Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors: Proceedings of the NATO Advanced Research Workshop on Properties and ... II: Mathematics, Physics and Chemistry, 184) 1402029640, 9781402029646

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Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors

NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Division Sub-Series I. II. III. IV. V.

Life and Behavioural Sciences Mathematics, Physics and Chemistry Computer and Systems Science Earth and Environmental Sciences Science and Technology Policy

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The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized bij scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organised and there are currently Five Sub-series as noted above. Please consult the following web sites for information on previous volumes published in the Series, as well as details of earlier Sub-series. http://www.nato.int/science http://www.wkap.nl http://www.iospress.nl http://www.wtv-books.de/nato-pco.htm

Series II: Mathematics, Physics and Chemistry – Vol. 184

Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors edited by

Bogdan Idzikowski Institute of Molecular Physics, Polish Academy of Sciences, Pozna´n, Poland

ˇ vec Peter S Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia and

Marcel Miglierini Department of Nuclear Physics and Technology, Slovak University of Technology, Bratislava, Slovakia

Kluwer Academic Publishers Dordrecht / Boston / London Published in cooperation with NATO Scientific Affairs Division

Proceedings of the NATO Advanced Research Workshop on Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors Budmerice, Slovak Republic 9–15 June 2003 A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 1-4020-2964-0 (PB) ISBN 1-4020-2963-2 (HB) ISBN 1-4020-2965-9 (e-book)

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.

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CONTENTS

PREFACE .......................................................................................................................ix K. SUZUKI Fe-M-B (M = IVa to VIa Metal) Nanocrystalline Soft Magnetic Materials..................... 1 G. HERZER The Random Anisotropy Model..................................................................................... 15 J.M. BARANDIARAN Some Aspects of the Crystallization of FINEMETand NANOPERM-like Alloys........................................................................................ 35 T. KULIK, J. FERENC, A. KOLANO-BURIAN Magnetically Soft Nanocrystalline Materials Obtained by Devitrification of Metallic Glasses............................................................................ 47 B.V. JALNIN, S.D. KALOSHKIN, E.V. KAEVITSER, V.V. TCHERDYNTSEV, E.V. OBRUCHEVA The Initial Stage of Nanocrystallization in Fe-Cu-Nb-Si-B Ferromagnetic Alloys ....... 59 M. DEANKO, D. MÜLLER, D. JANIýKOVIý, I. ŠKORVÁNEK, P. ŠVEC Cluster Structure and Thermodynamics of the Formation of Nanocrystalline Phases ... 69 E. ILLEKOVÁ Kinetic Characterization of Nanocrystal Formation in Metallic Glasses ....................... 79 V.I. TKATCH, S.G. RASSOLOV, S.A. KOSTYRYA Kinetics of the Nonisothermal Primary Crystallization of Metallic Glasses: Nanocrystal Development in Fe85B15 Amorphous Alloy................................................ 91 S.D. KALOSHKIN, B.V. JALNIN, E.V. KAEVITSER, J. XU Structural Relaxation and Nanocrystallization in the Initial Stage of Amorphous Alloys Studied by Curie Temperature Measurements............................ 99 C.F. CONDE, J.S. BLÁZQUEZ, A. CONDE Nanocrystallization Process of the HITPERM Fe-Co-Nb-B Alloys ............................ 111 A. ĝLAWSKA-WANIEWSKA Low Temperature Magnetic Properties of Nanocrystalline Co-Nb-Cu-Si-B Alloys................................................................................................. 123 F. MAZALEYRAT, Z. GERCSI, L.K. VARGA Induced Anisotropy and Magnetic Properties at Elevated Temperatures of Co-Substituted FINEMET Alloys............................................................................ 135 v

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P. KOLLÁR, E. FECHOVÁ, J. FÜZER, J. KOVÁý, P. PETROVIý, V. KAVEýANSKÝ, M. KONý Structure and Magnetic Properties of the Fe-Cu-Nb-Si-B Powder Prepared by Milling...................................................................................................... 147 L.K. VARGA, F. MAZALEYRAT Magnetic Decoupling in Soft Magnetic Nanocrystalline Alloys.................................. 157 H. CHIRIAC, N. LUPU Design and Preparation of New Soft Magnetic Amorphous Ferromagnets.................. 165 B. IDZIKOWSKI Formation of Nanocrystalline Metastable Phases in Fe-Ni-Zr-B Amorphous Alloys ....................................................................................................... 177 R. HASEGAWA Applications of Amorphous Magnetic Alloys.............................................................. 189 S. ROTH, G. SAAGE, J. ECKERT, L. SCHULTZ Magnetic Crystalline Transition Metal Ribbons Prepared by Melt-Spinning and Reactive Annealing ................................................................ 199 YU.V. BARMIN, I.L. BATARONOV, A.V. BONDAREV Percolation and Fractal Clusters in Amorphous Metals ............................................... 209 J. DEGMOVÁ, J. SITEK, J.-M. GRENECHE Neutron Irradiation Effect on Fe-Based Alloys Studied by Mössbauer Spectrometry ......................................................................................... 219 K. SEDLAýKOVÁ, F. HAIDER, J. SITEK, M. SEBERÍNI Application of Different Analytical Techniques in the Understanding of the Corrosion Phenomena of Non-Crystalline Alloys.............................................. 229 K.W. WOJCIECHOWSKI Monte Carlo Simulations of Model Particles Forming Phases of Negative Poisson Ratio ............................................................................................ 241 O. CRISAN, J.-M. GRENECHE, Y. LABAYE, L. BERGER, A.D. CRISAN, M. ANGELAKERIS, J.M. LE BRETON, N.K. FLEVARIS Magnetic Properties of Nanostructured Materials........................................................ 253 L. BATTEZZATI, M. KUSÝ, M. PALUMBO, V. RONTO Al-Rare Earth-Transition Metal Alloys: Fragility of Melts and Resistance to Crystallization.................................................................................. 267 L. BATTEZZATI, V. RONTO, M. KUSÝ On Different Mechanisms of Primary Crystallization in Al-Ni-La-Zr Amorphous Alloys .............................................................................. 279 M. JAHNÁTEK, M. KRAJýÍ, J. HAFNER Atomic Structure, Interatomic Bonding and Mechanical Properties of the Al3V Compound...................................................... 289

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F. AUDEBERT Amorphous and Nanostructured Al-Fe and Al-Ni Alloys ............................................ 301 M. KOWALCZYK, J. LATUCH, T. KULIK, H. DIMITROV Bulk Amorphous Samples of Al-Mm-Ni System......................................................... 313 E. FAZAKAS, L.K. VARGA, T. KULIK Al-Based Amorphous Alloys at the Limit of Glass Forming Ability .......................................................................... 321 N. MITROVIC, S. ROTH, S. DJUKIC, J. ECKERT Magnetic Softening of Metallic Glasses by Current Annealing Technique ................. 331 V.I. DIMITROV Interpretation of the Glass Transition Temperature from the Point of View of Molecular Mobility ............................................................ 345 I. KOKANOVIû, A. TONEJC The Effect of Thermal Relaxation on the Short-Range Order in Melt-Quenched Zr-Co and Zr-Ni Alloys.................................................................. 353 R. RISTIû, Ž. MAROHNIû, E. BABIû Magnetic Properties of Zr-3d Glassy Alloy Systems ................................................... 363 J.-M. GRENECHE Intergranular Phase in Nanocrystalline Alloys: Structural Aspects and Magnetic Properties ............................................................................................... 373 J. BALOGH, D. KAPTÁS, L.F. KISS, T. KEMÉNY, K. TEMST, C. VAN HAESENDONCK, I. VINCZE Mössbauer Study of Fe Grains in Nanocomposites...................................................... 385 M. KOPCEWICZ Radio-Frequency Mössbauer Spectroscopy in the Investigation of Nanocrystalline Alloys ............................................................. 395 D.S. SCHMOOL Ferromagnetic Resonance in Amorphous and Nanocrystalline Materials.................... 409 M. MIGLIERINI, J. DEGMOVÁ, T. KAĕUCH, P. ŠVEC, E. ILLEKOVÁ, D. JANIýKOVIý Magnetic Microstructure of Amorphous/Nanocrystalline Fe-Mo-Cu-B Alloys........... 421 N. LUPU, H. CHIRIAC Microstructure – Magnetic Properties Relationship in Nano-Clustered Glassy Magnets .............................................................................. 437 INDEX OF AUTHORS.............................................................................................. 447 INDEX OF SUBJECTS ............................................................................................. 449 LIST OF PARTICIPANTS .......................................................................................... 453

PREFACE

Recent progress and development of complex nanocrystalline alloys and their metastable amorphous precursors has emphasised the need for bringing together the leading scientists in the field for the purpose of disseminating the latest achievements in order to ensure scientific know-how exchange. The focus of the present NATO Advanced Research Workshop (ARW) was put on the emerging aspects in nanocrystalline materials. In addition to the already known effects induced by the presence of nanocrystalline structure such as the interface effects, the influence of high content of grain boundaries or the decrease in the exchange length, the averaging of magnetic anisotropy, the existence of a two-phase structure at the atomic scale, particular attention was given to the special character of the local atomic ordering and to the corresponding inter-atomic bonding as well as to the anomalies and particularities in electron density distributions, and to the formation of metastable, nanocrystalline phases built from small grains with special properties. Another objective was the investigation of new material classes based not on new compositions but rather on the original and special crystalline structure in the nanoscale, and on the atomic interactions under special, usually metastable, thermodynamic conditions related to the origin of the new structures with respect to their (amorphous) precursors, using scientific knowledge-based approach supported by previous in-depth studies and general experience. Three major techniques of nanocrystalline state formation, namely: the sufficiently rapid melt quenching, the mechanical alloying, and the heat treatment of the amorphous precursor have been reviewed. The emphasis was placed on the relationship between the amorphous precursors, the thermodynamics of enhancement and the facilitation of the formation of nanocrystalline phases. The mastering of the knowledge (and control, whenever possible) of the thermodynamic conditions, necessary for inducing the metastability of the structures, which lead to uncommon physical effects and special properties of nanocrystalline materials, was treated as preferential and given a particular emphasis. During five days, 57 participants from 21 countries discussed a wide range of topics in the following areas: Development of New Alloys, Properties of Conventional Nanocrystalline Materials, Modelling and Simulations, Applications and Experimental Methods. In total, 38 key speakers delivered main lectures that were suitably extended by 14 contributing talks presented by other participants. The focused activities and well chosen workshop subjects attracted a number of young scientists. Among the 21 participants there were 15 PhD students and young post-doctorate researches representing 7 different countries. The scientific programme was complemented by two round-table discussions which included, apart from the instructions for the authors of the ARW Proceedings, topics foix

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cused on the methods of the atomic-resolution structure analysis in the research of metallic nanocrystalline systems, and on the future of the research in this field, including further industrial applications of nanocrystalline materials. Additional discussions in smaller groups were held as a natural continuation of the daily schedule, during meals and in the evening get-together. A detailed summary of the workshop was made by Dr. R. Hasegawa, a member of the organizing committee. Over 50 technical papers were presented during the workshop and they can be classified as follows: 1. Development of new alloys. Two approaches to the new alloy development were presented: (i) a macroscopic view on the Fe-M-B system where M is selected from IVa, Va, and VIa elements, (ii) the effects of Cu and Co (micro-alloying). Copper affects the nanophase formation whereas cobalt increases the saturation induction of the material. In the micro-alloying study, a 3D atomic probe was used to characterise Cu clusters in an effort to optimise their roles. The results were utilized in developing new alloys containing Co with high saturation inductions. Properties and specific applications were reported for materials in bulk (e.g. Nd-Fe-Al), powder (Fe-Cu-Nb-Si-B by milling) and wire (Ni-P/Co-P nanowires) forms. These new forms may open up new prospective applications. 2. Properties of conventional nanocrystalline materials. Both intrinsic and technological properties were reviewed. Some new results relating to magnetic microstructures, magnetic decoupling, electron transport, effects of neutron irradiation, and corrosion properties were presented. A number of Al-Transition Metal-based alloys were reported. These studies are of help in understanding the thermodynamic states of these materials, clarifying local structures and atomic bonding, viscosity/diffusion (relating to glass formability of some of the Al-based alloys) and opening up new possibilities in the design of new alloys. Several papers were presented on crystallisation kinetics and mechanical properties. Technical contributions in the area of Zr/Ni-TM alloys included a wide range covering electronic properties, superconductivity, magnetism, thermal relaxation/crystallization kinetics, and shape memory. The primary area of interest was in the combined properties, such as shape memory with magnetism, and superconductivity with magnetism. 3. Modelling and simulation. The random anisotropy model for nanocrystalline magnetic materials was reviewed, covering a comprehensive picture of the magnetism involved. The density-of-state calculations for Cr23C6 type unit cell (applicable to Ni23B6 and Fe23B6) are instructive; anomalously high Fe magnetic moments (up to 3 μB) were found at some non-equivalent positions in the crystal structure. The electronic structure calculations and nucleation thermodynamics considered on Al-TM based alloys shed light on the atomic bonding and mobility in these materials. These models of the local magnetic, electronic and thermodynamic states should be of assistance in designing new alloys. Monte Carlo simulations of mechanical behaviour, materials with negative Poisson’s ratio and magnetisation processes in magnetically mixed states found in nanocrystalline magnetic materials were presented. These simulations are becoming more realistic and useful in physics. A graphic presentation of the dislocation motion in the simulated system was instructive. Two experimental approaches to simulate the mixed magnetic states were presented: one through nanostructured metallic

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systems of Fe clusters made by the condensation in inert gas and the other through multilayers. The former study showed the importance of the grain boundaries which affect the magnetic properties of the peripheries of the nanograins. Although the magnetic heterostructures generated from the multi-layers are two-dimensional, their local magnetic states should represent them at the interface between the nanoparticles and amorphous matrix in a real nanocrystalline magnet. Caution, however, should be raised while some observation implies a dipole-dipole-like interaction. 4. Applications. A review of the use of amorphous alloys in various applications was given. They can be found in power electrical transformers, motors, pulse power devices for energy generation, power electronics, sensors, telecommunication devices, and medical diagnostic equipment. A number of new alloys and their shapes and forms which are currently under investigation will eventually find practical applications. Among them, bulk amorphous/nanocrystaline magnetic materials appear to be suited preferably for hard magnets or for soft magnetic applications in the operating frequency of up to 1 kHz. Other bulk materials are found useful in structural or mechanical applications. The results of the efforts in nanocrystalline magnetic alloys with higher saturation inductions will find applications in high temperature magnetism. 5. Experimental methods. The presented results were based on differential scanning calorimetry (DSC), on X-ray and neutron diffraction, on Mössbauer (both transmission and energy conversion) spectroscopy, electron transport including superconducting, magnetoresistance, magneto-impedance, and conventional magnetometry. In addition, a technique using ferromagnetic resonance was presented. This method is commonly used for basic magnetic characterisation but care must be taken in the sample preparation. One presentation showed that a combination of DSC and resistivity measurements is suitable for in-situ probing of the nanocrystallization process and the related postnanocrystallization state. This kind of combined observation should shed more light on the nanocrystallization processes. The interest in the workshop and the attractiveness of the topics ware documented by the fact that only two of the originally confirmed 41 key speakers excused themselves from participation due to health problems and one speaker provided a sufficiently qualified substitute in due time prior to the workshop. The social program included a guided visit to attractive sightseeing spots in the vicinity of the workshop site – an excursion to the medieval chateau and museum ýerveny Kamen and a visit to a ceramic and pottery folk manufacture in Modra. The task force of the workshop was represented by the choice of speakers (which included talented young researchers) the approach to selected topics (the relationship between the structure and the preparation conditions) the microstructure and e.g. the magnetic, mechanical, electrical or other properties using a variety of diverse experimental and/or theoretical techniques, methods, models, and approaches. The speakers represented a subcritical concentration of scientists sufficient for the assessment of recent knowledge stemming from the research in physics and chemistry of nanocrystalline materials, for the establishment of additional links, for the exchange of experience and for discussions on the prospects of future research in the field. The workshop and further contacts will certainly play an important role of a bridge between the researchers from the NATO and Partner countries and shall form a sound basis for common

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research in near the future, ranging from bilateral co-operation and personnel exchange to larger scale international projects. Even though not fully funded, the generous support of the NATO Scientific Affair Division is greatly acknowledged. Because of a very tight time schedule and shortness of time between the approval of the ARW, announced in early April, and its starting date on June 8, 2003 we are especially grateful for in-time receipts of the financial instalments. Support extended by the respective institutions of the co-directors of the ARW, even if modest, as well as the funding from other sources is also greatly appreciated. Several post-workshop activities and contacts are already functional, ranging from bilateral contacts and preparations of joint research projects to larger scale programmes within the framework of the European and transatlantic scientific agencies. We express our deepest gratitude to all the participants for the energy and efforts they put into the making of this workshop and proceedings very successful. We would also like to thank Professor R.A. Ferchmin for helpful discussions during the final preparation of these proceedings, I. Grenda, M.A. for proof-reading of the English texts and Dr. G. Sekretarczyk for technical assistance.

April, 2004

Bogdan Idzikowski Peter Švec Marcel Miglierini

Fe-M-B (M = IVa TO VIa METAL) NANOCRYSTALLINE SOFT MAGNETIC MATERIALS A Review of Alloy Development KIYONORI SUZUKI School of Physics and Materials Engineering, Monash University Clayton, Victoria 3800, Australia Corresponding author: K. Suzuki, e-mail: [email protected]

Abstract:

A novel approach employed in the development of soft magnetic materials is to reduce the structural correlation length (grain size) below the ferromagnetic correlation length (~ domain wall width). This approach has successfully been applied to the development of Fe-rich Fe-M-B (M = IVa to VIa metal) nanocrystalline soft magnetic alloys, commercially known as NANOPERM. In this paper, research on these nanocrystalline soft magnetic alloys is reviewed and the principles underlying alloy design are summarized. Some prospects for further alloy development in the Fe-M-B system are also discussed.

1. INTRODUCTION One of the most successful industrial applications of nanostructured materials prepared by crystallization of amorphous precursors is with magnetic materials. Although high saturation magnetization can be realized easily in conventional crystalline magnetic materials, when concentrations of Fe are increased, their soft magnetic properties are usually poor because of the large magnetocrystalline anisotropy of D-Fe (K1 = 47 kJ/m3). The effect of this large K1 is, however, suppressed dramatically by reducing the grain size to nanometer scales [1]. Therefore, exceptionally high saturation magnetization as well as excellent soft magnetic properties can be obtained for Fe-rich nanocrystalline alloys. Two major alloy systems in this family of nanocrystalline magnetic materials are Fe-Si-B-Nb-Cu [2] and Fe-Zr-B-(Cu) [3, 4], commercially known as FINEMET and NANOPERM, respectively. In this paper the alloy development of the latter Fe-M-B (M = IVa to VIa metal) based system is overviewed and the rationale underlying alloy design is summarized. Secondly, scope for further development of FeM-B based nanocrystalline soft magnetic alloys with improved magnetic core characteristics is discussed. 1 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 1–14. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

K. Suzuki

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2. NANOCRYSTALLINE SOFT MAGNETIC MATERIALS The development of magnetic materials has a history of over a century. During this period, soft magnetic properties of materials have been progressively improved by means of compositional and/or structural modifications. In this section, a number of approaches involved in the material development to date are summarized and the advantage of the approaches employed in nanocrystalline soft magnetic materials is discussed. 2.1. Advantage The technical magnetic characteristics such as the coercivity (Hc) and permeability (P) are primarily a function of the magnetocrystalline anisotropy constant (Kc) of the material. In addition, an extrinsic magnetic anisotropy is induced by the magnetoelastic effect. Therefore, alloy development has centred on attempting to achieve microstructures which reduce both Kc and the saturation magnetostriction (Os) to zero. A wide range of soft magnetic materials developed to date may be classified into three groups in terms of the approaches used for reducing the effects of Kc and Os. These three approaches are summarized in Table I. Until relatively recently, most of the development was performed by optimizing the chemical composition and heat treatment of alloys prepared by conventional melting and casting. A considerably large amount of additives is needed for realising small Kc and Os in this conventional approach and the saturation induction (Bs) is severely reduced. In the 1970’s it was discovered that the magnetocrystalline anisotropy of alloys could be dramatically reduced by amorphization [5, 6]. This discovery has set the materials development free from the quest for compositions having Kc ~ 0. However, amorphization is ineffective in reducing the saturation magnetostriction and small Os in amorphous alloys is limited to alloys with low Bs. On the other hand, both the effects of Kc and Os in Fe-based crystalline systems are suppressed by reducing the grain size below the exchange correlation length. Hence, small effective values of Kc and Os are realized in Fe-rich compositions in nanocrystalline soft magnetic

Figure 1. Saturation magnetic induction and initial permeability of various soft magnetic materials

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Table I. Approaches used for reducing the effects of magnetocrystalline anisotropy (Kc) and magnetostriction (Os) in bulk soft magnetic materials Approaches Preparation Material families methods Kc o 0 Os o 0 Conventional materials

Melting and casting

Composition control

Composition control

Amorphous alloys

Melt spinning (amorphization)

Amorphization

Composition control

Nanocrystalline alloys

Melt spinning (amorphization) and crystallization

Nano-crystallization and composition control

Nano-crystallization and composition control

alloys, having led to a new class of soft magnetic materials possessing both high P and high Bs (Fig. 1). 2.2. History The concept of nanocrystalline materials can be found as early as in 1981. However, there was little awareness of the effect of nanoscale grain sizes on magnetic softness in the early 1980’s as the focus of the earlier nanocrystalline materials was to generate a new class of disordered solids by introducing a high density of grain boundary defects. Historically, the effect of nanoscale grain sizes on the technical magnetic properties was first studied for Ni-Fe (PERMALLOY) thin films in the 1960’s. Hoffmann [7] predicted in his ripple theory that the soft magnetic properties of polycrystalline Ni-Fe films could be improved by refining the grain size. However, K1 of PERMALLOY is by nature small enough to realize good magnetic softness and hence, the ripple theory did not seem to have an impact large enough to stimulate attempts to reduce the large effect of K1 in Fe-rich alloys by grain refinement. The era of intense research on Fe-rich nanocrystalline soft magnetic materials has opened after the development of nanocrystalline Fe74.5Si13.5B9Nb3Cu1 by Yoshizawa et al. [2] and the extension of the random anisotropy model [5] to nanocrystalline systems by Herzer [8] in the late 1980’s. 3. ALLOY DEVELOPMENT OF NANOPERM A pilot project [9] aimed at preparing magnetically soft Fe-rich nanocrystalline alloy powders by mechanical alloying (MA) started in 1989 at Institute for Materials Research (IMR), Tohoku University. This was a collaborative project between IMR and ALPS Electric and the author was the participating researcher from ALPS. The project was a spin-off of another IMR-ALPS joint project on Fe-Zr nanocrystalline soft magnetic thin films [10]. Although there was a growing awareness of the effect of grain refinement on magnetic softness, the research team at that time believed that the formation of a supersaturated solid solution in nonequilibrium bcc-Fe(Zr) was another important condition to realize small intrinsic K1 in the Fe-Zr films. We confirmed in the pilot project that nonequilibrium bcc-Fe powders supersaturated with Zr can be prepared by MA [9]. However, their soft magnetic properties were rather poor presumably

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K. Suzuki

because of the contamination of impurities during the milling process. Hence, instead of mechanical alloying, I chose to employ the technique of using melt-spun amorphous alloys as precursors to nanostructures following the report by Yoshizawa et al. A range of additional elements including B, Si, Al and other transition metals were added to the base Fe-Zr amorphous alloys and the coercivity after crystallization was investigated. As a result, a magnetically soft nanostructure was confirmed in the Fe-Zr-B system in a composition rage of | 90 at.% Fe [3]. This was the first report on NANOPERM. 3.1. Fe-M-B system Our earliest investigation on the nanocrystalline Fe-Zr-B alloys showed that a small coercivity of less than 10 A/m was limited to the samples in which the precipitates after primary crystallization were bcc-Fe with a grain size of 10 to 20 nm. The magnetic softness of nanocrystalline Fe-Zr-B alloys deteriorated severely when compounds were formed upon crystallization. Since the thermodynamic driving force for the nucleation of magnetically harder compounds is enhanced in hypereutectic compositions, the magnetically soft nanostructure is limited in the Fe-rich hypoeutectic region. However, the presence of a deep eutectic is an essential condition for the formation of an amorphous phase by melt spinning and hence, the preparation of the amorphous precursor

Figure 2. Compositional dependence of initial permaebility (Pe at 1 kHz) and saturation induction (Bs) for nanocrystalline (a) Fe-Zr-B [3], (b) Fe-Hf-B [15] and [c] Fe-Nb-B [11] alloys

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tends to be arduous in the hypoeutectic region away from the eutectic point. Consequently, a high initial permeability above 104 in the Fe-Zr-B system is obtained in a relatively narrow composition range of 5 to 7 at.% Zr and 2 to 6 at.% B (Fig. 2a).

Figure 3. Differential thermal analysis of amorphous Fe93xM7Bx (M = IVa to VIa metal) alloys [11]

The direction of subsequent alloy development was to search for alloy systems which gave rise to the formation of nanoscale bcc-Fe precipitates upon primary crystallization. A possible direction was to try substituting Zr with other transition metals. We investigated the structures of melt-spun Fe93–xM7Bx (M = IVa to VIa metal) alloys. Our emphasis in this investigation was placed on the minimum boron content required for the formation of an amorphous phase as the formation of bcc-Fe upon primary crystallization was most likely in Fe-rich amorphous alloys. The M content of 7 at.% was chosen as the lowest coercivity in the Fe-Zr-B system was confirmed for Fe91Zr7B2 and Fe90Zr7B3. Figure 3 shows the results of differential thermal analysis (DTA) for amorphous Fe93-xM7Bx (M = IVa to VIa metal) alloys [11] along with that of amorphous Fe86B14. Each amorphous alloy contains the minimum boron content for the formation of an amorphous single phase. Multi-stage crystallization is evident on each DTA curve. The primary precipitates of the multi-stage crystallization reactions were identified by means of X-ray diffractometry and transmission electron microscopy and the following reactions were concluded for the first exothermic reaction [11]: for M = Zr, Hf, V, Nb, Cr and Mo: amorphous o bcc-Fe + residual amorphous; for M = Ti, Ta and W: amorphous o bcc-Fe, tetragonal-Fe3B + residual amorphous.

K. Suzuki

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Hence, the primary precipitates can be free of compounds for amorphous Fe93-xM7Bx (M = Zr, Hf, V, Nb and Cr) alloys. The first exothermic peaks on the DTA curves in Fig. 3 are broader than the 2nd or the 3rd peaks, reflecting the sluggish precipitation reactions typical of diffusion controlled primary crystallization. A direct evidence of the diffusion controlled crystal growth in NANOPERM can be found in a review by Hono et al. [12]. Assuming that the grain growth of the primary precipitates in the Fe-M-B alloys is governed by the diffusion of the solute atoms in the amorphous matrix and the diffusion field is similar to the grain radius (r), the time dependence of the grain radius is approximated by

§ C '  C am t · ¸, r | 2tDv ¨¨ am' ¸ © Cam  Cbcc ¹

(1)

where Dv is the diffusion coefficient of the solute atoms. Cbcc, Cam and Cam’ are the solute contents of the bcc precipitates, the amorphous matrix and the amorphous phase at the interface of the growing bcc precipitates, respectively. This steady state solution indicates that a small r is expected for a system with small Dv and large (Cam’ – Cbcc). Consequently, a small solubility of the M element in D-Fe is particularly important for the nanostructural formation upon primary crystallization. Kronmüller et al. [13] have measured the diffusion coefficients in an amorphous Fe91Zr9 alloy by using radioactive tracers and found that the diffusion coefficient of Zr is smaller than that of Fe by three orders of magnitude. This suggests that the M elements such as Zr can have a dramatic effect on reducing the grain size if their concentration is considerably higher than their solubility in D-Fe. In Figure 4 we show the relationship between the mean grain size of the primary bcc precipitates in the Fe-M-B alloys and the solubility of each M element in D-Fe [14] at the annealing temperature. A small grain size of 10 to 15 nm

Figure 4. Relation between the mean grain size and the solubility of M element in D-Fe at annealing temperature for amorphous Fe-M-B after primary crystallization [14]

is limited to the alloys containing M elements with a low solubility limit less than 1 at.% (i.e., M = Zr, Hf, Nb, Ta and W), reflecting the significance of the retarded growth rate induced by the partitioning of M elements. As discussed above the primary precipitates in the Fe-Ta-B and Fe-W-B systems contain tetragonal-Fe3B and therefore, the alloy systems of Cu-free NANOPERM is limited to Fe-M-B (M = Zr, Hf and Nb) alloys (Figs. 2a, 2b and 2c) [3, 11, 15].

Fe-M-B Nanocrystalline Soft Magnetic Materials

7

3.2. Fe-M-B-Cu system The two key alloying elements in FINEMET are Nb and Cu. The role of Nb can be explained in the same manner as Zr in NANOPERM, i.e., the retarded growth rate due to the slow diffusivity of Nb. Hono et al. [12] has shown that Cu in FINEMET forms clusters prior to primary crystallization and the Cu clusters act as heterogeneous nucleation sites for bcc-Fe(Si) precipitates. Yoshizawa and Yamauchi [16] reported that the crystallization products of amorphous Fe75.5Si13.5B9Nb3 (Cu-free FINEMET) were Fe3B and Fe23B6. Hence, Cu in FINEMET is an essential inoculant which alters the crystallization products dramatically from the iron borides to bcc-Fe(Si). On the other hand, NANOPERM can be Cu-free as their Fe concentrations reach as high as about 90 at.% and the primary crystallization of bcc-Fe can be promoted by the thermodynamic driving force. Naturally, the formation of iron borides takes place upon primary crystallization in the ternary Fe-M-B (M = Zr, Hf and Nb) systems when the solute content is increased. Cu was found to be the most effective microalloying

Figure 5. Change in initial permeability (Pe) as a function of boron content for Fe92–xM7BxCu1 alloys after primary crystallization

element for preventing the formation of compounds upon primary crystallization in the Fe-M-B (M = IVa to VIa metal) systems. The composition rage where the primary crystallization of bcc-Fe takes place in the ternary alloys is enhanced dramatically towards the B richer region by an addition of 1 at.% Cu. As a result, the magnetically soft nanostructure is obtained for a broader variety of M elements. Figure 5 shows the relative permeability (at 1 kHz and 0.4 A/m) of amorphous Fe92-xM7BxCu1 (M = IVa to VIa metal) alloys after primary crystallization. A high permeability value above 10,000 is evident for Fe-M-B-Cu (M = Ti, Zr, Hf, Nb, Ta and Mo) systems. The P values remain < 10,000 for M = V and Cr because these two elements have little effect on reducing the grain size. It has been confirmed by Zhang et al. [17] that the Cu atoms in Fe-Zr-B-Cu also form clusters prior to primary crystallization.

8

K. Suzuki

3.3. Co addition Adding Co to Fe-based alloys has been a standard approach of alloy design in a range of magnetic materials as the saturation magnetization can be enhanced by Co. The earliest examples of such an approach in FINEMET and NANOPERM may be found in the reports from the inventors of these alloys. In Fig. 6a we present the results taken from the work of Yoshizawa and Yamauchi [18] on the effect of Co on the relative permeability of Fe75.5Si13.5B9Nb3Cu1. Adding Co to FINEMET results in a marked deterioration of magnetic softness presumably because of the induced anisotropy due to the atomic pair ordering. We found a similar influence of Co in nanocrystalline Fe91Zr7B2 (Fig. 6b) [19].

Figure 6. Effect of Co or Ni or Fe substitution on the relative permeability (Pe) and saturation magnetization (V s), (shown in (b)) for different alloys: (a) Fe73.5-xMxSi13.5B9Nb3Cu1, M = Co, Ni [18], (b) Co91-xFexZr7B2 and Co1-xFex [19]

Although adding a large amount of Co to the nanocrystalline Fe-Zr-B alloys results in poor magnetic softness of the alloys, a small amount of Co is useful for finetuning the

Figure 7. Effect of Co substitution on the saturation magnetostriction (Os) of nanocrystalline Fe90Zr7B3 [20]

Fe-M-B Nanocrystalline Soft Magnetic Materials

9

saturation magnetostriction of NANOPERM. The local magnetostriction of individual grains in nanocrystalline soft magnetic materials is averaged out over many grains and the saturation magnetostriction (Os) of cubic nanocrystalline systems is given by

Os

2 3 O100  O111 , 5 5

(2)

where O100 and O111 are the magnetostriction constants in the [100] and [111] directions, respectively. Since the signs of O100 and O111 are opposite for D-Fe (O100 = + 20.7 u 10-6 and O111 = –20.2 u 10–6), a small Os of about –4 u 10–6 is expected for a single phase nanocrystalline pure-Fe despite the large O100 and O111 in the order of 10–5. Figure 7 shows changes in the magnetostriction (Os) as a function of Co content (x) in nanocrystalline (Fe1-xCox)90Zr7B3 alloys [20]. The Os value for x = 0 is about –1 u 10–6 after annealing at 923 K, slightly closer to zero as compared with the value expected for the single phase nanocrystalline Fe. This seems to be due to the positive contribution of the magnetostriction from the residual amorphous phase or a proposed interphase [21, 22]. The magnetostriction of the Fe-Co-Zr-B alloys increases linearly with x, reflecting the compositional dependence of O100 and O111 in Fe-Co binary alloys. The influence of residual stress, caused by moulding the samples in an epoxy resin, on the magnetic softness was examined [20] for the nanocrystalline (Fe1-xCox)90Zr7B3 alloys.

Figure 8. Relation between saturation magnetostriction (Os) and Pe (at 1 kHz and 1 MHz) before and after epoxy resin molding nanocrystalline (Fe1-xCox)90Zr7B3 [20]

Figure 9. Relation between saturation magnetostriction (Os) and saturation magnetization (Ms) for various amorphous [23], nanocrystalline Fe-Si-B-Nb-Cu [2] and nanocrystalline Fe(Co)-Zr-B [20] alloys. The saturation magnetization of the Fe-based amorphous alloys in Ref. [23] was given in emu/g and the plots here are the 4SMs values with an assumed density 7.2 g/cm3

K. Suzuki

10

The residual stress was estimated to be –1.4 u 108 Pa from the stress induced magnetic anisotropy (0.67 kJ/m3 at Os = 3.1 u 10–6). Figure 8 shows the changes in Pe at 1 kHz and 1 MHz for the samples before and after moulding. The smallest influence of the residual stress is confirmed at Os = 0 and a high Pe value above 10,000 is obtained even after epoxy resin moulding. The zero-magnetostrictive (Fe1-xCox)90Zr7B3 samples are obtained for x = 0.01 to 0.015 and they exhibit a high Bs of 1.65-1.7 T. The combination of high Bs ~ 1.7 T and Os = 0 cannot be realised in other material families and this is a unique characteristic of NANOPERM (Fig. 9). Another important effect brought about by an addition of Co in nanocrystalline Fe-Zr-B-(Cu) alloys is an enhanced thermal stability. Willard et al. [24] investigated the effect of Co on the magnetic properties of nanocrystalline Fe88Zr7B4Cu1. The alloy studied was Fe44Co44Zr7B4Cu1 and is named HITPERM. The Curie temperatures of both the crystalline and the residual amorphous phases in HITPERM are higher than those of NANOPERM. Skorvanek et al. [25] demonstrated that HITPERM could be Cu-free. Moreover, they found that the coercivity of Cu-free HITPERM was lower than that of Fe44Co44Zr7B4Cu1. The primary application of HITPERM is with an actuator operated at elevated temperatures and hence, the saturation magnetization above room temperature is the central focus, rather than the soft magnetic properties at room temperature. 4. WAY FORWARD In this section, we briefly overview the alloy compositions and magnetic properties in a range of nanocrystalline soft magnetic alloy families reported to date. Secondly, the magnetic core characteristics distinctive of NANOPERM are discussed, followed by the prospects of further alloy development in the Fe-M-B based nanocrystalline soft magnetic alloys. Some of the alloy families whose magnetic core properties are similar or inferior to those of Fe-based amorphous alloys (i.e., Pe at 1 kHz < 10,000 or Hc > 10 A/m at room temperature) are left out in this discussion. 4.1. Nanocrystalline alloys developed to date Major alloy systems reported so far may be listed chronologically as: Fe-Si-B-Nb-Cu [1], Fe-Si-B-Nb-Au [26], Fe-Si-B-V-Cu [27], Fe-(Zr or Hf)-B [3], Fe-(Ti, Zr, Hf, Nb or Ta)-B-Cu [4], Fe-Si-B-(Nb, Ta, Mo or W)-Cu [28], Fe-P-C-(Mo or Ge)-Cu [29], Fe-GeB-Nb-Cu, Fe-Si-B-(Al, P, Ga or Ge)-Nb-Cu [30], Fe-Al-Si-Nb-B (Sendust-Nb-B) [31], Fe-Al-Si-Ni-Zr-B (Supersendust-Zr-B) [32] and Fe-Si-B-Nb-Ga [33]. The compositions of these alloys can be described by the following formula:

FM M ML LM ª º ª Ti V Cr º ªB C º ª Cu º «Fe Co Ni » « Zr Nb Mo » « Al Si P » «Ag » , « » « » « » « » «¬ »¼ «¬Hf Ta W »¼ «¬Ga Ge »¼ «¬ Au »¼ 66 ~ 91 2~8 2 ~ 31 0 ~1

(3)

where the elements given in bold letters are found most commonly in the developed alloys. FM in Eq. (3) are ferromagnetic elements. The approach to improve magnetic core properties by nanocrystallization is insignificant for Co- or Ni-rich systems from

Fe-M-B Nanocrystalline Soft Magnetic Materials

11

a technological view point since small K1 and Os values have already been realized in Co-rich amorphous or Ni-rich PERMALLOY. Hence, Co and Ni were used exclusively as additives in Fe-based nanocrystalline systems [34]. M denotes early transition metals, i.e. IVa to VIa metals, which are the slowest diffusive elements in the system, providing retarded crystal growth. ML are metalloids, semi-metals and simple metal elements. LM are late transition metals whose enthalpy of mixing with Fe is positive. The developed alloys may be divided into two groups; their precursors are based on either FM-M or FM-ML amorphous alloys. The vast majority of alloy systems developed to date are classified into the former group while perhaps NANOPERM is the only example of the latter. The highest saturation magnetization (Bs) of 1.7 T in the nanocrystalline soft magnetic alloy family is found in Fe91Zr7B2 or (Fe, Co)90Zr7B3 with effective permeability (Pe) | 3 u 104. On the other hand, the highest value of Pe (| 15 u 104) is obtained for Fe73.5Si13.5B9Nb3Cu1 with Bs of | 1.3 T. 4.2. Prospects It has been predicted in Herzer’s random anisotropy model (RAM) that varies as K14 in nanocrystalline systems. Thus, a rational approach to better soft magnetic properties in NANOPERM is to try reducing the intrinsic K1 of the bcc-Fe nanocrystallites. Hayashi et al. [35] reviewed various thin-film crystalline materials and summarized that K1 = 0 is expected in Fe-Ga-Si, Fe-Al-Ge, Fe-Co-Ga-Si and Fe-Co-Al-Ge, along with classical Fe-Ni and Fe-Al-Si. Consequently, the addition of Al, Si, Ga and Ge to Fe-M-B may result in a further reduction of . However, a substantial amount of ML addition in Fe-M-B will be accompanied by a serious decrease in the saturation magnetization, making NANOPERM featureless from the viewpoint of technological applications as the high saturation magnetization is one of the distinctive characters of NANOPERM. Hence, it is advisable to minimize the amount of ML in this approach. The amount of ML elements may be minimized if the ML atoms are preferentially incorporated into the bcc-Fe precipitates upon primary crystallization. The selection of the M element seems to be the key to such a preferential partitioning behaviour. An influential parameter for good magnetic softness, besides small grain size, small K1 and large exchange stiffness, is the volume fraction of the residual amorphous phase (Vam). Our two-phase RAM [36] predicts that small Vam is preferable when the Curie temperature of the residual amorphous phase (TCam) is substantially lower than that of the nanocrystalline phase (TCcr), whereas moderate Vam may reduce if TCam is close to TCcr. The coercivity of nanocrystalline soft magnetic alloys near T ~ TCam could vary as the –6th power of the spontaneous magnetization of the intergranular region when Vam is large. This suggests that further improvements of the soft magnetic properties are possible in alloy systems with relatively low TCam through an appropriate microalloying. Elements that incorporate preferentially into the residual amorphous phase following the nanostructural formation process may have greater effect upon the promotion of the intergranular magnetic coupling. In addition to the random magnetocrystalline anisotropy (), the extrinsic uniaxial anisotropies (Ku) induced chiefly by the residual stress and annealing are also

K. Suzuki

12

influential to the soft magnetic properties of NANOPERM [37]. An improvement of the magnetic softness by controlling Ku is another possible approach. 5. SUMMARY The distinctive magnetic core properties of Fe-M-B based nanocrystalline soft magnetic alloys, commercially know as NANOPERM, are the combination of the following characteristics: (i) a high saturation magnetization up to 1.7 T, (ii) a high permeability well above 10 000 and (iii) zero-magnetostriction. The combination of these excellent core properties is primarily due to the formation of nanoscale bcc-Fe with alloys having exceptionally high Fe concentrations. In order to maintain this distinctive character of NANOPERM, further alloy development should focus on microalloying effects or processing, rather than substantial modifications of alloy compositions. ACKNOWLEDGEMENTS The development of nanocrystalline Fe-Zr-B alloys commenced at the Institute for Materials Research (IMR), Tohoku University under the supervision of Professors N. Kataoka, A. Inoue and T. Masumoto. The author is grateful to Professor A. Makino who was his mentor at ALPS and allowed him to work at IMR. He also wishes to thank the Australian Research Council for its continuing financial support. REFERENCES 1. 2. 3.

4.

5. 6. 7. 8. 9. 10.

Herzer, G. (1997) Nanocrystalline soft magnetic alloys, in Handbook of Magnetic Materials, K.H.J. Buschow (ed.), Vol. 10, Elsevier Science, pp. 415-462. Yoshizawa, Y., Oguma, S. and Yamauchi, K. (1988) New Fe-based soft magnetic alloys composed of ultrafine grain structure, J. Appl. Phys. 64, 6044-6046. Suzuki, K., Kataoka, N., Inoue, A., Makino, A. and Masumoto, T. (1990) High saturation magnetization and soft magnetic properties of bcc Fe-Zr-B alloys with ultrafine grain structure, Mater. Trans. JIM 31, 743-746. Suzuki, K., Makino, A., Inoue, A. and Masumoto, T. (1991) Soft magnetic properties of nanocrystalline bcc Fe-Zr-B and Fe-M-B-Cu (M = transition metal) alloys with high saturation magnetization, J. Appl. Phys. 70, 6232-6237. Alben, R., Becker, J.J. and Chi, M.C. (1978) Random anisotropy in amorphous magnets, J. Appl. Phys 49, 1653-1658. Hasegawa, R. (1991) Amorphous magnetic materials – a history, J. Magn. Magn. Mater. 100, 1-12. Hoffmann, H. (1973) Static wall coercive force in ferromagnetic thin films, IEEE Trans. Magn. 9, 17-21. Herzer, G. (1989) Grain structure and magnetism of nanocrystalline ferromagnets, IEEE Trans. Magn. 25, 3327-3329. Kataoka, N., Suzuki, K., Inoue, A. and Masumoto, T. (1991) Magnetic properties of ironbase bcc alloys produced by mechanical alloying, J. Mater. Sci. 26, 4621-4625. Kataoka, N., Hosokawa, M., Inoue, A. and Masumoto, T. (1989) Magnetic properties of Fe-based binary crystalline alloys produced by vapor quenching, Jpn. J. Appl. Phys. 28, L462-L464.

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12. 13. 14.

15. 16. 17.

18.

19.

20. 21. 22.

23. 24.

25.

26.

27. 28. 29. 30.

13

Suzuki, K., Makino, A., Inoue, A. and Masumoto, T. (1994) Formation of nanocrystalline structure by crystallization of amorphous Fe-M-B (M = IVa to VIa group metal) alloys, Sci. Rep. RITU A39, 133-140. Hono, K. (1999) Atom probe microanalysis and nanoscale microstructures in metallic materials, Acta mater. 47, 3127-3145. Kronmüller, H., Frank, W. and Hörner, A. (1991) Diffusion and structural-relaxation mechanisms in metallic glasses, Mater. Sci. Eng. A133, 410-414. Suzuki, K., Sahajwalla, V., Cadogan, J.M., Inoue, A. and Masumoto, T. (1996) The role of the M element in nanocrystalline Fe-M-B (M = Zr, Hf and Nb) soft magnetic alloys, Mater. Sci. Forum 225-227, 665-670. Suzuki, K., Makino, A., Inoue, A. and Masumoto, T. (1993) Soft magnetic properties of Fe-Hf-B ternary alloys with nanoscale bcc structure, J. Jpn. Inst. Metals 57, 964-971. Yoshizawa, Y. and Yamauchi, K (1989) Fe based soft magnetic alloys composed of ultrafine grain structure, J. Jpn. Inst. Metals 53, 241-248. Zhang, Y., Hono, K., Inoue, A. and Sakurai, T. (1996) APFIM studies of nanocrystalline microstructural evolution in Fe-Zr-B(-Cu) amorphous alloys, Mater. Sci. Eng. A217-218, 407-413. Yoshizawa, Y. and Yamauchi, K. (1989) Magnetic properties of Fe-M-Cu-Nb-Si-B (M = Co, Ni) alloys, Abstracts of the 104th Spring Meeting of the Japan Institute of Metals, The Japan Institute of Metals, Sendai, p. 97. Kimura, H., Murakami, Y., Suzuki, K., Inoue, A. and Masumoto, T. (1991) Formation of nanocrystalline non-equilibrium phase by controlling crystallization of an amorphous phase, The 2nd Reports on the Cooperative Research Programs of the Laboratory for Advanced Materials, Institute for Materials Research, Tohoku University, Sendai, 155-157. Suzuki, K., Makino, A., Inoue, A. and Masumoto, T. (1994) Soft magnetic properties of nanocrystalline Fe-Co-Zr-B alloys, J. Magn. Soc. Jpn. 18, 800-804. ĝlawska-Waniewska, A. and Lachowicz, H.K. (2003) Magnetostriction in soft magnetic nanocrystalline materials, Scripta Mater. 48, 889-894. Miglierini, M. and Greneche, J.M. (1997) Mössbauer spectrometry of Fe(Cu)MB-type nanocrystalline alloys: II. The topography of hyperfine interactions in Fe(Cu)ZrB alloys, J. Phys,: Condens. Matter 9, 2312-2347. Ito, S., Aso, K., Makino, Y. and Ueda, S. (1980) Magnetostriction and magnetization of iron-based amorphous alloys, Appl. Phys. Lett. 37, 665-666. Willard, M.A., Laughlin, D.E., McHenry, M.E., Thoma, D., Sickafus, K., Cross, J.O. and Harris, V.G. (1998) Structure and magnetic properties of (Fe0.5Co0.5)88Zr7B4Cu1 nanocrystalline alloys, J. Appl. Phys. 84, 6773-6777. Skorvanek, I., Svec, P., Marcin, J., Kovac, J., Krenicky, T. and Deanko, M. (2003) Nanocrystalline Cu-free HITPERM alloys with improved soft magnetic properties, Phys. Stat. Sol. A196, 217-220. Kataoka, N., Matsunaga, T., Inoue, A. and Masumoto, T. (1989) Soft magnetic properties of bcc Fe-Au-X-Si-B (X = early transition metal) alloys with fine grain structure, Mater. Trans. JIM, 30, 947-950. Sawa, T and Takahashi, Y. (1990) Magnetic properties of FeCu(3d transition metals)SiB alloys with fine grain structure, J. Appl. Phys. 67, 5565-5567. Yoshizawa, Y. and Yamauchi, K (1991) Magnetic properties of Fe-Cu-M-Si-B (M = Cr, V, Mo, Nb, Ta, W) alloys, Mater. Sci. Eng. A133, 176-179. Fujii, Y, Fujita, H., Seki, A. and Tomida, T. (1991) Magnetic properties of fine crystalline Fe–P–C–Cu–X alloys, J. Appl. Phys. 70, 6241-6243. Yoshizawa, Y., Bizen, Y., Yamauchi, K. and Sugihara, H. (1992) Improvement of magnetic properties in Fe-based nanocrystalline alloys by addition of Si, Ge, C, Ga, P, Al elements and their applications, Trans. IEE Jpn. A112, 553-558.

14 31. 32. 33. 34.

35.

36. 37.

K. Suzuki Watanabe, H., Saito, H. and Takahashi, M. (1993) Soft magnetic properties and structures of nanocrystalline Fe-Al-Si-Nb-B alloy ribbons, J. Magn. Soc. Jpn. 17, 191-196. Chou, T., Igarashi, M. and Narumiya, Y. (1993) Soft magnetic properties of microcrystalline Fe-Al-Si-Ni-Zr-B alloys, J. Magn. Soc. Jpn. 17, 197-200. Tomida, T. (1994) Crystallization of Fe-Si-B-Ga-Nb amorphous alloy, Mater. Sci. Eng. A179-180, 521-525. Kopcewicz, M. and Idzikowski, B. (2003) Nanocrystalline Fe81–xNixZr7B12 (x = 10-40) alloys investigated by Mössbauer spectroscopy, in Material Research in Atomic Scale by Mössbauer Spectroscopy, M. Mashlan et al. (eds.) Kluwer Academic Publishers, pp. 147158. Hayashi, K., Hayakawa, M., Ishikawa, W., Ochiai, Y., Matsuda, H., Iwasaki, Y. and Aso, K. (1987) New crystalline soft magnetic alloy with high saturation magnetization, J. Appl. Phys., 61, 3514-3519. Suzuki, K. and Cadogan, J.M. (1998) Random magnetocrystalline anisotropy in two-phase nanocrystalline systems, Phys. Rev. B58, 2730-2739. Suzuki, K., Herzer, G. and Cadogan, J.M. (1998) The effect of coherent uniaxial anisotropies on the grain size dependence of coercivity in nanocrystalline soft magnetic alloys, J. Magn. Magn. Mater. 177-181, 949-950.

THE RANDOM ANISOTROPY MODEL

A Critical Review and Update GISELHER HERZER Vacuumschmelze GmbH & Co. KG D-63450 Hanau, Germany Corresponding author: G. Herzer, e-mail: [email protected] Abstract:

The random anisotropy model provides the theoretical basis for understanding the soft magnetic properties of amorphous and nanocrystalline ferromagnets. The arguments are surveyed, updated and illustrated in detail with the help of both an analytical model and numerical simulations. Questions how to extend the original model to a multi-phase system and how to include more uniform anisotropies are discussed. The results are related to the experimental findings for coercivity and permeability.

1. INTRODUCTION The soft and hard magnetic properties of a ferromagnetic material are intimately related to its structure. The key to this is the magneto-crystalline anisotropy energy. The latter is determined by the symmetry axis of the local atomic structure. The actual microstructure leads to a distribution of magnetic easy axes varying their orientation over the scale of the structural correlation length (grain size) D. When these structural variations occur on a large scale, like in conventional polycrystalline materials, the magnetization will follow the individual easy magnetic directions of the structural units. The magnetization process is thus determined by the local magneto-crystalline anisotropy constant K1 of the grains. For short structural correlation lengths, however, ferromagnetic exchange interaction forces the magnetic moments more and more to align parallel, thus impeding the magnetization to follow the easy axis of each individual structural unit. As a consequence the effective anisotropy for the magnetic behaviour will be an average over several structural units and be thus reduced in magnitude. The consequences for coercivity and permeability are shown in Fig. 1. The critical scale where exchange interaction energy starts to balance the anisotropy energy is given by the ferromagnetic exchange correlation length L0

M0 A K1 , 15

B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 15–34. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

(1)

G. Herzer

16

μi

Hc (A/m)

where A is the exchange stiffness, K1 is the local magnetic anisotropy constant and M0 is a proportionality factor in the order of one. It represents a characteristic minimum scale below which the direction of the magnetization cannot vary appreciably and, for example, determines the order of the domain wall width. Typical values are L0 | 5-10 nm for Co-based and L0 | 20-40 nm for Fe-based alloys. Thus, both amorphous (D | atomic scale) and nanocrystalline alloys (D | 5-20 nm) fall into the regime D < L0.

10

3

10

2

D6 + Fe2B

10 1

10

5

10

4

10

3

10

2

Fe-Cu1Nb1-3Si13B9 Fe-Nb3Si13.5B9 Fe-Cu1V3-6Si12.5B8 Fe-Cu1VxSi19-xB8 Fe-Cu0-1Zr7B2-6

Figure 1. Coercivity Hc and initial permeability μ i of Fe-based nanocrystalline alloys as a function of the average grain size D (cf. [1]). The open circle corresponds to an “overannealed” Fe73.5Cu1Nb3Si13.5B9 alloy with a small fraction (less than 10%) of Fe2B precipitates

1/D6

10

50

100

Grain Size, D (nm)

200

The degree to which the anisotropy of the grains within the exchange coupled volume is finally averaged out has been successfully addressed by the so-called random anisotropy model [2-4]. The model rationalizes the most complex problems of random anisotropies by a relatively simple but most efficient scaling analysis. As a result, the averaged anisotropy constant scales down as K1

6

K1 ˜  D L0 ,

(2)

which is well reflected in the coercivity Hc (v ) and permeability μ (v 1/) of nanocrystalline materials (cf. Fig. 1). The original arguments were based on a single phase system. In real materials, however, we deal with various structural phases. Thus, in typical soft magnetic nanocrystalline materials the randomly oriented crystallites of about 10 nm in size are embedded in an amorphous matrix [3]. The latter is made up again of structural units with magnetic easy axes randomly fluctuating on a much smaller scale determined by atomic distances. Moreover, real materials reveal additional anisotropies, such as magneto-elastic and field induced anisotropies which are uniform on a scale much larger than L0. Such long-range anisotropies ultimately determine the soft magnetic properties of optimized

The Random Anisotropy Model

17

amorphous or nanocrystalline alloys where the contribution of the random anisotropies is negligible. The original model has been extended respectively [1, 5-7]. We will revisit these extensions and illuminate in more details the reasoning behind them. 2. THE MODEL Basically, the random anisotropy model is an analysis of the interplay of exchange energy and magnetic anisotropy energy which contribute to the free energy density as

I

A

¦  ’m i

2

 I K (u ˜ m)  ... ,

(3)

i x, y, z

where A is the exchange interaction constant, m is the direction of the magnetization vector, IK is the anisotropy energy density and u denotes the (local) symmetry axis. The lowest order expansions of IK for uniaxial and cubic symmetry are

IK

­ 2 1 °°m3  3 K1 ˜ ® °m 2 m2  m2 m2  m 2 m 2  1 2 3 3 1 °¯ 1 2 5

uniaxial (4)

cubic

where mi = m˜ui are the normalized magnetization components with respect to an orthogonal coordinate system adopted to the crystalline axes ui. The latter are given by the c-axis or the directions for uniaxial and cubic symmetry, respectively. K1 is the magneto-crystalline anisotropy constant. By convention, we hereby have shifted the absolute energy scale so that the average anisotropy energy vanishes for a uniformly magnetized system with randomly oriented anisotropy axis. By that we simply avoid having to carry along irrelevant additive constants in the energy terms. For the analytical treatment of the problem, we will assume that the magnetization vector m and the anisotropy axis u are lying within a plane. However, we still allow the in-plane anisotropy axis to fluctuate along the coordinate perpendicular to that plane. The latter keeps the model three dimensional. This simplified approach may be physically justified for a typical ribbon shaped sample where the large out-of-plane demagnetizing factor forces the magnetization process mainly into the ribbon plane. Anyway, the major purpose of this assumption is to keep the mathematics as transparent as possible. Accordingly, the free energy density simplifies as

I ( x)

2

A ˜  ’M 

Ku K ( x) cos 2M ( x)  1 cos 2 M ( x)  T ( x)  ... 2 2

(5)

where M is the magnetization angle1 with respect to the easy axis of the uniform anisotropy Ku. The statistically independent quantities K1(x) and T(x) represent the magnitude and orientation of the randomly fluctuating anisotropy. The anisotropy is 1

The angle M should not be confused with the pre-factor of the exchange length for which we use the same symbol. The corresponding meaning should be evident from the context

G. Herzer

18

assumed to be uniaxial whereby we have rewritten the usual form for the angular dependence, i.e. sin2(M  T), using the trigonometric identity sin2y = (1  cos 2y)/2. The general case where we admit the full set of spherical angles for both magnetization and anisotropy axis is supplemented by numerical simulations. For this purpose, we have numerically averaged the anisotropy energy for N randomly oriented anisotropy axes u keeping the direction m of the magnetization constant. We hereby chose up to one million random axes. The latter is about the number of grains within the exchange volume of a nanocrystalline Fe-based alloy with optimized soft magnetic behaviour. The anisotropy constant KN of the N grains was calculated from the energies along the resulting easiest and hardest magnetic axis. This procedure was repeated for several thousand statistically independent sets of each N randomly oriented units. The average anisotropy constant was then evaluated as the ensemble average over the results for the individual sets of each N grains. Such a statistical ensemble corresponds to the sample volume which is made up of a huge number of exchange coupled regions. 2.1. The basic concept The model is ultimately based on a scaling analysis of the average free energy for a situation when exchange interaction dominates and thus forces the magnetization to align largely parallel on a scale Lex larger than the structural correlation length D. The effective anisotropy constant relevant to the magnetization process results from averaging over the N = (Lex/D)3 units within the volume Vex = Lex3 defined by the exchange correlation length Lex. For a finite number of grains there will always be some easiest direction left, determined by statistical fluctuations. Thus the averaged anisotropy constant is determined by the mean square fluctuation amplitude of the anisotropy energies of the N grains, i.e. K1

K1

N

K1 ˜  D Lex

3/ 2

.

(6)

Within each exchange coupled unit, the magnetization will align parallel to the corresponding easiest axis. Thus the exchange interaction energy scales as (’m)2 | (D/Lex)2, where D is an effective average angle between the easiest directions of the exchange coupled units. Accordingly, the averaged total free energy of the ground state scales as 2

I | A ˜ D Lex  12 E K1 ˜  D Lex

3/ 2

(7)

where E is a constant basically related to the symmetry and distribution of the random anisotropy axis. The minimization of with respect to Lex yields Lex

M A K1

L0  L0 / D

3

with

M0

D 8 3E ,

(8)

where is the averaged anisotropy constant as introduced by Eq. (6) and L0, as defined in Eq. (1), is the basic exchange length related to the local anisotropy constant

The Random Anisotropy Model

19

K1. The renormalized exchange length Lex, results from the basic exchange length L0 by self-consistently substituting the averaged anisotropy for the local anisotropy constant K1. In other words, the scale on which the exchange interaction dominates expands at the time as the anisotropy is averaged out. By combining Eqs. (6) and (8), can be finally expressed as shown in Eq. (2). The minimized total energy itself results as min = min/4. That makes an essential difference to the classical uncoupled multi-particle systems where the total minimum energy is only determined by the minimum anisotropy energy min. It should be noted that the pre-factors D and E via their combination in M0 can be rationalized into the basic exchange length L0. The latter ultimately remains the only open parameter within the above scaling analysis. It is therefore more appropriate to write down the results for or Lex in a rationalized form involving the ratio (D/L0) rather than in the explicit form as given in the original papers [2-4] involving all the individual material parameters and, in particular, more or less arbitrary pre-factors. 2.2. Average magnetic anisotropy So far, the argument for the average anisotropy is rather intuitive and based on general statistical concepts. Furthermore we still have to extend the model to a random multi phase system as well as to the case of a superimposed uniform anisotropy. Both is mainly a question of understanding how to add anisotropies. 2.2.1. Random anisotropies We start with purely random anisotropies averaged over the volume Vex = Lex3 of the exchange length within which the magnetization vector m is assumed to be constant. The average anisotropy energy can therefore be written as

IK



N

1 Vex

³

K1 ( x) f  m ˜ u ( x) d 3 x

Vex



1 N

N

¦ k (i) f  m ˜ u(i) 1

(9a)

i 1

with k1 (i ) : K1 (i ) ˜ :(i ) N Vex

(9b)

where K1(xi) is the magnitude, u(xi) the random axis and f(m˜ui) the angular dependence of the anisotropy energy for an individual grain (more precisely “structural unit”) located at the site xi. In the second step, we converted the integral into a discrete sum over the N exchange coupled grains and defined, as a convenient abbreviation, an effective local anisotropy constant k1(i) where : (i):= D(i)3 denotes the volume of the grain at the site i. In our planar anisotropy model we can explicitly write

IK

N



1 N

¦ i

k1 (i ) ˜ cos 2 M  T (i ) 2



kN ˜ cos 2 M  T N 2

(10)

where T (i) is the random orientation of the individual units. The sum over the grains can be rewritten as a single anisotropy expression with magnitude kN and orientation TN

G. Herzer

20

using trigonometric relations. The resulting easiest orientation TN is still a random angle if we look at different statistical sets of each N coupled grains. The resulting anisotropy constant kN is kN

k12 1  2 N N

¦ ¦ k (i)k ( j) cos 2 T (i)  T ( j ) 1

i

1

(11a)

j ( zi )

with k12 :

xQ K Q DQ ˜ N ¦ Q 2 1,

3

L3ex .

(11b)

While the indices i, j in Eq. (11a) run over the location of the individual grains, the index Q in Eq. (11b) refers to the structural phases where xQ is the corresponding volume concentration. The term “structural phase” here refers to all grains with the same anisotropy constant K1Q and the same size DQ which allows to handle a grain size distribution. The definition of k1 in Eq. (11b) rationalizes the random anisotropies of different structural phases into a single effective anisotropy constant. The only assumptions are that the anisotropy constants k1(i) are statistically independent of the random orientation T (i) and that the average number of grains within the exchange volume is larger than that for each phase, i.e. NQ = xQ˜(Lex/DQ)3 > 1. The randomness is ultimately reflected in the circumstance that k1 is determined by the mean squares of the local anisotropy constants rather than by a linear average. The anisotropy constant kN of the N grains is still statistically fluctuating around an average value v k1/N1/2. The fluctuations arise from the second expression under the square root in Eq. (11a), i.e. from the sum over all anisotropy cross terms between grains at different sites. Their relative orientation (Ti-Tj) is a random phase. Therefore the individual anisotropy cross terms mutually cancel and their average sum scales down proportionately to k12/N. Accordingly, the fluctuations of kN around its average value are proportional to the average itself. For an ensemble of statistically independent sets of each N coupled grains, the averages of the anisotropy constant kN and the minimum anisotropy energy IKmin are thus given by kN

E k1

N

IKmin

E

xQ K Q DQ ¦ Q 2 1,

3

L3ex

 12 k N

(12a)

(12b)

and the standard deviation of the anisotropy constants within the ensemble is

VK :

k N2  k N

2

K ˜ kN .

(13)

The parameter E involves higher order angular moments like originating from the anisotropy fluctuations within the ensemble. Its meaning is the same as in Eq. (7). An analytical expansion to the first relevant order yields E | 1  /4 = 0.875

The Random Anisotropy Model

21

and K | (1/E 2 – 1)1/2 = 0.553 which is close to the results of the numerical simulations. The latter yield E | 0.90r0.04 and K | 0.50r0.05, for an ensemble with 2000 statistically independent sets of each N (= 2-219) grains. The simulations show that the results apply already to an ensemble with statistically independent sets of only two coupled grains. Figure 2 shows the results of numerical simulations for a single phase system of cubic and uniaxial anisotropies. The simulations demonstrate that the relations found for the ensemble averages also apply very well to anisotropies oriented randomly over all spherical angles. Accordingly, we find E | 1.06r0.03 (K | 0.31r0.05) for uniaxial and E | 0.393r0.003 (K | 0.22r0.03) for cubic anisotropies, respectively. The indicated errors arise from the finite ensemble size (about 4000 statistically independent sets of N coupled grains). It should be noted, however, that the relation given by Eq. (11a) for the anisotropy constant kN of one particular set of N randomly oriented grains is restricted to our simplified model. In particular, the angular expressions in the anisotropy crossterms are much more complex in the general case. 1 uniaxial

p

0.1

E= 1.06 -1

-/|K1|

Figure 2. Numerical simulation of the minimum anisotropy energy of N coupled cubic (squares) and uniaxial (circles) grains with randomly oriented anisotropy axis. The full symbols are for K1 > 0, the open symbols for K1 < 0; the lines are the theoretical average. The results represent the average over statistical ensembles with about 4000 sets of each N randomly oriented grains. The inset shows the typical distribution p of the anisotropy constants kN within the ensemble (the example shown is for N | 16400)

10

0

cubic

0

E = 0.393

-2

1

k N/

10

-3

IKmin

10



2

E K1 2

N

-4

10

1

1

10

2

10

3

10

N

4

10

5

10

6

10

The rather distinct value of E for the cubic case is largely a consequence of common conventions for the anisotropy energy (cf. Eq. (4)). The latter result in 'IK = |K1|/3 for cubic and 'IK = |K1| for uniaxial anisotropies where 'IK = IKmax  IKmin is the energy difference between the hardest and easiest axis. If we redefined the cubic anisotropy constant as K1' = IKmax  IKmin = K1/3, we would actually find E’ | 1.17, i.e. a value close to the one for the cubic case as well. The remaining difference involves corrections from random fluctuations. Accordingly, we would approximately have E’ ~ 1 in all cases. In order to stay with the conventional nomenclature for the local anisotropy constants, I have so far adopted the definition of the averaged anisotropy constant to the conventions used for the underlying symmetry, like in Eq. (6). That is, was introduced in such a way that it is equal to K1 for N = 1. This is the most convenient way if we deal mainly with one single phase and I will come back to it where appropriate. However, here and in the following discussion, I will mainly use the notation := E = IKmax  IKmin for the average anisotropy constant and the conventional nomenclature for the local anisotropy constants K1. This convention is actually more appropriate when we generalize the model to mixed symmetries.

G. Herzer

22

As for the minimum of the average anisotropy energy, Eq. (12b) is actually trivial for our simplified model. But it is non-trivial for the general case of random spherical angles. It represents the finding that the ensemble averages of the minimum and maximum anisotropy energy density are arranged symmetrically around the energy for an infinite number of grains. The latter corresponds to the energy for the homogeneously magnetized state. This contrasts the situation for uncoupled grains where the local magnetization is aligned parallel to each individual random anisotropy axis. Then, the average minimum or maximum anisotropy energy simply equals the corresponding value of the individual grains. As a result, the minimum and maximum anisotropy energies, in general, are arranged asymmetrically around the homogeneously magnetized state. From Eq. (4) one can see, for example, that IKmin/K1 = 2/3 and IKmax/K1 = +1/3 for uniaxial and IKmin/K1 = 1/5 and IKmax/K1 = +2/15 for cubic anisotropies with K1 > 0 and, vice versa for K1 < 0 (cf. Fig. 2 for N = 1). A related finding, to be discussed in more detail now, is that the energy surface of randomly oriented coupled grains no longer has the high symmetry exhibited by a pure uniaxial or cubic anisotropy: Random uniaxial anisotropies can be largely characterized analytically. The corresponding energy density of Eq. (4) can be alternatively written as IK = m˜K1˜m, where K1 is a symmetric second rank tensor with zero trace2. The average over the N coupled grains assumes the magnetization m to be constant and, hence, simply results in N = m˜KN˜m with KN being still a symmetric second rank tensor with zero trace. The eigenvectors of the anisotropy tensors K define the anisotropy axes and the eigenvalues the anisotropy constants. In a coordinate system defined by its eigenvectors, KN can always be represented as

KN

0 0 · §u ¨ ¸ k N ˜ ¨ 0 1  2u 0 ¸. ¨ 0 u  1¹¸ ©0

(14)

The coordinates have been chosen in such a way so that the x-axis is defined by the magnetic hardest and the z-axis by the easiest axis. The anisotropy constant kN denotes the energy difference between the hardest and easiest direction and is positive by definition. For a single grain we would simply have k1 =|K1|, while for N grains the ensemble average is given by = E |K1|/N 1/2 with E | 1.06 as just discussed. The parameter u describes the symmetry and, with the above choice of the coordinate axes, is restricted to the range 1/3 d u d 2/3. The boundaries u = 1/3 and u = 2/3 correspond to a magnetic easy axis with hard a plane and a magnetic hard axis with an easy plane, respectively (cf. Fig. 3). In the more traditional notation of Eq. (4), this distinction is made by the sign of K1, where K1 > 0 corresponds to u = 1/3. However for N coupled grains, we find from our numerical simulations that u is distributed around an average value given by | 0.50 with a standard deviation of Vu | 0.07, no matter whether we start from an easy (u = 1/3) or a hard axis (u = 2/3). As illustrated in Fig. 3 2

The trace of K corresponds to the anisotropy energy of a uniformly magnetized system with random anisotropies. This value was set to zero by convention

The Random Anisotropy Model

23

here we deal with three preferred axes perpendicular to one another, corresponding to a minimum, a saddle point and a maximum of the anisotropy energy. For cubic anisotropies the corresponding arguments would involve a more complicated analysis of a fourth rank tensor which still has to be done. We can therefore only discuss the still somewhat preliminary numerical results and argue in a more visual way with the help of the typical random energy surfaces shown in Fig. 3. uniaxial

u = 2/3

u = 1/3

z

r I  I min

u = 1/2 (random average) cubic

K1 > 0

N=1

x

y

K1 < 0

N = 1 Mio (random average) Figure 3. Energy surfaces for uniaxial and cubic anisotropies. The distance from the origin corresponds to the anisotropy energy difference IK  IKmin for a certain orientation of the magnetization vector. The scale of each plot is adopted to the maximum energy difference. The color scale (see electronic version of this paper) ranges from black over blue, green and red to white for increasing energy differences. Blue colors indicate the orientations around the minimum and red colors around the maximum of IK. The thin black lines indicate the magnetic easiest axis. For random cubic anisotropies, we have additionally marked the magnetic hardest axis by thin red lines

G. Herzer

24

For one single cubic grain we have 3 easy axes along the directions and 4 hard axes along the directions for K1 > 0 and vice versa for K1 < 0. However, this distinction disappears for randomly oriented grains. A random energy surface produced by a set of N grains with K1 > 0 can be always reproduced by another set of N grains with K1 < 0. Thus, the random average again breaks the high original symmetry and ultimately results in only one easiest axis and one hardest axis forming an average angle of about 50° with each other. Yet, there are a number of intermediate easy and hard directions which still remind of the original cubic symmetry. Typically, the various easy axes form an angle of about 80°-90° with one another and their energies are relatively close together, differing by about 10%-20%. 2.2.2. Mix of random and uniform anisotropies Figure 4 illustrates how an additional uniform anisotropy of magnitude Ku significantly changes the situation as soon as it dominates over the random anisotropy contribution. Ku K1

N

=0

0.2

5 K1

z

Ku

1

N

1 K1

x

0.4

2

3

N

y 5 K1

N

Figure 4. Energy surfaces when a uniform uniaxial anisotropy is added to the anisotropy of N coupled, randomly oriented cubic grains (N = 10 000). The original easy axes of both uniform and average random anisotropy are indicated in the coordinate system. The resulting easiest axis is shown in blue (see electronic version of this paper). The horizontal bars indicate the energy scale. Note the change of scale in the bottom row

In practice, such a uniform anisotropy may be typically due to field or creep induced anisotropies, magneto-elastic anisotropies or shape anisotropies originating from both the sample geometry and surface roughness. But it may also originate from some degree of crystalline texture. It has not necessarily to be perfectly homogeneous in space, but it is allowed to fluctuate on a length scale much larger than the exchange length Lex. In our analytical model the total average anisotropy energy of the N coupled grains can be written as

The Random Anisotropy Model

IK

N

25

 12 K u cos 2M  12 k N cos 2(M  T N )

 12 K cos 2(M  -N )

(15a)

where kN and TN refer to the random contribution discussed in the previous section and Ku is the strength of the uniform anisotropy. All angles are chosen relatively to the easy axis of the uniform anisotropy at M = 0. The sum of both contributions can be again rewritten as a single anisotropy expression with the help of trigonometric relations. The resulting anisotropy constant K and new easiest orientation -N are K u2  k N2  2 K u k N cos 2T N

K

-N

1 2

arctan

(15b)

k N sin 2T N K u  k N cos 2T N

With similar arguments as in the previous section, the ensemble average of K follows as K

K u2  f u k N

2

(16)

where is the average random contribution given by Eq. (12a). The parameter fu denotes a correction arising from the randomly fluctuating cross term between the random and uniform anisotropy. It is a function of Ku/ which, in general, equals one for Ku = 0 and evaluates to a constant value for Ku >> . It can be reasonably approximated as fu | 1  cu (Ku/)2 in the lowest significant order. We find cu | = 0.5 for our planar anisotropy model. A spherical distribution of random angles involves just more complicated expressions for the angular moments. From the numerical simulations we find cu | 0.5 for the uniaxial and cu | 0.2 for the cubic case, i.e. approximately cu | E/2 in either case. 1.0 0.8

- (rad)

Figure 5. Numerical calculation of the average angle - (:= arccos) between the easiest and the macroscopic easy axis as a function of the uniform anisotropy constant Ku normalized to the average anisotropy constant := K1/N1/2 for randomly oriented cubic (full symbols) and uniaxial (open symbols) grains. The dashed line is the limit for Ku = 0. The results represent averages over statistical ensembles with up to 4000 sets of each N (= 4 to 220) grains; Ku was varied in the range Ku = 0.00125 to 0.64 K1

cubic

uniaxial

0.6

Ku

0.4

- easiest axis

0.2 0.0 0.01

0.1

1

10

Ku/

As illustrated in Fig. 4, the easiest axis is rotated towards the macroscopic anisotropy axis as soon as Ku approaches and finally exceeds the order of the random contribution. Figure 5 supplements the average orientation of the easiest axis as a function of Ku, for both uniaxial and cubic random anisotropies. Accordingly, the magnetic moments are forced to align more and more parallel, but this time as a consequence of the uniform anisotropy. The decreasing angular dispersion - 2 reduces the amount of exchange energy. Accordingly, the averaged total free energy density is now given by

G. Herzer

26 2

I | A ˜ H 2 D Lex  12 K ,

(17)

where H = - /T is the average ratio between the easiest angle - for Ku > 0 and the random angle T. It is related to the anisotropy constants by

H2

fH ˜ k N

2

K

2

.

(18)

By definition, H 2 equals one for Ku = 0. But it scales down as 1/N = (D/Lex)3 for dominating Ku, thus modifying the scaling behaviour of the exchange energy. The parameter fH denotes a correction from the anisotropy cross terms similar to fu in the average anisotropy constant. Like fu, it equals one for Ku = 0 and evaluates to a constant value for Ku >> . It can be again reasonably approximated as fH | 1  cH (Ku/)2 in the lowest significant order. For our planar model we find cH | = 0.5. For a spherical distribution of random angles, the numerical simulations yield cH | 0.8 for both the uniaxial and cubic case. The minimization of with respect to Lex again relates the renormalized exchange length to the average anisotropy constant in the usual form3, i.e. Lex = M0(EA/)1/2. The minimum energy min itself results as min | (1 3H2/4)min. When the uniform anisotropy is dominating over the random contribution, the average anisotropy constant evaluates as – Ku v 1/N. This changes the scaling behaviour of the random contribution from a D6 to a D3 law. Figure 6 shows the corresponding result obtained by numerical simulations for random cubic anisotropies. The numerical results for the average anisotropy energies are very well described by the theoretical relations. The theoretical estimate of the anisotropy angle is reasonable only for Ku < and Ku > , but relatively crude in the intermediate range where Ku | . The corresponding fit is much better for random uniaxial anisotropies. The figure actually shows an effective anisotropy constant Keff defined as the energy difference needed to rotate the magnetization from its easiest direction (1) into the macroscopically hard axis (3). This definition is introduced here because the average anisotropy constant itself involves the hardest axis determined by Ku and the random contributions which is virtually inaccessible in experiment. Accordingly, Keff corresponds rather to the experimental situation, i.e. to the area under the hysteresis loop when magnetizing the sample perpendicular to the uniform anisotropy axis starting from the demagnetized state. The difference GK = Keff  Ku reflects the average dispersion GK of the anisotropy constant due to random fluctuations. It determines the coercivity which for domain wall displacements, is approximately given by 1 wJ W G K Lex (19) Hc | | 2 J s wx max Js O 3

The literal procedure of minimization actually introduces minor corrections arising from the anisotropy cross terms. This causes M0 to deviate slightly from the value given in Eq. (8) as a function of Ku/. However, in view of the simplifying assumptions entering into the scaling analysis, we have discarded this nominal result in order not to overdraw the simplified approach

The Random Anisotropy Model

27

where JW = 4 (A/K)1/2 is the domain wall energy, Js the saturation magnetization and O the fluctuation length of the anisotropies. For exchange coupled grains, the latter equals to the exchange length, i.e. O | Lex. The coercivity is thus directly proportional to the anisotropy dispersion GK. Hence, we expect Hc v D3 if Ku is dominating. A corresponding behaviour was indeed observed by Suzuki et al. [6] e.g. for nanocrystalline Fe91Zr7B2 in the range D | 12-18 nm. If the random anisotropies are dominating, GK is simply proportional to the average anisotropy itself which results in Hc v D6 as shown in Fig. 1. It is most instructive to study the corresponding arguments of Alben et al. [2] who arrive at the essentially same results for both situations.

Figure 6. Effective anisotropy constant Keff (:= IK(3)  IK(1)) and angular dispersion - 2 (:=arccos2) for a cubic single-phase system as a function of the normalized grain size D/L0. The random anisotropies were superimposed with a uniaxial anisotropy of magnitude Ku = 0.01˜K1. The symbols are the numerical averages for a statistical ensemble with 3300 sets of each N = 2 to 218 grains; the lines are the theory. The small open squares supplement the results for Ku = 0 (Nmax = 220). The ratio D/L0 was calculated from the average anisotropy constant as D/L0 = (EK1/)1/2/N 1/3 which results by combining the relations for L0 and Lex with N = (Lex/D)3. It covers the relevant grain size range (D | 4 – 40 nm) for typical iron based nanocrystalline materials (L0 | 40 nm)

More long-range anisotropy fluctuations on a scale O > Lex can of course contribute to Hc as well. Actually, these more classical mechanisms play a dominant role in optimized FeCuNbSiB alloys and overshadow the grain size dependence expected from the random contribution. Most relevant to this are surface roughness, magneto-elastic anisotropies as well as a distribution of anisotropies induced during annealing along the orientation of the magnetization in the domains at elevated temperatures. The permeability μ, depends in general upon the angle between the applied field and the uniform anisotropy like in the more classical case. If the sample is magnetized perpendicularly to the uniform anisotropy axis μ is inversely proportional to the total anisotropy, i.e. μ v 1/Keff, and, therefore, grain size independent if Ku is dominating. If

28

G. Herzer

magnetized parallel to the uniform axis, it is determined by GK, i.e. μ v 1/GK, with a corresponding grain size dependence. This distinction vanishes for dominating random anisotropies and we arrive at the 1/D6 dependence shown in Fig. 1 since Keff = GK. 2.3. Material parameters As pointed out earlier, the basic exchange length L0 remains an open parameter of the scaling analysis. From the formal point of view, the precise value of this length scale is ultimately irrelevant for characterizing the scaling behaviour of with the structural correlation lengths. I was therefore rather generous with respect to that issue in previous publications where I put the pre-factors for L0 simply to one (cf. [3-6]). Similarly, the work of Alben et al. [2] should be also read generously with respect to the actual pre-factors. However, from a practical point of view it is highly desirable to relate L0 to the actual material parameters as close as possible. For this purpose we need to look more closely at the exchange interaction energy. The latter was simplified as = A(D /Lex)2 in order to extract its scaling behaviour. This actually involves two questions: (i) What is the average exchange constant A for multi-phase systems? (ii) What is the effective angle D between the easiest axes of exchange coupled regions? The exchange constant A has to be ultimately understood as an effective average value on the scale of the exchange length. However, as demonstrated by experiment, it is not a simple volume average. It is rather determined by the “weakest link” in the exchange chain which, for example, is the amorphous intergranular phase in typical nanocrystallized materials [3]. Hence, it should result from some kind of “inverse averaging” of the local exchange constants, similar to the way how parallel resistors are adding. We are leaving that theoretical issue open here and refer to the work of Suzuki et al. [7] who have proposed the most reasonable physical approach to the problem so far. Here we simply use the experimental value of the nanocrystallized material. The latter should be preferred over the value for the crystalline phase which I originally used to estimate the average anisotropy constant for room temperature (cf. [3, 4]). The parameter D is defined as D2: = . Accordingly, we need to estimate the magnetization gradient between two neighboring regions of coupled grains. Let T denote the smallest angle enclosed by the corresponding easy axes. We assume that the magnetization is rotating on a cone from one easy axis to the other easy axis in a strayfield free way similar to the situation in a domain wall (cf. [8]). This yields (’m)2 = sin2- (’I)2 where - is the polar angle of the cone. The azimuth angle I (= I0...I0v + GI) describes the rotation of the magnetization. From geometry, GI is given by cosGI = (cosT  cos2-)/sin2- where - may be any angle between T/2 to S/2. Like in a domain wall, the azimuth angle I changes approximately linearly on the scale of Lex, i.e. (’I)2 | (GI/Lex)2. The minimum exchange energy results for a “flat cone”, i.e. for - = S/2. The effective angle D between the easiest axis is thus given by D = 1/2. Statistically, the angles between the easy axes themselves are equivalent to the polar angles between the individual easy axes and a macroscopic direction.

The Random Anisotropy Model

29

Accordingly, can be calculated by averaging over the angles T of the easy directions nearest to the polar axis, similar to the classical calculation of the remanence for multi particle systems (cf. [8]). The result is D | 1.068 for uniaxial and D | 0.561 for cubic symmetry. For mixed symmetries D will be determined by the symmetry of the dominating anisotropy contribution. The cubic case needs some more reasoning: The random average results in only one easiest magnetic axis, i.e. we would have the same value for D as for uniaxial anisotropies. Yet, there are a number of easy directions which still remind of the cubic symmetry and which are energetically close together. The exchange plus anisotropy energy can be ultimately minimized if the magnetization is parallel to any of these easy axes. The latter can be of or type, irrespective of the sign of the local anisotropy constant K1. Accordingly we assumed = (100 + 111)/2. In the preceding arguments, we considered Lex as the scale on which the magnetization is coherently rotating from the easy axis of one exchange coupled region to the easy axis of the neighboring region. In contrast to this, we assumed the magnetic moments of the coupled grains to be oriented perfectly parallel in the arguments for the average anisotropy. This apparent ambiguity may be resolved as follows: Let us think of a second scale L1 < Lex on which the magnetization is largely parallel. Both L1 and Lex are determined by the interplay of exchange and anisotropy energy and, hence, are proportional to each other. The minimum anisotropy energy on the scale of L1 would be IKmin(L1) | –K1˜(D/L1)3/2. However, the corresponding easiest axes are determined by the local anisotropy fluctuations and, hence, are randomly oriented. The magnetization cannot follow these random orientations along the scale of Lex due to the smoothing effect of the exchange interaction. Consequently, the anisotropy is averaged out additionally and its average minimum density approaches IKmin(Lex) | –K1˜(D/Lex)3/2. Thus, the distinction between L1 and Lex disappears, at least to a certain extent. The mechanism can be approximately confirmed for simplified model situations where the total energy can be minimized analytically. It thus appears legitimate to assume that the average over the random anisotropies of N grains with perfectly parallel magnetization is approximately the same as the corresponding average for the case where we allow a coherent variation of the magnetization m over the same scale. Actually, the same conclusion is obtained if we suppose that the variation of m on the scale of Lex is statistically independent of the random orientation of the local easy axis. Possible corrections to this assumption would result in somewhat larger values of the parameter E or, vice versa, in somewhat smaller values for D. Yet this remains an uncertainty which still has to be clarified. Table I summarizes the results for a, E and M0 obtained by way of the preceding arguments. Table II gives the corresponding estimate of the basic exchange length L0 for nanocrystalline FeCuNbSiB alloys together with some relevant material parameters. However, it must be noted that some of the reasoning behind these parameters is not free from some uncertainties. The numerical precision given in the tables is therefore apparent and only valid within the corresponding assumptions. The values represent ultimately only a best guess and should be handled with the appropriate precaution.

G. Herzer

30 Table I. Estimated pre-factors a, E and M0 for cubic and uniaxial anisotropies Cubic Uniaxial a

0.56 0.39 1.46

E M0

1.07 1.06 1.70

Table II. Material parameters for the possible crystalline phases in nanocrystalline FeCuNbSiB alloys. For the estimate of L0 we assumed A = 5.7-6.2 u 1012 J/m which is the experimental exchange constant for the nanocrystallized state (the larger value applies to “overannealed” samples with small fractions of Fe2B)

D-Fe80Si20 Symmetry K1 (kJ/m3) L0 (nm) * interpolated from the data in [9]

Fe2B uniaxial –430 [10] 6.5

cubic 8.2* 39

Let us finally discuss how our theoretical estimate compares with the experiment. The basic exchange length L0 of the bcc crystallites can be determined from the upper critical grain size Dc where coercivity Hc and permeability μ no longer follow a D6 or 1/D6 law, respectively. This is the most unambiguous way if we want to avoid additional uncertainties related to the precise relation between the average anisotropy constant and Hc or μ, respectively (cf. [4]). From Fig. 1 we can estimate the upper critical grain size for the bcc crystallites as Dc ~ 35-45 nm. As discussed later, Dc is related to the basic correlation length by L0 | x1/6Dc, where x is the crystalline volume fraction. Assuming typical fractions of x ~ 0.7-0.8 (cf. [1]) we thus arrive at L0 ~ 33-43 nm. With K1 and A from Table II, this would yield M0 ~ 1.3-1.6 in approximate agreement with the theoretical estimate for cubic anisotropies. Yet, this experimental evaluation is not totally unambiguous either, since the material parameters are not too precisely known. In particular, the grain size cannot be varied in a straight forward way without slightly changing the local material constants or the crystalline fraction simultaneously.

3. CONCLUSIONS We propose that the average anisotropy constant of a coupled multi phase system with randomly oriented anisotropies is given by K



K u2  ¦ xQ EQ2 K1,2Q ˜ DQ Lex Q



3

(20)

where is defined as the difference between the maximum and minimum anisotropy energy density. Ku represents a uniform anisotropy which may fluctuate on a scale much larger than Lex. The random contributions are represented by the local anisotropy constants K1,Q, the grain sizes DQ and the volume fractions xQ of the individual structural

The Random Anisotropy Model

31

phases labeled by the index Q. The result includes a grain size distribution if “structural phase” refers to all grains with the same anisotropy constant K1,Q and the same grain size DQ. The parameters EQ mainly involve conventions used for defining the anisotropy energy for different symmetries, but also include some statistical corrections in the order of 10-20%. They sharpen our previous results [3-6]. The final relation has been generalized to include mixed symmetries by weighing the structural phases with their individual symmetry moments EQ. Numerical summations for a single phase system result in E | 1 for uniaxial and E | 0.4 for cubic symmetry. We have omitted less relevant corrections from anisotropy cross terms between the uniform anisotropy Ku and the random contributions. The latter can be taken into account in the lowest order by the substitution E 2 o E 2˜(1 0.5 E (Ku/)2). The result is based on statistical concepts which apply as long as the average number of coupled grains 3

xQ  Lex / DQ ! 1

NQ

(21)

is larger than the one for each individual phase. So far coupling only specifies that the magnetization is parallel within the volume defined by the magnetic correlation length Lex. If the coupling is dominated by exchange interaction, this magnetic correlation length can be self-consistently related to average anisotropy constant by Lex

M A K .

(22)

In the general case, the average anisotropy has to be determined by iteration. Explicit solutions can be obtained in the limiting cases of a vanishing or dominating macroscopic anisotropy Ku. The results are K

§ ¨ ¦ xQ EQ K1,Q © Q



DQ L0,Q



3

· ¸ ¹

2

(23)

for Ku = 0, and



K | K u  12 ¦ xQ EQ K1,Q K u DQ L0,Q Q



3

(24)

if the uniform anisotropy is dominating over the random contributions. The latter is accompanied by a change of the scaling behaviour of the random anisotropy contribution from D6 to D3. In both relations L0,Q : M0,Q A K1,Q with M0,Q : M

EQ

(25)

define the basic exchange lengths related to the local anisotropies of the individual structural phases. The corresponding pre-factors are expected to be about M0 ~ 1.5. Figure 7 illustrates the expected grains size dependence on the average random anisotropy for typical Fe-based nanocrystalline alloys with a majority phase of bcc crystallites. The figure basically sketches two situations which correspond to the opti-

G. Herzer

32

mized nanocrystalline state and the initial second stage of crystallization when small fractions of Fe2B are precipitating (cf. [1]). In the regime where the contribution of the bcc crystallites is dominating, the expressions for and Lex simplify drastically, i.e. K : E K1 Lex

E K1 ˜ x 2  D L0 3

L0  L0 / D x .

6

(26) (27)

(J/m3)

The only modification compared to a single phase system is that the relations involve the crystalline volume fraction x. Both and Lex are hereby scaling with the volume fraction in the same way as with the crystalline volume D3. The relations are identical to those for exchange coupled crystallites diluted in an ideally soft magnetic matrix. The contribution of the amorphous phase is virtually negligibly small, although its local anisotropy has been assumed to be more than an order of magnitude higher than that of the bcc crystallites. This is related to the circumstance that the corresponding anisotropies are fluctuating on a much shorter scale determined by atomic distances (Dam | 0.5 nm). 10

4

10

3

10

2

10

1

5% Fe2B: DFeB = 6 nm 5% Fe2B: DFeB = 4 nm

D3

1 10

-1

10

-2

10

-3

10

-4

5% Fe2B: DFeB = 2 nm

25% amorph.

D6 1

5

10

D (nm)

Figure 7. Theoretical estimate of the average anisotropy for a system of randomly oriented crystallites of bcc Fe80Si20 with grain size D and volume fraction x = 0.75. The crystallites are embedded in an amorphous matrix where a small fraction (5%) of Fe2B with a size of 2-6 nm is assumed to precipitate. Only the random anisotropy contributions are shown. The material parameters are given in Tables I and II. The atomic scale anisotropy constant of the amorphous 50 phase was assumed to be the same as that of Fe2B

The condition NQ > 1 is always fulfilled for the amorphous matrix. For the crystallites it simplifies to D  L0 x1/ 6 .

(28)

The critical grain size below which the averaging process takes place is thus somewhat enhanced due to the dilution effect4. For the optimum nanocrystallized state with no boride precipitates, is scaling with D6 down to grain sizes of about 5 nm. The random anisotropy of the amorphous matrix becomes only visible for very small grains resulting in a grain size independent 4

The somewhat different dilution effect (x1/4 instead of x1/6) given in [5] was related to the anisotropy fluctuations and not to average anisotropy , which makes a difference for D > Lex

The Random Anisotropy Model

33

anisotropy. However, the related coercivity (Hc ~ 0.001 A/m) is so small, that the situation shown for small grain sizes in Fig. 7 remains academic. In real materials, whether amorphous or nanocrystalline, the minimum Hc is ultimately determined by more long range anisotropy fluctuations which have been not considered in the figure. The lower limit where there is no more benefit of reducing the grain size is ultimately located at grain sizes of about 10 nm for typical FeCuNbSiB alloys (cf. Fig. 1). Yet, a very small volume fraction of a phase with high anisotropy and a grain size somewhat larger than the atomic scale can change the picture significantly. This is illustrated in Fig. 7 assuming a small fraction of Fe2B precipitates with different grain sizes. The example explains at least qualitatively the familiar finding that Fe2B precipitates significantly deteriorate the soft magnetic properties although the grain size of the bcc crystallites may remain virtually unchanged (cf. Fig. 1). The transition regions where the average anisotropy of bcc grains starts to dominate can be approximately characterized by a D3 law in a limited range of grain sizes. One can thus speculate whether a D3 dependence on Hc, so far related to the presence of a uniform anisotropy, might be also attributed to an “improper” intergranular matrix in certain cases. Yet this, like many other details, still needs further investigation. The focus of this review was on how to sum up random anisotropies. The essential assumption here has been was that the magnetization is largely parallel over a sufficiently large number N of grains. The coupling mechanism does not necessarily have to be exchange interaction but could also be dipolar interaction. In the latter case “Lex” should be understood as magnetic correlation length which is not necessarily proportional to 1/1/2 like it is for exchange interaction. But many of the arguments and results for the average anisotropy still apply as long as we leave the relation between “Lex” and open. Dipolar interactions, without any doubt, become increasingly important when the exchange interaction between the crystallites is largely interrupted, e.g. when the amorphous intergranular phase becomes paramagnetic (cf. [5]). It is still open how to incorporate them correctly into the scaling analysis of the total energy. Another open question for multi-phase systems is how to relate the effective exchange constant A to the local material parameters in general. Suzuki's model [7] assumes that the crystalline phase is completely surrounded by the amorphous phase. In many cases the latter reflects the typical situation in nanocrystallized materials. But what is the appropriate model if, for example, the crystallites were only one or two atomic distances apart or even were touching one another more or less frequently? The answer is not given yet, while the arguments for averaging the individual anisotropies are still the same. The problems of quantifying the effective exchange constant or the ferromagnetic correlation length for dipolar interactions are therefore still profound theoretical challenges which appear to be far more complex than the statistical summation procedure for random anisotropies.

G. Herzer

34

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Herzer, G., (1997) Nanocrystalline soft magnetic alloys, in K.H.J. Buschow (ed.), Handbook of Magnetic Materials, Vol. 10, Elsevier Science, pp. 415-462. Alben, R., Becker, J.J. and Chi, M.C., (1978) Random anisotropy in amorphous magnets, J. Appl. Phys. 49, 1653-1658. Herzer, G., (1989) Grain structure and magnetism of nanocrystalline ferromagnets, IEEE Trans. Magn. 25, 3327-3329. Herzer, G., (1990) Grain size dependence of coercivity and permeability in nanocrystalline ferromagnets, IEEE Trans. Magn. 26, 1397-1402 Herzer, G., (1995) Soft magnetic nanocrystalline materials, Scr. Metall. Mater. 33, 1741-1756. Suzuki, K., Herzer, G. and Cadogan, J.M., (1998) The effect of coherent uniaxial anisotropies on the grain size dependence of coercivity in nanocrystalline soft magnetic alloys, J. Magn. Magn. Mater. 177-181, 949-950. Suzuki, K. and Cadogan, J.M., (1998) Random magnetocrystalline anisotropy in two-phase nanocrystalline systems, Phys. Rev. B 58, 2730-2739. Chikazumi, S. and Charap, H., (1964) Physics of Magnetism, Robert E. Krieger Publishing Company, Malabar, Florida. Gengnagel, H. and Wagner, H., (1961) Magnetfeldinduzierte Anisotropie an FeAl- und FeSi-Einkristallen, Z. Angew. Phys. 8, 174-177. Iga, A., Tawara, Y., and Yanase, A., (1966) Magnetocrystalline anisotropy of Fe2B, J. Phys. Soc. Japan 21, 404.

SOME ASPECTS OF THE CRYSTALLIZATION OF FINEMET- AND NANOPERM-LIKE ALLOYS

J.M. BARANDIARAN Universidad del Pais Vasco (UPVEHU), Departamento de Electricidad y Electrónica P.O. Box 644, E-48080 Bilbao, Spain Corresponding author: J. M. Barandiaran, e-mail: [email protected]

Abstract:

Nanocrystallization in FINEMET- and NANOPERM-like alloys has been studied by less commonly used methods, as resistivity, EXAFS and magnetoelastic measurements. The results are compared with those of classical methods. The less conventional methods show a non-linear relationship of the measured parameter with the transformed fraction. Also evolved heat, as recorded in DSC experiments, is shown to display a similar non-linear relationship in primary crystallization. A common feature of the kinetics of nanocrystallization in all studied compounds is the large tails obtained in the isothermal and non-isothermal treatments, currently described by an Avrami index that changes during the crystallization. In an alternative model, justified by very basic assumptions that should apply to all primary crystallization processes, the observed kinetics is attributed to the change of the activation energy during the transformation.

1. INTRODUCTION FINEMET- and NANOPERM-like nanocrystalline alloys [1-3], with compositions FeMSiCuB and FeMCuB, where M is a refractory metal or a mixture of them (M = Nb, Mo, W, Ta, Zr, Hf, ...), are extremely good soft magnetic alloys. This is because of the averaging out of the crystal magnetic anisotropy due to the grain size being lower than the exchange correlation length [4, 5]. The usual method for obtaining nanocrystalline alloys is heat treatment in a furnace under inert atmosphere. Joule heating by means of a current flowing through the sample is also a useful method, as crystallization is accomplished in very short times and requires no inert atmosphere because oxidation has no time to take place, and, therefore, it can be performed in air. Higher temperatures result in lower grain sizes as compared with conventional, longer, treatments [6-9] (Table I). The composition of the phases, the quantity of each of them, the grain size and other parameters are to be monitored during crystallization in order to obtain an optimized 35 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 35–45. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

J. M. Barandiaran

36

mixture of crystalline grains and amorphous remaining phase for best magnetic properties. The above alloys have been studied by a number of classical techniques including DSC, X-ray, neutron diffraction, TEM, Mössbauer, magnetic measurements and others [10-18]. Table I. Effect of current and furnace annealing on two typical nanocrystalline alloys

Fe73.5Cu1 Nb3Si13.5 B9

c.a. (41 MAm-2, 30 s.) f.a. (550ºC, 1 h.)

Fe-Si (DO3), Fe2B Fe-Si, Fe2B

Grain size (nm) 8-9 12

Fe86Cu1 Zr7B6

c.a. (50 Mam–2, 30 s.) f.a (600ºC, 1 h.)

D -Fe, Fe2B, Fe3B

12

10.2

D -Fe, Fe2B, Fe3B

30

8.2

Alloy composition

Treatment*)

Crystalline phases

Hc (Am–1) 0.8 1.2

*) c.a. = current annealing (current density, time), f.a. = furnace annealing (temperature, time)

In this paper we shall concentrate on less common methods such as EXAFS, resistivity and elastic modulus measurements through magnetoelastic resonance experiments. These methods are not commonly used because the relationship between the studied parameter and the transformed fraction is not straightforward, as it is for the above mentioned classical ones, but they can give an insight into different aspects of nanocrystallization that are not covered by traditional methods. Crystallization of amorphous alloys runs by segregation of an excess of a metal rich phase (D-Fe or DO3-FeSi) [1, 2, 10-18]. This is a primary crystallization process, with specific characteristics that makes kinetic studies somewhat difficult. In the second part of the paper we shall concentrate on some models giving reasonable pictures of the nanocrystallization kinetics in these alloys.

2. NANOCRYSTALLIZATION STUDIES BY NON-CONVENTIONAL METHODS 2.1. Resistivity Resistivity measurements are largely used for the study of structural transformations as it is a sensitive and easy to implement method (relative changes of a few ppm can be easily detected) [19-22]. The resistivity difference between the amorphous precursor and the nanocrystalline alloy can be one order of magnitude at room temperature, but it is much reduced at the crystallization temperature at which it can be negligible (Fig. 1). This is especially true for FINEMET, as the Fe-Si crystals have much higher resistivity than the D-Fe ones. The relationship between the measured resistivity and the transformed fraction is not simple and, even more, it is morphology dependent [23]. The resistivity derivative is

Some Aspects of the Crystallization of FINEMET- and NANOPERM-like Alloys

37

Figure 1. Resistivity of two typical nanocrystalline alloys (left) and comparison between DTA and resistivity plots showing the differences in intensity for the crystallization processes (right)

comparable to the DSC heat flow [20], but the intensity of the different processes is very different. Some details are amplified while others very much reduced (Fig. 1). 2.2. EXAFS EXAFS (Extended X-ray Absorption Fine Structure) [24] is an atom sensitive method that can give an insight into the evolution of the neighbourhood of a single

Figure 2. Mössbauer spectra (left) and EXAFS deduced radial distribution function ) ( R) (right) for Fe91Zr9 glasses after annealing at the temperatures shown (bcc-Fe is displayed for comparison)

J. M. Barandiaran

38

species inside a multi-component alloy. The data treatment and extraction of information is, however, cumbersome [25] and little use of this technique has been made so far when studying crystallization. In order to compare the sensitivity and possibilities of this technique, the crystallization of Fe91Zr9 amorphous alloy was followed simultaneously by EXAFS on Fe K-edge (Station 7.1 at Daresbury Laboratory) and 57Fe Mössbauer spectroscopy [26]. Samples with different degrees of crystallization were measured at room temperature to obtain information about the structural changes at early stages of crystallization (Fig. 2). A close inspection of the Mössbauer spectra shows that the crystallization process began after annealing at 400ºC, but for temperatures below 773 K the amount of crystalline phase was very low: D about 3% at 400ºC, and D about 10% at 475ºC. The EXAFS spectra, however already show the appearance of a bump around R = 4.5 Å, characteristic of the bcc structure of the D-Fe, and a shift of the main peak (at about 2 Å) towards the bcc position. EXAFS allows establishing that, from the very beginning of the crystallization, a crystalline phase with bcc structure appears. The EXAFS method can be useful for the study of different atomic species in a single alloy. 2.3. Magnetoelastic resonance The use of elastic measurements to follow the nanocrystallization is also uncommon, probably because the classic experimental set-up is relatively heavy, and brittle samples make clamping and pulling as required in conventional measurements difficult. However, the use of Fe rich amorphous alloys precursors with relatively large magnetostriction allows us to use the non-contact method of magnetoelastic resonance (MER) [27-29]. The resonant frequency fR of an strip of length L, with free ends, is related to the Young modulus (E) and density U by the expression [30]: f

1 2L

E

U

(1)

The value of E at magnetic saturation, ES, is easy to follow during crystallization. Such a plot can be seen in Fig. 3, which indicates a rapid increase before saturation for

Figure 3. Left: Saturation Young modulus (Es) as a function of the crystalline fraction for Fe73.5Nb3Cu1Si13.5B9. Right: Evolution of Es upon annealing for Fe64Ni10Nb3Cu1Si13B9

Some Aspects of the Crystallization of FINEMET- and NANOPERM-like Alloys

39

a typical FINEMET alloy [31]. Also in Fig. 3 is represented the value of ES as a function of the annealing temperature for a Fe64Ni10Nb3Cu1Si13B9 alloy. The rise of ES for TANN above 400ºC indicates the starting of the nanocrystallization [32], but the relationship of ES with the transformed fraction is not a simple one. 3. DSC AT THE PRIMARY CRYSTALLIZATION 3.1. Enthalpy evolution during primary crystallization In contrast with the above methods that are difficult to trace to the exact amount of the transformed fraction, DSC is assumed to be the most direct method for kinetic studies of crystallization. Differential Scanning Calorimetry (DSC) is able to evaluate the enthalpy, 'H, released during isothermal or non-isothermal crystallization, which is assumed to be a direct measure of the transformed fraction [33, 34]. However during the growth of the primary crystals, as in nanocrystallization, the amorphous matrix undergoes compositional changes. Thus, free enthalpy difference between the amorphous and crystalline phases also changes, and the evolved heat can no longer be proportional to the fraction transformed. This can also affect the derivation of kinetic parameters from DSC traces. For simplicity, we can consider an amorphous binary alloy of composition A1 – x1 Bx1 whose primary crystallization results in precipitation of crystals of pure A. When metastable equilibrium is attained, the glass has a composition A1-x1 Bx2 : A1 – x1 Bx1 (amorphous) o A(crystalline) + A1 – x1 Bx2 (amorphous)

(2)

This can be true for NANOPERM alloys, but should be somewhat modified for FINEMET ones, where the primary crystals are DO3 Fe-Si rather than pure Fe. During the transformation the instantaneously transformed crystalline fraction, D, is related to the composition of the remaining amorphous phase, x, by:

D = (x2/x)(x – x1)/(x2 – x1)

(3)

We will assume (as is common for liquid binary alloys) a parabolic composition dependence for the enthalpy H of the amorphous alloy [34]. Similarly, we assume to a first approximation, that the composition dependence of the free enthalpy G = H – TS, at a given temperature T, is also parabolic and proportional to the enthalpy. So that G approximately equal to H and: H(x) = K(x0 – x)2 + H0

(4)

The tangent to the G(x) § H(x) curve that passes through the origin of the coordinate system gives the “equilibrium” glass composition at the end of primary crystallization. This is equivalent to the common tangent rule if the point for crystalline A is considered to be the lowest point of a very narrow parabola having the enthalpy of the crystalline A-B alloy with very low equilibrium solubility of B in A (see Fig. 4). This gives the condition: K(x2 – x0)2 + H0 = 2Kx2(x2 – x0)

(5)

J. M. Barandiaran

40

3.2. Evolved heat vs. transformed fraction During the precipitation of crystalline A, the enthalpy of the mixture can be calculated to obtain the evolved heat as recorded by DSC. By normalising of the total enthalpy released 'H(x2) at the end of the primary crystallization, and using the “equilibrium” condition (5), we obtain [35]: 'H N

1

(1  D ) 2 1  D (1  x1 / x2 )

(6)

The above indicates a non-linear relationship between the transformed fraction and the evolved enthalpy The right hand part of Fig. 4 shows the relationship between 'HN and D for selected values of x1/x2 as well as the experimental determination of the same quantity for a FINEMET alloy. In the experimental curve the evolved enthalpy measured in a DTA apparatus was compared with the “true” transformed fraction, as deduced from Mössbauer spectroscopy [36]. The latter is assumed to give an accurate value of the transformed fraction, provided the recoil-less fraction of the crystalline phase is constant during the transformation. The experimental points lie outside the upper bound for the calculated deviation. This is probably due to the crude approximations used in the calculation above.

Figure 4. Enthalpy of a binary nanocrystalline alloys (left) and comparison between DTA signal and transformed fraction, theoretically obtained from Eq. (5) or as experimentally obtained from Mössbauer experiments in FINEMET (right)

The shapes of the curves for the time dependence of the enthalpy release under isothermal conditions have been calculated and compared with those for the transformed fraction, supposed to obey a Johnson-Mehl-Avrami kinetics. Surprisingly, even in the extreme case of non-linearity, for x1 | x2, they have the same slopes as the transformed fraction, indicating that the Avrami index derived from the enthalpy is the actual one for the transformation. In the worst (unreal) case, the plots based on the enthalpy release data are shifted upwards, so that they result in an apparent rate constant a factor of two greater than the actual value, irrespective of the magnitude of the Avrami exponent.

Some Aspects of the Crystallization of FINEMET- and NANOPERM-like Alloys

41

4. KINETICS OF THE PRIMARY CRYSTALLIZATION 4.1. General considerations In contrast to the polymorphous or eutectic crystallization, the kinetics of a primary crystallization reaction is very difficult to fit to any established model of phase transformations, such as the well known Johnson-Mehl-Avrami model [37]. In terms of the Johnson-Mehl-Avrami kinetics, under isothermal conditions, the transformed fraction at time t is given by [33]

D 1  exp   >K I , u t @ n

(7)

where K(I, u) is a rate constant depending on the nucleation (I) and growth (u) rates and n is the so-called Avrami exponent which, in most cases, has a value in the range 1-4. These kinetic equations are derived under very general assumptions for all kinds of solid state transformations. The derivative curves (dD/dt), as obtained by DSC under isothermal or continuous heating treatments, have characteristic shapes of asymmetric peaks with a rapid decrease at the high time/temperature side. In nanocrystalline systems, as well as in other primary crystallization processes, however, large tails are obtained for long times or temperatures, in the isothermal and non-isothermal treatments. These tails are difficult to fit to JMA kinetics, and can only be accounted for by anomalous values of the transformation index or large changes in the index during the crystallization [38-42] (see below). This is mainly because, during the growth of the primary crystals, the matrix phase undergoes compositional changes. For instance solute species, e.g. B in FeB, FeBSi and FeZrB [43] based glasses, are rejected into the glassy matrix during the transformation. Thus free enthalpy difference between the crystalline and the amorphous phases also changes, so that the corresponding driving force for crystallization is then dependent on the fraction of transformation completed. Also the kinetic parameters, such as diffusion coefficients and other factors, are composition dependent and will change as the crystallization proceeds. Clearly, the overall process and its quantification are complex and few attempts have been made to clarify the thermodynamic aspects in detail since the description by Herold and Köster [43]. 4.2. Kinetics of nanocrystallization as a variable activation energy process A simple phenomenological model can assume, in Eq. (7), a variable rate constant for the primary crystallization of the form [44]: K (T, D) = K0 exp {–E(D)/kBT}

(8)

where we have condensed the different effects of the composition change of the amorphous matrix in a variable activation energy E(D) which increases steadily as the transformation proceeds, reaching very high values (eventually infinity) at the end.

J. M. Barandiaran

42

There are several functions that fulfil such conditions but we have chosen the simplest one, depending on a single parameter, in order to fit the experimental data. The best fits have been found when using: 2

E (D ) = E0 + C D /(1 – D )

(9)

With this expression, the fit of both isothermal and non-isothermal DSC curves, such as those in Fig. 5, is possible in most of the transformation range (at least up to about D = 0.90). Typical parameters are found in Table II. The evolution of E(D), as given by Eq. (9) is also depicted in Fig. 5. At D = 0.90 the change in E amounts only to about 25% of the starting value. Table II. Kinetic parameters for the nanocrystallization of Fe73.5Nb3Si22.5 – xBxCu1 alloys Composition x=5 x=6 x=9 x=9

Study IIsothermal Scan IIsothermal Scan

Temperature range (K)

E0 (eV)

760-780 760-870 790-825 760-870

3.57 4.5 3.98 4.04

C (eV) 0.15 0.1 0.2 0.2

n 4 ± 0.2 2 ± 0.1 1.3 ± 0.3 2 ± 0.2

A possible origin of the above variable activation energy can be traced to the expression of the nanocrystalline growth rate, u, which is of the form [33, 45]: U = u0 exp{–E/kBT}[1 – exp{–'G/RT}]

(10)

where E is the activation energy for diffusionand'G, the molar free enthalpy difference between the amorphous and crystalline phases. The latter can be taken as 'G § 'H = 1 – 'HN (from Eq. 6). If (10), with this value of 'G, is introduced in the rate constant (8) the growth is completely stopped at the end of the transformation, where 'G = 0.

Figure 5. Energy variation along the crystallization process for E0 = 4eV and different values of the constant C in Eq. (9)

Some Aspects of the Crystallization of FINEMET- and NANOPERM-like Alloys

43

The actual mechanism, however, must be related to the atomic mechanisms at the interface of the grains, where some species accumulate and completely hinder the diffusion through the interface, stopping the growth [46, 47]. The above expressions, based on very general arguments, can only give approximate trends due to the lack of specific details and to the large simplifications made in order to allow for simple calculations. A similar approach to deal with the kinetics of the primary crystallization has been used by P. Svec and co-workers [48]. They assume a broad activation energy distribution available for atomic jumps involved in the crystallization plus a variation of the activation energy with temperature, but the final effect is quite similar. 5. CONCLUSIONS The study of nanocrystallization processes can be done by a number of methods each of them having a different relation with the transformed fraction. This allows different aspects of the process to be amplified. On the other hand even well established methods like DSC or DTA are not free from misleading effects. This is so because in the primary crystallization processes, the amorphous precursor of the nanocrystalline alloy undergoes compositional changes during the crystallization. In consequence the evolved heat is no longer proportional to the transformed fraction. Regarding the kinetics of the nanocrystallization (and other primary crystallization processes) the well-established Johnson-Mehl-Avrami description needs modifications, like a variable activation energy in the rate constant. ACKNOWLEDGEMENTS The nanocrystallization studies presented in this work were performed in collaboration with a number of other researchers like: I. Tellería, F. Plazaola, M. L. Fernández Gubieda, J. Gutiérrez, A. García, I. Orúe, J.S. Garitaonandía, (Univ. Pais Vasco), J.C. Gómez Sal, L. Fernández Barquín (Univ. Cantabria), P. Gorria (Univ. Oviedo), D.S. Schmool (Univ. Porto), and others. I would like to thank especially Prof. Hywel Davies (Univ. of Sheffield) who suggested that in the primary crystallization, DSC signals probably were not proportional to the transformed fraction. REFERENCES 1. Yoshizawa Y., Oguma S., and Yamauchi K. (1988), J. Appl. Phys. 64, 6044. 2. Suzuki K., Makino A., Kataoka N., Inoue A., and Masumoto T. (1991), Mater. Trans. JIM 32, 93. 3. Suzuki K., Makino A., Tsai A.P., Inoue A., and Masumoto T. (1994), Mat. Sci. Eng. A 179-180, 501. See also: Suzuki K., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec, and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 1-14. 4. Herzer G. (1989), IEEE Trans. Mag. 25-5, 3327. See also: Herzer G., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec, and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 15-34.

44 5. 6. 7. 8. 9.

10.

11. 12.

13.

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

J. M. Barandiaran Hernando A. and Kulik T., (1994) Phys. Rev. B 49, 7064. Gorria P., Orue I., Plazaola F., and Barandiarán J.M. (1993), J. Appl. Phys. 73(10), 6600-6602. Zabala N. and Barandiarán J.M. (1995), J. Phys. D: Appl. Phys. 28, 2607-2611. Gorria P., Fernández-Barquín L., Gariatonandia J.S., Barandiarán J.M., García-Arribas A., and Convert P.: Physica B, 276-278 (2000) 461-462. Mitrovic N., Roth S., Djukic S., and Eckert J., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 331-344. Allia P., Baricco M., Tiberto P., and Vinai F., (1992), in: Studies of Magnetic Properties of Fine Particles and their Relevance to Material Science, by J.L. Dormann and D. Fiorani (eds.), Elsevier Science Publishers B.V., 411. Rixecker G., Schaaf P., and Gonser U., (1992), J. Phys.: Condens. Matter 4, 10295. Greneche J.M. (1998), in Non-Crystalline and nanoscale Materials, J. Rivas and M.A. López-Quintela (eds.), World Scientific, Singapore. See also: Greneche J.M., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 373-384. Miglierini M., (1994). J. Phys.: Condens. Matter. 6, 1431. See also: Miglierini M., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 421-436. Gorria P., Garitaonandia J.S., and Barandiarán J.M. (1996), J. Phys.: Condens. Matter. 8, 5925. Borrego J.M., Conde A., Todd I., Frost M., Davies H.A., Gibbs M.R.J., Garitaonandia J.S., Barandiaran J.M., and Greneche J.M. (2001); J. Non Crys. Solids 287 (1-3), 125-129. Gorria P., Orue I., Plazaola F., Fdez-Gubieda M.L., and Barandiarán J.M. (1993): IEEE Transactions on Magnetics, MAG-29, 2682-2684. Orue I., Gorria P., Plazaola F., Fernández-Gubieda M.L., and Barandiarán J.M. (1994), Hyperfine Interactions, 94, 2199-2205. Fernández Barquín L., Gorría P., Barandiarán J.M., Gómez Sal J.C., and Rodriguez Carvajal J. (1996), Physica B 234-236 418-420. Fernández Barquín L. (1992), PhD. Thesis, Univ. Cantabria. Barandiaran J.M., Fernández Barquín L., Gómez Sal J.C., Gorria P., and Hernando A., (1993), Solid State Commun. 88, 75. Barandiarán J.M. (1994), Physica Scripta T55, 194-198. Pekala K. and Pekala M. (2003), Proceedings of Intern. Workshop on Non Crystalline Solids Mexico DF to be published in J. Non Cryst. Solids. Rossiter J.W., (1987), The Electrical Resistivity of metals and alloys. Cambridge Univ. Press, Cambridge. Stern E.A. and Heald S.M. ,(1983), “Basic principles and applications of EXAFS”, in Handbook of Synchrotron Radiation, E.E. Koch (ed.), Vol. 1, North Holland, Amsterdam. Lengeler B. and Eisenberger P. (1980), Phys. Rev. B 21, 4507. Gorria P., Orue I., Fdez-Gubieda M.L., Fernández Barquín L., and Barandiarán J. M. (1997), J Phys. IV France 7 C2-1125-1126. Modzelewski C., Savage H.T., Kabakoff L.T., and Clark A.E. (1981), IEEE Trans. on Magn. MAG-17 2837. Wun-Fogle M., Clark A.E., and Hathaway K.B. (1986), J. Magn. Magn. Mat. 54-57 893. Kaczkowski Z., Lanotte L., and Muller M., (1995), J. Magn. Magn. Mat. 140-144, p. 0325. Barandiarán J.M., (2000), “Magnetoelasticity in amorphous ferromagnets”. In: Modern Trends in Magnetostriction Study and Application, M.R.J. Gibbs (ed.), Kluwer Academic Publ., Amsterdam, 71-95.

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31. Gutiérrez J., Gorría P., Barandiarán J.M., García-Arribas A., Squire P.T., and Atkin-son D., (1995) in: Nanostructured and non-crystalline materials. M. Vázquez and A. Hernando, (eds.), World Scientific, Singapore 500-504. 32. Gutiérrez J., Barandiarán J. M., Mínguez P., Kaczkowski Z., Ruuskanen P., Vlasák G., Svec P., and Duhaj P. (2003), Proceedings of the EMSA2002, Sensors and Actuators in press. 33. Christian J.W., (1975), The theory of transformations in metals and alloys, Pergamon Press, Oxford. 34. Porter D.A. and Easterling K.E., (1981), Phase transformations in metals and alloys, Van Nostrand, Wokingham. 35. Barandiarán J.M., Tellería I., Garitaonandía J.S., and Davies H.A., (2003), Proceedings of the VII Int. Workshop on Non Crystalline Solids, Mexico DF, to be published in J. Non Cryst. Solids. 36. Garitaonandia J.S., (1998), PhD thesis, Universidad del País Vasco, Bilbao. 37. Avrami M. (1941), J. Chem. Phys. 9, 177. 38. Tellería I. and Barandiarán J.M., (1995), in: Nanostructured and non-Crystalline Materials, M. Vázquez and A. Hernando (eds.), World Scientific, Singapore, pp. 399. 39. Illekova E., Kuhnast F.A., Fiorani J.M., and Naguet C., (1995), J. Non Cryst. Solids 192-193, 556. See also Illekova E., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 79-90. 40. Hampel G., Pundt A., and Hesse J., (1992), J. Phys.: Condens. Matter 4 , 3195. 41. Crespo D., Pradell T., Clavaguera-Mora M.T., and Clavaguera N., (1997), Phys. Rev. B 55, 3435. 42. Blázquez J.S., Conde C.F., and Conde A., (2003), Appl. Phys. A 76, 571-575. 43. Köster U. and Herold U., (1981), in Glassy metals I, H.J. Güntherodt and H. Beck (eds.), Springer-Verlag Berlin 225-259. 44. Tellería I. and Barandiarán J.M., (1998), in Non-Crystalline and nanoscale Materials, J. Rivas and M.A. López-Quintela (eds.), World Scientific, Singapore, 302. 45. Battezzati L. (1994), Mat. Sci. Eng. A178, 43. 46. Yavari R., (1995), in: Nanostructured and Non-crystalline Materials, M. Vázquez and A. Hernando (eds.), World Scientific, Singapore, 35. 47. Hono K., Hiraga K., Wang Q., Inoue A., and Sakurai T., (1992), Acta Metall. Mater. 40, 2137. 48. Deanko M., Müller D., Janiþkovic D., Škorvánek, I., and Švec P., (2005) in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 69-78.

MAGNETICALLY SOFT NANOCRYSTALLINE MATERIALS OBTAINED BY DEVITRIFICATION OF METALLIC GLASSES T. KULIK, J. FERENC, and A. KOLANO-BURIAN Faculty of Materials Science and Engineering Warsaw University of Technology Woáoska 141, 02-507 Warsaw, Poland Corresponding autor: T. Kulik, e-mail: [email protected] Abstract:

This paper presents the main features of magnetically soft metallic glasses and nanocrystalline materials obtained by controlled crystallization of metallic glasses, a brief description of the principal methods of nanocrystallization as well as the recent developments in nanocrystalline materials for high-temperature applications. Two groups of alloys were investigated: (Fe, Co)-Si-Nb-Cu-B (FINEMET-type) and (Fe, Co)-(Zr, Nb, Hf)-Cu-B (HITPERM-type). For FINEMETtype alloys it was found that the optimum combination of magnetic properties (coercivity, Curie temperature, magnetostriction) is obtained when Fe:Co ratio is about 1:1. For HITPERM-type alloys, the best performance and stability are observed when alloys contain Hf, and the worst in the case of Nb. Optimum Hf content is 7 at.%, and 6 at.% B. The HITPERM-type alloys exhibit good stability of properties at 500°C for at least 700 hours.

1. INTRODUCTION Metallic glasses, ever since they were developed, have exhibited outstanding mechanical, physical or chemical properties. One of the groups of metallic glasses with great application potential are magnetically soft engineering materials. The main components of these alloys are iron and cobalt, and nickel which also sometimes is used. These materials exhibit a low coercive field, low core losses, high magnetization and high permeability, just to mention the principal properties. These very good soft magnetic properties are obtained because metallic glasses match the classical rules for soft magnetic alloys: the single phase, minimum grain boundaries. One of the reasons of a potential increase of the coercive field is the magnetoelastic anisotropy, Kı, which is given by the equation:

KV

3 ˜Os ˜ V 2

where Os – coefficient of saturation magnetostriction and V – stress. 47 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 47–57. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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The presence of residual stresses induce relatively high magnetoelastic anisotropy, as was shown in the case of e.g. as-cast Co-Si-B glasses, both O z 0. There are two ways of avoiding this phenomenon – see Fig. 1: reduction of the residual stresses or reduction of the magnetostriction coefficient value. The former may be achieved by stress relieving annealing (below crystallization temperature), the latter by the addition – in the case of Co alloys – of Fe atoms. But in both cases it is possible to reduce the coercive field and to increase the remanence several times.

Figure 1. Dependence of (a) coercive field and (b) squareness of a hysteresis loop for Co-Fe-Si-B alloys annealed at various temperatures [1]

The heat treatment of metallic glasses must be carried out very carefully, because they tend to crystallize, i.e. crystals appear in the structure, and the soft magnetic properties are irreversibly destroyed. For each amorphous alloy there is a critical temperature of annealing for a certain period of time, which must not be exceeded, otherwise devitrification occurs and the magnetically soft amorphous alloy is killed. However, this year is the fifteenth anniversary of the development of a completely new class of soft magnetic materials, two-phase nanocrystalline alloys produced by controlled crystallization of amorphous precursors [2]. These materials break the classical rules of a large grain size of crystalline soft magnetic alloys and of adverse impact of crystallization on magnetic softness of metallic glasses. The first alloy of this group, FINEMET, with the chemical composition of Fe73.5Si13.5Cu1Nb3B9, after isothermal annealing at 550°C for 1 hour consists of bcc-Fe(Si) crystals embedded in the residual amorphous matrix. The size of the crystals should not exceed 20 nm and

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the smaller the grains, the lower is the coercive field. This alloy is based on a typical Fe-Si-B metallic glass, and contains little amounts of copper enhancing crystals nucleation and niobium retarding crystals growth. In the result, the coercive field of FINEMET is of the order of 1 A/m, which is comparable to the best amorphous cobaltbased magnetically soft alloys. Nanocrystalline soft magnetic materials combine the advantages of Fe- and Co-based metallic glasses: high saturation magnetization, low magnetostriction and vanishing effective magnetocrystalline anisotropy. The latter is possible only when the size of crystals is smaller than the length of the exchange interaction which is around 35 nm for pure iron. In such a case, the magnetocrystalline anisotropy of single grains is averaged out and the material behaves like a soft magnet. Also the average coefficient of magnetostriction may be adjusted to be near zero, thanks to the control of a crystalline volume fraction:

Oeff s

Vcr ˜ Ocrs  (1  Vcr ) ˜ Oam s

(2)

where: Os – coefficient of saturation magnetostriction, Vcr – crystalline volume fraction; superscripts: eff – effective for the alloy, cr – of a crystalline phase, am – of an amorphous phase. Usually, nanocrystallization is performed by isothermal annealing for 1 hour at temperatures slightly lower than the onset crystallization temperature obtained from continuous heating experiment. Such treatment may be applied both in fundamental research in scientific laboratories, and in industrial conditions. The advantages of this method are reproducibility and easy control of the heat treatment process. Another similar method of crystallization is continuous heating to the maximum temperature just after the first stage of crystallization and subsequent cooling. This method is frequently used in laboratories, and is less practical in mass production. The above mentioned two methods are the methods of conventional crystallization, i.e. crystallization at typical, medium temperatures. However, there are other, non-conventional methods of controlled devitrification of metallic glasses: high-temperature and low-temperature nanocrystallization. The former is performed by rapid heating and rapid cooling, with or without the isothermal stage. In the case of “flash-annealing”, a current pulse is conducted through a ribbon sample submerged in the liquid nitrogen or cooled by the rapid flow of helium [3]. The pulse intensity and duration are adjusted to provoke primary crystallization at temperatures about 700°C. The advantage of this technique is that the alloying elements, like Cu and Nb are not necessary to produce the nanocrystalline structure, because rapid heating causes the formation of a very large number of nuclei, and subsequent cooling freezes the crystals denying their further growth. On the other side of temperature axis there is low temperature annealing. In this case, the annealing temperature is 100-200°C lower than in conventional crystallization, allowing the quenched-in nuclei, which are stable at this temperature range, to grow. The high density of quenched-in nuclei and a low temperature prevent from the formation of a coarse crystals structure [4]. In both cases of non-conventional crystallization methods, alloying elements are not necessary to generate a nanocrystalline structure, which results in higher saturation magnetization [5, 6]. Regretfully, these non-conven-

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tional methods are investigated in scientific laboratories, as they are not reproducible yet. There have been two groups of soft magnetic nanocrystalline alloys under development since late 1980’s: FINEMET (Fe-Si-B-Cu-Nb) [2] and NANOPERM (Fe-Zr-BCu) [7], both having very good soft magnetic properties. FINEMETs are characterized by a very low coercive field (around 1 A/m), but only moderately high saturation magnetization (1.24 T), and NANOPERMs exhibit a higher coercive field (3-6 A/m), but very high saturation magnetization – 1.6 T or higher [8]. Recently research has been carried out to extend the temperature range of application of nanocrystalline soft magnetic alloys to about 500-600°C. FINEMET and NANOPERM contain amorphous matrix, which has a relatively low Curie temperature. The best method to increase the Curie point of amorphous and crystalline phase is to substitute a part of iron with cobalt. The new group of modified NANOPERM alloys is called HITPERM [9, 10]. The result is very interesting: the Curie temperature of an amorphous phase is shifted from 350 to 800°C. The room temperature measurements revealed that HITPERM alloys exhibit the coercive field of about 25-50 A/m, which is significantly worse in comparison with the alloys without Co. Nevertheless it should be underlined that Co modified alloys preserve good soft magnetic properties at much higher temperatures and this is the main reason for their application. Apart from the good soft magnetic properties at elevated temperatures, it is important that these properties and the structure of the alloy are stable in time, and do not deteriorate over the period of operation of the element to be built from the nanocrystalline alloy. This requires an addition of the elements that stabilize the structure – the grains embedded in the remaining amorphous matrix must remain sufficiently small and the remaining matrix should stay amorphous. Usually, these elements are zirconium, niobium, hafnium, tantalum, i.e. these having low solubility in bcc-(Fe, Co) crystals and low diffusivity in the amorphous matrix. It is also vital that during nanocrystallization the first stage of crystallization is complete, otherwise the structure and properties will change during the first period of operation of the final product. In this work, studies of crystallization of FINEMET and NANOPERM, both modified with Co, were carried out in order to evaluate their suitability for high-temperature applications. The aim of this work was to obtain materials with good and stable performance at temperatures up to 500°C. Two groups of alloys were investigated: HITPERM-type, with chemical composition of Fe45Co43Cu1B3.6Zr7.4–xRMx (RM = Hf, Nb), (Fe0.5Co0.5)99–x–yCu1By(HfvZr1-v)x and FINEMET-type, (Fe1–xCox)73.5Cu1Nb3Si13.5B9. 2. EXPERIMENTAL Alloys of the following chemical composition (in at.%): Fe45Co43Cu1B3.6Zr7.4-xRMx (x = 0 and 3.7; RM = Hf, Nb), (Fe0.5Co0.5)99-x-yCu1By(HfvZr1-v)x (x = 5, 6, 7 and 9; y = 4, 6 and 8; v = 0.5 and 1) and (Fe1–xCox)73.5Cu1Nb3Si13.5B9 (x = 0.14, 0.27, 0.41, 0.54, 0.68 and 0.80) were arc melted and melt-spun. They were subjected to calorimetric measurements of crystallization temperatures (by DTA and DSC) with the heating rate of 20°C/min. As-quenched ribbons were subjected to isothermal annealing at temperatures from 400 to 700°C for 1 hour in order to find the optimum annealing

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temperature, i.e. the temperature of annealing assuring the lowest coercive field measured at room temperature. The following magnetic properties of the alloys were measured: coercive field, Curie temperature, magnetostriction constant. The structure of the alloys was investigated using X-ray diffractometry and transmission electron microscopy. 3. RESULTS AND DISCUSSION 3.1. FINEMET modified with cobalt The FINEMET-type alloys, (Fe1-xCox)73.5Cu1Nb3Si13.5B9 (x = 0.14, 0.27, 0.41, 0.54, 0.68 and 0.80), investigated by DSC show that the cobalt content lowers the crystallization temperatures, although the impact of Co content on the second crystallization stage is insignificant [11]. The dependence of peak crystallization temperatures, T1 for the first stage and T2 for the second stage, is shown in Fig. 2. 740

Crystallization temperature, T [°C]

720 700 680

(Fe1-xCox)73.5Cu1Nb3Si13.5B9

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dT/dt = 20°C/min

620 600 580 560 540 520 0.1

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Figure 2. Crystallization temperatures of (Fe1-xCox)73.5Cu1Nb3Si13.5B9 alloys as a function of cobalt content, x

Figure 3. Dependence of coercive field of (Fe1-xCox)73.5Cu1Nb3Si13.5B9 alloys on cobalt content, x, and on annealing temperature, Ta

The as-quenched alloys were subjected to isothermal annealing for 1 hour at the temperatures from the range 440-560°C. For each alloy the optimum temperature was found, for which an alloy exhibited the minimum coercivity after annealing at that temperature. The dependence of coercivity on cobalt content and annealing temperature is presented in Fig. 3. It is worth to underline that similarly to primary crystallization temperature the optimum annealing temperatures depend on Co content – the more cobalt contained in an alloy, the lower the optimum temperature. The investigated alloys after optimum annealing exhibited a two-phase structure: the nanocrystals of bcc-(Fe, Si, Co) were homogeneously distributed in an amorphous matrix. The average size of the nanocrystals was between 7 and 10 nm, and seemed to be independent of cobalt content, x. The structure of selected alloys after optimum annealing is presented in Fig. 4.

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The diffraction patterns suggest that the higher cobalt content, the less crystalline phase is present in the structure of the optimally annealed alloy. This may be attributed either to the lower temperature of annealing, or to the more suitable crystalline volume fraction assuring the lowest achievable coercive field.

a) x = 0.14, 520°C/1h

b) x = 0.68, 490°C/1h

Figure 4. Structure of (Fe1-xCox)73.5Cu1Nb3Si13.5B9 alloys after optimum annealing

Figure 5. Dependence of coercive field, Hc, magnetostriction constant, Os, and Curie temperature, TC, on the cobalt content, x for (Fe1-xCox)73.5Cu1Nb3Si13.5B9 alloys after optimum annealing

Figure 5 shows the dependence of coercive field (Hc), magnetostriction constant (Os) and Curie temperature of amorphous matrix (Tc) for the alloys investigated. The local maxima of Hc and Os for the optimally annealed alloys appear for different cobalt content. This may be attributed to the different crystalline volume fraction for these

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samples, because the value of the average magnetostriction constant depends on both phases’ properties and their volume fractions in the structure. The above presented results indicate that from the point of view of soft magnetic behaviour at elevated temperatures, the optimum combination of properties have the alloys with the cobalt content x around 0.4-0.6, although they exhibit relatively high magnetostriction constant. Their medium value of coercive field (around 4-5 A/m) and the highest Curie temperature of amorphous phase (around 380°C) suggest that these alloys will satisfactorily meet the requirements of low a coercive field and high magnetization at elevated temperatures. It should be noted that in comparison with a cobalt-free FINEMET the alloys investigated herein exhibit worse soft magnetic properties at room temperature, but they are designed for operation at higher temperatures, where FINEMETs cannot be applied due to quite low Curie temperature. 3.2. NANOPERM MODIFIED WITH COBALT A series of alloys with the composition Fe45Co43Cu1B3.6Zr7.4-xRMx (x = 0, 3.7 and 7.4; RM = Hf, Nb) was prepared. The amorphous alloys containing Zr and Hf exhibit similar crystallization temperatures (Tx1 | 500°C, Tx2 | 695°C); Nb reduces Tx1 to 435°C and increases Tx2 to 750°C, suggesting that the addition of Nb should improve high temperature stability of the alloys’ structure and properties [12]. The amorphous alloys were annealed for 1 hour at temperatures ranging from 400 to 700°C to find the optimum annealing conditions. The dependence of coercive field of the alloys after the heat treatment on annealing temperature and chemical composition is presented in Fig. 6.

Figure 6. Dependence of coercive field, Hc, on the chemical composition and the annealing temperature Ta for the Fe45Co43Cu1B3.6Zr7.4-xRMx alloys

The optimum temperatures of annealing of the alloys are between 500 and 600°C, and the optimally annealed alloys exhibit the coercive field around 20-40 A/m. The worst soft magnetic properties are observed for the alloys containing niobium, and the best – the alloys containing hafnium. The abrupt rise of coercive field is related to the formation of the phases occurring in the second stage of crystallization. This is proved by the diffraction patterns of the alloys after annealing, presented elsewhere [13].

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The structure of the optimally annealed alloys consists of bcc-(Fe, Co) crystals with 5-40 nm in diameter, homogeneously distributed in an amorphous matrix, similarly to the structures pictured in Fig. 4. The Fe45Co43Cu1B3.6Zr7.4-xRMx alloys after nanocrystallization at 500 and 600°C were subjected to long-term annealing in order to investigate the influence of the refractory metal (RM) choice and nanocrystallization conditions on the stability of their magnetic properties. The results of measurements of the coercive field of the alloys after long-term annealing are presented in Fig. 7. All the alloys exhibit similar behaviour – initially Hc increases, and then reaches a stable level. The starting level of Hc (just after nanocrystallization) is higher for the alloys annealed at 600°C, but after several hundred hours of annealing at 500°C the differences between samples annealed at different temperatures become negligible, as pictured in Fig. 7a. This may be explained by the reaching of a stable state after the completion of the first crystallization stage. The alloys nanocrystallized at 500°C are farther from this stable state in comparison with these after 600°C, hence the increase is larger. This effect suggests that for the stability of properties of final products it is preferred that the alloys are nanocrystallized at higher temperatures. 100

50

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Fe45Co43Cu1B3.6 Nb7.4 Zr7.4 Hf7.4 Zr3.7Hf3.7 Nanocrystallized at 600°C for 1h

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Figure 7. Dependence of coercive field of Fe45Co43Cu1B3.6Zr7.4-xRMx alloys on the time of long-term annealing: a) Fe45Co43Cu1B3.6Zr3.7Hf3.7 alloy nanocrystallized at 500 and 600°C; b) Fe45Co43Cu1B3.6Zr7.4-xRMx alloys after annealing at 600°C

It is important that the alloying metal addition has a big impact on the magnitude of coercive field after long-term annealing. Figure 7b shows the dependence of Hc for the investigated alloys nanocrystallized at 600°C. It is evident that the alloys with niobium are characterized by high coercive fields and the alloys containing hafnium have the lowest Hc. At this stage it is difficult to explain this effect, but most probably

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hafnium is the most efficient in the hindering of the bcc-(Fe, Co) grain growth, ensuring the lowest grain size and thus the lowest Hc (including the state only after nanocrystallization). Grain size assessment from XRD experiments confirms this assumption, proving that grains in the alloy with Zr are 1.5 times larger than in the case of the alloy with Hf. In the next stage of the study the influence of boron, zirconium and hafnium content on the magnetic properties after nanocrystallization was investigated. The series of (Fe0.5Co0.5)99-x-yCu1By(HfvZr1-v)x (x = 5, 6, 7 and 9; y = 4, 6 and 8; v = 0.5 and 1) alloys was prepared. At first, having fixed Hf content to 7 at.%, boron addition was changed according to the formula (Fe0.5Co0.5)92-yCu1ByHf7 (y = 4, 6 and 8). DSC measurements proved that B content has negligible impact on the temperature of the first crystallization stage, but the increase in B amount significantly lowers the temperature of the second crystallization stage [14]. For 4 at.% of B, it was difficult to obtain fully amorphous ribbons. The results of measurement of coercive field of the (Fe0.5Co0.5)92-yCu1ByHf7 alloys after 1 hour annealing are presented in Fig. 8. The optimum annealing temperatures for the three alloys were around 550-600°C, with the tendency of lowering the optimum temperature with the increase of boron content. However, the differences between the coercive field for the optimally annealed samples were rather small – from 26 A/m for 4 at.% of B to 17 A/m for 8 at.% of B. The y = 6 alloy exhibits the widest range of nanocrystallization temperatures where Hc is almost constant, so this B content is the most versatile if for other reasons the annealing temperature must be modified. On the basis of the manufacturing, thermal stability and magnetic softness information it was concluded that the optimum B content was 6 at.%. Having established boron content at 6 at.%, a series of (Fe0.5Co0.5)93-xCu1B6 (HfvZr1-v)x, where x = 5, 6, 7 and 9; v = 0.5 and 1, alloys were prepared to assess the optimum content of refractory metals, hafnium and zirconium (RM). At the stage of production of amorphous ribbons it turned out that for the alloys containing 5 and 6 at.% of RM it was impossible to obtain fully amorphous products. This result suggests that the minimum refractory metal content is 7 at.%. DTA results of the amorphous alloys with x = 7 and 9 and v = 0.5 and 1 prove that for the investigated alloys, the first stage crystallization temperature depends on the total amount of RM, but is less sensitive to the type of alloying metal. The more alloying metal, the higher is the crystallization temperature. In the case of the second crystallization stage, the onset (Tx2) and peak (T2) temperatures depend on the type of alloying metal, not on its content. Hafnium increases Tx2 and T2 more efficiently than zirconium [14]. These results indicate that an addition of pure hafnium is more favorable for preventing the second stage of crystallization from occurring during the hightemperature long-term annealing. A higher amount of RM will also be preferred if the grain size stability is concerned, although increasing of the RM content reduces the saturation magnetization. The (Fe0.5Co0.5)93-xCu1B6(HfvZr1–v)x alloys were subjected to 1 hour annealing at temperatures from the range between 400 and 700°C. The dependence of the coercive field on the RM content and the annealing temperature is presented in Fig. 9.

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Figure 8. Dependence of the coercive field of (Fe0.5Co0.5)92–yHf7Cu1By alloys after annealing for 1 hour at different temperatures, Ta

Figure 9. Dependence of the coercive field of Fe45Co43Cu1B3.6Zr7.4–-xRMx alloys after annealing for 1 hour at different temperatures, Ta

It is clearly seen that the coercive field of the investigated alloys is lower if only Hf is added to the alloys. A partial replacement of Hf by Zr causes an increase of Hc in the optimal nanocrystalline state. Similarly, the more refractory metals are present in the alloy, the higher is the value of Hc after nanocrystallization. Moreover, for 7 at.% Hf content, there is the widest range of nanocrystallization temperatures assuring low coercivity, which makes these alloys flexible in the heat treatment. Hence, from the point of view of a soft magnetic behaviour, the preferred RM addition is 7 at.% of hafnium. 4. SUMMARY AND CONCLUSIONS (i) (ii)

(iii) (iv) (v)

For the FINEMET based alloys modified with cobalt, the optimum magnetic properties are obtained when Fe:Co ratio is around 1:1. For the HITPERM alloys, the best magnetic performance was found for the alloys containing Hf, which retain low coercivity after nanocrystallization (500600°C) and isothermal annealing at 500°C for 700 hours (usually below 50 A/m, the minimum of 23 A/m). Probably Hf is the best inhibitor of the growth of the crystallites, assuring the lowest values of Hc. The optimum nanocrystallization temperature for most of the investigated HITPERM-type alloys was 550°C. From the viewpoint of applications and manufacturing process, the best properties were obtained for the alloy containing 6 at.% of B and 7 at.% of Hf. Preliminary results show that the alloys studied are stable at 500°C at least up to 700 h. This will be confirmed for the wide series of alloys and for longer time.

ACKNOWLEDGMENTS This work was supported by the EC GROWTH programme, research project “HiT-Fcore”, contract No. G5RD-CT-2001-03009, and the Polish State Committee for Scientific Research, grant No. PBZ-KBN-013/T08/07.

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REFERENCES 1. Kulik, T., Matyja, H., and Lisowski, B., (1984) Influence of annealing on magnetic properties of Co-based glasses, J. Magn. Magn. Mater. 43, 135. 2. Yoshizawa, Y., Oguma, S., and Yamauchi, K., (1988) New Fe-based soft magnetic alloys composed of ultrafine grain structure, J. Appl. Phys. 64, 6044. 3. Kulik, T., Horubaáa, T., and Matyja, H., (1992) Flash annealing nanocrystallization of Fe-SiB-based glasses, Mater. Sci. Eng. A 157, 107. 4. Kulik, T., Ferenc, J., and Matyja, H., (1997) Low temperature nanocrystallization of ironbased amorphous alloys, Mater. Sci. Forum 235-238, 421. 5. Kulik, T., (1998) Annealing temperature dependence of size, morphology and composition of primary crystals created in Fe76.5Cu1Si13.5B9 glass, Mater. Sci. Forum, 269-272, 707-712. 6. Kulik, T., (2001) Nanocrystallization of metallic glasses, J. Non-Cryst. Sol. 287, 145-161. 7. Suzuki, K., Kataoka, N., Inoue, A., and Masumoto, T., (1990) High saturation magnetization and soft magnetic properties of bcc Fe-Zr-B alloys with ultrafine grain structure, Mater. Trans. JIM, 31,743. 8. McHenry, M.E., Willard M.A., and Laughlin D.E., (1999) Amorphous and nanocrystalline materials for applications as soft magnets, Progress in Materials Science, 44, 291-433. 9. Willard, M.A., Laughlin, D.E., McHenry, M.E., Thoma, D., Sickafus, K., Cross, J.O., and Harris, V.G., (1998) Structure and magnetic properties of (Fe0.5Co0.5)88Zr7B4Cu1 nanocrystalline alloys, J. Appl. Phys. 84, 6773. 10. Willard, M.A., Laughlin, D.E., and McHenry, M.E., (2000) Recent advances in the development of (Fe,Co)88M7B4Cu1 magnets, J. Appl. Phys. 87, 7091. 11. Kolano-Burian, A., Ferenc, J., and Kulik, T., (2002) Structure and magnetic properties of high temperature nanocrystalline FeCoCuNbSiB alloys, to be published in Mater. Sci. Eng. A 12. Kulik, T., Wlazlowska, A., Ferenc, J., and Latuch, J., (2002) Magnetically Soft Nanomaterials for High-Temperature Applications, IEEE Trans. Magn. 38, 3075-3077. 13. Wlazáowska, A., Ferenc, J., Latuch, J., and Kulik, T., (2002) Nanocrystallization of Soft Magnetic Fe-Co-Zr-Cu-B Alloys, Acta Phys. Polon. A, 102, 323-328. 14. Ferenc, J., Latuch, J., and Kulik, T., (2003) Magnetic properties of partially crystallized Fe-Co-Hf-Zr-B-Cu alloys, to be published in J. Magn. Magn. Mat.

THE INITIAL STAGE OF NANOCRYSTALLIZATION IN Fe-Cu-Nb-Si-B FERROMAGNETIC ALLOYS B. V. JALNIN, S. D. KALOSHKIN, E. V. KAEVITSER, V. V. TCHERDYNTSEV, and E. V. OBRUCHEVA Moscow State Institute of Steel and Alloys Leninsky prospect, 4, 119049 Moscow, Russia Corresponding author: B.V. Jalnin, e-mail: [email protected] Abstract:

The reversible and irreversible heat flow phenomena during the pre-crystallization relaxation process of amorphous Fe73.5Nb3Cu1Si13.5B9 alloy have been studied. The pre-crystallization and the initial stages of crystallization with the redistribution of the elements of a rapidly quenched alloy were studied using differential scanning calorimetry (DSC), thermomagnetic analysis (TMA), Mössbauer spectroscopy (MS) and X-ray diffraction (XRD). MS allowed us to detect the beginning of the formation of Fe-deficient areas as iron-rich nanocrystals were appearing. The peak at 5 T hyperfine field value was found to appear when the samples were annealed at 733 K. This effect corresponds to Fe-deficient areas, and, probably to Cu-enriched cluster, as well. On the basis of this detailed research we discuss the model of decomposition of the amorphous phase with the subsequent formation of iron-enriched nanocrystals.

1. INTRODUCTION In our recent studies [1, 2] of rapidly quenched Fe-Nd alloys we have found that crystallization by formation of D-Fe nanocrystals takes place at the initial stage of the process. The Fe-Nd system is characterized by a positive value of mixing enthalpy, so the amorphous phase is unstable because of thermodynamic reasons and tends to the decomposition. Dissimilarly to other binary alloys of transition metals, the decomposition of Fe-Nd rapidly quenched alloys can be observed in the diffraction spectra. That is why in these alloys we observe decomposition of the amorphous phase into the couple of amorphous phases just before nanocrystallization. It is known that amorphous alloy Fe73.5Nb3Cu1Si13.5B9 consists of two couples of elements (Fe-Cu and Cu-Nb), which have the positive value of mixing enthalpy. So, can we talk with the same confidence about the decomposition of amorphous phase in Fe-Cu-Nb-B-Si alloy as we do regarding the Fe-Nd system? The content of copper and niobium dopants to the alloy is just 1 or 3 at.%, respectively. Therefore it is extremely difficult to find Cu and/or Nb composition fluctuations in the amorphous phase after 59 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 59–68. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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structural relaxation, even if they exist. Nevertheless, we applied the following methods to try to test this hypothesis experimentally: (i) The XRD data in order to define some of the parameters of nanocrystalline structure formation, providing that sizes of nanocrystalline grains depend on the density of crystallization centers, i.e. the number of crystallization nuclei per volume unit is equal to the number of nano-grains which have been formed in this volume during crystallization. (ii) The Mössbauer data so as follow changes in the nearest iron atoms’ environment during the relaxation and at the earliest stage of nanocrystallization. (iii) Temperature dependencies of magnetization, as well as close to Curie temperature thermal capacity of amorphous phase were measured in order to reveal the possibility of pre-crystallizational fluctuational state of the amorphous phase. 2. EXPERIMENTAL PROCEDURE FINEMET-type quenched Fe73.5Nb3Cu1Si13.5B9 ribbon of 20 Pm thick and 1 mm width was used in our experiments. The Curie point was measured using DSM-2M calorimeter at the heating rate of 32 K/min. Temperature dependencies of the magnetization were measured using the dynamic mode of magnetization reversal. The X-ray diffraction (XRD) analysis of the samples was done with a DRON-3 diffractometer using CoKD radiation. The volume fractions of the nanocrystalline phase were calculated using the computer approximation of experimental diffraction spectrum by linear combination of theoretical spectra of D-Fe(Si) phase containing various concentrations of Si, the experimental spectra of amorphous alloy and polynomial background. The Mössbauer spectroscopy was performed using a Co57 source in Cr matrix. The source moved with constant acceleration on a two-side saw. The samples for diffraction and MS studies were treated in a calorimeter under the same conditions. 3. BASIC APPROACH TO THE DESCRIPTION OF PRE-CRYSTALLIZATION DECOMPOSITION IN AMORPHOUS ALLOYS In our previous works [3, 4] we defined the average size and volume fractions of the particles of D-Fe(Si) nanocrystalline phase from diffraction data. It is easy to calculate the number of crystals generated per volume unit or the volume density of nucleation centers. By analyzing a number of our data and the data of other researchers, and by taking into account one of the major results of the recent investigations of nanocrystallization, i.e. the fact of D-Fe(Si) phase nucleation on copper clusters [5], we have come to the conclusion, that it must be copper fluctuations in Fe73.5Cu1Nb3Si13.5B9 amorphous alloy that predetermine the sizes of upcoming D-Fe(Si) nanocrystals. Really, in this case the centre to centre distance of nanoparticles (which can be inferred from the volume fractions and sizes of crystals) corresponds to the wavelength of copper fluctuations. The acceptance of the nucleation of crystalline phase taking place on fluctuations arising at decomposition makes it clear that the nucleation and growth of crystalline phase become possible when the fluctuation spectrum includes a general wavelength O | 2Dc (Dc – critical nuclei size). Therefore, it occurs that the possibilities for nanocrystals to grow are limited by their interlocking with the surrounding phase which

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separates neighbour grains. Under the conditions of our experiment when heating up to a certain temperature is followed by accelerated cooling, there may be such a situation that nanocrystals have already being formed but the duration of the heat treatment is not sufficient for their competitive growth. The same situation is realized in rapidly quenched binary Fe-Nd alloys, where at a temperature of about 470 K Į-Fe crystals appears [1]. It is clear that the nanocrystals’ sizes correspond to the wave characteristics of the compositional fluctuations required for crystals nucleation. It is possible to express the relation between the value of the wave vector for the first maximum of the static structural factor kp of nanocrystalline structure and the size of crystals and their volume fraction by the simple expression: kp ~ 2S/O | 2S(1 + z/2)–1/3(1 – vD)1/3/D, 3

3

3

(1)

3

which follows directly from the condition O vD | O – D – zD /2, where z is the average number of particles in the nearest environment, and vD – volume fraction of D-Fe. Later on it will be assumed that the wavelength of fluctuations growing with maximal velocity is Omax ~ 2S [(–w2G/wc2)(1/2K)]–1/2 [6] and at the temperature close to spinodal: 

Omax~ (Tsp– T)–1/2

(2)

(G – Gibbs energy, K – energy gradient constant, c – is a solved component concentration, Tsp is the spinodal temperature, where w2G/wc2 = 0). Hence the plot 1/O2 via T near Tsp is linear and crosses the temperature axis just at Tsp. Such linearization is shown in Fig. 1, from which follows that the temperature Tsp = 997 K (724qC) for FINEMET corresponds to the spinodal decomposition of amorphous alloy (1 at.% Cu).

Figure 1. The plot of 1/O2 via T for treated nanocrystalline Fe73.5Nb3Cu1Si13.5B9 (opened circles) and Fe67Nd33 rapidly quenched alloys (closed circles); explanation in the text

It is important that the calculations based on the spinodal decomposition model perfectly describe both the regular solution (Fe-Nd) and the copper-deficient solution (Fe-Cu in FINEMET) with overcooling of about 200 K below the spinodal temperature. Anyway, let us try to clear up the role of other elements during the fluctuation decomposition. We remind that niobium has a positive enthalpy when mixing with copper (in the Cu-Nb diagram the liquid phase decomposes at 2070 K), and the copper segregation process can be accompanied by the segregation of niobium atoms. According to the expression (2), the estimation of the wavelength of Cu-Nb oscillations of the concentration gives the value of wavelength of niobium concentration almost half as much as that for Fe-Cu (0.59-0.64), taking into account the temperature of stability of 2070 K and the correction for average interatomic distance. The consequence of this fact

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is proved to be able to result in a rather interesting situation. Namely, firstly, the process of copper segregation (Cu-Fe decomposition) can be accompanied by the niobium running from the copper-rich zones (Cu-Nb decomposition), and also, secondly, the set of Nbenriched zones between Cu-rich ones is supposed to form due to the smaller wavelength of Nb fluctuations. Thus the niobium outflow reduces the stability of the amorphous phase, as regards the crystalline phases formation. It becomes clear, that the centers of primary crystallization are zones devoid of copper and niobium. In terms of the model of nucleation and growth of a spherical nucleus these zones with a deficient niobium concentration become “supercritical nuclei” of primary crystallization. It is necessary to remind, that in accordance with [7] the nanocrystal growth in FINEMET is controlled by the niobium characteristics of diffusivity, that is in good agreement with the above reasons. 4. THE STUDY OF PRE-CRYSTALLIZATION AND THE INITIAL STAGE OF CRYSTALLIZATION OF Fe-Cu-Nb-B-Si AMORPHOUS ALLOYS BY CURIE POINT MEASUREMENTS The above consideration shows rather convincingly the adequacy of the description of fluctuation processes in terms of the model of spinodal decomposition, whose parameters actually maintain nanoscale crystallization. The oscillations of dopants Cu and Nb, though present in very small amounts (1 and 3 at.% respectively), play a significant role, which can obviously be measured using the Curie point measurements. We have reviewed the data of the composition influences on the Curie temperature of Fe-B-Si-based amorphous phase in the work [3, 4]. Up to 1 at.% Cu addition does not change its value, while the niobium reduces it (by 22 K/at.% Nb). The addition of boron and silicon, providing (B + Si) < 30%, increases Curie temperature by 14 K per 1 at.% of the addition. Therefore, there is little chance of detecting the changes in Curie temperature, which are caused by copper fluctuations, whereas the changes caused by niobium and/or boron can be well registered. However, when measuring temperature dependences of magnetization, it is necessary to bear in mind that the system with the nanoscale fluctuations of the exchange interaction and of the magnetic moment has a peculiar behaviour. It should be noted that: (i) The ensemble of exchange-isolated and magnetically decoupled ferromagnetic areas (particles) behaves as superparamagnetic material. (ii) The existence of magnetic interaction results in the fact that ferromagnetic particles appear in a random field (Hrnd ~ J*N–1/2, J – magnetization, N – number of the neighbours) and orientation of their moment by the external magnetic field is possible if the external field exceeds the local value of the random field. (iii) At the transition from the paramagnetic to the ferromagnetic phase the exchangecoupled condition for the particles forms. An additional interaction occurs, which tends to orient the magnetic moment of a particle and matrix and works, in fact, against the random field. This orientation establishes at a certain magnetization value of interparticle area. From the above it follows that the measurement of temperature dependence of magnetization discloses decoupled ferromagnetic nano-areas as the high magnetic field is

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applied, which obviously excludes the observation of the fluctuation effects. That is why we have chosen a calorimetric method of measurement of the Curie temperature. 4.1. Ferromagnetic transformation at DSC measurements From the thermodynamic viewpoint, at the equilibrium, the value of ferromagnetic contribution to specific heat CPfm will be determined only by the entropy term of free energy with equilibrium values of magnetization Ieq(T) or the magnetic ordering parameter Jeq(T) = I(T)/I(0). CPfm = R((1 + Jeq)ln(1 + Jeq) + (1 – Jeq)ln(1 – Jeq))

(3)

However, if the magnetic system is under the influence of any force or process, we can expect that the magnetic system will be in a dynamic equilibrium. In this case we shall take into account the additional energy term, which generally includes Jn. It is easy to show that the addition of a slow process with energy Eadd = p(t, T)*Jn to CPfm results in the expression: CPfm = R((1 + J)ln(1 + J) + (1 – J)ln(1 – J)) – RJ*ln((1 + J)/(1 – J))/n + +(1/n)RT*[–2J/(1 – J2) + (n – 1)ln((1 + J)/(1 – J)) + 2(n – 2)Tc/T]*dJ/dT,

(4)

where n > 0. The strongest influence is expected near the Curie temperature due to the extremal behaviour of dJ/dT via temperature at T | Tc. It is clear that dJ/dT is a negative function but the multiplier before dJ/dT depends on n, namely it is negative for n = 1 and positive for n > 1. So in accordance with (4) at n = 2 extremal behaviour is never to be expected, there can be just an inflexion. The behaviour of the CPfm for n = 1 can be noticed on Fig. 2 at T | TcA. For example, it can mean, that at T | TcA the areas with TcA are under the influence of random magnetic field Hrnd (p(T, t) = Hrnd(T, t)*I(T), n = 1) from areas with Tc > TcA, whose magnetization I(T) slightly depends on temperature close to TcA. Moreover, the lightly coupled ferromagnetic particles with the large dispersion of the Curie temperature show a similar behaviour. Thus the DSC method allows precise and perfect detecting of the Curie temperature of an amorphous alloy. 4.2. Structural relaxation and pre-crystallization effects in Fe73.5Nb3Cu1Si13.5B9 alloys It is known that the structural relaxation process is partially irreversible. The structural relaxation of the as-quenched amorphous alloy is accompanied by a release of the free volume and hence by a reduction of the average interatomic distance with the changes of energy of ferromagnetic ordering and Curie temperature. The DSC measurements usually show a significant difference between the as-quenched and relaxed amorphous alloys. Such a difference is shown in Fig. 3 (curves A), where the short time annealing at 673 K of as-quenched alloy leads to the decrease in the heat flow at the recurring heating. Moreover, the irreversibility of the relaxation process is clearly illustrated by the following experiment. After the interruption of heating at

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623 K and during the repeated heating from room temperature up to 773 K we can see that the effect of structural relaxation is only observed above 623 K (see Fig. 3, curves B). It shows that the relaxation process of an as-quenched amorphous alloy is characterized by the broad activation energy spectrum. Now we shall consider the behaviour of the alloy at annealing below the crystallization temperature. For the as-quenched alloy, as has already been mentioned, the thermograms demonstrate both the background irreversible relaxation and the reversible effect. The last one coincides with the TMA data and corresponds to the Curie temperature of an amorphous alloy. At the same time almost in every thermogram of an as-quenched alloy the addition effect is observed in the temperature interval from 563 K up to the crystallization temperature 733 K. In Figure 4 the development of this effect at the annealing at 723 K is shown (signed as TcB). A detail investigation has revealed the following relationships between this effect and the heat treatment: (i) In the as-quenched alloys this peak is dim or split. The main component of TcB is located at 623 K. An additional component is traced up to 673 K. (ii) The repeated heating amplifies the component TcB of at 673 K and lowers the component at 623 K. The broadening and sometimes splitting of TcA peak is observed. (iii) Additional effects are registered more clearly, if the annealing temperature is closer to the crystallization temperature. (iv) Due to the beginning of crystallization at the annealing at the temperatures 733-773 K, the effect TcB is weakening, being located at 700 K with simultaneous appearance of Tc2.

Figure 2. DSC curves for the Fe73.5Nb3Cu1Si13.5B9 alloy heated up 733 K (1) and annealed for 10 min (2) and 40 min (3) in comparison with the temperature derivative of magnetization for the same alloy heated up 733 K (1) and annealed for 20 min (2) and 40 min (3)

Figure 3. DSC curves for the as-quenched Fe73.5Nb3Cu1Si13.5B9 amorphous alloy (scanning rate 32 K/min) and for repeated heating with annealing durations (from above downwards) for 10 s, 2 min and 5 min at 773 K (A). DSC curves for the as-quenched state with interruption of heating at 623 K and repeated heating (B)

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Figure 4. DSC curves for the Fe73.5Nb3Cu1Si13.5B9 amorphous alloy annealed at 720 K for 10-30 min. In addition to Curie temperature TcA another effect at TcB is observed

Taking into account that the annealing at 723 K does not result in the occurrence of a crystal phase we prefer to interpret these data as development of the decomposition stage of the amorphous phase. If we assume that the phenomenon TcB is caused by the ferromagnetic ordering in zones with the changed composition, the estimation of the difference TcB – TcA (40 K for as-quenched alloy) gives us the difference in niobium concentration of about 2 at.%. For the partially relaxed at 723 K alloy this difference becomes 90 K (4 at.% Nb), and at the continuation of annealing it achieves 120 K, that corresponds to 5.5 at.% Nb difference. The latter corresponds to the occurrence of the fluctuations of the Nb contents with the amplitude of almost 3 at.% Nb and decomposition of amorphous phase into the Nb-rich and Nb-free zones. But such an interpretation of TcB peak as Curie temperature of the Nb-free areas needs additional investigation and independent confirmation by other methods. 4.3. The initial stage of crystallization in Fe73.5Nb3Cu1Si13.5B9 alloy The X-ray diffraction shows the beginning of crystallization at 733 K of heat treatment. Comparing the annealing at 733 K with annealing at lower temperatures we notice that the behaviour of TcA demonstrates the acceleration of TcA rising and reflects the saturation of the amorphous matrix by boron displaced from Į-Fe nanocrystals. DSC curves also show the second peak (Tc2) in the temperature range of 510-540 K (see Fig. 2). A similar effect was previously obtained [8] by DSC studies of FINEMETtype glass-coated microwires. An increase in the annealing duration results in the shift of the Tc2 to higher temperatures. This effect can be explained by Nb-rich layer having gathered near the surface of Į-Fe crystals. Magnetization measurements did not show the presence of the Tc2. It is necessary to note that the TMA signal was measured using a weak external magnetic field (~1 Oe) and the saturation magnetization is slightly sensitive due to the broadening of the temperature interval of the ferromagnetic transformation under random field influence, and due to the small value of magnetization of these Nb-rich areas. 4.4. Mössbauer study of the pre-crystallization effects in Fe73.5Nb3Cu1Si13.5B9 alloy and the initial stage of crystallization Some additional information about the redistribution of the elements in the investigated alloys may be obtained from the Mössbauer data. Figure 5 shows the

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hyperfine field Bhf distribution P(Bhf) for the samples after various thermal treatments. The shape of the P(Bhf) curve for the as-quenched sample is a broad peak with a maximum of Bhf at about 23 T. Annealing for 40 min at 673 K results in insignificant changes of the P(Bhf) character which entails a slight increase in the Bhf density at 27 T and its corresponding decrease at the Bhf | 15 T. These changes correspond to the elements redistribution in totally amorphous alloys during the structure relaxation.

Figure 5. Hyperfine field distribution of Fe73.5Nb3Cu1Si13.5B9 alloy, in as-quenched state and annealed at several temperatures. The upper plot demonstrates the changes 'P between the distribution for the annealed sample and as-quenched one

Thus, we can note, that in some parts of the sample the number of iron atoms has increased (Bhf = 23 T) and in another one the quantity of Fe-deficient areas (Bhf = 15 T) has decreased (see the plot of P(Bhf) in Fig. 5 for changes after heat treatments). It seems that there as a result of annealing there was a movement of iron atoms from the Fe-deficient to Fe-rich zones. However, taking into account that the measurements show only the nearest environment of iron atoms, it is also possible to regard this fact as a movement, for example, of Nb and/or Cu atoms from Fe-rich zones to Fe-deficient ones. Consequently, these changes can be related to the spatial redistribution of elements during the compositional fluctuations at the decomposition process. More information can be obtained from the P(Bhf) curves for partially crystallized alloys. For the samples annealed at 733 K 40 and 60 min, the following tendency to change of P(Bhf) is observed. Firstly, an increase in P(Bhf) for high values of Bhf, corresponds to the crystalline phase appearance. Secondly, the P(Bhf) peak at Bhf | 5 T appears. Its intensity is found to increase with the increase in the length of annealing. We associate this peak with the formation of the Cu-rich and/or Nb-rich zones. According to [9] such a low magnitude of Bhf corresponds to copper environment of iron atoms with Fe: Cu ratio 30:70. We cannot exclude the possibility of Bhf = 5 T be

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due to the Nb-rich areas (for example, to Nb-rich layer around the nanocrystals). However, according to our studies [3, 4] Nb-rich zones are formed around -Fe and then they extremely slowly return the niobium to the residual amorphous phase. The decrease in TcA related to the niobium inflow was detected after 1 hour of annealing at 823 K. The occurrence of 5 T peak at 733 K and its disappearance at 773 K allows us to interpret this process as a reduction of iron quantity in u-rich zones rather than in Nb-rich areas. As the iron-free zones are not able to contribute something into the MS spectrum, a further decrease in this low-field peak is a result of the Fe outflow from these areas. 5. CONCLUSIONS The measurements of the ferromagnetic anomaly of specific heat of as-quenched Fe73.5Nb3Cu1Si13.5B9 amorphous alloys. proved that the Curie temperature increased by about 15 K due to the structural relaxation. The relaxation process of the investigated amorphous alloy is characterized by a broad distribution of activation energies. During the relaxation process the additional effects, apparently related to the ferromagnetic transformation of compositional fluctuations were found. The Mössbauer study showed that the changes in the hyperfine field Bhf distribution P(Bhf) take place during the structural relaxation of the alloy under investigation. The increase in Bhf density at 27 T and the corresponding decrease in the Bhf 15 T were observed. These facts allow us to conclude that the hypothesis of the decomposition of amorphous alloy at precrystallization stage may hold true. The model description of this decomposition stands the relation between the thermodynamic characteristics and the scale parameters of composition fluctuations and parameters of following nanoscale crystallization. The nanocrystallization process in Fe73.5Nb3Cu1Si13.5B9 alloys is found to start at 730 K. The redistribution of the elements during the nanocrystallization process proves to result in the formation of Fe-free nano-areas, and presumably, to Cu-clusters formation. The Mössbauer spectroscopy allows us to infer that the formation of the Fe-deficient zones goes in parallel with the crystallization process. In the temperature range of 510-560 K a certain additional effect was found, when using DSC measurements. It may relate to the Curie point of Nb-rich zone in the nanocrystal surrounding. REFERENCES 1. Jalnin, B.V., Obrucheva, E.V, and Obruchev, D.V., de Campos, M.F., Teresiak, A., Hermann, R., Shurack, F., Schultz, L. (2000) Phase condition and structure, formed at an annealing of quenched Fe-Nd alloys, in Proc. of the 11th Int. Symp. on Magnetic Anisotropy and Coercivity in Rare-Earth Transition Metal Alloys, H. Kaneko, M. Homma and M. Okada (eds.), The Japan Institute of Metals, Sendai, Japan, pp. S165-S172. 2. Jalnin, B.V. and Obrucheva, E.V. (1998) Nanocrystalline structure formation at crystallization of Fe-Nd films, in L. Schultz and K.-H. Müller (eds.), Proc. of the tenth Int. Symp. on Magnetic Anisotropy and Coercivity in Rare-Earth Transition Metal Alloys, Dresden, Werkstoff-Informationsgesellschaft mbH, Frankfurt, vol. 2, pp. 1051-1055.

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3. Jalnin, B.V., Kekalo, I.B., Skakov Yu.A., and Shelekhov E.V. (1995) Phase Transformations and Variation of Magnetic Properties during the Formation of Nanocrystalline State in IronBased Metallic Glass. The Physics of Metals and Metallography 79, 5, 536-544. 4. Kaloshkin, S.D., Tomilin, I.A., Jalnin, B.V., Kekalo, I.B., and Shelekhov, E.V. (1995) Influence of amorphous alloys composition on kinetics of crystallization with the nanocrystalline structure formation, Mater. Sci. Forum 179-181, 557-562. 5. Hono, K., Ping, D.H., Ohnuma M., and Onodera, H. (1997) Cu clustering and Si partitioning in the early crystallization stage of an Fe73.5Si13.5B9Nb3Cu1 amorphous alloy, Acta Materialia 47, 997. 6. Cahn, R.W. and Haasen, P., (1987) Physical metallurgy, vol. 2, Metallurgija, Moscow (in Russian). 7. Köster, U., Schünemann, U. et. al., (1991) Nanocrystalline materials by crystallization of metal-metalloid glasses, Mat. Sci. And Eng. A133, 611-615. 8. Zhukova, V., Kaloshkin, S., Zhukov, A., and Gonzalez, J. (2002) DSC studies of finemet-type glass-coated microwires, J. Magn. Magn. Mater. 249, 108-112. 9. Marci, P.P., Rose, P., Banda, D.E., Cowlam, N., Principi, and G., Enzo, S. (1995) Mater. Sci. Forum 179-181, 249.

CLUSTER STRUCTURE AND THERMODYNAMICS OF THE FORMATION OF NANOCRYSTALLINE PHASES M. DEANKOa, D. MÜLLERa, D. JANIýKOVIýa, I. ŠKORVÁNEKb, and P. ŠVECa a

Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia a,b Center of Excellence NANOSMART Corresponding author: P. Švec, e-mail: [email protected] b

Abstract: The formation of amorphous metallic systems by rapid quenching is influenced in a significant manner by the detailed path of the corresponding alloy from the melt through undercooled liquid down to the amorphous state. The thermodynamic history of the formation of an amorphous system (quenching the liquid state with specific structure, interatomic bonding and short range ordering) forces a specific template, reflecting the presence of ordered polyatomic clusters, into its potential energy structure. Subsequent transitions from amorphous to the (nano)crystalline state which then take place respect the existing potential energy landscape with such quenched-in local-scale heterogeneities. It will be shown that using a model-free continuous approach for the estimation of the distributions of initial energetic states (reflecting the cluster structure) it is possible to obtain information about the types of micromechanisms controlling the transformation processes as well as to use this information to obtain control of the phase selection during the transformation into the nanocrystalline state. A generalized view of the process of nanocrystallization from a clustered amorphous state will be presented. A special focus will be put on the nucleation processes and on the methods of their quantification. Two methods will be discussed.

1. INTRODUCTION Metallic alloy systems with outstanding properties advantageously exploit the enhancement of properties and special phenomena through the decreasing the size of structural units present in the matter. Nanocrystalline alloys obtained by crystallization from a metastable amorphous rapidly quenched state are an exemplary case of such systems. The size of crystalline grains is typically few nanometers or few tens of nanometers. The influence of nanocrystal dimensions, their structure, chemical composition and their overall volume content on thermodynamic parameters, e.g. heat capacity, thermal conductivity or diffusion coefficient and different physical, especially 69 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 69–78. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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magnetic, properties is well known. Further effects are related to the number of interfaces between the nanocrystals and the surrounding (usually amorphous) matrix, i.e. the nanocrystal surface-to-volume ratio. Other important factors worth of consideration are the size distribution and the spatial distribution of nanocrystals. In contrast to an ideal monodisperse system with nanocrystals of one size only, in real systems obtained by rapid quenching of the melt the nanocrystal size distribution is given by a complex interplay of the processes of nucleation and grain growth from disordered amorphous or undercooled liquid states with local atomic ordering on the scale of nanometers. The average size and size distribution of nanograins are closely related to the physical parameters such as the length of exchange interactions, the mean free path of charge carriers, correlation lengths, the interfacial structure and the interface induced stresses, the local magnetization processes, etc. and are reflected in the resulting properties of the complex systems containing nanocrystals embedded in an amorphous matrix. Among the most important general features of the amorphous rapidly quenched systems is the coexistence of a high degree disorder characteristic for amorphous metastable state together with the specific local ordering on atomic scales between different types of atoms. The presence of such relatively stable local structural heterogenities, denoted as clusters and containing several atoms or tens of different atomic species distributed in size and arrangement, leads to a specific heterogeneous thermodynamic behaviour and plays a crucial role for the stability, phase selection and micromechanisms of the formation of crystalline phases. We shall demonstrate the impact of different types of nucleation regimes on the process of transformation from the clustered amorphous to the nanocrystalline state and on the grain size distribution in these systems. Fundamental knowledge of thermodynamics of nucleation and growth processes will be shown to provide a method for control of grain size distribution and, consequently, of a selected physical property, by suitable time-temperature regime of the transformation. The application of this approach will be presented on selected iron and cobalt based systems with excellent soft magnetic properties as well as on systems prepared by computer simulation. The establishment of convenient size distributions of nanocrystalline grains via a specific timetemperature treatment derived from the information on transition thermodynamics will be correlated with the enhancement of magnetic properties in these systems. The discussion will focus on the nucleation and growth processes involving polyatomic cluster units and on the possibilities of quantification of these processes using transmission electron microscopy and measurements of the nucleation-induced electrical noise. 2. TRANSFORMATIONS FROM THE CLUSTERED AMORPHOUS STATE: PROCESSES DISTRIBUTED IN ACTIVATION ENERGIES In amorphous metastable metallic systems the transition to a more stable-(nano)crystalline-state is in most cases controlled by the formation of stable nuclei from an amorphous matrix and by their further growth. These processes are as a rule thermally activated and are usually approached through the notion of the activate state. In simple systems the activation energy E of the process has one single value and can be

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considered as constant. The kinetic parameters as well as the transformation behaviour can be estimated using the general exponential formula for the time dependence of the process rate [1] with the usual Arrhenius temperature dependence. In such simple cases the isothermal time evolution of the crystalline volume fraction x(t) in a nucleation-and-growth transformation is given by the Avrami equation x(t) = 1 – exp[–(tȜ)n], where n is the Avrami exponent. Then the generalized process rate Ȝ = Ȝ0 exp(E/kT) has also one single value and reflects the transition from a single initial energy state through the activation barrier at a given temperature T. The preexponential factor Ȝ0 is constant. The validity of this approach is limited to simple “homogeneous” cases. Whenever the transformation involves structurally or dynamically heterogeneous regions, a spread of values of the initial energetic states has to be considered [2, 3], especially in clustered media with clusters of a different size, composition, local ordering and interatomic bonding within the cluster atoms. Such a situation leads to the distribution of activation energies pdf(E) due to the distribution of initial free-energy states of the system. Then the transformation can be more correctly described by an Avrami-like analogue for complex systems f

x(t , T )

1  ³ pdf (O ) exp[ (t ˜ O ) n ]dO ,

(1)

0

where the formation of crystalline phases takes place by the contribution from all available process rates Ȝ with their respective probability density function pdf(ln Ȝ) = pdf(E)/kT obtained from the normalization condition. The isothermal annealing to the arbitrary annealing time, t, leads to irreversible annealing-out of a part of the processes, Pout, which is represented by the subintegral function of Eq. (1). Then the processes active at this annealing time, Pact, are given by the difference of processes annealed out between the time t and t + dt (in logarithm of time) as Pact

wPout / wt | (Ot ) n exp[ (Ot ) n ] pdf (O ) ,

(2)

which represents a product of a steeply increasing power function and a steeply decreasing power exponential function representing the “observation” window for the rate distribution pdf(Ȝ) with a maximum at t ~ 1/Ȝ and a width of about half order of magnitude in log Ȝ. Thus at any time t only a relatively narrow portion of the entire rate distribution with Ȝ ~ 1/t can be active and “visible”. The experimentally observed transformation rate at this time, f

dx / dt

³P

act (t , T ) dO ,

(3)

0

however, provides only integral information about the active process rates. Processes with Ȝ < t–1 are “sleeping” processes, to be activated as the observation window is shifted to lower process rates with increasing time. This phenomenon is closely related to the information content of the transformation curves and the capability of predicting the transformation behaviour [3]: unless the process obeys a simple law similar to

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the Avrami equation in its simplest form, the knowledge of the entire process rate (or activation energy) distribution is necessary. Otherwise, the predictability can range only to times within one order of magnitude above the longest observation time or the slowest process rate. In potential energy landscape terminology this is equivalent to the necessity of probing the entire clustered, energy-distributed landscape for the thermodynamic behaviour of all cluster types and sizes. The approach was tested on sets of very simple simulated isotherms of a nucleationand-growth transformation [4] with different, physically plausible, yet very narrow, pdf(E) with the spread of E being below 3%. It was shown that even narrow distributions of E, almost beyond the detection limit and accuracy of determination of activation energies of the majority of experimental methods, which is ~5%, have a drastic effect on the transformation kinetics. The values of kinetic parameters of transformation, namely the Avrami exponent n and the (temperature-independent) Arrhenius activation energy obtained on these isotherms by the commonly used classical time-to-transformation formulae differed drastically from those which served as input values for the simulation. Besides, very attractive dependences of these parameters on crystallinity content, x, were observed. Especially the decrease of the Avrami exponent n with increasing x could tempt to interpret the results via a decrease of nucleation rate accompanied by a diffusion-controlled grain growth. However, none of these interpretations reflected the simulation conditions, these being input as normal homogeneous nucleation and a 3D grain growth, corresponding to n = 4 during the entire transformation. The use of the K-S approach (named by the authors’ initials) outlined in [3, 5] infallibly yielded the correct values as well as the true and by classical methods of kinetic analysis inaccessible pdf(E) dependencies. 3. TEMPERATURE DEPENDENCE OF ACTIVATION ENERGIES An additional complication in the transitions from an amorphous to a nanocrystalline state is the temperature dependence of activation energies, leading to the case where pdf(E) = pdf(E(T)). In the first approximation E(T) can be described by the first two terms of its Taylor-series expansion around a mean activation energy E(T0) = E0 active at a mean annealing temperature T0 as E(T) § E0 + E’(T – T0), where E’ = dE/dT at T0. In processes controlled e.g. by a viscous flow, the activation energy decreases with increasing T, thus E’ < 0. The activation energy of the formation of the critical nucleus, W ~ TM/(TM – T) increases as T approaches the melting temperature TM. The normalized temperature coefficient of W(T) can be taken as KW = (dW/dT)/W = W’/W = 2/(TM – T). For most amorphous alloys the values of W(T) and KW are ~0.2-0.5eV and ~0.003 K-1, respectively. Thus in the interval of annealing temperatures T0 ± 30 K, W(T) = W(T0)[1 + KW(T – T0)] = W(T0) ± 10%. Taking the activation energy of nucleation-and growth process as a weighted sum of activation energies of nucleation, W + EG, and 3D growth, EG, with EG ~ 2 eV, we can compute E(T) = E0[1 + KE(T – T0)]. The value KE = E’/E0 | 5u10–4 K–1 and E(T) = E0 ± 1.5% for the same temperature interval, which represents a very small change. The effect on the transformation kinetics, however, is significant. A simulation of the transformation process at ~685 ± 35 K (Fig. 1) with Gaussian distribution of the activation energy centered

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around 2 eV with FWHM ~0.03 eV and KE as above leads to a very small shift in the pdf(E). Due to E’>0 the shift of pdf(E) is towards higher values of E with increasing temperatures and vice versa, as shown in the inset of Fig. 1. Thus the transformation curves x(t) (thick lines and full symbols) are shifted towards longer times at higher temperatures and towards shorter times at lower temperatures in comparison to the x(t) dependences for the same case without a temperature dependence, as described in [4, 5]. Effectively, this leads to an apparent acceleration of the kinetics, i.e. with a lower

720K s lo w e r

2

fa s te r

0 .5

0 .9 5

1 .0 0 E (T ) / E 0

pdf(E) * 10

transformed fraction

T 0= 6 8 5 K 650K

pdf(E(T))

1 .0

1 .0 5

in p u t p d f(E 0 ) K -S a p p ro a c h c la s s ic a l A v r a m i

2

1

650K

720K

0 .0

0

1 E -3

0 .0 1

0 .1 tim e [m in ]

1

1 .3

1 .5

1 .6 1 .8 E [ eV ]

2 .0

Figure 1. Transformation curves x(t) for the temperature-dependent (full lines and symbols) and temperature independent (open symbols) crystallization with Gaussian pdf (E) centered at 2 eV. The effect of temperature on the shift of pdf (E) is shown in the inset, the effect on x(t) is emphasized by the arrows. The results of the determination of pdf(E) using K-S approach are shown on the right, together with the results from the classical Avrami/Arrhenius analysis

activation energy. Such a result is indeed obtained when the kinetic analysis is performed using the classical kinetic analysis via Avrami/Arrhenius-type equations, as shown in the right part of Fig. 1. The use of K-S approach yields true values of E, E’ and pdf(E) as input into the simulations. In the case of E’ < 0 the effect would be opposite – the apparent slowing down of the transformation kinetics would be observed. It is to be noted again that the widths of pdf(E) as well as the values of KE (or E’) are very small. 4. CLUSTERS AND ENERGY DISTRIBUTIONS IN REAL SYSTEMS As mentioned above as well as in [5], the sign of the temperature dependence of activation energies can aid in identifying the microprocesses controlling (nano)crystallization. Positive or negative E’ can at least suggest a nucleation-like or viscous flow-like character of the transformation, respectively, allowing also to infer on the type of clusters and their role in the formation and growth of crystalline nuclei. Using this notion and the KS-approach for the determination of pdf(E) and E(T), three of the bestknown nanocrystal-forming systems, FINEMET [6], NANOPERM [7] and HITPERM [8], were analyzed. In all three cases the transformation kinetics and the values of pdf(E) and E’ using K-S approach were determined mainly from the time evolution of electrical resistivity R(t) during isothermal annealing in a wide temperature interval;

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a check of the validity of kinetic behaviour reflected by R(t) was performed also using DSC, however, in a much narrower temperature interval. 4 FeCuNbSiB FeZrB FeCuZrB FeCoZrB

2

4

-1

KE [10 K ]

3

1 0

Figure 2. The relative temperature dependence of activation energies, KE = E’/E0 as a function of relative activation energy for the FINEMET, NANOPERM and HITPERM systems

-1 0.95

1.00 E/E0

1.05

The combined dependences of E’, or KE = E’/E0, for all mentioned systems, FINEMET (FeCuNbSiB), NANOPERM (FeZrB and FeCuZrB) and HITPERM (FeCoZrB) are shown in Fig. 2 normalized against the mean activation energy E0, being 4.2 eV, 2.9 eV, 3.7 eV and 3.8 eV, respectively. As can be seen, the spread of activation energies in all cases is within 5% and the values of KE are of the order of 10–4K–1, similar to those estimated in the preceding paragraph; slightly higher values observed during the initial stages of nanocrystallization in FINEMET were ascribed to the clustering of Cu with nucleation-like character. Negative values of KE in NANOPERM correspond to the viscous flow of medium-range ordered regions without need for their nucleation-like rearrangement; a subsequent increase in KE to positive values in Cucontaining NANOPERM was interpreted again in terms of nucleation-like activation of clusters with Cu. In all cases the behaviour of E’ could be traced in a straightforward manner to the expected cluster structure and composition. 5. PHASE SELECTION BY SELECTIVE ENHANCEMENT OF CLUSTER CONTENT – THE APPLICATION OF SEQUENTIAL ANNEALING A special case of FINEMET alloyed with Ni substituting Fe was analyzed in [9] with respect to the changes of cluster types and short range ordering related to the Fe/Ni content. Different temperature intervals favoring alternatively the reordering of Fe-Ni rich clusters in an amorphous state from bcc-like into fcc-like and vice versa were determined in [10]. It was shown that a martensitic-like behaviour can be observed in amorphous state and that enhancement of the formation of different phases can be achieved by suitable preannealing of the amorphous matrix leading to the atomic rearrangement in the originally bcc-like clusters. A similar effect induced by sequential annealing was observed in the Fe-Co-Zr-B (HITPERM) alloy. A set of isotherms shown in Fig. 3 was used for determining the activation energy distributions and E(T), as described above. Using the detailed thermodynamic information on the transformation process and time evolution of crystal sizes, it was possible to suggest a special two-step sequential annealing along the transformation isotherms, monitoring simultaneously selected magnetic properties. The values of coercive field obtained during different

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annealing sequences shown in Fig. 3 are in the enclosed table. It can be seen that classical annealing at ~740 K (point 1) leads to a stable and reasonably low value of HC. Annealing at lower temperature (point 2) yields a slightly higher HC value. At higher

1.0

3

Sample

2

R(t)/R(t=5sec)

4 0.9

0.8

0.7 723K 798K

1

0.6 0.1

1

10 100 time [min]

Coercivity HC [A/m]

1 2 3 4

28 30 14 16

2o1 3o1 4o1

34 24 18

1000

Figure 3. The evolution of electrical resistivity in the course of nanocrystallization of HITPERM alloy in the temperature range 723-798 K. The thick curve represents the isotherm at 740 K, the horizontal line shows the times necessary to obtain equal crystallinity content of ~15 vol.% at different temperatures, indicated by full squares and numbers. The values of room temperature coercivity obtained after annealing at each point are shown in the table; the values obtained after sequential annealing are shown in the bottom rows

temperatures and shorter times HC is lower, however, not stable due to unfinished nanocrystallization processes. An optimized annealing sequence (to point 4 at higher temperature and then along the 740 K isotherm down to point 1) leads to almost 50% improvement of HC and a stable nanocrystalline structure with grain sizes slightly smaller than those obtained by simple single-step annealing at 740 K. 6. NUCLEATION AND GROWTH IN NANOCRYSTALS FORMING AMORPHOUS SYSTEMS Special tools are necessary for detailed quantification of the grain size distribution and subsequent estimation of the crystallinity content as well as of the nucleation and growth rates. A calibration of any algorithm for these purposes is necessary, preferably on a suitable sample with a well-defined crystallinity, grain size distribution and transformation process. The main problems with structure quantification (e.g. by microscopy), besides the pattern recognition and grain boundary thickness, are the polishing (or focal plane) effect and the effect of the sample thickness.

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Figure 4. The effect of focal plane (left) and sample thickness (right) on the apparent grain size distribution and crystallinity content, which is 40 vol.% in all frames. Left: sequence of frames with different focus values (0, +10, +20 and +40 nm from top to bottom) showing the apparent change in size of a selected grain (marked by dashed lines) having diameter of 80 nm. Right: sequence of frames with different sample thickness (or focal depth) ranging from 0 to 45 nm (see marker); increase of focal depth drastically changes the apparent crystallinity content

A convenient way of simulating the nanocrystalization process even in a clustered amorphous matrix is direct nucleation at random sites and spherical growth of nuclei in a sufficiently large volume of the sample. The processes of the nucleation and growth may be easily prescribed; however, it was shown that even the simplest mechanism of homogeneous nucleation and 3D growth with constant rate reproduced the real transformation [4] quite accurately. The only assumption, reflecting the fact that after nanocrystallization usually ~50 vol.% of the amorphous matrix remained untransformed, was that the grain growth ceased for grains coming to contact with another

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grain. If necessary, such an approach allows also for easy refinement of simulation conditions to include effects analogous to soft impingement, etc. The grain structure obtained by a simulation experiment is well defined with the exact number of grains of known sizes, thus both grain size distributions and crystallinity content are unambiguous. The results of such a simulation and especially the focal plane and sample thickness effects are shown on a series of frames in Fig. 4 on series of frames with the same magnitification. The crystallinity content is 40 vol.% in all frames. Depending on the focal plane it is possible to observe the same grain with apparently different diameters; the effect is identical to the polishing effect, however, in the case of nanocrystalline materials the polishing effect is less important. Even a more drastic effect may be observed on the apparent crystallinity content due to the different thickness layer (or sample). With the increasing thickness or focal depth crystalline grains with a higher contrast than the remaining amorphous matrix may lead to significant overestimation of the crystallinity content. It is therefore necessary to use additional techniques, e.g. determination of a layer thickness, observations in different diffraction conditions in dark field together with other methods (X-ray diffraction or fluctuation microscopy [11]) to obtain a correct estimate of the crystallinity content. 1 .0

R(t)/R(3 sec)

820K 740K

0 .9

0 .8

0 .7 0 .1

1

10

100

1000

tim e [m in ]

Figure 5. A principal scheme for the determination of nucleation and growth rates via the detection of the electrical noise during isothermal transformation (Al-Fe-V system)

Additional possibilities of obtaining direct information on nucleation and growth processes taking place during the transition from the amorphous to the (nano)crystalline state are the monitoring of electrical manifestations of the formation of crystalline nuclei and their size increase. In general, the forming crystalline phase has electrical resistivity different from that of the amorphous matrix. Thus although the time evolution of electrical resistivity is usually observed as a smooth curve evolving in time or temperature and can give information about the overall kinetics, minute parts of the curve can be considered as composed of steps corresponding to the appearance of additional scattering centers and to their size increase, leading to still another change. An illustration of this situation is in Fig. 5. The use of convenient electronics able to produce a derivative of the R(t) signal and analyze its frequency spectrum depending on the transformation rate and the sample volume (~10–12m3) together with special coincidence circuitry is capable of providing information for the direct determination of the nucleation rates.

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7. CONCLUSIONS Clustered amorphous state exhibits specific features due to its inherent nature and genesis. The distribution in size, local ordering and composition of clusters is reflected in the distribution of the initial thermodynamic potential of the system and thus in its transformation behaviour. It was shown that even very narrow distributions with a slight temperature dependence of the corresponding activation energies leads to significant effects in the crystallization kinetics. Narrow distributions were observed and determined in a real system. The control of heterogeneities as a convenient tool for tailoring specific properties of materials sensitive to nanoparticle size effects was illustrated. Some problems related to quantification of processes controlling nanocrystallization were assessed. ACKNOWLEDGEMENTS Support of the Slovak Grant Agencies for Science (projects no. VEGA 2/2038, 4/4065, APVT51-021102, APVT-51-052702 and SO 51/03R8 06 03) is acknowledged. The research was partly supported by the SAS Center of Excellence “Nanosmart”. REFERENCES 1. Primak, W. (1955) Kinetics of Processes Distributed in Activation Energies, Phys. Rev. B 100, 1677. 2. Debenedetti, P. G., Stillinger, F. (2001) Supercooled Liquids and the Glass Transition, Nature 410, 259. 3. Krištiakova, K., Svec, P. (2001) Continuous Distribution of Thermodynamic Microprocesses in Complex Metastable Systems, Phys. Rev. B 64, 184202. 4. Švec, P., Krištiaková, K. (2002) Influence of Spatial Heterogeneity on (Nano)crystallization of Rapidly Quenched Iron and Cobalt Systems, J. Optoelectronics Advanced Mater. 4, 223. 5. Krištiaková, K., Švec, P. (2002) Calculations of Temperature-Dependent Model Activation Energy Distributions, Czech J. Phys. 52A, 133. 6. Krištiaková, K., Švec, P. (2001) Distribution of Thermodynamic Processes Controlling (Nano)crystallization of Iron-Based Metallic Glasses, Scripta Materialia 44, 1275. 7. Švec, P., Krištiaková, K., Duhaj, P., Janiþkoviþ, D. (2002) Energetics of Formation of Nanocrystalline Structures in Finement, Nanoperm and Hitperm Alloys, Czech J. Phys. 52, 145. 8. Krištiaková, K., Švec, P., Janiþkoviþ, D. (2001) Short Range Order and Micromechanism Controlling Nanocrystallization of Iron-Cobalt Based Metallic Glasses, Mater. Transaction JIM 42, 1523. 9. Duhaj, P., Švec, P., Sitek, J., Janiþkoviþ, D. (2001) Thermodynamic, Kinetic and Structural Aspects of the Formation of Nanocrystalline Phases in FeNiCuNbSiB Alloys, Mat. Sci. Eng. A 304-306, 178. 10. Švec, P., Krištiaková, K., Deanko, M. (2003) Cluster Structure of the Amorphous state and Nanocrystallization of Rapidly Quenched Iron and Cobalt Based Systems, in Synthesis, Functional Properties and Applications of Nanostructures, T. Tsakalakos, I. Ovidko (eds.), NATO ASI Series, vol. 128, Kluwer Acad. Publishers, Dordrecht, pp. 271-294. 11. Li, J., Gu, X., Hufnagel, T.C. (2003) Using Fluctuation Microscopy to Characterize Structural Order in Metallic Glasses, Microsc. Microanal. 9, 509.

KINETIC CHARACTERIZATION OF NANOCRYSTAL FORMATION IN METALLIC GLASSES E. ILLEKOVÁ Institute of Physics, Slovak Academy of Sciences Dúbravská cesta 9, 842 28 Bratislava, Slovakia Corresponding author: E. Illeková, e-mail: [email protected] Abstract:

Fe-Mo-Cu-B, FINEMET-type and Al-based ribbons were investigated by differential scanning calorimetry (DSC) in both scanning and isothermal regimes. The devitrification of rapidly quenched ribbons is a multistage process. Our studies have established that the kinetics of the nanocrystal formation stage (being the primary crystallization, R1, or the main transformation stage) is characterized by four principal peculiarities: (i) The scanning exothermal DSC peak has the large high temperature part. (ii) Any pre-annealing at temperatures below the R1 peak shifts the peak to higher temperatures, decreasing its enthalpy. (iii) The isothermal transformation exotherm does not shape any peak. (iv) The thermograms taken at all heating rates and at each annealing temperature follow the unique Suriñach plot master curve. This curve is a straight line indicating the normal-grain-growth exponent < 2. The nanocrystal formation in metallic glasses does not follow the conventional Johnson-Mehl-Avrami kinetics. The normal-grain-growth kinetic law, proposed for coarsening of extremely fine crystalline grains in heterogeneous thin films, could also in the case of R1 nanocrystalline formation stage in metallic ribbons rationalize all peculiar results without any correction.

1. INTRODUCTION In the last decade, the relation between the shift in the exothermic crystallization differential thermal analysis (DTA) peak as a function of the pre-DTA isothermal heattreatment and the crystallization kinetics has been found [1]. This recognition accounts for the increased significance of the DTA investigations of crystallization in glasses. The demand of the modern times for minimalization has actualized the advance of new materials with extremely fine microstructures. Accordingly, the FINEMETs, NANOPERMs, HITPERMs and some aluminium based heat-treated ribbons symbolize the particular category of the nanocrystalline alloys in which the development of the three-dimensional nanostructure can be controlled by a special thermal treatment of rapidly quenched precursors. The nanocrystalline metallic ribbons are characterized by an extremely high nanocrystal density at a relatively low total crystalline content, sufficiently high thermal stability, extraordinary magnetical, corrosion and mechanical 79 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 79–89. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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properties. The continuous-heating as well as the isothermal nanocrystal formation being the main transformation stage, R1, in metallic ribbons, is characterized by distinct kinetics which does not follow the conventional nucleation-and-growth Johnson-MehlAvrami (JMA) kinetic law [2]. In this presentation the kinetics of nanocrystal formation is investigated in the NANOPERM-type Fe76Mo8Cu1B15 metallic ribbon prepared by planar flow casting. Differential scanning calorimetry was used in both continuous-heating (heating rates from 5 to 80 K min1) and isothermal (at temperatures from 603 to 873 K) regimes. The samples were isochronaly (up to 60 minutes) pre-DSC heat-treated. Equivalent measurements were performed on FINEMET-type ribbons, namely Fe73.5Cu1Nb3Si13.5B9 one and seven other samples, varying Cu (0 or 1 at.%), Nb (from 0 to 7 at.%) and Si (from 0 to 14.5 at.%) contents, as well as Fe64Ni10Cu1Nb3Si13B9 and also the Al90Fe7Nb3 ribbon. 2. EXPERIMENTAL The Fe76Mo8Cu1B15 metallic ribbon, 6 mm wide and 20 Pm thick, was prepared by the planar-flow casting technique (the quenching rate ~106 K s1) in the air. The inductively coupled plasma spectroscopy analysis (±1% of element content) verified the real chemical composition. The diffraction X-ray (XRD) patterns, transmission electron microscopy (TEM) and Mössbauer spectroscopy (MS) did not determine any crystalline phase in the as-cast ribbons [3]. The calorimetric signals from phase transformations were monitored by DSC using Perkin-Elmer DSC7 (±0.5 K; ±2 J g1) system. Continuous-heating regime from 290 to 973 K (with the heating rates, w+, ranging from 5 to 80 K min1) and an isothermal regime (at Tx – 50 K to Tx + 50 K range, where Tx is the onset peak temperature) with a heating ramp w+ = 40 K min1 were used. The samples were investigated in the asquenched state and also after isothermal in situ DSC pre-annealing (for annealing time, ta = 60 min at annealing temperatures, Ta, from Tx  50 K to Tx + 50 K and at 40 K min1 ramp, the cooling rate was 200 K min1). Samples of about 2 – 13 mg placed in the Pt pan, the empty reference pan and flowing Ar as well as N2 atmosphere were used. The DSC instrument was calibrated for all heating rates using the In and Zn standards. The subtracted first measuring run and the subsequently following second run was always used for the kinetic calculations in the continuous-heating regime while only the first measuring run was used in the isothermal measuring regime. As has been previously found, the classical JMA kinetic laws fail in the case of the continuous-heating nanocrystal formation stage, R1, in metallic ribbons [4]. Besides, the same crystallization stage often reveals the bimodal character in the isothermal regime [5]. Therefore the Suriñach curve fitting procedure [6, 7] might help to specify the complex character of the R1 stage. In this way, each single DSC curve (continuousheating or isothermal), represented in an appropriate coordinate system, namely

ª dD (T , t ) º 'E *  ln w ln « » ¬ dT ¼ RT (t ) or

ª dD (t ) º 'E * ln « » ¬ dt ¼ RT

versus

 ln>1  D (T , t )@

versus  ln>1  D T (t )@

(1)

(2)

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Figure 1. Suriñach plots [6] for different theoretical kinetic equations summarized in Table I. Full lines correspond to the JMA kinetics [6], exponent n being the parameter. Dashed lines correspond to the NGG kinetics [5], exponent m is the parameter. The dotted line corresponds to the long-range diffusion kinetics [6]. JMA model lines are shifted to show the maxima at the same level

Table I. JMA versus NGGDand long-range diffusion kinetics: f (D) – differential kinetic equation according to [8], g(D) = ,0 d(D)f (D), and yT(t) = [dD (t)/dt]T (e.g. proportional to the isothermal DSC signal) and YT (t) = DT (t) (e.g. proportional to the isothermal electrical resistivity or thermogravimetry signal), if T = const Symbol

JMA(n)

NGG(m)

(d)

Rate controlling reaction mechanism

JMA crystallization (Johnson-Mehl-Avrami)

Normal-graingrowth (Atkinson)

Three-dimensional diffusion (Ginstling-Brounstein)

§ dD · ¸ © dt ¹

f D W ¨

g D

D

dD

³ f D 0

y t

dD t dt

n1  D > ln 1  D @

t

1

W

n

mr0

ª r0 º m « 1  D »  r0 ¼ ¬

n

ª § t ·n º 1  exp «  ¨ ¸ »

m

m

1

> ln1  D @n

ª §t· º exp «  ¨ ¸ » t n 1 n W ¬ ©W ¹ ¼ n

1  D m 1

n 1 n

r0W



1 m m

m t  r0 W

1  º ª «¬1  D 3  1»¼

2 3ª 2 º 1  D  1  D 3 » « 2¬ 3 ¼

# 1 m m



1

1

3 1

W t 2 1

§ r mW · m § 6t · 2 #¨ ¸ 1¨ 0 m ¸ W ¨ ¸ ¹ © ©W ¹ ¬« ¼» © t  r0 W ¹ W > 0, n > 0, m > 0, - parameters of individual models, r0 – initial grain radius Y t D t

is compared with the theoretical ones. Here, dD (T,t)/dT and [dD (t)/dt]T are directly proportional to DSC continuous-heating and isothermal signals, dH/dt, namely (dD/dT) = (1/'Hw+)(dH/dt) and [dD/dt]T = (1/'H)(dH/dt), D, 'H, 'E* and R being the degree of W > 0, n > 0, transformation, the degree of transformation enthalpy, the transformation activation energy and the gas constant, respectively. Theoretically

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possible kinetic laws are described in Table I and their Suriñach curves are shown in Fig. 1, namely the conventional JMA kinetics, the NGG kinetics, that is insinuated both in the continuous-heating and isothermal measurements [5], and the diffusion that some authors suppose to be a major controlling mechanism. 3. RESULTS The devitrification in the Fe76Mo8Cu1B15 metallic ribbon is a multistage process. Our experimental studies [9] have established that in the temperature interval 573-1000 K, it proceeds in four independent stages, R0, R1, R2 and R3 (see Fig. 2). In the R0 stage, XRD and TEM observations did not record the presence of any crystalline phase and MS suggests the presence of distinct structural rearrangements different to the classical structural relaxation ones [3]. Within the R1 stage, the exhausting annealing provides the formation of only 35 vol.% of D-Fe crystalline grains reaching barely 10 nm. The R2 and R3 stages where crystallization of the other autonomous phases as J-Fe(Mo) and the borides, respectively, has been proposed after analyse of MS results [10], will be the aim of our future complex studies.

Figure 2. DSC trace from as-quenched Fe76Mo8Cu1B15 ribbon and its decomposition [9] into five independent exothermal effects being structural relaxation and R0, R1, R2 and R3 crystallization stages. The heating rate, w+ = is 40 K min1

Figure 3. Influence of pre-annealing on the continuous-heating DSC signal of Fe76Mo8Cu1B15 ribbon taken at the heating rate w+ = 40 K min1. The pre-annealing temperature, Ta is the parameter

The D-Fe nanocrystal formation stage is the primary crystallization, R1, or the main transformation stage. Its thermodynamically specific onset, peak and endset temperatures are Tx1 = 764.2 K, Tp1 = 804.6 K and Tx2 = 860.9 K, respectively and the enthalpy – change is 'H1 = – 62 J g–1 at w+ = 40 K min 1. Its activation energy (calculated from w+ – * dependence of Tp [11]) is 'E = 511 r 24 kJ mol 1. Its kinetics is characterized by four principal peculiarities: (i) The continuous-heating DSC transformation exotherm has anomalous shape with the leading edge steeper than the trailing one (see Figs. 2 and 3). (ii) The relation between the continuous-heating transformation kinetics and the isothermal pre-heating treatment is such that any pre-annealing partially reacts out therelevant initial part of the main transformation exotherm without any influence on its

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residue (see Fig. 3). (iii) In the isothermal experiments, the DSC signal after a steep negative increase monotonically decreases without shaping any peak (see Fig. 4). A higher temperature accelerates the isothermal main transformation kinetics making the initial DSC signal larger and the transformation half time shorter. (iv) The Suriñach plot of each continuous-heating DSC main transformation exotherm follows (independently of w+) a unique master curve which is a straight line (see Fig. 5).

Figure 4. Isothermal calorimetry traces at various temperatures, Ta, of as-quenched Fe76Mo8Cu1B15 ribbons

Figure 5. Suriñach plots for the continuous-heating DSC main transformation exotherm of Fe76Mo8Cu1B15 ribbon taken at 40 K min 1. correspond to experimental data (not all data points are shown), - - - - and —— to the theoretical NGG kinetics for m = 2 and 1.5, — - — and — - - — to the theoretical JMA kinetics for n = 1 and 4, respectively

Equivalent characteristic results have been found for the main transformation forming stable nanocrystalline structures in many rapidly quenched ribbons. Namely, in the case of all FINEMET-like ribbons [4, 5], the continuous-heating R1 peak is wide, asymmetrical, with a long high temperature tail (Fig. 6a); any pre-annealing at a temperature below the main transformation shifts the R1 peak to higher temperatures (Fig. 6b); the isothermal main transformation exotherm has a bimodal character (Fig. 6c) where the monotonically decreasing DSC signal being the dominant one is controlled by the rearrangement of Nb and the peak mode is related to lower Ta and to the complex chemical composition of the sample; the Suriñach plot follows the straight line in the continuous-heating regime (Fig. 6d) and reflects the bimodal character of the master curve in the isothermal case. In the case of the Al 90Fe7Nb3 ribbon [12], both the -Al nanocrystal formation stage (R1) and the eutectic-like crystallization of the amorphous matrix into intermetallics in a polycrystalline -Al matrix (R3) take place in the temperature range of the DSC measurements. One can simply relate the R1and R3 kinetics. Namely, the R1 peak is narrower and shifted to higher temperatures while the R3 peak is wider and shifted to lower temperatures after the appropriate isothermal preannealing (Fig. 7); the DSC signal is decaying and temperature independent for R1 stage and a it is a peak the time scale of which significantly prolongs with decreasing Ta

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Figure 6. Kinetics characterizations of the FINEMET-type ribbons. a) Continuous-heating DSC signal of: 1 – Fe80.5Nb7B12.5, 2 – Fe77.5Cu1Nb4.5B17, 3 – Fe78Cu1Nb3Si4.5B13.5 (dashed line 3’’ refers to the isothermally pre-annealed at 713 K for 200 min sample), 4 – Fe73.5Cu1Nb3.2Si7B15.3, 5 – Fe74.6Cu1Nb3.2Si9.2B12, 6 – Fe74.7Nb3.1Si12.7B9.5, 7 – Fe73.5Cu1Nb3Si13.5B9. 0 – Fe75.6Cu1Si14B9.4, being a classical metallic glass. The vertical scale for the sample Fe75.6Cu1Si14B9.4 (curve 0) is shrunk by the factor of 4. (Reprinted from [5].) b) Effect of pre-annealing on the continuousheating DSC signal of Fe73.5Cu1Nb3Si13.5B9. The pre-annealing temperature, Ta is 788 K and the pre-annealing time ta is the parameter. (Reprinted from [4].) c) Isothermal calorimetry traces at various temperatures, Ta, of Fe73.5Cu1Nb3Si13.5B9 (Ta being the parameter). The dotted line is the baseline, obtained as a second run under identical conditions after finishing the transformation. The baseline signal was shifted down to seen in the picture. (Reprinted from [4].) The heating rate in a) and b) and the heating ramp in c) was 40 K min1. d) Suriñach plots for the continuous-heating DSC transformation exotherms of Fe73.5Cu1Nb3Si13.5B9 taken at various heating rates, w+, being 20, 30, 40, 50, 60 and 80 K min1. u correspond to the theoretical data obtained for NGG kinetic equation with exponent m = 1.5 (primary results for Table I in [5])

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for R3 stage in the isothermal regime (Fig. 8); the Suriñach plots are straight lines (since D = 0.1) for R1 stage; however, they are convex curves (with a maximum at D = 0.54) for R3 stage (Fig. 9). 4. DISCUSSION

Generally, the crystallization of glasses follows the nucleation-and-growth JohnsonMehl-Avrami (JMA) kinetic law ([2] and Table I). Even though the JMA kinetics does not correspond to the experimental data ideally in the case of heterogeneous rapidly quenched metallic ribbons characterized by the cluster type medium range order, since the times of appropriate fitting of the crystallization of the Fe80B20 ribbon by Greer [13] and of Pd82Si18 ribbon by Kelton and Spaepen [14], the classical JMA kinetics has been generally accepted also for the case of crystallization of conventional amorphous metallic ribbons. The theoretically calculated shape of the continuous-heating DSC peak corresponding to the classical JMA kinetics is asymmetrical, with, independently of the parameter n, always a slower rise on the low-temperature side (see e.g. Fig. 3 in Ref. [15] or Fig. 10 for n = 3 in this paper). Besides, such asymmetry is characteristic also for all simple interface- or long-range-diffusion-controlled processes (see e.g. Fig. 12.17 in Ref. [8]). A pre-annealing of a sample increases its initially transformed fraction, which shifts the JMA peak to lower temperatures and broadens it (Fig. 10). If n > 1, the JMA-like isothermal DSC signal shows a peak for a nonzero degree of conversion, Dmin = 1 – exp [(1  n)/n] i.e. at a nonzero time, tmin = W [(n – 1)/n]1/n, which due to the Arrhenius W (T) is dependent on temperature. The spherulitic morphology of the R1 nanocrystalline phase in the metallic ribbons rules out the eventually decreasing isothermal DSC signal (n d 1) resulting from a JMA-like one- or two-dimensional growth from a fixed number of specially distributed pre-existing nuclei [2]. The nanocrystal formation is usually assumed to be the primary crystallization in initially homogeneous amorphous matrix. Accordingly, several proposals involving the crucial influence of the supposed long-range diffusion controlling the rate of the growth of the grains have been advanced to account for the specific peculiarities in both continuous-heating and isothermal kinetics, the high nanocrystal density, remarkable thermal stability and relatively low crystalline content in specific rapidly quenched metallic ribbons. Such are the rapid diffusion field impingement model of Allen et al. [16], the critical grain size effect approach of Hermann et al. [17] or the coupled flux model of Kelton [18]. Thus the Barcelona group model [19], for example, the gradual reduction of the actual growth rate accounts for the change of the reaction mechanism from the interface controlled to the long-range-diffusion controlled one in a certain moment in the case of the nanocrystallization of FINEMETs. Lately, Gupta et al. [20] in their model of modified-JMA primary crystallization in glasses took into account the isotropic homogeneous nucleation, the diffusion-controlled growth, the Gibbs-Thompson effect and the mean field soft-impingement correction during the growth and they simulated also the pre-annealing effects on the continuous heating DSC peak shift. In this case, the peak initially significantly shifts to higher temperatures when the grain radius is close to the critical nucleus radius and afterwards it falls down. Such a result

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might correlate with the experimentally observed increase in the DSC peak during the low temperature pre-annealing in our metallic ribbons assuming another reason for suppression of the grain growth.

Figure 7. DSC trace from as-quenched and heat-treated Al90Fe7Nb3 ribbons. The inset shows an expanded view of the peaks from low-temperature pre-annealed samples. Numbers in parentheses indicate annealing temperature in K and annealing time in minutes. (Reprinted from [12])

Figure 8. Isothermal calorimetry traces at various temperatures of as-quenched Al90Fe7Nb3 ribbons. Numbers in parentheses indicate annealing temperature in K and annealing time in minutes. (Results presented at RQ11, 11th Int. Conf. on Rapidly Quenched & Metastable Materials, 25-30th August 2002, Oxford, England)

Figure 9. Suriñach plots for the continuousheating DSC transformation peaks R1 and R3 from Fig. 7 and for isothermal peaks R3i from Fig. 8 of as-quenched Al90Fe7Nb3 ribbons. o , and + correspond to experimental data, (not all data points are shown), —— to the theoretical NGG kinetics for m = 0.15, — - — and — - - - — to the theoretical JMA kinetics for n = 1 and 4, respectively. (Results presented at RQ11)

An alternative to the JMA crystallization is the normal-grain-growth (NGG) process [21] reflecting the coarsening in the microcrystalline R1 phase (if the grains are less than about 10 nm). The DSC exothermal signal is different in several principal respects, in the NGG and JMA processes [15]. Thus the isothermal DSC signal is monotonically decreasing for NGG process unlike the peaked signal for transformations by JMA kinetics. The continuous-heating DSC signal from a NGG process has asymmetry that is

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reversed to the JMA kinetics one (see Figs. 10 and 11). The clearest effect is that of the pre-annealing (increasing the initial grain radius), which shifts the onset of the NGG peak to higher temperatures and leads to a narrower transformation range (Fig. 11).

Figure 10. Effect of an initial transformed fraction, x0 on the computed dx/dt vs. T curve (proportional to the continuous heating DSC signal) for a transformation with the JMA kinetics. Heating rate w+ = 10 K min1, n = 3, x0 being the parameter is proportional to the isothermal pre-annealing time. (Reprinted Fig. 13 from [13], ¤ 1982, with permission)

Figure 11. Effect of pre-annealing (increasing the initial grain radius r0) on the computed continuous-heating DSC signal from the NGG process. Heating rate w+ = 40 K min1, m = 2, r0 is the parameter. (Reprinted Fig. 4a from [15], ©1991, with permission of American Institute of Physics)

Table II. Structural characterization (nanocrystalline phase and final grain diameter) and kinetic parameters (Kissinger activation energy and the normal-grain-growth exponent) of the nanocrystal formation stage in metallic ribbons Sample Fe76Mo8Cu1B15 Fe73.5Cu1Nb3Si13.5B9 Fe87-xCu1Nb3SixB9 Fe63.5Ni10Cu1Nb3Si13.5B9 Al90Fe7Nb3 **

Product

D [nm]

E* [kJ mol1]

m

Reference

D-Fe D-Fe(Si) D-Fe(Si) D-FeNi(Si) D-Al

10

511 r 24 418 r 8** ~300-600** 429 r 5** 162 r 24

1.7 1.5 1 0.5 0.15

[present results] [4, 5] [5] [unpublished results] [12]

E* is heat-treatment dependent because of the bimodal character of R1 stage

While the conventional idea of the NGG mechanism [21], where larger grains in the already fine-crystalline sample increase their size at the expense of smaller ones, does not correlate well with the structural observations in our heterogeneous two-phase systems, its related kinetic law (see Tab. I) could rationalize all our peculiar DSC results without any correction. The desired kinetic parameters m and other characteristics of the nanocrystal formation stage R1 in herein investigated metallic ribbons are summarized in Table II. It is seen that m < 2 may well reflect the presence of a second phase

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being the amorphous matrix (Tab. I in Ref. [21]) a fact, which might also be related to the final grain radius of the R1 phase. 5. CONCLUSIONS The devitrification of nanocrystal forming rapidly quenched ribbons is a multistage process. Our studies have established that the kinetics of the nanocrystal formation stage (being the primary crystallization, R1, or the main transformation stage) is characterized by four principal peculiarities: (i) The continuous heating exothermic DSC peak has anomalous asymmetrical shape with a large high temperature part. While the minimum of the peak shifts significantly to higher temperatures, with increasing the heating rate, the shift of its onset is insignificant. (ii) Any pre-annealing at the temperatures below the main transformation shifts the peak to higher temperatures decreasing its enthalpy. (iii) The isothermal transformation exotherm is anomalous without shaping any peak. (iv) The thermograms taken at all heating rates and at each annealing temperature follow the unique Suriñach plot master curve. This curve is not convex but it is a straight line indicating the NGG exponent, m, between 2 and 0.15, which is related to the morphology of the actual nanocrystalline structure. The nanocrystal formation in metallic glasses does not follow the conventional JMA kinetics. The use of the JMA model requires essential corrections in both nucleation and growth micromechanisms, which should be specific for each sample. The NGG kinetic law, proposed for coarsening of extremely fine crystalline grains in heterogeneous thin films, could also in the case of R1 nanocrystalline formation stage in metallic ribbons rationalize all peculiar results without any correction. ACKNOWLEDGEMENTS The work was supported by the Slovak Scientific Grant Agency (contract 2/2038/22) and EC HPRN-CT-2000-00038 project. REFERENCES 1. 2. 3.

4.

5.

Weinberg, M.C. (1991) Interpretation of DTA Experiements Used for Crystal Nucleation Rate Determinations, J. Amer. Ceram. Soc. 74, 1905-1909. Christian, J.W. (1975) The Theory of Transformations in Metals and Alloys, Pergamon Press, Oxford. Miglierini, M., Degmová, J., KaĖuch, T., Švec, P., Illeková, E. and Janiþkoviþ, D. (2004) Magnetic Microstructure of Amorphous/Nanocrystalline FeMoCuB Alloys, in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, 421-436. Illeková, E., Kuhnast, F.A., Fiorani, J.M. and Naguet, Ch. (1995) Peculiarities of the Crystallization Kinetics of Fe73.5Cu1Nb3Si13.5B9 Ribbon to the Nanostructured Phase, J. NonCryst. Solids 192&193, 556-560. Illeková, E. (2002) FINEMET-type Nanocrystallization Kinetics, Thermochim. Acta 387, 47-56.

Kinetic Characterization of Nanocrystal Formation 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

19.

20. 21.

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Suriñach, S., Baró, M.D., Clavaguera-Mora, M.T. and Clavaguera, N. (1983) Kinetic Study of Isothermal and Continuous Heating Crystallization in GeSe2-GeTe-Sb2Te3 alloy glasses, J. Non-Cryst. Solids 58, 209-217. Illeková, E. (1996) The Crystallization Kinetics of Fe80Si4B16 Metallic Glass, Thermochim. Acta 280/281, 289-301. Šesták, J. (1984) Thermodynamical Properties of Solids, Academia Prague, Praha. Illeková, E., unpublished results. Miglierini, M., unpublished results. Kissinger, H.E. (1957) Reaction Kinetics in Differential Thermal Analysis, Anal. Chem. 27, 1702-1706. Illeková, E., Janiþkoviþ, D., Kubeþka, P., Švec, P. and Gachon, J.C. (2003) Thermodynamic Limitations of the Clustering in the Al90Fe7Nb3 Alloy, Mat. Sci. Eng. A. (in print). Greer, A.L. (1982) Crystallization Kinetics of Fe80B20 Glass, Acta Metall. 30, 171-192. Kelton, K.F. and Spaepen, F. (1985) A Study of the Devitrification of Pd82Si18 over a Wide Temperature Range, Acta Metall. 33, 455-464. Chen, L.C. and Spaepen, F. (1991) Analysis of Calorimetric Measurements of Grain Growth, J. Appl. Phys. 69, 679-688. Allen, D.R., Foley, J.C. and Perepezko, J.H. (1998) Nanocrystal Development During Primary Crystallization of Amorphous Alloys, Acta Mater. 46, 431-440. Hermann, H., Mattern N., Roth, S. and Uebele, P. (1997) Simulation of Crystallization Processes in Amorphous Iron-Based Alloys, Phys. Rev. B56, 13888-13897. Kelton, K.f., Croat, T.K., Gangopadhyay, A.K., Xing, L.-Q., Greer, A.L., Weyland, M., Li X. and Rajan K. (2003) Mechanisms for Nanocrystal Formation in Metallic Glasses, J. Non. Cryst. Solids 317, 71-77. Clavaguera-Mora, M.T., Clavaguera, N., Crespo, D. and Pradell, T. (2002) Crystallisation Kinetics and Microstructure Development in Metallic Systems, Progress in Materials Science 47, 559-619. Gupta, P.K., Baranta, G. and Denry, I.L., (2003) DTA Peak Shift Studies of Primary Crystallization in Glasses, J. Non. Cryst. Solids 317, 254-269. Atkinson, H.V. (1988) Theories of Normal Grain Growth in Pure Single Phase System, Acta Metall. 36, 469-491.

KINETICS OF THE NONISOTHERMAL PRIMARY CRYSTALLIZATION OF METALLIC GLASSES: NANOCRYSTAL DEVELOPMENT IN Fe85B15 AMORPHOUS ALLOY

V.I. TKATCH, S.G. RASSOLOV, and S.A. KOSTYRYA Physics and Engineering Institute of NAS of Ukraine 72, R. Luxemburg str., Donetsk, 83114, Ukraine Corresponding author: V.I. Tkatch, e-mail: [email protected]

Abstract:

The formation of the D-Fe solid solution crystallites in the melt-spun Fe85B15 metallic glass under constant rate heating has been studied by X-ray diffraction and differential scanning calorimetry (DSC). The model of nonisothermal primary crystallization kinetics based on combination of Kolmogorov kinetic crystallization equation and the relation between the diffusion-controlled crystal growth on the one hand and the temperature and heating rate on the other has been developed. From the comparison of the experimental and calculated rates of crystallization the values of the model parameters have been estimated and the conditions of the nanoscale structure formation in the alloy investigated have been predicted.

1. INTRODUCTION The formation of structures with nanoscale grain size during crystallization of metallic glasses is of a great interest from both the fundamental and the technical point of view. Fundamental studies of the mechanisms of crystal nucleation and growth as well as kinetics of transformation will to a certain degree aid in optimizing the structure and excellent physical (magnetic and mechanical) properties of nanostuctured materials attractive for practical applications [1-3]. As it has been shown by Köster et al. [4] the primary crystallization mode of metallic glasses is the most suitable process for the well controlled production of nanophase composites. In the primary crystallization the growing crystals have a composition different from that of the parent (amorphous) phase and the rate of this process is controlled by the volume diffusion. During the growth the rejection of some kinds of atoms causes the formation of a concentration gradient and results in the time91 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 91–98. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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dependent rate of growth. Despite the importance of the primary crystallization process and recent efforts, the theoretical model of this process has not yet been developed to the same quantitative level as it has been done for polymorphic and eutectic modes of crystallization [5]. Currently, the most usual way to produce nanocrystalline structures from amorphous precursors is isothermal annealing at temperatures near the crystallization temperature. However, from many points of view the nonisothermal treatment of glasses is a more convenient and effective procedure to create nanophase structures [3]. However, the rigorous analytical description of nonisothermal crystallization kinetics is more complicated in comparison with that of the isothermal process and can be made in some cases only [6, 7]. Recently, the theoretical analysis of the diffusion-controlled crystal growth in metallic glasses at continuous heating has been performed and the relatively simple analytical equation for the growth velocity has been derived [8]. Using this equation offers an opportunity for an analytical description of the nonisothermal primary crystallization of glasses. In this paper we attempt to describe the experimentally measured kinetics of the formation of the D-Fe solid solution crystals in the well-known Fe85B15 metallic glass under linear heating and to evaluate the grain sizes in the partially crystallized specimens in a wide range of heating rates. 2. EXPERIMENTAL PROCEDURE AND RESULTS Glassy ribbons (2-3 mm width and 22 Pm thick) of nominal composition of Fe85B15 were prepared by melt spinning from a glass silica nozzle onto a copper wheel, 30 cm in diameter, rotating at 2000 rpm. X-ray diffraction using Co KD radiation in a DRON-3M diffractometer was used to verify the amorphous state and to characterize the crystalline phases. The semiempirical Selyakov-Scherrer analysis was used to estimate the grain size in the partially crystallized specimens using the equation [9]:

d

0.9O / B cos Ĭ B ,

(1)

where O is the wavelength, B is the X-ray peak breadth and 4B is the Bragg angle. The thermal analysis of the melt-spun ribbons was performed in protective argon atmosphere using a Perkin-Elmer DSC7 calorimeter. The kinetics of crystallization was studied by dynamic thermal treatment at scan rates ranging from 0.083 to 0.67 K/s. Rapid heating at approximately 200 K/s was carried out by immersing of the ribbons into a salt bath held at 1123 K with the temperature controlled within r1 K. The final temperature of heating corresponding to the end of the first crystallization stage was chosen empirically. The X-ray diffraction studies confirmed the amorphous structure of the as-prepared Fe85B15 specimens without any observable differences in the diffraction patterns obtained both from contact and free surfaces of the ribbons. The DSC scans (Fig. 1) contain two separated peaks (at T1 = 685 K and T2 = 767 K for the heating rate of 0.167 K/s) which implies a two-stage mode of crystallization process well established for this amorphous alloy [10]. The X-ray diffraction of the samples heated just above

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the first stage crystallization temperatures T1 showed co-existence of a bcc crystalline phase and a residual amorphous phase. The lattice parameter of the crystalline phase was about 0.2864 r 0.002 nm, i.e. close, but somewhat lower to that of pure D-Fe. Additional Bragg peaks corresponding to the body centered tetragonal boride Fe3B were observed at diffraction patterns of the specimens heated up to T2.

Figure 1. The DSC thermogram for Fe85B15 glass measured during linear heating at 0.167 K/s

The experiments also showed that the increase in the heating rate up to 0.67 K/s only shifts these maxima along the temperature axis (to 715 and 794 K for the first and second stages, respectively). Note, that these results are in a good accordance with the data reported for this alloy and reviewed in [10], which allows us to use the data of other researchers for subsequent quantitative analyzes of D-Fe solid solution crystallization process. 3. DISCUSSION Among a variety of experimental techniques used for the investigations of the metallic glass crystallization, the most reliable results are obtained from the measurements of the transformation kinetics. A comparison of the experimental kinetic curves with the appropriate kinetic equation allows elucidating of details of the crystal nucleation and growth processes. For this reason we attempted to develop an analytical approach for the description of the primary crystallization kinetics at constant rate heating and to verify its validity by comparison with the above presented results of kinetic and structural studies for the Fe85B15 amorphous alloy. According to [10, 11], the formation of the D-Fe solid solution crystals in a hypoeutectic Fe-B amorphous alloy occurs via homogeneous nucleation and diffusionlimited growth. For a quantitative description of kinetics of this crystallization stage in the present study the approach based on Kolmogorov model [12] was proposed:

X

>

@

1  exp  S / 3 IU 3 t 4 ,

(2)

where X is the volume fraction transformed, I is the nucleation frequency, U is the rate of crystal growth, t is time. Strictly speaking, the existence of concentration gradients

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developing in diffusion layers by the atoms rejected by the nucleating and growing crystallites can modify the driving force for the crystallization and indicates that a classical analysis of transformation kinetics cannot be used for the crystallization process. Nevertheless, the analysis made by Belen’kij [13] showed that in this case the kinetic equation (2) is valid as an upper estimation of the volume fraction transformed. To modify Eq. (2) for linear heating conditions at the rate of q we used the nonisothermal form of equation for diffusion growth UD derived in Ref. [8]:

U D (T )

On / 2 >D(T )qQ / T 2 @ 1 / 2

(3)

where On is a dimensionless parameter depending on the matrix concentration at (CI) and far (CM) from the interface and that of the crystal (CP), D is the diffusivity which depends on the temperature through the time and Q is the activation energy for a diffusion jump. It is noteworthy, that if a quantity of T 2 ( qQ ) is considered as certain effective time teff for linear heating conditions equation (3) formally coincides with that for the rate of growth at constant temperature obtained by differentiating of well-known Zener equation for parabolic growth [6]. Note, that a similar parameter was obtained earlier [14] for the description of nonisothermal glass kinetic crystallization via the interface-controlled (with time-independent rates) crystal nucleation and growth. For linear heating conditions the value of On depends on CP, CI and CM as [8]:

On kn

>

(1 / 4)k n 1  1  16 / k n

1/ 2

@

(4a)

2C I  C M / C P  C I .

(4b)

A substitution of Eq. (3) into (2) and replacement of t by teff yields the nonisothermal kinetic equation of primary crystallization in the form:

^

>

@ `.

X (T ) 1  exp  S / 3 IU D3 T 2 / qQ

4

(5)

To test the applicability of this equation to the nonisothermal crystallization process the calculated kinetic curves were compared with the X(T) dependences derived from the experimental DSC scans. In the quantitative analysis several approximations were used. The frequency of homogeneous nucleation was calculated using the classical equation (see [6]) in the form given in [14]:

I (T )

§ 16S V 3Vm2 · NV D ¨ ¸, exp ¨ 3 kT'G 2 ¸ a02 © ¹

(6)

Here NV is the number of atoms per unit volume, a0 is the distance of diffusion jump (average atomic diameter), V is the specific crystal-liquid (glass) interfacial energy, Vm is the molar volume, k is the Boltzmann constant and 'G is the molar Gibbs free energy difference between the glassy and the crystalline phases. For calculations of the 'G(T) dependence the approximation proposed by Thompson and Spaepen [15] was used:

Kinetics of the Nonisothermal Primary Crystallization of Metallic Glasses

'G (T )

2'H m T (Tm  T ) , Tm (Tm  T )

95

(7)

with 'Hm and Tm being the molar enthalpy of the fusion and the melting temperature respectively. The values of parameters in equations from (3) to (7) required for calculations of D-Fe solid solution crystallization kinetics in Fe85B15 were taken from Handbooks [16, 17] and earlier published papers [11, 14, 18]. To some extent the melting temperature was taken to be equal to the liquidus temperature (1513 K) of this alloy [17], while the 'Hm was adopted to be as that for pure Fe (13280 kJ/mol) [16]. As it was shown by Köster et al. [11] the rate of growth of D-Fe crystals in amorphous hypoeutectic alloys may be described using the values of the diffusivity from Ref. [18]: D (T )

6.5 exp 26820 / T [m2/s].

(8)

The estimations of V for pure Fe (0.18 J/m2) [19] and for Fe80B20 (0.2 J/m2) [14] show that the nucleus-melt interfacial energy is a slowly varying function of the composition and the latter value of V was used in calculations. Taking On = 1.4 [11] the rate of the first stage of Fe85B15 amorphous alloy crystallization dX/dT at heating rate of 0.167 K/s was calculated and compared with the experimental DSC curve (Fig. 2). As it is seen in Fig. 2 the temperatures of the maxima of the calculated and experimental curves coincide within 1 K. However, for the heating rate of 0.67 K/s the calculated temperature of the first stage of crystallization lies at approximately 9 K below the experimental one. Note, that in this case the good agreement between the calculated and experimental kinetic data may be reached assuming a somewhat lower value of parameter (On = 0.86) as shown by the dashed line in Fig. 2. Considering that in this model the parameter On is essentially adjustable the good agreement between the calculated and experimental data implies that equations from (3) to (8) may be used for the description of the primary crystallization kinetics in metallic glasses upon linear heating and that the chosen values of the parameters involved for Fe85B15 are quite reasonable. From Eq. (4) it follows that a decrease in On with the heating rate may be caused by the increasing CP, i.e. by increasing boron concentration in the D-Fe solid solution. To verify this assumption we studied the structure of the specimen rapidly (approximately at 200 K/s) heated to a temperature somewhat below that at the beginning of second stage of Fe85B15 glass crystallization (formation of the Fe3B crystals). As it is seen in Fig. 3 the (110) reflection of D-Fe solid solution in the rapidly heated specimen shifts to large diffraction angles, which indicates that the lattice constant further decreases from that for pure Fe in accordance with the above made suggestion. Besides, the increase in the heating rate results in the appreciable line broadening (Fig. 3) indicating the decrease in the D-Fe solid solution grain sizes. The last result is in general agreement with the experimental observations [3, 20] and, at the first sight, directly follows from the analytical expression for the radius of diffusion-controlled growing crystallite dependent on temperature and constant rate heating [8]:

V.I. Tkatch et al.

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R(T , q )

>

@

On DT 2 / qQ

1/ 2

.

(9)

However, increasing the heating rate rises the temperatures of the glass crystallization and, hence, crystal growth occurs at enhanced values of the diffusion coefficient.

Figure 2. A comparison of the experimental (dots) and calculated (lines) dependencies of the crystallization rates dX/dT of D-solid solution in Fe85B15 metallic glass at heating rates of 0.167 K/s (1) and 0.67 K/s (2). The calculated curves were obtained using nonisothermal kinetic equation (5) and values of parameter On equal to 1.4 (solid lines) and 0.86 (dashed line)

Figure 3. Details of the (110) peaks of the X-ray diffractograms (Co KD-radiation) for the samples of the Fe85B15 amorphous alloy heated to temperatures of the first stage of crystallization end at the rates of 0.167 K/s (solid line) and ~ 200 K/s (dashed line)

In order to analyze the effect of the heating rate q on the size R of the primary formed crystallite, the values of R(T) as a function of T for the different heating rates following equation (9) were calculated. The calculations of R for the selected values of q were terminated at the temperatures corresponding to the end of the first stage of transformation, which were roughly estimated by extrapolating the DSC data to higher heating rates. The model calculations have shown that the grain size (2R) of D-Fe solid solution formed in binary Fe85B15 glass monotonically decreases from 320 to 48 nm as the heating rate increases from 0.167 to 104 K/s (Fig. 4). Note, that the results of the simulations agree as well with the data presented in Fig. 3 as with those reported in literature [3, 20]. In particular, Abrosimova et al. [20] showed that the sizes of D-Fe solid solution crystallites in Fe85B15 amorphous alloy crystallized at a heating rate about 104 K/s ranged between 10-30 nm. Besides, if the experimentally observed broadening of the (110) diffraction peak in the specimen heated at 200 K/s (Fig. 3) is to be ascribed to the grain size reduction then. The value of d estimated from equation (1) amounts to about 100 nm which is close to the calculated value 2R = 120 nm. Taking into account the uncertainties involved both in the experimental estimations and in the values of the model parameters (e.g. the above mentioned tendency of lowering On with increasing of heating rate) the agreement between the calculations and experimental data appears to be reasonable.

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Figure 4. Variations of the radius of D-Fe solid solution grains in metallic glass Fe85B15 vs. temperature calculated for different heating rates: 1-0.167 K/s, 2-200 K/s, 3-104 K/s

It follows that the rapid heating processing of amorphous alloys leads to an appreciable decrease in sizes of the crystals formed by the primary mode of crystallization. It implies that a number of alloys with nanocrystalline structures can be extended not only at the expense of alloying, but also by a proper choice of an annealing treatment regime.

4. CONCLUSIONS The analytical approach based on the combination of the Kolmogorov equation and the relation for the rate diffusion-limited crystal growth rate vs. temperature and the heating rate is developed for the description of the primary metallic glass crystallization kinetics at linear heating. Good agreement of the calculated dependencies of the crystallization rates on temperature with the experimental DSC thermograms for the Fe85B15 amorphous alloy is evidence for the validity of the proposed model. The results of model calculations have shown that the size of D-Fe solid solution crystals formed during the primary crystallization monotonically decreases as the heating rate increases and at heating with the rates above 103 K/s the nanocrystalline structure in the alloy investigated must be formed, which is in accordance with the experimental data. ACKNOWLEDGMENTS The authors wish to thank Prof. A. Grishin (RTI, Stockholm) for the provision of laboratory facilities and Dr. V. Kameneva for assistance with the X-ray analysis. REFERENCES 1. 2.

Inoue, A. (1998) Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Progress in Materials Science 43, 365-520. McHenry, M.E., Willard, M.A., Laughlin, D.E. (1999) Amorphous and nanocrystalline materials for applications as soft magnets, Progress in Materials Science 44, 291-433.

98 3. 4. 5. 6. 7.

8. 9. 10.

11. 12. 13. 14.

15. 16. 17.

18.

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V.I. Tkatch et al. Kulik, T. (2001) Nanocrystallization of metallic glasses, J. Non-Crystalline Solids 287, 145-161. Köster, U., Meinhardt, J., Alves, H. (1995) Formation of nanocrystalline materials by crystallization of metallic glasses, Material Science Forum 179-181, 533-538. Clavaguera-Mora, M.T. (1998) The use of metastable diagrams in primary crystallization kinetics study, Thermochimica Acta 314, 281-289. Christian, J.W. (1975) The Theory of Transformations in Metals and Alloys, Pergamon, New York. Ruitenberg, G., Woldt, E., Petford-Long, A.K. (2001) Comparing the Johnson-MehlAvrami-Kolmogorov equations for isothermal and linear heating conditions, Thermochimica Acta 378, 97-105. Rassolov, S.G., Tkatch, V.I., Selyakova, N.I. (2001) Diffusion-limited growth in metallic glasses under continuous heating, J. Applied Physics 92, 6340-6342. Umanskij, Ya.S., Skakov, Yu.A., Ivanov, A.N., Rastorguev, L.N. (1982) Crystallography, X-Ray Analysis and Electron Microscopy, Metallurgija, Moscow (in Russian). Köster, U., Herold, U. (1981) Crystallization of metallic glasses, in: H.-J. Guntherodt and H. Bek (eds.), Glassy Metals 1, Topics in Applied Physics, New York, Springer-Verlag, Berlin Heidelberg, pp. 325-371. Köster, U., Herold, U., Hillerbrand, H.-G., Denis, J. (1980) Diffusion in some iron-based metallic glasses, J. Material Science 15, 2125-2128. Kolmogorov, A.N. (1937) To statistical theory of crystallization of metals, Izvestiya Akademii Nauk SSSR Seriya Matematika 3, 355-360 (in Russian). Belen'kij, V.Z. (1980) Geometry-probabilistic models of crystallization, Nauka, Moscow (in Russian). Tkatch, V.I., Limanovskii, A.I., Kameneva, V.Yu. (1997) Studies of crystallization kinetics of Fe40Ni40P14B6 and Fe80B20 metallic glasses under non-isothermal conditions, J. Material Science 32, 5669-5677. Thompson, C.V., Spaepen, F. (1979) On the approximation of the free energy change on crystallization, Acta Metallurgica 22, 1855-1859. Handbook, (1976) Properties of Elements, Metallurgija, Moscow (in Russian). Kubashewski, O. (1982) Iron-binary alloy systems, Springer, Berlin. Borisov, V.T., Golikov, I.N., Scherbedinskij, G.V. (1964) About relation of the diffusion coefficients with the grain boundary energy, Fizika Metallov i Metallovedenije 14, 881-885 (in Russian). Kelton, K.F. (1991) Crystal nucleation in liquids and glasses, in: H. Ehrenreich and D Turnbull (eds.), Advances in Research and Application, Solid State Physics, Academic Press, New York, 45, pp. 75-177. Abrosimova, G.Ye., Aronin, A.S., Stelmuh, V.A. (1991) Crystallization of Fe85B15 amor phous alloy above the glass transition temperature, Fizika Tverdogo Tela 33, 3570-3576 (in Russian).

STRUCTURAL RELAXATION AND NANOCRYSTALLIZATION IN THE INITIAL STAGE OF AMORPHOUS ALLOYS STUDIED BY CURIE TEMPERATURE MEASUREMENTS S. D. KALOSHKINa, B. V. JALNINa, E. V. KAEVITSERa, and J. XUb a

Moscow State Institute of Steel and Alloys, Leninsky prosp., 4, 119049 Moscow, Russia Shenyang National Laboratory for Materials Sciences, Institute of Metal Research Chinese Academy of Science, Shenyang, 110016, China

b

Corresponding author: S. D. Kaloshkin, e-mail: [email protected]

Abstract:

Structural relaxation and the beginning of crystallization of amorphous iron-based alloys were studied by Curie temperature (TC) measurements. Apparent values of activation energy of relaxation were evaluated from the TC time-temperature dependencies. It was observed that the average value of activation energy increases with the relaxation process. It was shown that the measurements of TC evolution allow distinguishing the relaxation and crystallization process, which could have a practical benefit of determination of the optimal thermal treatment to achieve the best soft magnetic properties. TC measurements may help to detect the initial stage of amorphous phase crystallization. TC data correlate with structural alterations which are accompanied by the redistribution of elements in amorphous phase during annealing.

1. INTRODUCTION The mechanism of the formation of amorphous-crystalline and nanocrystalline structures by crystallization from the amorphous state depends on the structural relaxation during pre-crystallization annealing. Thermal relaxation may result in both: relative stabilization of amorphous structure or, on the contrary, chemical decomposition of the amorphous phase, formation of segregations – precursors of future crystalline precipitations. That is why it is very important to develop methods which allow studying the structural changes during relaxation, when the crystallization itself has not yet started. One of the most popular methods often used for structural relaxation study is differential scanning calorimetry (DSC). It allows recording of exothermal and endothermal effects which accompany relaxation or measuring the characteristic points of heat capacity, such as the Curie point. The results of investigation of relaxation processes in Fe-Si-B based amorphous alloys below the crystallization temperature are 99 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 99–110. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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presented here. An exothermic effect is considered to be the result of surface oxidation of amorphous samples. Besides that, for alloys based on two or more transition metals we observed an endothermic effect, which could be attributed to the so-called “crossover” effect [1]. However, we do not discuss these results here. The main attention is paid to TC measuring by DSC in order to control the structural state of the amorphous phase and chemical segregations. The Curie temperature (TC) is very sensitive to structural changes in amorphous ferromagnetic phases, which accompany relaxation and crystallization processes during heating. So measurements of TC may give much information about kinetic parameters of these processes. In combination with a structural investigation it becomes a powerful method of kinetic analysis of all kinds of transformations in alloys with amorphous or partially amorphous structures. It is interesting that DSC provides one of the most convenient and fast methods of TC determination, often easier than the measurements of thermomagnetic characteristics, because of a very precise control of temperature in the standard DSC method. During the structural relaxation, the variation of TC can amount to tens of degrees, while the accuracy of TC measuring is not worse than r0.5 K. 2. EXOTHERMAL EFFECT In Figure 1 the calorimetric curves recorded by scanning calorimeter DSM-2M (“SKB BP”, Russia) for amorphous alloys of Fe-TM-B systems are given. For all compositions, the first curve corresponds to the heating of an initial alloy up to the temperature slightly lower than the starting point of crystallization, and the second one – to repeated heating of the same sample in the calorimeter.

Figure 1. Pre-crystallization DSC curves for Fe-TM-B amorphous alloys. 1 and 2 – first and second heatings correspondingly

For Fe80Mn5B15 alloy on the first and on the repeated heating curves the heat capacity peaks, related to the Curie temperature of amorphous phase, are visible. Structural relaxation during the first heating results in an increase in TC. The effective values of activation energy for a number of iron-based amorphous alloys, derived by Kissinger's method from the shift of the maximum of the exothermic effect by variation of heating rate [2], lay in the interval of 60-100 kJ/mol. That is much less than the values of crystallization activation energy for corresponding alloys. Many researchers have observed the broad exothermic peak in low-temperature interval during heating of amorphous alloys [3-6]. They usually associated these effects

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with processes of structural relaxation in the amorphous phase. Only a few investigators explained this effect as a reaction of surface oxidation of amorphous samples [5, 6]. Our experiments confirm the connection of the exothermic effects with oxidation processes. Figure 2 shows experiments with the consecutive heating of sample of Fe78Si9B13 amorphous ribbon below the temperature of crystallization (numbers of heating runs are marked by figures). After the first and the second heating the exothermic effect disappeared. Third heating was made for the same sample after the removal of the surface layers by etching the sample in diluted nitric acid. Calorimetric curve 3 shows the presence of a broad exothermic effect again.

Figure 2. Pre-crystallization DSC curves for Fe78Si9B13 amorphous alloy in air. The sequences of heatings are marked by figures

Figure 3. Pre-crystallization DSC curves for Fe78Si9B13 amorphous alloy in Ar (1, 2) and in air (3, 4). The sequence of heatings is marked by figures

It has been noticed that the formation of an oxide layer on the surface of amorphous ribbon embrittle it. However, after chemical etching the oxide film from the ribbon surface the sample becomes more ductile again. Another DSC experiment was carried out for the same alloy but in different atmospheres (Fig. 3). A small exothermic effect could be observed by comparing the calorimetric curves of the first and the second heating of the initial sample in argon (1, 2). After that the sample was heated up in air. An exothermic effect, very similar to that obtained for the first heating in air, appeared again (3, 4). It is worth mentioning, that for the experiment we used argon of high purity, but certain oxidation did nevertheless occur. This means, that the surface of amorphous alloy is very active to the oxidation consequently special methods for additional argon cleaning should be applied. Probably the heat effect from the process of nonreversible structural relaxation of amorphous alloys at heating also contributes to this exothermic process, but the main part of heat emission is caused by an interaction of the alloy surface with oxygen. Surface investigations of amorphous alloys by the method of electron spectroscopy for chemical analysis confirmed the oxidation of alloys. These experiments have shown that the thickness of oxidized layers on the surface of as-quenched amorphous ribbon is usually about 30 Å [6]. After chemical etching the thickness of this oxidized layer is about 10 Å, while heating of the alloy to 700 K resulted in an increase in the oxidized layer up to 60 Å.

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3. KINETICS OF STRUCTURAL RELAXATION STUDIED BY TC MEASUREMENTS It is interesting that magnetic transformation in TC could not be detected by scanning calorimetry in case of zero magnetostriction of amorphous phase. For instance, there was no visible peak of heat capacity corresponding to Curie temperature at heating in a calorimeter of Co70Fe5Si10B15 amorphous alloy, which is known as zero magnetostrictive alloy. Of course, the disordering of magnetization vectors in the vicinity of the Curie point should be probably accompanied by heat capacity increase for all types of alloys. However, such peak seems to be too small for zero magnetostrictive alloys to detect them by standard DSC method. We have not heard about other investigations where DSC method was used for TC determination for similar alloys. It seems that the usually measured maximum of the heat capacity in the TC point reflects the work of the magnetic forces on the deformation of the material due to magnetostriction. That is why the peak of heat capacity on a calorimetric curve becomes higher in the case of higher value of magnetostriction. According to published data TC may change in different ways: to increase and then decrease through a curve with a maximum [7], to increase in two stages [8], cyclically – at a cyclic change of temperature [9] etc. It specifies both: the compositional and topological evolution of local atomic structure at the structural relaxation, and the tendency of amorphous structure to establish the “equilibrium” short-range order at each temperature. The reversible effects were found in alloys consisting of several metallic components. For all amorphous alloys studied in the present investigation, TC was higher after annealing than for the initial state. The experimental procedure was the following: an initial amorphous alloy was heated in a calorimeter at a rate 32 K/min up to the definite temperature and annealed during a certain time. After that a sample was cooled down and then again heated up to the same or new temperature for the next annealing. The Curie point was measured as a peak on the calorimetric curve during every heating. Fig. 4a-c shows the results of these measurements. The same trend was observed for all isothermal curves: at each temperature of annealing the TC quickly increases at first, then slows down and gradually achieves the saturation value. Alloying of Fe-Si-B amorphous phase by Cr and Mo results in a decrease of the Curie temperature, only 3 at.% Olead to decrease of the TC on 128 K. The Curie temperature strongly depends on short-range order composition in amorphous structure. We can assume, that the Curie temperature increases with the number of neighbouring Fe-Fe atoms in an amorphous structure and with the reduction of distances between them. The topological ordering of an amorphous structure during annealing leads to the decrease of the average distances between iron atoms, and subsequently results in increase in TC. Further annealing stimulates the processes of compositional short-range ordering with an increase in the numbers of Fe-Fe atomic pairs, that also causes the increase of TC value. The kinetics of the relaxation process was studied in the frames of two different approximations: using the single effective activation energy approach and using the distribution of activation energy values. For the first case the apparent value of

Structural Relaxation and Nanocrystalization of Amorphous Alloys

Figure 4. Curie point of Fe-Si-B based alloys depending on time for isothermal annealing at different temperatures

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Figure 5. Activation energy distribution derived from TC data for Fe-Si-B based amorphous alloys

the relaxation activation energy E can be defined from the TC time-temperature dependencies using one of the following equations ln (dTc/d )Tc = const = ln (dTc/d )

= const

ln ( )Tc = const =

=

E/RT + const1

(1)

E/RTann + const2

(2)

E/RTann + const3

(3)

The calculations of the activation energy under Eqs. (1-3) show a reasonable coincidence. The following results were obtained: Alloy Fe78Si9B13 Fe75Mo3Si9B13 Fe75Cr5Si5B15

[kJ/mol] 90 120 150

Basing on the same experimental data, the relaxation process was described using the model of a spectrum of activation energy values [11, 12]. The amorphous state was considered to be a multi-level system corresponding to a continuous distribution of all possible atomic configurations. These configurations transfer one into another during structural relaxation. Each configuration has its definite energy and the spectrum of activation energies corresponds to the given configurational spectrum.

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The multi-level system can be supposed to be an ensemble of two-level systems with the Arrhenius’ relaxation time W = W0 exp (E/RT) for each two-level system, respectively. So it is possible to consider the macroscopic change of the Curie temperature during annealing as a result of the Curie temperature changes in the microscopic elementary volumes ɌCel. The degree [W (t) of the relaxation for each elementary volume is equal to

[Wel ( t )

TCel ( t )  TCel ( 0) TCel ( 0)  TCel (D )

1  exp(  t / W )

(4)

where ɌCel(0), ɌCel(t) and ɌCel(D) accordingly: initial, at the moment t and ultimate value of ɌCel. The macroscopic value of ɌC(t) corresponds to the average value of relaxation degree [ av (t): D

[ av (t )

³

D

[W (t ) ˜ P(W )dW

1

D

³ exp(t / W ) ˜ P(W )dW

(5)

D

or: E max

[ av (t ) 1 

³ exp[t / W

0

exp(  E / RT ] ˜ P ( E )dE

(6)

0

where: P(t) and P(E) – distribution function of probability density of times and activation energy of relaxation, respectively. The problem of the definition of relaxation times spectrum relates to the method of reconstruction of subintegral function in accordance with the experimental data. It is possible to apply for this purpose a method of representation of an integral curve as a linear superposition of continuously distributed elementary functions differing by some parameter, for example by the relaxation time. As many physical properties change during the structural relaxation by the logarithmic law it is convenient to use ln(t) as a parameter. Then: D

³

[ av (t ) 1  P (ln W ) ˜ exp( t / W )d (ln W )

(7)

D

The density function of probabilities P(ln t) can be expressed as a superposition of the orthogonal functions [12]: N

P (ln W )

¦ a [cos(i ˜ S ˜ ln W / ln W i

max

)  ( 1) i ] .

(8)

i 1

The calculation consists in the minimization of root-mean-square deviations of experimental data from the calculated function [ av (t). If we accept that E = kT ln (W/W0) and P(E) = kT P(lnW), it is possible to proceed to the activation energy spectra of relaxation (Fig. 5a-c). These spectra are unsymmetrical. The portion of relaxation processes with high values of activation energy increases with

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an increase in relaxation temperature. The spectra tend to higher values of activation energy with annealing temperature increase that specifies involving the processes with high activation energies into structural relaxation. Therefore, the long-term low-temperature annealing is not equivalent to the short-term annealing at high temperature – the more significant structural alterations occur in the amorphous phase at higher temperature. For the selection of annealing regimes of amorphous materials in order to achieve specified level of properties (especially magnetic) it is important to control not only the degree of structural relaxation, but also the way in which this degree was achieved. 4. CONTROL OF RELAXATION IN MAGNETIC AMORPHOUS ALLOYS USING TC DATA The data obtained in the examination of relaxation processes in magnetic amorphous alloy Fe81Si4B13C2 using TC measurement are presented below. Figure 6 shows the trends of TC with increase of annealing time at various temperatures. Conditionally it is possible to divide the change of TC into two stages: at the first one there is a process of TC increase with retardation; at the second stage – an increase of TC is again accelerated. A fast increase in TC at the second stage is accompanied by the degradation of the heat capacity peak in the Curie point, so it can be related to the occurrence of segregations with close, but different TC values. The activation energy calculated from the data of the first stage of TC change (section I of Fig. 6) has relatively low value 100 r 15 kJ/mol, which is typical of the processes of amorphous phase relaxation. Correspondingly, the activation energy value on the second stage is found to be 290 r 25 kJ/mol. This value is in a good agreement with the crystallization activation energy determined for this alloy by Kissinger's method from DSC data (260 r 20 kJ/mol). This means that the section I in Fig. 6 corresponds to the structural relaxation of an amorphous phase, while section II is the region where crystallization process starts. It is interesting that X-ray diffraction detects the presence of crystalline phase only at later stages of crystallization, so that the Curie temperature is a very sensitive parameter for detecting the most initial moments of crystallization. In practice it is very difficult to maintain all the parameters of amorphous ribbon production absolutely identical. There are always some deviations which result in deviations of properties for different production pieces. Therefore, an identical annealing of these series of amorphous alloy cannot give an identical level of magnetic properties and there is an optimal heat treatment for every piece resulting in the maximal level of properties. The aim of this part of the research was to compare the kinetic parameters of relaxation and crystallization of amorphous alloys obtained from TC measurements with specific magnetic losses after heat treatment. The specific losses depending on the temperature of isochronous annealing for the different series of the Fe81Si4B13C2 alloy are presented in Fig. 7. The ribbons with the widest variation of properties were taken for this experiment. The minimal losses for each ribbon were achieved at different temperatures. The correlation between the optimal temperature of annealing related to the minimal losses, and the Curie temperature

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Figure 6. Dependencies of Curie point of Fe81Si4B13C2 amorphous alloy for isothermal (a) and isochronal (b) annealings

S.D. Kaloshkin et al.

Figure 7. Specific loss in Fe81Si4B13C2 amorphous ribbons depending on temperature for isochronal annealings

Figure 8. Correlation between Curie temperature and optimal temperature of annealing of Fe81Si4B13C2 alloy (Fig. 7)

of alloy (Fig. 8) was found. So, from TC measurements it is possible to pick an optimal temperature of heat treatment corresponding to minimal level of magnetization losses. There are two main factors, which mostly affect the magnetization losses in amorphous alloys. The first one is connected with the level of strains in amorphous structure. These are the strains, which appear during the quenching process, as well as during the deformation at winding of toroidal magnetic core. The magnetic losses decrease with reduction of strains and depend on a degree of completeness of relaxation processes in an amorphous structure during annealing. The second factor is associated with the

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formation of segregations and start of crystallization of amorphous structure, which result in a sharp increase of magnetization losses. Hence, the problem of optimizing the annealing is that the relaxation in amorphous phase should be completed as much as possible, while the process of crystallization has not begun yet. The dashed line between (I) and (II) regions in Fig. 6a corresponds to this transitive state of the alloy. Therefore, using the Curie temperature measurements it is possible to determine the optimal regime of heat treatment without examinating magnetization losses. This method does not allow to determine the heat treatment parameters knowing only one TC magnitude for the as-quenched amorphous alloy, it is necessary to measure the time dependence of TC. However it allows detecting the initial moment of crystallization process at chosen temperature. 5. TC OF FINEMET-TYPE AMORPHOUS ALLOYS: RELAXATION AND NANOCRYSTALLIZATION Annealing of FINEMET-type alloys at temperatures below the crystallization point results in an increase of TC [13-15]. The Curie temperature change is caused as by structural relaxation as by segregations and nanosized clusters in amorphous phase, so the measurement of the Curie point is an effective method for studying of these processes. Due to a 3 at.% Nb addition, the magnetostriction of amorphous phase of FINEMET-type alloys is lower than of above studied iron-based alloys. That is why the heat capacity peak in the Curie point is not so visible as for those alloys. Anyway it can also be detected by DSC method with comparatively high accuracy. Figure 9 shows the allowable correspondence of TC measured by DSC and magnetization data obtained for the Fe73.5Nb3Cu1Si13.5B9 amorphous alloy. In general, TC changes with time and temperature of annealing in a similar way as for other above described iron-based alloys, it increases with both these parameters. The dependencies of TC on time are shown in Fig. 10. These data could not be linearized in coordinates TC = f (ln t), as it sometimes occurs (for example in [15]). The very fast initial increase slows down when annealing continues. The apparent activation energy of relaxation was determined from these data using the Eq. (2). For the initial moment of relaxation process this value is found to be 40 kJ/mol. It is in a good agreement with the value 42 kJ/mole, determined for the FINEMET glass-coated microwires using the same method [16]. However, the data corresponded to the moment W = 5 min the apparent activation energy is found to be 75 kJ/mol. This means that at the earliest stage of relaxation, the processes with low activation energies prevail while at later stages the processes with higher activation energies are involved into the relaxation. The kinetics of the relaxation cannot be described by a few definite parameters as reflects complicated chain of structural transformations in multilevel system. Comparing the curves for 723 and 733 K in Fig. 10 one can almost see the coincidence up to 15 minutes of annealing, but then the curve for 733 K deviates to higher TC values. Such a behaviour is similar to that observed above for other Fe-Si-B based alloys (Fig. 4). According to X-ray diffraction data, of D-Fe phase has appeared in the samples annealed at 733 K for more than 20 minutes – changes of the Curie temperature allow to detect the earliest stage of nanocrystallization.

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Figure 9. Curie temperature determined from calorimetric (a) and magnetization data (b)

S.D. Kaloshkin et al.

Figure 10. Curie point of Fe73.5Nb3Cu1Si13.5B9 alloy depending on time for isothermal annealing at different temperatures

The splitting of the heat capacity peak corresponding to Curie temperature into two peaks was observed at annealing of FINEMET amorphous alloy below the crystallization temperature [16, 17]. However, the separation of the amorphous phase into two phases with different Curie temperatures was not confirmed by magnetic methods [17]. It is very difficult to detect such fine effect by magnetization measurements and DSC can be useful as a more sensitive method. The Curie temperature is also sensitive to the redistribution of elements between amorphous and crystalline phases during crystallization. Unfortunately for partially (more than 20%) crystallized FINEMET-type alloy, due to the reduction of magnetostriction of enriched by niobium amorphous phase, it is impossible to measure its TC by DSC. The heat capacity peak corresponding to TC becomes negligible. However, TC of the amorphous phase can be determined by magnetic methods [18]. The dependency of TC on annealing duration at various temperatures is shown in Fig. 11. For some annealing temperatures the Curie point demonstrates a nonmonotonous evolution with the annealing time, passing through the maximum. It is known that the addition of Nb to iron based amorphous alloys results in the decrease in the Curie point by 25 K/at.% [19], while an addition of Si and/or B results in an increase in Curie point by 14 K/at.% [20]. The presence of copper practically does not practically affect TC. Thus the increase in the Curie point of amorphous phase with increasing of D-phase volume fraction is caused by its enriching with boron. The process of enriching of amorphous phase by niobium proceeds much slower and results in a gradual decrease in the Curie point at later stages of annealing. This process continues after the D-phase precipitation. There is no niobium in the crystalline phase as the lattice parameter of D-phase at all stages of crystallization remains practically constant (0.5688 nm). Apparently, niobium concentrates near the phase boundaries and then slowly diffuses into the surrounding amorphous phase, which causes the decrease in the Curie temperature of the amorphous matrix. The niobium concentration on the phase boundaries may be very significant; it

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Figure 11. Curie temperature of the remained amorphous phase during nanocrystals formation in Fe73.5Nb3Cu1Si13.5B9 alloy

stabilizes the remaining amorphous phase. Only at rather high temperatures (960 K or above), when the diffusibility of atoms strongly increases, the transformation of the remaining amorphous phase into a mixture of borides becomes possible. So TC measurements allow studying of elements of redistribution kinetics during the crystallization process. The alloying of the amorphous phase only by copper does not result in a formation of a nanocrystalline structure by crystallization. The basic role in the nanostructure formation belongs to niobium, which is not able to dissolve in D-phase and has very low mobility. Thus Nb atoms form protective layers around D-phase crystals, which do not only slow down their further growing, but even stop it. The 4-d and 5-d transition elements, such as Nb, Zr, Mo, Hf, Ta, being added to amorphous alloys stimulate the nanostructures formation. The role of boron consists in the stabilization of the amorphous, and then of amorphous-crystalline structure, and silicon influences on the magnetostriction and provides high level of magnetic properties. 6. CONCLUSIONS The measurement of the Curie temperature of the ferromagnetic amorphous alloys is a very powerful method of compositional and structural state control of the ferromagnetic amorphous phase. The DSC is especially convenient for such an investigation because it gives very fast and precise method of measuring TC as a heat capacity peak. However, it is possible to use DSC for this purpose only for alloys with non-zero magnetostriction. It is possible to study kinetics of relaxation, distinguish the processes of relaxation and crystallization. The Curie temperature is a very sensitive parameter allowing determination of optimal heat treatment regimes in order to achieve the maximal level of functional properties. For FINEMET-type alloys the Curie temperature is sensitive also to the decomposition of amorphous phase and redistribution of components between amorphous phase and growing nanocrystals. ACKNOWLEDGEMENTS This work was supported by RFBR (02-02-39028-GFEN_a).

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Greer, A.L., Leake, J.A., (1979) Structural relaxation and crossover effect, J. Non-Cryst Sol. 33, 291-297. Kissinger, H.E., (1957) Reaction kinetics in differential thermal analysis, Anal. Chem. 29, 1702-1706. Battezzati, L., Riontino, G., Baricco, M., Lucci, A., Marino, F., (1984) A DSC study of structural relaxation in metallic glasses prepared with different quenching rates, J. NonCryst. Solids 61-62, 1021-1026. Chen, H.S., Inoue, A., Masumoto, T., (1985) Two-stage enthalpy relaxation behaviour of (Fe0,5Ni0,5)83P17 and (Fe0,5Ni0,5)83B17 amorphous alloys upon annealing, J. Mater. Science 20, 2417-2438. Calca, A., Radlinski, A.P., (1987) DSC study of surface induced crystallization in Pd-Si metallic glasses, Acta Met. 35, 1823-1829. Tomilin, I.A., Kaloshkin, S.D., Hoang, P.D., (1990) The investigation of processes before crystallization in amorphous alloys by DSC (oxidation or relaxation), Key Engineering Materials 40-41, 203-208. Greer, A.L., Gibbs, M.P.J., Leake, J.A., Evetts, J.E., (1980) Structural relaxation of transition metall-metalloid glasses, J. Non-Cryst. Solids 38-39, 379-384. Walter, G.L., Luborsky, F.E., (1978) The ductile-brittle transition of some amorphous alloys, Mater. Sci. Eng. 33, 91-94. Katayama, T., Nishihara, Y., Miyazaki, M., Ogawa, S., (1983) Structural relaxation in (Fe-Cr) based glasses, J. Magn. Magn. Mater. 31-32, 1561-1562. Gibbs, M.R.G., Evetts, J.E., Leak, J.A., (1983) Activation energy spectra and relaxation in amorphous materials, J. Mater. Sci. 18, 278-288. Van den Beukel, A., (1985) Structural relaxation in amorphous alloy Fe40Ni40B20, Rapidly Solidified Materials. Proc. Int. Conf. (San Diego),193-203. Window, B., (1971) Hyperfine fields distributions from Mössbauer spectra. J. Phys. E: Scientific Instruments 4, 401-402. Gorria, P., Garitaonandia, J.S., Barandiaran, J.M., (1996) Structural and magnetic changes in FeNbCuSiB amorphous alloys during the crystallization process. J. Phys.: Condens. Matter 8, 5925-5939. Lovas, A., Kiss, L.F., Balogh. I., (2000) Saturation magnetization and amorphous Curie point changes during the early stage of amorphous-nanocrystalline transformation of a FINEMET-type alloy, J. Magn. Magn. Mater. 215-216, 463-465. Conde, C.F., Miranda, H., Conde, A., (1991) Annealing effect on the Curie temperature of a Fe77Cr2B16Si5 glass, Mater. Lett. 10, 501-503. Zhukova, V., Kaloshkin, S., Zhukov, A., Gonzalez, J., (2002) DSC studies of finemet-type glass-coated microwires, J. Magn. Magn. Mater. 249, 108-112. Kaevitser, E.V., Kaloshkin, S.D., Jalnin, B.V., Tcherdyntsev, V.V., Baldokhin, Yu.V., (2003) Structure transformation and elements redistribution at heating of Fe73.5Nb3Cu1Si13.5B9 amorphous alloy, J. Magn. Magn. Mater. 258-259, 539-542. Kaloshkin, S.D., Tomilin, I.A., Jalnin, B.V., Kekalo, I.B., Shelekhov, E.V., (1995) Influence of amorphous alloys composition on kinetics of crystallization with the nanocrystalline structure formation, Mater. Sci. Forum 179-181, 557-562. Antonione, C., Batezatti, L., Cocco, G., Marino, F., (1984) Thermochemical and structural investigation of crystallization in Fe-B and Fe-Si-B metallic glasses, Z. Metallk. 75, 714-718. Luborsky, Fred, E., Becker, Joseph, J.; Walter, John, L.; Liebermann, Howard, H., (1979) Formation and magnetic properties of Fe-B-Si amorphous alloys. IEEE Trans. Magn., MAG-15, 1146-1149.

NANOCRYSTALLIZATION PROCESS OF THE HITPERM Fe-Co-Nb-B ALLOYS Influence of Cu and Co alloying C.F. CONDE, J.S. BLÁZQUEZ, and A. CONDE Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales CSIC-Universidad de Sevilla, Apartado 1065, 41080-Sevilla, Spain Corressponding author: C.F. Conde, e-mail: [email protected] Abstract:

Crystallization behaviour, nanocrystallization kinetics and nanostructure characteristics of Nb containing HITPERM alloys are reviewed. The influence of the Fe/Co ratio in the alloy and the role of Cu as nucleant agent and refiner of the nanostructure are analysed. Clustering of Cu in the pre-crystallization stages is evidenced in these Nb-containing alloys from atom probe results. No difference in Co concentration between nanocrystals and the remaining amorphous phase has been found. The crystalline volume fraction at the end of the nanocrystallization process decreases for high Co content alloys and the mean size of nanocrystals decreases as the Co content increases for the Cu-free alloys whereas it is independent of Co content for Cu-containing alloys. A recrystallization process involving the bcc-Fe,Co phase occurs at the second crystallization stage and (FeCo)23B6-type crystals form. An addition of Mn affects mainly the Curie temperature of the amorphous phase and Mn is rejected from nanocrystals and partitioned into amorphous residual phase.

1. INTRODUCTION Nanocrystalline alloys obtained in primary crystallization of melt-spun amorphous of specific families of Fe(Co),B based alloys exhibit excellent soft magnetic properties owing to their peculiar two-phase microstructure of randomly oriented nanosized ferromagnetic crystals of a bcc-Fe(Co),X phase embedded in a ferromagnetic amorphous matrix with a lower Curie temperature. A refinement of crystal grain size below 20 nm is necessary to obtain low coercivity in nanocrystalline soft magnetic alloys. According to the Herzer´s random anisotropy model [1] when the grain size is much lower than the exchange length, the crystalline anisotropy is averaged out and soft magnetic behaviour occurs. Nanocrystals are exchanged coupled via the ferromagnetic intergranular amorphous phase. Consequently the Curie temperature of the amorphous matrix is an important parameter in the temperature dependence of the magnetic behaviour: above 111 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 111–121. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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that Curie temperature nanocrystalline grains are decoupled and the soft magnetic properties of the material deteriorate. Several nanostructured materials of similar microstructure have been developed since the first report in 1988 of FeSiBCuNb alloys [2], known as FINEMET, that show the highest permeability resulting from the Si content of the bcc phase that reduces magnetostriction [3]. The FeMB(Cu), (M = Zr, Nb, Hf) alloys [4] named NANOPERM, with a higher iron content, exhibit higher saturation magnetization and lower permeability. More recently, to increase the saturation magnetization and the Curie temperature, Co was partially substituted by Fe in (Fe,Co)MBCu, (M = Zr, Nb, Hf) nanocrystalline alloys, called HITPERM [5], with significantly improved high temperature magnetic properties with respect to the former two alloy families [5, 6]. Nanocrystalline microstructure in these Fe,B-based alloys can be easily obtained by partial crystallization of an amorphous precursor. Devitrification process consists of two well separated transformation stages and primary crystallization yields nanocrystalline microstructures when copious nucleation and hindered growth of the crystals formed occur at the same time. Cu addition is revealed as necessary to achieve nanocrystalline microstructure in FINEMET alloys [1, 7]: Cu atoms form clusters having near fcc symmetry, at pre-crystallization stages [8, 10] that serve as heterogeneous nucleation sites for the bcc-Fe,Si primary crystals [11-12]. In NANOPERM alloys the nanocrystalline microstructure can be obtained in Cu-free alloys but Cu addition produces a refinement of the microstructure [4]. Atom probe results have confirmed the formation of Cu clusters prior to the crystallization in FeZrB alloys [13]. The refractory metal (Nb, Zr, Hf) limits the growth of the bcc grains due to its partition to the grain boundaries resulting from its very low solubility in the emerging crystallites and its low diffusivity [3, 14]. For HITPERM alloys, a different role of Cu in the nanocrystallization process of Zr and Nb containing alloys has been reported. Whereas for Nb containing HITPERM alloys Cu addition produces a refinement of the microstructure [15, 16] in a similar way as observed for NANOPERM alloys, for Zr containing alloys Cu shows no significant role in the grain size of the nanocrystalline phase, which has been attributed to the absence of Cu-clustering in these alloys [17]. In fact, for the HITPERM alloy of composition Fe44Co44Zr7B4Cu1, Cu clustering is not observed and Cu atoms are homogeneously distributed in the amorphous matrix [18] whereas for the Nb containing alloy Fe39Co39Nb6B15Cu1 atom probe results clearly reveal the presence of Cu-clusters [19]. For FINEMET alloys with partial substitution of Co by Fe, atom probe results show that the driving force for Cu-clustering decreases as Co content increases [17, 20]. These results should indicate that in Co-containing alloys Cu clustering is a complex phenomenon affected by different parameters as the Co content, the early transition metals added and the mixing enthalpies of the alloy components. As the soft magnetic properties of these nanocrystalline alloys are strongly correlated with microstructural features (grain size, crystalline volume fraction, thickness and chemical composition of the intergranular amorphous phase) good knowledge of the nanocrystallization mechanisms is the key for a fine control of the optimal final microstructure.

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The present work attempts to review results on crystallization behaviour, nanocrystallization kinetics and nanostructure features of Nb containing HITPERM alloys and the influence of alloying. Two types of compositional changes are analysed: alloys with Fe/Co ratio values higher and lower than the typical 50:50 were studied to explore the role of Co content and Cu-added and Cu-free alloys are compared in order to elucidate the significance of the role of Cu as nucleant agent and grain refiner in these Nb containing HITPERM alloys. Also, the effects of the Mn addition are contemplated. 2. CRYSTALLIZATION BEHAVIOUR Devitrification of Nb-containing HITPERM alloys [15, 21-24] occurs in two transformation stages, evidenced by well-resolved exothermic peaks in differential scanning calorimetry (DSC) curves (Fig. 1). The first crystallization stage, above 700 K, is characterized by a large and highly asymmetric DSC exotherm, as usually found for nanocrystallization processes, and consists in a precipitation of bcc Fe,Co crystals embedded in a residual amorphous phase. Crystallization is completed after a second stage, above 900 K, with the formation of boride phases. Thermal stability of both ascast amorphous and nanocrystalline alloys decreases as the Co content of the alloy increases. Cu alloying decreases the crystallization onset by about 25 K and shifts to higher temperatures the second crystallization stage. Therefore, the thermal stability of the nanocrystalline two-phase system, measured as the temperature splitting of the two crystallization peaks, is increased in Cu containing alloys. Mn addition (up to 4 at.%) only slightly increases the crystallization onset [21]. For (FeCo)ZrB alloys a similar crystallization behaviour has been reported: primary crystallization occurs above 750 K and a decrease of the crystallization onset as the Co/Fe ratio in the alloy increases is also observed [5, 25]. The two main phases present after the secondary crystallization are bcc-Fe,Co and (FeCo)23B6 but (FeCo)2B and (FeCo)3Nb phases are also detected [15, 21]. The amount and grain size of the (FeCo)23B6-type phase increase as the Co content in the alloy increases but the bcc-FeCo crystals after the second crystallization stage remain at a nanometric size [26]. The occurrence of a 23:6 type phase was observed in the nanocrystallization of FINEMET-type alloys [27, 28] and Hf-containing HITPERM alloys [29].

Figure 1. DSC (left) and thermomagnetic (right) curves of (FeMn)78–xCoxNb6(BCu)16 alloys

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DSC results show that the enthalpy of the first crystallization stage is larger for Co/Fe balanced alloys and decreases for higher and smaller Co content alloys, whereas the enthalpy fraction of the first stage, defined as 'H1/('H1 + 'H2) where 'H1 and 'H2 are the enthalpies of the first and the second stages, decreases as the Co content in the alloy increases, suggesting a smaller volume fraction of bcc-Fe,Co crystals at the end of the nanocrystallization for high Co content alloys. Thermomagnetic measurements in the course of devitrification (Fig. 1) show a nearly constant magnetization in a large temperature range (up to above 400 K), falling at the Curie temperature of the amorphous phase (higher than 600 K) that increases with the Co content of the alloy [15]. Mn addition provokes a decrease in the Curie transition of the amorphous phase [21]. It is worth noticing the high value of the Curie temperature of the amorphous phase in HITPERM alloys, significantly higher than the found for Co-free precursors of NANOPERM alloys (about 300 K) [30, 31]. The crystallization onset is evidenced by an increase in magnetization, due to the formation of the bcc-Fe,Co ferromagnetic phase. As Curie transition of the amorphous phase and crystallization onset temperatures are close, compositional changes can provoke that the rise in magnetization due to the ferromagnetic Fe,Co crystals overlaps in temperature the fall in magnetization due to the ferro-paramagnetic transition of the amorphous phase, if crystallization starts before the magnetic transition of the amorphous phase. In fact, for low Co content alloys magnetization has a zero value below the crystallization onset but progressive overlapping can be observed as the Co/Fe ratio in the alloy increases. Magnetization increases during the nanocrystallization process but, above 900 K, at temperatures that coincide with the second crystallization stage, a fall in magnetization is observed. This abrupt decrease in magnetization cannot be associated to a Curie transition because the only ferromagnetic phase present at this stage is the bcc-Fe,Co phase, with a much higher Curie temperature. The irreversible and thermally activated character of the fall in magnetization characterizes without ambiguity this feature as a recrystallization reaction provoking a decrease in the volume fraction of Fe,Co phase: some of bcc-Fe,Co crystals contribute to the boride phases formed at this stage, mainly a (FeCo)23B6-type phase, with a lower Curie temperature. A decrease in volume fraction of Fe,Co crystals after the second crystallization stage, derived from X-ray data, corroborates their partial transformation [32]. Thermomagnetic curves for fully crystalline samples show a fall in magnetization above 750 K at the magnetic transition of the (FeCo)23B6 phase [26]. This Curie temperature decreases with Mn additions by about 25 K/at.% Mn, regardless the Cu content of the alloy, suggesting that Mn is mainly contained in this (FeCo)23B6-type phase after crystallization [21]. 3. NANOCRYSTALLIZATION KINETICS Crystallization of amorphous metallic alloys is a nucleation and growth process and the overall rate of transformation accounts for the time and temperature dependence of both mechanisms. Kinetics of isothermal crystallization has been described in a large

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number of cases in the Johnson-Mehl-Avrami theory [33]. If the Avrami exponent is constant throughout the whole transformation, a log-log plot of [–log(1–x)] against t (JMA plot) gives a straight line of gradient n. In terms of a crude model [34] the Avrami exponent may be written as n = a + bp, where a accounts for the nucleation rate, b defines the dimensionality of the growth and p refers to the mechanism controlling the growth. Typically, a = 0 for athermal growth of quenched-in nuclei and a = 1 for steady state nucleation; p = 0.5 for primary diffusion-controlled growth. However, whereas values of n = 2.5, consistent with this model, are usually found for primary crystallization of conventional Fe,B based amorphous alloys, significantly lower values, even smaller than unity, have been found for some nanocrystalline Fe,B based alloys. Isothermal nanocrystallization kinetics of Nb-containing HITPERM alloys was studied by analysing the time dependence of magnetization throughout the process [35]. For low Co content alloys crystallization starts above the Curie temperature of the amorphous phase and the effective volume fraction x of crystals is obtained as x(t) = M(t)/M(f), where M(t) is the magnetization at t and M(f) is the long time saturation value for the isothermal run but for high Co content alloys a deconvolution [35] of the overlapped contributions to M of amorphous phase and emerging nanocrystals is necessary. JMA plots for these HITPERM alloys are clearly non linear but can be approximated by two linear steps with different slopes in all the studied alloys and annealing temperatures. The first step, corresponding to the low-transformed-fraction range, has a slope close to unity, whereas the second step, for high-fraction range, exhibits a slope value significantly lower than unity, which decreases as the annealing temperature increases. Low values for the Avrami exponent, even below 1, and a slowing down kinetics behaviour have been usually found for FINEMET type alloys [36-39] but n values above 2 have been reported for NANOPERM alloys of the FeZrB type [40]. However, low values of n have also been found in Fe80Nb6B14 alloys [41]. From these results it is easy to infer that a significant parameter responsible for this peculiar kinetic behaviour should be the Nb content because this element, of low diffusivity and insoluble in the bcc-Fe,Co phase, would hinder the grain growth. The decrease of n with the annealing temperature can be explained because for lower temperatures the crystalline fraction reached in a given time is smaller and thus the effect on growth inhibition should be smaller. The effect of Cu addition is only observed in the first step of the JMA plots. In Cu containing alloys the Avrami exponent is slightly increased at the beginning of the crystallization and the slope change occurs at a higher value of x. These results should agree with the role of the Cu clusters as nucleation sites for Fe,Co crystals in the early stages of nanocrystallization. This Cu effect on the kinetics has been found to be independent of the Co content in the alloys. Regarding the influence of Co alloying, the Avrami exponent of the first step of JMA plots does not show a dependence with the Co content of the alloy but for the second step n decreases as the Co content in the alloy increases. This slowing down of the kinetics at the last stages of the nanocrystallization in high Co content alloys can be associated to the lower content of the amorphous matrix in Fe, necessary for the grain growth [35].

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4. NANOCRYSTALLINE MICROSTRUCTURE The microstructure of nanocystalline alloys consists of two major phases: bcc-Fe, Co nanosized crystals embedded in a residual amorphous matrix. The final grain size and volume fraction of Fe,Co crystals are well defined because the transformation rate is not significant up to the onset of the secondary crystallization thermally well separated of the primary one. For Cu-containing alloys a third minority phase, present since pre-crystallization stages, consists of Cu-rich clusters that catalyses the nucleation of Fe,Co crystals. In this section microstructural features and partitioning of the alloying elements in the phases are analysed. 4.1. Fe-Co nanocrystals The lattice parameter of the bcc-(FeCo) crystals does not show appreciable changes in the course of the nanocrystallization process but decreases as the Co content in the alloy increases, following the same behaviour as that found in Fe,Co binary alloys [42]. This result suggests a correlation between the Co content of the nanocrystals and that of the alloy. A similarity in the atomic scattering factors of Co and Fe makes it difficult to remove the ambiguity between and -Fe,Co (B2 type) phases with conventional XRD. The -Fe,Co phase was detected in Zr containing HITPERM alloys from synchrotron radiation diffraction [31] and low values of the hyperfine field found in Mössbauer studies on Nb containing HITPERM alloys suggest the presence of the ordered -Fe,Co phase in these alloys [43]. The crystalline volume fraction derived from deconvolution of the X-ray integral intensity profile of amorphous halo and (110) crystalline peak is, after a correction for the different scattering power of both phases [44], 55% for alloys with Fe/Co ratio up to 50:50, and decreases for higher Co content alloys (45 for 60 at.% Co content alloy). No significant differences in crystalline fractions have been found for Cu free and Cu containing alloys with the same Co content. Mössbauer spectrometry results on the fraction of probe atom (Fe) in the different phases show a decrease in the crystalline atomic fraction for high Co content alloys [43] in a similar way as in the volume fraction derived from XRD data. The observed decrease in the crystalline fraction in high Co content alloys can be explained, if we assume that the Fe exhaustion of the matrix stops the nanocrystallization process [45]. Transmission electron microscopy (TEM) images (Fig. 2) show that a Cu addition clearly refines the final nanostructure in Nb containing HITPERM alloys with low Co content. Large irregular crystals are observed in Cu-free low Co-content alloys [16, 21] but these particles are aggregates of smaller grains with the same orientation as shown by convergent beam electron diffraction patterns [16]. This feature, also found in NANOPERM alloys [13], indicates that heterogeneous nucleation occurs at the bcc(FeCo) crystals/amorphous interfaces of the particles nucleated earlier in Cu-free alloys. The microstructure refinement effect of Cu in these alloys is reduced when the Co content increases. The mean grain size is of about 5 nm for Cu added alloys independently of Co content, whereas for Cu free alloys the mean grain size decreases as the Co

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Figure 2. TEM images of Cu-free (left) and Cu-added (right) 18 at.% Co alloys

Figure 3. FeCo nanocrystals size distribution profiles in Fe78-xCoxNb6 (BCu)16 alloys

content increases (a 20 nm for 18 at.% Co alloy and a 5 nm for 60 at.% Co alloy). Cu addition also induces a narrower grain size distribution profile with respect to the Cu free alloys (Fig. 3), the effect being more apparent for low Co content alloys [16]. A microstructure refinement in these alloys is obtained by adding Cu or by increasing Co content. A smaller grain size implies a greater number of crystals, provided that the crystalline fraction is the same, and an enhancement of the nucleation with respect to the growth process. 4.2. Partitioning of alloying elements The partitioning behaviour of alloying elements during the primary crystallization of Nb containing HITPERM alloys has been analysed from three-dimensional atom probe

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(3DAP) experiments [19]. For Cu-free alloys isoconcentration surfaces of Fe enclose volumes enriched with this element that correspond to bcc-(FeCo) crystals whereas the other regions constitute the remaining amorphous matrix. The results for the Fe18Co60Nb6B16 alloy show a very low density of Fe-rich particles for samples in the early stages of crystallization but the number density of these Fe-rich particles is highly increased for samples annealed up to the end of the primary crystallization. Concentration depth profiles show that Nb and B are depleted in the bcc-(FeCo) phase but, while nearly all the atoms of Nb are excluded from the Fe-rich particles, some amount of B should remain in those crystals. An interesting result is that no apparent difference of Co concentration between FeCo crystals and amorphous matrix is found. This can be explained by the high solubility of Co in bcc-Fe phase. For FeCoZrBCu alloys, however, Co preferentially partitions in the amorphous phase [18], so the enthalpy of mixing for Co and Nb (or Zr) should be significant. No difference in the partitioning of elements throughout crystallization is observed and composition of FeCo crystals is constant.

Figure 4. Three-dimensional map of Cu atoms (a), isoconcentration surfaces of 30 at.% Cu (b) and 50 at.% Fe (c) and concentration depth profiles for a selected volume

For Cu added alloys three-dimensional mapping of Cu atoms (Fig. 4) clearly show Cu clusters in Fe39Co39Nb6B15Cu1 alloy. A few FeCo particles are observed in the isoconcentration surface of Fe, indicating an early stage of crystallization. Concentration depth profiles from a selected region containing both a Cu cluster and a FeCo particle (Fig. 4), show that Nb and B are depleted in the FeCo crystals but Co is homogeneously distributed in FeCo and amorphous phases, similar to the observed for Cu-free alloy. In the Cu cluster the concentrations of both Fe and Co are greatly reduced as expected since the mixing enthalpy of Cu and Fe (or Co) is positive. In Fig. 4 can be seen that FeCo crystal is just on a side of a Cu cluster, confirming that Cu clusters provide nucleation sites for bcc-(FeCo) crystals.

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5. CONCLUSIONS The results of the crystallization of Nb containing Hitperm alloys allow to conclude that there are some differential features with respect to Zr added alloys: first, there is the significant role of Cu that forms clusters enhancing nucleation of FeCo crystals and refining the nanocrystalline microstructure. Second, Co is uniformly distributed in FeCo nanocrystals and amorphous matrix. The microstructure refinement obtained by increasing the Co content in the alloy is more important for Cu-free alloys. ACKNOWLEDGEMENTS This work was supported by the Spanish Government and EU FEDER (project MAT 20013175) and the PAI of the Regional Government of Andalucía. REFERENCES 1. 2. 3. 4.

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14. Yoshizawa, Y., and Yamauchi, K. (1991) Magnetic-properties of FeCuCrSiB, FeCuVSiB, FeCuMoSiB, alloys, Mater. Sci. Eng. A 133, 176-179. 15. Blázquez, J.S., Conde, C.F., and Conde, A. (2001) Crystallization process in (FeCo)78Nb6(BCu)16 alloys, J. Non-Cryst. Solids 287, 187-192. 16. Blázquez, J.S., Franco, V., and Conde, A. (2002) The influence of Cu addition on the crystallization and magnetic properties of FeCoNbB alloys, J. Phys.: Condens. Matter 14, 11717-11727. 17. Hono, K. (2002) Atom probe characterization of microstructures of nanocrystalline and nanocomposite magnetic materials, in Advanced Magnetic Materials: Characterization and simulation of advanced magnetic materials, Y. Liu, D.J. Sellmyer, D. Shindo, J.G. Zhu and G.C. Hadjipanayis (eds), Springer-Verlag (to be published). 18. Ping, D.H., Wu, Y.Q., Hono, K., Willard, M.A., McHenry, M.E., and Laughlin, D.E. (2001) Microstructural characterization of (Fe0.5Co0.5)Zr7B4Cu1 nanocrystalline alloys, Scripta Mater. 45, 781-786. 19. Zhang, Y., Blázquez, J. S., Conde, A., Warren, P. J., and Cerezo, A. (2002) Partitioning of Co during crystallization of Fe-Co-Nb-B(-Cu) amorphous alloys, Mater. Sci. Eng. A 353, 158-163. 20. Ohnuma, M, Hono, K., Abe, T., Onodera, H., Linderoth, S., Pedersen, J.S., and Yoshizawa, Y. (2001), Microstructure of nano-crystalline soft-magnetic (Fe,Co)-Si-B-Nb-Cu alloys, in Proc. 22nd Riso Inter. Symp. on Materials Science: Science of metastable and nanocrystalline alloys structure, properties and modelling, A.R. Dinesen, M. Eldrup, D. Juul Jensen, S. Linderoth, T.P. Pedersen, N.H. Pryds, A. Schroder Pedersen, J.A. Wert (eds.), Roskilde, Dinamarca, pp. 341–346. 21. Conde, C.F., Conde, A., Svec, P., and Ochin, P. (2003) Influence of the addition of Mn and Cu on the nanocrystallization process of HITPERM FeCoNbB alloys, Mater. Sci. Eng. A in press. 22. Kane, S.N., Gupta, A., Sarabhai, S.D., and Kraus, L. (2003) Influence of Co content on structural and magnetic properties of CoxFe84-xNb7B9 alloys, J. Magn. Magn. Mater. 254, 495-497. 23. Kraus, L., Soyka, V., Duhaj, P., and Mat'ko, I. (1998) Magnetic properties on nanocrystalline CoFeNbB alloys, J. Phys. IV 8, 95-98. 24. Kraus, L., Haslar, V., Duhaj, P., Svec, P., and Studnicka, V. (1997) The structure and magnetic properties of nanocrystalline Co21Fe 64-xNbxB15 alloys, Mater. Sci. Eng. A, 226, 626-630. 25. Willard, M.A., Laughlin, D.E., and McHenry, M.E. (2000) Recent advances in the development of (Fe,Co)88M7B4Cu1 magnets, J. Appl. Phys. 87, 7091-7096. 26. Blázquez, J.S., Lozano-Pérez, S., and Conde, A. (2002) A study of the fcc-(FeCo)23B6 phase in fully crystallized Fe-Co-Nb-B-Cu alloys, Phil. Mag. Lett. 82, 409-417. 27. Borrego, J.M. and Conde, A. (1997) Nanocrystallization behaviour of FeSiBCu(NbX) alloys, Mat. Sci. Eng. A 226, 663-667. 28. Borrego, J.M., Conde, C.F. and Conde, A. (2000) Phil. Mag. Lett. 80, 359-365. 29. Iwanabe, H., Lu, B., McHenry, M.E., and Laughlin, D.E. (1999) Thermal stability of the nanocrystalline Fe–Co–Hf–B–Cu alloy, J. Appl. Phys. 85, 4424-4426. 30. Gorria, P., Orue, I., Plazaola, F., Fernández-Gubieda, M.L., and Barandiarán, J.M. (1993) Magnetic and Mössbauer study of amorphous and nanocrystalline Fe86Zr7Cu1B6 alloys, IEEE Trans. Mag. 29, 2682-2684. 31. Willard, M.A., Laughlin, D.E., McHenry, M.E., Thoma, D., Sickafus, K., Cross, J.O., and Harris, V.G. (1998) Structure and magnetic properties of (Fe0.5Co0.5)88Zr7B4Cu1 nanocystalline alloys, J. Appl. Phys. 84, 6773-6777.

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32. Blázquez, J.S., Conde, C.F., and Conde, A. (2003) Thermomagnetic detection of recrystallization in FeCoNbBCu nanocrystalline alloys, Appl. Phys. Lett. 79, 2898-2900. 33. Christian, J.W. (1975) The Theory of Transformations in Metals and Alloys, Pergamon Press, D.W. Hopkins (ed.). 34. Ramanan, V.R.V., and Fish, G.E. (1982) Crystallization kinetics in Fe-B-Si metallic glasses, J. Appl. Phys. 53, 2273-2275. 35. Blázquez, J.S., Conde, C.F., and Conde, A. (2003) Kinetic of nanocrystallization in FeCoNbB(Cu) alloys, Appl. Phys. A 76, 571-575. 36. Rixecker, G., Schaaf, P., and Gonser, U. (1992) Crystallization behaviour of amorphous Fe73.5Cu1Nb3Si13.5B9, J. Phys.: Condens. Matter 4, 10295-10310. 37. Conde, C.F., and Conde, A. (1994) Crystallization of a FINEMET-type alloy: nanocrystallization kinetics, Mater. Lett. 21, 409-414. 38. Mat'ko, I., Duhaj, P., Svec, P., and Janickovic, D. (1994) Formation of nuclei of metastable phases in nanocrystalline materials, Mat. Sci. Eng. A 179/180, 557-562. 39. Conde, C.F., Millan, M., Borrego, J.M., Conde, A., Capitan, M.J., and Joulaud, J.L. (1998) An in situ synchrotron study of nanocrystallization in (Fe, Cr)-Si-B(-Cu-Nb) alloys, Phil. Mag. Lett. 78, 221-227. 40. Suzuki, K., Makino, A., Tsai, A.P., Inoue, A., and Masumoto, T. (1994) The role of boron in nanocrystalline Fe-Zr-B soft-magnetic alloys, Mater. Sci. Eng. A 179, 501-505. 41. Suzuki, K., Cadogan, J.M., Dunlop, J.B., and Sahajwalla, V. (1995) 2-stage nanostructural formation process in Fe-Nb-B soft-magnetic alloys, Appl. Phys. Lett. 67, 1369-1371. 42. Bozorth, R.M. (1968 ) Ferromagnetism, Van Nostrand-Reinhold, Princeton, N.J. 43. Blázquez, J.S., Conde, A., and Greneche, J.M. (2002) Mössbauer study of FeCoNbBCu HITPERM-type alloys, Appl. Phys. Lett. 81, 1612-1614. 44. Blázquez, J.S., Franco, V., Conde, C.F., and Conde, A. (2002) Microstructure and magnetic properties of Fe78-xCoxNb6B15Cu1 (x =18,39,60) alloys, J. Magn. Magn. Mater. 254255, 460-462. 45. Blázquez, J.S., Borrego, J.M., Conde, C.F., Conde, A., and Greneche, J.M. (2003) On the effects of partial substitution of Co for Fe in FINEMET and Nb-containing HITPERM alloys, J. Phys.: Condens. Matter 15, 3957-3968.

LOW TEMPERATURE MAGNETIC PROPERTIES OF NANOCRYSTALLINE Co-Nb-Cu-Si-B ALLOYS A. ĝLAWSKA-WANIEWSKA Institute of Physics, Polish Academy of Sciences al. Lotników 32/46, 02-668 Warsaw, Poland Corresponding author: A. ĝlawska-Waniewska, e-mail: [email protected]

Abstract: Co66Nb9Cu1Si12B12 metallic glass is used as a parent material for nanocrystalline magnets exhibiting low Curie temperature of the amorphous matrix (100-140 K). Precipitation of Co nanoparticles destroys the ferromagnetic ordering in the amorphous alloy and leads to a low-temperature cluster-glass state. At higher temperatures, the grains embedded in the paramagnetic matrix exhibit a superparamagnetic behaviour. In the fully crystallized state the magnetic properties of the material, composed of two crystalline phases with their Curie points above the room temperature, are mainly governed by the inter- and intra-phase magnetic interactions which lead to a preferential ferromagnetic ordering.

1. INTRODUCTION Nanocrystalline materials, produced by a devitrification of the amorphous alloys, display a variety of magnetic states and their magnetic properties can be adjusted to special requirements by tailoring the intrinsing properties of the constituent phases as well as the microstructure [1-3]. At temperatures below the Curie point of the amorphous matrix (which for the most widely studied materials is above or even far above the room temperature) the magnetic properties of the created multiphase nanocrystalline materials are mainly determined by a competition between the strength of the interphase and intraphase exchange interactions and the anisotropy of individual nanocrystals. In FINEMET [4] and NANOPERM [5] alloys at high crystalline fraction, the exchange interactions lead to a substantial reduction of the effective anisotropy and magnetic softening [1]. In these alloys the exchange coupling between the crystals is mediated throughout a very thin layer of the intergranular amorphous phase and it is preserved even at temperatures above the Curie point of the amorphous matrix [6]. However, in partly crystallized alloys, where the intergrain distances are larger, with the reduction of the exchange stiffness of the amorphous matrix, the averaging of the effective anisotropy over the exchange coupled regions becomes incomplete and results in magnetic hardening [6-10]. Around the Curie point of the matrix the magnetic decoupling between the crystalline and amorphous phases takes place and at higher 123 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 123–134. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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temperatures on the nanocrystalline material can be considered as a system of ferromagnetic nanoparticles dispersed in a paramagnetic matrix. The magnetic behaviour of such nanostructure depends on the competition between the energy tending to stabilize the magnetic structure (i.e. the anisotropy of the individual grains and strength of the dipolar interactions) and the thermal energy. For small fraction of crystallites, when the grains are well separated and the dipolar coupling between them is negligible, the thermal effects become dominant and the nanostructure can display a superparamagnetic behaviour [11, 12]. But with the increase of the grain content and corresponding reduction of the intergrain distances, the magnetostatic interactions prevent thermal fluctuations and dominate the overall magnetic behaviour of the nanocrystalline sample [13]. In the widely studied Fe-based nanocrystalline alloys the Curie temperature of the amorphous matrix is above the room temperature and issues of the small particle magnetism can only be studied at elevated temperatures. But the recently developed devitrified Co66Nb9Cu1Si12B12 alloys have the Curie point of the amorphous phase below 150 K [14]. This enables analysing the particulate properties of these nanocrystalline magnets at low temperatures where the thermal fluctuations are suppressed. Moreover, it may be expected that, due to largely reduced exchange stiffness of the intergranular phase, these nanostructure can display a behaviour not observed in strongly correlated systems. 2. MATERIAL CHARACTERIZATION Amorphous ribbon of the nominal composition Co66Nb9Cu1Si12B12 was produced by a conventional single-roller planar-flow casting method; its devitrification process and basic magnetic properties have already been published [14-16]. The nanocrystalline

Figure 1. TEM micrographs of Co66Nb9Cu1Si12B12 samples annealed at 843 K (a) and 903 K (b)

samples were prepared by the isothermal annealing of the as-spun precursor under vacuum for 1 h at temperatures 843 K (sample A1) and 903 K (sample B1). Their microstructure, obtained with the TEM, is shown in Fig. 1. The sample annealed at 843 K consists of isolated grains embedded in an amorphous matrix with the volume fraction of the crystalline phase of about 5%. The nanocrystalline phase, composed of Co crystallites in which the metalloid atoms (mainly Si) are partitioned, have the Curie temperature of around 1100 K (less than the one of pure Co ~1400 K). The heat

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treatment at 903 K results in the total crystallization of the sample and creation of two crystalline phases with different Curie points: one at ~1000 K and the other at ~360 K. 3. EXPERIMENTAL RESULTS 3.1. dc magnetic measurements Magnetic measurements were performed with the VSM (Oxford Instruments Ltd.) on the amorphous and nanocrystalline Co66Nb9Cu1Si12B12 alloys over the temperature range 4-300 K. Thermal evolutions of the selected hysteresis loops of the samples A1 and B1 are shown in Figure 2a and 2b, respectively.

Figure 2. Selected hysteresis loops for the samples annealed at 843 K (a) and 903 K (b)

For the sample A1 at low temperatures, where both phases – grains and matrix are ferromagnetic, the hysteresis loops are nearly rectangular. As the temperature rises and the grains become surrounded by the paramagnetic matrix, the loop shape changes to the one characteristic of non–interacting magnetic nanoparticles tending to a superparamagnetic state with zero coercivity HC and remanence MR. In turn, for the fully crystallized sample B1 the loops are broad and with increasing temperature a continuous gradual decrease of the coercivity and remanence is observed as expected for the collective magnetic behaviour.

Figure 3. Temperature dependence of the coercivity in partly crystallized Co66Nb9Cu1Si12B12 alloy (sample A1)

The temperature dependence of the coercive field in sample A1 is plotted in Fig. 3. The coercivity shows a general tendency to decrease with the increase of the tem-

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perature. However, at temperatures close to TC (am) two local maxima, at ~95 K and ~135 K, are observed. At T >TC (am) the observed coercivity as well as remanence decay are consistent with the enhanced role of the thermal fluctuations of magnetic moments of the grains surrounded by the paramagnetic medium. Above the blocking temperature, the magnetocrystalline anisotropy of nanosize, non-interacting, randomly oriented grains is overcame by thermal activation. Thus, nanoparticles do not display any hysteresis.

Figure 4. Temperature dependencies of the ZFC-FC magnetization in amorphous (a) and nanocrystalline alloys with low (b) and high fraction (c) of the crystalline phase; (d) shows the enlarged region of elevated temperatures for sample A1 as well as the fit of MFC(T) curve to the equation (1)

The temperature dependencies of the magnetization measured in 10 Oe applied field in the standard zero-field-cooled (ZFC) and field-cooled (FC) regime are presented in Fig. 4: (a) for the relaxed amorphous precursor (annealed at Tan < 800 K i.e. below the crystallization transformation), (b) and (c) for nanocrystalline samples annealed at 843 and 903 K, respectively. For Co66Nb9Cu1 Si12B12 alloy in the amorphous state the ZFC-FC magnetization curves overlap (Fig. 1a) and are characteristic of a ferromagnetically ordered material with the ferromagnetic-paramagnetic phase transition at TC (am) | 175 K. For a sample A1 at the early stage of crystallization strong low temperature irreversibility is observed and the ZFC-FC curves show splitting from 4 K up to 235 K

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(Fig. 2b, d). The splitting arises due to the differences between the random freezing of magnetic moments when cooling in the zero magnetic field and more ordered state reached when cooling in the applied field. The observed peak in MZFC(T) dependence is smeared, suggestive of sluggish response of the material. The ZFC magnetization first increases with increasing temperature up to a certain characteristic temperature Tf | 50 K and this initial increase is well correlated with the local anisotropy reduction and the corresponding decrease of the coercivity (see Fig. 3). At T >Tf the ZFC magnetization shows a pronounced plateau almost up to TC (am) that points to the existence of stable ferromagnetic interactions in this sample. The FC magnetization increases sharply below TC (am) as the temperature decreases and MFC(T) does not saturate even at 4 K. Thus, in sample A1 the full alignment of magnetic moments in a field direction within the thermal fluctuation effects cannot be achieved even at very low temperatures. Contrary to the partly crystallized sample A1, the fully crystallized sample B1 exhibits only slight ZFC-FC irreversibility in the temperature range 4-300 K. This indicates the predominantly ferromagnetic interactions in such nanostrusture where the reduced irreversibility can be related with the disordered grain surfaces and intercrystallite regions. 3.2. ac susceptibility studies Measurements of the ac susceptibility give a detailed insight into the reversible magnetization dynamics. The temperature dependencies of the real Ȥƍ and imaginary ȤƎ components of the ac susceptibility in the amorphous and fully crystallized samples are shown in Fig. 5 (a) and (b), respectively. They confirm the ferromagnetic ordering of the amorphous precursor and the collective magnetic behaviour of fully crystallized sample, in agreement with dc magnetization studies. However, the partly crystallized sample A1 shows a complex magnetic behaviour – the temperature dependencies of the real and imaginary components of the suscep tibility measured at different amplitude and frequency of the ac field are shown in Fig. 6 and 7, respectively. The observed peak in the real component Fc(T) is very broad and rounded and its shape remains almost unchanged, independently on the field strength.

Figure 5. Thermal evolution of the ac susceptibility in the amorphous (a) and fully crystallized (b) samples

The initial increase of Fc(T) is observed for T from 4 K up to Tf* | 20 K. The real and imaginary components of the susceptibility measured at low frequency (1 kHz), are

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1.0 0.8 0.6 0.4 0.2 0.0

0

20

40

60

80

100

120

140

T [ K]

Figure 6. Temperature dependencies of the real part of the ac susceptibility of the sample A1 measured in different ac fields at 1 kHz (a) and at different frequencies in 2.5 Oe (b)

Figure 7. Temperature dependencies of the imaginary part of the ac susceptibility of the sample A1 measured in different ac fields at 1 kHz (a) and at different frequencies in 2.5 Oe (b)

field dependent (Fig. 6a and 7a). With the increase of the ac field the maximum in Fc(T) curve shifts towards higher temperatures, from ~17 to ~27 K (see the inset in Fig. 6a). Additionally, for the real component a small kink is observed at around 110-120 K (which correlates with the local decrease of the coercivity observed in the same temperature range (see Fig. 3) and its amplitude decreases with the increase of the ac field. The imaginary component of the susceptibility Fs(T) exhibits a complex structure (distinctly noticeable for 1 and 2.5 Oe) and consists of three overlapped maxima. It is very sensitive to the amplitude of the ac field (Fig. 7a) that changes the intensity of the relative contributions from the respective overlapping maxima. The first (low temperature) maximum, seen at Tf* | 20-40 K, dominates at high ac fields and the decrease of its intensity with decreasing ac field is observed simultaneously with the increase of the third maximum. This third maximum, seen at 100-110 K, just below TC(am), dominates the observed behaviour for very low ac fields. The intensity of this maximum is effectively suppressed when measured in higher fields, and only small inflection in Fs(T) curve is observed at about 110 K for the highest ac field of 15 Oe. Fc(T) dependence does not show any significant dependence on the frequency (slight dispersion is only observed in the range 80-120 K, as shown in Fig. 6b) that, generally, is in contrast with the behaviour observed for spin–glasses. However, the imaginary component Fs(T) shows a significant dependence on the frequency. As can be seen from Fig. 7(b) at small frequencies of about 600-1000 Hz the first maximum at Tf* is almost

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indistinguishable. With the increase of the frequency from 1 to 6 kHz, the well defined cusp appears at Tf* | 27 K and with a further increase of the frequency up to 10 kHz the intensity of the cusp increases and, simultaneously, it shifts towards higher temperatures (Tf*(10 kHz) | 35 K). Such a behaviour is reminiscent of a random spinglass-like freezing [17]. The second and third maxima are strongly overlapped and, as a result, one broad peak is observed. Therefore, the third cusp in Fc(T) could only be distinguished as a kink at around 110 K. 4. MAGNETIC ORDERINGS IN CO66NB9CU1SI12B12 ALLOYS The investigated as-quenched and nanocrystalline Co66Nb9Cu1Si12B12 alloys exhibit a variety of magnetic states, depending on the microstructure and temperature. The amorphous material displays pure ferromagnetic ordering. On the other hand, the fully crystallized ribbon (sample B1) containing two crystalline phases (both with their TC above the room temperature) reveals a collective magnetic behaviour. In this sample the two constituent crystalline phases remain magnetically coupled and this coupling leads to the predominantly ferromagnetic ordering. The small ZFC-FC irreversibility observed in this sample can be caused by the disturbed surface/interface regions with non-collinear magnetic arrangements found both for small particles [18, 19] and nanocrystalline alloys [20]. In turn, the overall behaviour of the partly crystallized alloy (sample A1), composed of Co grains embedded in the amorphous matrix which, depending on the temperature, is either in paramagnetic or ferromagnetic state, depends first and foremost on the magnetic state of the matrix. Thus, the interpretation of the presented experimental data is divided into two parts: one deals with the elevated temperature region (above TC (am)), while the other discusses the low temperature magnetic behaviour of this material being at early stage of crystallization. 4.1. Isolated nanocrystallites in paramagnetic matrix On heating above TC (am), the single domain Co grains embedded in the paramagnetic matrix (sample A1) gain some thermal energy which enables easier reorientation of their magnetic moments with an external field and a continuous transition to the superparamagnetic state. This transition manifests itself as a peak in both ZFC magnetization (Fig. 4d) and ac susceptibility (Fig. 8) as well as the corresponding decrease of the coercivity above TC (am) (Fig. 3). In the superparamagnetic regime from the fit of the experimental M(H; T) dependencies by a superposition of the Langevin functions it has been found that the mean diameter of the grains | 7.4 nm with the distribution width V (D) | 0.56, assuming that it is log-normal. The room temperature magnetization of the grains was found to be Mcr | 1360 emu/ccm, i.e. only slightly smaller than that of pure cobalt (1420 emu/ccm) [14]. For T > TC (am), the MZFC(T) curve of the sample A1 shows a typical blocking behaviour. The magnetization increases up to its maximum value at TB | 200 K, which is the mean blocking temperature. With further increase of the temperature, the ZFC magnetization drops and above TBmax | 235 K (the maximum blocking temperature) both ZFC and FC curves overlap and all crystallites turn to superparamagnetic state. The MZFC(T) peak is

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relatively broad which is mainly due to the distribution of particle sizes and, consequently, the distribution of blocking temperatures. The theoretical analysis of the MZFC(T) curve was performed within a model for noninteracting spherical single–domain particles based on the distribution of blocking temperatures, as originally proposed by Gittleman [21] where the ZFC magnetization is given by: M ZFC (T , H )

M S2 H 1 3kT Q

Vmax

VB ( T )

³

U (V )V 2 dV 

Vmin

M S2 H 1 U (V )VdV 3K Q V ( T )

³

(1)

B

U(V) represents the volume distribution function, VB is the volume corresponding to the blocking temperature TB (the so-called blocking volume) in the time scale Wm of magnetization measurements, K is the magnetic anisotropy constant and Vmax

Q

³ VU V dV .

(2)

Vmin

The first integral in the above equation represents the contribution from the superparamagnetic particles, while the second one corresponds to the blocked grains. The experimental ZFC curve was analyzed in the framework of this model assuming the log-normal size distribution with the average diameter of crystallites obtained from the fit of the superparamagnetic magnetization curves. The fitted MZFC(T) dependence [16] obtained for the effective anisotropy constant KA = 2.7 u 105 J/m3 is shown in Fig. 4d. The obtained KA value is only slightly smaller than the magnetocrystalline anisotropy constant of pure bulk cobalt (4.5 u 105 J/m3) and this reduction can be caused by: (i) the symmetry reduction of the crystal lattice in Co-based grains due to the admixture of metalloid atoms (mainly Si) and (ii) surface anisotropy contribution.

Figure 8. Out-of-field component of the ac susceptibility in partly crystallized sample at T > TC (am) for different frequencies and amplitudes of ac field

The superparamagnetic behaviour of Co grains separated by the paramagnetic matrix is also evidenced by the ac susceptibility measurements and manifests itself by an additional peak at temperatures above the Curie point of the amorphous matrix; the temperature dependence of this peak obtained for the imaginary component is shown in

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Fig. 8. The mean blocking temperature corresponding to the susceptibility maximum is TB* | 250 K. As expected for a system of superparamagnetic particles, this temperature is higher than the one obtained from the static ZFC magnetization curve and, additionally, with the increase of the frequency from 1 to 10 kHz, it shifts towards higher temperatures from ~250 K to ~270 K. Additionally, as can be seen from Fig. 8, the maximum of Fs(T) slightly shifts towards lower temperatures with the increase of the field amplitude to 15 Oe. This is in agreement with the theoretical Monte–Carlo simulations of a field dependence of the blocking temperature of a system of Co nanoparticles [22]. 4.2. Low temperature ordering in partly crystallized alloys Since at low temperatures the amorphous alloy exhibits ferromagnetic ordering, the irreversible magnetization effects observed in the partly crystallized alloy do not originate from mechanisms related to the intrinsic properties of the amorphous medium such as inhomogenities (regions of low- and high-density amorphous arrangement [23]), or reentrant spin-glass behaviour (as found in the well-known FeZrB systems [24]). In turn, Skorvanek et al. [9] observed the low temperature magnetic hardening and magnetization irreversibility in Fe-Nb-B-(Cr)-(Cu) alloys with medium degree of crystallinity and ascribed these effects to the reduced exchange coupling between the grains and the matrix due to the freezing of the distorted grain-matrix interfaces. But this mechanism cannot explain the strong irreversibility observed in the sample A1 that contains only 5% of the crystalline phase. Therefore, the low temperature behaviour observed in this sample is connected with the peculiar nanostructure in which small Co crystallites precipitate in the amorphous matrix. It may be clarified within the framework of a simple model in which magnetic clusters are formed from small randomly oriented, strongly magnetic crystallites and the surrounding magnetic spins from the amorphous matrix, which are strongly coupled to the individual crystallites. Spin configurations in different clusters are different and the clusters are weakly related. As a result, there is a large number of configurations of the cluster magnetic moments separated by energy barriers into which the system could be found on lowering the temperature. Therefore, in the low temperature regime the freezing of a disordered arrangement of cluster magnetic moments can be expected. The disorder, which leads to the cluster-glass behaviour of the whole system, arises from a random distribution of the easy axes of strongly anisotropic grains. Additionally, the interactions between different phases which results in a wide distribution of relaxation times [25] as well as the interactions between Co clusters (of a magnetostatic origin or via the metallic matrix), which could randomly assume both signs, lead to the frustration of spins of the amorphous matrix, mainly in the inter-clusters regions, that enhances the effects of the overall magnetic irreversibility in the partly crystallized alloy. The main static experimental observations: (i) the initial increase of ZFC magnetization up to the freezing temperature Tf, (ii) long-range relaxation effects below Tf, (iii) a significant difference between MZFC and MFC curves, (iv) the lack of magnetic saturation of MFC even at very low temperatures, and (v) the increase of the coercivity at T < Tf are consistent with the proposed cluster-glass behaviour of the material [26, 27]. A deeper insight into the spin structure and magnetic transformations in the partly crystallized material can be derived from the susceptibility data. The initial increase of

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Fc(T) with increasing temperature up to the freezing temperature Tf*, which correlates with the initial increase of ZFC magnetization as well as with the corresponding reduction of the coercivity is a distinctive feature of complex magnetic systems such as cluster–glasses, re-entrant spin–glasses, etc. i.e., systems in which below Tf * the susceptibility shows long–range relaxation effects, not observed for ferromagnetic ordering. However, the in–field magnetic behaviour of the Fc(T) dependencies is different from the one typical of the spin–glass or re-entrant spin–glass [17] but is rather characteristic of an inhomogeneous ferromagnet [28] in which the broad Fc(T) peak is the result of a superposition of ferromagnetically ordered and magnetically disordered frustrated regions. The non–homogeneous nature of the partly crystallized sample in which, besides the frustrated clusters, also the ferromagnetic amorphous phase (located between the clusters) is present, manifests itself both in Fc(T) and Fs(T) curves at temperatures just below the Curie point of the amorphous matrix. The kink observed in Fc(T) and the corresponding peak in Fs(T) (the third maximum) observed just below TC (am) reveal features specific of the Hopkinson maximum, which is characteristic of the magnetization processes in a ferromagnet. The Hopkinson peak does not depend on the ac field frequency but is very sensitive to the field amplitude [29]. As presented in Fig. 7(a), at low fields Fs(T) rises sharply at the Curie temperature of the amorphous matrix, has a broad maximum and then diminish with decreasing temperature. An application of higher fields suppresses this maximum and shifts it to lower temperatures, as expected for ferromagnetic ordering. Suppression of the Hopkinson peak facilitates the observation of other critical peaks in Fs(T) curve. It is known that in the paramagnetic phase the interactions between spins exist and a short-range order progressively occurs by lowering the temperature. This picture is even more reliable in the case of weakly magnetic matrix with the magnetically blocked Co nanocrystallites inside. These highly anisotropic, strongly magnetic crystallites induce the polarization of the surrounding matrix along their easy axis and act as the cores of created magnetic clusters. Therefore, a random distribution and inhomogeneous growth of clusters, formed from the nanosized grains and matrix spins coupled to the individual grains by bonds stronger than the thermal energy, is expected when decreasing the temperature below TC (am). With the temperature decrease the clusters grow in size and take on diverse shapes based upon the distribution of competitive interactions among the various spins in their immediate neighbourhood. This implies that the transition to the cluster–glass state is smoothed and gives a distribution of cluster sizes and, hence, a distribution of the transition temperatures TCG. As a result, at TCG | 70 K ( 900 K) results in a formation of two crystalline phases (both with their Curie point above room temperature) and high crystalline fraction. The nanostructure, created during the heat treatment, is the main factor affecting the magnetic properties of the material. The Co66Nb9Cu1Si12B12 amorphous material displays the ferromagnetic ordering below the Curie temperature TC (am) | 175 K. In a fully crystallized ribbon the two constituent crystalline phases remain magnetically coupled over the whole low temperature range and this coupling leads to a collective magnetic behaviour and predominantly ferromagnetic ordering. The most interesting behaviour is found in Co66Nb9Cu1Si12B12 material at small crystalline fraction. In such a partly crystallized alloy at temperatures above the Curie point of the matrix, the isolated Co grains display superparamagnetism. In turn, at low temperatures the competition between the strength of exchange interactions and the effective anisotropy of individual grains causes magnetic polarization of the matrix around the grains leading to the cluster-glass state. For a low fraction of the crystalline phase the material reveals a ferromagnetic contribution (originating from the matrix not coupled to the clusters) superimposed on the cluster-glass contributions and behaves as an inhomogeneous ferromagnet. The unusual cluster-glass ordering of the partly crystallized alloy results from the peculiar nanostructure of randomly oriented, strongly magnetic and anisotropic Co grains and isotropic matrix with largely reduced exchange stiffness constant. Although ferromagnetism by itself is well known, clustering behaviour of inhomogeneous ferromagnets is still far from being well understood. Little is known about such ordering in nanomaterials and, therefore, the present

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studies reveal new important aspects of this unusual magnetic state in nanocrystalline alloys. ACKNOWLEDGEMENTS This work was partly supported with funds available the European Community programme ICA1-CT-2000-70018 (Center of Excellence CELDIS). Special thanks go to Dr. P. Didukh for carrying out some of the measurements and the numerical fitting. REFERENCES 1. Herzer, G. (1996) J. Magn. Magn. Mater. 158, 133. 2. McHenry, M.E., Willard, M.A., Laughlin, D.E. (1999) Prog. Mater. Sci. 44, 291. 3. Hernando, A. (1999) J. Phys: Cond. Matter 11, 9455. 4. Yoshizawa, Y., Oguma, S., Yamaguchi, K. (1988) J. Appl. Phys. 64, 6044. 5. Suzuki, K., Makino, A., Inoue, A., Masumoto, T. (1991) J. Appl. Phys. 70, 6232. 6. ĝlawska-Waniewska, A., Nowicki, P., Lachowicz, H.K., Goria, P., Barandiaran, J.M., Hernando, A. (1994) Phys. Rev. B 50, 6464. 7. Hernando, A., Kulik, T. (1994) Phys. Rev. B 49, 7064. 8. Suzuki, K., Cadogan, J.M. (1998) Phys. Rev. B 58, 2730. 9. Skorvanek, I., Skwirblies, S., Kötzler, J. (2001) Phys. Rev. B 64, 184437. 10. Suzuki, K., Cadogan, J.M., Cochrane, J.W. (2003) Scripta Mater. 48, 875. 11. ĝlawska-Waniewska, A., Gutowski, M., Lachowicz, H. K., Kulik, T., (1992) Phys. Rev. B 46, 14594. 12. ĝlawska-Waniewska A. (1995) in Nanostr. & Non-Cryst. Materials, M. Vazquez, A. Hernando (eds.) World Sci. Publ., Singapore, p. 495. 13. ĝlawska-Waniewska A., Popáawski, F., Greneche, J.M., Lachowicz, H.K., Inoue, A. (1999) J. Magn. Magn. Mater. 196, 171. 14. ĝlawska-Waniewska, A., Didukh, P., Lachowicz, H.K., Kulik, T. (2000) J. Magn. Magn. Mater. 215, 495. 15. Didukh, P., Nedelko, O., ĝlawska-Waniewska, A. (2002) J. Magn. Magn. Mater. 242, 1077. 16. Didukh, P. (2002) PhD Thesis, Warszawa. 17. Maydosh, J.A., Spin glasses: an experimental introduction (1993) Taylor & Francis, London, p. 203. 18. Kodama, R.H., Berkowitz, A.E., McNiff Jr, E.J., Foner, S. (1996) Phys. Rev. Lett. 77, 394. 19. Bonetti, E., Del Bianco, L., Fiorani, D., Rinaldi, D., Caciuffo, R., Hernando, A. (1999) Phys. Rev. Lett. 83, 2829. 20. ĝlawska-Waniewska, A., Greneche, J.M. (1997) Phys. Rev. B 56, R8491. 21. Gittleman, J.I., Abeles, B., Bozowski, S. (1974) Phys. Rev. B 9, 3891. 22. Chantrel, R.W., Wamsley, N.S., Gore, J., Maylin, M. (1999) J. Appl. Phys. 85, 4340. 23. Kaul, S.N., Siruguri, V., Chandra, G. (1992) Phys. Rev. B 45, 12343. 24. ĝlawska-Waniewska, A., Pont, M., Lazaro, F.J., Garcia, J.L. (1995) J. Magn. Magn. Mater. 140, 453. 25. Restrepo, J., Perez Alcazar, G.A., Gonzalez, J.M. (2000) J. Appl. Phys. 87, 7425. 26. Lähderanta, E., Efimowa, K., Laiho, R., Al. Kanani, H., Booth, J. (1994) J. Magn. Magn. Mater. 130, 23. 27. Anil Kumar, P.S., Joy, P.A., Date, S.K. (1998) J. Phys.: Condes. Matter 10, L487. 28. Kondo, Y., Swieca, K., Pobel, F. (1995) J. Low Temp. Phys. 100, 195. 29. Kisatake, K., Miyazaki, T., Takahashi, M., Maeda, K., Hattoari, T., Matsubara, I. (1986) Phys. Stat. Sol. A 93, 605.

INDUCED ANISOTROPY AND MAGNETIC PROPERTIES AT ELEVATED TEMPERATURES OF Co-SUBSTITUTED FINEMET ALLOYS F. MAZALEYRATa, Z. GERCSIa, b, and L.K. VARGAb a

SATIE, Ecole Normale Supérieure de Cachan 61, avenue du Président Wilson 94235 Cedex, France b RISSPO, Hungarian Academy of Science P.O. Box 49, 1525 Budapest, Hungary Corresponding author: F. Mazaleyrat, e-mail: [email protected] Abstract:

In order to go an insight in the mechanism of induced anisotropy we systematically investigated Fe73.5-xCoxSi13.5Nb3B9Cu1 and Fe78-xCoxSi9Nb3B9Cu1 alloys in a large composition range. The samples were annealed with both longitudinal and transversal fields and tensile stress. The transversal induced anisotropy was measured using usual techniques and we had developed a new method to measure the longitudinal induced anisotropy based on the application of a transversal bias field superimposed to the longitudinal sweeping field. A plotting strategy allows to get rid of the shape effect and finally to measure directly the longitudinal induced anisotropy. The preliminary results show good high temperature properties of Comodified alloys. These experiments clearly show that the annealing temperature has to be chosen as a function of the targeted working temperature. Indeed, the optimal annealing temperature from the room temperature softness point of view (~520°C) does not give sufficient structural stability. If one wants to apply these alloys at high temperature, the annealing must be performed near 600°C in order to stabilize the remaining amorphous phase.

1. INTRODUCTION In the early years after the discovery of FINEMET, various experiments have been conducted with the objective to induce an uniaxial anisotropy ( K U ) in nanocrystalline materials. As it was expected from previous experiments with amorphous materials, longitudinal and transverse anisotropies were successfully induced by longitudinal and transverse field annealing, respectively [1]. G. Herzer has shown that this phenomenon is related to the Fe-Si pair ordering during the crystallization stage [2] although some contribution from the remaining amorphous phase is expected. The amplitude of the induced anisotropy in nanocrystallized FeSiBNbCu alloys is strongly dependent on the 135 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 135–145. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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Si content through the type of long range order in the nanophase. In FINEMET (x = 13.5-16.5 at.%) the ordering into a DO3 structure is determined to magnetic pair ordering which results in a low KU . The possibility of inducing anisotropy by stress annealing was first attested by Glaser [3] and was proved to be transversal and strikingly strong. Some authors have also explained this phenomenon by using quantitative arguments in the frame of Néel's theory [4]. A major objection to this scheme is that such a high induced anisotropy due to magnetic atom pair ordering should be explained only by an uniaxial long range order which is not possible because the DO3 structure is attested. However, a more realistic explanation was given by Herzer [5], who attributes the stress induced anisotropy to a magnetoelastic effect produced by the back stresses exerted by the anelastically deformed amorphous matrix. This elongation of the ribbon is mainly due to the viscous mechanical behaviour of amorphous phase which is in the supercooled liquid state at the annealing temperature (the annealing is performed above the glass transition temperature). It was demonstrated, in effect, a marked slowing down of the elongation at the onset of crystallization [6]. However, in FeZrBCu NANOPERM type materials (in which the magnetostriction coefficient of grains is negative) and FeCoZrBCu HITPERM (in which the magnetostriction coefficient of grains is positive) the stress annealing causes the hysteresis loop to be perfectly rectangular, i.e. KU to be negative [7]. Qualitatively, HITPERM alloys obeys Herzer's rule whereas the back-stress concept is difficult to apply to NANOPERM because pure iron crystals undergo plastic creep while amorphous phase flows. Iron creep is due to the high dislocation mobility from which results its mechanical softness. On the contrary, Fe-Si and Fe-Co are mechanically hard compounds [7]. Independently of the mechanism responsible for KU and its sign, it is generally accepted that thermomechanical treatment was more effective than magnetothermal treatment to induce anisotropy since maximum values of 8000 Jm-3 and 150 Jm-3 are obtained in amorphous and (nano)crystalline materials, respectively. This thinking was recently shaken by Yoshizawa who has recently observed the induced anisotropy as high as 1800 Jm-3 in Fe 8.8 Co 70Si 9 B 9 Nb 2.6 Cu 0.6 by transverse field annealing. This paper aims at comparing the strength of anisotropies induced by stress and field annealing in traditional (13.5 at.% Si) and lower Si content (at. 9%) FINEMET alloys where Fe was partly replaced by Co. A new method developed for the measurement of the anisotropy field in square loop materials is also presented. Finally the high temperature behaviour will be discussed. 2. EXPERIMENTAL TECHNIQUES A series of (Fe1- x Co x ) 73.5 Si13.5 B9 Nb 3Cu 1 alloys, where x = 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.8 were prepared. The alloys were melt-spun in the form of 4 mm-wide 20 μm-thick ribbons. The thermomagnetic curves were recorded by means of a Faraday balance up to 800°C with a heating rate of 10 K/min. In order to precipitate the nanocrystalline phase, the samples were annealed for 1 h at 550°C under Ar atmosphere. The microstructure was checked by X-ray diffraction (XRD) using the Cu radiation. The spectra were fitted using Lorenz and pseudo-Voigt functions for the crystalline and amorphous phases respectively, in order to split the two contributions. The grain size

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was calculated applying Halder-Wagner plot with the computed integral width. The crystallized fraction was deduced from relative intensities of the crystalline (110) and amorphous lines. Further investigations by means of TEM allowed one to visualize the microstructure and to check the size and the dispersion of the nanograins. For comparison, another series of Fe-Co based alloys was cast. The compositions were very close to that investigated by Yoshizawa [8]: (Fe1- x Co x ) 78 Si 9 B9 Nb 2.6 Cu 0.6 with x = 12, 19, 25, 31, 38, 50, 64, 70, 76, 82, 88, 95, 100 and the samples were annealed accordingly at 520°C for 1 h. Uniaxial anisotropy was induced by stress and field annealing. The stress annealing was performed by applying 200 MPa tensile stress on single ribbons during the whole duration of the thermal treatment. The longitudinal field annealing was applied to 1 m single ribbons in order to minimize the demagnetizing factor and the 800 A m-1 dc-field was generated by a solenoid. The transverse field annealing was conducted by placing the furnace in a 25 cm Helmholtz coil set in order to produce a 12 kA m-1 in plane transversal field, homogeneous along the length of the samples.

Figure 1. Crystallization temperatures and Curie points of the Co-doped FINEMET alloys

Figure 2. Saturation magnetization of the amorphous precursor, annealed material and crystals. The latter is deduced from calculations. The induction at 1 kAm-1 is shown for comparison

The specific saturation magnetization was measured in a VSM with a field up to 0.9 T. The saturation magnetostriction was evaluated by means of a Small Angle Magnetization Rotation set-up with a dc-field of 3500 A/m in the as-cast and annealed states. The hysteresis loops where recorded in a single sheet tester at low frequency using a fully digital loop tracer based on a 12 bit oscilloscope. 3. CRYSTALLIZATION, STRUCTURE AND BASIC MAGNETIC PROPERTIES In order to choose the proper annealing treatment of the present alloys, thermo-magnetization measurements were performed. The plots drawn in Fig. 1 show that the crystallization temperature varies little (about 20 K) with the cobalt content. It is remarkable that for x > 20% the crystallization consists in the simultaneous precipitation

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of two phases having a huge difference in Curie point values [9]. This second crystallization temperature can be determined neither from our plots nor by DSC but, as suggested by the Curie points around 720-740°C, the first crystalline phase has a composition nearly independent of that of the amorphous precursor at least while x < 50%. In contrast, the second crystalline phase has a Curie point varying from 800 to almost 900°C as far as it can be linearly extrapolated from the thermomagnetization curves at the power 1/E (with E = 0.36). This suggests that the second crystalline phase is richer in Co, poorer in Si and that its composition depends on the composition of the mother alloy. The XRD patterns show the characteristic lines of bcc-Fe broadened by the small size of crystals. The composition of the bcc-crystals is difficult to evaluate but since the lattice parameter does not vary appreciably in Fe-Co alloys up to 20 at.% of Co [10], the Si content can reasonably be deduced for the low Co concentration range from Fe-Si lattice parameters around 22% (a = 0.2833 nm). The decrease of the lattice parameter (a = 0.2820 for x = 80%) is consistent with the Co enrichment but gives no information on the Si content. As seen in Tab. 1, the estimated crystallized volume shows no clear tendency upon Co considering the accuracy of the method employed. Also the grain size is more or less constant and the standard deviation in Halder-Wagner plot may indicate a broadening of the size distribution as it was confirmed by TEM [145]. The alloy having the same Fe and Co content exhibits two resolved (110) diffraction peaks. Although this diffractogram is very difficult to interpret due to the proximity of the lines, two chemically different phases can be distinguished as it was suspected from thermo-magnetization curves. The larger lattice parameter (0.2853) corresponds to that of FeCo or Fe8Si compounds. Table I. Grain size and crystallized fraction x (%)

50

80

0

10

20

30

40

a (nm)

0.2833

0.2834

0.2835

0.2826

0.2824

DXRD (nm)

12 r 1

14 r 1

12.5 r 1.5

18 r 3

13 r5

13/34

16 r 6

vC (%)

67 r 5

71 r 5

67 r 5

62 r 5

80 r 10

84 r 10

64 r 2

0.2824/ 0.2853 0.2820

As it is well known in Fe-Co based amorphous alloys, the saturation magnetization in the as-cast state continuously decreases with Co content. In contrast, there is a plateau around x = 30% after annealing. Based on the assumption that the magnetization of the amorphous phase remains constant after annealing, the magnetization of the crystalline phase was calculated as J Scr >J SnX  (1  vC ) J Sac @ , where ac, cr and vC denote the as cast and crystals values and the crystallized volume fraction, respectively. Independently of the approximations, a clear maximum of J Scr appears near x = 30% as it is expected from the classical data on Fe-Co alloys (Fig. 2).

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4. MEASUREMENT OF UNIAXIAL ANISOTROPY The transversal induced anisotropy can be evaluated by two different techniques. If the hysteresis loop is linear up to saturation, the magnetization occurs by rotation only and KU can be easily deduced from the area on the left of the loop. A more general method applicable for random easy axis distribution consists in the computation of the second derivative of the return branch of the hysteresis loop [12] and multiplying by the field yields the distribution of anisotropy fields [13]. In the case of longitudinal induced anisotropy, one should take care of the shape anisotropy not to be confused with the induced one. Indeed, traditional methods require samples to be anisotropic or at least square in shape. For this purpose, a method originally proposed by Weber et al. [14] was adapted to long samples. The ac-field (H) is applied along the longitudinal easy axis and the magnetization is measured within the same direction. When the transversal bias field (HB) is applied, the hysteresis loop is flattened until a critical value at which the magnetization switch is shifted at H S r H C (see Fig. 3). When two perpendicular fields are applied and the easy axis is parallel to the measurement direction, the total magnetic energy is: E (M )

KU sin 2 M  P 0 M S H cos M  P 0 M S H A sin M

(1)

where M is the angle between the magnetization and the measurement direction. The magnetization has 3 stable positions of the magnetization M = 0 and M = S/2 and the switch from one to another (at H H S ) occurs when: E (0)

P0 M S H

E (S / 2)

KU  P 0 M S H A

For a constant H A the anisotropy constant is: KU sotropy field is: H K 2( H S  H A )

(2)

P 0 M S ( H S  H A ) and the ani(3)

Figure 3. The shape of the hysteresis cycle as Figure 4. Sketch of the two experimental a function of increasing bias current at constant set-up. 50 cm solenoid +30 cm Helmoltz maximum sweeping field coils (a) and two perpendicular silicon steel yokes (b)

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For long samples, the longitudinal field is equal to the applied one because the demagnetizing factor is negligible and the perpendicular inner field is H A H B  N A M A . For

H < HS, the material is perpendicularly saturated and the loop is linear so that M A FHB and HK

2>H S  (1  N A F H B )@ 2( H S  D H B )

(4)

The parameter D is highly dependent on the demagnetizing factor and the rotational susceptibility which are difficult to determine. To escape this difficulty, several hysteresis loops are recorded with various values of the biasing field and HS is plotted as a function of HB . According to (4) H S is found by extrapolation at H B 0 , so H K 2 H S (0).

Figure 5 . Loops recorded with constant bias Figure 6. The switching fields plotted as a field and varying maximum sweep field. function of a bias current field for selected materials

The experimental set-up is composed of a solenoid generating the longitudinal ac-field, in the middle of which the sensing coil and the sample are positioned, and a perpendicular Helmholtz coils set (Fig. 4a). This coils set is about 35 kg and HB = 12 kA m-1 is not sufficient for all the samples. Another set-up composed of two perpendicular iron yokes in which HB can reach 100 kAm-1 is also employed (Figure 4b). In this case, the perpendicular field at a given position is H A v nI B /d , where n and d are the turns number and air gap length, respectively. Equation (4) becomes H K 2( H S  D ' H B ), where again the knowledge of D’ is not necessary. A first important point is to verify the independence of HS upon the maximum sweeping field Hmax in particular if the sample is not fully saturated. For this purpose, several loops were recorded with a constant HB and varying Hmax (see Fig. 5). HS was proved to be independent of Hmax if the latter was sufficient to produce the switching of the magnetization. This problem is important because for large HB the samples are not saturated as illustrated in Fig. 5. From these split loops, the values of HS are extracted and plotted as a function of bias current IB v HB in Fig. 6. The perfect alignment of points allows an accurate extrapolation to zero which gives the values of HK by a mean least squares linear fit with a remarkably low standard deviation.

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5. UNIAXIAL INDUCED ANISOTROPY Table II summarizes the HK and KU values of selected materials. The coercive fields are also reported. It is to notice that there is no clear relationship between the magnitude of the anisotropy fields and the coercivity of different materials. For instance, the results obtained with Fe-Co based nanocrystalline alloys suggest that the coercivity is basically linked to the magnetization process (rotation or domain wall displacement) and weakly to the magnitude of induced anisotropy. Table II. Anisotropy fields measured by the presented in this paper (KU < 0) and other (KU > 0) techniques JS (T) 1.24

KU (Jm-3) -41 r 3

-68 r 3

1.16

-40 r 2

8.4

Long. H

-158 r 15

1.16

-92 r 1

8.0

(Fe0.9Co0.1 )73.5 Si13.5B9 Nb3Cu1

Stress

+331 r 15

1.16

+192 r 10

13.5

(Fe0.9Co0.1 )73.5 Si13.5B9 Nb3Cu1

Transv. H

+40 r 4

1.16

+23 r 2

5.8

Material Fe 73.5Si13.5 B9 Nb

Annealing Long. H

(Fe0.9Co0.1)73.5Si13.5B9 Nb3Cu1

No field

(Fe0.9Co0.1 )73.5 Si13.5B9 Nb3Cu1

HK (Am-1) -66 r 5

HC (Am-1) 5.5

The original FINEMET composition exhibits a slightly higher value of KU (41 Jm-3) compared to transverse field annealing (10-20 Jm-3) [2], which can be explained by the shape anisotropy contribution. Relatively large KU were induced in the Co doped alloys as expected in an earlier work [8]. It is however noticeable that only the samples with x = 0, 10, 20, 30 and 80 were sensitive to the longitudinal field annealing. The reasons of this will be discussed below. A surprising effect is the notable long range uniaxial anisotropy of Co-doped sample annealed without field showing a value comparable to that of field annealed FINEMET sample. This “self-induced” anisotropy is of great importance in the theory of random anisotropy model proposed by Suzuki et al. [15]. Indeed the change from the classical D6 dependence of the coercive field to a D3 law for some alloys (e.g. NANOPERM) was explained by the introduction of a long range KU in the model which had never been directly measured. Concerning the origin of this self-induced anisotropy two explanations are possible. A first one would involve the magnetoelastic origin linked to the different thermal dilatation coefficients of both amorphous and crystalline phases but it should be a priori a short range contribution subject to the averaging out. Another explanation would be the self magnetic field annealing in the region of large domains persisting at the temperature of nanocrystallization [16] specially in the case of Co-doped samples with high magnetization at high temperature [11]. It is worth noticing that this effect is missing with FINEMET because the Fe-Si crystallites are in the super-paramagnetic phase during annealing [17]. 5.1. Field induced anisotropy In Figure 7, the transverse field annealed samples having Co content less than x = 30% show very similar values compared to the samples annealed in the longitudinal

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field. In fact these values are systematically 10-20 J m-3 smaller (with opposite sign) probably due to a shape contribution. Above 20%, KU increases quite rapidly and decreases again at 80%. This situation is quite surprising compared to the results of

Figure 7. The field and stress induced anisotropy as a function of Co content in (Fe1- x Co x ) 73.5 Si13.5 B 9 Nb 3 Cu 1 alloys

Figure 8. Comparison between the field induced anisotropy in 13.5% Si, 9% Si FINEMET (open symbols) and similar alloy in [8] (full symbols)

Yoshizawa. In spite of a markedly different composition we should expect a similar behaviour in the whole compositional range and not only in the low concentration range (see Fig. 8). In order to check this, we used a series of transverse field annealed alloys with a very similar composition to that of Yoshizawa and his results were recovered only in 50%. The huge difference between our measurements and Yoshizawa's is undoubtedly explained by the inadequate intensity of applied field. In order to be effective, the field applied during annealing must exceed NMS (TA) the demagnetizing field at the annealing temperature, a value which is easily reached in the case of low Co samples having a Curie point close to the annealing temperature. This explains why much smaller fields are necessary for longitudinal field annealing ( N A | 10 2...10 3 , N II 10 7 ). Indeed, it is clear that the samples with high magnetization and Curie point ( x t 50%) are less sensitive to field annealing. 5.2. Stress induced anisotropy The substitution of cobalt rapidly diminishes the value of the stress induced transverse anisotropy which drops to zero at x = 20%. Higher Co concentrations exhibit rather low longitudinal KU up to at least 50% whereas the anisotropy becomes transversal again for the sample having x = 80%. According to Herzer, the stress induced anisotropy is correlated to the magnetostriction coefficient of the nanocrystals (OScr ) but in this case, it is extremely difficult to evaluate. First, the magnetostriction of the as-cast material O Sac was measured and it was found to decrease continuously with increasing Co content. This was not expected since a low Co substitution in Fe-based amorphous alloys usually yields a sensitive enhancement of OSac . This may be due to a lack of saturation in the measurement process or to the effect of Nb which modifies the magnetostrictive behaviour even at low concentrations. Second, the coefficients of

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the nanocrystallized samples OSnX were measured, and OScr was calculated by O Scr >O SnX  (1  vC )O Sac @ which has to be taken only as a tendency. After comparison with KU reduced to the applied stress, 3K U / 2V , one can observe in Fig. 9 that the correlation is found quantitatively only for x = 0 and 10% and qualitatively up to 50%. The low level of longitudinal anisotropy (x = 30 to 50) may be explained by the mechanical behaviour of the sample measured during annealing: above the glass transition temperature, the amorphous material extends by a viscous flow process up to the crystallization temperature at which the process is practically stopped due to the smaller fraction of amorphous component and its compositional change. From the plot of 'L / L in Fig. 10, it is clear that the elongation of the ribbons drops when Co is added which

Figure 9. Magnetostriction coefficients compared to the reduced anisotropy and the elongation produced by stress annealing

Figure 10. In-situ measurement of the elongation of ribbons during stress annealing

probably partly explains the phenomenon. It is however difficult to explain the positive KU found for x = 80% since a negative magnetostriction is not expected in this compositional range. 6. HIGH TEMPERATURE BEHAVIOUR The high temperature measurements were conducted with various samples. The discussion will be restricted to samples having x = 0 and 30% the latter showing an interesting behaviour. The high temperature of FINEMET has been extensively studied and one the most important figures is the so called decoupling temperature at which the random anisotropy is destroyed as revealed by the strong enhancement of the coercive field. This decoupling temperature is not dependent on the annealing condition (i.e. vC ) since it remains about 600 K (330°C) [17]. This remark is not valid for the sample annealed at 625°C, for which the minimum in HC is due to the anisotropy compensation of Fe2B (see also [18]). Concerning the Co-doped alloy, the decoupling temperature is the same for a sample annealed between 500 and 550°C (see Fig. 11). In contrast, annealing the same alloy at 600°C shifts this decoupling temperature to 900 K (~630°C). This shift of the decoupling temperature cannot be explained by such an enhancement of the amorphous phase Curie point. In fact, the amorphous reminder represents probably a relatively low fraction that would be still polarized by the high

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induction of the Fe-Co-Si crystallites (~0.4 T at 600°C). In addition, this “over-annealing” improves the structural stability which is crucial for high temperature devices. As

Figure 11. Temperature dependence of induction and coercive field for Co containing and Co free FINEMET-type samples annealed at various temperatures. Left x = 30%, right x = 0

a consequence, the Co-substituted alloys must be annealed at a higher temperature than that corresponding to the room temperature optimum if applied in high temperature devices. 7. CONCLUSIONS Methods for measurements of transverse and longitudinal anisotropy induced by field or stress annealing have been presented and the ability of various alloys to have their hysteresis loops tailored has been checked. These induced anisotropies have been measured in a wide range of Co content in two FINEMET type alloys having 9 and 13.5 at.% of Si. In contrast to the crystalline and amorphous materials the highest field induced anisotropy has not been found for equal quantity of Fe and Co. This contradiction with atom pair ordering theory should be explained by the presence of a third element (Si) besides Fe and Co in the nanoparticles. The high ability to field annealing of the sample with lower Si content might be explained by its chemically disordered bcc-structure which is more suitable for pair ordering than the rigid DO3 structure, the latter being imposed by the larger Si concentration (15-25%) in nanocrystals. This ability to show induced anisotropy is, however, paid by lower magnetic softness (i.e. HC is 1 or 2 orders of magnitude higher compared to high Si content FINEMET) which may impede the high frequency applications. The convenient ability of FINEMET to show very large stress induced anisotropy is destroyed by Co substitution to Fe. This behaviour can be understood within the back stress theory by the change in the sign of magnetostriction coefficient as a function of Co content. The addition of Co is motivated by the increase in the working temperature by 100°C provided by the increase in Curie temperature of the amorphous matrix and the stronger coupling between grains due to the higher saturation magnetization of crystallites. The interpretation of the above experimental statements, however, must remain very careful. Indeed, very little is known about the composition of the nanocrystallites and a fortiori about their intrinsic properties. For this reason, similar work has to be conducted

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in Si free nanocrystalline systems. In spite of worse soft magnetic properties, the intrinsic magnetic parameters of Co-Fe crystallites are well known and will simplify interpretation of the observed phenomena. REFERENCES 1. 2. 3.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18.

Yoshizawa, Y., Yamaguchi, K., (1989) Effect of magnetic field annealing on magnetic properties in ultrafine crystalline Fe-Cu-Nb-Si-B, IEEE Trans. Magn. 25, 3324-26. Herzer, G., (1994) Magnetic field induced anisotropy in nanocrystalline Fe-Cu-Nb-Si-B, J. Magn. Magn. Mat. 133, 248-250. Glaser, A.A., Kleynerman, N.M., Lukshina, V.A., Patapov, A.P., Serikov, V.V., (1991) Thermomechanical treatment of nanocrystalline alloy Fe-Cu-Nb-Si-B, Phys. Met. Metal. 72, 719-724. Hofmann, B., Krönmuller H., (1995) Creep induced magnetic anisotropy in Fe-Cu-Nb-Si-B, Nanostruct. Mat. 6, 961-964. Herzer, G., (1994) Creep induced magnetic anisotropy in nanocrystalline Fe-Cu-Nb-Si-B, IEEE Trans. Magn. 30, 4800-02. Mazaleyrat, F., Faugières, J.C., Rialland, J.F., (1998) High temperature behaviour of stress annealed anisotropy nanocrystalline Fe-Cu-Nb-Si-B, J. Phys. IV France 8, 159-162. Varga, L.K., Gersci, Z., Kovacs G., Kakay, A., Mazaleyrat, F., (2003) Stress induced magnetic anisotropy nanocrystalline alloys, J. Magn. Magn. Mat. 254-255, 477-479. Yoshizawa, Y., Fujii, S., Ping, D.H., Hono, K., (2003) Magnetic properties of nanocrystalline FeMCuNbSiB (M: Co, Ni), Scripta Mater. 48, 863-868. Conde, C.F., Conde, A., (1998) Crystallization behaviour of (Fe, Co)SiB-CuNb, Mat. Sci. Forum 269-272, 719-724. Bozorth, R.M., (1951) Ferromagnetism, fac-simile reissue, IEEE Press, New York. The lattice parameters given in Bozorth are actually in KX and not Å (aÅ = 1.00202 aKx) Gersci, Z., Mazaleyrat, F., Ferenc, J., Kulik, T., Varga, L.K., (2003) Mat. Sci. Eng. A, in press. Asti, G., Rinaldi, S., (1972) Nonanalycity of the magnetization curve, Phys. Rev. 28, 1584-86. Barandiaran, M., Hernando, A., Vazquez, M., Gonzalez, J., Rivero, G., (1989) IEEE Trans. Magn. 25, 3330-32. Weber, W., Allenspach, R., Bischof, A., (1997) Determining magnetic anisotropies from hysteresis loop, Appl. Phys. Lett. 70, 520-522. Suzuki, K., Herzer, G., Cadogan, J.M., (1998) The effect of coherent uniaxial anisotropies on the grain size dependence of coercivity in nanocrystalline soft magnetic alloys, J. Magn. Magn. Mat. 177, 949-950. Herzer, G., private communication. Mazaleyrat, F., Varga, L.K., (2001) Magnetic transitions in two-phase nanocrystalline materials, IEEE Trans. Magn. 37, 2232-35. Herzer, G., (2005) The random anisotropy model: a critical review and update, in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 15-34.

STRUCTURE AND MAGNETIC PROPERTIES OF THE Fe-Cu-Nb-Si-B POWDER PREPARED BY MILLING P. KOLLÁRa, E. FECHOVÁa, J. FÜZERa, J. KOVÁýb, P. PETROVIýa, V. KAVEýANSKÝb, and M. KONýa a Institute of Physics, Faculty of Sciences, P. J. Šafárik University Park Angelinum 9, 041 54 Košice, Slovakia b Institute of Experimental Physics, Slovak Academy of Sciences Watsonova 47, 043 53 Košice, Slovakia

Corresponding author: P. Kollar, e-mail: [email protected] Abstract:

We have studied the influence of milling on the structure and magnetic properties of Fe73.5Cu1Nb3Si13.5B9 powder prepared in a vibratory micro-mill as a function of a long the milling time. Three powder samples were prepared and investigated (one prepared by the milling of an amorphous ribbon, one by the milling of the same ribbon in a partially nanocrystallized state and one by the milling of pure elements). The structural analysis showed a decrease in the grain size with the increasing time of milling. The average grain size was found to be in the range from about 8 Pm after 200 hours of milling down to below 1 Pm after 1700 hours. The coercivity of the samples prepared from pure elements increased almost linearly up to 1700 hours of milling while further milling lead to the saturation at 25 kA/m (at the milling time of 3500 hours). The coercivity of the samples milled from ribbons increased to its maximum of 8 kA/m for the milling time of 800 hours and then decreased.

1. INTRODUCTION An important group of soft magnetic materials is that consisting of nanocrystallites randomly nucleated in a soft amorphous matrix. This kind of soft two-phase materials can be obtained by the crystallization of conventional Fe-Si-B amorphous alloys with a small addition of Cu and Nb [1-3]. A well-established example is the alloy of chemical composition Fe73.5Cu1Nb3Si13.5B9 also called FINEMET. The FINEMET alloys are prepared in the form of ribbons by the melt-spinning technique followed by annealing at elevated temperatures in an Ar protective atmosphere to achieve a nanocrystalline structure. Unfortunately, nanocrystalline ribbons prepared by partial crystallization are very brittle, restricting their possible applications. Therefore it is logical to attempt to prepare such material in a more ,,bulk“ form, for example in the form of a cylinder or a ring, which would be more convenient for industrial applications. One of the methods 147 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 147–155. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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of preparing material in bulk is to compact the powder [4]. The preparation method and further processing of the powder determines its structure and magnetic properties [5, 6]. To obtain material with suitable magnetic properties it is necessary to know the influence of the milling time on the structure of powders. The scope of the present work is to investigate the structure and magnetic properties of FINEMET-type powder material prepared by a long-time mechanical milling and alloying in a vibratory micro-mill. 2. EXPERIMENTAL Three different samples with the same chemical composition of Fe73.5Cu1Nb3Si13.5B9 have been prepared and investigated. The first sample (sample I) was prepared by the milling of an amorphous ribbon prepared by the rapid quenching method, the second one (sample II) by milling the ribbon in a partially nanocrystalline state (ribbon annealed at 530oC for 1 hour in an argon protective atmosphere) and the third sample (sample III) was prepared by the milling of the appropriate amounts of Fe, Cu, Nb, Si, and B in a powder form in order to obtain the Fe73.5Cu1Nb3Si13.5B9 alloy. The milling procedure of the powder was performed in an argon protective atmosphere. The mechanical alloying was carried out in a hardened-steel mortar (inner diameter 9.3 cm) of a vibratory micro-mill Pulverisette 0, Fritsch, for 1700 hours (sample I and sample II) and for 3500 hours (sample III). The milling procedure was interrupted every 20 hours (up to 200 hours), then every 40 hours (up to 1700 hours) and then every 100 hours (up to 3500 hours of milling) to remove a part of the milled powder for further investigations. The crystallographic structure of the powders was observed by an X-ray diffractometer HZG 4/A using filtered Co-KD1,2 radiation (O = 0.17902 nm). The magnetic moment and coercivity of the powder at room temperature in a magnetic field of 0.6 T were measured by a vibrating sample magnetometer (VSM) as a function of the milling time. The dependence of the magnetic moment on the temperature (thermomagnetic curves) was measured in the constant magnetic field 300 mT in the temperature range 20-800oC. The heating and cooling rate was 10 K/min. Zero field and field cooling measurements were performed by VSM at constant magnetic field of 10 mT. The room temperature transmission Mössbauer spectra (using a conventional spectrometer with 57 Co/Rh J-source) were taken into 500 channels in a constant acceleration mode. The velocity scale r8 mm/s was calibrated by the natural D-Fe. The spectra were processed by the non-linear least-squares method. 3. RESULTS AND DISCUSSION We have found that the structure and magnetic properties of powder significantly depend on the milling time. The grain size decreases with the increasing of the milling time and produced particles are in such a wide range of sizes, that they cannot be observed by a single method. So we had to observe particles with a diameter of less than 200 nm by TEM and larger particles by SEM. The milling of sample I, which was amorphous and thus very elastic, was initially progressing very slowly, and the milling process became gradually more effective only after parts a greater of number of ribbon had become nanocrystalline [7]. Sample II was

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in a partially nanocrystalline state, so it was very brittle and thus the milling process was effective from its very beginning. In both samples the homogeneous distribution of small particles (of about 20 nm) was observed after 200 hours of milling. It was impossible to analyse sample III by TEM for milling times up to 200 hours due to a large diameter of Fe and Nb powders [7, 8]. The X-ray diffractograms (Fig. 1) document the crystallization process of the amorphous sample as well as the formation of the iron oxide (hematite-Fe2O3) phase as a result of longer milling (1700 hours), manifested in the appearance of the broad diffraction peak at about 38.5º, the shape of background and noise level. X-ray diffractograms of sample II are not shown here since they are similar to the diffractograms of sample I. X-ray patterns of sample III (Fig. 2) were fitted by means of the LeBail Rietveld crystal structure refinement method using GSAS software package [9]. The sample in the as-mixed state (Fig. 2a) was found to consist of D-Fe, Cu, Nb and Si phases (marked in Fig. 2a from down up). Boron is too light to be successfully detected by X-ray diffraction techniques. After a longer milling time an increase in the Fe2O3 (hematite) phase contribution as well as in the density of lattice distortions were documented (Fig. 2b, c). We would like to mention that the amount of the hematite phase, detected by the X-ray method, is very small (this phase is present only on the surface of the particles), and no ferrous oxide was detected.

Figure 1. X-ray diffractograms of sample I for different milling times

For the quantitative description of the real structure of the samples, the angular period of the pattern with the most resolved diffraction peak of the D-Fe phase (at about 2ș = 52º) was chosen. A profile analysis of the peak was performed using the fitting procedure which enabled us to determine numerical values of the parameters describing the diffraction peak shape, i.e. fwhm – the full width at half maximum, ȕ – the integral width of the peak, ȕC and ȕG – Cauchy and Gaussian components contributions to the integral width. Assuming that the influence of small average dimensions of coherent regions preferably influences the Cauchy component ȕC while the increasing of lattice distortions density causes growing of the Gaussian part ȕG, the dependence of the structural parameters on the milling process could be quantified (Table III) [10]. D is the average linear dimension of the coherent region (it is smaller than the average grain size determined by electron microscopy as the individual grains consist of more subgrains of which each shows a coherent crystal structure) and e

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represents a relative microscopical deformation (e = $d/d, where $d is the halfwidth of the distribution function of interplanar spacing d within a grain for a given set of plains {hkl}). The preliminary instrumental broadening correction was performed using the profile parameters taken for pure -Fe powder with sufficiently large coherent regions and a small density of lattice distortions, so the effect of the standard powder sample broadening could be neglected.

Figure 2. X-ray diffractograms of sample III for different milling times. The observed data are indicated by crosses and the calculated ones by the solid line. The positions of all possible Bragg reflections for all phases are indicated by the vertical marks in the middle while the lower curve shows the difference between the observed and calculated diffraction patterns

Table I. Resulting profile parameters for the -Fe (110) peak of sample III milling [h] as mixed 1700 3500

fwhm [2Q ] 0.12 0.80 0.83

[2 Q] 0.16 1.05 1.12

[2 Q] 0.09 0.60 0.65

G

C [2

Q]

0.09 0.63 0.68

D [nm] 220 40 30

e [10 3] 45 300 320

The coercivity of samples I and II increases up to 800 hours of milling, Fig. 3. This is caused by the decrease in the powder size, and the magnetization process is realised more and more by the rotation of magnetization vectors (the domain wall motion becomes less significant). The theoretical value of the maximum coercivity caused by the magnetocrystalline anisotropy of a single domain particle, magnetized by the rotation of the magnetization vector only, is Hc = 2K1/IS. If we assume that FeSi grains in a FINEMET type alloy typically contain 20 at.% Si, we obtain Hc = 10 kA/m (the constant of magnetocrystalline anisotropy is K1 = 8000 J/m3 and the spontaneous magnetic polarization is Is = 1.6 T) [11]. The coercivity dependence reaches its maximum at approximately this value, confirming that the powder consists of single domain particles. The coercivity of sample III increases with the increase in the milling time up to 1700 hours almost linearly and further milling leads (at 3500 hours) to the saturation at about 25 kA/m. We do not see here the maximum coercivity as in

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the case of milled amorphous and nanocrystalline ribbons [12]. Such a behaviour is maybe caused by the imperfect alloying of powders and by additional stress anisotropy. Magnetic moments of the samples measured at room temperature are shown in Fig. 4.

Figure 3. Coercivity as a function of the milling time for sample I, sample II and sample III

Figure 4. Magnetic moment dependence on the milling time for samples I, II and III

The magnetic moment of the samples prepared in the form of ribbons (sample I and II) decreases very slowly as a function of milling time up to 600 hours. Then it decreases significantly up to 1100 hours and then it decreases slowly. Sample I is more resistant to the milling because it is in an amorphous state and thus its magnetization begins to decrease only later in the process of milling. The magnetic moment of sample III decreases monotonously with the milling time, which is probably caused by the alloying of the elements without the magnetic moment with iron, by the decrease of the powder size and by the increase in the amount of the superparamagnetic phase. Figure 5 shows temperature dependence of the magnetic moment (zero field cooling and field cooling at 10 mT) for the sample I milled for various milling times.

Figure 5. Magnetic moment dependence on temperature for the sample I (milled for 100 h, 980 h and 1700 h) after field cooling (FC) and zero field cooling (ZFC). Measured at the magnetic field of 10 mT. TB is the blocking temperature

The decrease of the magnetic moment after zero field cooling shows the contribution of superparamagnetic particles to the total magnetic moment. The blocking temperature (superparamagnetic particle becomes ferromagnetic) decreases significantly with the milling time, which corresponds to the decrease in the particle size.

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Figure 6. Thermomagnetic curves in selected stages of milling of the sample I (a) and sample III (b) (heating rate: 10 K/min)

Figure 6a shows thermomagnetic curves of powder sample I for selected stages of the milling process. Thermomagnetic curves of powder sample II are similar to those of sample I. The magnetic moment decreases with the increase in the temperature up to the Curie point of the amorphous phase (TCam). The decrease of this point with the increasing milling time is caused by the increase of metalloids concentration in the amorphous phase. The crystallization process starts at approximately 520oC (TCR). However, the magnetic moment of both samples is not zero even between TCam and TCR and that is why we assume that the samples contain a small amount of the crystalline phases (with Curie a temperature higher than TCam). The presence of another crystalline phase is visible above 650oC. Figure 6b presents a set of thermomagnetic curves measured after different times of milling of sample III. On the sample milled for 500 hours a small increase in the magnetic moment is already observed at a temperature of about 530oC. With the prolongation of the milling time the linear decrease of the magnetic moment in the temperature range 180-530oC becomes more and more pronounced. We suppose that this decrease corresponds to the creation of a disordered intergranular phase during the milling. This phase recrystallizes into the D-Fe(Si) phase at higher temperatures and its contribution to the total magnetic moment can be seen in the temperature range between 600 and 700oC. The final decrease above 750oC represents the ferroparamagnetic transformation of the D-Fe(Si) phase. The temperature of this transformation decreases with the milling time from 766oC after 20 hours down to 746oC after 1500 hours. Further milling increases this value again up to 757oC after 3500 hours of milling. These variations suggest the changes of the Si content in the D-Fe(Si) phase generated during the milling process, from 0 to about 6 at.% of Si. In Figure 7 we see the evolution of Mössbauer spectra of sample I as a function of the milling time. Mössbauer spectra of sample II are similar to the spectra of the sample I.

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Figure 7. The evolution of the room temperature Mössbauer spectra as a function of the milling time of sample I

The coexistence of two phases in sample I and II was confirmed by Mössbauer spectroscopy investigations. The first phase, characterized by a magnetic dipole interaction, contributed to the spectrum with one sharp sextet of D-Fe and one broadened sextet with distributed hyperfine magnetic field. The distributed sextet represents different nearest surroundings of Fe-atoms, grain boundaries, intergranular and amorphous matrix. This phase represents a substantial part of the sample at the beginning of the milling and its fraction slowly decreases with the milling time. The fraction of the second phase, with superparamagnetic behaviour, characterized by a collapsed hyperfine magnetic field, increases with the milling time. The influence of the ferromagnetic phase seen as a sextet prevails up to 660 hours of milling. Above 1020 hours of milling a typical doublet of superparamagnetic phase particles is seen. Between 660 and 1020 hours of the milling the spectrum is a combination of the spectra of both phases [12]. The coexistence of the three phases containing Fe in the investigated sample III was confirmed by the room temperature 57Fe-transmission Mössbauer spectroscopy measurements. In Fig. 8 we can see the evolution of Mössbauer spectra of sample III as a function of the milling time. The sharp sextet line with the hyperfine magnetic field (HMF) induction of 33 T corresponds to the magnetic dipole interaction in ferromagnetic D-Fe crystalline grains. A relative amount of this phase decreases with the time of milling. The distributed

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sextet line of HMF corresponds to the grain boundaries and the intergranular phase. HMF distribution indicates the existence of two different surroundings of Fe-atoms:

Figure 8. The evolution of the room temperature Mössbauer spectra as a function of the milling timeof sample III

Fe-rich and Fe-poor parts, with approximately the same occurrence probability. However, Fe-poor part is overlapped by the smooth broadened doublet line in longermilled samples. The smooth broadened doublet line represents superparamagnetic behaviour of small particles characterized by collapsed HMF. After 2500 hours of milling it becomes the dominant feature of the spectra [8].

4. CONCLUSIONS The influence of the milling on the structure and magnetic properties of powder FINEMET-type material as a function of the milling time has been investigated. The results show that the structure and magnetic properties depend significantly on milling time. A study of the structure and magnetic properties allows us to conclude that: The milling of sample I (an amorphous ribbon, very elastic) initially proceeds very slowly. The milling of sample II (partially in a nanocrystalline state) is more effective due to the presence of the nanocrystalline phase. The milling of ribbons (sample I and sample II) leads to a single domain particle powder, which can be magnetized by magnetization vector rotation only. The coercivity Hc of this FINEMET type powder reaches the value 10 kA/m and then decreases with

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the milling time. The coercivity of sample III (prepared by the milling of pure elements) increases with the increase in the milling time up to 1700 hours almost linearly and further milling leads at 3500 hours to the saturation at 25 kA/m. The magnetic moment of the samples decreases monotonously with the milling time. This decrease is connected with the decrease in the powder size and the increase in the amount of the superparamagnetic phase detected by the temperature dependence of the magnetic moment measurement of field and zero field cooled samples. Thermomagnetic curves indicate a creation of a disordered inter-granular phase during the milling process and its subsequent crystallization. We can conclude that a shorter milling time is more suitable for the preparation of compacted-powder samples exhibiting soft magnetic properties. ACKNOWLEDGEMENTS

This work was supported by VEGA projects. We thank Mr. R. Mlýnek for helpful discussions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12.

Yoshizawa, Y., Oguma, S., and Yamauchi, K. (1988) J. Appl. Phys. 64, 6044. Herzer, G., (1989) IEEE Trans. Magn. 25, 3327. Yoshizawa ,Y. and Yamauchi, K., (1990) Mater. Trans. Jpn. Int. Metals 31, 307. Heczko, O. and Ruuskanen, P., (1993) Key Engin. Mat. 81-83, 195. Xu, H., He, K.Y., Qiu, Y.Q., Wang, Z.J., Feng, W., Dong, Y.D., Xiao, X.S., and Wang, Q., (2000) Mat. Sci. Eng. A, 286, 197. Chiriac, H., Moga, A.E., Urse, M., and Necula, F., (1999) Nanostrust. Mater. 12, 495. Sovák, P., Fechová, E., Kollár, P., Kaveþanský, V., and HorĖák, P., (2002) phys. stat. sol. (a) 189, 747-751. Kováþ J., Petroviþ, P., Fechová, E., Füzer, J., and Kollár, P., (2002) phys. stat. sol. (a) 189, 859-863. Larson, A.C. and Von Dreele, R.B., GSAS – Generalised Structure Analysis System, Tech. Rep. LAUR-86-748, Los Alamos National laboratory, Los Alamos NM-87545 (1990), Copyright 1985-2000, The Regents of the University of California, (2001). de Keiser, Th.H., Langford, J.I., Mittemeijer, E.J., and Vogels, A.B.P., (1982) J. Appl. Cryst. 15, 308-314. Herzer, G., (1993) Physica Scripta T49, 307. Fechová, E., Kováþ, J., Kollár, P., Füzer, J., and Konþ, M., (2001) J. Metast. Nanocr. Mat. 10, 577.

MAGNETIC DECOUPLING IN SOFT MAGNETIC NANOCRYSTALLINE ALLOYS

L.K. VARGAa and F. MAZALEYRATb a

Research Institute for Solid State Physics and Optics 1525 Budapest, P.O. Box 49, Hungary b SATIE, Ecole Normale Supérieure de Cachan 61, avenue du Président Wilson 94235 Cedex, France Corressponding author: L.K. Varga, e-mail: [email protected] Abstract:

For proper description of magnetic decoupling in two phase nanocrystalline alloys two modifications have been introduced in the Herzer model: the role of the shape anisotropy besides the crystalline anisotropy of nanoparticles and the contribution of the dipolar superferromagnetism to the average stiffness constant.

1. INTRODUCTION Nanocrystalline alloys (FINEMET [1] and NANOPERM [2] and their Co-doped derivatives [3, 4] are usually prepared by partial crystallization of an amorphous precursor developing excellent soft magnetic properties. This magnetic softness has been explained in terms of a reduction in the fluctuation of the magnetic anisotropy due to exchange coupling between randomly oriented nanograins mediated by the residual amorphous matrix [5, 6]. There is a temperature limit in these two-phase nanocrystalline soft magnetic alloys above which the nanograins become magnetically decoupled and the exchange softening is no more effective. This decoupling temperature TD is usually taken as the Curie temperature of the weakest link, the amorphous phase, although the expected composition of the residual amorphous phase provides a Curie temperature TCam much below that of the experimental found TD [7]. Actually, the residual intergranular amorphous phase has diffusion controlled variable composition with a corresponding distribution of its TC, which makes the assumption of a simple phase transition too simplistic. To account for the experimentally found higher decoupling temperature one must assume an intense internal field in

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the intergranular region originating both from exchange penetration [8] and dipolar fields of the neighbouring crystalline phases. The actual decoupling temperature can be determined from the behaviour of the hysteresis parameters as a function of temperature. The quantitative prediction of these temperature dependencies is a difficult task. The tendencies can be described qualitatively with the simple random anisotropy model of Herzer [5, 6] giving the effective anisotropy as

K!

x2

K14 D 6 , A3

(1)

where x is the volume fraction of the crystalline phase, K1 is the original anisotropy of the bulk crystalline phase, D is the diameter of the crystalline nanoparticle and A is the exchange stiffness constant. At the decoupling, the effective starts to increase due to the strong decrease in the exchange interaction A. The consequence is that the permeability is strongly reduced, the coercivity is strongly increased and the remanence ratio increases from the uniaxial induced anisotropy (Ku) governed low temperature value to high values, near 0.83 (cubic crystalline symmetry), after decoupling, where large dominates over Ku. Quantitatively however, the simple Herzer model and its improvement by Suzuki [9] predict an infinite increase of effective anisotropy and hence of the coercivity, which is in contradiction with the experiment. Moreover, the experimental Hc values are about two orders of magnitude lower than theoretical Hc values predicted in the StonerWohlfarth model for randomly oriented noninteracting particles. The situation is as if further averaging of anisotropy still persisted over the exchange decoupling which suppresses the effective anisotropy at high temperatures. The simple dipolar coupling of otherwise superparamagnetic particles is able to account for the values of otherwise superparamagnetic transition temperatures as it was shown by Herzer [6]. The quantitative evaluation of the coercivity upraise at decoupling, however, is still missing. In order to describe the temperature region between the decoupling temperature, TD, and superparamagnetic transition tempearure, Tsp, (the so called “superferromagnetic” region) we are going to use the concept of dipolar superferromagnetism [10], which takes over the role of the exchange in coupling the nanoparticles above the Curie temperature of the interphase region. Just as the exchange couples moments from one region to another, so does the dipolar coupling between particles. It acts as a spring to impose magnetic alignment between two particles whose magnetization lies along the direction from one particle to another. In this paper we present a modified Herzer model including besides this dipolar coupling a shape anisotropy term, which becomes important around and above the decoupling temperature. These modifications will be useful in describing the temperature dependence of coercive field above TCam and below the superparamagnetic transition temperature (Tsp).

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2. EXPERIMENTAL The ribbon samples a 4 mm wide and 20-25 Pm thick were prepared by melt spinning in a partial vacuum under H2 protective atmosphere. The annealing was performed in situ in the measuring head of the hysteresis loop tracer under Ar protection. The hysteresis loop tracer was a home-built piece of equipment based on a storage oscilloscope. The exciting current (10 Hz, up to 100 A) was applied to a copper rod placed in the center of the toroidal sample. The hysteresis loop was registered at each 5 degrees of increasing temperature with a heating and cooling rate of 7 K/min. The zero demagnetizing factor of a toroidal sample made it possible to measure the true hysteresis parameters. In Figure 1 we present the coercive field for FINEMET (Fe73.5Si13.5B9Nb3Cu1) after different annealing. The decoupling temperature remains almost constant very near to the initial TC of the precursor amorphous material (600 r 30 K).

Figure 1. The coercive field as a function of temperature, for FINMET samples annealed at different temperatures for 1 h

It can be observed that the rise of Hc diminishes with increasing annealing temperature, i.e. with increasing x. The ultra soft material (Hc < 1 A/m) below TD is still soft (Hc ~ 100 A/m) above TD in the optimal annealed state. The same behaviour of Hc was also observed for NANOPERM (Fe84.5Nb2Zr4B8.5Cu1) [11].

3. DISCUSSION The main concept of dipolar ferromagnetism can be formulated as follows: in a dipolar coupled nanogranular system, a ferromagnetic order cannot appear when the system can be reduced to a square lattice of point dipoles [12]. However, both kinds of symmetry breaking, in the particle environment and in the particle own shape, may favor the ferromagnetic ordering [13]. In this paper we present order of magnitude calculations only and a more general criterion will follow from simulations of a more extensive set of dipolar-coupled arrays.

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It is necessary first to show that this dipolar coupling of nanoparticles is an effect equal in its importance to the role of the exchange coupling between atomic moments. While the interaction energy for atomic dipoles situated at atomic distances “a” is only −24 2 μ 0 μ B2 ) − 7 (9.274 ⋅ 10 (2) 10 = = 3.18 × 10 − 25 J , −10 3 3 4π a (3 ⋅ 10 ) when one takes two cubes of iron with dimension 10 nm on a side, the magneto-static interaction is equivalent to the exchange coupling when the spacing between the two cubes each containing N atoms is about 1.5 nm:

E dat =

E dpart =

μ 0 N 2 μ B2 ( D / a)3 at = E d 4π ( D + δ ) 3 (1 + δ / D ) 3

(3)

for D = 10 nm, δ =1.5 nm it turns out that Edpart/Edat = 24352, i.e. Edpart= 7.74×10–21 J. This interaction energy between two cubic dipoles lying in line and pointing to the same direction is of same order of magnitude as the exchange energy between the atomic moments: E exchange = A ⋅ a = 1.5 × 10 −11 ⋅ 3 × 10 −10 = 4.5 × 10 −21 J, and is sufficient to overcome both the thermal excitation above the exchange decoupling temperature and also the tendency of random directions of the anisotropy of the particles to misalign the magnetizations of the two particles. The collective response of the ensembles of dipolar-coupled particles can give rise to magnetization processes that show the general characteristics of ferromagnetism such as remanence and coercivity. One of the features of the replacement of the exchange interactions between the nanoparticles by the dipolar coupling is the maintenance of what is generally called exchange softening, but which now can be termed dipolar softening. The main parameter in anisotropy averaging is the effective stiffness constant, so in the following we derive the stiffness constant contribution, Ad, of dipolar ferromagnetism. The dipolar interaction energy of two nanoparticles & & & & & & μ μ ⋅μ ⎛ μ ⋅μ 3( μ1 ⋅ r12 ) ⋅ ( μ 2 ⋅ r12 ) ⎞ ⎟⎟ (4) E d = 0 1 3 2 ⋅ ⎜⎜ 1 2 − 4π r12 μ1 ⋅ μ 2 ⋅ r122 ⎝ μ1 ⋅ μ 2 ⎠

Figure 2. Schematic representation of dipolar interaction of two particles with diameter D, situated at distance r12 = D + δ. The interaction tends to diminish the angle θ between the dipole moments

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can be expressed in terms of the mx component of relative magnetization, m = M/Ms, as

Ed

P 0 P1 ˜ P 2 § 2T · ¨ cosT  3 cos ¸ 3 4S r12 © 2¹

where m x

cos

T 2

| 1

1 §T · ¨ ¸ 2©2¹

2



P 0 P1 ˜ P 2 § 2T · ¨1  cos ¸ 3 4S r12 © 2¹



1 1  T 2 and consequently 'm x 8

P 0 P1 ˜ P 2 (1  m x2 ) 4S r123 1  T2. 8

The variation of the dipole energy per unit volume as a function of mx is given by: 1 wEd V wmx

1 ( D  G )3

§ P 0 P1 ˜ P 2 · 1 ¨ ¸ ˜ ¨ 4S r 3 2mx 'mx ¸ | ( D  G ) 3 12 © ¹

§ P 0 P1 ˜ P 2 1 2 ·¸ ¨ . (5) ˜ ¨ 4S r 3 2 8 T ¸ 12 © ¹

Similarly to the expression of the exchange energy as a function of a rotation angle per unit length we express the density of dipolar energy variation with the help of an effective stiffness constant as 2

§ T · Ad ˜ ¨ ¸ . ©D G ¹

1 wEd V wm x

(6)

From the equivalence of expressions (5) and (6) comes the effective dipolar stiffness

Ad

P 0 P1 ˜ P 2 1 . 3 4S r12 4( D  G )

(7)

Considering identical nanoparticles (P1 = P2 = P) and expressing Ad as a function of saturation polarization J s P o P / D 3 we obtain J s2 D 3 ˜x , 16SP 0 D  G 1

Ad

(8)

where x is the crystallized fraction which determines the spacer G = D(x–1/3 – 1) and finally we obtain J s2 D 2 4 / 3 ˜x . 16SP 0

Ad

(9)

In a two-phase system the effective stiffness constant (A) can be written in different ways using different models. Here we adopt the approach of K. Suzuki [9] with a small modification, namely, the amorphous stiffness is augmented by the dipolar stiffness: 1

1

A

ACR



G /D AAM  Ad

,

(10)

where ACR and AAM are the stiffness constants for crystalline and amorphous phases, respectively.

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In order to obtain a proper quantitative agreement with the experimentally found upraise of coercive field, we introduce a second modification into the Herzer model: besides the “intrinsic” K1, we take into account the shape anisotropy, Kd as N eff J CR  J AM 2 , Kd (11) 2P0

where Neff is the effective demagnetizing factor of a non-spherical nanoparticle. Kd can be even larger than the K1 above the decoupling temperature. Extending the Herzer model [5, 6] for both exchange and dipole ferromagnetism, the local anisotropies K1 and Kd of the nanoparticles will be averaged out in the whole temperature range, up to the superparamagnetic transition temperature, Tsp

K!

2

2

x ( K1  K d )

D3 § A · ¸ ¨ © K !¹

2

3/ 2

 Ku ,

(12)

where Ku is a large scale (domain size) induced anisotropy, which appears during the heat treatment of the amorphous precursor material. Above the decoupling, the large domain structure characteristic for the ultrasoft low temperature state get broken in small domains [14], which shows that Ku is no more effective and can apart from K1 and Kd, be neglected. This is why, at this stage of simulating the rise of coercive force at decoupling we neglect Ku and Eq.(12) can be solved directly as

K!

x2

( K12  K d2 ) 2 6 D , A3

(13)

where A is the effective average stiffness given by Eq. (10). The temperature dependence for K1 and JSCR of the bcc nanograin can be taken from the literature experimental data [15]. The high temperature values of JSCR were corrected to take into account the superparamagentic transition at Tsp, which was calculated from the balance between the thermal and the magnetostatic energy in the Lorentz field of dipole-dipole interaction of nanograins

TSP

S xV 2 J SCR (TSP ) . 54 P 0 k B

(14)

The saturation polarization of the amorphous phase was calculated from the Arrott-Noakes equation [16] to take into account the enhancement of the TCam due to the neighbouring strong magnetic nanograins. Finally, the temperature dependence of the coercive force, Hc can be calculated, following Herzer [5], as 2 K av , (15) H c pH J where J = xJSCR + (1 – x)JSAM and pHc are constants useful to fit the calculated values to the experimental ones. The coercivity, Hc depends mainly on Neff at a given x. c

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163

In Figure 3 the calculated values of Hc for different crystalline fractions are presented taking Neff = 0.02. It is worth mentioning that Neff may depend on the x and on the particular annealing treatment applied.

Figure 3. Simulated coercive field for a model FINEMET material

In comparison with Fig. 1, good agreement can be observed with the experimental results as far as the order of magnitude of the Hc rise is concerned. The reproduction of the asymmetric shape of the Hc maximum needs further simulation taking into account the details of the superparamagnetic transition. It is worth mentioning that at a high crystalline fraction (x > 68%), where the nanoparticles can touch one another directly through a ferromagnetic inter-granular layer (enriched in Nb), the exchange averaging once again prevails over the dipolar interaction. The dipolar ferromagnetism dominates the interaction of nanoparticles at intermediate values of x, below the maximum closed packing fraction of spherical like nanoparticles (x < 68%) and above a certain value of x at which the distance between the particles is small enough to make the dipolar interaction effectively strong (for G = D corresponds x ~ 12%). 4. CONCLUSIONS We can conclude that the dipolar ferromagnetic interaction in a system of closepacked monodomain nanoparticles (D/10 < G < D) is sufficiently strong to replace the exchange interaction in averaging out the local anisotropy above the decoupling temperature. The effective dipolar stiffness constant, as it was introduced here, can be used to characterize the temperature behaviour of coercive field around the decoupling temperature in two-phase nanocrystalline alloys. For order of magnitude simulations beside the crystalline anisotropy K1, the shape anisotropy of the nanoparticles proved to be an important factor to be averaged out above the decoupling temperature. Using these fundamental results, a magnetic nanocomposite core can be developed composed of nanosized metallic magnetic particles and a nonmagnetic insulator coating. This granular material may be relatively soft owing to the dipolar softening from room

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temperature up to superparamagnetic transition and can be used for high frequency applications. ACKNOWLEDGEMENTS This work was supported by EU- G5RD-CT-2001-03009 and Hungarian OTKA-T 034 666 grants. L.K. Varga thanks the ENS de Cachan for one month hospitality as visiting professor. REFERENCES [1] Yoshizawa, Y., Oguma, S., and Yamauchi, K., (1988) J. Appl. Phys. 64, 6044. [2] Suzuki, K., Kataoka, N., Inoue, A., and Masumoto, T., (1990) Mater. Trans. JIM 31, 743. [3] Willard, M.A., Laughlin, D.E., McHenry, M.E., Thoma, D., Sickafus, K., Cross, J.O., and Harris, V.G. , (1998) J. Appl. Phys. 84, 6773. [4] Gomez-Polo, C., Marin, P., Pasqual, L., Hernando, A., and Vazquez, M. (2001), Phys. Rev. B 65, 024433. [5] Herzer, G., (1989) IEEE Trans. Magn. 25, 3327 and (1990) 26, 1397. [6] Herzer, G., (1995) Scr. Metall. Mater. 33, 1741. [7] Yavari R. and Negri, D., (1997) Nanostruct. Mat. 8: 969. [8] Hernando, A., Vazquez, M., Kulik, T., and Prados, C., (1995) Phys. Rev. B 51, 3581. [9] Suzuki, K. and Cadogan, J., (1998) Phys. Rev. B 58, 2730. [10] Hauschield, J., Elmers, H.J., and Gradmann, U., (1998) Phys. Rev. B 57, R677. [11] Varga, L.K., Mazaleyrat, F., Kovács, G., and Kákay, A., (2001) J. Magn. Magn. Mater. 226-230, 1550. [12] Luttinger, J.M. and Tisza, L., (1946) Phys. Rev. 70, 954. [13] Costa, M.D. and Pogorelov, Y.G., (2001) phys. stat. sol. (a) 189, No. 3, 923. [14] Schafer, R., Hubert, A., and Herzer, G., (1991) J. Appl. Phys. 69, 5325. [15] Chikazumi, S., (1964) Physics of Magnetism, John Wiley (ed.), p. 151. [16] Arrott, A. and Noakes, J.E., (1967) Phys. Rev. Lett. 19, 786.

DESIGN AND PREPARATION OF NEW SOFT MAGNETIC AMORPHOUS FERROMAGNETS Bulk Amorphous Alloys; Amorphous Wires, Microwires and Nanowires H. CHIRIAC and N. LUPU National Institute of Research and Development for Technical Physics 47 Mangeron Blvd., P.O. 3, P.O. Box 833, 700050 Iasi, Romania Corresponding author: H. Chiriac e-mail: [email protected] Abstract:

DC and AC magnetic properties of Fe-based bulk amorphous alloys as thick meltspun ribbons, cast rods and torroids are investigated. The influence of the preparation conditions, composition, frequency, and treatments on the electrical and magnetic characteristics is discussed. The magnetic behaviour of amorphous wires and microwires is presented. The correlation between the diameter of the wires, the magnitude of the GMI effect and the surface magnetic permeability is discussed. Arrays of amorphous NiP and CoP nanowires with diameters near 200 nm have been obtained using electrodeposition. The microstructure and magnetic properties of the nanowire arrays strongly depend on the composition.

1. INTRODUCTION The specific magnetic behaviour of amorphous soft magnets combined with good mechanical performances and high corrosion resistance make them competitive with their crystalline counterparts in applications as transformers, sensors, transducers, etc. Modern electronic devices such as power supplies and digital equipment for the telecommunications or IT industry demand magnetic cores or inductive components with compact volume, good magnetic properties, and the ability to fabricate in different geometries. Although there are a few limitations of magnetic metallic glasses in applications mainly due to their shape limitation (thin films, melt-spun ribbons with thicknesses usually no larger than 50 Pm, conventional wires or glass-coated microwires, powders), their main advantage is the wide range and the flexibility of compositions. Moreover, in the last decades they have been widely used as precursors for nanocrystalline or quasicrystalline alloys that exhibit remarkable magnetic and mechanical properties owing to their very complex structure. In this paper we will describe some of our recent materials developments related to the potential use of amorphous alloys. 165 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 165–176. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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2. BULK AMORPHOUS ALLOYS Nowadays, there are tremendous efforts to prepare bulk amorphous alloys in different systems, with different geometries and good soft magnetic characteristics for specific applications [1-6], because these materials have a potential to open up the market either by replacing the conventional Fe-Si laminas and melt-spun amorphous or nanocrystalline ribbons or by triggering the development of new devices. Their main advantage consists of the ease of formation in bulk shapes by both casting and powder consolidation methods thanks to their large glass-forming ability. 2.1. Sample preparation For the processing of bulk amorphous alloys, we prepared master alloys of 5-10 g each by arc melting pure elements (99.99%) in an argon atmosphere. The alloys were re-melted several times for homogenization. Melt-spun ribbons with thicknesses up to 200 Pm and widths of 2-4 mm were prepared by melt-spinning technique in an Ar atmosphere. Glassy rods with diameters no larger than 3 mm were prepared by suction casting method, whereas glassy rings having internal diameter, external diameter and height of 6, 10 and 1 mm, respectively, were obtained by mould casting method. The master alloy was melted in a quartz crucible using an induction coil system and pushed when melted with a pressure of 0.5-0.8 atm. in a water cooled Cu mould. 2.2. Large glass-forming ability The ability to fabricate Fe56Co7Ni7Zr6M1.5Nb2.5B20 (M = Zr, Ti, Ta, Mo) bulk amorphous alloys by the conventional Cu mould casting method is settled on the large glass-forming ability of these alloys, i.e. the supercooled liquid regions achieving 80-90 K (Table I) in comparison with 30-40 K as previously observed for conventional Fe-based and Co-based metallic glasses. Table I. The evolution of the glass transition temperature (Tg), crystallization temperature (Tx) and supercooled liquid region ('Tx = Tx – Tg) on the difference between the main components atomic radii (rZr – rM)/rM (%) (rM – rFe)/rFe (%) (rM – rB)/rB (%) 'Tx = Tx – Tg (K) Tg (K) Tx (K)

M = Zr – 27 63 80 773 853

M = Ta 7 18 52 85 768 853

M = Ti 8 16 50 85 733 823

M = Mo 13 10 42 90 743 833

By increasing the difference between the atomic radii of Zr and addition elements (rZr = 0.16 nm, rTi = 0.147 nm, rMo = 0.139 nm), the supercooled liquid region ('Tx) is increased despite of the decrease in the difference in atomic radii between the main components (rFe = 0.126 nm; rB = 0.098 nm) and the addition elements. Consequently,

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we expect a different magnetic behaviour as a function of the nature of the addition element. 2.3. DC and AC magnetic properties DC-magnetic measurements were carried out using an extraction DC-fluxmetric method. Primary and secondary coils were wound on the torroids using enamel-coated copper wire. Magnetic characteristics as AC magnetic permeability (Pe), electrical resistivity (URT), saturation induction (Bs) and coercive field (Hc), as well as their variation vs. temperature were measured using an AC fluxmetric method in fields up to 25 kA/m. The saturation magnetostriction constant (Os) was measured by the small angle magnetization rotations (SAMR) method. The hysteresis losses for a given frequency were determined by the area within the hysteresis loop. They were assumed to be constant with frequency. The eddy current losses are defined by (S d Bˆ ) 2 We ˜f

EU RT U

where d is the thickness of the sample, Bˆ is the peak value of the sinusoidal flux density, URT is the electrical resistivity, U is the density, and f is the frequency. E is a geometrical coefficient [7]. For sheets of thickness d, E 6 , while for rods of diameter d, E 16 [8]. For ring shaped samples, E is calculated using the following formula [9]:

E

6 , w h· § 1  0.663 tanh¨1.58 ¸ h w¹ ©

where w and h represent the width and the height of the torroid, respectively. For the Fe56Co7Ni7Zr7.5Nb2.5B20 amorphous torroid with Dext = 10 mm, Dint = 6 mm and h = 1 mm, E is 6.1065. Table II presentes the electrical resistivity and magnetic characteristics of Fe56Co7Ni7Zr6M1.5Nb2.5B20 bulk amorphous alloys. Table II. Magnetic characteristics and room temperature electrical resistivity as a function of the addition element in amorphous Fe56Co7Ni7Zr6M1.5Nb2.5B20 cast rods and melt-spun ribbons

P0Ms (T) M = Zr M = Ti M = Ta M = Mo

1.01 0.89 1.06 1.07

Hc (A/m) 9.5 6.06 6.1 7.43

Pe (500 Hz) TC (K) 21500 18000 19000 17000

554 560 603 560

URT (:Pm) 1.51 2.08 1.87 1.76

Os (u 10–6) 7 9 9 10

Whereas the saturation magnetization, P0Ms, does not change significantly by the partial substitution of Zr, the effective magnetic permeability, Pe, decreases drastically. The Curie temperature increases for the alloy containing Ti probably because of the increase in the strength of the interactions between the unfilled 3d (for Ti

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and Fe) and 4d (for Zr and Nb) electronic shells. This also seems to be the cause for the largest values of the electrical resistivity for the samples with 1.5 at.% Ti. The coercive field, Hc, decreases when 1.5 at.% Zr is replaced with Mo, Ta or Ti. From these results one can conclude that Ti seems to be the most suitable element to improve the softness of the bulk amorphous samples prepared in (Fe, Co, Ni)70(Zr, M, Nb)10B20 multicomponent system. Moreover, the magnetic properties of the amorphous torroids are comparable with those of FeSiB and CoFeSiB melt-spun amorphous ribbons (Table III), often used as magnetic cores, shielding elements, and inductive components. Figure 1 presents the variation of the DC magnetic permeability as a function of the applied field for the Fe56Co7Ni7Zr7.5Nb2.5B20 amorphous torroid. PDC slowly decreases by increasing the applied field above 5 A/m, but increases very rapidly when the applied field approaches to zero. Table III. DC and AC magnetic characteristics in the as-cast state for bulk amorphous Fe-based torroids and amorphous Fe-based and Co-based melt-spun ribbons P0Ms (T) Hc (A/m) PDC (105) PAC, 5 00 (104) PAC, 1 0k (104) Sample / Geometry / Thickness Fe56Co7Ni7Zr7.5Nb2.5B20 Torroid/1 mm

1.01

1.44

1

2.15

0.56

Fe77.5Si7.5B15 Melt-spun ribbon/30 Pm

1.56

3.2

–

–

–

Co68.25Fe4.5Si12.25B15 Melt-spun ribbon/30 Pm

0.76

0.48-160

–

1

1

PAC, 5 00 is the relative magnetic permeability at 500 Hz, whereas PAC, 1 0k represents the relative magnetic permeability at 10 kHz

Figure 1. DC-magnetic permeability vs. applied field for Fe56Co7Ni7Zr7.5Nb2.5B20 amorphous torroid

Figure 2. Magnetic permeability as a function of the AC-applied field frequency, f, for Fe56Co7Ni7Zr6M1.5Nb2.5B20 (M = Zr, Ti, Ta, Mo) bulk amorphous torroids

The large values of both DC and AC magnetic permeability measured for Fe56Co7Ni7Zr6M1.5Nb2.5B20 (M = Zr, Ti, Ta, Mo) bulk amorphous alloys in the as-cast state are strongly related to the large electrical resistivities of 180–230˜10–8 :˜m, in comparison with 110 and 150 ˜10–8 :˜m for FeSiB and CoFeSiB melt-spun amorphous ribbons. Coercive fields (Hc) in the as-cast state are below 8 A/m, whereas the saturation induction (Bs) reaches 0.9-1.2 T for Fe56Co7Ni7Zr6M1.5Nb2.5B20 (M = Ti,

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Ta, Mo) amorphous torroids. The Curie temperature varies between 550 and 605 K depending on the addition element (M), that being a very important point to be considered when defining new materials for applications. The frequency dependence of the AC-magnetic permeability for Fe56Co7Ni7Zr6M1.5Nb2.5B20 bulk amorphous alloys is presented in Fig. 2. The magnetic permeability of Fe56Co7Ni7Zr7.5Nb2.5B20 amorphous torroid increases by about 50% by decreasing the frequency from 500 Hz to 5 Hz and decreases about 4 times when the frequency increases to 10 kHz. The partial substitution of Zr results in a less pronounced frequency variation of the magnetic permeability, indicating these bulk amorphous alloys with additions as suitable candidates for frequency applications. The decrease of the permeability with the increase of the frequency is especially due to the classical eddy current losses and anomalous (excess) eddy current losses. The hysteresis losses also contribute to the deterioration of the magnetic characteristics vs. frequency, but their contribution is significantly smaller (Fig. 3). The most significant increase of the classical eddy current losses is observed for the amorphous torroids containing Zr, for which the hysteresis losses are also the largest. Consequently, the magnetic permeability of Fe56Co7Ni7Zr7.5Nb2.5B20 amorphous torroid decreases more rapidly in comparison with the magnetic permeability of the Fe56Co7Ni7Zr6M1.5Nb2.5B20 (M = Ti, Ta, Mo) bulk amorphous torroids. The eddy current losses are smaller when adding Ti and Ta in comparison with the ring-shaped samples containing Zr or Mo, but they are comparable with those reported in the literature for other metallic glasses with large glass-forming ability [9, 10].

Figure 3. Frequency dependence of hysteresis losses (Wh) and classical eddy current losses (We) for the as-cast Fe56Co7Ni7Zr6M1.5Nb2.5B20 amorphous torroid measured at f= 50 Hz and maximum flux density Bˆ 0.5 T

Figure 4. The hysteresis loop shape dependence on the treatment, for Fe56Co7Ni7Zr7.5Nb2.5B20 melt-spun amorphous ribbons, 120 Pm thickness

Thermal and thermomagnetic treatments may strongly affect the magnetic properties of amorphous alloys, especially the shape of the hysteresis loop, the magnetic permeability and the coercive field. The modification of the shape of the hysteresis loop after thermal and thermomagnetic treatments at relaxation temperature (748 K) for Fe56Co7Ni7Zr7.5Nb2.5B20 thick amorphous ribbons (120 Pm) are shown in Fig. 4. The direction of the applied magnetic field is relative to the long axis of the ribbon. One

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observes that the rectangularity of the hysteresis loop as well as the saturation magnetization and coercive field are changing with the direction of the applied magnetic field. The thermal treatment without magnetic field, just below glass transition temperature (Tg = 773 K), leads to a slight increase in the coercive field and to the elongation of the hysteresis loop. The presence of an external magnetic field results in better magnetic properties leading to the magnetic softness of the amorphous samples. The best response is obtained when the applied field is parallel to the long axis of the ribbon because of the easy axis induced on the parallel direction with the applied field. When the external field is perpendicular to the ribbon long axis the induced anisotropy is smaller owing to the competition of the magnetoelastic anisotropy induced during the melt-spinning preparation process and oriented parallel with the long axis. Consequently, the coercive field increases. Further experimental work along this line is expected in the near future. 3. MAGNETIC AMORPHOUS WIRES In addition to bulk amorphous alloys with soft magnetic properties, the low dimension soft magnetic amorphous materials also represent a very exciting field of research for both fundamental studies and applications. In this category, amorphous wires and glass-covered microwires, and very recently amorphous nanowires are extremely important. 3.1. Amorphous wires and glass-covered microwires Amorphous wires with diameters up to 200 Pm and glass-covered amorphous metallic wires having diameters of the metallic core of 1 to 80 Pm and the glass cover thickness of 1 to 20 Pm, with positive, negative, and nearly zero magnetostriction, have been extensively studied over the last years, and their magnetic properties have been found to be extremely attractive for sensors applications [11]. Their specific magnetic properties are strongly dependent on composition through the manetostriction value, on the magnitude and the direction of the induced anisotropies either during the preparation process or by annealing, on the magnetic permeability, on their diameter and on the internal and superficial stresses distribution. In the following we will focus on the influence of the composition and dimensional characteristics on the magnetic properties, mainly on the GMI effect, of nearly zero magnetostrictive Co-based amorphous wires and glass-covered wires 3.1.1. Preparation Amorphous wires with nominal compositions Co72.5–xFexSi12.5B15 (x = 5.5-6.2) were obtained by two different methods, namely the in-rotating water spinning and the glasscoated melt-spinning [11], at the National Institute of Research and Development for Technical Physics of Iasi, Romania. The diameter of the conventional amorphous wires (CAW) ranges from 90 to 150 Pm, whereas the glass-covered amorphous wires (GCAW) consists of a metallic core having diameters between 15 and 80 Pm, coated by a glass cover ranging from 5 to 20 Pm. The saturation magnetostriction constant (Os)

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changes the sign from negative (Os = –0.23˜10–6 for x = 5.5) to small positive (Os = +0.05˜10–6 for x = 6.2) values when the Fe content increases, passing through zero for x ~ 6.0. 3.1.2. The influence of the composition and microwires diameter on the GMI effect GMI measurements were performed in the high frequency range (100 kHz-10 MHz) for driving AC currents up to 5 mA using a digital oscilloscope coupled with a computer, which allowed automatic frequency control, data acquisition, and processing. For comparison, we carried out GMI measurements on CAW and GCAW having different compositions and saturation magnetostriction constants. Additionally, we investigated the influence of the cold rolling process on the GMI response of the CAW. GMI effect in low magnetostrictive amorphous wires is mainly influenced by two factors: the specific circumferential magnetic domain structure and dynamic magnetization processes [12]. Iac passes only through a superficial layer of the wires, owing to the skin effect that occurs at frequencies of the order of MHz. The depth of this layer is determined by the magnetic penetration depth Gm, given by

Gm

U , SQPT

where U is the electrical resistivity, Q the frequency, and PT the circular permeability. The circular magnetization is driven by the circular AC field created by Iac while Gm is usually of the order of several micrometers at megahertz frequencies. The glass cover induces an additional anisotropy, which strongly influences the magnitude of the GMI effect in low magnetostrictive amorphous glass-covered wires [13]. From the point of view of sensing applications, the amorphous glass-covered wires are often preferred against the conventional amorphous wires due to their more reduced dimensions, i.e. the diameter of the metallic core varies from a few micrometers to a few tens of micrometers [11, 14]. The axial DC field dependences of the impedance (Q = 10 MHz) for Co72.5-xFexSi12.5B15 (x = 5.5; 5.95; 6.0; 6.2) CAW and GCAW are illustrated in Fig. 5. It is important to note that the GMI curves exhibit only one central peak for positive magnetostrictive GCAW with x = 6.2, independent of the frequency [15], due to the non-formation of the circumferential magnetic domains structure in the positive magnetostrictive glass-covered amorphous wires [16]. The impedance shows two maxima whose positions change to high dc fields with the frequency increase, for negative magnetostrictive GCAW (x < 6) [15]. This displacement is mainly caused by the supplementary induced anisotropy as the effect of the negative magnetostriction constant. For nearly zero magnetostrictive composition (x = 6) the GMI behaviour is very sensitive to the ac field frequency. The two maxima on the impedance curves correspond to the anisotropy field, Hk. It is worthwhile to note that the best response of the GMI effect is obtained for x = 5.95 in the case of GCAW and at x = 6 for CAW. This different behaviour, which is

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strongly dependent on the saturation magnetostriction constant value, is caused by the variation of the penetration depth of the ac current, i.e. the magnetic domain structure and the existence or non-existence of the closure surface magnetic domains in GCAW.

Figure 5. GMI curves for CAW and GCAW with different compositions and saturation magnetostriction constants measured at 10 MHz

The influence of the metallic core diameter on the GMI effect for both CAW and GCAW with the nominal composition Co68.18Fe4.32Si12.5B15 (x = 5.95) is presented in Fig. 6. The GMI response monotonously decreases with the increase of the metallic core diameter. 180

100

d= d= d= d= d= d=

160 140 120 Impedance (:)

Impedance, Z (:)

80

d = 90 Pm d = 100 Pm d = 110 Pm d = 120 Pm d = 130 Pm d = 140 Pm d = 150 Pm

60

40

30 Pm 40 Pm 50 Pm 60 Pm 70 Pm 80 Pm

100 80 60 40

CAW 20 -2000

-1000

0

Hdc (A/m)

1000

2000

GCAW tg = 7 Pm

20 0

-2000

-1000

0

1000

2000

Hdc (A/m)

Figure 6. DC field dependence of the impedance for Co68.18Fe4.32Si12.5B15 CAW and GCAW as a function of the metallic core diameter (Q = 10 MHz)

This effect is ascribed to the decrease of the volume of the external circumferential magnetic domains with respect to the volume occupied by the axially magnetized metallic inner core. The GMI effect diminishes much stronger for GCAW because the volume occupied by the axially magnetized central magnetic single domain is comparable with the volume occupied by the circumferentially magnetized magnetic domains on the surface. The GMI response is strongly affected by the type of treatment applied on the conventional wires, and especially if cold rolling treatments are present, as shown in Fig. 7. The cold rolling process modifies the distribution of the stresses induced in

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Figure 7. DC field dependence of the impedance for Co68.18Fe4.32Si12.5B15 CAW as a function of the applied treatment (Q = 10 MHz)

the superficial layer during the preparation. Consequently, the GMI curves are broadened. The reduction of the diameter to 100 Pm results in the increase in the GMI response and the broadening of the field dependence (Fig. 7a). This increase is even much more pronounced when subsequent thermal treatments are applied. The superficial polishing of the conventional wire combined with specific thermal treatments give rise to a supplementary increase of the GMI response, but narrow the field dependence. The reduction of the diameter to 25 Pm by cold rolling (Fig. 7b) leads to the increase of the GMI response of about 3 times and the important broadening of the field dependence, which can be partially reduced by choosing a suitable combination of thermal and thermomechanical treatments. 3.2. Nanowires Nowadays, arrays of magnetic nanowires are widely investigated in order to understand their magnetic behaviour and to estimate their potential use in applications such as patterned recording media, nano-sensors and nano-devices [17, 18]. 3.2.1. Samples preparation In this work, arrays of about 200 nm diameter amorphous Ni100–xPx and Co100–xPx nanowires were obtained by electrodeposition into the nanometre-sized pores of tracketched polycarbonate or anodic alumina oxide (AAO) membranes using a twoelectrode electrochemical cell. The pore diameters and the thickness of both the polycarbonate and AAO membranes were 200 nm and about 6 μm, respectively. Prior to the electrodeposition of NiP and CoP nanowires in polycarbonate or AAO membranes, a 800 nm Ag film was deposited by thermal evaporation on the membrane surface to act as a substrate and working electrode [19]. The metallic layer was insulated from electrolyte solution by a special insulator film. Thus, the metallic layer used as a cathode was in direct contact with the electrolyte through the membrane pores. A platinum wire was used as an anode. The current densities ranged between 0.1 and 0.6 mAcm–2. For comparison, Co80P20 amorphous thin films having 200 nm in thickness were electrodeposited on alumina substrates covered with a thin layer of Cr/Ag deposited in the process of vacuum evaporation.

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3.2.2. Structure and morphology Figure 8 shows the X-ray diffraction patterns of the electrodeposited Ni80P20 nanowire arrays and of the AAO membrane, on which the Ag thin film was deposited, respectively. The presence of just one broad peak onto the X-ray diffraction pattern of the nanowire arrays and no additional sharp peaks are features characteristic of the amorphous phase.

Figure 8. X-ray diffraction data obtained from the electrodeposited Ni80P20 nanowire arrays

Figure 9. SEM micrograph of electrodeposited Co80P20 200 nm diameter nanowire arrays

The morphology of the electrodeposited Co80P20 200 nm diameter nanowire arrays, obtained after the dissolution of the AAO membrane in chloroform, is shown in Fig. 9. 3.2.3. Magnetic results The reduced hysteresis loops as well as the temperature dependence of the reduced magnetiation were carried out using a vibrating sample magnetometer (VSM) in a maximum applied field of 1260 kA/m. The measurements were conducted on the asdeposited samples and with the external field applied in the plane. The magnetic properties of the amorphous NiP and CoP nanowire arrays are strongly dependent on the P content, i.e. electrodeposition conditions. Figure 10 presents the hysteresis loops of the electrodeposited Co80Fe20 and Ni100–xPx 200 nm diameter nanowire arrays as a function of P content. The data for Ni100–xPx nanowire arrays were normalized to pure Ni magnetization. The coercive field value of about 5 kA/m measured for the in-plane field direction for amorphous Co80P20 nanowire arrays was comparable with the ones published recently on amorphous CoP 100 nm cylinder arrays [20]. Significant differences in the coercive field were observed depending on the samples morphology and the direction of the external field, as shown in Fig. 11. While the coercive field reaches 0.2 kA/m for Co80P20 amorphous thin films with the field parallel on the film plane, the 200 nm nanowire arrays show coercive fields of 1.5 kA/m when the external field is parallel to the long axis of the nanowires. This behaviour is given by the presence of magnetostatic interactions between nanowires, as proposed previously [21].

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Figure 10. Magnetic hysteresis loops of electrodeposited Ni100–xPx and Co80P20 (inset) 200 nm diameter nanowire arrays

0.50

Magnetic moment (emu)

Co 80 P 20

0.25

thin layer nanowire arrays

0.00

-0.25

-0.50 -100

H parallel

-50

0

50

100

H (kA/m)

Figure 11. Magnetic hysteresis for both sample morphology in two applied field direction for Co80P20 amorphous thin film and nanowire arrays

Figure 12. Temperature dependence of the reduced magnetization of electrodeposited Ni100–xPx 200 nm diameter nanowire arrays

The temperature dependence of the reduced magnetization as a function of P content in Ni100–xPx nanowire arrays is presented in Fig. 12. Both samples containing 10.56 and 16 wt% P are amorphous, but the increase of the P content over 15 wt.% diminishes the ferromagnetic behaviour of NiP amorphous alloys. Consequently, the magnetization and Curie temperature decreased, whereas the coercive field increased. However, the value of Hc is still below the one of the Ni electrodeposited nanowire arrays. Thus, the magnetic properties of the electrodeposited NiP and CoP nanowire arrays are very sensitive to the P content, i.e. the electrodeposition conditions.

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ACKNOWLEDGMENTS This work was supported in part by the Romanian Ministry of Education, Research and Youth – Department of Research under Contract CERES 3/15.10.2001.

REFERENCES 1. Inoue, A., Takeuchi, A., Zhang, T., Murakami, A., and Makino, A. (1996) Soft magnetic properties of bulk Fe-based amorphous alloys prepared by copper mold casting, IEEE Transactions on Magnetics 32, 4866-4871. 2. Inoue, A., Koshiba, H., Itoi, T., and Makino, A. (1998) Ferromagentic Co-Fe-Zr-B amorphous alloys with glass transition and good high-frequency permeability, Applied Physics Letters 73, 744-746. 3. Shen, T.D. and Schwarz, R.B. (1999) Bulk ferromagnetic glasses prepared by flux melting and water quenching, Applied Physics Letters 75, 49-51. 4. Chiriac, H. and Lupu, N. (1999) Structure and magnetic properties of some bulk amorphous materials, Journal of Non-Crystalline Solids 250-252, 751-756. 5. Chiriac, H. and Lupu, N. (2001) New bulk amorphous magnetic materials, Physica B 299, 293301. 6. Stoica, M., Degmova, J., Roth, S., Eckert, J., Grahl, H., Schultz, L., Yavari, A.R., Kvick, A., and Heunen, G. (2002) Magnetic properties and phase transformations of bulk amorphous Fe-based alloys obtained by different techniques, Materials Transactions 43, 1966-1973. 7. Pfützner, H., Schönhuber, P., Erbil, B., Harasko, G., and Klinger, T. (1991) Problems of loss separation for crystalline and consolidated amorphous soft magnetic materials, IEEE Transactions on Magnetics 27, 3426-3432. 8. Bozorth, R.M. (1993) Ferromagnetism, Piscataway, NJ: IEEE Press, 3rd Edition. 9. Shen, T.D., Harms, U., and Schwarz, R.B. (2002) Bulk Fe-based metallic glass with extremely soft ferromagnetic properties, Materials Science Forum 386-388, 441-446. 10. Mizushima, T., Makino, A., Yoshida, S., and Inoue, A. (1999) Low core losses and soft magnetic properties of Fe-Al-Ga-P-C-B-Si glassy alloy ribbons with large thicknesses, Journal of Applied Physics 85, 4418-4420. 11. Chiriac, H. and Óvári, T.-A. (1996) Amorphous glass-covered magnetic wires: preparation, properties, applications, Progress in Materials Science 40, 333-407. 12. Panina, L.V., Mohri, K., Bushida, K., and Noda, M. (1994) Giant magneto-impedance and magneto-inductive effects in amorphous alloys, Journal of Applied Physics 76, 6198-6203. 13. Chiriac, H., Óvári, T.-A., and Marinescu, C.-S. (1997) Comparative study of the giant magnetoimpedance effect in CoFeSiB glass-covered and cold-drawn amorphous wires, IEEE Transactions on Magnetics 33, 3352-3354. 14. Humphrey, F.B. (1994) Applications of amorphous wire, Materials Science and Engineering A179/A180, 66-71. 15. Chiriac, H., Murgulescu, I., and Lupu, N. (in press) The influence of the composition on the GMI effect in low magnetostrictive amorphous microwires, Journal of Magnetism and Magnetic Materials. 16. Pirota, K.R., Kraus, L., Chiriac, H., and Knobel, M. (2001) Magnetostriction and GMI in Jouleheated CoFeSiB glass-covered microwires, Journal of Magnetism and Magnetic Materials 226, 730-732. 17. Fert, A. and Piraux, L. (1999) Magnetic nanowires, Journal of Magnetism and Magnetic Materials 200, 338-358. 18. Raposo, V., Garcia, J.M., Gonzales, J.M., and Vazquez, M. (2000) Long-range magnetostatic interactions in arrays of nanowires, Journal of Magnetism and Magnetic Materials 222, 227-232. 19. Chiriac, H., Moga, A.E., Urse, M., and Ovari, T.A. (2003) Preparation and magnetic properties of electrodeposited magnetic nanowires, Sensors and Actuators A 106, 348-351. 20. Shima, M., Hwang, M., and Ross, C.A. (2003) Magnetic behaviour of amorphous CoP cylinder arrays, Journal of Applied Physics 93, 3440-3444. 21. Sorop, T.G., Untiedt, C., Luis, F., de Jongh, L.J., Kroll, M., and Rasa, M. (2003) Magnetization reversal of individual Fe nanowires in alumites studied by magnetic force microscopy, Journal of Applied Physics 93, 7044-7046.

FORMATION OF NANOCRYSTALLINE METASTABLE PHASES IN Fe-Ni-Zr-B AMORPHOUS ALLOYS

B. IDZIKOWSKI Institute of Molecular Physics, Polish Academy of Sciences M. Smoluchowskiego 17, 61-179 PoznaĔ, Poland Corresponding author: Bogdan Idzikowski, e-mail: [email protected]

Abstract:

The paper presents a comprehensive review of our recent experimental and theoretical investigations in the processing of nanocrystalline soft magnetic materials made from an amorphous precursor with a nominal chemical composition of Fe81 – x –yNixZr7B12Au1, x = 10-40, 64; y = 0, 1. The transformation from the amorphous into the nanocrystalline state was investigated by means of structural (DSC, XRD, TEM) measurements as well as by transmission and conversion electron Mössbauer spectroscopy (CEMS). Additionally, magnetic (VSM) measurements were performed. The annealing favours the emergence of a fine grain fraction of magnetically ordered metastable cubic FexNi23 – xB6 phase in an amorphous matrix. The relationship between the structures of the metastable and equilibrium phases and their transformations are discussed. The magnetic behaviour of pure Ni23B6 and Fe23B6 phases was studied theoretically using the spin polarized tight binding linear muffin-tin orbital (TB-LMTO) method. Anomalously high magnetic moments of Fe atoms were found in some inequivalent positions in the crystal structure. The possibilities of increasing the saturation magnetization value by applying an optimal chemical composition and a crystal structure as well as decreasing the coercive force of the nanocrystalline alloys utilizing intergranular exchange coupling are discussed.

1. INTRODUCTION Nonocrystalline soft magnets are prepared by heat treatment in inert atmosphere of amorphous precursors in the form of ribbons. This paper summarizes the most recent experimental and theoretical investigations in the processing of such magnetic materials. It gives an overview of the relevant classes of extremely soft magnets together with a description of the appropriate manufacturing methods, and focuses on important parameters for their application. Particular attention will be given to the magnetic behaviour of melt-spun Fe-Ni-Zr-B-(Au) samples subsequently annealed for one hour at 177 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 177–188. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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different temperatures in order to form a nanostructure, and to the comparison of the above with our theoretical predictions. High saturation magnetization can be achieved in many crystalline magnetic materials by increasing the iron concentrations. Soft magnetic properties of Fe-based alloys are usually insufficient for applications because of large magnetocrystalline anisotropy of bcc-Fe. A large anisotropy constant of Fe could be suppressed in composite materials by reducing the diameters of the grains. Owing to the magnetic exchange interactions nanocrystalline alloys consisting of magnetic grains placed in amorphous matrix can reveal a smooth magnetization curve with extremely small values of coercive force. Very successful in the development of a new type of soft magnetic materials was a reduction of the ratio of the structural correlation length depending on the diameters of the grains to the ferromagnetic correlation length which should be in the range of the domain wall width. Up to now nanocrystalline alloys produced by partial crystallization of amorphous precursors have exhibited a multiphase structure with nanocrystalline body-centredcubic (bcc) grains dispersed into a residual amorphous matrix. Well-known soft magnetic nanocrystalline alloys consist of a homogeneous phase of nanosized bcc-Fe, bcc-Fe(Si) or bcc-(FeCo) grains (see e.g. [1-3]) that are 3-15 nm in diameter. During the devitrification processes the amorphous part of the alloys becomes inhomogeneous showing some, sometimes significant, gradients of chemical composition. However, due to the magnetic exchange interactions via this matrix, nanocrystalline systems consisting of magnetic grains not exceeding several nanometers in diameter can exhibit extremely small coercivities. This magnetic softening phenomenon in nanocrystalline materials was explained by Herzer [4], who proposed a successful extension of the previous random anisotropy models [5, 6]. The magnetic properties as well as the crystallization behaviour of Ni-containing amorphous alloys were studied earlier (e.g. [7-10]) but these alloys were unsuitable for being used for the formation of a nanocrystalline phase or phases. The presence of elements like Nb, Zr, Mo, Ti, which are inhibitors of crystallization processes in the precursor alloy, is needed to prevent grain growth. The very fine nanocrystalline structure is expected if clusters of e.g. Cu or Au are present in the amorphous alloys. A nanostructured phase was found by XRD [8] to be the product of the crystallization in Fe40Ni38Mo4B18 system. The presence of Mo atoms in the alloy plays a crucial role in the nanostructure formation process. It is consequently of particular interest to study such alloys in an attempt to understand the details of the complex crystallization process leading to the formation of new fcc-structure based soft magnetic nanostructured systems. The existing papers overview on metastable Cr23C6-type phases is presented in Table I, which collects the structural and magnetic parameters of the crystallization products found in Fe-Ni-Co-M-B systems after annealing (M is crystallization inhibitor metal). The unit cell parameter for the different crystallization products corresponds to different compositions of amorphous precursors, different crystallization conditions and a different thermal pre-history, giving a possibility of receiving unequal unit cell parameters, and in consequence, a relatively bright spectrum of magnetic properties. The structural transformation scheme for Fe(Ni)-M-B systems connected with the first

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exothermic reaction could be as follows: amorphous state amorphous state + bcc-Fe bcc-Fe + borides ± Fe23B6 bcc-Fe + borides bcc-Fe + borides + Fe23B6 [12, 13]. In this scheme, the first and/or second transitions corresponds to the first crystallization stage and if the composition of the growing crystal differs from the composition of the amorphous matrix, then there occurs a primary crystallization process. The values of Avrami exponent discussed from Ref. [12] show the process with a decreasing nucleation rate for the diffusion controlled (primary crystallization) process. During the crystallization and/or re-crystallization transitions, the volume fraction of nanocrystals of each phase changes its volume in accordance with the conservation law. Table 1. Lattice constants and Curie temperature for Fe-Ni-Co-B alloys with Cr 23C6-type structure (*value extrapolated – see text) Composition

Fe23B6

Ni23B6 (FeNi)23B6 Co23B6 (FeCo)23B6 (FeCoNi)23B6

a (nm) 1.067 1.0761 1.059, 1.069 1.039 1.062 0.953* 1.051, 1.068 1.105 – –

TC ( C) [9] [11] [12] [13] [15] [16, 17] [18]

375-389

[14]

– – – 502 307-327 400

[15] [18] [19]

For detailed investigations of Cr23C6-type phases in nanocrystalline form, we prepared amorphous alloys with low and high Ni concentrations using a melt-spinning technique. Subsequent annealing allowed us to form a nanostructure. The significant presence of Ni in those alloys resulted in the formation of metastable Ni-rich fcc-phases containing both the transitions elements and the boron. 2. EXPERIMENTAL Melt-spun alloys with the appropriate nominal composition were prepared by a single roller (40 cm in diameter) technique in Ar protective atmosphere. High-purity elements (Ni 99.995, Fe 99.998, B 99.8, Zr 99.95, Au 99.995) were used for making pre-alloys. Each ingot was moved round several times and melted by induction heating in a water cooled boat to assure homogeneity. The ribbon was 3 mm wide and 0.35 μm thick. The structure of the samples was characterized by XRD analysis in a Seifert diffractometer using Co-KD and Cu-KD radiations. The crystallization behaviour of asquenched ribbons was examined by differential scanning calorimetry using Netzsch DSC 404 apparatus under flowing Ar at various heating rates for scans up to the preselected temperatures. The temperature and heat flow calibrations of the DSC cell were checked against pure metal standards (In, Zn).

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Transmission 57Fe Mössbauer measurements were performed at 300 K with a Co(Rh) source using conventional constant acceleration equipment. The spectra were described by means of a discrete number of quadrupolar doublets or magnetic sextets in accordance with their hyperfine structure. The isomer shift values are expressed in relation to those of bcc-Fe at 300 K. The microstructure was examined by transmission electron microscopy (TEM) after electrolytic thinning of the samples. 57

3. RESULTS AND DISCUSSION A set of similar experimental procedures was applied in our investigations and the results were analysed in order to understand the nanocrystallization processes in low and high nickel concentration ribbons containing iron and 7 at.% Zr and 12 at.% B. For optimal annealed samples the structural and magnetic properties were compared and discussed. 3.1. Ribbons with nickel content x = 10-40 The crystallization of amorphous Fe81–xNixZr7B12 (x = 10-40) alloys, as investigated by DSC linear-heating curves clearly indicates two crystallization stages with two characteristic crystallization temperatures. Such behaviour is typical of amorphous alloys serving as the precursors for the formation of the nanocrystalline alloys. The crystallization temperatures of the first and second stage depend on the alloy composition. They decrease from about 510°C and 730°C for low Ni-content (x = 10) to about 480°C and 650°C for high Ni-content (x = 40).

Figure 1. DSC traces measured for the Fe81–xNixZr7B12, x = 40 ribbon with different heating rates q = 10-50 K/min [20]

Figure 2. Kissinger’s plot for Fe81-xNixZr7B12, x = 40 alloy; q denotes the heating rate, Tx is maximum crystallization rate and the points are from the experiment [20]

The DSC curves taken at different heating rates are presented in Fig. 1. The enthalpy of crystallization H was determined from DSC measurements and was found to be approximately 43 and 82 J/g for the first and second stage, respectively. The enthalpy value with error accuracy (about 10%) did not change at different heating rates. For the concordance with the crystallization/re-crystallization scheme in the case of the

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Fe41Ni40Zr7B12 alloy a successive investigation, e.g. an isothermal heat treatment is necessary to determine the crystallization products of the first crystallization stage. The diffusivity coefficient in the Arrhenius equation D(T) = D0exp(–Q/T) was determined from the Kissinger’s plot ln (Tx2 /q ) vs. 1/Tx and is presented in Fig. 2. It was found that for the first stage the activation energy Q = 296.6 kJ/mol and pre-exponent W0 = 8.75 × 10–20 s (characteristic diffusion time). Figure 2 also shows that the crystallization processes of the first and second stages are interdependent, their parameters of the linear fitting are the slope of the line (36 ± 2) u 103 and (34.6 ± 0.6) u 103 and the intercept is about –33 ± 2 and –24.5 ± 0.7 for the first and second stage, respectively. The interdependence of the crystallizations processes in Fe41Ni40Zr7B12 alloy during the heat treatment at the first and second stage suggests a transformation of the existing phase(s) to metastable (FeNi)23B6 phase at the beginning of the second crystallization stage. Fe41Ni40Zr7B12 (1203) 1.00

1.00

e

a

as-q

595C 0.95

Figure 3. Room temperature Mössbauer spectra of as-quenched Fe41Ni40Zr7B12 alloy and annealed for one hour at indicated temperatures [17]

Relative transmission

0.96 1.00

1.00

b

f 0.96

620C

470C

0.92 0.96 1.00

1.00

c

g

570C

670C 0.95 1.00

0.96 1.00

d

h

800C 0.95

582C 0.96

-8

-4

0

4

8 -8

-4

0

4

8

Velocity [mm/s]

The transmission Mössbauer spectra recorded for the as-quenched Fe41Ni40Zr7B12 alloy and annealed at indicated temperatures for one hour are shown in Fig. 3. As can be seen, the crystalline bcc-Fe phase was formed in the sample annealed at 470qC, in addition to the amorphous phase (Fig. 3b). The increase in the annealing temperature causes the increase in the spectral contribution of the bcc-Fe phase and then at Ta t 570qC a decrease in this component, associated with the simultaneous change of the spectral component related to the broadened sextet which now corresponds both to the residual amorphous phase and to the Ni-containing nanostructure. The Hhf of this sextet slightly decreases which suggests a substantial Ni-content in the nanocrystalline phase (Fig. 3c, 3d). The XRD measurements suggest that the nanograins of the

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(FeNi)23B6 phase are formed at Ta | 570qC. At Ta | 595qC the single-line component appears in the spectrum (Fig. 3e) and the Hhf of the magnetic component decreases further. The single-line component dominates in the spectra recorded for Ta = 620-640qC (Fig. 3f). The increase in Ta above the temperature of the second crystallization peak in DSC curve causes complete crystallization of the sample and the single-line component disappears (Fig. 3g, 3h). The phase formed at Ta t 700oC (Fig. 3h) is most probably fccFeNi. The origin of the single-line component (Fig. 3e, 3f) can be related to the superparamagnetic relaxation in the nanograins of FeNi-containing phase as revealed by the gradual transformation of this component to the magnetic pattern at low temperatures. The crystallization behaviour of samples with lower Ni-content (not shown here) proceeds in a simpler way, typical of other NANOPERM alloys. Conventional Mössbauer measurements allow the identification and estimation of the relative abundance of phases formed in the heat treatment of the amorphous precursors. They do not, however, provide information regarding either the magnetic properties (anisotropy fields and magnetostriction), or the size of the grains. The unconventional rf-Mössbauer technique, in which the rf-collapse and sideband effects are exploited, permits us to distinguish the magnetically soft nanocrystalline phase from the magnetically harder microcrystalline one. The qualitative information concerning the distribution of the anisotropy fields related to the distribution of the size of the nanograins can be inferred from the dependence of the rf-collapsed spectra on the rf-field intensity. The rf-Mössbauer results show that the nanocrystalline (FeNi)-type phase, being magnetically very soft has, however, in most cases markedly larger anisotropy than that of the parent amorphous phase. The complete rf-collapse of the magnetic hyperfine structure occurs only in the amorphous precursor or in the retained amorphous fraction in the nanocrystalline alloy. However, in clear distinction to the results obtained for x d 30 samples, the rf-Mössbauer measurements have shown that the Fe41Ni40Zr7B12 nanocrystalline alloy annealed at 580qC has exceptional soft magnetic properties, i.e. very small anisotropy accompanied by the vanishing magnetostriction. For this alloy a complete rf-collapse effect was observed for the first time both for the residual amorphous phase and the nanocrystalline one [21].

Figure 4. A high resolution TEM bright field image of melt spun Ni41Fe40Zr7B12 alloy after annealing at 640qC/1h [22]

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A TEM picture for heat-treated Ni41Fe40Zr7B12 sample is shown in Fig. 4. A fraction of very small grains (several nanometers in diameter) is present among relatively big grains. The annealed nanocrystalline ribbons became magnetically soft because of the exchange interaction between these small grains with a fcc-structure composition. A fast Fourier transformation (FFT) performed for the areas belonging to big and small grains fully confirm the existence of the phases found by XRD investigations [22]. A detailed study of the crystallization process of the amorphous Fe81–xNixZr7B12 (x = 10-40) alloys revealed a two-step crytstallization behaviour for all compositions. Despite the fact that the hyperfine field in the Fe41Ni40Zr7B12 nanocrystalline alloy is reduced as compared with the bcc-Fe phase in NANOPERM alloys, an improved magnetic softness combined with a much reduced brittleness of the samples offer new attractive possibilities for technical applications of these novel Ni-containing nanocrystalline alloys. 3.2. Ribbons with nickel content x = 64 For an as-quenched fully amorphous Ni64Fe16Zr7B12Au1 ribbon, the DSC linearheating curve at heating rate of 20 K/min (not shown here) exhibited two main exothermic peaks with that were very similar to the ribbons with a lower Ni content. The first crystallization peak onset occurred at T1 = 448qC while the second one was at T2 = 492qC. Up to 900qC on DSC trace no other distinct thermodynamic events were found. Small anomalies around 350qC and 620qC can be related to the magnetic transitions and the final crystallization step, respectively. These onset temperatures for primary crystallization are associated with the nucleation process and the growth of new crystalline phase(s).

Figure 5. Mössbauer spectra recorded at 300 K on as-quenched amorphous Ni64Fe16Zr7B12Au1 alloy and on different crystalline states resulting from the annealing treatments at reported temperatures and corresponding hyperfine field distribution on the right [23]

The first fitting model consists of a pure discrete distribution of hyperfine fields which are presented in Fig. 5. In the case of as-quenched amorphous sample, the hyperfine field distribution maximum is shifted towards low fields by comparing to those usually observed on NANOPERM amorphous alloys. Such a reduction of field

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values is unambiguously attributed to the presence of Ni atoms homogeneously distributed in the amorphous matrix. The mean hyperfine field, estimated at about 14 T, is qualitatively explained by the large Ni content. For the nanocrystalline states, the hyperfine structure has to be interpreted in conjunction with the X-ray diffraction results (see Fig. 6). The shift of the high field peak towards high fields is attributed to the progressive transformation of the amorphous matrix into crystalline fcc-FeNi and then into crystalline (FeNi)23B6 grains. Indeed, the addition of Ni atoms favours the presence of different iron neighbours giving rise to broadened sextet lines and a decrease in the mean magnetic moment at Fe site, i.e. of the hyperfine field. In addition, the recent calculations of Fe23B6, Ni23B6 and (FeNi)23B6 allow us to estimate the magnetic moment at two main Fe sites. Taking into account the fact that 2.2 PB corresponds to the hyperfine field of 33 T, we performed the fitting of four additional magnetic subspectra (Zeeman sextets) corresponding to four inequivalent positions of Fe atoms in Fe23B6 unit cell, and succeeded in obtaining hyperfine fields at 33 T and 27.8 T. The two other hyperfine fields can be attributed to the atomic disorder around 57Fe site. In addition, the Ni enrichment of the amorphous matrix is fairly consistent with the presence of a low field component which progressively transforms into a paramagnetic phase. Thus, the Mössbauer data agree with XRD data. From the present study one can see the evolution of the volumetric crystalline fraction in terms of the Fe content.

Figure 6. XRD pattern of as-quenched Ni64Fe16Zr7B12Au1 ribbon and after annealing at different temperatures Ta for one hour. Black points denote an unidentified phase (or phases)

Figure 7. Magnetization vs. temperature for melt spun Ni64Fe16Zr7B12Au1 alloy in as-quenched state and after annealing [23]

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Figure 7 shows the temperature dependence of magnetization for Ni64Fe16Zr7B12Au1 alloy taken in an external magnetic field of 300 mT. The Curie temperature of asquenched ribbon is 405 K and slightly decreases for the amorphous fraction of partially recrystallized at 420°C and 435°C samples while low temperature magnetization is nearly the same. Heat treatment at the temperature range from 460°C to 500°C causes a formation of a nanostructure with optimal soft magnetic properties (Hc of about several Oe and relatively high saturation magnetization at room temperature), good thermal stability of the structure and favourable mechanical properties. 3.3. Calculations from the first principles For comparison of the magnetic measurements with the theory, the spin polarized tight binding linear muffin-tin orbital (TB-LMTO) method in the atomic sphere approximation (ASA) [24, 25] was used to computate the electronic band structure of Fe23B6 and Ni23B6 compounds. In this approximation, the crystal is divided into spacefilling spheres, therefore with slightly overlapping spheres centred on each of the atomic sites. The standard combined corrections for overlapping [24] were employed to compensate for the ASA errors. In the calculations reported here, the Wigner-Seitz (WS) sphere radii are such that the overlapping is below 10%. The total volume of all spheres Sj (j = 1, …, N) equalled the equilibrium volume of the unit cell. The value of the lattice constant of Fe23B6 compound a = 1.0761 nm was taken from the Ref. [11]. The value for Ni23B6 compound (x = 0 in Fex Ni23 – xB6 formula) was extrapolated using the experimental data for x = 23 [11] and x = 18.5 [16]. The systems are a cubic (Fm(3)m space group, no. 225); their unit cells accommodate four formula units with 116 atoms. There are four inequivalent positions of Fe (Ni) atoms (see Table II). Table II. Structural parameters of Fe(Ni)23B6 compounds and WS radii Sj [Å] (lattice constant a = 1.0761 nm [11] for Fe23B6, and extrapolated value a = 0.953 nm for Ni23B6) Atom Fe or Ni Fe or Ni Fe or Ni Fe or Ni B

(position) (4a) (8c) (48h) (32f) (24e)

X

Y

Z

0 ¼ 0 0.3809 0.2765

0 ¼ 0.1699 0.3809 0

0 ¼ 0.1699 0.3809 0

Sj Fe23B6

Ni23B6

1.7007 1.5576 1.3852 1.3543 1.1908

1.5213 1.3942 1.2205 1.1930 1.0683

As a starting point, the atomic configurations were assumed as follows: core[Ar] + 3d64s2 for Fe, core[He] + 2p22s for B, and core[Ar] + 3d84s2 for Ni. A fully relativistic approach for the core electrons and a scalar relativistic approximation for valence electrons were used. The Min-Jang [26] scheme for calculating the spin-orbit effects was employed. The exchange-correlation potential was chosen in the form proposed by von Barth and Hedin [27]. The self consistent calculations were performed for 256 k-points in the irreducible wedge (1/48) of the Brillouin zone. The tetrahedron method [28] was used for the integration over the Brillouin zone. The iterations were repeated until the accuracy of the energy eigenvalues within the error of 0.01 mRyd was achieved. The shape of the total and local densities of states (DOS) depends on the type

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of atom, its position and the local environment. The values of total DOS at the Fermi level EF are equal to 10.589 and 4.385 states/(eV f.u.) for Fe23B6 and Ni23B6 compounds, respectively (see Figs. 8 and 9). Owing to their large numbers, the d electrons contribute significantly to the total DOS for E = EF: about 90%. The calculated total magnetic moments for Fe23B6 and Ni23B6 compounds are equal to 48.758 and below 10–4 PB/f.u., respectively. Local contributions provided by particular atoms are collected in Table III.

Figure 8. Total and local DOS plots for Fe23B6 compound

Figure 9. Total and local DOS plots for Ni23B6 compound

Table III. Local magnetic moments for Fe, Ni, and B atoms in Fe23B6 and Ni23B6 compounds Compound Fe23B6 Ni23B6

Magnetic moments [PB/atom] for given position 4a 8c 48h 32f 24e 2.982 2.553 2.222 1.877 –0.167 41 u 10–6 9 u 10–6 7 u 10–6 7 u 10–6 1 u 10–6

Especially high values of magnetic moments are located on Fe(4a) and Fe(8c) atoms, higher than those for bulk bcc-Fe system (about 2.2 PB/atom). The values of the magnetic moments depend on the local environment of Fe atoms: the types of neighbours and the distances between the atoms. In the case of 4a and 8c positions, inter-atomic distances larger than those for bcc-iron lead to larger Wigner-Seitz radii and larger magnetic moments. These data can be interpreted qualitatively as showing a tendency toward the localization of the d electrons [29]. With increasing WS radii, the magnetic

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moments approach values closer to the value of the moment of an isolated Fe atom. By increasing the number of neighbouring boron atoms we may reduce the magnetic moment of iron. In the case of Ni23B6 compound the magnetic moments are reduced (in fcc-Ni about 0.6 PB/atom) to zero.

4. CONCLUSIONS We have studied the influence of the annealing temperatures on the nanostructure formation and magnetic behaviour of amorphous and nanocrystalline Ni-containing alloys. The initial temperature of crystallization was determined by DSC and VSM measurements. After annealing, the ribbons became magnetically soft. Moreover, in a nanocrystalline state they show good mechanical properties when compared with the FINEMET, NANOPERM or HITPERM. Room temperature 57Fe Mössbauer results carried out in transmission geometry show a distribution of hyperfine fields that is consistent with FeNi atomic disorder in the crystalline phase and with the magnetization data. The saturation of magnetization does not depend much on the crystal structure (even in amorphous or nanocrystalline states). Band structure calculations have shown that the local magnetic moments of Fe and Ni atoms in Fe23B6 and Ni23B6 compounds depend on their local environments. The iron magnetic moments are enhanced up to about 3 PB/atom and for nickel reduced (in fcc-Ni about 0.6 PB/atom), even to zero. The presence of this metastable phase as a nanocrystalline fraction in an amorphous matrix is responsible for the soft magnetic behaviour of these composites. Especially, an amorphous precursors with high Ni-content (e.g. Ni64Fe16Zr7B12Au1) exhibit particularly good soft magnetic properties after an optimal crystallization procedure. ACKNOWLEDGEMENTS I am indebted to many people for helpful discussions during the preparation of a series of papers on those new nanocrystalline phases. Especially, I wish to thank Dr. A. Szajek for numerical calculations of the metastable phases parameters, Professor M. Kopcewicz and Dr. J.-M. Greneche for Mössbauer effect investigations, Professor M. Giersig for TEM and electron diffraction experiments and Dr. Z. Horvath for many valuable suggestions.

REFERENCES 1. Yoshizawa, Y., Oguma, S., and Yamauchi, K., (1988) J. Appl. Phys. 64, 6044. 2. Suzuki, K., Makino, A., Inoue, A., and Masumoto, T., (1991) J. Appl. Phys. 70, 6232. 3. Willard, M.A., Laughlin, D.E., McHenry, M.E., Thoma, D., Sickafus, K., Cross, J.O., and Harris, V.G. , (1998) J. Appl. Phys. 84, 6773. 4. Herzer, G., (1993) Phys. Scr. T 49, 307. 5. Alben, R., Becker, J.J., and Chi, M.C. (1978) J. Appl. Phys 49, 1653. 6. Harris, R., Plischke, M. and Zuckermann, M.J., (1973) Phys. Rev. Lett. 31, 160. 7. Mizgalski, K.P., Inal, O.T., Yost, F.G., and Karnowsky, M.M., (1981) J. Mater. Sci. 16, 3357. 8. Li, J., Su, Z., Wang, T.M., Ge, S.H., Hahn, H., and Shiari, Y., (1999) J. Mater. Sci. 34, 111.

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Nakamura, T., Koshiba, H., Imafuku M., Inoue, A., and Matsubara, E., (2002) Mater. Trans. 43, 1918. Suzuki K., Kataoka, N., Inoue, A., Makino, A., and Masumoto, T., (1990) Mater. Trans. JIM 31 743. Khan, Y. and Wibbeke, H., (1991) Z. Metalkd. 82, 703. Chen, W.Z. and Ryder, P.L., (1995) Mat. Sci. Eng. B, 34, 204. Chen, W.Z. and Ryder, P.L., (1997) Mat. Sci. Eng. B, 49, 14. Borrego, J.M., Conde, C.F., and Conde, A., (2000) Phil. Mag. Lett. 80, 359. Blazquez, J.S., Conde, C.F., and Conde, A., (2001) Appl. Phys. Lett. 79, 2898. Monnier, G., Riviere, R., and Ayel, M., (1967) Comptes rendus 264 C, 862. Kopcewicz, M., Idzikowski, B., and Kalinowska, J., (2003) J. Appl. Phys. 94, 638. Gloriant, T., Surinach, S., and Baro, M.D. (2004) J. Non.-Cryst. Solids 333, 320. Uriarte, J.L., Yavari, A.R., Surinach, S., Rizzi, P., Heunen, G., Barrico, M., and Baro, M.D., (2003) J. Mag. Mag. Mater. 254-255, 532. Kostyrya, S., ĝniadecki, Z., and Idzikowski, B. (2005) phys. stat. sol. (b), in print Kopcewicz, M., (2005) Radio-Frequency Mössbauer Spectroscopy in the Investigation of nanocrystalline Alloys, in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec and M. Miglierini (eds.), Kluwer Academic Publishers, Dordrecht, 395-407. Idzikowski B., and Giersig, M., in preparation. Idzikowski, B., Greneche, J.-M., Szajek, A., and Kovaþ, J. (2004) Appl. Phys. Lett. 85, 1392. Andersen, O.K., Jepsen, O., and Šob, M., Electronic Structure and its Applications, M. Yussouff (ed.), Springer, Berlin (1987), p. 2. Krier, G., Jepsen, O., Burkhardt, A., and Andersen, O.K., The TB-LMTO-ASA Program (source code, version 4.7). Min, B.I. and Jang, Y.-R., (1991) J. Phys.: Condens. Matter 3, 5131. von Barth U., and Hedin, L., (1972) J. Phys. C 5, 1629. Blöchl, P., Jepsen, O., and Andersen, O.K., (1994) Phys. Rev. B 49, 16223. Bagayoko, D. and Callaway, J., (1983) Phys. Rev. B 28, 5419.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

22. 23. 24. 25. 26. 27. 28. 29.

APPLICATIONS OF AMORPHOUS MAGNETIC ALLOYS

RYUSUKE HASEGAWA Metglas, Inc, 440 Allied Drive, Conway, SC 29526, USA Corresponding author: R. Hasegawa, e-mail: [email protected] Abstract:

Examples of several recent developments in the use of amorphous magnetic alloys are summarized. They include from such devices as utility transformers for energy conservation, charged particle accelerators for energy generation, sensors to monitor energy flow and the environment, and telecommunication devices. Specific properties of the amorphous materials that lead to these applications are pointed out.

1. INTRODUCTION Amorphous magnetic alloys are used in many areas, including transformers for electric power distribution, power electronics for small and large-scale power management, pulse power devices, telecommunication devices, and sensors. The energyefficient nature of amorphous magnetic materials has a great impact on global energy savings when large devices such as transformers are in use. The ubiquitous use of power electronics in information technologies demand ever-more efficient electronic devices in which amorphous soft magnets play a major role. These devices, however, introduce harmonic distortions in the electrical power lines, which in turn increase total transformer losses. Although this has been recognized, its impact on the total losses of conventional transformers has been found to be considerably larger than on amorphous metal-based transformers [1]. Thus, the use of amorphous metal-based electrical transformers is becoming increasingly significant. In the power electronics area, small-size saturable cores using non-magnetostrictive amorphous alloys have been widely utilized as magnetic amplifiers to control output voltages of switch-mode power supplies in PCs and the like. The trend in the small-size power supplies is toward dc-to-dc conversion with low output voltages (~1 volt) and high currents (10-100 A), which requires low-loss electrical chokes. These components are usually based on high induction Fe-based alloys [2]. The magnetic characteristics of these components can be utilized in power factor correction to maximize electrical power usage in power conditioning devices. 189 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 189–198. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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Large-size saturable cores feature the unique combination of fast-flux reversal and a large flux swing achievable in amorphous magnetic alloys, and have been used in devices handling large pulse-power ranging from kilo- to tera watts. The end usages are found in power supplies for lasers and in particle accelerators. Future applications of these devices will be found in the area of energy generation which needs to be lessfossil-fuel dependent. In telecommunication systems, signal transmission in wide-frequency ranges must be distortionless. Low magnetic loss and fast-flux reversal of amorphous soft magnets achieve this requirement. Thus far small pulse transformers with these characteristics have been used in ISDN. Recently it has become necessary to utilize conventional telephone lines more effectively. For example, one line can carry two independent communication signals, which is known as DSL. This requires frequency band-pass filters. It has been found that amorphous soft magnetic alloys with relatively linear BH behaviours are well suited for this application. In the area of sensors, the use of amorphous magnetic metals in electronic article surveillance has been around for sometime. Some new, better performing materials, which extend the scope of this application, have been introduced [2]. Noted development is the use of similar materials in a number of sensing elements for temperature, pressure, magnetic field, and current/voltage. The high magnetic permeabilities achievable in these materials are also useful in magnetic shielding, the need for which is ever increasing due to the wide use of electronic devices in smaller spaces. Representative examples of the wide varieties of applications mentioned above are covered in this presentation, emphasizing new developments. 2. POWER SYSTEMS An enormous amount of electrical power is being consumed worldwide with an annual increase in the rate of consumption of about 2-3% in industrial countries and more than 5% in developing countries. Of all the electric energy generated, about 2-3% is lost in distribution transformers. This lost energy amounts to about 61 TWh in the U.S. alone, according to the International Energy Agency (IEA) [3]. If we use energy-efficient transformers such as amorphous metal-based units, we can reduce the loss by at least 1/2. A by-product of the loss reduction is the decrease in the emission of hazardous gas such as CO2. Each country has set different specifications for transformer losses, and the degree of energy savings differs from country to country. Estimated transformer loss, energy savings and resultant CO2 gas reduction for some selected countries are given in Table I [4]. If we add the numbers for developing countries, worldwide distribution transformer loss would exceed 200 TWh if we keep using conventional transformers. Considerable global energy savings of ~100 TWh are possible by adopting energy-efficient transformers with CO2 emission reduction of about 50-100 million tons annually. Everincreasing energy need with added loss impacts from harmonic distortions in the energy distribution systems and increased use of less efficient smaller transformers due to decreased energy-distribution distances (a by-product of deregulation) will make it necessary to adopt low-loss transformers.

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Recognizing the benefits of energy-efficient transformers, many countries have launched “initiatives”. However, most of the proposed programs are voluntary, as in the case of “the Energy Star” labelling scheme introduced by the Environmental Protection Agency of the U.S. At the moment, Mexico is the only country where minimum energy standards are implemented according to the IEA [3]. Japan has launched a “Top Runner Scheme” which will be legally implemented in 2006 [5]. In this program, “the energy efficiency standards for equipment are set at higher levels than the performance of the best-efficient equipment among currently commercialized products for each equipment category, including transformers”. Table I. Transformer losses, energy savings and reduction of CO2 emission for selected countries Country EU Former Eastern Block US China Japan

Transformer loss [TWh] 40-50 * 61 * 27

Potential savings [TWh] 22 10 45 47 24

CO2 emission reduction [Mt/y] 9 10 34 52 10**

*data not available, **an estimate of 0.4 kg CO2 / kWh used as in Europe

The main characteristic of amorphous metal-based distribution transformers is their exceptionally low core- (or no-load) loss. In the rural electricity distribution systems in which load factors are low, this feature is well noted. A recent study in Brazil shows a considerable reduction in the total cost for these energy-efficient units used in rural areas [6]. In areas with mixed-load characteristics in rural and industrial settings, the impacts of harmonic distortions mentioned above become apparent as shown in a study conducted in India [7]. 3. PULSE POWER DEVICES Pulse power can be conveniently generated by compressing pulses; concepts based on magnetic switches have been implemented successfully using amorphous soft magnetic materials with relatively high-saturation inductions [8]. The advantage of using this kind of magnetic switch includes the capability of attaining high voltages of several hundred kVs and shorter pulse widths of less than 500 ns. Thus far these applications have been mostly used in pulse sources for lasers and some particle accelerators in the U.S. national labs. The basic principle is based on a succession of typical LC resonant circuits with decreasing resonant time at each stage of pulse compression, forming a successive energy transfer circuit. Thus as the pulse width decreases, the voltage increases, giving more acceleration for the charged particles as discussed below. Recent advances in the field include the use of pulse devices in heavy-ion induction accelerators [9]. These accelerators are being developed with a goal of driving inertial fusion energy power plants to generate electricity without generating CO2. Heavy-ion inertial fusion energy has several advantages: Accelerators provide high-reliability, long life-time, high repetition-rate, and high efficiency. All of them are desirable in a power

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plant. A lower-cost, more rapid-development path is possible because the accelerator, the fusion chamber and the target factory can be developed independently. Thick liquidwalled chambers using salts consisting of low-atomic-number elements give the potential of low-activation power plants. Fuel, deuterium, heavy-hydrogen from water and tritium, are available in every country and no green-house gases are produced during the operation of a fusion-power plant. Induction accelerators have been chosen by the U.S. heavy-ion fusion program because of the high beam currents that can be accelerated. Present designs call for accelerating the current of the of order of 100 A, typically in about 100 beams of about 1 A each, near the injector. Pulse compression raises the beam current to the order of 10 kA by the end of the accelerator. Such dense currents can be readily handled with induction accelerators which has already been demonstrated in electron accelerators. The beam in an induction accelerator can be thought of as a secondary transformer; a voltage pulsed across the primary appears along the beam and accelerates the charged particles in it. From Faraday’s law, the acceleration voltage V is given by ('B/'t)S, where 'B is the flux change in the ferromagnetic induction core, 't is the duration of the voltage pulse, and S is the cross-sectional area of the core. It is clear that higher voltage can be achieved with a higher flux-swing material, with a shorter duration pulse, and a larger area core. Other electric and magnetic fields, usually DC, confine and transport the current with low losses, utilizing Lorentz’ force. Combining these two basic physics rules, one can construct a device in which a beam of charged particles can be confined and accelerated at the same time. Figure 1 shows one such example: a high DC voltage is supplied into a pulse compression network composed of saturable reactors SR and capacitors C, the output of which is a short high-energy pulse and is fed into the one-turn primary winding of a magnetic inductor with a square BH loop. This, in turn, generates a flux swing 'B in the inductor, inducing a voltage V (~'B/'t) across an ion beam. A constant flux B supplied by the superconducting magnets confines the beam along the direction of the flux B, and the induced voltage V accelerates the ions in the beam. Given the accelerator configuration of Figure 1, one can optimize the device design according to our needs. For example, depending on the acceleration voltage necessary for the overall operation, the number of stages or inductors can be varied accordingly. The paragraph below describes the current effort. The magnetic material suited for the present application must have a large flux swing with a small magnetic loss under a high rate of magnetization change. In addition, because a large amount of the material is needed for the actual operation of the device, the cost of the material has to be taken into consideration. In the light of these requirements, iron-based alloys with relatively high saturation inductions such as crystalline Si-Fe alloys, Fe-based amorphous and nanocrystalline alloys have been considered and studied. Figure 2 summarizes the results reported in Ref. 9 on the coreloss vs. magnetization rate for the representative materials with similar thicknesses (20-25 Pm). Their flux swing 'B varied between materials and ranged from 2.4 T for the amorphous and nanocrystalline materials to 3.0 T for 3% Si-Fe. Since the flux reversal is considered through magnetization rotation, eddy-current is the major source of the core loss. Larger resistivities by a factor of about 3 of the amorphous and nanocrystalline materials compared with the crystalline material are reflected in the core

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losses of the data obtained. When the material cost is considered, the data indicate that amorphous Fe-based alloys are the best candidates for a core material to accelerate charged particles in a heavy-ion fusion device. It has been reported that these materials exhibit an acceleration efficiency exceeding 50% for pulses shorter than 1 Ps in a 3.3 MJ, 1.3 GeV Kr + driver [10].

Figure 1. Schematic diagram of a simple charged particle accelerator (simplied diagram of Fig. 1 of Ref. 9). Depending on the magnetic properties of the inductor core and its physical dimension, the accelerating voltage of each inductor stage can be determined. To achieve a desired final acceleration voltage, additional inductor stages are placed accordingly

Figure 2. Core loss as a function of magnetization rate for a crystalline 3% Si-Fe (A), amorphous Fe-B-Si alloy (B), amorphous FeB-Si-C (C) and nanocrystalline Fe-based alloy (D). The thickness of these materials is 1825 μm. (Data taken from Figure 6 of Ref. 9)

An alternative approach to charged particle acceleration has been considered utilizing an rf technology [11]. The accelerators in this study were for 3 and 50 GeV proton synchrotrons operated at 2-3.4 MHz with the required high-frequency voltages of 420 and 270 kV, respectively. The high frequency current is fed into a central conductor of a co-axial line with a magnetic inductor forming a LC resonant circuit. The voltage appearing in the gap in the cavity is used as a particle-accelerating voltage. Ferrites were used for the core material of the inductor, but had some drawbacks, including dynamic property degradation by disaccommodation, permeability change with the amplitude of high-frequency excitation and its resultant non-linear oscillation in the resonant cavity. In addition, constructing a large ferrite core with a certain level of uniformity is relatively difficult. In this situation, a new core material is being sought. Considering the high-frequency properties needed for this application, the investigators of Ref. 11 have evaluated amorphous and nanocrystalline materials. The per-

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Figure 3. Performance factor μ’Qf as a function of frequency for a nanocrystalline Fe-based alloy (A), amorphous Co-base alloy (B) and amorphous Fe-base alloy (C)

formance of a resonator is determined mainly by the real part of the permeability, μ’, of the core material, quality factor Q of the circuit and the operating frequency f. Since the product, μ’Qf is proportional to the shunt impedance of the resonant cavity, this quantity represents the overall characteristic of the device. Figure 3 compares the results obtained for Fe- and Co-based amorphous alloys and a nanocrystalline alloy. The high μ’Qf values obtained for a Co-based amorphous alloy and a nanocrystalline Fe-based alloy indicate that these materials result in more compact cores than an Fe-based amorphous alloy. 4. SENSORS Several sensors using amorphous materials have been mentioned in earlier publications [2, 12, 13] and a recent development in this field is summarized below. The general trend has been to utilize high permeabilities achievable in these materials. The new development includes current sensors which require relatively low permeabilities and sensors based on the features combining high permeabilities and other unique properties of amorphous materials such as magnetoelastic properties.

Figure 4. Linear BH loops for an amorphous Fe-B-Si (A) and Co-Fe-B-Si alloy (B)

Accurate sensing of the current in electrical power distribution systems is important in power metering for utility purposes and in current monitoring to control equipment accurately. When a current level is low, a simple current by-pass circuit is sufficient. However, monitoring a large current requires a current transformer which isolates the large current-carrying wire. The function of this transformer is to accurately monitor the current in the primary winding in terms of the voltage appearing in the secondary

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winding. This requires a magnetic core for the transformer to have a linear BH characteristic. There are several ways to achieve linearity in the BH behaviour of a magnetic material. The most straightforward technique is to field anneal a magnetic material so that its easy axis is 90 degrees away from the magnetic field direction of a device in operation. This is relatively easy for a material with a low magnetic anisotropy, which is the case with Co-rich low magnetostrictive amorphous alloys. Because of the low magnetic anisotropies, their permeabilities are high, and the current sensors based on these materials saturate with low currents. When the saturation induction is relatively low, it limits the upper current level to be monitored. The upper limiting current can be increased if the core material has a higher saturation induction, as in the case with Fe-based material. Examples of the linear BH loops obtained for Coand Fe-based amorphous alloys are compared in Fig. 4. It is noticed that the upper field (corresponding to the upper current to be measured) is higher for the Fe-based core than the Co-based one [14]. For a much higher current sensor, a low linear permeability of the core material is required with a high saturation induction so that it does not magnetically saturate. To meet these requirements, magnetic cores made from Fe-based amorphous alloys were heat-treated with high magnetic fields applied perpendicular to the cores’ circumference direction or were gapped [15]. Some of the gapped cores could handle currents to about 800 A. A recent work based on a study of compacted cores using nanosize amorphous magnetic powders obtained by a borohydride chemical reaction indicate that the upper current limit can be further extended to a magnetic field exceeding well over 100 Oe [16]. This results from the particles being 10-50 nm in size and single magnetic domains, and the forming the chain-like structures. Thus the permeabilities of the compacted cores depend mostly on the shapes of the chains. In the present case, the permeability of the cores ranges from 10-15 irrespective of the saturation induction of the particles. Because of low permeability, the upper limiting field can be as high as 500 Oe [17].

Figure 5. Resonance frequency, fr, and signal level as a function of a dc bias field, Hb, for an amorphous metal strip with magnetoelastic properties. T1 and T2 are the temperatures of the strip provide a caption for this figure

A temperature sensor has been developed taking advantage of the temperature dependence of the higher harmonic response of amorphous metal strips with high permeabilities [18]. A variety of excitation and sensing modes can be adopted because since the harmonic response is limited to odd harmonics of the exciting field when the non-linear BH loop of the sensing element is symmetric (corresponding to the case in which there is no dc bias) or includes even harmonics when the BH loop is asymmetric (corresponding to the case where a dc bias field is applied to the sensing element). Another temperature sensor, based on the magnetoelastic effect of the amor

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phous metal strip, has been proposed [19]. The operation principle of this sensor is illustrated in Fig. 5. When a magnetoelastic amorphous metal strip with a density ȡ and a Young’s modulus E is placed in an oscillating magnetic field, the strip resonates mechanically at a frequency fr = (E/ȡ)1/2/2l, where l is the length of the strip. The resonance frequency depends on the dc bias field Hb applied along the strip length direction as depicted by the lower curves of Fig. 5, in which its temperature dependence is shown. The sensing voltage shown by the upper curve does not change too much with a relatively small change in temperature. As noticed in this figure, the resonance frequency decreases with an increase in the sensing element temperature for a bias field well below Hb2 at which fr is a minimum. The opposite holds when the bias is well above Hb2. Thus measuring fr at a given bias field level, one can determine the temperature of the sensor. In this magnetomechanical resonance, the frequency fr can be determined with a high accuracy (better than 0.01%) making this a reliable temperature sensor. A bimetallic temperature sensor has been demonstrated utilizing the magnetostrictive effect of certain amorphous metal strips in conjunction with the thermal expansion coefficient difference between metals, [20]. Most of the magnetostrictive amorphous metal ribbons show thermal expansion coefficients, ț, of (5-10) × 106/oC, which are smaller than those of typical metals such as Al (ț ~ 24 × 106/oC) and Cu (ț ~ 17 × 10–6/oC). Thus a bimetallic layer based on Al and amorphous alloy ribbon should result in an effective temperature-sensing element as suggested in Ref. 20. The choice of the magnetostrictive amorphous metal layer, on the other hand, should be made by considering the magnetomechanical coupling constant, Ȝ2/K, where Ȝ and K are the magnetostriction and the anisotropy energy of the ribbon material, respectively. A smaller K also implies a larger magnetic permeability, resulting in a larger sensing signal. Thus a larger Ȝ alone is not sufficient. 5. TELECOMMUNICATION DEVICES Due to the increased demand for telecommunication lines, a single line is now divided frequency-wise to carry multiple bands covering frequency spectrum from the conventional telephone to modem lines. To avoid cross-talking between different lines, effective band-pass filters are needed. These filters are based on conventional LC resonance circuits and their resonance frequencies must be relatively constant with varying signal amplitudes. For this type of applications, the BH behaviours depicted in Fig. 4 are useful as disclosed previously [21]. When used as the core material of the inductor of a simple band-pass filter shown by the inset of Fig. 6, the linear BH behaviour of Fig. 4B taken on a Co-based near zero magnetostriction alloy results in the shift of the resonance frequency with varying field as shown by the curve B in the figure. As shown in Figures 4 and 6, the linearity breaks down abruptly with an applied above 10 Oe, whereas the curve A taken on an Fe-based amorphous alloy maintains the linearity above 10 Oe, extending its usefulness to a higher field. Additional advantages of the Fe-based filter core is its lower inductance which varies with the ambient temperature because of its higher Curie temperature compared with the Co-based one.

Applications of Amorphous Magnetic Alloys

Figure 6. Resonance frequency shift as a function of applied field for the filters using the core materials A and B from Fig. 4. The inset shows a simple bandpass filter based on aLC resonant circuit

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Figure 7. A tunable SAW device utilizing a magnetostrictive amorphous film with the magnetic hard axis along the wave propagation direction. The device configuration was originally proposed in Ref. 23

Another type of filter needed in cellular and cordless telephone systems is based on magnetomechanical resonance. In this case, the central resonance frequency covers 1-2 GHz region and a new approach to the frequency tuning has been recently proposed [22]. The tuning method utilizes a surface acoustic wave (SAW) propagation, as shown schematically in Fig. 7. In this device, the resonance frequency is shifted by changing the propagation velocity of an SAW through a giant ǻE effect which is depicted in Fig. 5. The same magnetomechanical resonance frequency, fr, defined above, applies to the magnetostrictive film of Fig. 7. An amorphous magnetostrictive Fe-based magnetic film is attached to a piezo-electric film, a ZnO film in the case of Ref. 22, which serves as a transducer. Thus the frequency shift ǻf/f = (1/2)(ǻE/E) can be controlled by the applied magnetic field, resulting in a magnetically tunable resonator. Since the frequency shift in this case is an order of magnitude higher than that due to the temperature change, the temperature-resonance frequency shift utilized in the temperature sensor mentioned above does not affect the operation of the present SAW device. The SAW device of Fig. 7 was originally proposed to make a conventional SAW delay line tunable [23].

6. CONCLUSIONS Amorphous magnetic alloys find wide use in components of devices for energy generation and conservation, sensors to monitor the environment and to control electrical and electronic devices, and telecommunication devices. These are just a few examples from the recent development in the field. All of these achievements are mainly the result of the unique combination of the electromagnetic and mechanical properties of amorphous materials, which are readily varied by changing the chemical composition of the alloys. ACKNOWLEDGEMENTS Technical advice given to the author by Dr. A.W. Molvik of University of California Berkeley and correspondence with Dr. P. Smole of Vienna University of Technology are greatly appreciated.

R. Hasegawa

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Hasegawa, R. and Pruess, D.C. (2001) Impact of amorphous metal based transformers on efficiency and quality of electric power distribution, Proceedings of the the Summer Meeting of IEEE Power Engineering Society (Vancouver, Canada; 15-19 July 2001). Hasegawa, R. (2000) Present status of amorphous soft magnetic alloys, J. Magn. Magn. Materials 215-216, 240-245. Lebot, B. (2002) Energy-efficient distribution transformers: a hidden opportunity for large scale energy savings, Proceedings of the 3rd International Workshop on Distribution Transformer Efficiency (Treviso, Italy, 17 September 2002), p. 15-24. Targosz, R. (2002) Central European perspective, ibid , p. 121-128. Hoshino, M. (2002) Latest standards for transformer efficiency in Japan, ibid, p. 91-100. Luciano, B.A., Nóbrega, R.S., Gama dos Santos, M.B. and Cavalcanti, L.F. (2002) Amorphous alloy core transformers: an experience in the Celb rural distribution system, Proceedings of the International Congress and Exhibition on Electrical Distribution (Cidel, Argentina, 03-05 December 2002), paper 3.9.74. Trivedi, U. C., Gupta, V., Ramamoorty, M. and Hasegawa, R., presented at the International Power Engineering Conference, September 2003, Singapore. Smith, C.H. (1990) Application of amorphous magnetic materials at very-high magnetization rates, J. Appl. Phys. 67, 5556-5561. Molvik, A.W. and Faltens, A. (2002) Induction core alloys for heavy-ion inertial fusionenergy accelerators, Phys. Rev. Special Topics-Accel. & Beams 5 , 080401-1-20 Molvik, A.W. and Faltens, A. (2001) Nucl. Instrum. Methods Phys. Res., Sect. A464, 445-451. Nakayama, H., Uesugi, T., Ezura, E., Ohmori, C., Kanei, Y., Kiba, K., Saito, K., Sato, Y. Sauda, M., Takagi, A., Tanabe, T., Tanabe, Y., Toda, S., Fujieda, M., Matsumura, R., Mori, Y., Yamamoto, M., and Yoshii, M. (1999) Summary of the measurement of magnetic materials for JHF RF cavity (2)-FINMET-, KEK (High Energy Accelerator Research Organization, Japan) Report 98-13 (in Japanese), p. 1-36. Hasegawa, R. (2001) Applications of amorphous magnetic alloys in electronic devices, J. Non-Crystal. Solids 287, 405-412. Hasegawa, R. (2003) Applications of amorphous magnetic alloys, J. Mater. Sci & Eng. (to be published). Hasegawa, R. and Martis, R.J. (2003) U.S. Patent (pending). Hasegawa, R. and Martis, R.J. (2003) U.S. Patent (pending). Hasegawa, R., Hammond, V.H. and O’Reilly, J. M., (2003) Magnetic inductor based on nanosize amorphous metal powder, (submitted for publication). Because of the instrument limitation, a linear BH dependence could be measured up to about 100 Oe in Ref. 16. Ong, K.G., Grime, D.M., and Grimes, C.A. (2002) Higher-order harmonics of a magnetically soft sensor: Application to remote query temperature measurement, Appl. Phys. Lett. 80, 3856-3858. Mungle, C., Grimes, C.A., Breschel, W.R. (2002) Magnetic field tuning of the frequencytemperature response of a magnetoelastic sensor, Sensors & Actuators A 101, 143-149. Mehnen, L., Pfützer, H., and Kaniusas, E. (2000) Magnetostrictive amorphous bimetal sensors, J. Magn. Magn. Mat. 215-216, 779-781. Hasegawa, R, Tatikola, S., and Martis, R. J. (2003) U.S. Patent (pending). Smole, P., Ruile, W., Korden, C., Ludwig, A., Quandt, E., Krassnitzer, S. and Pongratz, P. (2003) Magnetically tunable SAW-resonator, Proceedings of 2002 IEEE Frequency Control Symposium (to be published). Webb, D.C., Forrester, D.W., Ganguly, A.K., and Vittoria, C. (1979) Applications of amorphous magnetic layers in surface acoustic wave device, IEEE Trans. Mag. 15, 1410-1415.

MAGNETIC CRYSTALLINE TRANSITION METAL RIBBONS PREPARED BY MELT-SPINNING AND REACTIVE ANNEALING S. ROTH, G. SAAGE, J. ECKERT, and L. SCHULTZ IFW Dresden, Institute for Metallic Materials P.O. Box 27 01 16, D-01171 Dresden, Germany Corresponding author: S. Roth, e-mail: [email protected] Abstract:

Transition metal alloys are often difficult to be prepared as amorphous ribbons by conventional methods. If boron is added to these alloys, amorphous ribbons may be prepared by melt spinning. These amorphous ribbons have a better workability than the crystalline ones. However, their composition is different from the target composition. Upon annealing treatments in flowing hydrogen the boron may be extracted and the ribbon crystallizes. Thermodynamically, the extraction of boron proceeds by the reaction of hydrogen with the borides formed during the crystallization of the ribbons. In order to investigate this extraction in more detail Fe80B20 amorphous ribbons were used. Thermogravimetric measurements were performed at three different heating rates, which permitted to develop a thermokinetic description of the extraction process. It is controlled by chemical reactions and diffusion. The description allows to calculate the degree of boron extraction for various annealing procedures. After the extraction of boron the ribbon becomes a single phase. Various soft magnetic alloys can be prepared by this method. For Fe15Co10Si, the coercivity is 36 A/m and the saturation polarization is 1.45 T. Core losses in sinusoidal magnetic field measured at 50 Hz to 500 Hz at 1 T are 1.36 W/kg to 18 W/kg.

1. INTRODUCTION It is often difficult to prepare ribbons of transition metal alloys with brittle behaviour by conventional methods. The possibility to prepare such alloys as ribbons by melt spinning is achieved by adding a certain amount of glass formers, e.g. boron, to the initial composition. The initial state of the ribbons is amorphous with good bending ductility. After the preparation of the ribbons in the desired shape, the glass former is extracted by annealing the ribbons in a reactive atmosphere. A similar method was first mentioned by Maringer and Vassamillet [1]. There, the reactive atmosphere was air or wet hydrogen. This permitted selected oxidation of the glass formers without oxidizing the iron. After the heat treatment, the oxide “skin” was removed by chemical etching. Roth [2] for the first time, reported on the extraction of 199 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 199–207. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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boron from transition metal-boron alloys by a two step annealing process in wet and dry hydrogen to prepare soft magnetic alloys. The annealing in wet hydrogen produces to an oxidation layer on the surface which, in the case of Si-containing alloys, cannot be removed by the second annealing in dry hydrogen. In previous papers [3-5] we presented the results of the preparation of Fe-Co-Si ribbons by adding boron to the base composition and removing the boron after the processing. In these studies, the reactive atmosphere was dry hydrogen. Boron was nearly completely extracted from the ribbons. The extraction was caused by gas-solid reactions between the hydrogen and the ribbon, and by the formation of boron hydrides which, being gaseous, escape. In our previous study [6], the gas-solid reactions were investigated from a more fundamental point of view using Fe80B20 as a model alloy in order to determine the type of the reactions and the corresponding activation energies. These studies gave the basis for the preparation of crystalline soft magnetic alloy ribbons by rapid solidification and subsequent annealing in a reactive atmosphere.

2. EXPERIMENTAL 2.1. Preparation Ingots of various iron TM-Si-B (TM = transition metal) alloys were prepared by arc melting. High purity starting materials were used. Ribbons of 10 mm width and about 20 μm thickness were prepared by planar flow casting. These ribbons were cut into stripes of about 100 mm length which were subjected to annealing in dry or wet flowing hydrogen at various temperatures for various times. 2.2. Characterization The boron content of the samples was determined spectroscopically. Soft magnetic properties were measured in a long solenoid in external fields up to 5 kA/m. The coercivity was taken from quasistatic hysteresis loops with a field amplitude of 1 kA/m. The saturation magnetization as a function of the temperature was measured by a Faraday magnetometer in a field of 0.7 T at a constant heating rate of 10 K/min. Some annealing states of an Fe-Si-B-alloy were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to characterize their phase composition. The extraction process was investigated in more detail by a thermogravimetric investigation with a simultaneous analysis of the gas atmosphere by mass spectrometry. In order to develop a mathematical description of the boron extraction, simultaneous thermogravimetric and single differential thermal analyses (sDTA) were performed in a NETZSCH STA 429 analyser using 600 mg samples of Fe80B20 placed into alumina crucibles under the hydrogen flow. The mass loss vs. time was measured at heating rates of 2.5, 5 and 10 K/min from room temperature up to 1150°C. These data were analysed using the NETZSCH Thermokinetics – Program [7]. This description was used to pre-

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dict the amount extracted boron for samples which were annealed for different times at different temperatures. In this case, the mass loss was determined by weighing the samples prior to and after annealing. 2.3. Results 2.3.1. 2B7.9(Fe-Si) wt.% ribbons Figure 1 shows the coercivity for different annealing states of a 2B7.9(Fe-Si) wt.% alloy. The duration of the first annealing has little influence on the coercivity, if the first annealing temperature is above 800°C. The coercivity after the first annealing decreases with a increasing annealing temperature. The second annealing at 1100°C in dry hydrogen causes a remarkable decrease in the coercivity for all preliminary annealing

Figure 1. Coercivity of a 2B7.9(Fe-Si) wt.% alloy after annealing in wet H2 at TA for 0.5 or 2 h, and after subsequent annealing at 1100°C in dry H2 for 2 h

Table I. Boron content of the 2B7.9(Fe-Si) wt.% ribbons after annealing in wet and dry hydrogen 1st annealing (wet H2) 2nd annealing (dry H2 ) B T (°C)/t (h) T (°C)/t (h) (wt.%) – 1100/2 1.22 900/0.5 1100/2 0.01 900/2 1100/2 not detectable

Table II. Constitution of the 2B7.9(Fe-Si) wt.% ribbons after annealing in wet and dry hydrogen determined by X-ray diffraction minor phase 2st annealing (dry H2 ) main phase 1st annealing (wet H2) (2nd phase) T (°C)/t (h) T (°C)/t (h) (1st phase) Fe2B, and traces 700/0.5 – bcc-Fe(Si) not identifiable 900/0.5 – bcc-Fe(Si) Fe2B 900/2 – bcc-Fe(Si) Fe2B 700/0.5 1100/2 bcc-Fe(Si) little Fe2B 900/0.5 1100/2 bcc-Fe(Si) traces of Fe2B 900/2 1100/2 bcc-Fe(Si) none

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treatments. Coercivities of less than 100 A/m are obtained as a result of two step annealing, if the first annealing in wet hydrogen has taken place at a temperature above 800°C followed by annealing in dry hydrogen at 1100°C. If the first annealing temperature is above 800°C it is of little influence on the coercivity after the second annealing. The results of the chemical analysis for some annealing states are given in Table I. For this alloy two step annealing seems to be necessary to achieve a complete boron extraction. The results of XRD analysis are given in Table II. After annealing at 900°C for 2 hours in wet hydrogen followed by annealing at 1100°C for 2 hours in dry hydrogen, the alloy becomes a single phase and no boron can be detected by chemical analysis. 2.3.2. Fe-Co-Si-TM-B ribbons (TM = Mn, Cr, Ni) A more detailed analysis of the boron extraction was made for ribbons containing Cr, because the chemical bond of B to Cr is stronger than to the other elements, and the boron extraction is expected to be more difficult in comparison with other transition metal elements. Investigating the thermogravimetric curves of 22.5Co3Si3Cr4.2(Fe-B) wt.% ribbon (Fig. 2) we observe that the mass of the ribbon changes in two steps. The first step begins before crystallization and is limited to the amorphous state. During the crystallization the mass changes become smaller and attain a limit value. The second step occurs near 850°C, and the mass change increases until the ribbon begins to melt, where we stopped to measure. The spectrometric analysis of the gaseous products (Fig. 2) suggests that compounds such as HB, H2B, H3B, and H6B2 developed. The mass numbers 12-16 and 28 correspond to the boron hydride ions: HB+, H2B+, H3B+, H4B+, H5B+and H6B2+ respectively. H6B2 appears with the highest probability.

Figure 2. The temperature dependence of the mass changes of a 22.5Co3Si3Cr4.2(Fe-B) wt.% ribbon, heating with 10 K/min in dry hydrogen

Figure 3. Spectrometric analysis of the gas products obtained for 22.5Co3Si3Cr4.2(Fe-B) wt.% ribbon during annealing a in flowing hydrogen at a heating rate of 2.5 K/min

Figure 4 shows the cross-section of the 22.5Co3Si3Cr4.2(Fe-B) wt.% ribbon after annealing at 900°C for 9 h. The extraction starts from the surface and is not complete in

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this case. The surface is boron-free, but in the bulk some borides are still visible. For longer annealing times and/or higher temperatures the boride phase disappears.

Figure 4. Scanning electron micrograph of the cross section of a 22.5Co3Si3Cr4.2(Fe-B) wt.% ribbon annealed at 900°C for 9 h in flowing dry hydrogen

Table III. Hc and Js values for the ribbons annealed in flowing hydrogen at 300°C for 9 h and at 1000°C for 9 h After boron extraction Initial composition No. [wt.%] Js [T] Hc [A/m] 1 4.5Co6Si4.2(Fe-B) 73 1.73 2 13.5Co6Si4.2(Fe-B) 78 1.82 3 22.5Co6Si4.2(Fe-B) 81 1.86 4 4.5Co3Si3Mn4.2(Fe-B) 38 2.07 5 13.5Co3Si3Mn4.2(Fe-B) 44 2.10 6 22.5Co3Si3Mn4.2(Fe-B) 41 2.12 7 4.5Co3Si3Cr4.2(Fe-B) 51 1.97 8 13.5Co3Si3Cr4.2(Fe-B) 48 2.03 9 22.5Co3Si3Cr4.2(Fe-B) 50 2.04 10 15Co10Si2(Fe-B) 36 1.45 Table IV. The losses measured at sinusoidal field for 15Co10Si2(Fe-B) wt.% after boron extraction P (1.0 T) f P (0.5T) [Wkg–1] [Hz] [Wkg–1] 50 0.4 1.4 100 0.8 2.9 200 1.6 6.3 500 4.7 18.0 1000 10.0 41.0 2000 24.0 100.0 5000 79.0 353.0 10000 208.0 960.0

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The magnetic properties of the ribbons were measured after annealing in flowing hydrogen at 300°C for 9 h followed by annealing at 1000°C for 9 h. The cooling rate was 100 K/h. It was checked by XRD and SEM that all these ribbons were free of borid phases. The results are given in Table III. We find that increasing the Co content increases Js, if the TM and Si content is constant. Replacing Si by Cr or Mn increases Js further, where Mn is more effective. The coercivities of all ribbons are smaller than 100 A/m. Alloy No. 10 in Table III has the lowest coercivity of 36 A/m. The composition of this alloy after boron extraction is expected to have zero magnetostriction [8]. In Table IV losses measured on stripes of this alloy as a function of frequency at sinusoidal field excitation are given. 3. DEVELOPMENT OF A THERMOKINETIC DESCRIPTION OF THE EXTRACTION PROCESS 3.1. Experimental data Figure 5 shows the mass change of the Fe80B20 ribbon as a function of temperature together with the sDTA signal during heating at a constant rate of 10°C/min in flowing hydrogen. In order to demonstrate the influence of the surface the as-cast ribbon as well as a ribbon with polished surface were investigated. A first a mass decrease is observed in the amorphous state between 300°C and the crystallization temperature, Tx. This effect depends on the quality of the surface and is enhanced by polishing away a thin layer from the surface. Beginning at about 440°C, i.e. above Tx (see sDTA-signal in Fig. 5), the mass begins to increase. One possible reason for this increase is the absorption of hydrogen. The mass increase is reduced by polishing the surface of the ribbon. At temperatures above 800°C the mass of the ribbon decreases again, with a stronger effect for the ribbon with the polished surface. This mass decrease is caused by a more rapid boron extraction at elevated temperatures.

Figure 5. Temperature dependence of the mass and heat changes in the Fe80B20 ribbon (heating rate 10°C/min)

Figure 6. Mass change of a Fe80B20 ribbon as a function of temperature for different heating rates (the lines are the results of the model calculation)

The results of thermogravimetric (TG) measurements in flowing hydrogen at different heating rates are given in Fig. 6. The mass change of each reaction step de-

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pends on the heating rate. An analysis of these curves allows to construct a theoretical description of the behaviour in the framework of the temperature dependence of the reaction kinetics. 3.2. Thermokinetic model Only the boron extraction after the crystallization is taken into account within the model. In this case, the model contains three reactions: The first reaction describes the mass increase caused by hydrogen absorption, and the other two reactions describe the boron extraction. The first reaction is of a second order, the second reaction is also of a second order, and the third reaction is a diffusion-dependent reaction. The latter two reactions are competing reactions and describe the decomposition of the borides and the diffusion of boron to the surface and the boron hydride formation at the surface (see Fig. 7).

Figure 7. Schematic description of the extraction process with three reactions

Formally, these reactions are described by a set of equations which is given by: reaction 1 (2nd order): A ——(1)—— B, dxA/dt = A1exp(–E1/RT)xA2,

(1)

reaction 2 (2nd order): C ——(2)—— D, dxC/dt = A2exp(–E2/RT)xC2,

(2)

reaction 3 (diffusion dependent): C ——(3)—— E, dxE/dt = A3·exp(–E3/RT)[1.5xE 1/3 (xE –1/3 –1)].

(3)

The mass as a function of time is then given by m(t) = m(0) – mmodel mBoron ,

(4)

with mmodel = W1 (1 – xA) + (1 – W1)[W2(1 – xC) + W3xE];

(5)

where mBoron is the initial amount of boron in the alloy, xA, xC and xE are the concentrations of the formal model reactants A, C, and E, respectively, and An, En, and Wn are

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206 Table V. Values of the model parameters n (1) (2) (3)

lg(An/s) –0.8 22.24 1.77

En [J/mol] 57.7 623.05 196.04

Wn –0.07 0.01 1

the frequency factor, the activation energy and the relative weight of the nth reaction, respectively. Their values are given in Table V. 3.3. Prediction of the annealing effect The model was tested to predict the amount of extracted boron for various annealing procedures using equations (1) to (5). The amount of extracted boron was determined by

Figure 7. Prediction of the boron extraction for various annealing procedures

analysing the mass of the sample before and after annealing. The results are summarized in Fig. 7. There is a good agreement between the experimental data and the prediction. Thus, the model describes the extraction process properly and it can be used to optimize the annealing process. 4. CONCLUSIONS Boron can be extracted from amorphous TMxBy ribbons by annealing in H2. For Fe80B20, the boron extraction can be described by a model with three reactions. The model allows us to predict the effect of annealing. At low temperatures the extraction is mainly diffusion controlled. At high temperatures the controlling mechanism is a 2nd order reaction (e.g. decomposition of Fe2B). Crystalline soft magnetic ribbons can be prepared by addition of boron to the alloy prior to planar flow casting. In the second step the boron is extracted by annealing in H2. An oxide layer (e.g. B2O3) may affect the extraction process. By this method, alloys which are difficult to be cold rolled may be shaped to thin foils.

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ACKNOWLEDGEMENTS The authors are grateful for the help of N. Mattern, U. Kühn and V. Michel, who performed X-ray diffraction, ribbon preparation, and chemical analysis, respectively. Especially, the help of K. Jaenicke-Rößler, who made the thermogravimetric (TG) measurements in hydrogen, is acknowledged. This study was supported by the Deutsche Forschungsgemeinschaft under grant Ro 962/3. REFERENCES 1. 2. 3. 4. 5. 6.

7. 8.

R. E. Maringer and L. F. Vassamillet; Proc. 4th Int. Conf on Rapidly Quenched Metals (Sendai, 1981), p. 629. S. Roth, (1997) Mater. Sci. Eng. A226-228, 111. G. David, S. Roth, J. Eckert, and L. Schultz, (2000) J. Magn. Magn. Mater. 215-216, 434. G. David, S. Roth, J. Eckert, and L. Schultz, (2000) J. Metastable and Nanocryst. Mater. 8, 835. G. Saage, S. Roth, J. Eckert, and L. Schultz, (2003) J. Magn. Magn. Mater. 254-255, 26. G. David, S. Roth, J. Eckert, L. Schultz, THERMEC 2000, Las Vegas/USA, 4.-8.12.00, in Proceedings of the International Conference on Processing and Manufacturing of Advanced Materials: CDROM, Section D3 (6 p.); Special Issue: Journal of Materials Processing Technology, T. Chandra, K. Higashi, C. Suryanarayana, and C. Tome (eds.), Elsevier Science, 117/3 (2001). Netzsch thermokinetics, NETZSCH Gerätebau GmbH, Wittelsbacher Strasse 42, D-95100 Selb, (2000). N. Tsuya, K. I. Arai, K. Ohmari and T. Honma, (1982) J. Appl. Phys. 53, 2422.

PERCOLATION AND FRACTAL CLUSTERS IN AMORPHOUS METALS YU.V. BARMINa, I.L. BATARONOVb, and A.V. BONDAREVb a Department of Solid State Physics, Voronezh State Technical University 14 Moskovski prospekt, 394026 Voronezh, Russia b Department of Higher Mathematics and Physico-Mathematical Modelling Voronezh State Technical University 14 Moskovski prospekt, 394026 Voronezh, Russia Corresponding author: Yu. V. Barmin, e-mail: [email protected]

Abstract:

The atomic structure of binary amorphous alloys (AA) was investigated by X-ray diffraction and computer simulation methods. The analysis of the atomic structure of AA was performed in the framework of percolation theory and fractal geometry. Atomic clusters were determined as groups of atoms of one species that are in immediate contact with each other. The distribution of clusters by size, the probability of belonging given atom to the greatest cluster, the fractal dimensionality of the percolation cluster and the concentration dependence of the percolation radius were calculated. The correlation between the magnetic properties of AA and their cluster structure was established.

1. INTRODUCTION The atomic structure of amorphous metallic alloys was studied by X-ray diffraction method. However, as it is known, the diffraction experiment allows to obtain only averaged information on the atomic structure of amorphous alloys (AA): such structural characteristics as the radial distribution functions (RDF) and the parameters of shortrange order calculated from the RDF. This drawback causes the necessity of construction and analysis of computer models of atomic structure of AA because such a model gives the atomic coordinates in the system. Therefore the molecular dynamics simulation of the atomic structure of AA is widely used. However, diffraction experiments and traditional computer models do not allow to establish the rules of atomic arrangement for amorphous materials. As it is known, crystals possess translation symmetry and quasicrystals have rotational symmetry (Penrose tessellation). But in amorphous structures the laws of spatial arrangement of atoms are unknown. In this connection we used a new method for the analysis of the structure of AA based on the application of the percolation theory and fractal geometry. This method allowed us to obtain long-range information on the structure of AA. 209 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 209–218. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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2. X-RAY DIFFRACTION EXPERIMENT The atomic structure of AA was studied on the standard X-ray diffractometer in reflection geometry. We used an X-ray tube with molybdenum anode and a graphite monochromator in the diffracted beam. The measured intensity of X-ray radiation was corrected to the air background, polarization and absorption. Then the intensity was normalized into electronic units. The structure factor was calculated taking into account the intensity of incoherent radiation and corrections to the anomalous dispersion of the atomic scattering factor [1]. The basic characteristic of the atomic structure of AA is the radial distribution function which is obtained as the sine Fourier transform of the structure factor. The direct Fourier transform is sensitive to experimental errors in the structure factor as the statistical dispersion and the measurement on the finite interval. To reduce the contribution caused by these errors the following algorithm was used: the experimental structure factor was smoothed with a set of basic functions (Hermite [2] and Laguerre [3]) and then the Fourier transform of the smoothed solution was performed. In this work we used a method based on the separation of the structure factor into several intervals which correspond to different peaks of the structure factor. In each interval the experimental structure factor is approximated with a wave package (a set of basic functions). The application of this method considerably increases the accuracy of the reconstruction of the RDF and provides stabile way of smoothing to random experimental errors. 3. SIMULATION TECHNIQUE Simulation of the atomic structure was carried out using the molecular dynamics method. As an initial atomic configuration we chose a random distribution of 7000 atoms inside the basic cube with periodical boundary conditions. For numerical solving equations of motion the Verlet algorithm in the velocity form was used. The integration – step was 2˜10 15 s, the relaxation was conducted during 5000 time steps. The simulation was conducted at constant temperature 300 K with correction of temperature at each time step. For the description of the interatomic interaction in amorphous metallic alloys we constructed a model potential represented as a polynomial of the fourth power [4]:

­°C1 ˜ r  rk 4  C2 ˜ r  rk 3  C3 ˜ r  rk 2

at r d rk

°¯0

at r ! rk

M r ®

(1)

Here rk is the cut-off radius of the potential. Coefficients C1, C2, C3 were found as a solution of a system of three linear equations which connected the potential and its first and second derivatives with the parameters for crystalline analogues:

­ °M a  A ˜ Ea ° ®M ca 0 ° 18 K v °M cca a2 ¯

(2)

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where Ea is the atomization energy, A is the coefficient of the order of unity, a is the equilibrium interatomic distance, K is the bulk modulus, va is the atomic volume. The introduction of the coefficient A is caused by the fact that the potential energy in amorphous and crystalline state is not equal. The value of A was so chosen as to achieve the coincidence of the model and experimental RDF. As an example we chose amorphous alloys of the Re-Ta system. The numerical values of coefficients for this system are given in the Table I. Table I. Parameters of the polynomial potential ɋ2

ɋ1

Type of the potential

10 eV/nm

URe-Re URe-Ta UTa-Ta

3

4

3

ɋ3 3

2

rk 2

–1

A

10 eV/nm

10 eV/nm

10 nm

– 6.4188

– 3.9867

– 4.5543

3.699

1.82

– 4.0450

– 2.8247

– 3.4076

3.827

1.47

–2.6950

– 2.0074

– 2.5144

3.942

1.15

We experimentally studied the atomic structure of the amorphous alloys of Re100–xTax system with six compositions: x = 10, 17, 23, 31, 39 and 45 at.% Ta. The reduced distribution functions for these alloys are shown in Fig. 1. It can be seen that he positions of the peaks change systematically with the changing of the composition. Radial distribution functions calculated for the models are in good agreement with the experimental ones. They also reproduce the changes of the structure with changing composition of the alloys [5]. 4. CLUSTER STRUCTURE AND PERCOLATION THRESHOLD OF AMORPHOUS ALLOYS We analysed the model using the percolation theory and fractal geometry. For the atomic configurations obtained by computer simulation of Re100–x Tax (x = 3-31 at.%) AA we analysed the structural details of the subsystem of the atoms of one type. Atomic clusters were defined as follows: the cluster is a group of atoms of one type which are in direct contact with one another, i.e. they are the nearest neighbours [6]. If we consider a crystal, then the percolation radius (parameter determining the belonging of an atom to the cluster) is equal to the atomic diameter. In the case of an amorphous structure, atoms are the nearest neighbours if they are within the first coordination sphere of one another, i.e. the distances between them do not exceed the first minimum of the partial RDF gTaTa(r). Therefore in our model the percolation radius rc was chosen equal to the distance to the first minimum of the partial RDF gTa-Ta(r): rc =1.31 dTa. We show in Fig. 2 the partial structure of the subsystem of Ta atoms (the projection on one side of the cube) for several compositions and the corresponding cluster distribution by sizes N–nN, where N is the number of atoms in the cluster and n is the number of clusters having the size N. The greatest cluster is shown with links between the neighbouring atoms. In Figure 2a the subsystem of Ta atoms for 15 at.% Ta is shown. The black circles represent atoms in the greatest cluster in the model. White circles represent the rest of

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Figure 1. Reduced distribution functions G(r) for Re100–xTax amorphous alloy

Ta atoms. The Re atoms are not shown here. It is seen that at 15 at.% Ta a great number of small clusters exist, all the clusters are friable and extensive, and there are no compact ones. The greatest cluster is also small. Then we increased the concentration of Ta atoms by 2 at.% only (Fig. 2b). At a concentration of 17at.% Ta one large cluster was formed which connected two opposite sides of the basic cube. Thus, a percolation cluster was formed near this concentration and the percolation transition took place. For checking the presence of the percolation effects the thin boundary layer was analysed near each side of the cube. The percolation was registered only when the same cluster had at least two atoms in the boundary layers belonging to the opposite sides of the cube. The shape of the distribution of clusters by sizes changes when the concentration of Ta atoms is changed. At 17 at.% Ta one large cluster is distinguished, while the number of small clusters rapidly decreases. As it is known from the percolation theory, the percolation cluster is a fractal object. Fractal properties of the percolation cluster are related to its scale invariance (selfsimilarity): such a cluster has pores of all sizes, from the atomic diameter up to the size of the basic cube, as it is seen from Fig. 2b. Then we increased the concentration of Ta atoms by 3 at.%. In Fig. 2c the subsystem of Ta atoms for 20 at.% Ta is represented. At this concentration almost all the atoms

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Figure 2. An image of a subsystem of Ta atoms for Re100–x Tax (x =15, 17 and 20 at.%) and distribution of clusters by sizes. N is the number of atoms in a cluster, n is the number of clusters with size N

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belong to the greatest cluster. With increasing the concentration of Ta atoms the number of small clusters abruptly decreases. Small clusters associate with the greatest cluster. The large and then small pores in it disappear, the cluster becomes compact. The dependence of the probability of belonging of an atom to the greatest cluster Ɋ(x) on the composition of the alloy is shown in Fig. 3. It has a shape which is characteristic for geometrical phase transitions and represents a diffuse step. The value of Ɋ(x) was determined as a ratio of the atomic number in the greatest cluster to the total number of tantalum atoms in the system. 5. FRACTAL DIMENSIONALITY OF THE PERCOLATION CLUSTER The number of particles N(L), or mass M(L), of a fractal cluster increases according to the power law as the characteristic dimension L of the system increases:

N (L ) ~ LD ,

(3)

where D is the fractal dimensionality [7, 8]. Formula (3) is correct only asymptotically at a large system dimension. The length of the edge of the basic cube is small for our models (L = 0.627-0.811 nm). Increasing the linear dimensions of the system leads to considerable expenses of the simulation time, thus the calculation of the asymptotic dependence (3) seems to be impossible for our model. The following method was used for the calculation of fractal dimensionality. The percolation cluster obtained in a model of a finite size is a fragment of some cluster cut from a hypothetically infinite structure. The cluster being considered can be a part of a finite as well as infinite cluster. But it is known that even finite clusters on the percolation threshold have in the definite length scale the same dimensionality as the infinite percolation cluster [7]. The characteristic length on which the fractal properties of the cluster are revealed is within the gyration radius Rg R g2 (N ) =

&

1 2N 2

∑ (r − r ) , &

&

i

j

2

(4)

i, j

where ri is a radius vector of the i-th atom in the cluster. The gyration radius is a meansquare radius of the cluster measured from its center of gravity. For the percolation cluster the center of gravity and gyration radius Rg were calculated. Around the center of gravity the central sphere with the radius Rcent=Rg/2 was constructed. Around each atom situated within the central sphere we constructed spheres with the radius R consecutively increasing from 0 to Rg – Rcent. The step of changing R was 2.74⋅10-3 nm. Then we calculated the number of atoms N inside the sphere of the radius R. The obtained values of N were averaged over the calculation results for all the atoms in the central sphere. Periodic boundary conditions were not taken into account. Tangent of the slope angle of the linear part of the dependence lnN = f(lnR) determines fractal dimensionality. The dependence lnN = f(lnR) for one of the realizations of the percolation cluster is shown in Fig. 4. Points on the left from the vertical

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dotted line were not taken into consideration because of a considerable deviation from the linear dependence at small values of R. Approximating the right part of the plot with

Figure 3. Dependence of probability of belonging an atom to the greatest cluster on composition of the alloy

Figure 4. Calculation of fractal dimensionality of the percolation cluster. R is radius of the sphere, N is number of atoms of the percolation cluster in the sphere of radius R

a straight line by the least squares method, we obtained the value of fractal dimensionality of the percolation cluster D = 2.5 averaged over many realizations of the model. This value is close to the theoretical value D = 2.54 for well-known lattice percolation problems. Since the value of dimensionality is closely connected with the values of critical exponents E and Q then we can come to a conclusion that the universality of critical exponents taking place for lattice problems also extends to the amorphous structure. At the concentration of Ta atoms over the percolation threshold the dimensionality of the greatest cluster coincides with Euclidean dimensionality of space (D = 3). 6. CONNECTION OF THE CLUSTER STRUCTURE OF AMORPHOUS ALLOYS WITH MAGNETIC PROPERTIES The proposed percolation model can be useful for the description of physical properties of amorphous alloys in which the atoms having their own magnetic moment are randomly distributed in a paramagnetic matrix. Additionally, we constructed computer models of atomic structure of Re100-xTbx (x = 1-100 at.%) the amorphous alloys. The structural analysis of the model using the percolation theory was conducted. It was established that for the Re-Tb system the percolation threshold is observed near 13 at.% Tb. For Re-Tb amorphous alloys in the wide compositional range a maximum on temperature dependence of dynamic magnetic susceptibility F(T) (see Fig. 5) and irreversibility of magnetization M(T) are observed [9]. It testifies the magnetic phase transition typical for mictomagnets, or cluster glasses. The transition temperature T0 increases with increasing the concentration of magnetic ions (Fig. 6). A mictomagnet is similar to an ideal spin glass. However, local correlations of magnetic ions dominate in it. The direct exchange interaction is short-ranged and essen-

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tial only in distances compared with interatomic distances. Therefore clusters in the model were determined naturally as groups of atoms which are the nearest neighbours [10].

Figure 5. Temperature dependence of dynamic magnetic susceptibility F(T) of the Re100-x-Tbx amorphous alloys: (1) x = 30, (2) x = 40, (3) x=70, 4 – x= 94 at.%

Figure 6. Dependence of the freezing temperature on composition of the Re-Tb amorphous alloys

It should be noted that the transition is observed only in the alloys containing more than 13 at.% of magnetic atoms, i.e. the magnetic ordering is observed only above the percolation threshold in this system. Thus we established a connection between the cluster structure and the magnetic properties of these alloys. 7. CONCENTRATION DEPENDENCE OF THE PERCOLATION RADIUS Different physical interactions can have different characteristic radii. Therefore, in general, the percolation radius rc is not constant. At any concentration of Ta atoms r > 0 we can find the value rc at which this composition will be situated on the percolation threshold. For the investigation of the dependence rc(x), the models of Re100-xTax (x = 1, 2, 3, 5, 10, 15, 17, 20, 31, 45, 70 and 100 at.%) AA were constructed. The results were averaged over 10 realizations for every composition. In order to analyse the influence of a short-range order on the concentration dependence of the percolation radius we also calculated the concentration dependence of the percolation radius on the model of random arrangement of atoms, which is uniform over all the simulation volume. This problem of random sites is completely equivalent to the known from literature problem of spheres [11]. The sizes of the cube and the number of Ta atoms were given according to the compositions indicated above. The results of the calculation were also averaged over 10 realizations for every composition. In Fig. 7 the concentration dependence of the percolation radius is given, i.e. at each concentration of Ta atoms such a value of the percolation radius was determined at which the percolation cluster is formed the first time. In other words, this cluster is on the percolation threshold. Such a dependence is calculated for the models of Re-Ta amorphous alloys (black circles) and for random distributions of atoms (white circles).

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The percolation radius depends on the concentration of Ta atoms and the volume of the simulation cube V. But the volume of the cube V, in its turn, also depends on the number of Ta atoms. For random arrangements of atoms the following equality must be fulfilled because of the scale invariance of the problem rc A , (5) 3 3 V x where A is constant. It is expedient to consider another dimensionless parameter which does not depend on the number of atoms. It is expressed by formula

Bc

4 S C rc3 , 3

(6)

where C is the volume atomic concentration. In Figure 8 we present the concentration dependence of the Bc parameter. It is known that for random arrangement of atoms (for the problem of spheres) the value of Bc is constant and equal to 2.7 r 0.1 [11]. From Fig. 8 it is seen that for x = 15-100 at.% Ta the value of Bc does not depend on the concentration of Ta atoms and its mean value is Bc = 2.8. At low concentrations (x = 1-10 at.% Ta) considerable deviations from the mean value are observed due to the scale effect connected with a small system size [11].

Figure 7. Dependence of the percolation radius on the concentration of Ta atoms

Figure 8. Dependence of the Bc parameter on the concentration of Ta atoms

For the amorphous structure the statistically valuable deviations from the rc(x) and Bc(x) curves for random distribution of atoms are observed in Figs. 7 and 8. These deviations are connected with the presence of a short-range order in the amorphous structure. Decreasing of the amplitude of the curves with the amorphous structure at x = 16-50 at.% Ta is connected with the proximity of the percolation radius to the first maximum of the partial RDF gTa-Ta(r). In the distances r | rc a great number of Ta atoms exists, facilitating the formation of the percolation cluster. Thus, the Bc and rc are structure-sensitive parameters and their dependence on the concentration of Ta atoms correlates with the RDF. Moreover, the values of fractal dimensionality averaged over all compositions for amorphous structure and of random arrangement of atoms coincide ( D = 2.5) and are close to the theoretical value D = 2.54

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for three- dimensional lattice problems. This agrees with the fact that critical exponents are determined by properties of the system with infinite increasing of its size and thus they cannot be sensitive to the structure of a short-range order. The obtained result confirms the assumption [11] that the critical exponents for continuous percolation have the same values as for lattice problems, since they do not depend on the geometry of a lattice. ACKNOWLEDGEMENTS The work was partly supported by the Russian Foundation for Basic Research, Grants No 02-02-16267 and 03-02-06005. REFERENCES 1. Wagner, C.N.J., (1978) Direct methods for the determination of atomic-scale structure of amorphous solids (X-ray, electron and neutron scattering), Journal of Non-Crystalline Solids 31, 1-40. 2. Krylov A.S. and Vvedenskii A.V., (1995) Software package for radial distribution function calculation, Journal of Non-Crystalline Solids 192&193, 683-687. 3. Samoilov, V.G., Bataronov, I.L., Roshchupkin, S.A., and Barmin Yu.V., (1995) Smoothing experimental data to solve the inverse problems of mathematical physics, Bulletin of the Russian Academy of Sciences 59, 1729-1732. 4. Bataronov, I.L., Bondarev, A.V., and Barmin, Yu.V., (2000) Numerical simulation of the atomic structure of amorphous metal alloys, Bulletin of the Russian Academy of Sciences 64, 1329-1332. 5. Bondarev, A.V., (2002) Atomic Structure of Amorphous Alloys of Rhenium with Transition Metals of the Sixth Period, Abstract of Ph.D. Thesis, Voronezh. 6. Barmin, Yu.V., Bataronov, I.L., and Bondarev, A.V., (1999) Cluster structure of amorphous alloys, Abstracts of the 2nd Russian Seminar “Non-linear Processes and Self-organization Problems in Modern Materials Science”, Voronezh, 38-39. 7. Feder, J. (1988) Fractals, Plenum Press, New York. 8. Stauffer, D. and Aharony, A., (1994) Introduction to Percolation Theory, Taylor & Francis, London. 9. Barmin Yu.V., Zolotukhin I.V., and Soloviev A.S., (1991) Preparation and properties of amorphous terbium–rhenium films, Digest booklet of the 13th International Colloquium on magnetic Films and Surfaces, Glasgow, 68-69. 10. Hurd, C.M., (1982) Varieties of magnetic order in solids, Contemporary Physics 23, 469493. 11. Shklovskii, B.I. and Efros, A.L., (1984) Electronic Properties of Doped Semiconductors, Springer Verlag, Heidelberg.

NEUTRON IRRADIATION EFFECT ON Fe-BASED ALLOYS STUDIED BY MÖSSBAUER SPECTROMETRY

J. DEGMOVÁa, J. SITEKa, and J.-M. GRENECHEb a

Department of Nuclear Physics and Technology Faculty of Electrical Engineering and Information Technology Slovak University of Technology, Ilkoviþova 3, 812-19 Bratislava, Slovakia b

Laboratoire de Physique de l´Etat Condensé, UMR CNRS 6087, Université du Maine Faculté des Sciences, 72085 Le Mans Cedex 9, France Corresponding author: J. Degmova, e-mail: [email protected]

Abstract:

Two types of nanocrystalline alloys, FINEMET and NANOPERM, were irradiated by different neutron fluences. Changes in the structure and microstructure were experimentally investigated by means of Mössbauer spectrometry which is well suited for studying the local environments of iron in the crystalline grains, the interfacial and the amorphous remainder. The reorientation of the texture of ferromagnetic domains was observed in both systems but structural changes were found either in the crystalline phase or the amorphous remainder under neutron irradiation, depending on the type of nanocrystalline alloys.

1. INTRODUCTION In the recent years, nanocrystalline alloys have become attractive for applications owing to their functional properties. The most prominent examples such as FINEMET (FeCuNbSiB) and NANOPERM (FeZr(Cu)B) have been most frequently investigated because they exhibit excellent soft magnetic properties combining high magnetic permeability and large saturation magnetization [1, 2]. Magnetic properties are strongly dependent on the microstructure of nanocrystalline alloys i.e. the volumetric crystalline fraction and the magnetic behaviour of crystalline grains created during the primary crystallization. Recent investigations dealt with the influence of the neutron irradiation damage on the structural and magnetic properties of the amorphous as well as the nanocrystalline alloys [1-3]. Our paper is focused on the structural as well as the local magnetic modifications induced into FINEMET and NANOPERM alloys by irradiation with different neutron fluences. Using Mössbauer spectrometry, our main interest was 219 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 219–228. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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oriented on the changes in the orientation of the net magnetic moment, in the values of the magnetic hyperfine fields as well as in the volumetric fraction of the crystalline and the amorphous components after irradiation. Thanks to its sensitivity, 57Fe Mössbauer spectrometry is able to distinguish iron atoms in different sites and phases and to detect short-range order changes in the iron-based alloys caused by neutrons. 2. NEUTRON IRRADIATION EFFECT Metallic glasses were thought to be resistant to radiation damage by neutrons due to their amorphous structure. However, as it was shown in [6], some physical properties of metallic glasses are more or less affected by neutron irradiation. Such magnetic parameters as the exchange constant, the magnetic moment and the coercive force were found to be modified by a neutron irradiation. These deviations in a magnetic structure are supposed to be a consequence of the changes in the short-range order as a result of atom mixing caused by elastic stress centers produced during the process of neutron irradiation. Changes in the orientation of the average magnetic moment were observed in neutron-irradiated metallic glasses [7]. Indeed, the particle bombardment produces defects that may cause a realignment of magnetic domains implying a reorientation of magnetic moments. Changes in the local neighbourhoods of resonant atoms affect the average hyperfine field as well as the shape of hyperfine field distributions. A modification of the electrical resistivity by the irradiation is considered to be affected by topological and compositional defects. In boron-containing alloys the capture of thermal neutrons produces high energy D and Li particles in accordance with the reaction 10 B(n, D)7Li + 2.31 MeV. These particles modify the composition because at least the D-particles agglomerate to form helium bubbles [3]. Some boron can also be transformed into lithium. In the case of crystalline material, the interaction of neutrons with the atoms of irradiated material leads to a dynamic disturbance and reconstruction of the crystalline lattice regular atomic ordering [8]. In the case of nanocrystalline alloys, which consist of crystalline nanograins embedded in an amorphous intergranular matrix, one expects that irradiation by neutrons will lead to: (i) redistribution of atoms in the amorphous matrix, (ii) disturbance of regular atomic ordering of the crystal lattice and (iii) atom exchange between the amorphous and crystalline component [9]. These processes are accompanied by the damage of the material structure and we can distinguish two types of damage: (i) displacement damage-production of atoms shifted out of their original position. In this case, the energy is transferred to the nucleus by collision of the neutron with the atomic nucleus. (ii) capture of the neutron in the atomic nucleus with a consequent decay producing particles or photons. The mechanism of the radiation damage of nanocrystalline materials by neutron is dependent on the constituent elements. Each of them possesses different cross-sections to thermal and fast neutrons.

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3. EXPERIMENTAL DETAILS A specimen of the master alloy was prepared by planar flow casting in the form of ribbons (about 22-35 Pm thick and 10 mm wide). The nominal compositions were Fe73,5Cu1Nb3Si13,5B9 and Fe87,5Zr6,5B6. Subsequent annealing was carried out in a vacuum at the 550°C for 1 hour. The neutron irradiation was carried out in a nuclear pile by a whole neutron spectrum to the total fluence of 1016 up to 1019 n/cm2. The samples were sealed in Al foils prior to irradiation and the irradiation was carried out below 343 K. The ratio of fast and slow neutron was approximately 8:1. 57Fe Mössbauer experiments were performed at different temperatures (from 77 to 500 K). Mössbauer spectra were collected in transmission geometry by a conventional constantacceleration spectrometer with a 57Co(Rh) source. The ribbon plane was oriented perpendicularly to the J-beam. The spectra were evaluated by both the NORMOS [10] and MOSFIT [11] programs, which allowed simultaneous treatment of crystalline, residual amorphous matrix and interface by means of single individual components and a distribution of hyperfine components. The isomer shift values were quoted in relation to the spectrum for D-Fe at 300 K. Mössbauer spectrometry was used as a basic method for studying the changes in the material caused by neutron irradiation. Indeed, this method allows to perform the phase analysis and to map the changes in the vicinity of iron nuclides. In the case of neutron irradiated nanocrystalline alloys one can see the changes in the contributions of the amorphous and crystalline components, in the short range order, in the orientation of the net magnetic moment and in the distributions of internal magnetic fields. The fitting procedures used in this paper for evaluation of amorphous as well as nanocrystalline samples were described in [12]. 4. RESULTS AND DISCUSSION 4.1. FINEMET-alloys 4.1.1. Amorphous FINEMET- alloys Mössbauer spectra of FeCuNbSiB as-cast non-irradiated and irradiated (1019 n/cm2) samples taken at 77 K are shown in Fig. 1. In both cases the spectra exhibit very well resolved six line patterns typical of an amorphous structure. At the first sight, it was not possible to distinguish significant differences. The most relevant Mössbauer parameters obtained after application of fitting procedure are listed in Table I. The results for FeCuNbSiB samples irradiated by 1017 n/cm2 were also included for comparison. The obtained values confirm: (i) only a small variation of angle ȕ (which defines the direction of the hyperfine field with respect to the J -beam direction, and which is given by the relative areas of the 2nd and 5th lines of the spectra) with the increase of neutron fluence, (ii) a slight increase in isomer shift values and decrease in average hyperfine field values with the increase of neutron fluence. Changes in the orientation of the net magnetic moment are consistent with the reorientation of the ferromagnetic domains out of the ribbon plane. It might be a conse-

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Figure 1. Mössbauer spectra of non-irradiated (a) FeCuNbSiB amorphous samples and samples irradiated by neutron fluence of about 1019 n/cm2 (b) taken at 77 K

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Figure 2. Mössbauer spectra of non-irradiated FeCuNbSiB nanocrystalline samples (a) and samples irradiated by neutron fluences of about 1017 n/cm2 (b) and 1019 n/cm2 (c)

quence of the reorientation of iron magnetic moments in the vicinity of the stress centres or of the thin surface crystallization caused by irradiation. A slight increase of isomer shift with an increase of neutron fluence is consistent with the reduction of Fe-electron density while the decrease of average hyperfine field values could be caused by the volume expansion of the amorphous phase due to irradiation. The shape of the obtained distributions of the hyperfine field P(B) does not change significantly with the increasing neutron fluence [13]. Summarizing all results mentioned above, one can conclude that the highest neutron fluence 1019n/cm2 can modify the local ennvironment but it remains not sufficiently high to induce significant changes in the amorphous FINEMET-alloys. 4.1.2. Nanocrystalline FINEMET-alloys Figure 2 shows Mössbauer spectra of irradiated (1017 and 1019 n/cm2) and non-irradiated FeCuNbSiB nanocrystalline alloys taken at 300 K. The applied fitting procedure consisted of 5 sextets of sharp lines corresponding to FeSi crystalline grains and one sextet with broad lines attributed to amorphous matrix [14]. From Table I and Fig. 2, one can see that the contribution of the amorphous component in the Mössbauer spectra became almost unchanged with the increasing fluence of neutrons. No significant changes in the amount of the crystalline volumetric fraction in the samples were observed after irradiation. Only the highest fluence of 1019 n/cm2 causes quite a significant reduction of the sharp lines in the spectrum with respect to the spectrum of nonirradiated sample. Taken into account the results from the fitting procedure (listed in Table I), one can suppose that neutron irradiation mostly causes disturbances of the regular atomic ordering of the FeSi crystal lattice.

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In addition, the E values would suggest some changes in the texture of ferromagnetic domains. Those changes occur probably due to a new distribution of stress induced by the neutron irradiation as it was discussed in [7] which is in good agreement with the slight decrease in the average values of the hyperfine field of the amorphous component with the increasing fluence of neutrons. It is important to emphasize that the value of E is totally independent of the fitting assumptions. Table I. Mössbauer parameters corresponding to the amorphous (A) and nanocrystalline (A1) FeCuNbSiB samples irradiated with difference fluences of neutrons (1017 and 1019 n/cm2). ISOam is the isomer shift for the amorphous component, Eam (r 5) is the angle determining the orientation of the net magnetic moment of the amorphous component, Aam (r 2) is the relative area of the amorphous component, (r 0.03) is the average hyperfine field of the amorphous component, Acr (r2) is the relative area of crystalline components of Mössbauer spectra Sample A1 A1-17 A1-19 A A-17 A-19

T 300 K 300 K 300 K 77 K 77 K 77 K

ISOam [mm/s] – 0.10 – 0.09 0.04 0.06 0.06 0.10

Eam [%] 63 71 60 54 57 56

Aam[%] 58 56 59 100 100 100

[T] 18.9 18.3 17.6 24.7 24.1 24.4

Acr[%] 42 44 41 0 0 0

Summarizing the behaviour of nanocrystalline samples, we suppose that the neutron fluence of about 1019 n/cm2 is not sufficiently high to destroy the crystalline FeSi grains but remains sufficiently high to disturb the atom ordering in crystalline grains. This can be seen from the different contributions of sharp lines in the spectra with the increasing neutron fluence while the amount of the crystalline phase remains almost unchanged. 4.2. NANOPERM-alloy 4.2.1. Amorphous NANOPERM-alloys The effect of the neutron irradiation studied on FeZrB amorphous ribbons irradiated by different neutron fluences ranging from 1017 to 1019 n/cm2 shows that significant changes occur only in the case of 1019 n/cm2. Mössbauer spectra and parameters of nonirradiated as well as irradiated samples (obtained at 300 K) are depicted in Fig. 3 and in Table II. It is important to emphasise that no satellite lines emerge out of the amorphous absorption range. Such a feature is consistent with the non-occurrence of the Fe-based crystalline grains due to the irradiation process. As can be seen from Fig. 3 and Table II, the relative areas of the 2nd and 5th lines decrease with the increase of neutron fluence which implies a tendency of the net magnetic moment to turn out of the ribbon plane after irradiation. This is supposed to be a consequence of defects produced by irradiation, which are responsible for the reorientation of the magnetic moment. A decrease in the average hyperfine field values () with an increase in the neutron fluence was also observed. A detailed temperature study was prepared on non-irradiated FeZrB samples and on samples irradiated

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by the highest neutron fluence 1019 n/cm2 in the temperature range from 77 K up to 360 K [15]. The temperature dependences in Fig. 4 compare the average values of the hyperfine field before and after irradiation. One can observe that the magnetic to paramagnetic transformation was completely achieved at about 335 K in both cases. However, the hyperfine parameters obtained from the fitting of experimental Mössbauer spectra show that the mixture of ferromagnetic and paramagnetic states can be observed over 20 K for the non-irradiated as-quenched sample, and 30 K for the irradiated sample, respectively. This broadening after irradiation can be attributed to the formation of different local structural environments.

Figure 3. Mössbauer spectra of amorphous non-irradiated (a) and irradiated (b-d) FeZrB alloys where: (b) corresponds to irradiation by 1017 n/cm2, (c) to 1018 and (d) to 1019 n/cm2

Figure 4. Temperature dependences of the average values of hyperfine fields for nonirradiated sample (X0) and sample irradiated by fluency of 1019 n/cm2 (X0-19)

Table II. Mössbauer parameters of as-cast FeZrB alloys (where: X0-FeZrB are non-irradiated alloys, X0-x-FeZrB are alloys irradiated with the fluence of 10x n/cm2, is the average hyperfine field, A is the area, E is the angle determining the orientation of the net magnetic moment and ISO is the isomer shift for an individual component of Mössbauer spectra) Sample X0

IS [mm/s]

[T]

E [°]

[n/cm ]

r0.01

r0.03

r5

0

– 0.17 – 0.15

9.3

63

9.3

67

– 0.12

8.6

26

Fluence 2

17

X0-17

10

X0-19

1019

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4.2.2. Nanocrystalline NANOPERM-alloys Mössbauer spectra and parameters of non-irradiated FeZrB nanocrystalline samples and samples irradiated by different fluences of neutrons (from 1017-1019 n/cm2) taken at room temperature are shown in Fig. 5 and in Table III, respectively. One can quite easily identify some of the effects of neutron irradiation directly from the spectra, e.g. a significant increase in the relative area of sharp lines corresponding to D-Fe. After irradiation, changes in the orientation of the net magnetic moment and in the value of average hyperfine field of amorphous phase take place. With the increasing neutron fluence, the angle E decreases from about 43° for non-irradiated sample up to about 33° for the neutron fluence of 1019 n/cm2, indicating that the net magnetic moment of the amorphous component is strongly oriented out of the ribbon plane. One can conclude that the magnetic domain structure of amorphous alloys as well as the magnetization processes are governed by both microstructural defects and their stress fields [16]. Consequently, the above results suggest that the SRO and the distribution of magnetic dipoles are affected by stresses in the irradiated regions [17].

Figure 5. Mössbauer spectra of FeZrB nanocrystalline samples taken at room temperature for: (a) non-irradiated sample and irradiated samples with neutron fluence of about 1017 (b) and 1019 n/cm2 (c)

Figure 6. Determination of Tc for non irradiated (X0-1) and irradiated (X0-1-19) nanocrystalline FeZrB alloys

Changes in the average value of hyperfine fields of amorphous as well as interfacial components were also observed. A slight decrease in the average hyperfine field and

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a significant decrease in the volumetric fraction of the amorphous component can indicate a movement of Fe atoms from the amorphous matrix to the interface or to the crystalline part, contributing thus to the slight increase in after irradiation. We suppose that these free Fe atoms originate either from the neutron capture by boron or from the recoil atom displacement. We cannot a priori exclude that a part of the crystalline iron got damaged, meaning that it contains vacancies and interstitial atoms. The fluence of 1019 n/cm2 is still not sufficiently high to amorphize the crystalline iron grains. Both the increase in the volumetric fraction in the interfacial zone and the rapid decrease in the amorphous rest confirm that the Fe-B coordination was reduced. Table III. Mössbauer parameters corresponding to the nanocrystalline FeZrB samples irradiated with difference fluences of neutrons. Where: (r 0.03) is the average hyperfine field, A (r 2) is the relative area, E (r 5) is the angle determining the orientation of the net magnetic moment for an individual component of Mössbauer spectra. A – amorphous, IF – interfacial and cr – crystalline component

Ea X0-1 X0-1-17 X0-1-18 X0-1-19

43 39 39 33

11.3 11.4 11.5 10.6

Aa 82 71 79 67

EIF 40 39 44 41

27.4 28.2 29.9 28.2

AIF 4 5 3 5

Ecr 73 78 81 69

33.1 33.1 33.0 33.0

Acr 14 24 18 28

After summarizing all results obtained in the fitting procedure, the changes in the hyperfine parameters caused by neutron fluence of 1019 n/cm2 were considered as the most important ones [13]. Subsequently, non-irradiated samples and samples irradiated by the neutron fluence 1019 n/cm2 were submitted to Mössbauer experiments in the temperature range from 77 K up to 500 K [15]. The results of the applied fitting procedure described in [18] show that in both cases, i.e. for the non-irradiated and irradiated samples, the average hyperfine field of amorphous remainder decreased with increasing temperature, but it differed from zero at temperatures considerably higher than the Curie temperature of the amorphous precursor (~400 K). The situation can be analysed more easily by plotting B1/EH in reduced coordinates using Heisenberg formula, where EH is an empirical parameter. In the case of 3D Heisenberg system EH is assumed to be equal to 0.36 [19]. The two curves are illustrated in Fig. 6 after enlargement of the B coordinates. Figure 6 shows that after neutron irradiation with the fluence 1019 ncm2 the ferromagnetic order disappears at a lower temperature of measurement. If for the irradiated sample the paramagnetic state starts to be dominant at about 390 K, then for the nonirradiated sample it is at about 420 K. These results indicate that the amorphous matrix is rather strongly influenced by the neutron irradiation.

5. CONCLUSIONS The present study shows that the irradiation effects are dependent on the nanocrystalline alloy. In the amorphous component of FINEMET-alloys, the irradiation induced the reorientation of magnetic domains and redistributions of the atoms, as observed from small changes in the intensities of the spectral lines and from a slight

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decrease in the hyperfine field of amorphous component after the irradiation. One can conclude that the highest neutron fluence 1019 n/cm2 is still not sufficient to destroy the crystalline FeSi grains but is sufficiently high to disturb the atom ordering in crystalline grains from their regular positions. The magnetic moments of NANOPERM amorphous alloys turn out of the ribbon plane after neutron irradiation. The interval for observation of the mixture of the magnetic and paramagnetic state of the amorphous component is longer for the irradiated sample. But the Curie temperature is the same for the irradiated as well as nonirradiated amorphous samples. In the case of nanocrystalline samples the volumetric fraction of the amorphous and interfacial components tends to increase after neutron irradiation at the detriment of the amorphous remainder. And for the amorphous remainder of the irradiated sample, the paramagnetic state starts to be dominant about a temperature lower than that of the non-irradiated sample. ACKNOWLEDGEMENTS The master ribbons were supplied by Dr. P. Duhaj. This work was partly supported by grants Vega 1/0284/03 and Vega 1/1014/04 and J. D. is grateful for a grant from the French Government for supporting her stay in Le Mans. REFERENCES 1. 2.

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Yoshizawa, Y., Oguma, S., and Yamauchi, K., (1988) New Fe-based soft magnetic alloys composed of ultrafine grain structure J. Appl. Phys. 64, 6044-6050. Makino, A., Inoue, A., and Masumoto, T. (1995) Soft Magnetic Properties of Nanocrystalline Fe-M-B (M = Zr, Hf, Nb) Alloys with High Magnetization, Nanostruc. Mat. 2, 985-988. Shimansky, F.P., Gerling, R., and Wagner, R., (1988) Irradiation-induced defects in amorphous Fe40N40P20 97, Mat. Sci. Eng. 97, 173-176. Miglierini, M. and Sitek, J., (1990) Neutron irradiation of metallic glasses and Mössbauer spectroscopy, Eng. Mat. 40&41, 281-285. Miglierini, M., Nasu, S., and Sitek, J., (1992) Influence of neutron irradiation on ferromagnetic metallic glasses, Hyperfine Interaction 70, 885-888. Schimansky, F.P., Nagorny, K., Gerling, R., and Wagner, R., (1985) Rapidly Quenched and Metastable Materials, Elvice Science Publishers, Amsterdam, pp. 779-182. Sitek, J., Miglierini, M., (1985) Mössbauer Spectroscopy on Amorphous FexNi80–x B20 after Neutron Irradiation, Phys. Stat. Sol. (a) 89, K31. Kautský, J. and Koþík, J. (1994) Radiation Damage of Structural Materials, Academia, Prague. Sitek, J., Seberini, M., Lipka, J., Tóth, I., and Degmová, J., (1997) Rapidly Quenched and Metastable Materials, Elvice Science Publishers, Amsterdam, pp. 179-182. Brand, R.A., (1989) NORMOS program 1989 version, unpublished. Teillet, J. and Varret, F., MOSFIT program unpublished. Degmová, J., (2000) Radiation Damage of Amorphous and Nanocrystalline Fe-based Alloys, Thesis, FEI STU, Bratislava. Sitek, J. and Degmová, J., (1999) Mössbauer Spectroscopy in Material Science, Kluwer Academic Publishers, Dordrecht, V6, 273-283. Borrego, J.M., Conde, C.F, Conde A., and Greneche, J.M., (2001) Crystallization of Cocontaining FINEMET-alloys, J. Non-Cryst. Sol. 287, 120-124.

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Degmová, J., Sitek, J., Grenèche, J.M., Mössbauer study of neutron irradiated NANOPERM alloys (to be published). Kronmuller, H., (1980) Magnetization Processes and the Microstructure in Amorphous Metals, J. Phys. Paris 41, C8-618. Gupta, A., Habibi, S., and Principi, G., (2001) Study of short range order in Fe-Si-Ni-B amorphous alloys, Mater. Sci. Eng. A 304-1306, 1056-1061. Miglierini, M. and Grenèche, J.M., (1997) Mössbauer spectrometry of Fe(Cu)MB-type nanocrystalline alloys: I. The fitting model for the Mössbauer spectra, J. Phys.: Condens. Matter 9, 2303-2319. Slawska-Waniewska A., Grenèche, J.M. (1997) Magnetic properties of interface in soft magnetic nanocrystalline alloys, Phys. Rev. B 56, R8491-8494.

16. 17. 18.

19.

APPLICATION OF DIFFERENT ANALYTICAL TECHNIQUES IN THE UNDERSTANDING OF THE CORROSION PHENOMENA OF NON-CRYSTALLINE ALLOYS

K. SEDLAýKOVÁa, b, F. HAIDERb, J. SITEKa, and M. SEBERÍNIa a

Department of Nuclear Physics and Technology Slovak University of Technology Ilkoviþova 3, 812 19 Bratislava, Slovakia b Institute of Physics, Experimentalphysics I, University of Augsburg Universitätsstrasse 2, 861 59 Augsburg, Germany Corresponding author: J. Sitek, e-mail: [email protected]

Abstract:

The aim of this paper is to discuss the applicability of different analytical techniques to study the corrosion phenomena and mechanisms of amorphous and nanocrystalline metallic alloys. We focus here on atmospheric corrosion of soft magnetic Fe-based materials prepared by a plane-flow casting method followed by annealing. The samples were exposed at rural and industrial sites for 2 to 6 months. The techniques of (conversion electron) Mössbauer spectrometry, X-ray diffraction and transmission electron microscopy are considered. These analytical techniques provide useful information regarding the nature, composition, morphology and crystallinity of the corrosion film and are, moreover, highly suitable for understanding the possible structural rearrangement of noncrystalline materials. Substantial differences in the corrosion resistance according to the alloy composition and crystallinity have been observed. The most resistant Si-containing, partly crystallized alloy proved the presence of a pure amorphous protective oxide film on the surface. Fe oxide particles in other systems showed a needle-like morphology and poor crystalline order and were identified as lepidocrocite.

1. INTRODUCTION Corrosion is a widespread phenomenon, responsible for many functional failures in service. It may take many forms, depending on the corrosion conditions and individual features of the material. Especially corrosion caused by various atmospheric conditions, which is nearly unavoidable during a long-term operation, accounts for more failures (involving cost and tonnage) basis than any other environment [1]. Although there are 229 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 229–239. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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several techniques for accelerating corrosion under laboratory conditions, none of them has been found satisfactory to duplicate the composition of the corrosion products produced under atmospheric exposure [2]. The aim of the study was to prove the diagnostic potential of several analytical methods to understand the corrosion mechanism of amorphous and nanocrystalline metallic alloys. The nanocrystalline materials exhibit great fundamental and technological interests because of their unique microstructural characteristics, resulting in excellent soft magnetic properties. Even though the number of papers devoted to the corrosion of these alloys is unfortunately very low (and none was found to be handling the mechanism of atmospheric rusting), a partial deterioration of their unique magnetic features observed in laboratory corrosion tests has been already indicated [3]. 2. MATERIALS AND EXPERIMENTAL METHODS Fe-based metallic alloys of the nominal composition of Fe73.5Cu1Nb3Si13.5B9 and Fe87.5Zr6.5B6 were investigated in the amorphous and nanocrystalline state. The amorphous precursor was prepared by the plane-flow casting method at the Institute of Physics, Slovak Academy of Sciences, Bratislava, in the form of ribbons several millimetres wide and about 20 to 30 micrometers thick. To obtain the nanocrystalline structure, controlled annealing treatment of the ‘as-cast’ samples in a vacuum at a temperature of 540qC was carried out. Accordingly, annealed Fe73.5Cu1Nb3Si13.5B9 (so called FINEMET) and Fe87.5Zr6.5B6 (so called NANOPERM) alloys were composed of ultrafine bcc-Fe and DO3-Fe(Si) grains with DO3 structure, respectively. The shiny sides of the amorphous and nanocrystalline samples of both compositions were exposed at rural and industrial sites for 2 to 6 months. To analyse the corrosion mechanism and products, the methods of X-ray diffraction (XRD), Mössbauer spectrometry (MS) and transmission electron microscopy (TEM) were employed. The X-ray diffraction patterns were recorded with the Enraf-Nonius Diffractis 585 diffraction analyser using Co KD radiation. The incidence angle of the direct beam with respect to the specimen plane remained constant during the entire measurement, i.e. 11 degrees. For the selected specimens, the X-ray patterns were collected at lower incident angles as well, down to approximately 3 degrees. Mössbauer spectra were recorded in transmission geometry by a conventional constant-acceleration spectrometer with 57Co(Rh) source at room temperature and for the selected samples, at liquid N2 temperature. Apart from transmission measurements, the conversion electron Mössbauer spectrometry (CEMS) was engaged. CEM spectra were taken with a back-scattering type gas-flow proportional counter, designed at our laboratory. For evaluation of all the recorded Mössbauer spectra, the NORMOS program was used [4]. The specimens for TEM observations were prepared by ion-polishing using GatanPIPS 691. The samples of shiny (corroded) surfaces were prepared by ion-milling of the ribbons from the wheel-contacted side only. The corrosion products and the grainstructure of the materials were investigated using a Philips CM 120 electron microscope. The TEM accelerating voltage was 120 kV.

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3. RESULTS AND DISCUSSION 3.1. X-ray diffraction The microstructure of nanocrystalline alloys was widely investigated by X-ray diffraction in the sense of crystalline fraction, the nature of the grains and grain size determination [5]. XRD is a simple and comfortable method, which is easily applicable even to quite brittle, ribbon-shaped nanocrystalline specimens. For corrosion studies, the composition of the rust scale can be determined quite reliably using X-ray diffraction. X-ray patterns of iron oxides can be fitted using different line profiles – preferably Voight, Pseudo-Voight or Pearson VII function – to yield accurate line positions, widths and intensities, these being the three important parameters. From these, information is obtained about the nature of the oxide, its quantity (in a mixture), its unit cell parameters and its crystallinity. Deviations from the unit cell parameters obtained from an X-ray pattern may be used to quantify the extent of Fe substitution by other cations; the line broadening provides information on the average crystal size (Scherrer formula); the changes in relative intensities of the peaks point at preferential orientation etc. In many cases, however, the oxide film is too thin for this technique to be applied and the identification of these phases requires grazing incidence measurements or other sensitive surface chemical methods, such as electron diffraction, Auger, Mössbauer and Raman spectrometry, XPS and EXAFS. Another drawback of this method can arise when corrosion products are of a low crystallinity and for this reason, they cannot be analysed accurately. Even though, the differences in the broadening of various reflections due to different degrees of development of small crystals in various directions can provide information about their crystal shape [6]. Concerning actual results, the XRD patterns of the as-quenched samples showed the presence of only broad halos confirming their amorphous structure. For the nanocrystalline samples, the presence of rather well defined Bragg peaks corresponding to the structurally ordered crystalline grains superimposed on very broad lines typical for disordered amorphous matrix was observed. The crystalline peaks are associated with either bcc-Fe in case of NANOPERM alloys or with DO3-Fe(Si) nanograins in case of FINEMET alloys. Diffraction patterns were analysed by Rayflex program. The most intense peak of the first diffuse maximum was decomposed using Pseudo-Voight profiles in order to estimate the crystalline/amorphous fraction from the integral intensities of respective peak areas. The results as compared with those obtained by MS are listed further in Table II. From the full width at half maximum of the strongest peak assigned to the crystalline phase, the average grain size was assessed using the Scherrer equation (Table I). The surface appearance of all corroded samples was inspected under optical microscope before further investigations. The Si-containing nanocrystalline specimens showed, even after 6-months outdoor exposure, no visible continuous oxide layer on the surface. XRD analysis yielded no information on the composition of the potentially present passive film, either. On the other hand, the amorphous precursor of FeCuNbSiB was covered by a massive orange-coloured rust layer as early as after 2 months weathering. A relatively continuous oxide film was observed on FeZrB ‘as-cast’ samples as well;

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however, their nanocrystalline counterparts, unlike in the case of FINEMET, were corroded to the largest extent.

Figure 1. The XRD pattern of nanocrystalline FeZrB specimen after a 6-month exposure recorded at an incident angle of ca. 3 degrees Table I. Average crystal sizes of the bcc-Fe and bcc-Fe(Si) grains of NANOPERM and FINEMET samples, respectively; and mean oxide particles sizes obtained using XRD unexposed nanocrystals

Sample FeCuNbSiB

11

FeZrB

12

Crystal size (nm) after 6-months exposure nanocrystals J-FeOOH 12 – 13

13

Table II. Comparison of the amorphous phase fraction of nanocrystalline samples obtained using XRD and MS Amorphous phase fraction (%) Sample unexposed after 6-months exposure XRD MS XRD MS FeCuNbSiB 53 50 52 53 FeZrB

62

69

34

39

The XRD analysis of the amorphous samples indicated a very low crystallinity of the oxide film preventing its identification even at lower incident angles. This method offered some relevant results on the composition of the corrosion film only in the case of the most intensively corroded nanocrystalline NANOPERM. The respective diffraction pattern, illustrated in Fig. 1, was found to be consistent with the orthorhombic structure of J-FeOOH, i.e. lepidocrocite (Rayflex card Nr. 74-1877). The presence of D-FeOOH (goethite), which displays a similar diffraction pattern as lepidocrocite, cannot be strictly excluded; even though the reflection (130) is missing in the diffraction

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pattern. Since from the appearance of the XRD spectra it was obvious that the oxide particles were of a very small size (broad, low intensity peaks), the Scherrer equation was applied to the most intense peaks (031 reflection) in order to get a rough estimate of their average crystal size. The mean particle size is shown in Table I together with the average sizes of Fe-nanocrystals. 3.2. Mössbauer spectrometry 57 Fe Mössbauer spectrometry seems an excellent tool to investigate iron-based nanocrystalline alloys, because this local technique is able to elucidate the nature of hyperfine interactions of the different resonating iron nuclei and to probe the nature of their immediate surroundings [5]. This technique can easily be applied to the thin and brittle ribbon-shaped samples over a wide temperature range due to a high recoilless factor [7]. Identification of Fe-containing phases, which are created during the annealing process as well as elucidation of their structural (e.g. volumetric fraction of individual phases) and magnetic properties (the orientation of the net magnetic moment, the average hyperfine field, etc.), can be performed very effectively. The delicate stage of this analytical method is, however, the choice of the fitting procedure of the Mössbauer spectra. They can be, in general, quite complex due to the structural disorder, embracing up to 7 sextets attributed to different iron neighbourhoods (e.g. in case of FINEMET alloys) as well as the amorphous phase describing the distribution of hyperfine field/quadrupole splitting. From the corrosion point of view, MS is particularly useful in systems where the iron oxide may be too low in concentration or in crystallinity to be detected by XRD. MS is the only technique, which can identify uniquely all the iron oxides (hydroxides) including the measurement of the fraction of each phase present in the corrosion coating and to obtain information about the particle size and its isomorphous substitution. For example, the size and size distribution of small particles of superparamagnetic Fe oxides can be estimated from the Mössbauer spectra by recording the transition from the doublet spectrum into a magnetically split spectrum as the temperature decreases. The temperature of such a transition decreases with decreasing the particle size [6]. The phase analysis in the transmission geometry is, however, hindered, when the oxide films are very thin and the sub-spectrum of the substrate is predominant in the Mössbauer pattern. Moreover, such a layer cannot be scraped off the surface for studying in this geometry. Here, a surface-sensitive variant of MS, i.e. conversion electron Mössbauer spectrometry (CEMS), which collects electrons associated with the 7.3 keV conversion after resonance absorption of 14.4 keV J-rays comes in handy providing useful information about the corrosion products, grown to the thickness of more than 100 nm, in a non-destructive way. The specific results showed that particularly the CEMS variant is very useful in the identification of the corrosion products. For the quite intensively corroded amorphous specimens, where the identification of corrosion products by XRD was impossible, the CEM spectra manifested the presence of a well-resolved, slightly broadened paramagnetic doublet having Mössbauer parameters of Fe(III) in the form of ferric oxyhydroxide J-FeOOH (lepidocrocite). However, from the room temperature

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Mössbauer spectra, lepidocrocite and small superparamagnetic particles of goethite (DFeOOH) or maghemit (JFe2O3) cannot be identified accurately. In order to distinguish between these three possible paramagnetic compounds, low temperature measurements are required. The relative fraction of paramagnetic (hydro)oxides registered on amorphous specimens varied between 6 and 49%. The diagnostic potential of this method is, however, hindered when the more complex spectra are to be analysed. This is the case of nanocrystalline FINEMET, where the spectra complexity obscures the fitting procedure and further oxide describing component becomes ‘invisible’ in lower concentrations even for CEMS.

Figure 2. Changes in the structural arrangement of the nanocrystalline FeZrB alloy after 2 to 6-months exposure to the atmosphere revealed by transmission MS

Figure 3. Transmission spectra of nanocrystalline NANOPERM untreated (a) and exposed in industrial area for 6 months measured at (b) room temperature and spectra recorded at 77 K (c). Corresponding distributions of hyperfine fields are plotted at the right hand side of each graph

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Relatively simpler features of NANOPERM spectra facilitate their interpretation. The CEMS showed that the surface of the samples even after a 2-month exposure was composed exclusively of a (hydro)oxides describing doublet. In the case of such an advanced stage of corrosion, the transmission measurements can render interesting information on the corrosion damage as well. In addition to the possibility of distinguishing the oxide component, the bulk spectra offer unique characteristics of structural rearrangement (Fig. 2). We observed a growth of a crystalline, interfacial and paramagnetic phase component at the expense of the residual amorphous matrix. The contribution of the doublet up to ca. 10% was manifested. This phenomenon could be related to the corrosion-induced growth of the existing crystalline grains. Since, as mentioned above, lepidocrocite and other potentially superparamagnetic oxides cannot be identified separately in the Mössbauer spectrum at room temperature, the 77 K transmission spectra of NANOPERM were recorded (Fig. 3). Low temperature measurements unveiled, however, an absence of magnetically ordered iron oxides. Furthermore, the significant increase in quadrupole splitting of the doublet can attribute this component to lepidocrocite, which has a Néel temperature of about 77 K [6]. Mössbauer measurements were correlated with X-ray diffraction results mentioned above and no significant discrepancies about the fraction of the crystalline phase were observed (Table II). 3.3. Transmission electron microscopy Transmission electron microscopy is also very useful for studying the microstructure of non-crystalline materials. In addition to the grain size determination, it offers complementary information on the grain shape as well as their homogeneity, density and distribution within the amorphous matrix. TEM is applied routinely to determine crystal morphology of common corrosion products as well. Besides the imaging mode, the electron diffraction mode is also available. The electron diffraction pattern can, unlike that of X-rays or neutrons, be related to an image of a crystal, thus enabling the structure of a particular region to be investigated. An advantage is that as electrons are scattered more efficiently than X-rays, shorter exposure times are required. In addition, comparatively small samples can be examined (selected area diffraction, SAD). On the other hand, since electrons do not penetrate the matter as easily as X-rays, only relatively thin samples (50-100 nm) can provide an electron diffraction pattern [6]. To prepare samples with such properties for the electrons transparent region is, however, critical in this method due to brittleness of the material. This can be achieved relatively successfully when ion-polishing technique is used to prepare the TEM specimens. If the samples are thinned from one side only, one can inspect the properties of the very thin, initially wheel-contacted or free surface. As far as e.g. grain size is concerned, however, these can vary significantly within the whole sample cross-section, usually being the largest on the free side and the smallest in the inner part [8]. Hence, the information on the average grain size could be obtained only if cross-section specimens are prepared by the common sandwich technique.

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The main problem arises, when corroded samples are to be investigated. The atmospheric rusting results in formation of a strongly inhomogeneous oxide film, which is therefore quite difficult to analyse. Moreover, as the corrosion film is usually thicker than 50 nm, analysing of the influence of the corrosion damage on structural rearrangement can be difficult as well. The preliminary TEM observations confirmed absence of the crystalline phase in the ‘as-cast’ FeCuNbSiB specimens. Figure 4 shows the TEM micrographs of the shiny surface of nanocrystalline FINEMET. The grain size of the nanocrystals determined by an image analysis was approximately 10 nm, which was in a good agreement with the X-ray diffraction results. The early stage of the corrosion process of amorphous FeCuNbSiB was investigated and it revealed a presence of an amorphous passive film, which is to be identified (Fig. 5a). Concerning the composition, one could expect the presence of SiO2 protective layer [9]. The ‘as-cast’ specimen, after a 6-month weathering, showed the presence of a similar amorphous region too; however, in addition, some fibrous structure and needle-like particles yielding no sharper diffraction patterns were observed as well (Fig. 5b).

Figure 4. Bright-field TEM image with the a corresponding electron diffraction pattern (EDP) of the shiny surface of the annealed FeCuNbSiB alloy ribbon

Figure 5. TEM pictures of corroded ‘as-cast’ FeCuNbSiB ribbon: amorphous film observed at the early stage of the corrosion process (a); fibrous structure of the corrosion film of a 6 month weathered specimen (b)

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Figure 6. TEM images of a 6 months corroded nanocrystalline FeCuNbSiB specimen; an amorphous region with round particles (a), the interface between nanograins containing interface region and amorphous area (b)

On the corroded surface of a nanocrystalline FINEMET, an amorphous passive film was observed, showing scattered small round particles of the size of about 20 nm (Fig. 6a). The film thickness was, however, even after 6 months, so small that the Fe(Si) grains were still discernible in the inspected region (Fig. 6b). It was found that the nanocrystal grain size remained practically unaltered.

Figure 7. Bright-field (a) and dark-field (b) TEM image of untreated nanocrystalline FeZrB sample with corresponding SAED pattern

From the free surface of a nanocrystalline NANOPERM shown in Fig. 7, large grains of D-Fe of the diameter ranging from ca. 100 to 200 nm are observable. When compared with grain size obtained by XRD (ca. 12 nm), the structure of their surface is found to be very much different from that of the inner part. Figure 8a shows the surface of the 6-months corroded NANOPERM sample. One can notice the oxide particles with needle-like morphology, showing a discernible internal structure. According to the corresponding SAED pattern shown in Fig. 8b, these can be identified as lepidocrocite. Table III summarizes the TEM investigations aimed at grain size determination.

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Figure 8. A bright-field TEM image of needle-like oxide particles observed on a corroded surface of nanocrystalline FeZrB ribbon (a) and the corresponding SAED pattern (b) Table III. Approximate crystal sizes of the bcc-Fe and bcc-Fe(Si) grains of NANOPERM and FINEMET samples, respectively, and average size of oxide particles obtained using TEM (shiny side) Sample FeCuNbSiB

unexposed nanocrystals 10

FeZrB

200

Crystal size (nm) after 6-months exposure nanocrystals J-FeOOH 10 – 10 nm wide, – up to 60 nm long

The TEM observations indicate that further investigation of the corrosion products is necessary to provide relevant information on their morphology and crystallinity. 4. CONCLUDING REMARKS The capabilities of three different analytical techniques, namely the X-ray diffraction, Mössbauer spectrometry and transmission electron microscopy, of obtaining information on the corrosion behaviour of non-crystalline Fe-based alloys were discussed. The engagement of complementary techniques can lead to a better understanding of relevant phenomena, even though each method has its own shortcomings as far as its practical application is concerned. Although X-ray diffractometry is a typical analytical technique for the identification of the corrosion products, it becomes unusable if the corrosion layer is very thin as is the case of the initial corrosion stage and if the corrosion products are in an amorphous state. On the other hand, TEM is able to yield relevant results even if the passive film is very thin, but the drawback appears during the preparation of specimens in advanced stages of corrosion, where the oxide film can be very inhomogeneous in its composition and depth profile. The utility of Mössbauer spectrometry techniques for the corrosion study, comprising transmission measurements and CEMS variant, was demonstrated as well. While CEMS is very suitable for different Fe-phases identification, the trans-

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mission mode can provide relevant information on the bulk rearrangement. This can also be proved by XRD. ACKNOWLEDGEMENTS Contribution of the grants SGA 1/1014/04, 1/0284/03 and DAAD 08/2003 is acknowledged. REFERENCES 1. 2. 3. 4. 5. 6. 7.

8.

9.

Fontana, M.G. (1987) Corrosion Engineering, McGraw-Hill Book Comp., New York. Oh, S.J., Cook, D.C., and Townsend, H.E. (1999) Atmospheric corrosion of different steels in marine, rural and industrial environments, Corrosion Science 41, 1687-1702. Sousa, C.A.C., Kiminami, C.S. (1997) Crystallization and corrosion resistance of amorphous FeCuNbSiB, J. Non-Cryst. Solids 219, 155-159. Brand, R.A. (1987) NORMOS programs, internal report, Angewandte Physik, Universität Duisburg (unpublished). Greneche, J.M. (1997) Nanocrystalline iron-based alloys investigated by Mössbauer spectrometry, Hyp. Interactions 110, 81-91. Cornell, R.M., Schwertmann, U. (1996) The Iron Oxides, VCH Verlagsges. mbH, Weinheim. Greneche, J.M., Miglierini, M., and Slawska-Waniewska, A. (2000) Iron based nanocrystalline alloys investigated by 57Fe Mössbauer spectrometry, Hyp. Interactions 126, 27-34. Wu, Y.Q., Bitoh, T., Hono, K., Makino, A., and Inoue, A. (2001) Microstructure and properties of nanocrystalline Fe-Zr-Nb-B soft magnetic alloys with low magnetostriction, Acta Mater. 49, 4069-4077. Sousa, C.A.C., Kuri, S.E., Politti, F.S., May, J.E., and Kiminami, C.S. (1999) Corrosion resistance of amorphous and polycrystalline FeCuNbSiB alloys in sulphuric acid solution, J. Non-Cryst. Solids 247, 69-73.

MONTE CARLO SIMULATIONS OF MODEL PARTICLES FORMING PHASES OF NEGATIVE POISSON RATIO

K.W. WOJCIECHOWSKI Institute of Molecular Physics, Polish Academy of Sciences M. Smoluchowskiego 17, 60-179 PoznaĔ, Poland Corresponding author: K. Wojciechowski, e-mail: [email protected] Abstract:

Systems with negative Poisson ratio (NPR) behave in a counterintuitive way: when pulled (pushed) in one direction, they expand (shrink) in all directions. In this lecture we discuss application of computer simulations to study NPR systems and sketch an idea – based on the Cauchy relations – of systematic studies of mechanisms which may lead to NPR. Roughly speaking, the NPR systems can be divided into three groups: (i) systems of artificial structures (on micro-, mezo- or macroscopic scale), (ii) systems at special conditions (e.g. systems at negative pressure, systems near some phase transitions, etc.), and (iii) thermodynamically stable phases. We concentrate on the third group and study a class of twodimensional model particles forming isotropic solid phases which exhibit the NPR. Depending on the interaction potential used, they show periodic or aperiodic structures. The Poisson ratio of the aperiodic solids can be decreased by transforming them into periodic crystals.

1. INTRODUCTION Mechanical properties of materials are important not only in traditional applications, like the construction industry or light and heavy industry, but also in modern advanced technologies. New materials of desirable magnetic or electric properties should also posses proper mechanical properties. In this context, searching for materials and models of unusual mechanical properties is not only interesting from the point of view of fundamental research but also important from the point of view of potential practical applications. This paper concerns computer simulation studies of one of such classes of systems, namely those which show negative Poisson ratio (NPR). When we stretch a piece of rubber, it shrinks in dimensions perpendicular to the stretching direction (see Fig. 1a). The negative ratio of the change of transverse dimension to the change of longitudinal dimension is known as the Poisson ratio [1]. By 241 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 241–252. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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definition, this ratio is positive for rubber. Everyday experience shows that the behaviour of rubber is typical of common materials, like leather, plastics, metals, etc. All these materials when pulled (pushed) in any direction, shrink (expand) in directions transverse to the pulling (pushing) direction. Although the opposite behaviour, when a stretched (compressed) material sample expands (shrinks) transversely, i.e. when the material exhibits a negative Poisson ratio (NPR), is in conflict with our intuition, the elasticity theory does not exclude it, even in isotropic systems [1]. Some mechanical [2, 3] and thermodynamic [4] models showing NPRs have been studied in the eighties of the last century. In 1987 first NPR foams were manufactured by Lakes [5]. These facts were, however, very slowly spreading in the scientific community, which for a long time believed that no isotropic NPR materials existed in nature [1].

Figure 1. Deformation corresponding to horizontal stretching of samples made of common materials (left) and a negative Poisson ratio material (right). The initial states of the samples are represented by dashed lines

Manufacturing of the NPR materials [5] has proved that theoretical models [2-4] exhibiting such an unusual property are not merely mathematical curiosities. Since that time an increasing interest in studies of NPR materials and models has been observed (for reviews see e.g. [6-9]). It is caused not only by their counterintuitive properties [10] which are of interest from the point of view of the fundamental research but also, if not mainly, by various applications. The examples are: air filters, strain sensors, press-fit fasteners, pads under carpeting, wrestling mats, doubly curved panels of synclastic shapes, vascular implants, fillings for highway joints, shock and sound absorbers, packing materials, and other [6-10]. The existing NPR materials and models can be divided into three groups [11]: (i) The first of them concerns systems of special, usually artificial (on macro-, mezo- or micro-scale), structures. Such NPR structures were discussed in numerous papers reviewed in [6-9] as well as in some recent papers [12-16]. (ii) The second group corresponds to systems which show the NPR under special conditions, e.g. in the vicinity of phase transitions [17-19], near percolation thresholds [20, 21] or at “negative” pressures’ [22-24]. (iii) The third group is related to thermodynamically stable phases exhibiting NPRs. In this case the crucial point is to ‘construct’ a proper molecule (or molecules) forming a NPR phase. Such molecules will be further referred to as the NPR molecules. The systems representing the last group above can be thought of as the most fundamental NPR systems. It is so because the equilibrium structure of any thermodynamically stable phase is fully determined by the molecular interaction potential. The attractive feature of the latter NPR structures is that they should be homogeneous down to the molecular level. They should have also well defined stability ranges and their properties should be tuneable, at least to some extent, e.g. by mixing them with some usual molecules.

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One can notice that it is relatively easy to find real materials showing NPR in some directions (see e.g [25, 26]). It has been also possible to find an anisotropic crystal which Poisson ratio averaged over orientations is negative; this interesting example is the D-crystobalite [27]. However, no real, thermodynamically stable phase has been found as yet which is elastically isotropic (i.e. its elastic properties do not depend on the direction) and shows a NPR. Thus, the question whether it is possible to construct a molecule (or molecules) forming such a phase can be posed. This problem is of theoretical interest and, if the answer is positive, can have practical consequences. At the initial stage of solving this problem various simplifications are acceptable, like considering very artificial “molecules” and reducing the system dimensionality. In this paper we will restrict ourselves to the two-dimensional version of this problem. The paper is organized as follows. In Section 2 basic definitions of the elasticity theory are reminded and the simulation method is sketched. In Section 3 the Poisson ratio of isotropic systems is discussed. In Section 4 a strategy of systematic investigations which may lead to constructing systems of NPR is presented. In Section 5 an example of a model particle is described, which forms elastically isotropic (i.e. of elastic properties not depending on the direction) NPR phases in two dimensions. The final Section 6 contains a summary and conclusions. 2. DETERMINATION OF ELASTIC PROPERTIES OF SOLIDS BY COMPUTER SIMULATIONS 2.1. Basic definitions Elastic deformations of a body can be described by the (Lagrange) strain tensor

Hij = (wiuj + wjui + 6k wiuk wjuk)/2. The displacement vector ui is the difference between the system coordinates after and before the deformation, 6k denotes the summation with respect to the index k and wi means differentiation with respect to the system coordinates before the deformation (further referred to as the reference state) [1]. Elastic properties of solids can be determined by expanding the free energy change 'F(H) corresponding to a (small) strain H with respect to the components of the strain: 'F(H)/Vref = 6ij V ij H ij + 6ijkl Cijkl Hij H kl /2 ,

(1)

where V ij are the components of the stress tensor, Cijkl are the components of the tensor of the elastic constants, Vref is the volume of the reference state of the system and 6ij, 6ijkl denote the summations over the indices ij, ijkl, respectively. When the system is under isotropic pressure, V ij = –pGij (where Gij is the Kronecker delta), instead of expanding the free energy it is more convenient to expand the free enthalpy 'G(H)/Vref = '(F + pV)/Vref = 6ijkl Bijkl Hij H kl /2 ,

(2)

where the reference state corresponds to the equilibrium state at the pressure p, and the elastic constants Bijkl and Cijkl are related by the formula [28, 22]

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Bijkl = Cijkl – p (Gik Gjl + Gil Gjk – Gij Gkl) .

(3)

If a solid is deformed by applying a small tensile or compressive load 'V xx in the direction x, the changes of the strain tensor components in this direction and in a direction y perpendicular to it are equal 'Hxx = Sxxxx 'V xx ,

(4a)

'Hyy = Syyxx 'V xx ,

(4b)

where the matrix of elastic compliances Sijkl is the inverse of the matrix Bijkl 6klBijkl Sklmn = (Gim Gjn + Gin Gml)/2

(5)

It follows from (4) and the definition of the generalized Poisson ratio (defined as the negative ratio of the strain change in the direction y to the strain change in the direction x), that the Poisson ratio measured for the x,y directions can be written as Qyx = –'Hyy/'Hxx = –Syyxx /Sxxxx ,

(6)

which means that the Poisson ratio depends on both directions, in general. We should add here that the (perpendicular to each other) directions x and y can be chosen arbitrary. This means that, in general, when x and y are not crystalline axes, the formula (6) can be quite complex as it will involve all the components of the tensor of elastic compliances (or elastic constants) describing the system. 2.2. Monte Carlo simulations of elastic constants The elastic constants of static periodic structures interacting through analytic potentials can be determined by analytic methods. The presence of disorder, introduced e.g. by positive temperature or defects, requires using computer simulations, in general. The sample representing a simulated system is usually of a form of periodic box which can be oblique, in general, and which is described by the, so called, box matrix h of columns formed by vectors defining the box edges [29]. Denoting the reference state of the box by H one can write the strain tensor in the form [29]

H = (H–1 h h H–1 – I)/2 , where H–1 is the inverse of the matrix H and the matrices h, H are symmetric. When the box is allowed to fluctuate at a constant stress and H the equilibrium of the system, there is a simple relation between the the matrix of elastic compliances and the average fluctuations of the the strain tensor [29]

(7)

assumed to be corresponds to components of components of

H { ³dHD(D+1)/2 Hij H kl exp(–'G(H))/³dHD(D+1)/2 exp(–'G(H)) = = k T Sijkl/Vref ,

(8)

where the integration in Eq. (8) is over all the components of the strain and the reference state corresponds to the equilibrium state of the system. As the strain fluctuations

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can be measured during the simulations, the formula (8) allows one to determine elastic properties of the system. If the external stress corresponds to isotropic pressure it is not necessary to know the equilibrium (reference) structure of the studied system prior to simulations. The precise formulas for obtaining the compliances from the strain fluctuations in such a case can be found, e.g., in Ref. [30] where one can also find references to other methods of the elastic constants determination by computer simulations. 3. ELASTICITY OF ISOTROPIC BODIES To describe elasticity of isotropic bodies one needs only two elastic constants: the bulk modulus B and the shear modulus P. In this case the expansion in the Eq. (2) can be reduced to 'G(H)/Vref = (B/2) 6i Hii2 + P 6ij [Hij – (1/D) Gij 6k H kk]2

(9)

and the Poisson ratio, which obviously does not depend on the direction, is expressed by the formula [22]

Q = (D B – 2P)/[D(D – 1) B + 2 P]

(10)

where D is the dimensionality of the system. An isotropic system is stable when any deformation increases its free enthalpy, i.e. when the quadratic form in (9) is positive definite. This is equivalent to the requirement that B and P are positive. Thus, the requirement of the system stability implies that the Poisson ratio fulfils the following inequalities –1 d Q d 1/(D – 1) . It follows from Eq. (10) that the Poisson ratio is a decreasing function of the (positive) ratio of the system rigidity to its bulk modulus, P/B. There are some special cases worth mentioning. (i) When P/B o 0 then Q = 1/(D – 1) and one can check that the volume of the system is preserved when the system is stretched or pulled in one direction. In three dimensions this case is well approximated by rubber. (ii) When P/B = D/2 then Q = 0, i.e. the transverse dimensions of the systems are preserved at uniaxial stretching/pulling. In reality, such behaviour is well approximated by cork. (iii) When P/B o f then Q = –1 what means that the system shape is preserved when the system is uniaxially stretched/pulled. Equation (10) indicates that at a given B more rigid systems show lower Poisson ratios. As the rigidity (tendency to preserve shape) is important in various practical applications, like constructions of buildings, airplanes, cars, etc., the materials of negative Poisson ratio are of practical interest.

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4. CAUCHY RELATIONS AND NEGATIVE POISSON RATIOS The symmetry of the strain tensor Hij = Hji implies that the tensor of elastic constants Cijkl must be invariant with respect to the following index interchanges: i l j, k l l and ijlkl. At zero pressure, if the tensor of elastic constants is invariant with respect to all replacements of the indices, i.e. when equalities known as the Cauchy relations (CRs) [31] are fulfilled, then the equality Biijj = Cijij = Cijij = Bijij holds true. Combining this equality with the obvious relations fulfilled by the bulk modulus and the shear modulus, B { (6i Biijj)/D, P { Bijij, and with the requirement Bijij = (Biiii – Biijj)/2 which follows from the isotropy of the system at zero preassure, one obtains

Q = 1/(D + 1) ,

(11)

which means that when the CRs hold true then the Poisson ratio is positive for any finite dimensionality. The conditions sufficient for the CRs have been discussed extensively in the literature [31]. These conditions are collected in the left-hand side column of the Table I. In the right-hand side column of that table some contradictory conditions are shown. The latter conditions imply that the Poisson ratio may be different from its value given by Eq. (12) and, in particular, its value may be negative. Table I. Sufficient conditions for the Cauchy relations and some conditions being in contradiction with them are collected in the left column and right column, respectively. The conditions in the right column offer possibilities for obtaining negative Poisson ratios Sufficient conditions for the CRs

Chances for obtaining Q < 0

Central interactions between point ‘atoms’

Anisotropic particles Non-central interactions

Static structures (T = 0)

Positive (high) temperatures (T > 0) Non-convex structures

Affine deformations

‘Collapsing’ inclusions

Pair-wise interactions

Many-body interactions

No external pressure (p = 0)

Non-zero (large) external pressures (positive or negative)

Periodic structures (perfectly ordered crystals)

Defects (vacancies, interstitials, ...) Disordered systems (glassy systems, degenerate crystals, quasi-crystals, ...) Percolation, phase transitions

The discussion in this paper will be focused on the negation of the first two conditions sufficient for the CRs. The systems of anisotropic particles interacting through non-central potentials will be discussed both at zero and non-zero pressure or temperature. Examples of periodic and aperiodic solid phases formed by the anisotropic

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particles will be given. Systems representing other conditions will be discussed elsewhere. 5. TWO-DIMENSIONAL MODEL PARTICLES FORMING PHASES OF NPR The first known model of the NPR molecule was the cyclic hexamer [4, 32, 33]. Although the NPR phase formed by the hexamers is elastically isotropic, it does not show the mirror symmetry i.e. it is chiral (see Fig. 2), with the chiral axis being perpendicular to the system plane. Despite that any chiral axis can be thought of as not much relevant for structures of two-dimensional NPR systems discussed in this paper, presence of such an axis can complicate modelling of highly symmetric NPR phases in three dimensions. Thus, it is interesting whether one can construct elastically isotropic two-dimensional NPR phases, which show the mirror symmetry. Recently, a positive answer to this question has been found [24, 34, 35]. Hard cyclic trimers constitute an example of a class of such NPR molecules; a NPR phase, which is elastically isotropic at presence of the mirror symmetry, is shown in Fig. 3. Elastic properties and (mechanical and thermodynamic) stability of this phase are discussed in the following two subsections.

Figure 2. Geometry of the NPR phase of cyclic hexamers. Each hexamer is consisted of six discs of the same diameter b = 0.7 which centres are fixed at the vertices of a hexagon of unit side length. It can be seen that this structure does not show the mirror symmetry because of the non-zero angle between the molecular axis (thick dotted line) and the crystalline axis (dashed line)

Figure 3. Geometry of the NPR phase of the cyclic trimers. Each trimer consists of three discs of the same diameter b = 0.7 which centres are fixed at the vertices of a triangle of unit side length; the interior of the triangle is further referred to as the molecular core. It can be seen that this structure shows the mirror symmetry because of the angle between the molecular axis (thick dotted line) and the crystalline axis (dashed line) is equal to zero. The molecular anisotropy parameter is defined as D = 1/(2b) and changes between zero (the case of the isotropic discs) and unity (the maximum anisotropy for which the molecular cores do not overlap in this structure)

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5.1 Analytic studies of cyclic trimers Periodic structures of the cyclic trimers with various interaction potentials have been solved exactly in the static (zero temperature) limit in Ref. [24]. In Figure 4 the Poisson ratio, the bulk modulus and the shear modulus are shown as functions of the molecular anisotropy parameter D (defined in the description of Fig. 3) when only the nearestneighbouring trimers interact by the n-inverse-power ‘atom-atom’ interaction potential u(r) ~ 1/rn. It can be seen that at sufficiently small distances between the nearestneighbouring atoms of the neighbouring molecules (i.e. when the density is large or, in other words, when the trimer anisotropy is large) the system shows negative Poisson ratio.

Figure 4. (a) The Poisson ratio, (b) the bulk modulus and (c) the shear modulus as functions of the trimer anisotropy. The curves representing the bulk (shear) modulus are drawn only for its positive values. The curves for the Poisson ratio are drawn only when the system is mechanically stable (i.e. both the bulk and the shear modulus are positive)

In the limit of n o f, i.e. when the trimers can be seen as the hard bodies of the atomic diameters equal to the distance between the centres of the nearest-neighbouring discs of different molecules, the Poisson ratio is a particularly simple function of the molecular anisotropy parameter [24]

Q = (1 – 2D2)/(3 – 2D2) .

(12)

5.2. Monte Carlo simulations of cyclic trimers Monte Carlo simulations have been used to study the elastic properties of the trimer system at positive temperature [35]. Various interaction potentials have been studied [35]. In this paper we restrict our attention to the case of hard trimers at the anisotropy D = 0.5, i.e. when the disc diameter is equal to the side length of the molecular core. Two kinds of such “molecules” are shown in Fig. 5. The fluid of simple hard cyclic trimers (see Fig. 5a) freezes spontaneously into an aperiodic molecular solid whose close packed structure is shown in Fig. 6a. At present it is not known, however, if this solid structure (which at close packing corresponds to hexagonal lattice of hard discs) is a metastable glass or a thermodynamically stable

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phase. (The latter possibility occurs, e.g., in the case of two-dimensional hard homonuclear dimers, for which the thermodynamically stable solid phase is aperiodic [36, 37].)

(a)

(b)

Figure 5. Geometry of (a) the simple trimer interacting through the ‘atom-atom’ hard disc potential only and (b) the centred trimer being the simple trimer with an extra hard disc potential interaction between the molecular mass centres

(a)

(b)

Figure 6. Structures of the hard cyclic trimers at the anisotropy parameter D = 0.5: (a) aperiodic crystal near close packing, (b) periodic crystal with the 3-fold symmetry axis near melting. Both these structures are elastically isotropic by the symmetry arguments

When an extra interaction between the molecular mass centres is introduced, apart from the atom-atom interactions characterizing the simple trimers, the obtained centred hard cyclic trimers (Fig. 5b) crystallize into the periodic molecular solid whose close packed structure is shown in Fig. 6b. The elastic properties of the isotropic solid structures of the simple and centred hard trimers have been obtained in the full range of (meta)stability of the solid phases, i.e. between the close packed structures and melting [35]. The computed Poisson ratios show a linear (within the simulation accuracy) dependence on the relative “volume” (i.e. on the two-dimensional area divided by the area at close packing). The Poisson ratio grows from Qa = –0.019 r 0.011 at close packing to about 0.26 near melting for the aperiodic structure and from Qp = –0.135 r 0.009 at close packing to about 0.04 near melting for the periodic structure.

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It is worth adding that the static limit for the close packed periodic structure of hard trimers is given by the Eq. (12); for D = 0.5 one obtains Qstatic = 0.2. This means that near close packing the molecular motions of hard trimers substantially decrease the Poisson ratio with respect to the static limit. Similar decrease of the Poisson ratio near close packing has been obtained for other anisotropies and for other interaction potentials of cyclic trimers [35] and in various other hard body systems in two and three dimensions; some examples are described in [19, 30, 37, 38]. 6. SUMMARY AND CONCLUSIONS The considered system of hard cyclic trimers constitutes a very simple model which can freeze into an elastically isotropic, aperiodic NPR structure. By modifying the interaction potential of the trimers, the aperiodic structure crystallizes into a periodic NPR phase, which is also elastically isotropic. The transformation is accompanied by a strong reduction of the Poisson ratio of the system. Systems of other particles forming elastically isotropic NPR phases have been also studied in two dimensions [35]. It has been observed that by increasing the molecular anisotropy and non-central interactions one can decrease the measured Poisson ratio to any negative value allowed by the stability conditions. The two-dimensional elastically isotropic NPR structures of the hard trimers can be thought of as planar layers in three dimensions. By stacking such layers one on another, three-dimensional NPR structures of elastically cylindrical symmetry can be obtained [24]. Studies of three-dimensional NPR phases currently in progress, indicate that as it was also observed in the case of two-dimensional systems, molecular motions can substantially reduce the Poisson ratio of hard-body systems near close packing. This result should have interesting consequences for some granular systems [35]. Closing, let us notice that measurements of the Poisson ratio of real materials can be of interest not only in the context of searching for the NPR systems. Recently it has been pointed out that the Poisson ratio is sensitive to subtle structural changes in some model systems [39]. This encourages the checking whether the Poisson ratio can be used as a simple indicator of structural changes in real materials, e.g. in nanocrystalline alloys. ACKNOWLEDGEMENTS The work was partially supported by the (Polish) Committee for Scientific Research (grant No. 4T11F01023) and by the Centre of Excellence for Magnetic and Molecular Materials for Future Electronics within the European Commission contract No. G5MA-CT-2002-04049. REFERENCES 1. Landau, L.D. and Lifshits, E.M. (1993) Theory of Elasticity, Pergamon, Oxford. 2. Almgren, R.F. (1985) An isotropic three-dimensional structure with Poisson's ratio = –1, J. Elasticity 15, 427-430.

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3. Kolpakov, A.G. (1985) Determination of the average characteristics of elastic frameworks, PMM USSR 49, 739-745. 4. Wojciechowski, K.W. (1987) Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers, Molec. Phys. 61, 1247-1258. 5. Lakes, R.S. (1987) Foam structures with a negative Poisson’s ratio, Science 235, 1038-1040. 6. Lakes, R.S. (1993) Advances in negative Poisson’s ratio materials, Advanced Materials 5, 293-296. 7. Wojciechowski, K.W. and BraĔka, A.C. (1994) Auxetics: Materials and Models with Negative Poisson's Ratios, Molec. Phys. Reports 6, 71-85. 8. Evans, K.E. and Alderson A. (2000) Auxetic materials: Functional materials and structures from lateral thinking, Advanced Materials 12, 617-628. 9. Grima, J.N., Jackson, R. Alderson, A. and Evans, K.E. (2000) Do zeolites have negative Poisson’s ratios?, Advanced Materials 12, 1912-1918. 10. Lipsett, A.W. and Beltzer, A.I. (1988) Reexamination of dynamic problems of elasticity for negative Poisson's ratio, J. Acoustical Soc. America 84, 2179-2186. 11. Wojciechowski, K.W. (1998) Isotropic systems of negative Poisson ratios, in Statistical Physics: Experiments, Theories, and Computer Simulations, Tokuyama, M. and Oppenheim, I. (eds.) World Scientific, p. 107. 12. Grima, J.N. and and Evans, K.E. (2000) Auxetic behaviour from rotating squares J. Materials Sci. Letters 19, 1563-1565. 13. Ishibashi, Y. and Iwata, M. (2000) A microscopic model of a negative Poisson’s ratio in some crystals J. Phys. Soc. Japan 69, 2702-2703. 14. Bowick, M., Cacciuto, A., Thorleifsson, G. and Travesset A. (2001) Universal negative Pois son ratio of self-avoiding fixed-connectivity membranes, Phys. Rev. Lett. 87, 148103_1-4. 15. Alderson, A. and Evans, K.E. (2002) Molecular origin of auxetic behaviour in tetrahedral framework silicates, Phys. Rev. Lett. 89, 225503_1-4. 16. Vasiliev, A.A., Dmitriev, S.V., Ishibashi, Y. and Shigenari T. (2002) Elastic properties of a two-dimensional model of crystals containing particles with rotational degrees of freedom, Phys. Rev. E 65, 094101_1-7. 17. Hailing, T., Saunders, G.A., Yogurtcu, Y.K., Bach, H. and Methfesse, S. (1984) Poisson’s ratio limits and effects of hydrostatic pressure on elastic behaviour of Sm1-xYxS alloys in the intermediate valence state, J. Phys. C: Solid State Physics 17, 4559-4573. 18. Hirotsu, S. (1991) Softening of bulk modulus and negative Poisson’s ratio near the volume phase transition of polymer gels, J. Chem. Phys. 94, 3949-3957. 19. Tretiakov, K.V. (2000) Monte Carlo simulation studies of mechanical and thermodynamic stability of selected molecular models, PhD Thesis, IFM PAN, PoznaĔ. 20. Novikov, V.V. and Wojciechowski, K.W. (1999) Negative Poisson coefficient of fractal structures, Solid State Physics 41, 1970-1975. 21. Wojciechowski, K.W. and Novikov, V.V. (2001) Negative Poisson’s ratio and percolating structures, TASK Quarterly 5, 5-11. 22. Wojciechowski, K.W. (1995) Negative Poisson ratios at negative pressures, Molec. Phys. Reports 10, 129-136. 23. Wojciechowski, K.W. and Tretiakov, K.V. (1996) Determination of elastic constants by Monte Carlo simulations, Computational Methods in Science and Technology 1, 25-29. 24. Wojciechowski, K.W. (2003) Non-chiral, molecular model of negative Poisson ratio in two dimensions, J. Phys. A: Math. & Gen. 36, 11765-11778 25. Milstein, F. and Huang, K. (1979) Existence of a negative Poisson ratio in FCC crystals, Phys. Rev. B 19, 2030-2033. 26. Kittinger, E., Tichy, J. and Bertagnolli, E. (1981) Example of a negative effective Poisson’s ratio, Phys. Rev. Lett. 47, 712-714.

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27. Yeganeh-Haeri, A., Weidner, D. J. and Parise, J.B. (1992) Elasticity of alpha -cristobalite: a silicon dioxide with a negative Poisson’s ratio, Science 257, 650-652. 28. Wallace, D.C. (1972) Thermodynamics of Crystals, Wiley, New York. 29. Parrinello, M. and Rahman, A. (1982) Polymorphic transitions in single crystals: A new molecular dynamics method, J. Applied Phys. 52, 7182-7190. 30. Wojciechowski, K.W., Tretiakov, K.V. and Kowalik, M. (2003) Elastic properties of dense solid phases of hard cyclic pentamers and heptamers in two dimensions, Phys. Rev. E 67, 036121_1-14. 31. Weiner, J.H. (1983) Statistical Mechanics of Elasticity, Wiley, New York. 32. Wojciechowski, K.W. (1989) Two-dimensional isotropic system with a negative Poisson ratio, Phys. Lett. A 137, 60-64. 33. Wojciechowski, K.W. and BraĔka, A. C. (1989) Negative Poisson ratio in a two-dimensional 'isotropic' solid , Phys. Rev. E 40, 7222-7225. 34. Wojciechowski, K.W. (2003) Remarks on “Poisson ratio beyond the limits of the elasticity theory”, J. Phys. Soc. Japan 72, 1819-1820. 35. Wojciechowski, K.W. and Tretiakov, K.V. (2003) in preparation. 36. Wojciechowski, K.W., Frenkel, D. and BraĔka, A.C. (1991) Non-periodic solid phase in a two-dimensional hard dimer system, Phys. Rev. Lett. 64, 3168-3171. 37. Wojciechowski, K.W., Tretiakov, K.V., BraĔka, A.C. and Kowalik, M. (2003) Elastic properties of two-dimensional hard discs in the close-packing limit, J. Chem. Phys. 119, 939-946. 38. Wojciechowski, K.W. and Tretiakov, K.V. (2002) Elastic properties of the f.c.c. hard sphere crystal free of defects, Computational Methods in Science and Technology 8(2), 84-92. 39. Tretiakov, K.V. and Wojciechowski, K.W. (2002) Orientational phase transition between hexagonal solids in planar systems of hard cyclic pentamers and heptamers, J. Phys.: Cond. Matter 14, 1261-1273.

MAGNETIC PROPERTIES OF NANOSTRUCTURED MATERIALS Monte Carlo Simulation and Experimental Approach for Nanocrystalline Alloys and Core-Shell Nanoparticles O. CRISANa,b, J.-M. GRENECHEc, Y. LABAYEc, L. BERGERc, A.D. CRISANb M. ANGELAKERISb, J.M. LeBRETONd, N.K. FLEVARISb a

National Institute for Materials Physics, P.O. Box MG-7, 76900 Bucharest, Romania Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece c LPEC, UMR 6087 CNRS, Université du Maine, 72085 Le Mans, France d GPM, UMR 6634 CNRS, Université de Rouen, 76801 St. Etienne du Rouvray, France Corresponding author: O. Crisan, e-mail: [email protected] b

Abstract:

The magnetic properties of FINEMET-type nanocrystalline alloys and isolated ferromagnetic AgCo nanoparticles are investigated both experimentally and numerically. Theoretical models of spins that simulate ideal nanocrystalline alloys and isolated nanoparticles are considered while their magnetic properties are derived from Monte Carlo simulation of low-temperature spin ordering. Interesting features such as magnetic polarization of the matrix due to penetrating fields arising from nanograins and the role played by the crystalline fraction in the overall magnetic behaviour, in the case of nanocrystalline alloys are investigated. For isolated nanoparticles it is shown that the competition between surface and bulk anisotropy gives rise to surface spin disorder that, together with finite-size effects, is responsible for the experimentally observed lack of saturation of the magnetization in high applied fields. These simulation results are confirmed by experimental data obtained on FINEMET nanocrystalline alloys and isolated ferromagnetic AgCo colloidal nanoparticles.

1. INTRODUCTION A great deal of interest has been devoted recently to the magnetic properties of nanocrystalline materials from both the experimental [1-8] and the theoretical [9-12] point of view. These nanomaterials have a huge potential in technological applications in many fields. Besides this, they may also be regarded as model systems for studying fundamental issues such as quantum tunneling of magnetization, spin dependent magneto-transport, and so on. Nowadays there are several patented systems based on nanocrystalline alloys, such as FINEMET (or VITROPERM) with the nominal composition Fe73.5Cu1Nb3Si13.5B9, or NANOPERM (Fe-Nb-Cu-B or Fe-Zr-Cu-B). Usually, 253 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 253–266. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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these materials are obtained by a subsequent annealing of rapidly quenched amorphous ribbons. The microstructure consists thus of ferromagnetic crystalline nanograins dispersed within a weakly ferromagnetic amorphous matrix. Such nanocrystalline alloys have received great attention during recent years mostly because of their outstanding potential as soft ferromagnets or magnetostrictive materials. The so-called FINEMET [1]. Nanocrystalline Fe73.5Cu1Nb3Si13.5B9 ribbons, obtained after subsequent annealing of the amorphous precursor, consist of Į-Fe(Si) or Fe3Si nanocrystalline grains dispersed into an amorphous residual Fe-Nb-B matrix, and exhibit excellent soft magnetic properties (high permeability, high saturation magnetization, low losses and low magnetostriction). These soft magnetic properties are mostly related to the exchange coupling between nanocrystalline grains through the amorphous matrix if the exchange correlation length does not exceed the nanocrystalline grain size [2]. The annealing parameters, such as temperature/time, atmosphere and/or applied field need to be strictly controlled. Tailoring of desired macroscopic properties for specific applications requires a deep insight in the magnetic features of these nanocrystalline Febased ribbons. For this purpose one has to elucidate the correlation between the microstructural evolution of both the nanocrystalline and amorphous residual phase, and the magnetic behaviour of the ribbons. The key issue for understanding the magnetic macroscopic properties, such as magnetization or susceptibility, would be to investigate the contributions arising both from the nanograins and from the amorphous residual matrix, but also to study the role played by the nanograin surface and the interfacial zone between the nanograins and the matrix. 57Mössbauer spectroscopy studies of FINEMET-type [4] and NANOPERM-type [5-8] nanocrystalline alloys provide evidence for an interfacial zone between the nanograins and the amorphous residual matrix. This interface exhibits a disordered atomic structure and spin-glass-like behaviour and has a chemical composition that differs strongly from those of both the nanograin and the matrix [8]. In addition, contrary to the low-temperature case where both intergranular and nanocrystalline grains behave as strongly coupled ferromagnets, the high temperature magnetic behaviour, i.e. above the Curie temperature of the amorphous matrix, is strongly dependent on the crystalline volume fraction [13-15]. Another key issue in understanding the magnetic properties of such systems is related to the surface and finite-size effects. Both effects have a stronger influence on the magnetic properties of the assemblies of nanograins, either isolated or interacting, as the size of nanograins decreases. Several theoretical studies of the magnetic behaviour of oxide nanoparticles have been reported [9-12]. It has been shown that broken exchange bonds at the nanoparticles surface, resulting in lower coordination compared to the bulk, give rise to a surface spin disorder and hence an increased surface anisotropy [9]. This surface spin disorder is particularly important in the case of isolated nanoparticles, which can be described by a core-shell model. It has been reported that in the case of CoRh nanoparticles, strongly enhanced magnetic moments are obtained and the magnetization does not saturate even at pulsed applied fields (of the order of 35 T) [16]. This unusual result can be explained in terms of surface spin disorder imposed by strong surface anisotropy and can be understood by observing the spin configurations in theoretical systems of spins, obtained by Monte Carlo simulation. The influence of the competition between bulk and surface energies resulting in finite-size effects on

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the magnetic behaviour of oxide nanoparticles has also been evidenced [9, 10]. The method of Monte Carlo simulation of low-temperature spin ordering was used for studying the surface and finite-size effects in oxide nanoparticles [11, 12]. Unlike micromagnetic [17, 18] or molecular dynamics calculations [19], the Monte-Carlo simulations (MCS) take into account the atomic structure of the lattice and the shortrange nature of the exchange interactions. The present work is structured in two main parts. In the first one we report the usual observed magnetic behaviour and phase structure in the case of FINEMET-type alloys with an emphasis on the chemical nature of the nanograin – matrix interfaces and the consequently modified magnetic behaviour compared with those of the nanograin core and of the matrix. Monte Carlo simulations of low-temperature spin ordering of a single ferromagnetic grain immersed into a weak ferromagnetic environment, identified with the amorphous matrix, will allow to evidence the two-phase magnetic behaviours, as observed in real systems. Thermodynamic quantities such as susceptibility, magnetization, energy-per-spin as well as parameters such as the Curie temperature, are investigated as a function of the crystalline fraction and exchange coupling inside the nanograin core, the matrix and at the interfaces. The other part is devoted to the investigation of surface and finite size effects occurring in the magnetic behaviour of the isolated nanoparticles. Spin ordering at low temperatures obtained by Monte Carlo simulation is studied as depending on surface anisotropy and exchange interactions between spins. The theoretical data are then corroborated with experimental magnetic measurements on core-shell-type AgCo nanoparticles obtained by colloidal chemistry. 2. STATE-OF-THE-ART It has already been mentioned that FINEMET-type nanocrystalline alloys exhibit excellent soft magnetic properties that are related to the exchange coupling between the nanograins [2]. Therefore, a crucial parameter that directly influences the high- and lowtemperature magnetic behaviour of the nanocrystalline alloys is considered to be the crystalline volumetric fraction. The crystalline volume fraction, as well as the interfaces between nanocrystalline grains and matrix, significantly influences the magnetic properties of these alloys. It has been shown that this interface features a disordered atomic structure and a spin-glass-like magnetic behaviour [5]. For temperatures above the Curie point of the amorphous matrix, the magnetic behaviour is strongly dependent on the crystalline fraction. A low crystalline fraction leads to the occurrence of hightemperature superparamagnetic (SPM) single-domain grains while for a high crystalline fraction, the paramagnetic intergranular phase is polarized by penetrating fields arising from the nanocrystalline grains [4, 13, 15]. The magnetic polarization of the amorphous matrix and the interfacial regions by the nanocrystalline grains have a significant influence on the macroscopic magnetic behaviour of the nanocrystalline alloys. In the case of Fe-based nanocrystalline alloys, this crystalline fraction can be quite conveniently derived from Mössbauer spectrometry. It is known that such nanocrystalline alloys are often described as two-phase (amorphous + nanocrystalline grains) materials. Nevertheless, one should take into account that the amorphous intergranular phase is

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chemically and structurally heterogeneous, originating from the atomic diffusion mechanisms which have occurred during the transformation from the crystalline into the nanocrystalline state. For this purpose since both the local atomic density and the coordination in the boundary regions are different from those of bulk crystalline and amorphous phases. It seems that a third Mössbauer component corresponding to Fe sites located at the grain surfaces and/or in the interphase boundaries has to be considered. For NANOPERM-type alloys, besides the magnetic sextet for the nanocrystalline phase (in that case Į-Fe) and the low-field hyperfine field distribution for the amorphous phase, a third contribution corresponding to the interfacial regions between nanograins and amorphous matrix [5] was introduced to fit the Mössbauer spectra. In the case of FINEMET-type alloys, due to the complexity of the hyperfine structure of the crystalline component and to the high spectral overlapping of the different contribution, this third component cannot be accurately estimated, even though evidence for distinct magnetic behaviour of the interfacial regions compared with the nanograins and the amorphous matrix has been provided [5-8]. To come to the point, for FINEMET alloys the contribution of the magnetically disordered crystalline interface would be included in the contribution due to nanocrystalline grains. The nanograin exchange field penetration into the matrix is still an open issue [20-22]. 57Fe Mössbauer spectrometry data [7] and thermomagnetic data [23] obtained on two-phase nanocrystalline alloys provided evidence for exchange coupling between the grains even above the Curie temperature of the matrix. This exchange field penetration has been also observed and modeled by several authors using random anisotropy concept [14], molecular field approach [21, 22] and assuming an exponential decay of exchange interactions through the amorphous matrix [15, 24]. Nevertheless, all these approaches are based on experimental features (either Mössbauer or magnetic measurements) performed on the integrality of the samples. By using Monte Carlo simulation, one can directly obtain the magnetic behaviour of outer shells of the nanocrystalline grain or of the interfacial regions (2-3 successive atomic layers covering the nanocrystalline grain) and their behaviour could be correlated with the evolution of physical parameters hardly tunable in real materials, such as the matrixnanograin exchange coupling, or surface anisotropy. For this reason and many more, Monte Carlo simulation (MCS) seems to be a suitable approach to predict magnetic features of real materials, even by using simple assumptions, idealized systems of small sizes. The overall magnetic response of the systems submitted to extreme conditions that eventually cannot be achieved in laboratories, i.e. high magnetic fields or huge surface anisotropies, may be obtained via MCS. The magnetic properties of nanostructured materials in general, and of the nanoparticles in particular are, as it has already been underlined, strongly altered comparing to the bulk. This altering may occur in different ways and may lead to unexpected new phenomena related to technological applications. Besides their enhanced interest in catalysis, nanoelectronics [25], biomedical applications [26] or magnetic recording media [27, 28], magnetic nanostructures obtained by self-organization of nanoparticles onto substrates can be used as model systems for studying fundamental aspects arising from nanoscopic scaling of different magnetic features. Two main effects that originate from the spatial confinement in nanostructured materials, i.e. surface and finite size

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effects, have been previously considered in order to explain anomalous magnetic behaviour of nanomaterials. It has been found [29] strong variation of perpendicular magnetic anisotropy and increased orbital magnetic moments for small SPM Co clusters on Au(111) surface, this being attributed to finite size effects which directly influence the 3d electronic structure. For iron nanoparticles [30] it has been established that the surface spins are noncollinear and ferromagnetically coupled to the core. Interesting fundamental issues such as enhanced exchange bias in Fe/FeRh bilayers [31] and at Fe/oxide interfaces [32] have been also corroborated with the spin flop coupling of the interfacial spins and with the surface spin-glass-like state, respectively. Evidence of surface spin disorder and finite size effects has been found in ferrite and metallic oxide nanoparticles [33-35] and the influence of surface spins on the overall magnetic behaviour has been modelled [9] considering enhanced surface anisotropy due to broken exchange bonds at the surface. Also, in the case of maghemite nanoparticles, both experimental and simulation studies [11, 12, 36] have proved that highly disordered surface layers dominate the magnetic properties for small sizes of nanoparticles. Colloidal Co [37] and CoRh [16] nanoparticles have been shown to exhibit greatly enhanced magnetic moments comparing to the bulk, and their magnetization does not saturate even at applied pulsed field as high as 35 T. This anomalous behaviour could also be associated with the surface spin disorder and finite size effects. An attempt to give evidence of the influence of such surface and finite size effects on the magnetic behaviour of isolated nanoparticles will consist in investigating the low-temperature spin configurations for a single ferromagnetic nanoparticle via Monte Carlo simulation. These results will be consequently corroborated with experimental data on colloidal AgCo magnetic nanoparticles. 3. CASE OF NANOCRYSTALLINE FINEMET ALLOYS 3.1. Framework of the simulation The model considered for Monte Carlo simulation consists of a spherical nanograin embedded in a matrix of cubic shape. This cubic box contains 153 sites on a simple cubic lattice, i.e. each i site has six nearest neighbours. To each cubic lattice site, a classical spin Si that interacts with its j nearest-neighbours via an exchange coupling constant Jij will be assigned. Contained in the box, a sphere of radius R (in units of interatomic distance) is defined. The sites belonging to the sphere (nanograin) and to the matrix, are denoted as A and B sites, respectively. Moreover, two non-equivalent atomic layers at the nanograin surface are defined: the first one consists of A sites having at least one first-nearest-neighbour of B type and denoted AB, and the other consists of B sites having at least one first-nearest-neighbour of A type, denoted BA. These two atomic shells represent the nanograin surface and the matrix-nanograin interface, respectively, featuring magnetic behaviour different from that of the bulk (AA and BB regions). Taking into account the broken symmetry (lower coordination) for the sites in the surface that leads to a distribution of magnetization over the whole system, one has to consider JAA z JBB z JAB (for reasons of symmetry JAB = JBA). The macroscopic thermodynamic properties, such as the temperature dependence of magnetization, specific heat and magnetic susceptibility for our system, are obtained

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from a Heisenberg-type hamiltonian which contains several terms corresponding to different energy contributions: exchange, anisotropy, magnetostatic and dipolar. In the present study, only the first two prevailing energy contributions are considered: the hamiltonian defined at a given site i thus reads as: Hi

 ¦ J ij S ˜ S j  K V ( S i , V ˜ yˆ ) 2  K S ( S i , S ˜ nˆ ) 2

(1)

j V

V is the nearest-neighbourhood of site i, Jij are the exchange coupling constants, Si, Sj the spins corresponding to the i and j sites, Ki the site dependent anisotropy constant (Ki = KS for AB sites and Ki = KV elsewhere), y and n denote the directions chosen for the anisotropy (uniaxial for the bulk and normal for the surface). The grain had different radii, ranging from 4 (N | 268 sites) to 7 (N | 1436 sites), leading to an atomic crystalline fraction of 7 and 40%, respectively. We associate the same spin value S = 1 to each site in both regions. The ferromagnetic exchange coupling constants (only over the nearest-neighbours) considered for calculations equal JAA = 3 (inside the nanograin) and JBB = 1/2 (inside the matrix), a choice consistent with two phases exhibiting significantly different Curie temperatures.

Figure 1. Simulated total magnetization vs. T for 153 cubic box, for JAB = 2 and different nanograin radius

Figure 2. Simulated total magnetization vs. T for 153 cubic box, for nanograin radius R = 6 and different matrix-nanograin exchange coupling JAB

The high ratio JAA /JBB allows thus to separate clearly the two phases because the magnetic behaviour is worth to be discussed for temperatures ranged between the two Curie temperatures. The exchange coupling constant between the nanograin and the matrix JAB ranges from 0.01 to 50. The calculations were performed using periodic boundary conditions. Moreover, the anisotropy is considered uniaxial along the y-axis and equal for all sites: KV = 0.3 while surface anisotropy was considered radial to the surface and equal to KS = 3.0. By neglecting the dipolar term, each computation needs less CPU time. This gain allows thus a greater number of Monte Carlo steps (2 u 105 steps per spin and per temperature) to be taken, in order to obtain better statistics and a better estimate of magnetic parameters such as Curie temperatures. Figure 1 shows the temperature dependence of total magnetization (normalized) of the 153 site cubic box, with different values of nanograin radius (different crystalline fractions), for JAB (exchange coupling between the matrix and the nanograin) equal 2.

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All the curves exhibit a two-phase behaviour, typical for nanocrystalline soft magnetic alloys. The two contributions that show distinct behaviour could unambiguously be attributed to the matrix and the nanograin, respectively. The effect of increasing the crystalline fraction is obvious in the magnetization curves, i.e. higher magnetization values above the Curie temperature of the matrix (hereafter denoted TCM) up to the Curie temperature of the nanograin (hereafter denoted TCN). It is worthwhile noticing that the magnetization apparently does not vanish at temperatures above TCN. This is an illustration of the size effects acting on the magnetic state of the system. When one deals with finite-sized magnetic objects, the magnetic correlation established through exchange coupling between reversal spins does not completely disappear even at temperatures above TCN, where thermally activated magnetic fluctuations should prevent the local alignment of the spins. For the nanograin radius R = 6 (Fig. 2) the magnetization curve with JAB = 0.01 shows a very sharp transition between the matrix and the nanograin contributions, typical of a system with completely decoupled magnetic phases. With increasing JAB, the transition between the two contributions becomes more and more smooth and one can observe that the exchange coupling in the surface influences the matrix and the nanograin differently.

Figure 3. Simulated magnetization of the nanograin surface AB (top) and of the matrix-nanograin interface BA (bottom) for different nanograin radius and JAB = 2

Figure 4. Magnetization vs. T for ascast (open circles) and annealed (open squares) FINEMET sample [42]. Continuous line: nanograin contribution. Dashed line: matrix contribution

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In Fig. 3 the normalized magnetization vs. temperature curves obtained for the nanograin surface shell (AB) and the matrix-nanograin interface (BA) for different nanograins radius, for JAB = 2, are shown. Increase of TC (compared with the corresponding values in case of almost decoupled system, i.e. JAB = 0.01) with the crystalline fraction is observed for both regions. This indicates a magnetic polarization of the matrix by exchange coupling in the matrix-nanocrystalline grain interface. The observed small fluctuations around TC are due to the finite-size effects, important in such systems. An interesting behaviour here is exhibiting by MBA dependence. MBA not only vanishes far above TCM of the matrix (see Fig. 1) – in fact, it vanishes at TCN, just as the nanocrystalline grain core and surface contribution, providing thus an increase of its TC of more than 300% – but also the dependence is far from the expected ferromagnetic profile, exhibiting a rather paramagnetic-like behaviour instead. Evidences about paramagnetic behaviour of the interface in various nanocrystalline (either FINEMET or NANOPERM type) alloys have been reported by several authors [22, 23] and explained by boron enrichment of the interface during annealing [22]. As in our simulation, no difference is assumed between atoms in nanocrystalline grain, matrix or interface. This suggests that the high degree of magnetic disorder (apparent paramagnetism) of the shell considered as matrix-nanocrystalline grain interface, in real materials, could also be due to the difference in exchange coupling values of its neighbourhood (weak for the matrix and strong for the nanocrystalline grain) and also to the competition between enhanced surface anisotropy and exchange coupling inside the nanocrystalline grain.

3.2. Experimental results The magnetic behaviour of the FINEMET samples, as-cast and annealed, has been investigated by thermomagnetic measurements. The specific magnetization vs. temperature for both the as-cast sample (open circles) and for the sample annealed at 510qC (open squares) is presented in Figure 4. It is well established that the specific magnetization of a single-phase ferromagnet decreases with temperature according to the following Heisenberg-type dependence: V T V 0 1  T TC E (2) where ı(0) is the specific magnetization at zero temperature, TC the Curie temperature and ȕ the critical exponent (typically ȕ = 0.36 for Heisenberg ferromagnets). The thermomagnetic curve of the as-quenched sample shows weak ferromagnetic features, typical of the topologically disordered Fe-rich amorphous ribbons, i.e. a decrease of the magnetization towards zero at a temperature value TC corresponding to the Curie point of the amorphous precursor of about 390qC. The sample shows zero magnetization up to about 475qC. Then the magnetization starts to increase. This is due to the onset of crystallization at 475qC. When the sample begins to crystallize and the number of progressively formed magnetically ordered nanocrystallites increases with the temperature, the nanocrystals net magnetization overcomes the thermally induced spin reversal and the total specific magnetization of the sample increases up to a value corresponding to the end of primary crystallization, point from which the nucleation process has finished (|550ºC from the DSC curves for same samples [38, 39]). At higher temperatures, it can be assumed that the magnetization of the as-cast sample vanishes. The specific

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magnetization vs. temperature curve for the nanocrystalline sample annealed at 510qC exhibits typical ferromagnetic features – a decrease due to the thermally induced spin disorder in the sample – with an inflection point, characteristic of a two-phase behaviour, with well separated Curie temperatures, which is usually the case in nanocrystalline alloys. The decrease of magnetization with increasing temperature is slower than in the case of the as-cast amorphous sample and the magnetization values are higher for the nanocrystalline sample than for the amorphous precursor, for any given temperature. It is well established [40, 41] that below the observed inflection point the curve comprises the magnetization contribution of the amorphous residual matrix together with the nanocrystalline grains contribution. It should nevertheless be mentioned that in this temperature range the nanocrystals, being ferromagnetically coupled strongly than in the amorphous, have a less important contribution to the magnetization decrease than the amorphous. Above the inflection point, the amorphous contribution to the magnetization vanishes and only the nanocrystals contribute to the net magnetization of the sample. By separating the low temperature profile (contribution of the amorphous phase) from the high temperature profile (contribution of only the nanocrystalline grains) and numerically fitting them using Eq. (2), one can roughly estimate the Curie temperatures of the amorphous as well as of the nanocrystalline phase. The fittings are shown in Fig. 4 by solid line (nanocrystalline contribution) and a dashed line (amorphous part), respectively. The amorphous contribution has been obtained by the subtraction of a nanocrystalline contribution (solid line) from the experimental data, for temperatures below the inflection point. The numerical fitting results show that the Curie temperature of the Į-Fe(Si) nanocrystalline grains is about 590qC, while the Curie temperature of the residual amorphous is about 440qC. If one compares this value with that obtained for the amorphous precursor (390qC), with iron content obviously higher than the amorphous residual matrix, the Curie temperature increases at about 12% [42]. This increase is a further indication of the magnetic polarization of the amorphous residual matrix by penetrating fields arising from nanocrystalline grains. It is expected to be even larger if one compares the amorphous residual matrix with an amorphous as-quenched alloy of identical composition. Some authors [15, 24] have reported an increase of TC by up to 100 K for the amorphous residual matrix compared to the amorphous as-cast samples with identical composition, in the case of Fe-Zr-B-Cu and Fe-Nb-B-Cu (NANOPERM) alloys. However, unlike the NANOPERM alloy, in the case of FINEMET nanocrystalline alloys, the exact composition of the amorphous residual matrix and the heterogeneous behaviour are difficult to be estimated from Mössbauer data, mainly due to the lack of estimation of the interfacial region. 4. CASE OF ISOLATED AGCO NANOPARTICLES 4.1. Framework of the simulation The isolated ferromagnetic nanosphere was modelled as a sphere with radius R = 15 and containing N = 14328 atoms in a cubic symmetry with a surface-to-volume ratio of 0.16. The same hamiltonian as in Eq. (1) is used to obtain the equilibrium spin configuration. The exchange coupling in the nanograin core (AA region) is taken the same as in the nanograin surface (AB region): JAA = JAB = 1000, KV = 20

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while KS is ranging between 20 and 2000. The spin configuration calculated in the demagnetized state exhibits distinct features as the surface anisotropy increases. For KS/KV = 10 the surface spins tend to be radially oriented, a tendency which is propagated (via exchange coupling) inside the core where it competes with the uniaxial orientation along Oz imposed by the bulk anisotropy. This competition gives rise to a “throttled” spin configuration that has the surface spins oriented inward for upper hemisphere and outward for the lower hemisphere [43]. The surface spin reversal that occurs at the equator takes place over several interatomic distances. For KS/KV = 60 the surface spin reversal takes place only over one interatomic distance by creating vortex-type reversal centers (Fig. 5). The calculated spin configuration in the case of isolated ferromagnetic nanoparticles shows the occurrence of different equilibrium orientation for surface spins than for the core spins, essentially due to the increased surface anisotropy. This surface spin disorder may be responsible for the peculiar magnetic behaviour observed in the low-dimensional systems, and, in particular, for the enhanced magnetic moments and the lack of saturation of the magnetization in high applied fields. 4.2. Experiment and discussions The AgCo nanoparticles have been obtained via colloidal chemistry techniques [44]. Their composition shown by energy dispersive spectroscopy (EDS) has been found to be Ag30Co70. Their morphology and structure have been studied by XRD and HRTEM [45]. The nanoparticles are deposited onto Si(100) substrates and self-organize into quasi-regular arrays. The structure of a single nanoparticle is determined to be of fcc-Ag core with incomplete hcp-Co shells. The magnetism of this system is essentially determined by the Co spins in surface states. From this point of view, the surface spin orientation is crucial for determining the overall magnetic properties of the system. Hysteresis loop of Ag30Co70 / Si(100) has been recorded using a SQUID device at 293 K in applied field up to 5.5 T, parallel to the sample plane and is shown on a reduced

Figure 5. Spin configuration in the central plane of R = 15 nanoparticle, obtained by MCS [43]

Figure 6. Hysteresis loop for Ag30Co70 nanoparticles at 293 K [46]. Inset: full cycle up to 5.5 T

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scale in Fig. 6. A very interesting result is the fact that the magnetization (inset of Fig. 6) exhibits no saturation up to 5.5 Tesla and the increase of magnetization for applied fields above 0.3 T looks quite similar to paramagnetic-like materials. This anomalous magnetic behaviour resembles the previously reported investigations on CoRh nanoparticles [16] and could be attributed both to the unusual multiphase polycrystalline structure of nanoparticles favoring noncollinear arrangement of magnetic moments and to the highly disordered magnetic surface layer, as we have seen in the simulated spin configuration (Fig. 5). The shape of the M(H) curve suggests that the sample exhibits at least two different magnetic components: one is ferromagnetic and gives a sharp increase at very weak applied fields (up to ~ 1500 Oe) and the other is paramagnetic at 293 K and gives a continuous increase of magnetization at higher applied fields. The surface spin disorder arising from the competition between the surface and the bulk anisotropy may constitute one of the reasons for the experimentally observed lack of saturation for the magnetization and the peculiar behaviour of the M(H) curve in the case of isolated AgCo nanoparticles. 5. CONCLUSIONS AND PROSPECTS Using a simple model consisting of systems of spins in a cubic symmetry and a Hamiltonian composed of exchange coupling and surface and bulk anisotropy terms, thermomagnetic data are obtained by Monte Carlo simulation of low-temperature spin ordering. In the case of a single ferromagnetic nanograin immersed in a weakly ferromagnetic matrix (assimilated to the nanocrystalline alloys), the magnetic behaviour is investigated as a function of the crystalline fraction and exchange coupling between nanograin and matrix. The peculiar behaviour of the interfaces between nanograin and matrix, i.e. the very strong increase of the Curie temperature of the interfacial layer as observed both theoretically and experimentally, is proven to be due to the polarization of the matrix via penetrating fields arising from the nanograins. The simulated thermomagnetic curves are corroborated with the experimentally obtained phase structure and magnetic data to give a coherent image of the different behaviour of both nanograin surface and interface between matrix and nanograin. The equilibrium spin configuration of an isolated nanoparticle with cubic symmetry is obtained by Monte Carlo simulation and is shown to be extremely sensitive to the competition between surface and bulk anisotropy. This competition yields a particular, so-called “throttled”, low-temperature spin ordering, where surface spins reversal takes place via vortex-type pinning centers. This surface spin disorder is shown to be responsible for the lack of saturation of magnetization at applied high magnetic fields (5.5 T) and peculiar multiphase magnetic behaviour, experimentally observed in AgCo nanoparticles. Further simulation studies implying the use of supplementary (dipolar) terms in the hamiltonian and detailed magnetic and structural data are necessary to clarify the influence of the finite-size and surface effects and to understand the issues regarding interfacial states and matrix polarization by pinning fields, on the magnetic features of nanocrystalline alloys and nanoparticles.

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264 ACKNOWLEDGEMENTS

The financial support for the postdoc fellowship of O. Crisan from Region Pays de Loire, at the Universite du Maine, Le Mans, France, is gratefully acknowledged. Part of this work has been performed under the EU funded RTN no. HPRN-CT-1999-00150. The simulations were made using Lotus, a 95 processors Beowulf class parallel computational facility: http://weblotus.univlemans.fr/w3lotus REFERENCES 1. 2. 3.

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42. Crisan, O., Grenèche, J.-M., LeBreton, J.M., Crisan, A.D., Labaye, Y., Berger, L., and Filoti, G., (2003) Magnetism of nanocrystalline FINEMET alloy: experiment and simulation, Eur. Phys. J. B 34, 155-162. 43. Labaye, Y., Crisan, O., Berger, L., Grenèche , J.M., and Coey, J.M.D., (2002) Surface anisotropy in ferromagnetic nanoparticles, J. Appl. Phys. 91, 8715. 44. Sobal, N.S., Hilgendorff, M., Mohwald, H., Giersig, M., Spasova, M., Radetic, T., and Farle, M., (2002) Synthesis and Structure of Colloidal Bimetallic Nanocrystals: The NonAlloying System Ag/Co, Nano Letters 2, 621. 45. Crisan, O., Angelakeris, M., Flevaris, N.K., Sobal, N., and Giersig, M., (2003) Anisotropies in ferromagnetic nanoparticles: simulation and experimental approach, Sensors & Actuators A 106, 130-133. 46. Crisan, O., Angelakeris, M., Nogues, M., Papaioannou, E., Flevaris, N.K., Komninou, Ph., Kehagias, Th., Sobal, N., and Giersig, M., (2003) Correlation of structure and magnetism of AgCo nanoparticle arrays, Proceedings of ICM 2003, Rome, Italy, to appear in J. Magn. Magn. Mater.

Al-RARE EARTH-TRANSITION METAL ALLOYS: FRAGILITY OF MELTS AND RESISTANCE TO CRYSTALLIZATION L. BATTEZZATI, M. KUSÝ, M. PALUMBO, and V. RONTO Università di Torino, Dipartimento di Chimica IFM P. Giuria 9, 10125 Torino, Italy Corresponding author: L. Battezzati, e-mail: [email protected]

Abstract:

The stability of Al-transition metal (TM)-rare earth (RE) alloys is considered with reference to transport and thermodynamic properties of the melt. The mobility of species or groups of atoms is described above the melting point and in the proximity of the glass transition. Viscosity is analysed at first in the frame of the strong/fragile classification of liquids. Al-based glass-formers are shown to be fragile systems. Evidences that for some molecular and metallic glass-formers the Stokes-Einstein equation does not hold below and above Tg are reviewed. The alloys are, however, resistant to crystallization on rapid quenching. Some of them display also peculiar devitrification behaviour, often, but not always, with formation of primary compact nanocrystals. Analysing the transformation paths it can be inferred that mobility is belated by composition gradients in the amorphous matrix. The resistance to crystallization may result from the shape and relative position of free energy curves because crystal and liquid phases are such that the driving force for nucleation of intermetallics does not increase steadily but tends to level off on undercooling.

1. INTRODUCTION Al-based amorphous alloys occur in systems containing at least a transition metal (TM) and a rare earth (RE) [1, 2]. Contrary to the general rule for metallic glasses, they can be obtained in composition ranges where no deep eutectic exists. In most cases their composition falls off a shallow eutectic and corresponds to a field of a phase diagram where Al coexists with intermetallic compounds and there is a steep liquidus curve [3, 4]. A primary intermetallic compound starts the equilibrium solidification. Because a driving force for crystallization builds up below the liquidus temperature, it may even be surprising that these melts can undercool to the extent of forming glasses. On the other hand, rapid solidification results either in amorphisation or in the production of a two-phase material containing Al crystals in an amorphous matrix. This indicates that the melt can be undercooled well below the eutectic temperature at which a driving force for Al nucleation appears. At variance, Al crystallization may occur in a trans267 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 267–278. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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formation of the glass. DSC analyses reveal that Al precipitation from glassy matrices takes place at temperatures just above 150°C [1-4]. As for intermetallics, a contrasting behaviour is found for two groups of alloys. In the binary Al-RE and the RE-rich ternary systems, metastable compounds with different structures are formed on quenching from the melt and on heating the glass [5]. The possibility of nucleating various phases can represent a “confusion principle” for the alloy helping in glass formation. The production of Al nanocrystals in spite of a substantial driving force for nucleation of other phases, can be the outcome of homogeneous fluctuations in the undercooled melt or glass and be driven by the higher mobility of Al with respect to transition and rare earth elements. For the other group of alloys, those rich in transition metal or ternaries containing Fe, a “confusion principle” may still operate since several intermetallic phases exist. However, the same phases are found both during quenching, in competition with the glass, and during devitrification. The driving force for their formation should predominate in any case as suggested by the higher liquidus point with respect to the other group of alloys. They can then trigger crystallization of Al as observed in the foundry practice of inoculation. The formation of glassy or nanocrystalline phases is, therefore, the outcome of a subtle interplay of thermodynamic [6], i.e. driving forces for transformation, and kinetic, i.e. atomic mobility, factors. Progress in understanding these issues is reviewed by considering transport and thermodynamic properties of the melt. 2. VISCOSITY OF UNDERCOOLED LIQUIDS. STRONG AND FRAGILE MELTS Non-glass forming liquids usually have K = 103 Pa˜s at the equilibrium melting point, Tm, whereas, for metallic glass-formers, K is of the order of a101 Pa˜s at Tm. During the undercooling of glass-forming liquids, viscosity shows an extraordinary increase up to a1012 Pa˜s in correspondence of the glass transition, Tg. As a consequence, their mobility is reduced, nucleation is retarded and the system can be vitrified [6]. A general pattern of the viscosity of glasses and glass-forming liquids over a broad temperature range involves three regimes. Below Tg the viscosity shows an exponential behaviour § E1 · ¸; © RT ¹

K K 01 exp¨

(1)

the values of Tg and K(Tg) depend on the cooling rate: when it is decreased, K(Tg) increases and Tg decreases. Analogously, an exponential behaviour is found above Tm, with different pre-exponential and activation energy parameters. Experimental data for the viscosity of metallic melts cannot be obtained in the whole temperature range between Tm and Tg due to the tendency of the liquid to crystallize, so the data obtained at low and high temperature must be fitted using an appropriate function. Here, K is described by the Vogel-Fulcher-Tamman (VFT) relationship

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K

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ª º B A exp « » ¬« (T  T0,K ) ¼»

(2)

where A and B are constants and T0,K is the temperature where the viscosity would diverge because the liquid freezes to an amorphous solid. In order to compare data relative to different systems, the viscosity is plotted as logK vs. Tg/T: the so-called Angell plot (Fig. 1) [7]. The few cases found to date are those of SiO2 showing nearly Arrhenian behaviour (Eq. 1), and of o-terphenyl presenting VFT behaviour (Eq. 2). In the Angell classification of glass-forming liquids these represent limiting “strong” and “fragile” behaviour, respectively. From a structural point of view, strong liquids contain tetrahedral three-dimensional networks (e.g. SiO2, GeO2 and BeF2), that confer resistance to thermal disruption of the structure; the fragile systems on the contrary usually do not present strong directional bonding. Figure 1. The viscosity of various glassformers reported as a function of normalised temperature (Tg/T). The network glassformer SiO2 display “strong” behaviour (upper full line) whereas the molecular oterphenyl glass-former (lower full line) is “fragile”. Alloys fall in between the two extremes being relatively fragile: Zr46.75Ti8.25Cu7.5Ni10Be22.5 (dashed line); Mg65Cu25Y10 (dotted line); Pd40Ni40P20 (dot-dashed line), Al87Ni7Ce6 (full bold line)

The kinetic properties have a thermodynamic counterpart in the rate of entropy loss on undercooling which is faster when the fragility of the melt increases. Using the Kauzmann paradox which implies that the entropy of the liquid and crystal phases (having specific heat difference 'Cp) [8] becomes equal at temperature, T0, below the experimental Tg, Tm

'S

³

'S m  'C p d ln T

0

(3)

T0

fragile systems are found to approach T0, the Kauzmann temperature, more rapidly than the strong ones. So, the fragile/strong behaviour of glass-formers can be quantified by the ratio Tg/T0: the higher the fragility the lower is Tg/T0. This assessment of the thermodynamic fragility gives similar results as the ratio Tg/T0, K, with T0,K the parameter entering the VFT equation, representing the kinetic fragility. The resistance of the strong glass to structural changes is also shown by the small changes in heat capacity taking place at Tg (Cp(liq)/Cp(glass) | 1.1), while fragile ones present higher jumps (60-80% of the glass specific heat) [9].

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The fragile/strong behaviour of the supercooled liquids can be also classified by means of dimensionless parameters: m and D. The former is defined as the slope of the viscosity curve reported in an Angell plot in the vicinity of Tg: m

ª d (logK ) º « » «¬ d (Tg / T ) »¼ T

(4)

. Tg

Using the VFT equation, the slope of log(K) versus 1/T is given by E(Tg) = RBTg2/(Tg  T0, K)2 so, the fragility at the glass transition can be quantitatively expressed as m = BTg/2.3(Tg  T0, K)2. D is the fragility parameter entering the modified VFT equation,

K

ª DT0, K º A exp « », ¬« (T  T0, K ) ¼»

(4a)

where the product DT0, K replaces the parameter B in the conventional expression. Strong glasses present low values of m and high values of D (e. g. m = 20 and D = 100 for SiO2), whereas the reverse occurs for fragile ones (e.g. m = 81 and D = 6.8 for o-terphenyl). Table I. Fragility parameters m, D and Tg/T0 for different glass-formers. Metallic glasses fall in between strong (SiO2) and fragile glasses (o-terphenyl) Glass

m

D

Tg/T0

SiO2

20

100

Zr46.75Ti8.25Cu7.5Ni10Be22.5

33

22.7

1.72

Mg65Cu25Y10

45

22.1

1.58

Pd40Ni40P20 Fe40Ni40P14B6 Al87Ni7Ce6 o-terphenyl

46 69 127 81

18.1 10.1 5.6 6.8

1.44 1.28 1.15 –

–

The fragility concept can be also applied to metallic melts, e.g. Al87Ni7Ce6. This alloy is taken as a representative example of glass-forming liquids based on Al-rare earth elements-transition metals for which viscosity data are not available. They can be estimated by deriving suitable parameters for the VFT equation. The relevant transformation temperatures and enthalpies are: Tm = 911 K. This is the eutectic melting. The liquidus occurs at higher temperature, but it is not considered here because it refers to the primary formation of an intermetallic which does not compete with glass formation, Tx = 523 K, Tg = 513 K (both data collected at the heating rate of 40 K/min); 'Hm = 9.8 kJ/mol and 'Hx = 5.3 kJ/mol [10]. Assuming that the specific heat difference between the liquid and crystal phases can be expressed by 'Cp = C/T 2 in the temperature range from Tm to Tx, the condition of vanishing entropy difference between the liquid and crystal phases, Eq. (3), is imposed, and the T0

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temperature is found at 444 K. 'Cp at Tg is found as high as 21 J/mol˜K indicating thermodynamic fragility. The pre-exponential factor A is taken as NAh/Vm = 3.8˜105 Pa˜s, with NA the Avogadro constant, h the Planck constant and Vm the molar volume. Using the Andrade formula for the viscosity at the melting point [11]

K Tm

AC

w a Tm Vm2 / 3

,

(5)

where AC is the proportionality coefficient and wa the average atomic weight, and assigning the AC coefficient the average value 6.5˜107 (JK1mol1/3)1/2 for metallic glassformers at the eutectic temperature, we obtain: K (Tm) = 7.8˜103 Pa˜s. Finally K (Tg) is taken as 1.0˜1012 Pa˜s. With the latter two positions, the quantities B and T0.K are obtained as B = 2474 K and T0.K = 447 K, remarkably close to T0. The viscosity is then expressed as K = 3.8˜105 exp [2472/(T  447)] Pa˜s. The fragility parameters m and D turn out to be 127 and 5.6 respectively, indicating that the ternary Al87Ni7Ce6 is a fragile melt. Although there are differences in the glass-forming tendency when substituting other transition metals and rare earth elements for Ni and Ce or when changing the alloy composition, the present result is indicative of the behaviour of this family of alloys. The above expression (5) for viscosity provides values in agreement with the experimental ones obtained above the liquidus for a number of Al-Ni-RE alloys [12]. The viscosity parameters of Al87Ni7Ce6 are compared with literature findings for some glassy substances and alloys in Tab. I. The general strong/fragile scheme is followed; note that strong melts need a critical cooling rate much lower than fragile ones to be vitrified [6]. The undercooled melts scale in strength in the order Zr46.75Ti8.25Cu7.5Ni10Be22.5> Mg65Cu25Y10> Pd40Ni40P20 >> Al87Ni7Ce6. 3. THE RELATIONSHIP BETWEEN VISCOSITY AND DIFFUSIVITY When diffusion and viscous flow occur with the same brownian mechanism, the Stokes-Einstein equation (SE) is employed:

KD

kT , 6Sr

(6)

where k is the Boltzmann constant and r is an ionic radius. The SE equation is valid at high temperatures near the melting point, but the correlation may fail when the liquid approaches the glass transition [6, 13]. Illustrative data are displayed in Fig. 2 for molecular glass formers: a clear breakdown of the SE relationship can be noticed in correspondence of about 1.3˜Tg. The measured self-diffusion coefficients are larger than those calculated by means of the SE equation using the experimental shear viscosity values. In correspondence to the SE breakdown de-coupling takes place between the translational diffusion and viscosity on the one hand, and rotational diffusion and viscosity on the other. In fact, while at high temperatures both Drot and Dtrans are inversely proportional to the viscosity, for high undercooling this relationship is lost; near Tg the molecules translate faster (two

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orders of magnitude) than suggested by the SE equation. Figure 3 also shows data for a metallic alloy above Tg in the limited range where they could be collected. It is to be remarked that the points for Fe40Ni40P14B6 refer to viscosity and an apparent diffusion coefficient derived from the measurements of the rate of crystal growth, i.e. of the size of eutectic colonies as a function of time at various temperatures. The points appear to show a trend analogous to that of molecular glasses.

Figure 2. A plot showing the breakdown of the Stokes-Einstein equation for various glassformers. The logarithm of the quantity (KD/T) is plotted vs. a normalised temperature (T/Tg). The points referring to salol (+) and o-terphenyl (’) (translational diffusion coefficients) conform to SE behaviour for T/Tg > 1.3. The points referring to o-terphenyl (’) (rotational diffusion coefficients) conform to SE immediately above Tg. The points referring to the Fe40Ni40P14B6 alloy (diffusion coefficients derived from the rate of crystal growth) deviate from SE behaviour up to T/Tg = 1.17

The recent discovery of bulk metallic glasses having high thermal resistance to crystallization allows us to verify the K-D relationship in a larger temperature range, above Tg. In the case of the Zr46.7Ti8.3Cu7.5Ni10Be27.5 bulk amorphous alloy, the SE equation appears to lose its validity, since there is a discrepancy between the experimental translational diffusion coefficient of various elements and the one computed via the SE equation. This is shown in Fig. 3 where the experimental trend of diffusion coefficient of various elements [14] is shown together with that obtained by means of the SE equation. The discrepancy is apparent. The K-D behaviour found for the Zr46.7Ti8.3Cu7.5Ni10Be27.5 amorphous alloy appears to be very similar to that of many molecular glass-formers. The failure of the Stokes-Einstein law near 1.2-1.3 Tg can be explained by assuming a change in the diffusion mechanism. It has been speculated that the mechanism for mass transport passes from a co-operative diffusion process, typical of viscous flow, to activated “hopping” transitions (jump diffusion) involving a few molecular units. The jump diffusion occurring at high undercooling resembles the vacancy diffusion in crystals and does not contribute to viscous flow, so the measured diffusion coefficients are higher than those calculated using the SE equation.

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Figure 3. Arrhenius plot giving the tracer diffusion coefficient of various elements in Zr46.7Ti8.3Cu7.5Ni10Be27.5 (solid lines) and a diffusion coefficient computed as if the SE equation was valid (dashed line). There is no apparent correlation of diffusivity of alloying or other elements, such as Al with viscosity in this temperature range

Contrary to molecular substances where the mobility behaviour has been studied and modelled by investigating the liquid state, for metallic alloys the breakdown of the relationship between diffusion and viscosity was discovered and discussed at first for glasses below the glass transition. This is an outcome of studies on structural relaxation of amorphous alloys where free volume is lost on annealing via defect annihilation, the material increases its density and the ideal glassy state is approached. Measurements of the equilibrium viscosity and the diffusion coefficient of Fe and Au tracer atoms in Fe40Ni40B20 and Pd40Ni40P20 relaxed glasses, respectively, showed that at constant temperature the KD product is not constant [15]. It was proposed that the viscosity and the diffusivity do not follow the same mechanism and it was assumed that the atomic transport during a viscous flow involves a pair of defects, whereas, in the case of diffusion, only one defect is required; formally this leads to KD 2

const .

(7)

It was also verified that this correlation holds for a molecular glass-former above Tg. With the new findings on bulk metallic glasses illustrated in Fig. 3 it can be suggested that this correlation is general. The above considerations would turn useful in estimating diffusion coefficients from viscosity in the neighbourhood of Tg if the significance and value of the above product KD2 were elucidated. At present it has been ascertained that the product in Eq. (7) is constant at constant temperature, but it changes with temperature and diffusion couple studied. If various diffusing species in the same alloy, Zr46.7Ti8.3Cu7.5Ni10Be27.5, are considered, then the product scales roughly with the atomic mass of the diffusing atom. 4. CRYSTALLIZATION AND MOBILITY

If D is derived for an alloy from Eq. (7), its activation energy would be compatible with that found in the diffusion and growth studies. Crystallization is very frequently studied by thermal analysis and activation energies are easily obtained by means of non isothermal scans. These values are often difficult to rationalise unless they can be clearly referred to nucleation and growth processes. In most experiments a limited temperature range is spanned, so the data can be fitted with an Arrhenius equation. If

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above Tg the mobility were determined by viscous flow, the activation energy would approximate the curvature of the VFT function in the temperature range of interest. Therefore, it should become the higher the closer the temperature range is to Tg. As an example, the apparent activation energy for viscous flow in Al87Ni7Ce6, calculated from the example in paragraph 2, just above Tg is of the order of 640 kJ/mol. Such high activation energy would certainly be rate limiting for all processes involving atomic mobility, but values of this order have not been found in any crystallization or growth processes for this and related alloys. At the present stage Al-transition metal-rare earth alloys the activation energies reported so far are widely scattered. They range from 140-160 kJ/mol for some Al-Ni-Gd glasses to values in excess of 400 kJ/mol for Al86Ni5Co2Y8 according to their composition and heat treatment. Considering homogeneous nucleation, the activation barrier can be estimated of the order of 40-50˜RT at deep undercooling, again lower than the above value. In most instances nucleation is heterogeneous, so the barrier will be even lower with respect to the value for SE viscous flow [16]. In a series of experiments with Al87Ni7Ce6 and Al87Ni7Nd6 amorphous alloys [10], it has been recently found that Tg becomes manifest at heating rates above a certain value typical of each alloy when the onset of crystallization is displaced to sufficiently high temperatures. The kinetics of the transformation was then studied and the Kissinger plots showed a change in the mechanism as a function of the heating rate, i.e. of peak temperature as implied by a deviation from linearity in the points for the first DSC peaks. The Kissinger plots could be referred to definite processes. At low rates, the crystallization must precede or overlap Tg so the activation energies of 340-370 kJ/mol for the two alloys should be related to the motion of Al in a medium characterised by short range order of different species, and therefore by the need of cooperative displacements of the alloy constituents. Above Tg, the viscous flow in the highly undercooled melt apparently has no effect since lower values of activation energies, 140-190 kJ/mol, are obtained. This suggests that the need for cooperative diffusion is removed in the molten state and that the hopping of single Al atoms suffice for promoting crystallization. It is apparent that estimating diffusivities via the SE equation is not appropriate for these materials. Extending the work to an Al87Ni7La6 alloy confirms these findings [17]. Concluding, a mobility different from that expressed by the SE relationship is relevant for crystallization of Al based glasses. The SE supplant (cf. Eq. (7)) may be operative or crystallization may depend on single diffusion steps not related to viscous flow. 5. FORMATION OF PRIMARY NANOCRYSTALS

In most alloys where primary nanocrystals are obtained from an amorphous matrix the transformation is reported to be fast and then to slow down progressively. This is reflected in highly asymmetric peaks in DSC. The glass transition is seldom detected before the onset of precipitation. It should be remarked that the primary phase is often, but not always Al. In fact, there have been findings in various laboratories that metastable intermetallics form as primary phases in Al-Ni-La and Al-Ni-Ce alloys [10, 18-21]. Examples of DSC traces are shown in Fig. 4 for Al87Ni7La6 and Al87Ni7La5Ti1

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Figure 4. DSC traces for the alloys listed in the insert at the heating rate of 20 K min1

amorphous alloys. The first crystallization step of the ternary alloy is due to the precipitation of a complex cubic phase, rich in the rare earth element. Substituting some Ti for La causes destabilization of such a phase and precipitation is then due to fcc Al. Nevertheless, both peaks are skewed and a substantial background signal occurs on their high temperature side indicating a similar mechanism of transformation. It has been shown that the background signal does not involve major precipitation of new crystals but rather the coarsening of those already existing, and homogenization of the remaining matrix where compositional gradients should occur because of solute rejection by the precipitates. It has been shown earlier that rare earth atoms can accumulate ahead of the nanocrystalline Al interface whereas transition metals diffuse faster in the matrix so their concentration is more readily homogenized. The new finding that a homogenization process occurs also when a primary La-rich phase forms, implies that a gradient in the Ni content of the matrix will retard its transformation as well. So, the two phase materials are resistant to crystallization because compositional gradients are established. It has been also suggested that during primary crystallization stress builds up around precipitates because of compositional gradients. This would be analogous to the stress effect occurring in multilayered thin film made of early and late transition metals where the interdiffusivity depends on the length scale of modulation, being fast for short distances, comparable to precipitate size, and dropping steadily for long range motion as implied in homogenization [22]. 6. NUCLEATION THERMODYNAMICS

Precipitation from the amorphous Al87Ni7Ce6 matrix involves only Al at low rates, i.e. below Tg, but it implies the formation of a metastable intermetallic, besides Al, when the transformation occurs above Tg. Therefore there is a clear change in the transformation mechanism across the glass transition. It is likely that below Tg only the growth of Al crystals occurs on pre-existing seeds whereas, in addition to Al growth, the two phases nucleate and grow in the undercooled melt. In Al87Ni7Nd6 the first transformation does not imply the formation of an intermetallic compound at any rate, so the change in the mechanism can be more clearly attributed to the formation of Al by either a growth in a glassy matrix or nucleation and a growth in a liquid matrix [10]. In addition, the tendency of the melt to undercooling shows that the nucleation of

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intermetallic compounds which is possible at high temperature, just below the liquidus, is sluggish.

Figure 5. The driving force for nucleation computed by means of the common tangent construction for fcc-Al and Al11Nd3 in the alloy Al91Nd9

The nucleation scenario in these alloys can be described thermodynamically by means of free energy curves representing the driving force for nucleation of either Al or Al11Nd3 computed according to the parallel tangent construction as a function of temperature (Fig. 5). The free energy of the liquid and crystal phases was optimized by means of a CALPHAD software and an appropriate account was made of the excess specific heat which is specific of glass-forming melts as well as of the occurrence of a glass transition [23]. At the glass-forming composition of 9 at.% Nd, the driving force for nucleation of the intermetallic builds up below the liquidus but levels off at high undercooling because of the progressive stabilization of the liquid phase due to the excess specific heat. Meanwhile, the driving force for nucleation of Al increases steadily and becomes close to that of Al11Nd3 at temperatures close to the glass transition. The two phases can actually compete for nucleation and factors such as glass (liquid)-crystal interfacial tension can become decisive in phase selection. It is expected that the simple fcc structure of Al will involve a lower interfacial tension with respect to the complex Al11Nd3 compound. On the other hand, metastable compounds may display short range order closer to that of the glass (liquid) and, therefore, nucleate preferentially. 7. CONCLUSIONS

Al-transition metal-rare earth melts have been suggested to be fragile in the Al-rich composition range where amorphisation can occur by rapid quenching. This is mostly determined by the low value of the ideal glass transition temperature, T0, corresponding to the point of vanishing entropy difference between liquid and crystal phases which was estimated from thermodynamic data. Although there is limited information on the viscosity of such alloys, referring to temperature ranges above the liquidus, the T0, K parameter entering the VFT for viscosity can be recovered. This stems from the assumption that the viscosity behaviour at the eutectic and glass transition temperature should be typical of glass forming alloys. The T0,K is close to the thermodynamic T0 and

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the overall viscosity in the undercooling regime conforms to the fragile type in Angell classification. Evidences have then been reviewed of the relationship between viscosity and diffusivity. At high temperature the proportionality expressed by the Stokes-Einstein equation appears valid within the scatter of experimental data but it breaks down close to Tg. In fact, the data obtained on the diffusion and the rate of crystal growth (including activation energies for crystallization) show that mobility is due to either single hopping jumps (vacancy-like mechanism) or the movement of groups of atoms (cooperative mechanism) instead of viscous flow. In Al-Ni-RE amorphous alloys, primary crystallization occurs frequently involving either fcc Al or an intermetallic compound. Such two-phase materials are rather stable kinetically in that they resist crystallization in a large temperature range. This has been attributed to sluggishness in nucleation of stable and metastable intermetallics depending on the existence of compositional gradients in the amorphous matrix which is enriched in the slow diffusing elements, and on the lowering of the driving force for nucleation due to the shape of the liquid free energy curve. ACKNOWLEDGMENTS

This work is funded by the Research Training Network of the European Commission “Nano Al” HPRN-CT-2000-00038. REFERENCES

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7. 8. 9. 10.

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Battezzati, L. and Greer, A.L., (1989) On the viscosity of liquid metals and alloys, Acta Metall., 37, 1791-1802. Yamasaki, T., Kanatani, S., Ogino, Y. and Inoue, A., (1993) Viscosity measurements for liquid Al-Ni-La and Al-Ni-Mm (Mm: Mischmetal) alloys by an oscillating crucible method, J. Noncryst. Solids, 156-158, 441-444. Chang, I., Sillescu, H., (1997) Heterogeneity at the glass transition: translational and rotational self-diffusion, J. Phys. Chem. B, 101, 8794-8801. Zumkley, T., Naundorf, V. Macht, M.-P., (2000) Diffusion in the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk glass: on the diffusion mechanism in supercooled liquids, Z. Metallkd., 91, 901-908. Duine, P.A., Sietsma, J., van der Beukel, A., (1993) Atomic transport in amorphous Pd40Ni40P20 near the glass transition temperature: Au diffusivity and viscosity, Phys. Rev. B 48, 6957-6965. Battezzati, L., Interplay of process kinetics in the undercooled melt in the proximity of the glass transition, Mater. Sci. Eng. A (in press) Battezzati, L., Rizzi, P., Ronto, V., The difference in devitrification paths in Al87Ni7Sm6 and Al87Ni7La6 amorphous alloys, Mater. Sci. Eng. A, (in press) Zhuang, Y.X, Jiang, J.Z., Lin, Z.G., Mezour M., Crichton, W. and Inoue, A., (2001) Evidence of eutectic crystallization and transient nucleation in Al89La6Ni5 amorphous alloy, Appl. Phys. Lett., 79, 743-745. Ye, F. and Lu, K., (1999) Pressure effect on crystallization kinetics of an Al-La-Ni amorphous alloy, Acta mater., 47, 2449-2454. Gangopadhyay, A.K. and Kelton, K.F., (2000) Effect of rare-earth atomic radius on the devitrification of Al88RE8Ni4 amorphous alloys, Phil. Mag. B, 80, 1193-1206. Abrosimova, G. E., Aronin, A. S., Zver'kova I. I., Kir'yanov, Y. V., (2002) Phase transformations upon crystallization of amorphous Al-Ni-RE alloys, Phys. Met. Metallov., 94, 113-118. Karpe, N., Krog J. P., Bottiger, J., Chechenin, N. G., Somekh, R. E., Greer, A. L., The thermodynamic factor in interdiffusion – A strong effect in amorphous Ni-Zr, Acta Met. Mater., 43, 551-558. Baricco, M., Gaertner, F., Rizzi, P., Battezzati, L., Cacciamani, G., Greer, A.L., (1998) Thermodynamics of homogeneous crystal nucleation in Al-RE metallic glasses, Mater. Sci. Forum, 269-272, 553-558.

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ON DIFFERENT MECHANISMS OF PRIMARY CRYSTALLIZATION IN Al-Ni-La-Zr AMORPHOUS ALLOYS

L. BATTEZZATI, V. RONTO, and M. KUSÝ Università di Torino, Dipartimento di Chimica IFM via P. Giuria 9, 10125 Torino, Italy Corresponding author: L. Battezzati, e-mail: [email protected] Abstract:

The devitrification sequences and mechanism are reported for a series of Al-Ni-Rare Earth amorphous alloys containing addition of Zr. The primary precipitation of a primitive cubic intermetallic occurs on continuous heating of amorphous alloys containing at least 6 at . % La as shown in Al87Ni7La6 and Al87Ni6La6Zr, whereas Al is formed in Al87Ni7La5Zr. The transformation can turn eutectic-like in both the above alloys with formation of the intermetallic and Al when it is accomplished on isothermal annealing. This induces a surprising effect on the subsequent matrix crystallization which is shifted to high temperature with respect to conventional scans made on continuous heating. The implications of the findings for diffusion in the matrix, nucleation and growth mechanisms are discussed.

1. INTRODUCTION Al-based amorphous alloys can be obtained by rapid solidification of systems containing a transition metal (TM) and a rare earth (RE) element. Once they are properly annealed, copious Al nanocrystals form, well dispersed in the amorphous matrix. The nanocrystalline alloys with such microstructure have attracted interest because of improved mechanical properties with respect to both conventional light alloys and amorphous Al alloys [1-4]. In the recent literature the devitrification behaviour of Al amorphous alloys has been thoroughly studied in view of microstructure optimization. The rare earth elements, as well as Y, are usually considered as vicariant in these materials although differences in the amorphising range and devitrification mechanism were demonstrated for binary Al-RE and ternary Al-TM-RE systems [1]. Fe and Ni are the most commonly used transition metals. However, several metastable intermetallic compounds compete with glass formation during rapid solidification when Fe is alloyed to Al and a rare earth. So, amorphisation is difficult [5]. Systematic studies on Al-Ni-Gd alloys have indicated 279 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 279–287. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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the Al87Ni7Gd6 composition as a good glass former [6]. When alloying different rare earth elements to Al and Ni in the same amount as Gd, a variation in transformation mechanism has been shown while there are two stages when using La or Ce, they become three when using Nd, Sm or Gd [6-8]. Furthermore, in the case of Al-Ni-La alloys of close composition, the primary formation of a metastable intermetallic phase was reported instead of Al [9, 10] at variance to a eutectic reaction [11]. In other works the presence of the metastable phase was not recognized since some of its most intense reflections coincide with those of Al [8, 12]. In all cases the nucleation rate is high, leading to formation of a high number of fine crystals, and growth becomes soon sluggish, possibly because of the occurrence of composition gradients in the matrix around the nanocrystals [13, 14]. A recent suggestion on transformation mechanism indicates a phase separation within the glassy phase as a possible precursor stage to devitrification [15]. To find evidence of this effect, addition of Ti and Zr was devised since they display positive heat of mixing with rare earth elements but strongly negative with Al and Ni, so the substitution might force the change in local order within the glassy phase. This paper reports an analysis of Al-Ni-La alloys containing Zr with the aim of exploring their glass forming tendency and devitrification behaviour. 2. EXPERIMENTAL Master alloys were prepared by arc melting of pure elements in Ar atmosphere using a rare earth as a getter. Lumps of the master ingots were then rapidly solidified by melt spinning under a protective atmosphere obtained by repeated evacuation and purging of the apparatus with Ar. The samples were contained in a silica crucible lined with a coating of rare earth oxide obtained by letting a portion of the alloy react with the crucible at high temperature. No further sign of reaction was detected during the use of the crucible. The alloy phases were studied by X-ray diffraction (XRD) employing CuKD radiation. The microstructure was examined by transmission electron microscopy (TEM) after electrolytic thinning of the samples. A power compensation differential scanning calorimeter (DSC) was used under flowing Ar at various heating rates for scans up to selected temperatures. The temperature and heat calibrations of the DSC cell were checked with pure metal standards (In, Zn). 3. RESULTS The devitrification behaviour of a series of Al-TM-RE alloys is shown in Fig. 1 as evidenced by DSC continuous heating experiments. The following main features have been found: (i) There is an increase in the number of peaks when Sm substitutes La in Al87Ni7RE6 alloys. (ii) The transformation sequence becomes more complex when 1 at.% Zr is used instead of either La or Ni, whereas it remains almost unaffected when 1 or 2 at.% Ti substitutes La [16].

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(iii) The first DSC peak is narrower and steeper for Al87Ni6La6Zr and Al87Ni7La6 with respect to that of Al87Ni7La5Zr and Al87Ni7Sm6 which are broader and shallower. In all cases the transformation starts rather abruptly and then continues in a large temperature range, as shown by highly asymmetric peaks. (iv) The addition of Ti or Zr shifts the primary transformation to low temperature with respect to the ternary alloys. (v) The glass transition temperature can be detected for some alloys by heating at suitable rates (10°C/min for Al87Ni7La6, 40°C/min for Al87Ni7Sm6 [9], and 80°C/min for Al87Ni7La5Zr).

Figure 1. DSC traces obtained with a series of Al-transition metals-rare earth amorphous alloys

Figure 2. a – Al87Ni7La6 heated after the first DSC peak; b – Al87Ni7La5Zr after annealing for 120 min at 197°C; c) Al87Ni6La6Zr heated after the first DSC peak

The series of TEM images of Fig. 2 shows the microstructure of representative alloys after primary crystallization in DSC at the heating rate of 20°C/min. The TEM image of Al87Ni7La6 (Fig. 2a) shows rather large crystals of irregular shape. From selected area diffraction (SAED) patterns as those shown in the insert and from XRD patterns (see below) it was ascertained that they belong to a metastable compound, rich in La [10]. It

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occurs as primary phase on continuous heating. Some of its reflections coincide with those of Al; their intensity, however, is much different and specific to the compound. The crystals grow to a considerable size during the DSC experiments. The primary crystallization of Al87Ni7La5Zr involves the precipitation of Al (Fig. 2b). On lowering the La content of the alloy there is no trace remaining of the metastable compound. The Al crystals, mostly appearing in the form of clusters of average size approximately 50 nm, are numerous and inhomogeneously dispersed in the matrix. The size of those observed in various areas of the sample ranged from 7 to 13 nm. The Al87Ni6La6Zr alloy presents SAED patterns compatible with formation of the same metastable compound as in the Zr-free alloy. The crystals, around 15 nm in size, are smaller than those of the ternary alloy (Fig. 2c). The XRD patterns reported in Fig. 3 confirm the TEM results. The pattern of Al87Ni7La6 has a series of reflections superimposed to a halo. All of them can be assigned to a primitive cubic structure. Details have been reported elsewhere [10]. A pattern of Al87Ni7Sm6 is reported for comparison in order to show the difference in intensity of the reflections occurring in the angular position of those of Al which is the primary phase in the latter alloy. Similarly, the reflections of Al87Ni7La5Zr show that Al is the primary phase.

Figure 3. XRD pattern of samples of the alloys listed in the figure, after primary crystallization. Stars indicate reflections of the primitive cubic phase. The haloes occurring around 2T degree are due to adhesive tape

On the contrary, the quaternary alloy rich in La, Al87Ni6La6Zr, presents reflections coincident with those found in Al87Ni7La6 which can be assigned to the same intermetallic compound. The kinetics of formation of Al and of the primary compound has been followed by letting the primary transformation occur in isothermal annealing at temperatures lower than the onset of transformation on continuous heating. Fig. 4a shows XRD patterns taken with Al87Ni7La6 annealed for various times at 230°C. It is apparent that the metastable compound forms from the very beginning of transformation. It can be noted, however, that the reflections corresponding to those of Al are more intense with respect to the pattern obtained with the same alloy on continuous heating. Therefore, on isothermal annealing, the two phases form together.

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The patterns reported in Fig. 4b for Al87Ni7La5Zr refer to the progressive formation of primary Al during isothermal annealing at 197°C with various holding times. From the absolute intensity of reflections and haloes shown in Fig. 4, the transformed fraction was derived as a function of time for all samples. The same quantity was also obtained from the amount of heat released in the first DSC peak by samples annealed for various times at low temperature. An example is reported in Fig. 5. The fraction transformed rises rapidly in both cases but hardly reaches completion. The DSC transformed fraction appears higher, probably because of a superimposed heat contribution from the diffusion controlled process of matrix homogenization. Extrapolation to nil transformed fraction of the curves which can be fitted to the points shows that there is an incubation time for the transformation.

Figure 4. a – XRD patterns taken with Al87Ni7La6 annealed for various times at 230°C; b – XRD patterns taken with Al87Ni7La5Zr annealed for various times at 197°C

Figure 5. Al transformed fraction during primary crystallization in Al87Ni7La5Zr as obtained from XRD and DSC measurements

Figure 6. DSC traces obtained with Al87Ni7La6 samples previously annealed for various times at 230°C and on continuous heating

The isothermal annealing performed to determine the fraction of alloy transformed in the primary reaction revealed an unexpected feature for Al87Ni7La6. Figure 6 reports DSC traces obtained with samples previously annealed for various times at 230°C

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below the first peak. After partial precipitation of the primary phase, the DSC peak is reduced. As usually found for alloys undergoing primary devitrification to a nanocrystalline phase with compositional gradients around it, depending on the length of the annealing time, its maximum shifts to higher temperatures. The surprising finding is that the second peak is much affected by the low temperature annealing. For short annealing times the peak is slightly changed but for longer annealing times a further peak develops some 15 degrees above the previous one which reduces in size and finally disappears. Annealing were performed in the temperature range from 210°C to 230°C and always gave the same results in different time periods. XRD patterns taken with samples annealed at intermediate stages of the transformation, present higher intensity of the reflections corresponding to the (200) and (311) angular position of Al, indicating that the formation of the metastable compound takes place together with that of some crystalline Al. The heat released during all transformations is constant and equals that produced by unannealed samples. The shift of the second peak does not occur to the same extent when the primary phase is Al. It has already been shown in a previous paper that there is no major change in the second and third peak of Al87Ni7Sm6 [17]. Here we report the behaviour of Al87Ni7La5Zr (Fig. 7). In DSC there are three major peaks, contrary to the ternary Al87Ni7La6 where only two peaks are found. When the first transformation is partially performed in isothermal pre-anneals, the first peak is reduced in size, and shifts to higher temperature, as found previously.

Figure 7. DSC traces obtained with Al87Ni7La5Zr samples previously annealed for various times at 197°C and on continuous heating

The small hump preceeding the second peak is shifted to low temperature. The second peak remains unchanged whereas the third one is decreased in height. Finally, the hump following the third peak is shifted to high temperature. It is shown by Rietveld refinement of XRD patterns that the low temperature hump is due to precipitation of Al11La3 and that at high temperature to precipitation of Al3Zr. The sequence of transformations of Al87Ni7La5Zr is demonstrated in the XRD patterns of Fig. 8. After precipitation of Al and the formation of a small quantity of Al11La3, probably caused by surface crystallization, there is massive formation of Al11La3 and then of Al3Ni. The two phases apparently originate from the amorphous matrix. It is not clear, however, if Al3Zr is the product of crystallization of a small

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Figure 8. XRD patterns showing the sequence of transformations of initially amorphous Al87Ni7La5Zr as a function of the temperature reached in heating experiments

portion of retained amorphous phase or of decomposition of supersaturated phases formed previously. 4. DISCUSSION AND CONCLUSIVE REMARKS In the devitrification of Al-based amorphous alloys containing La, there is the possibility of forming a primary intermetallic phase instead of pure Al. This occurs when the La content is of the order of 6 at.% as shown by different behaviours of Al87Ni7La5Zr and Al87Ni6La6Zr, confirming the findings reported for Al87Ni7La5Ti [16]. The precipitation of the intermetallic as a primary phase is the outcome of continuous heating experiments. The related DSC peak shifts regularly as a function of the heating rate and its minimum can be used for constructing a Kissinger plot. The transformation can turn eutectic-like with the production of some Al apart from the compound, when it is accomplished in isothermal annealing. It is likely that the compound is supersaturated with Al once it forms on continuous heating, but this could not be proven up to now. When a sufficient amount of the materials has transformed isothermally, the matrix becomes stabilized and another transformation is shifted to high temperature. If Al precipitates first, there are only minor effects on subsequent transformations due to the anticipated crystallization of some Al11La3, possibly on the surface, and a delayed formation of Al3Zr. The matrix homogenization after precipitation always produces a sizeable heat effect in DSC. Consequently the transformed fraction is overestimated. From DSC, TEM and XRD analyses it is apparent that all those phases are formed by a mechanism based on nucleation and growth. This is indicated by the abrupt start of the first DSC peak, the incubation time (found when analysing the fraction transformed on isothermal annealing), and the copious number of crystals dispersed in the matrix. Since the number of crystal of the intermetallic compound is lower than that of Al and the compound grows to a larger size than Al, it is possible that the compound forms on pre-existing seeds. Its faster growth should reflect the difference in the demixing paths, involving difference in diffusion paths, in the two processes. The density of Al crystals in partially crystallized alloys is large with sizes ranging from a few to some tens of nanometers. This is the result of copious nucleation. There

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has been discussion on the nature of the nucleation events. When analysing the crystallization of binary Al-Sm alloys it was suggested that, being the crystals so copious, nucleation might have been mostly homogeneous, in agreement with the shape of the size distribution of nanocrystals. In addition, the amount of impurities and inclusions found in the material would not have accounted for all crystals formed if they acted as heterogeneous nucleants. Subsequently, experiments on glassy Al92Sm8 [18] alloys either melt quenched and obtained by cold rolling foils of the elements, showed difference in crystallization mode between the two materials: the melt quenched samples contained the expected high population of nanocrystals after annealing through the primary crystallization whereas this was fully avoided in the cold rolled material. The conclusion was then drawn that the nanocrystals were produced by growth on preexisting seed which could have been formed during quenching whereas the seeds were not present in the solid state processed alloy [18]. However, later an analysis of the size distribution of the nanocrystals led to conclude that after an initial nucleation on quenched-in clusters thermal nucleation could have followed to complete the reaction [4]. So, it is likely that a single nucleation mechanism of Al does not apply [17]. There is no explanation yet for the observation that in Al87Ni7La5Zr the Al crystals appear in clusters. The use of 1% Zr instead of La was meant to enhance phase separation within the amorphous phase which has been claimed in some Al-Ni-RE alloys [15]. If there were demixing of phases within the glass, it could be envisaged that Al formation could be favoured in one of the phases. Up to now, however, no proof of demixing has been found for the present alloy since there is no thermal effect of it. The DSC trace after a short term annealing exactly overlap that obtained on continuous heating and XRD patterns do not appear affected by the annealing. ACKNOWLEDEGEMENTS This work is funded by the Research Training Network of the European Commission “Nano Al” HPRN-CT-2000-00038. REFERENCES 1. 2.

3.

4. 5.

Inoue, A., (1998) Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Progress in Materials Science 43, 365-520. Greer, A.L., Zhong, Z.C., Jiang, X Y., Rutherford, K.L., and Hutchings, I., (1997) Al-Y-Ni nanophase composites by devitrification – microstructure, hardness and abrasive wear resistance, in Proc. Symp. on Chemistry and Physics of Nanostructures and related NonEquilibrium Materials, E. Ma, and B. Fultz (eds.) The Minerals, Metals & Materials Society, 184 Thorn Hill Road, Warrendale, PA 15086-7514, USA. Battezzati, L., Pozzovivo, S., and Rizzi, P., (2003) Nanocrystalline Aluminium Alloys, in Nanoclusters and Nanocrystals, Nalwa, H.S. (ed.) American Scientific Publishers, 25650 North Lewis Way, Stevenson Ranch, California 91381-1439, USA. Wilde, G., Boucharat, N., Hebert, R.J., Rösner, H., Tong, W.S., and Perepezko, J.H., (2003) Nanocrystallization in Al-rich metallic glasses, Adv. Eng. Mater. 5, 125-130. Battezzati, L., Ambrosio, E., Rizzi, P., Garcia Escorial, A., and Cardoso, K., Complex transformation sequences in Al-TM-RE amorphous alloys, Proc. 22nd Risø Intern. Symp. on Materials Science, Science of Metastable and Nanocrystalline Alloys Structure Proper-

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ties and Modelling, A.R. Dinesen et al. (eds.), Risø National Laboratory, Roskilde, Denmark, 2001, 211-216. 6. Guo, F.Q., Poon, S.J., and Shiflet, G.J., (2000) Glass formability in Al-based multinary alloys, Mater. Sci. Forum, 331-337, 31-42. 7. Battezzati, L., Pozzovivo, S., and Rizzi, P., (2002) Phase Transformations in Al87Ni7Ce6 and Al87Ni7Nd6 amorphous alloys, Mater. Trans. 43, 2593-2599. 8. Battezzati, L., Rizzi, P., and Ronto, V., The difference in devitrification paths in Al87Ni7Sm6 and Al87Ni7La6 amorphous alloys, Mater. Sci. Eng. A, (in press). 9. Gangopadhyay, A.K. and Kelton, K.F., (2000) Effect of rare earth atomic radius on the devitrification of Al88RE8Ni4 amorphous alloys, Phil. Mag. A 80, 119-1206. 10. Ronto, V., Battezzati, L., Yavari, A.R., Tonegaru, M., Lupu, N., and Heunen, G., (2004) Scripta Mater., 50, 839-843. 11. Zhuang, Y.X., Jiang, J.Z., Lin, Z.G., Mezouar, M., Crichton, W., and Inoue, A., (2001) Evidence of eutectic crystallization and transient nucleation in Al89La6Ni5 amorphous alloy, Appl. Phys. Lett. 79, 743-745. 12. Ye, F. and Lu, K., (1999) Pressure effect on crystallization kinetics of an Al-La-Ni amorphous alloy, Acta Mater. 47, 2449-54. 13. Hono, K., Zhang, Y., Inoue, A., and Sakurai, T., (1995) Atom probe studies of nanocrystalline microstructural evolution in some amorphous alloys, Mater. Trans. JIM 38, 909-917. 14. Zhang, Y., Warren, P.J., and Cerezo, A., (2002) Effect of Cu addition to nanocrystallization of Al-Ni-Sm amorphous alloy, Mater. Sci. Eng. A327, 109-115. 15. Gangopadhyay, A.K., Croat, T.K., and Kelton, K.F., The effect of phase separation on subsequent crystallization in Al88Gd6La2Ni4, Acta Mater. 48, 4035-4043. 16. Battezzati, L. Kusý, M., Palumbo, M., and Ronto, V., (2005) Al-Rare Earth-Transition Metal alloys: fragility of melts and resistance to crystallization, in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec, and M. Miglierini (eds.), Kluwer Acad. Publ., Dordrecht, The Netherlands, 267-278. 17. Battezzati, L., Kusý, M., Rizzi, P., and Ronto V., Devitrification of Al-Ni-Rare Earth amorphous alloys, J. Mater. Sci. (in print). 18. Wu, R.I., Wilde, G., and Perepezko, J.H., (2001) Glass formation and primary nanocrystallization in Al-base metallic glasses, Mater. Sci. Eng. A301, 12-17.

ATOMIC STRUCTURE, INTERATOMIC BONDING AND MECHANICAL PROPERTIES OF THE Al3V COMPOUND M. JAHNÁTEKa , M. KRAJýÍa ,b, and J. HAFNERb a

Institute of Physics, Slovak Academy of Sciences Dúbravská cesta 9, SK 84228 Bratislava, Slovakia b Institut für Materialphysik and Center for Computational Materials Science Universität Wien, Sensengasse 8/12, A-1090 Wien, Austria Corresponding author: M. Jahnátek, e-mail: [email protected] Abstract:

On the basis of ab-initio calculations we analyzed the electron density distribution and investigated interatomic bonding in the elementary cell of Al3V compound. For Al3V crystallizing in the DO22 (Al3Ti) structure we found an enhanced charge density along Al-V bonds and certain Al-Al bonds that is characteristic for covalent bonding. We calculated elastical properties and investigated the effect of interatomic bonding on mechanical properties. The calculated strength of Al3V in tensile deformation was found significantly higher than that of fcc-Al or bcc-V crystals.

1. INTRODUCTION Transition-metal aluminides are known to be of great technological importance and high scientific interest. Al-based compounds of transition-metals (TM) are among the most promising candidates for high-performance structural materials [1]. The reported tensile strength of e.g. nanocrystalline Al94V4Fe2 is above 1300 MPa, which exceeds the strength of usual technical steels [2]. The physical interest in transitionmetal aluminides is trigerred by the wide variety of physical properties. Aluminides form an important class of quasicrystals, with exotic physical and chemical properties [3]. Transitionmetal aluminides may also exhibit true semiconducting behaviour [4, 5]. In this paper we present results of our study of the interatomic bonding and mechanical properties of the Al3V compound. The Al3V compound has the DO22 (Al3Ti) crystal structure which is a special decoration of a face-centered cubic lattice. The electronic density of the states of this compound exhibits unusually deep pseudogap, very close to the Fermi level. NMR studies suggest a strong directional bonding [7, 8] in this structure. This conjecture is further corroborated by the structural analysis: the unusually short Al-V distances [9] indicate that the bonding may have a covalent character. Recently, we have performed a detailed study of the electronic structure and bonding in Al3V [6]. We demonstrated that a special hybridization between the Al(s, p) and V(d) 289 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 289–300. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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orbitals which is responsible for forming a deep pseudogap near the Fermi level in the Al3V compound is also associated with the formation of covalent bonds. We analyzed the charge distribution in the elementary cell and found an enhanced charge density along the Al-V bonds and certain Al-Al bonds that is characteristic for covalent bonding. In the present work we calculated elastical properties and investigated the effect of interatomic bonding on mechanical properties. The calculated strength of Al3V in tensile deformation was found significantly higher than that of fcc-Al or bcc-V crystals. 2. METHODOLOGY The electronic structure calculations have been performed using two different techniques. The plane-wave based Vienna ab-initio simulation package VASP [10, 11] has been used for the calculations of the electronic ground-state and for the optimization of the atomic volume and unit-cell geometry. The VASP program has also been used to calculate charge-distributions. In its projector augmented-wave (PAW) version [11] VASP calculates the exact all-electron eigenstates, hence it can produce realistic electron-densities. The plane-wave basis allows to calculate Hellmann-Feynman forces acting on the atoms and stresses on the unit cell. The total energy may by optimized with respect to the volume and the shape of the unit cell and to the positions of the atoms within the cell. However, a plane-wave-based approach such as used in VASP produces only the Bloch-states and the total density of states (DOS), a decomposition into local orbitals and local orbital-projected DOS's requiring additional assumptions. To achieve this decomposition, self-consistent electronic structure calculations were performed using the tight-binding linear muffin-tin orbital (TB-LMTO) method [12, 13] in an atomicsphere approximation (ASA). The minimal LMTO basis includes s, p, and d-orbitals for each Al and V atoms. The two-center TB-LMTO Hamiltonian was constructed and diagonalized using standard diagonalization techniques. The TB-LMTO basis is used to construct the symmetrized hybrid orbitals from which the crystal-orbital overlap populations (COOP) [14] are calculated. 3. INTERATOMIC BONDING IN THE Al3V STRUCTURE 3.1. Crystal structure Al3V is an intermetallic compound with a DO22 (Al3Ti) crystal structure. The space group is I4/mmm (No. 139). The primitive cell contains 4 atoms. The orthorhombic elementary cell consists of two primitive cells, see Fig. 1. All atoms are located on the sites of a face-centered-cubic lattice (fcc). The elementary cell consists of two fcc units stacked along the z-direction. In the z = 0 plane the vertices of the cubic lattice are occupied by vanadium atoms and the face-centers by aluminum atoms. In the z = 0.5 plane the arrangement is just the opposite. The planes z = 0.25 and z = 0.75 are occupied by aluminum atoms only. In the elementary cell there are one vanadium crystallographic site V (Wyckoff notation 2a) and two aluminum sites Al1 (2b) and Al2 (4d). Each vanadium atom has

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Figure 1. An elementary cell of Al3V in the DO22 structure. Positions of aluminum atoms are represented by smaller spheres, position of vanadium atoms are represented by bigger spheres; Al1 atoms are black, Al2 atoms are gray

4 Al1 neighbours and 8 Al2 neighbours. Al1 neighbours are located in (x, y) plane at z = 0 and z = 0.5 on vertices of a square centered by the V atom. The distance between the central V atom and the Al1 atoms is dV-Al1 = 2.661 &. Al2 neighbours are located in z = 0.25 and z = 0.75 planes in vertices of a tetragonal prism centered again by the V atom at a distance dV-Al2 = 2.802 &. Considering only nearest neighbours the pointgroup symmetry of the V-site would be Oh, but nonequivalent neighbours from the second and higher shells reduce the point-group symmetry to D4h. An Al1 atom sees 4 vanadium atoms located at dAl1-V = 2.661 & on the vertices of a square and 8 Al2 neighbours located at dAl1-Al2 = 2.802 & forming a tetragonal prism centered by the Al1 atom. Al2 has four Al2 neighbours in the (x, y) plane forming together a square grid of aluminum atoms. The edge of the squares measures 2.661 &. Al2 has also 4 Al1 and 4 V neighbours, both with tetrahedral coordination at a distance of 2.802 &. In summary, the vanadium atom has 12 aluminum nearest neighbours, both aluminum atoms have 4 vanadium neighbours and 8 aluminum neighbours in the first coordination shell. 3.2. Charge densities and bonding Using the VASP program we calculated the charge-density distribution in the elementary cell of the DO22 structure. Figure 2a shows a contour plot of the valence-charge distribution in the (x, z) plane for y = 0.5. The high charge density in the center (dark region) corresponds to the vanadium atom. Positions of aluminum atoms are characterized by minimal charge densities light regions. If the character of the bonding is purely metallic, the charge distribution among atoms should be homogenous. A possible covalent bonding is indicated by enhanced charge distribution along connections between atoms. In Fig. 2a we see regions of enhanced charge-density halfway between the central V atom and four Al2 atoms. As the structure has tetragonal D4h symmetry around z-axis the same distribution exists also in the perpendicular (y, z) plane. To confirm the covalent bonding we investigated the difference electron-density, i.e. a superposition of atomic charge-densities is subtracted from the total charge density.

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Figure 2. a – (left) Contour plot of valence electron density in the (x, z) plane of the DO22 structure for y = 0.5. High charge density in the center – dark region corresponds to the vanadium atom. Positions of aluminum atoms are characteristic by minima of charge density – light regions. The islands of enhanced charge between the central V atom and four Al2 atoms (gray circles) indicate a possible covalent bonding. b – (right) Contour plot of the difference electron density in (x, z) plane for y = 0.5 (the same plane as in the previous figure). In the difference density a non-selfconsistent charge density obtained as a superposition of atomic charge densities is subtracted from the total charge density. In the figure we represent only regions of enhanced density. In blank regions among atoms the difference density is negative. One can clearly identify enhanced charge corresponding to bonding between V atom and Al2 atoms

The contour plot in Fig. 2b represents the regions of positive difference electron-density in the (x, z)-plane, in the blank space the difference density is negative. In Fig. 2b we can clearly identify the “bond-charges” between the V and Al2 atoms. The bonds are directed from the central vanadium atom to the eight vertices of a tetragonal prism formed by the Al2 atoms. The bonds are directed from the central vanadium atom to the four vertices of a square formed by the Al1 atoms. An enhanced charge density was also found in the planes at z = 0.25 and z = 0.75 where only Al2 atoms are located. In summary, there are three types of covalent bonds. The bonds are sketched in Fig. 3. Vanadium atom has two types of bonds: V-Al2 bonds are marked as dashed lines, V-Al1 bonds are displayed as dash-dotted line segments. The Al2 atoms, in addition to

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Figure 3. An elementary cell of Al3V in the DO22 structure. Positions of aluminum atoms are represented by smaller circles, position of vanadium atoms are represented by larger circles. Three types of covalent bonds are sketched: V-Al2 bonds are marked as dashed lines, V-Al1 bonds are displayed as dash-dotted lines, Al2-Al2 bonds are marked in by dotted line segments

the bonds with the V atom, have weak Al2-Al2 bonds marked in Fig. 3 by dotted lines. The character of the bonds is investigated in the next section. 3.3. Hybridized orbitals and bonding Bonding in an intermetallic compound can be very complex. Fortunately, in the DO22 crystal structure where the symmetries of atomic sites are relatively high, symmetry can help to identify the orbitals or hybridized orbitals that are most important for the forming of the bonds. To gain a deeper understanding, we constructed sets of symmetrized hybridized orbitals oriented along the bonds and calculated the density of states projected onto bonding and antibonding combinations of these symmetrized orbitals. The symmetrized orbitals are sets of hybridized orbitals possessing the pointgroup symmetry of a particular atomic site. Here we shall investigate V-bonds only. A set of bonds originating from a particular atom forms a reducible representation of the point group. Decomposition of the reducible representation into irreducible ones enables to select individual s, p or d orbitals whose linear combinations form the hybridized orbitals. From the symmetrized orbitals we constructed bonding and antibonding configurations and investigated the density of states projected on these orbital configurations. We note that the difference of these projected DOS is essentially equivalent to the differential crystal orbital overlap population (COOP) defined by Hoffmann [14]). Figure 4 shows the density of states projected on bonding (B) and antibonding (A) combinations of symmetrized orbitals located an neighbouring atoms. In addition to the bonding DOS and antibonding DOS (to which for sake of clarity a negative sign is assigned),

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Figure 4. The crystal orbital overlap population (COOP). The density of states is projected on bonding (B) and antibonding (A) combination of symmetrized orbitals located on atoms. In addition to the bonding density and antibonding density to which for sake of clarity a negative sign is assigned (both dotted lines) the difference (B-A) between bonding and antibonding densities is presented (thick line). a – Al2(sp2d)-Al2(sp2d) bonding, b – V(dxy)Al1(sp2d) bonding, c – V(d4)-Al2(sp3) bonding, and d – V(dzx)-Al2(sp3) bonding

the difference (B-A) between bonding and antibonding densities, i.e. the COOP, is presented. 3.3.1. Al2-Al2 bonds The bonding between two Al2 atoms is in the (x, y) plane, (see dotted lines in Fig. 3). Each Al2 atom has four Al2 neighbours located at the vertices of a square. The symmetrized orbitals correspond to an sp2d hybridization. The density of antibonding configuration is negligibly small in the whole studied energy region (Fig. 4a), the COOP is positive below and above Fermi level, as well. Although the bond has a covalent character it is only partially populated by electrons. This indicates that these bonds are not strong. The minimum around the Fermi level does not have the character of a bonding-antibonding splitting, but is a consequence of a low total density of states in this region induced by Al2-V bonding (see below). 3.3.2. V-Al1 bonds The vanadium atom interacts with four Al1 atoms in the (x, y) plane, (see dot-dashed line segments in Fig. 3). The Al1 atoms have four V neighbours located at the vertices of a square. The corresponding set of symmetrized hybridized orbitals is again sp2d with Al1 s, px, py and dxy orbitals. From the point of view of the vanadium atom the V-Al1 bonds are oriented from the central V atom to four Al1 atoms located at the vertices of a square. The corresponding set of symmetrized orbitals is again sp2d. However, as the contribution of p-states to the vanadium DOS is negligible and the contribution of s-states is small, the V(dxy) orbital is dominant.

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Figure 4b shows that below the Fermi level the bonding DOS is substantially higher than the antibonding one. The region above the Fermi level up to 2.7 eV can be considered as nonbonding, both bonding and antibonding DOSes are very close to zero. Above 2.7 eV the antibonding character becomes significant. 3.3.3. V-Al2 bonds The vanadium atom is bonded with two Al2 atoms located in opposite directions on the body diagonal of a tetragonal prism. Altogether there are four such bonds (see dashed lines in Fig. 3). The Al2 atoms have four V neighbours located at the vertices of a tetrahedron. The symmetrized orbitals on the Al2 atoms are thus sp3 hybrids formed by s, px, py and pz orbitals. The point group symmetry of the vanadium site is D4h. The orbitals oriented from the central vanadium atom to the eight Al2 atoms at the vertices of a tetragonal prism form a basis of a reducible representation of the D4h point group. We found that d4 hybrid-orbitals formed by dz2, dx2-y2, dzx, dyz states (or sd3 hybridization if we consider s orbital instead of dz2) dominate the bonding. It is remarkable that the symmetry here excludes the dxy orbital from bonding. This is the orbital which plays a dominant role in V-Al1 bonding as discussed in the previous section. Four d4 hybridized orbitals possessing inversion symmetry point towards the vertices of a tetragonal prism. The symmetrized d4 orbitals have a form similar to the dz2 orbital and differ only in orientation. While the dz2 orbital is oriented along the z axis, the symmetrized d4 orbitals are oriented along the body diagonals of the tetragonal prism. Figure 4c shows that while the bonding DOS below the Fermi level is substantial, the antibonding DOS is negligible in this region. At the Fermi level the bonding DOS decreases and above the Fermi level a nonbonding region extends to 1.5 eV. In this energy range a bonding contribution from the dx2-y2 component, and an antibonding DOS from the dz2 component almost compensate. Above 1.5 eV the antibonding character becomes dominant. A more detailed analysis of the V (d 4)–Al2(sp3) bonding shows that the main bonding contribution out of the four d 4 hybridized orbitals comes from the components dzx and dyz both belonging to the Eg irreducible representation. Figure 4d represents the bonding and antibonding densities corresponding to these states. Below the Fermi level (more exactly below 0.08 eV) the states have predominantly bonding character while above the Fermi level the character is antibonding. This demonstrates bondingantibonding splitting of the energy levels and confirms the covalent character of the bond. 4. INTERATOMIC BONDING AND MECHANICAL PROPERTIES The elasticity of a material is one of its fundamental properties important for technological applications. For a long time the elastic properties of materials have been extensively studied by various experimental methods. The progress in the ab-initio methods in the past decade allows us to approach this interesting topic also from the theoretical point of view. The elastic constants describe mechanical properties of materials in the linear region of deformation. Another important quantity, which describes the mechanical properties of the material beyond the linear region, is the ideal

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(or theoretical) strength. It represents the stress necessary for de-cohesion or fracture of the crystal [15, 16]. The ideal strength represents upper strength limit for a solid under a given load. For calculation of the ideal strength one has to deform the crystal along a path of the easiest deformation. For a fcc crystal it is a shear deformation in a direction in a {111} plane. For a bcc crystal it is e.g. a slip of {110} planes along the direction. The ideal strength corresponds to a saddle point in a path of the easiest deformation. Table I. Computed and experimental values of elastic constants and related material properties of Al, V and the Al3V compound; a and c are lengths of elementary cell in &, V0 is the equilibrium volume in &3/atom, B – bulk modulus in GPa, Cij – elastic constants, all in GPa, C' – shear modulus in GPa, relevant only for cubic structures, E – Young's modulus in GPa (two values correspond to strains along x and z axis) and V is Poisson ratio Struc. Sym.

Al cF4 exp. V cI2 exp. Al3V tI8 exp.

a

c

V0

B

C11

C12

C13

C33

C44

C55

C’

4.046

–

16.56 16.56

75 79

109 114

57 62

2.995 – 13.43 185 3.022 13.80 161 3.766 8.312 14.73 118 3.840 8.579 15.81

271 238 233

142 122 77

– – – – 46

– – – – 258

28 32 18 47 104

– – – – 129

26 70 26 70 65 174 58 155 – 204/205

4.045

E

V 0.34 0.35 0.34 0.33 0.30

To investigate the effect of bonding we stretched the Al3V crystal along z-direction and compared the maximal stress found along the deformation path with the same quantities found for tensile deformation of the fcc-Al and bcc-V crystals. As our primary interest was to investigate the effect of bonding on mechanical properties we stretched the elementary cells of Al, V and Al3V in one high-symmetry direction common for all three crystal structures and did not attempt to search for a path of easiest deformation. For calculation of the elastic constants we used the recently published symmetrygeneral least-squares extraction method [17]. The method allows to extract the elastic constants from the total energies calculated for several crystal deformations and to produce high reliable and consistent set of these constants for any crystal symmetry. We implemented the method in connection with VASP. This combination of programs provides a very powerful tool for the calculation of the elastic constants. The elastic constants and related quantities are listed in Table I. For cubic 7 systems the independent elastic constants are C11, C12 and C44 only, for tetragonal crystals C11, C12, C13, C33, C44 and C55. To calculate the elastic constants, the total energies as a function of small distortions of the lattice (typically of the order of 1% or less) have to be calculated. Highly accurate computations must be performed. The internal unconstrained atomic coordinates must be fully relaxed. A good check for the obtained elastic constants is a consistency test. The bulk modulus can be computed either from the elastic constants or independently, also from the energy vs. volume curve. A similar consistency test exists for the Young modulus. It can be calculated either from the elastic constants or extracted from the linear part of the stress-strain dependence.

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Figure 5 collects our results of the tensile deformations of fcc-Al, bcc-V and the Al3V compound. Full curves represent stresses induced by tensile strain applied on the elementary cells. Near the origin one observes a short region of a linear behaviour. The slope of the linear part of the stress-strain curve near the origin is related to the Young modulus. For each system the Young modules have has been calculated also from the elastic constants, in Fig. 5 they are is represented by dashed straight lines. The agreement of the slopes of the stress-strain curves obtained from our tensile experiments with the slopes of the dashed lines representing the Young modules demonstrates the consistency of both computational methods.

Figure 5. The results of the tensile deformations of fcc-Al, bcc-V and the Al3V crystals. Full curves represent stresses induced by tensile strain applied on the elementary cells. Near the origin one observes a short region of a linear behaviour. The slope of the linear part of the stress-strain curve near the origin is related to the Young modulus that can be calculated also from the elastical constants – dashed straight lines, cf. text

The stress-strain curve for a fcc-Al crystal deformed along the direction increases monotonously and reaches its maximum of 11.4 GPa at the tensile strain 34.3%. This maximal stress is higher than the value of the ideal shear strength of Al. Roundy et al. [18] reports the ideal shear strength for fcc-Al 1.85 GPa. The value of the Young modulus of 70 GPa extracted form the region of the linear deformation agrees well with the experimental value, see Tab. I. This agreement indicates that the Young modulus for fcc-Al has a relatively isotropic character. The stress-strain curve for a bcc-V crystal deformed along the direction behaves qualitatively differently from that of Al. This deformation path is known as the Bain path. At this path the crystal undergoes the bccofcc phase transition. The stress-strain curve reaches its maximum of 18.9 GPa at the tensile strain of 18.2%. At the tensile deformation 27.4% the c/a ratio of the tetragonally deformed bcc lattice is just equal to 21/2. At this point the lattice becomes fcc and the stress-strain curve

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intersects here the zero value. The calculated Young modulus E = 174 GPa is somewhat higher than the value of E = 155 GPa calculated from the experimental values of the elastic constants. The stress-strain curve for the Al3V crystal deformed along the direction has a simple shape, similar to that of fcc-Al. It increases monotonously and reaches its maximum of 28.2 GPa at the tensile strain 24.7%. The value of strength 28.2 GPa is significantly higher than the strength of V or Al crystals. As the structure of Al3V can be considered as a special decoration of a fcc lattice the topology of the atomic structures of deformed crystals is very similar. The observed increase of the strength of the Al3V crystal in comparison to the fcc-Al and bcc-V crystals must be therefore attributed to the increased strength of interatomic bonding. 5. DISCUSSION AND CONCLUSIONS In Al3V bonding of enhanced covalency exists between the Al2 atoms as well as between the V-atoms and both types of Al-atoms. The Al2-Al2 bonding is based on the sp2d hybrid-orbitals. These bonds are not fully saturated and are rather weak. The interaction of the sp2d hybrid-orbitals on the Al1-sites with the V-dxy states forms the basis for the covalent Al1-V bond. Al2-V bonding is based on sp3-hybrids on the Al-atoms and d4-hybrids on the V-sites. The strongest covalent bonds are in the crystal oriented in the diagonal direction. We calculated elastic properties and investigated the effect of interatomic bonding on mechanical properties. As our primary interest was the investigation of the effect of bonding on mechanical properties, we stretched the elementary cells of Al, V and Al3V only in one high-symmetry direction, common for all three crystal structures. We thus obtained a set of comparable results. We did not attempt to search for a path of weakest deformation that is different for each crystal structure. The calculated strength of Al3V in tensile deformation was found significantly higher than that of fcc-Al or bcc-V crystals. The observed increase in the strength of the Al3V crystal in comparison to the fcc-Al and bcc-V crystals is attributed to the increased strength of the interatomic bonding. For all investigated systems we calculated the elastic constants. As expected, for fcc-Al we found a good agreement with experiment. For bcc-V the agreement of the calculated elastic constants with the experimental values is not so satisfactory. The biggest discrepancy is found for the C44 constant. The calculated value of 18 GPa is considerably smaller than the experimental value of 47 GPa. This discrepancy is presumably a failure of the LDA approximation in case of V-V interaction. Such a failure has been reported also by other authors [19]. In the Al3V compound V atoms are not the nearest neighbours and therefore here one should not expect a similar discrepancy. In Al3V the values of diagonal elastic constants C11 and C33 are large, comparable to those of bcc-V. The off-diagonal constants C12 and C13 are substantially smaller. This indicates that the covalent bonds enhance the strength of the elementary cell for tensile deformations along the Cartesian axes, particularly along z-axis, but the cell remains unstable for a shear deformation, particularly in (x, z) plane. The Young modulus can be calculated directly from the elastic constants. It is also equal to the slope of the stress-strain curve near the origin. The values of the Young

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modules calculated from the elastic constants and the corresponding values extracted from the slopes of the stress-strain curves are in good agreement. If the stress-strain curve is a simple smooth curve, as it is in the case of Al, a higher slope of the curve at the origin, i.e. a higher value of the Young modulus, also means a higher maximum of a stress-strain curve, i.e. a higher strength of the crystal. From the calculated Young modules one can estimate that the strength of the Al3V crystal for tensile deformation along the x direction is weaker than that along z direction. Relatively large difference in the values of the strain for which the stress reaches its maximal value in cases of Al and V can also be interpreted by the character of the bonding. While in simple metals with s-p interaction the interatomic bonding is weaker but has a larger extent than in the case of transition metals where d-d interaction is strong but decreases faster with the interatomic distance. To conclude, we have used ab-initio methods to understand interatomic bonding in Al3V and investigated the effect of bonding on its mechanical properties. ACKNOWLEDGEMENTS We acknowledge support from the Grant Agency for Science in Slovakia (Grant No. 2/2038/22). REFERENCES 1. Inoue, A. and Kimura, H., (2000) High-strength aluminum alloys containing nanoquasicrystalline particles, Mat. Sci. Eng. A 286, 1. 2. Inoue, A., Kimura, H., Sasamori, K., and Masumoto, T., (1996) High mechanical strength of Al-(V, Cr, Mn)-(Fe,Co,Ni) quasicrystalline alloys prepared by rapid solidification, Materials Transactions, JIM 37, 1287. 3. Rapp, Ö., (1999) Physical Properties of Quasicrystals, ed. Z. M. Stadnik, Springer Series in Solid-State Sciences, Springer, Berlin. 4. Krajþí, M. and Hafner, J., (2002) Covalent bonding and band gap formation in transitionmetal aluminides: di-aluminides of group VIII transition metals, J. Phys.: Condens. Matter 14, 5755. 5. Krajþí, M. and Hafner, J., (2002) Covalent bonding and band gap formation in transitionmetal aluminides: Al4MnCo and related compounds, Phys.: Condens. Matter 14, 7201. 6. Krajþí, M. and Hafner, J., (2002) Covalent bonding and bandgap formation in intermetallic compounds: a case study for Al3V, Phys.: Condens. Matter 14, 1865. 7. Dunlop, J.B., Grüner, G., and Caplin, A.D., (1974) Dilute intermetallic compounds II: properties of aluminum rich aluminum-transition metal phases, J. Phys. F: Metal Phys. 4, 2203. 8. Lue, C.S., Chepin, S., Chepin, J., and Ross, Jr., J.H., (1998) NMR study of trialuminide intermetallics, Phys. Rev. B 57, 7010. 9. Caplin, A.D., Grüner, G., and Dunlop, J.B., (1973) Al10V: An Einstein solid, Phys. Rev. Lett. 30, 1138. 10. Kresse, G. and Furthmüller, J., (1999) Efficient iterative schemes for ab-initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11 160. 11. Kresse, G. and Joubert, D., (1999) From ultrasoft pseudopotentials to the projector-augumented wave method, Phys. Rev. B 59, 1758. 12. Andersen, O.K., Jepsen, O., and Götzel, D., (1985) Highlights of Condensed Matter Theory, F. Fumi, and M.P. Tosi (eds.), North Holland, New York.

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13. Andersen, O.K., Jepsen, D., and Šob, M., (1987) Electronic Band Structure and its Applications, M. Youssouff (ed.), Springer, Berlin. 14. Hoffmann, R., (1988) Solids and Surfaces: A Chemist's View of Bonding in Extended Structures, VCH, New York. 15. ýerný, M., Šandera, P., and Pokluda, J., (1999) Ab-initio calculations of ideal strength for cubic crystals under three-axial tension, Czech. J. Phys. 49, 1495. 16. Šob, M., Wang, L.G., and Vitek, V., (1997) Theoretical tensile stress in tungsten single crystals by full-potential first-principle calculations, Mater. Sci. Eng. A 234-236, 1075. 17. Page, Y.L. and Saxe, P., (2001) Symmetry-general least-squares extraction of the elastic coefficients from ab-initio total energy calculations, Phys. Rev. B 63, 17 4103. 18. Roundy, D., Krenn, C.R., Cohen, M.L., and Morris Jr., J.W. (1999) Ideal shear strengths of fcc aluminum and copper, Phys. Rev. Lett. 82, 2713. 19. Söderlind, P., Ahuja, R. Eriksson, O., Wills, J.M, and Johansson, B., (1994) Crystal structure and elastic-constant anomalies in the magnetic 3d transition metals, Phys. Rev. B 50, 5918.

AMORPHOUS AND NANOSTRUCTURED Al-Fe AND Al-Ni BASED ALLOYS

F. AUDEBERT Grupo de Materiales Avanzados, Facultad de Ingeniería, Universidad de Buenos Aires Paseo Colón 850, (C1063ACV), Buenos Aires, Argentina At present: Academic Visitor in the Department of Materials, University of Oxford. Parks Road Oxford, OX1 3PH, UK Corresponding author: F. Audebert, e-mail: [email protected] Abstract:

Al-based systems allow obtaining microstructures composed of different combination of several classes of phases: crystalline solid solutions, amorphous solid solutions, crystalline intermetallic compounds and quasicrystals. Many Al-Fe based systems are icosahedral phase formers, but non icosahedral phase was reported in Al-Ni based systems. The strong hetero-atomic interaction in the liquid of Al-based alloys appears to have a big effect on the amorphous forming ability. In order to analyse the amorphous forming ability and the amorphous structure of Al-Fe and Al-Ni based alloys, series of samples were produced by melt spinning. The structure was characterized by means of X-ray diffraction, Mössbauer spectroscopy and transmission electron microscopy. Clusters with medium range order in the Al-Fe based alloys were found and the icosahedral short range order in the amorphous structure is discussed. These alloys have a heterogeneous amorphous structure at nano-scale. The relationship among the different phases obtained by rapid solidification in the Al-Fe based systems is discussed considering the hetero-atomic interaction and the ability for clusters formation in the liquid.

1. INTRODUCTION Al-based alloys with very refined microstructures having great potential for technological applications have been developed in the last two decades. The technological interest in these Al-alloys arises from their low density and the ability to produce several kinds of microstructures with good combined properties. The Al-based systems give the possibility to obtain microstructures composed of different combinations of several classes of phases: crystalline solid solutions, amorphous solid solutions, crystalline intermetallic compounds and quasicrystals [1-3]. th Early in the 80 only few reports were published on fully amorphous Al-based alloys, but all of them reported brittle failure of those alloys. Meanwhile the advantage of the rapid solidification process for producing refined microstructures was used for elaborat301 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 301–312. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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ing the “nanocrystalline Al-based alloys” with high mechanical strength. The microstructure of those alloys basically consisted in a high volume fraction of small size intermetallics dispersoids embedded in a rich solute content Al matrix. Al-Fe and Al-Ni based alloys with different mechanical properties were developed [1, 4, 5]. In 1984, Shechtman et al. [6] published the first paper on a “quasicrystalline phase” in the Al-Mn system. Since that report many papers focused on the structure and properties of the quasicrystalline phases have been published [7]. In 1988, the first “ductile amorphous Al-based alloys” were reported by Shiflet et al. [8] in the Al-Fe-RE (RE: rare earth) systems and by Inoue et al. [9] in the Al-Ni-RE systems. Also, ductile amorphous alloys with high strength were produced in Al-FeETM systems (with ETM: Zr, V or Nb), [1, 5]. The existence of ductile amorphous Al-based alloys gave a great impulse for developing nanostructured alloys, particularly by crystallization process from an amorphous precursor. In this way, microstructures composed of D-Al nanograins embedded in an amorphous matrix can be produced [10]. These “nanostructured alloys with amorphous matrix” have up to 50% higher tensile strength than the precursor amorphous alloy [1], but they present a ductile-brittle transition related to the volume fraction of the D-Al nanograins [11]. During the crystallization process, whereas the DAl nanograins grow, the average chemical composition of the remaining amorphous matrix changes increasing the solute content which increase the mechanical strength [1, 11]. The resulting strength and the ductile-brittle transition have been explained, for the Al-Ni-Y system, by the simple rule of mixtures involving the strengthened amorphous matrix and the D-Al nanograins of ideal strength [11]. This kind of nanostructured alloys can be produced from the solid state easily controlled by means of heat treatments; however it has a limit temperature for application in order to avoid the ductile-brittle transition. Another class of nanostructured alloys are those called “nanoquasicrystalline alloys” which are composed of icosahedral particles embedded in a crystalline D-Al matrix [1]. This kind of microstructure is produced directly from the liquid state. The first report focused on the study of the microstructure and its properties could be that from Inoue et al. [12] in 1992 on Al-Mn-Ce system. This kind of alloys was developed also in Al-CrRE systems and more recently in the Al-Fe-Cr-ETM [3, 13, 14]. These alloys have metastable phases, while the alloys from the latter system have a good stability of the microstructure which allows to retain a high strength at temperatures ~350 C [13]. The “amorphous nanogranular Al-based alloys” are an intermediate class of nanostructured alloys between nanostructured alloys with amorphous matrix and nanoquasicrystalline alloys. These alloys have a microstructure composed of granules of an amorphous phase with 2 to 5 nm sized embedded in an D-Al matrix [1, 3]. Also these alloys are obtained directly from the liquid state, particularly in the Al-Fe-V and Al-FeTi systems [1]. It was suggested that the amorphous granules have an icosahedral short range order [1, 3], which could be explained as an initial stage of a nanoquasicrystalline alloy. It is known that the transition metals in the liquid Al produce a strong hetero-atomic interaction. This was earlier observed by Gebhardt et al. [15] in 1953 when they noted that low Fe concentration increase the viscosity of liquid Al. Maret et al. [16] have

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observed different structural arrangements in the local order in the liquid of Al80Ni20 (at.%) respect to that of the Al80Mn20 (at.%). Moreover, studies by neutron scattering on an icosahedral former alloy (Al-Mn-Pd) showed the icosahedral local order persists in the liquid state [17]. The Al-Fe based alloys are also icosahedral former, but no icosahedral phase is known in the Al-Ni based systems [7]. Therefore it is reasonable to think that the local order in the liquid state of both classes of systems is different and leads to different amorphous structures and, moreover, different classes of microstructures by rapid solidification processes. The knowledge of the atomic interaction and the cluster formation in the liquid state is very important for determining the phase selection in order to obtain a refined microstructure by rapid or moderate solidification processes. Changes in the chemical composition can lead to different local order, stabilize the undercooling liquid and decrease the growth of the icosahedral particles. The microstructure of these refined alloys is controlled basically by the nucleation process more than the growth process; therefore the study of the structure of the rapidly solidified samples allows us to get information of the atomic interaction and the clusters formation in the liquid state. In this work the structure of a group of rapidly solidified Al-based alloys studied by means of X-ray diffraction (XRD), Mössbauer spectroscopy and transmission electron microscopy (TEM) is analysed. The results are discussed considering the changes in the chemical composition of the alloys and the effect of the different components in local order of the liquid is proposed. 2. EXPERIMENTAL PROCEDURE Table I shows the code number and the chemical composition of the alloys selected for this study. Ingots as master alloys of each composition were prepared using pure elements: Al (99.99%), Fe (99.99%), Ni (99.99%), Sb (99.7%), Nb (99.7%) and Mischmetal (MM: solid solution of rare earth with 54 at.% of Ce). Table I. Alloy code and chemical composition of the alloy studied Alloy Code Fe-1 Fe-2 Nb-1 Nb-2 Nb-3 Sb-1

Alloy Composition (at.%) Al79Fe21 Al86Fe14 Al90Fe7Nb3 Al87Fe8Nb5 Al87Fe10Nb3 Al87Fe10Sb3

Alloy Code MM-1 MM-2 Ni-1 Ni-2 Cr-1

Alloy Composition (at.%) Al85Fe5MM10 Al90Fe5MM5 Al87Fe5Ni5Nb3 Al87Ni8.5MM3Nb1.5 Al93Fe4.2Cr2.8

Ingots of the binary Al-Fe alloys, with higher Fe content, were prepared in an arc furnace under Ar atmosphere. The other alloys were prepared in an induction furnace using a graphite crucible under Ar atmosphere. Rapidly solidified samples, with thickness of ~20 Pm, were produced by melt spinning technique using a Cu wheel and quartz nozzles with a BN coating. Structural characterization was carried out by means of XRD in a T-2T goniometer using Cu-KD radiation. The Al87Fe10Nb3 and Al87Fe8Nb5 melt-spun alloys were observed by TEM, the samples were prepared by electropolishing in 25 vol.% of nitric acid in methanol at –30qC. Also, Mössbauer spectra were recorded

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with a 57Co(Rh) source at room temperature in the transmission geometry. The spectra were fitted using the Normos program [18]. Lorentzian lines were used for fitting the ingot samples, and histograms distribution of the electric field gradient assuming the usual linear relationship between the isomer shift (IS) (relative to the D-Fe) and the quadrupole splitting (QS) [19] was used for fitting the melt-spun samples. The smoothing parameters for latter fitting were chosen to be as high as possible, and constrained to the lowest values of F2 and Hesse-Rübarsch parameters [20]. 3. RESULTS AND DISCUSSION 3.1

X-Ray Diffraction

Figure 1 shows the X-ray diffractograms of the melt-spun Al79Fe21 and Al86Fe14 samples and from the ingot of the Al79Fe21 alloy. The D-Al phase was identified in the ingots samples and in the as spun samples as well. The T-Al13Fe14 phase, clearly observed in the ingot samples, was also observed in the as spun Al79Fe21 sample. However, no clear peaks corresponding to the T-Al13Fe14 phase were identified in the diffractogram of the as spun Al86Fe14 sample. It is known that the monoclinic T-Al13Fe14 phase is a Mackaytype crystal which is easily twinned and distorted by rapid solidification as was reported for alloys close to the Al86Fe14 [21, 22]. Moreover, this phase is an approximant phase which contains periodic layers with local pseudo-five fold symmetry [23]. D- Al T- Al13Fe4 T D

Al86Fe14 As Spun

TD

T

Al79Fe21 T T T

T As Spun T

D

T T T T D TT Al79Fe21T T T T Ingot T T T T T TT T TTT T

10

20

30

40

2T

50

60

T

TD D

D

TD

TD D T TD

T 70

80

D

D- Al W- Al3Nb

C- AlSb *- Al3Ni i- Icosahedral Phase

C

D

C

Al87Fe10Sb3

C

90

C

* W *

10

20

W

WW

D

ii 30

40 2T 50

C

D

D

Al93Fe4.2Cr2.8 i

D

D

D

Al87Fe5Ni5Nb3

Figure 1. X-ray diffratograms of the Al-Fe

alloys

Melt Spun Intensity (a.u.)

Intensity (a.u.)

D

D

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W D

i

i 60

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Figure 2. X-ray diffractograms of the meltspun Al87Fe10Sb3, Al87Fe5Ni5Nb3 and the Al93Fe4.2Cr2.8 alloys

The Cr addition to the Al-Fe alloys enhances the icosahedral forming [14, 24] even at high Al content as can be seen in the X-ray diffractogram of the melt-spun Al93Fe4.2Cr2.8 sample, which shows peaks corresponding to the D-Al and the icosahedral phases (bottom level of Fig. 2). The X-ray diffractogram of the melt-spun Al87Fe10Sb3 sample showed the presence of the D-Al and the cubic-AlSb phases but no peak could be assigned to Al-Fe phases (top level of Fig.2). Similar results were observed previously for several alloy compositions in the Al-Fe-Sb system [25]. The Nb or MM addition to the Al-Fe alloys produces a glass forming region [1, 26]. The X-ray diffractograms of the melt-spun samples containing Nb or MM, selected in

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the present work, did not show sharp peaks, they had the feature of fully amorphous samples with a main broad peak, a weak secondary peak and particularly a small prepeak at ~20q in 2T (Fig. 3). The pre-peak is related to a strong chemical order as is inferred from the corresponding partial structure factor in the Bathia-Thorton formalism [27]. Moreover, the origin of the pre-peak in the Al-based alloys was related to a chemical order at medium range due to a strong hetero-atomic interaction [28, 29]. Therefore, the amorphous phase should be heterogeneous at a medium range order containing hetero-atomic clusters. This component of the structure factor is sensitive to the solute concentration and the scattering factor of the elements of the alloy. The scattering factor of the Fe atom doubles in respect to the Al one, and the corresponding to the Nb and RE atoms are also higher. Then if those alloying elements are forming clusters this should contribute to the increase in the area of the pre-peak in the diffractogram. The analysis of the (pre-peak area/main-peak area) ratio shows that this value increases when Fe or Nb content increases and when MM content decreases. This suggests that Fe and Nb atoms contribute to the increase in the volume fraction of clusters. However the rare earth elements, for an Fe/RE ratio higher than 1 are apparently dissolved in the regions with higher Al content in the amorphous phase.

Al85Fe5MM10

Intensity (a.u.)

Figure 3. X-ray diffractograms of the amorphous melt-spun samples, (Al-Fe-Nb and Al-Fe-MM alloys)

Al90Fe5MM5 Al90Fe7Nb3 Al87Fe10Nb3 Al87Fe8Nb5 Al87Ni8.5Nb1.5MM3

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The size of clusters (D) can be estimated by the Scherrer equation [30] applied to the pre-peak, also if the same equation is applied to the main-peak the correlation length (G) of the amorphous phase is obtained, which is related with the extension of the topological short range order of the amorphous structure. As can be seen in table II, the later parameter for the Al-Fe based alloys is as high as the characteristic of the amorphous phases with high grade of local order is [31]. The size of the hetero-atomic clusters increases with the Al content, up to 2 nm of cluster size for alloys with 90 at.% of Al (Table II). Table II. Estimated average values of the clusters size (D) and the correlations length (G) of the Al-Fe based amorphous samples Alloy (at.%) Al85Fe5MM10 Al90Fe5MM5 Al90Fe7Nb3 Al87Fe10Nb3 Al87Fe8Nb5

D (nm) ~1.1 ~2 ~2 ~1.5 ~1.2

G (nm) ~1.3 ~1.5 ~1.2 ~1.2 ~1.5

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The Al87Fe10Nb3 alloy is close to the centre of the glass forming region in the Al-rich corner of the Al-Fe-Nb system [26]. When half of the Fe content is substituted by Ni, the glass forming ability (GFA) is drastically reduced as can be seen in the X-ray diffractogram of the melt-spun sample (middle level in Fig. 2). The diffractogram of the Al87Fe5Ni5Nb3 alloy shows Bragg reflections from the D-Al, Al3Nb and Al3Ni phases, although no sharp peaks could be assigned to Al-Fe phases. However the melt-spun Al87Ni8.5MM3Nb1.5 sample resulted fully amorphous. The X-ray diffractogram of this amorphous sample does not show the pre-peak (bottom level in Fig. 3). The influence of the Nb and the MM on the GFA of the Al-Ni based alloys were previously studied [32] and also no pre-peak was observed on the amorphous samples. The lack of the pre-peak suggests that the corresponding amorphous phase does not contain clusters with a medium range order. 3.2. Mössbauer Spectroscopy

Relative Absortion (a.u.)

Relative Absrotion (a.u.)

The Mössbauer spectra from the ingots of the Al79Fe21 and the Al86Fe14 alloys showed the characteristic shape of the spectrum corresponding to the T-Al13Fe4 phase (Fig. 4a). These spectra are well fitted by a Lorentzian doublet (IS = 0.20 mmm/s, QS = 0.40 mm/s) and a Lorentzian single line with a IS = 0.20 mm/s. The effect of the rapid solidification on the local order around the Fe atoms in the Al79Fe21 and the Al86Fe14 alloys can be seen in the Mössbauer spectra showed in Fig. 4b and Fig. 5a respectively.

(a)

Ingot Al79Fe 21 -2.0

-1.5

-1.0

-0.5

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Figure 4. Mössbauer spectra of the Al79Fe21 alloy as ingot (a) and melt-spun alloy (b)

The melt-spun Al79Fe21 sample, which composition is near to the corresponding to the T-Al13Fe4 phase, showed a small disorder. The best fitting of the Mössbauer spectrum was achieved with an additional Lorentzian doublet (Fig. 4b). However the Mössbauer spectrum of the melt-spun Al86Fe14 sample have a different structure (Fig. 5a), like an asymmetrical doublet. Similar Mössbauer spectrum are also observed for amorphous and quasicrystalline phases in Al-based alloys [25, 33-35], which suggests that the rapid solidification on the Al86Fe14 alloy produced a higher disorder around of the Fe atoms, in agreement with the X-ray diffraction results (Fig. 1). The Mössbauer spectrum of the melt-spun Al86Fe14 sample was fitted using histograms distribution (Fig. 5b and 5c). In order to compare, the Mössbauer spectrum from the Al86Fe14 ingot sample, which is similar to that obtained for the Al79Fe21 ingot

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(Fig. 4a), was also fitted by histograms distribution and the corresponding QS and IS distributions were plotted together to those for the melt-spun sample (Fig. 5b and 5c respectively). The IS distribution for the ingot sample is observed to be very narrow and with an average value close to that corresponding to the T-Al13Fe4 phase, as was also obtained for the Al79Fe21 ingot sample (Fig. 4a). The IS distribution for the melt-spun sample is also very narrow, which means that all the Fe atoms in both ingot and meltspun samples have very similar chemical environment. The average IS value of the asspun sample is lightly lower than the ingot sample and can be related to a higher contribution of the Al atoms in the local order. The QS distribution for the ingot sample (Fig. 5b) shows two maximum (QS~0 and QS~40 mm/s) well defined as each one is a narrow individual distribution, which is in agreement with the fitting using Lorentzian lines. The values of both maximums in the QS distribution are the same of those obtained for the Al86Fe14 and Al79Fe21 ingot samples, that are the corresponding values of the T-Al13Fe4 phase using fitting by Lorentzian lines. This result shows the validity of the distribution fitting method used.

Figure 5. Mössbauer Spectrum (a) of the melt-spun Al86Fe14 sample and the corresponding QS (b) and IS (c) distributions, also is included the QS and IS distributions corresponding to the Al86Fe14 ingot sample (as cast)

The QS distribution for the Al86Fe14 melt-spun sample shows that the maximum at QS~0 was strongly reduced, which suggests that the highest ordered Fe site in the T-Al13Fe4 phase was topologically disordered by the rapid solidification process. Moreover it was observed that the QS distribution for both samples had a small shoulder at the higher QS side and a very small maximum at QS~0.85 mm/s, although the meltspun sample showed a smoother distribution. It is interesting to observe that the TAl13Fe4 phase have five icosahedral Fe sites, where two of then are very similar to each other [36]. Moreover a value of 0.19 mm/s for the IS was observed for a vapour deposited Al sample containing 10 at.% of Fe in solid solution [37]. Then, small topological differences among each Fe site in the T-Al13Fe4 and some Fe atoms dissolve in the Al solid solution can lead to a multimodal character of the QS distribution of the Al86Fe14 ingot sample. While the higher disorder in the environment of each Fe site produced by the rapid solidification can be the responsible for the broader and smoother QS distribution of the Al86Fe14 melt-spun sample (Fig. 5b).

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All the spectra from the melt-spun ternary samples show a doublet structure with broad lines (Fig. 6a), similar to that obtained for the melt-spun Al86Fe14 sample (Fig. 5a) and to those observed before for amorphous and quasicrystalline alloys as well [25, 3335]. This structure of the Mössbauer spectra suggests the existence of distributions, at least of the QS. Figures 6b and 6c show the corresponding QS and IS distributions.

Figure 6. Mössbauer spectra (a) of the melt-spun Al-Fe based samples and the corresponding QS (b) and IS (c) distributions

The IS distributions, obtained for the melt-spun ternary (and quaternary) alloys, are also narrow as was observed for the binary alloys, which indicates that all the Fe atoms in each alloy have similar chemical local environment. Consequently the QS values are related to the topological order around the Fe atoms. The QS distributions of the meltspun ternary (and quaternary) samples show a multimodal character (Fig. 6b). The Sb-1 alloy, which showed crystalline peaks in the X-ray diffractogram (Fig. 2), shows four maximums clearly determined, however the amorphous alloys have the smoother QS distribution. Multimodal QS distributions were found for quasicrystalline (icosahedral and decagonal) phases [34, 35]. Stadnik used two QS distributions for fitting the quasicrystalline alloys [34]. The multimodal character of the QS distribution suggests the existence of different “classes of Fe environments” [34], which should not be confused with Fe sites in a specific structure. A “class of Fe environment” is as a disordered Fe site with a distribution of the local order in the structure. This situation is reasonable to find in materials with several plastic deformation or produced by rapid solidification as was discussed above for the Al86Fe14 melt-spun sample (Fig. 5).

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The multimodal character of each QS distribution of the melt-spun Al-Fe based samples, containing Nb, RE, Sb or Cr, appear to be composed almost by four QS distribution components with average QS values around: 0-0.10, 0.35-0.42, 0.55-0.60 and 0.80-0.85 mm/s (Fig. 6b), which are close to those obtained for the melt-spun Al86Fe14 sample (Fig. 5b). It is interesting to note that the QS distribution of the Al-FeCr alloy (Cr-1) corresponds particularly to the icosahedral phase, in agreement with the phases observed by XRD (Fig. 2). Therefore the amorphous Al-Fe-X (X: Nb, RE) alloys appear to have the same classes of Fe environments that the icosahedral Al-Fe-Cr phase. Moreover, these classes of Fe environments should also be present in the melt-spun AlFe-Sb (Sb-1) and Al86Fe14 samples. Only the T-Al13Fe4 and the icosahedral Al-Fe phases have known an IS0.05 0.1

Width [mm] 5 1-5 1-5 5 1-5

Thickness [Pm] 40.0 49.5 33.2 75.0 31.2

Ductility/Brittlness Ductile Brittle Very Brittle Ductile Brittle

Figures 2 and 3 show the results of XRD and DSC measurements, respectively. As can be seen, all the ribbons were amorphous, except the alloy V (Al75Mm15Ni10), where sharp peaks corresponding to crystalline phases are visible. This result corresponds well to DSC measurements where no crystallization process was observed (only straight horizontal line – not shown in Fig. 3 – was recorded). These results indicate that the ribbons of the alloy V are completely crystalline. As can be seen from Fig. 1, the composition of alloy V is very close to the boarder of glass forming region. The crystallization process of the alloys studied varies for different alloy compositions. In the case of the first alloy three overlapping crystallization stages occur. In the alloy II two overlapping stages are visible. The increase of Ni content (alloy III) results in only one crystallization stage. It can be concluded that with the increase of nickel content the crystallization process becomes less complicated. The onset of the crystallization temperature Tx and the temperature of the first crystallization peak T1 increases with the increase of nickel content (Fig. 3 and Table V). It means that nickel

Bulk Amorphous Samples from Al-Mm-Ni System

Figure 2. XRD patterns of melt-spun ribbons

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Figure 3. DSC curves of the melt-spun ribbons (alloy no. V not shown)

Table V. The onset temperature Tx and the temperature of the first crystallization peak T1 Alloy no. I II III IV

Alloy composition Al85Mm10Ni5 Al80Mm10Ni10 Al75Mm10Ni15 Al85Mm5Ni10

Tx [K] 570 635 675 550

T1 [K] 585 658 705 557

stabilizes the amorphous structure of the alloys studied. There is also correlation between brittleness of the investigated ribbons and their composition. Lower ductility corresponds to lower aluminum content in the alloys. 3.2. Powders After the milling of the ribbons, XRD and DSC measurements were carried out. These results are shown in Figs. 4 and 5. X-ray diffraction results show that no structural changes occurred during the milling process. Moreover, either no changes or only very small differences are observed between DSC curves representing powders. This means that the materials studied are energetically stable enough and they do not change their structure during the milling process. 3.3. Bulk samples Bulk samples obtained by controlled consolidation of appropriate powders were again studied with XRD and DSC measurements and the results obtained are shown in

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dT/dt = 40 K/min

Alloy I powder Alloy I ribbon

Exothermal [a.u./g]

Alloy I ribbon Alloy I powder

Intensity [a.u.]

Alloy II ribbon Alloy II powder

Alloy III ribbon Alloy III powder

Alloy II powder Alloy II ribbon

Alloy III powder Alloy III ribbon

Alloy IV ribbon Alloy IV powder

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Figure 4. XRD patterns of the ribbons before and after milling (alloys I to IV)

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Alloy IV powder Alloy IV ribbon

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800

Temperature [K]

Figure 5. DSC curves of the ribbons before and after milling (alloys I to IV)

Figs 6 and 7, respectively. As it was mentioned in the experimental part, the exposition surface of the bulk samples was much smaller comparing to the ribbon and powder samples, presented in Figs. 2 and 4. This explains the unusual shape of the XRD patterns presented in Fig. 6. However, the results give some information about the structure of the material. It is seen that after compaction, no crystalline phases occur. All the materials, after compaction at elevated temperature, continue to be amorphous. Only in the case of alloy III, consolidated at temperature above the first crystallization peak, an admixture of the crystalline phases was detected, and manifests itself as sharp peaks in XRD patterns shown in Fig. 8. The crystallization process of the alloys studied is relatively complicated. This is mainly caused by a precipitation of metastable phases, not existing in the crystallographic phase diagrams. The DSC curves shown in Fig. 7, give almost no information about the decomposition of the amorphous phase. The structure of the bulk samples, compacted at temperatures above the first crystallization stage depends on the pressure, which is shown in XRD patterns (Fig. 8). The compaction at a lower pressure (2.5 GPa) leads to the precipitation of some crystalline phases (Fig. 8c). The same effect was observed for alloys from the Al-Mm-Ni-Fe system [8]. For samples compacted at 7.7 GPa another peak in XRD pattern is observed (Fig. 8b) indicating that at this temperature and pressure another phase can precipitate.

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dT/dt=40K/min

Exothermal [a.u./g]

Aloy I - Al85Mm10Ni5 T = 523 K

Intensity (a.u.)

Alloy II - Al80Mm10Ni10 T = 573 K

Alloy III - Al75Mm10Ni15 T = 623 K

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Alloy I bulk Alloy I powder Alloy I ribbon

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Alloy II bulk Alloy II powder Alloy II ribbon

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Alloy III bulk Alloy III powder Alloy III ribbon

Alloy IV - Al85Mm5Ni10 T = 523 K

Alloy IV bulk Alloy IV powder Alloy IV ribbon 523 K

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Figure 6. XRD patterns of the bulk samples consolidated at temperatures T

Figure 7. DSC curves of the alloys studied after each stage (ribbons, powder, bulk material). The arrows indicate temperatures of consolidation

c Alloy III

2.5GPa, 723K, 2' HV0.1= 632

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Al100-xMm10Nix

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Figure 8. XRD patterns of alloy III (Al75Mm10Ni15) consolidated in several conditions (shown in the graphs)

5

10 NI, x [at.%]

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Figure 9. Microhardness of bulk samples vs. nickel content

Finally, Vicker’s microhardness, as a mechanical parameter, was measured and the results are presented in Fig. 9. The relationship between the amount of nickel in the alloy and its hardness is clearly seen. The value of the microhardness is changing from about 400 for 5 at.% of Ni to more then 500 for the alloy containing 15 at.% of

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nickel. It should be noticed, however, that the alloy containing 15 at.% of Ni (alloy III) after partial crystallization (see Fig. 8c) exhibits the microhardness as high as 632. On the other hand, the microhardness of bulk materials corresponds to the brittleness of the ribbons (see Fig. 9 and Table IV). The density of bulk samples was also measured. The results show an increase in the density with the increase in the nickel and mischmetal content in the investigated alloys. This is probably because those two elements exhibit much higher densities than aluminum (Ni – 8.9 g/cm3, Mm – 6.49 g/cm3, Al – 2.8 g/cm3). The densities are: 3.8, 3.8, 4.0, 3.5 g/cm3 for alloys: I – Al85Mm10Ni5, II – Al80Mm10Ni10, III – Al75Mm10Ni15, IV – Al85Mm5Ni10, respectively. It is worth to noticing that even an alloy with a large amount of nickel, characterized by good mechanical properties, exhibits density only a little bigger than the density of pure aluminum (2.8 g/cm3). 4. CONCLUSIONS This work proved that bulk amorphous materials can be produced using a three-step technique (melt spinning, milling and compaction). The results obtained show that it is possible to mill the ribbons and consolidate the powder without losing the amorphous structure of the material. It was observed that an application of higher pressure during the compaction process, results in better compaction of bulk samples. At the same time higher pressure (7.7 GPa) enables to preserve the amorphous structure of bulk samples. It can be concluded that high pressure shifts the onset of the crystallization to higher temperatures. These studies have also shown the dependence between the hardness of the bulk materials and their structure. By choosing appropriate conditions during compaction (time and pressure) we may cause some crystalline phases precipitate enhancing the hardness even by up to about 20%. The evident influence of the nickel content in the alloy on its hardness was observed. A higher amount of nickel increases the brittleness of the initial amorphous ribbons but results in the enhanced hardness of the bulk amorphous samples. ACKNOWLEDGEMENTS The financial support from the Polish Committee of Scientific Research under project KBN No. PBZ/KBN/13/T08/99/21 is gratefully acknowledged. The authors also would like to thank TREIBACHER AUERMET Produktionsgesellschaft mbH for the supply of Mischmetal. REFERENCES [1] Inoue, A., (1998) Prog. Mater. Sci. 43, 365-520. [2] Zhong, Z.C., Jiang, X.Y., and Greer, A.L., (1997) Mater. Sci. Eng. A 226-228, 531. [3] Zhong, Z.C., Jiang, X.Y., and Greer, A.L., (1997) Mater. Sci. Eng. A 226-228, 789. [4] Ohtera, K., Inoue, A., Tarabayashi, T., Nagahama, H. and Masumoto, T., (1992) Mater.Trans. JIM, 33, 775. [5] Kawamura, Y., Inoue, A., and Masumoto, T., (1993) Scr. Metall. 29, 25. [6] Latuch, J., Kokoszkiewicz, A., and Matyja, H., (1998) Mater. Sci. Forum. 269-272, 755. [7] Latuch, J., Dimitrov, H., Audebert, F., and Kulik, T., (2003), Solid State Phenom. 94, 71. [8] Dimitrov, H., Blazquez, J.S., Latuch, J., and Kulik, T., (submitted to Acta Materialia).

Al-BASED AMORPHOUS ALLOYS AT THE LIMIT OF GLASS FORMING ABILITY E. FAZAKASa, b, L.K. VARGAa, and T. KULIKb a Research Institute for Solid State Physics and Optics of the Hungary Academy of Science 1525 Budapest, P.O.B. 49, Hungary b Faculty of Material Science, Warsaw University of Technology Woáoska 141, 02-507 Warsaw, Poland

Corresponding author: L.K. Varga, e-mail: [email protected] Abstract:

New Al based amorphous alloy compositions Al90Ni8Fe1Ce1, Al92Ni4Ce4, Al90Ni4Ce6, Al85Ni5Co2Y8 and Al85Ni5Co2Ce8 are reported at the edge of glass forming ability (GFA). Some of them, with the highest possible Al content are two-phased materials (Al nanocrystals and a residual amorphous phase) already in the as-cast state. Nevertheless, their crystallization characteristics resemble to those of fully amorphous samples. The characteristics of crystallization were determined by DSC and DTA and the structural properties of the nano- and of the fully-crystallized states were studied by XRD and SEM. Besides the usual kinetic characteristics ('H, Ea, Avrami exponent, etc.) the long term thermal stability was also studied using the DSC data and was compared with that of other Al amorphous alloys reported in the literature.

1. INTRODUCTION Ternary Al-based nanophase composites consisting of primary nanocrystallites dispersed in a residual amorphous matrix exhibit good thermal stability [1] and remarkable mechanical properties [2]. In general, their composition is of Al-TM(Ni, Co, Fe)RE(Y, Ce, Mm) type with more than 85 at.% of Al. Alloys with at least 85-90 at.% of Al can be prepared in a completely amorphous state and the primary crystallization of these ternary alloys has been studied extensively as it is a controllable method for production of nano-granular structures [3-5]. Alloys with the highest Al content (above 90 at.% Al) are marginal glass formers and nanosized D-Al grains embedded in an amorphous matrix appear in the as-cast state already during the rapid solidification processes. Avoiding the simultaneous precipitation of Al based compound phases (like Al3Ni, Al3Ce11 etc.) is necessary in both methods, to maintain the good mechanical properties. Above a certain concentration of the glass forming RE element (e.g. x > 3 at.% Ce in Al90–xNi10Cex [6]) the formation of a nano-Al 321 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 321–329. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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composite is no more possible due to the co-precipitation of relatively large (about 1050 nm) compound phases together with the nano-Al crystallites. The purpose of this paper is to study new Al based alloy compositions at the edge of glass forming ability (GFA) from the point of view of producing nanophase composites. Some of the selected compositions (Al90Ni8Fe1Ce1, Al92Ni4Ce4) proved to be nanocrystalline already in the as cast state. Nevertheless, the kinetics analysis of the crystallization behaviour of the residual amorphous phase gives an insight into the origin of the dispersed nanocrystal and amorphous matrix microstructures, and also provides effective assessment of the overall stability that is essential for microstructure control and further applications in a compact form. Some other compositions proved to be amorphous in as-cast state (Al90Ni4Ce6, Al85Ni5Co2Ce8 and Al85Ni5Co2Y8) with wellseparated crystallization stages and the nanocrystallized state was achieved by annealing below the first crystallization peak. 2. EXPERIMENTAL Al90Ni8Fe1Ce1, Al92Ni4Ce4, Al90Ni4Ce6, Al85Ni5Co2Y8, and Al85Ni5Co2Ce8 ingots were prepared by inductive-melting of a mixture of pure (99.99 wt.%) Al, Ni Fe, Ce, and Y. Rapidly quenched ribbon samples were prepared by melt spinning technique using a Cu-wheel (150 mm diameter) rotating at a peripheral velocity of 34 m/s (the same for all ribbons) in inert atmosphere. The ribbons were 4 mm wide and about 20-25 Pm thick. Perkin Elmer DSC-7 differential scanning calorimeter was used to investigate the structural transformations by linear heating up to 823 K. Continuous heating experiments were performed at scanning rates in the range of 2.5-80 K/min (see the results in Table II). Each measurement was immediately followed by a second run under the same conditions in order to determine the calorimetric baseline. From the change of the DSC signal as a function of the heating rate, the activation energy of the phase transformations was determined using the Gao-Wang analysis. Both the average and the local Avrami exponents have been determined. On the quaternary amorphous samples, isothermal calorimetric analyses were also performed. All the calorimetric measurements were carried out in argon (99.999% purity) flux. Graphite sample pans were used. The temperature and the energy release were calibrated using pure K2CrO4 and Zn. X-ray diffraction (XRD) patterns were measured on a Philips powder diffractometer in T-2T geometry using Cu-KĮ radiation with a graphite monochromator at the diffracted beam side. The step width was 0.01° in the range of 25-90°. 3. RESULTS AND DISCUSSION XRD were used to characterize the as-cast state (see Fig. 1). Samples with the highest Al content proved to be partially crystallized with nano-Al precipitates and those with high RE content proved to be fully amorphous. Besides the average kinetic parameters determined from the DSC peak positions, the “local” dependent kinetic parameters, i.e. the transformed fraction, x, were also

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Figure 1. XRD patterns of some amorphous samples and samples with nanoAl grains placed in amorphous matrix

determined. We present here two less frequently calculated “local” parameters, the local activation energy (E(x)) and the local Avrami exponent n(x) or morphology factor as they can be determined from non-isothermal DSC measurements. 4. LOCAL ACTIVATION ENERGY In order to deduce a formula to calculate the local activation energy one has to express the transformation rate dx/dt as a function of the already transformed fraction, x, and the temperature T only. This can be obtained from the usual Johnson–Mehl-Avrami (JMA) Eq. [6] written in a differential form: dx/dt = (1 – x)K(T) (t – t0)n ,

(1)

where t0 is the incubation time, n is the Avrami exponent and K(T) is the Arrhenius part of the transformation rate: KT = K0 exp(–E/kT),

(2)

where K0 is a constant, E is the apparent activation energy for the process. Taking into account that (t – t0) can be expressed uniquely as a function of x, the transformation rate (proportional to the heat evolution during the DSC measurement) can be written as dx/dt = Cf(x)exp(–E/kT),

(3)

where C is a constant, E is the local activation energy depending on x, k is the Boltzmann constant, x is the amount of transformed fraction up to temperature T. In logarithmic form: ln(dx/dt) = lnCf(x) –E/kT.

(4)

The functions E(x) and f (x) are not known but they can be determined from systematic measurements as a function of the heating rate: a given x is attained at different Ti temperatures for different Ei heating rates. Representing ln(dx/dt)i as a function of 1/Ti, the slope will give the local E(x) activation energy. In fact, this method can be considered as an extension of the Gao-Wang method for arbitrary x.

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Figure 2. Local activation energy vs. crystallization fraction

Figure 2 shows the experimentally determined local activation energies as a function of x for precipitation of nano-Al in a primary crystallization process. The corresponding average activation energies are collected in Table I. It can be observed that the local activation energies are in general decreasing with the evolution of nanocrystallization, except the case of Al85Y8Ni5Co2 sample where no overlapping of the first and second stages of crystallization can be observed.

5. LOCAL AVRAMI EXPONENT n(x) Taking the integral form of JMA equation, the crystallization kinetics of amorphous alloys is normally modelled by: x = 1 – exp[KT(t – t0)n].

(5)

The concept of the local Avrami exponent has been recently developed for isothermal measurements [7] and defined as: n(x) = G ln[–ln(1 – x)] / G ln(t – t0) .

(6)

The value of the local Avrami exponent (morphology index) n(x) gives information about the nucleation and growth behaviour when the crystallized volume fraction is x. In order to apply Eq. (6) for non-isothermal measurements as well, we must rewrite the temperature dependence x(T) obtained by non-isothermal DSC measurements in time dependence x(t) using t = T/E, and t0 = T 0 /E, where E is the scanning rate in K/s. This quasi-isothermal approximation (around the peak temperature) of a temperature scan experiment can be justified by the fact that the width of the transformation peak is negligible compared to the crystallization temperature expressed in K (about 5%). The values of the local Avrami exponent n(x) are presented in Fig. 3. and Table I. In Table I some isothermal Avrami exponent data shown also determined for x between 0.2 and 0.8. Isothermal measurements were carried out on some selected samples only, which were amorphous in as cast state (Al85Y8Ni5Co2 and Al85Ce8Ni5Co2).

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Table I. Kinetic parameters obtained from non-isothermal (Eni, nni) and isothermal (Ei, ni) analysis nni ±0.1 Gao-Wang 3

Eni ±0.2 (eV) Gao-Wang

Alloy Al90Ni8Fe1Ce1

1.6

Al92Ni4Ce4

1.85

Al90Ni4Ce6

ni ±0.5

Ei ± 0.6 (eV) –

–

0.8

–

–

1.3

0.84

–

–

Al85Y8Ni5Co2

1.85

1.2

4.7

1.9

Al85Ce8Ni5Co2

1.95

2.3

4.2

1.5

Figure 3. The local Avrami exponent as a function of the crystallized fraction

Table II. Crystallization parameters obtained from non-isothermal measurements (E = 10 K/min) Alloy

TP1 (K)

TP2 (K)

TP3 (K)

Al90Ni8Fe1Ce1

577

Al92Ni4Ce4

610

654

–

Al90Ni4Ce6

471

618

–

Al85Y8Ni5Co2

561

603

656

Al85Ce8Ni5Co2

–

572

592

'H1 (J/g) ±5 77

'H2 (J/g) ±5

'H3 (J/g) ±5 –

16

29 46

48

89 47

86

53 41

An Avrami exponent n t 2.5 would indicate that the transformation process could be taking place by the continuous nucleation and a three-dimensional diffusion-controlled parabolic growth. Such a large Avrami exponent can be observed only around the peak position (x ~ 0.5) for samples with partial crystallized as cast state (Al90Ni8Fe1Ce1) and for samples with the overlapping first and second crystallization stages (Al85Ce8Ni5Co2). Samples with well separated first and second stages where true nano Al-residual amorphous composite can be realized (Al85Y8Ni5Co2) show small a Avrami exponent, around 1, which denotes the domination of nucleation over the grain growth.

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6. LONG TERM-THERMAL STABILITY Studying the Kissinger expression [8] for determining the activation energy, one can notice that this method has a significant corollary, i.e. linearity of the (lnE/Tp2) vs. (1/Tp) plot which allows creation of the continuous heating transformation (CHT) diagrams at different heating rates using the linear fit of the Kissinger plot, i.e.,

ln

E T p2

§ 1 b¨ ¨ Tp ©

· ¸  c, ¸ ¹

(7)

where b (which is equal to –E/R) and c are the slope and the intercept constants, respectively. Thus, for any peak temperature Tp the corresponding E will be given as

E

T p2 ˜ e

b (1 / T p )  c

(8)

The heating time (th) can be then calculated by (Tp – 298)/E (considering that the heating starts from the room temperature) and the Tp vs. th diagrams can be determined from the experimentally determined b and c values [9]. From such a diagram (Fig. 4) the long time thermal stability can be inferred from the interception point of a constant temperature line on the Tp vs. th) curves.

Figure 4. Temperature-time diagram to determine the long-term stability

Comparing the long thermal stability of different compositions it turns out that some partial crystallized samples (Al92Ni4Ce4) can be more stable owing to the fact that the residual amorphous phase is more stable than the fully amorphous as-cast state (Al85Y8Ni5Co2). This is important taking into account the fact that the residual amorphous phase contains more of glass-forming elements than the as cast fully amorphous phase. 7. GLASS FORMING ABILITY

In order to evaluate the GFA of the studied alloys, the size-effect criterion was applied using the equation derived by Egami and Waseda [10]:

Al-Based Amorphous Alloys at the Limit of Glass Forming Ability

O

CB

§ R 1  ¨¨ B © RA

· ¸ ¸ ¹

3

 CC

327

§ R 1  ¨¨ C © RA

· ¸ ¸ ¹

3

,

(9)

where C is the concentration in the atomic fraction and R is the atomic radius. The subscript A refers to the matrix (in our case Al) while B (e.g. Ni), C (e.g. Y, Ce), D (e.g. Fe, Co) to the solute components. The minimum solute concentration required to form an amorphous phase is given by the criterion: O | 0.1. Using the metallic atomic radii, RAl = 144.5 pm, RNi = 124.6 pm, RCe = 182.5 pm, RY = 180.1 pm, RMm = 183.8 pm, RCo = 125.2 pm, RFe = 127.4 pm, one can determine the value of O for all the compositions. These calculated O values are summarized in Table III. The effective radii in the amorphous state, however differ from the metallic radii as it can be estimated from the extended X-ray absorption fine structure (EXAFS) measurements [11] and consequently the posterior calculated O values differ as well. In the Al-Fe-Ce system a dramatically reduced radius for Fe (Reff ( Fe) = 75 pm) and an increased radius for Al (Reff ( Al) = 172 pm) were determined in the amorphous state. The observed changes have been attributed to the transfer of electrons with s-p character of the Al atoms to the d states of the Fe atoms [12]. Nevertheless, the a-priori estimation based on the metallic radii is a useful guide to GFA. Table III. The GFA parameter, O, calculated according to Eq. (9) Alloy

O (using metallic radii)

Al90Ni8Fe1Ce1

0.042

Al92Ni4Ce4

0.055

Al90Ni4Ce6

0.075

Al85Y8Ni5Co2

0.1

Al85Ce8Ni5Co2

0.108

In accordance with the experimental situation, samples with the highest Al content proved to be partially nanocrystalline in as-cast state, while those with 85 at.% of Al proved to be amorphous. For some compositions with a large content of glass forming elements (Al85Y8Ni5Co2 and Al85Ce8Ni5Co2), endothermic glass transition can be observed before the crystallization onset. Such a sample is a good candidate for being prepared in a bulk amorphous state. In terms of thermal properties, the bulk glass forming ability (BGFA) is measured by the width of the supercooled liquid region ('T = Tx – Tg) between the crystallization temperature (Tx) and the glass transition temperature (Tg) and by the reduced glass transition temperature, Trg = Tg /Tm. Lu and Liu [13] have introduced a new reduced transition temperature, Tx/(Tg + Tm), where Tm is the melting temperature, which seems to be more relevant than Trg. When no Tg can be detected, Tg can be replaced by Tx in the new reduced transition temperature formula. We propose here

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a small modification of Tx/(Tx + Tm) formula, multiplying by two one can observe that the new reference temperature for Tx will be the arithmetic average of Tx and Tm. The results are summarized in Table IV and V. Table IV. Glass transition (Tg), crystallization (Tx) and melting (Tm) temperatures Alloy

Tg (K)

Tx1 (K)

Tx2 (K)

Al90Ni8Fe1Ce1

–

588

–

Al92Ni4Ce4

–

616

674

Al90Ni4Ce6

–

471

Al85Y8Ni5Co2

556

Al85Ce8Ni5Co2

566

Tx3 (K)

Tm1 (K)

Tm2 (K)

910

1034

–

913

–

618

–

914

–

563

607

679

919

–

572

–

–

909

1072

Table V. Reduced crystallization and glass transition temperatures Alloy Al90Ni8Fe1Ce1 Al92Ni4Ce4 Al90Ni4Ce6 Al85Y8Ni5Co2 Al85Ce8Ni5Co2

2Tx1/(Tx1 + Tm1) 0.79 0.81 0.68 0.76 0.77

2Tg/(Tx1 + Tm1) – – 0.75 0.76

Basing on the collected results of a variety of bulk amorphous alloys published by Lu and Liu [13] we have deduced an empirical correlation between 'T and this new reduced temperature 2 Tx/(Tx + Tm) obtaining zero 'T for 2 Tx/(Tx + Tm) = 2/3, which is equivalent to conclude that alloys with Tx > Tm/2 will form bulk amorphous state. For partially crystalline samples in the as cast state such criteria may be misleading; the apparently high Tx1 denotes the stability of residual amorphous phase and has nothing to do with the BGFA. Nevertheless, the relatively high Tx1 of the residual amorphous phase in as cast partially crystallized samples helps compaction at high temperatures (but below Tx) needed for preparation of nanophase composites. 8. CONCLUSIONS New kinetic parameters have been presented to characterize and to promote the preparation of nano-Al/residual amorphous composite materials from Al based amorphous precursor alloys with the highest Al content, above 85 at.%. Local activation energies and Avrami exponents have been determined from non-isotherm DSC data together with a T-t diagram extractable from the Kissinger plot. The Egami criteria proved to be useful for predicting the GFA. The collected data for the bulk glass forming ability of Lu and Liu could be extended for the Al based alloys as well, introducing a simplified criteria for the BGFA, namely Tx1 > Tm1/2 is necessary to observe the glass transition temperature in a usual DSC scan.

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ACKNOWLEDGEMENTS The authors are grateful for the financial supports from EU “Nano-Al” Research Training Network project HPRN-CT-2000-00038 and from the Hungarian Fund OTKA project T034666. REFERENCES 1. 2. 3. 4. 5. 6.

7.

8. 9. 10. 11.

12. 13.

A. Inoue (1998), Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Progress in Materials Science 43, 365-520. T.G. Nieh and J. Wadsworth (1991), High strain-rate superplasticity in Al matrix composites, Mater. Sci. Eng. A 147, 129-142. V. Kwong, Y.C. Koo, J. Thorpe, and T. Aust (1991), Crystallization behaviour of Al85Y10Ni5 by isochronal and isothermal annealing, Acta Metall. Mater. 39, 1563-1570. M. Gogebakan, P.J. Warren, and B. Cantor (1997), Crystallization behaviour of amorphous Al85Y11Ni4, Mat. Sci. Eng., A 226-228, 168-172. W.T. Kim. M. Gogebakan, and B. Cantor (1997), Heat treatment of amorphous Al85Y5Ni10 and Al85Y10Ni5, Mat. Sci. Eng. A 226-228, 178-182. M. Avrami, J. Chem. Phys., (1941) Kinetics of Phase Change I., General theory, 7, 1103-1112. (1941) Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei, 8, 212-224; (1941) Granulation, Phase Change and Microstructure, Kinetics of Phase Change III, 9, 177-184. A. Calka and A.P. Radlinski (1985), Decoupled bulk and surface crystallization in Pd85Si15 glassy metallic alloys: Description of isothermal crystallization by a local value of the Avrami exponent, J. Mater. Res. 3, 59-66. H.E. Kissinger (1957), Reaction Kinetics in Differential Thermal analysis, Analitical Chemistry 29, 1702-1706. D.V. Louzguine and A. Inoue (2002), Comparison of the long-thermal stability of various metallic glasses under continuous heating, Scripta Mater. 47, 887-891. T. Egami (1984), Universal criterion for metallic glass formation, Mat. Sci. Eng., A 226228, 261-267. A.N. Mansour, C.-P. Wong, and R.A. Brizzolara (1994), Atomic stucture of amorphous Al100-2xCoxCex (x = 8, 9 and 10) and Al80Fe10Ce10 alloys: An EXAFS study, Phys. Rev. B 50, 12401-12412. H. Y. Hsieh, B. H. Toby, T. Egami, Y. He, S. J. Poon, and G. J. Shiflet (1990) Atomic structure of amorphous Al90FexCe10-x, J. Mater. Res. 5, 2807-2812. Z.P. Lu and C.T. Liu (2002), A new glass-forming ability criterion for bulk metallic glasses, Acta Materialia, 50, 3501-3512.

MAGNETIC SOFTENING OF METALLIC GLASSES BY CURRENT ANNEALING TECHNIQUE N. MITROVICa, S. ROTHb, S. DJUKICa, and J. ECKERTb a Joint Laboratory for Advanced Materials of Serbian Academy of Science and Arts Section for Amorphous Systems Technical Faculty ýaþak, Svetog Save 65, 32000 ýaþak, Serbia b Leibniz-Institute of Solid State and Materials Research Dresden Institute of Metallic Materials P.O. Box 270016, D-01171 Dresden, Germany Corresponding author: M. Mitrovic, e-mail: [email protected]

Abstract: The current annealing (CA) method used for magnetic softening of amorphous alloys is observed by estimation of annealing temperature based on on-line infrared radiation and electrical resistivity measurements. Multi-step CA treatments were performed on FINEMET-type alloys as well as on novel Fe-based amorphous alloys with a large supercooled liquid region in order to attain different degrees of relaxation or nanocrystallization. Recent results on improvement of magnetoresistance and magnetoimpedance effects by applying this technique in ribbon and wire shaped samples are reviewed.

1. INTRODUCTION In the last decade alternative annealing techniques have been a subject of increasing attention due to exploring their usefulness for improvement of the magnetic properties of ferromagnetic metallic glasses. The very high sensitivity of excellent soft magnetic behaviour on grain size of nanocrystalline alloys obtained from amorphous precursors [1] underlines the importance of optimization of the annealing parameters. The current annealing (CA) technique is especially interesting as thermo-magnetic sample annealing of two the simultaneous effects: Joule heating and a magnetic field induced by the current [2]. Moreover, FINEMET-type alloy samples are characterized by some brittleness even in the as-cast state, thus limiting their practical application. Some attempts to overcome this problem were based on the precipitation of nanocrystalline phases by dc Joule heating of amorphous ribbons [3]. 331 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 331–344. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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Nowadays, there is a variety of methods to apply this technique: (i) single treatment with different current intensities and pulse duration [3, 4]; (ii) multi-step treatments with successive increase in current intensity with [5, 6] or without cooling [7] between the steps; (iii) application of high frequency currents [8]. However, apart from the method applied, the main problem in practice is the difficulty in estimating of the sample temperature [9, 10] as well as its (in)homogeneity throughout the specimen [11]. In this study we present our recent results on the magnetic softening of FINEMET-type alloys as well as novel Fe-based amorphous alloys with a large supercooled liquid region. Multi-step CA treatments were performed on ribbon and wire shaped samples in order to attain different degrees of relaxation and nanocrystallization [5, 12, 13]. An experimental method for determining the temperature of CA ribbons characterized by measuring the spectral response of a PbS detector on infrared radiation emitted during the treatment is compared with a method based on the on-line following of the electrical resistivity [9]. The evolution of soft magnetic properties obtained by controlled crystallization is investigated by X-ray diffraction (XRD), differential scanning calorimetry (DSC), hysteresis, magnetization, magnetoresistance and magnetoimpedance measurement. 2. ESTIMATION OF THE SAMPLE TEMPERATURE In experimental work, sample temperatures are estimated by monitoring the temperature dependence of chosen physical properties (usually magnetization M(T) [14] or electrical resistance R(T) [15]) and changes of these properties during the flow of different currents through the sample (M(I) or R(I)). The dependence T(I) is derived by comparing the values of these physical properties. In Fig. 1a the furnace annealed (FA) R(T)/R(300 K) curve of Fe73.5CuxNb3Si14.5xB9 (x = 1.5) and the M(T)/M(300 K) curve for the same system (x = 1) presented by Kataoka et al. [16] are given. The different crystallization steps can be clearly seen for both curves. Good agreement between these two curves can be seen for the region of Curie temperature TC (I) and the region of the onset of the crystallization process TX1 (II).

Figure 1. a) Temperature dependence of M(T)/M(300 K) (x = 1) [15] and R(T)/R(300 K) (x = 1.5) (FA) for Fe73.5CuxNb3Si14.5–xB9 amorphous ribbons, and b) comparison of estimated sample temperature vs. annealing current made by the first two methods (light symbols resistance data, black symbols theoretical model) for Fe73.5Cu1.5Nb3Si13B9 and Fe72Cu1V5Si14B8 alloys [5]

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In our experiments, the final temperature during the Joule heating was determined by three methods: (i) Using the temperature dependence of the relative electrical resistance R(T)/R(300 K), thus avoiding extrapolation for T > TC, which would be required if the magnetizationtemperature M(T) dependence were used. (ii) Solving the transcendent equation in the theoretical model proposed by Barandiaran et al. [10], for details see [5]. The disagreement of the values obtained by resistance data and theoretical model is about 10 K (Fig. 1b). (iii) Measuring the spectral response of a PbS detector on infrared radiation (IR) of the sample emitted during dc CA. A spectroradiometer SR-5000 was used. The principal scheme is given in Fig. 2. The calibration source of infra-red radiation (black body) was placed at a distance of lSC = 3 m (Fig. 2a); the optical system was focused on the central region of the sample in order to avoid the region of inhomogeneous temperature distribution (about a tenth of the length taken from both ends of the sample [17]) as it is shown in Fig. 2b.

Figure 2. a) Calibration of the spectroradiometer, and b) measuring the spectral response of the radiation of a source at an unknown temperature (ribbon sample) [9]

The unknown temperature of the CA sample TAN can be determined from the equation: O2

³

O1

O2

H O , T AN ˜ P O , T AN ˜ dO

U AN ( O ) S SC ˜ ˜ P O , TSC ˜ dO SC ( O ) S AN

³U

O1

ª W º « sr ˜ cm 2 » ¼ ¬

(1)

where: H (O,TAN) is the spectral emissivity (we used H | 1), P(O, TSC) is Planck’s function, USC(O) is the spectral response of the detector to a black body, UAN (O) is the spectral response of the detector to the ribbon during annealing, SAN is the active area of the sample, and SSC is the active area of the black body. Figure 3 shows the functions

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USC(O) and UAN(O) during the experiments on Fe75Ni2Si8B13C2 amorphous ribbons. The value on the right side of the Eq. 1 (:-radiance, i.e. radiation flux per unit solid angle per unit area) can be determined basing on the experimental data and using numerical methods for calculating a definite integral [18]. Finally, the sample temperature is calculated using an iterative procedure, where the iteration step 'TAN changes until the required accuracy r5 K is reached.

Figure 3. Spectral responses of the detector to a black body (USC) and to a ribbon sample (UAN) at the start of the annealing procedure [9]

Figure 4. Ia) Radiance during annealing of a sample of amorphous ribbon, and Ib) change of the relative electrical resistivity of a Fe75Ni2Si8B13C2 amorphous ribbon during CA (34 A/mm2). II) Temperatures of the sample during CA determined by: a) spectroradiometric measurements, and b) using curves R(t)/R(0) and R(T)/R(300 K) [9]

This method was combined with the comparative method based on the on-line following of the electrical resistivity R(t) of the amorphous ribbon during CA. As it can be seen from Fig. 4I excellent agreement between the radiance and the electrical resistivity methods was obtained. The maximum deviation of temperatures estimated by these methods is about 20 K (Fig. 4II).

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3. ELECTRICAL AND MAGNETIC PROPERTIES OF CURRENT ANNEALED AMORPHOUS ALLOYS 3.1. Electrical resistivity followed during current annealing treatment For the interpretation of the structural transformations during CA it is necessary to follow the electrical resistivity of amorphous alloys before, during and after annealing. In Fig. 5 selected curves of the relative electrical resistance during 60 s of dc CA for Fe72Cu1V5Si14B8 amorphous ribbon are given. The initial steep increase in resistivity is due to the increase of the sample temperature. For low current intensity (curves a and b) a plateau value exists, which is determined by the heat balance (the supplied power is equal to the speed of dissipation of heat by conduction, natural convection and radiation).

Figure 5. Relative electrical resistance during the first run of 60 s dc CA for amorphous Fe72Cu1V5Si14B8 ribbons [5]

Figure 6. Changes of relative electrical resistance for the sample (b – 1.9 A) of alloy Fe72Cu1V5Si14B8 during the second (b’ – 2.3 A) and third (b” – 2.5 A) heating run, and XRD patterns for the sample annealed with 2A during only 5 s and for the sample b” [5]

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The slight decrease observed with increasing annealing time may be due to the relaxation processes in the amorphous structure. Currents higher than 2 A (c-f), cause a resistance bump, shifting toward lower times with increasing current intensity. The maximum after this bump results from the crystallization energy, which is released during the exothermic phase transformation and raises the sample temperature. In order to confirm the state of the sample b (I = 9 A) after cooling, we performed a second and third heating run. The second heating with increasing current intensity (curve b’– I’ = 2.3 A in Fig. 6) leads to crystallization, i.e. a peak is recorded before the isothermal region. Curve b’’– I” = 2.5 A for the third run shows a plateau, indicating that the crystallization process is almost completed during the second heating run. The XRD pattern (b”) in Fig. 6 is for this sample after the third heating run. Besides strong peaks of a bcc D-Fe(Si) phase and very weak peak of the Fe2Si0.4B0.6, no Feborides (Fe2B and Fe3B) that precipitate after FA for 1 hour at 813 K [19] were noticed. The other XRD pattern in Fig. 6 for the sample heated with the current of 2 A for only 5 s confirms crystallization in the remaining amorphous matrix. 3.2. CA crystallization effect on longitudinal magnetoresistance During the last decade considerable experimental research on magnetoresistance and magnetoimpedance effect of amorphous and nanocrystalline alloys has been conducted, aiming at the optimization of the microstructure for sensing applications. Measurements of the longitudinal magnetoresistance give positive values for all three groups of amorphous alloys (Fe-based [20], Ni/Fe-based [21] and Co-based [22]). However, a model of magnetoresistance proposed by Balberg and Helman assumed it to be always negative for crystalline ferromagnets [23]. Kuzminski et al. [24] have examined the behaviour of the Fe-Cu-Nb-Si-B alloys, showing that a negative magnetoresistance in the nanocrystalline state can be obtained by conventional (furnace) annealing.

Figure 7. Field dependence of the longitudinal magnetoresistance in Fe72Cu1V3Si16B8: a – as-cast state and after successive heating runs (b – first 0.47 A; c – second 0.48 A; d – third 0.51 A ; e – fourth 0.52 A) [12]

In order to explore the longitudinal magnetoresistance of Fe72Cu1V3Si16B8 alloys, successive steps of dc CA were used to obtain a gradual transformation from the amor-

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phous to the nanocrystalline state. The field dependence of the longitudinal magnetoresistance (UII) of the sample normalized to the resistivity in zero magnetic field (U0) is shown in Fig. 7. With increasing magnetic field the absolute values of magnetoresistance increase. As the field is increased further all curves tend to saturate. The ascast saturated value (Fig 7a, 0.096%) is close to that of amorphous Fe-based Metglas 2605 and 2605A alloys with positive longitudinal magnetoresistance (0.128% and 0.083%, respectively [22]). After each heating run the magnetoresistance decreases. The decrease can be attributed to an increase of the content of nanocrystals in the residual amorphous matrix. The increase of the volumetric fraction of the crystallites was suggested by an increase of the relative electrical resistance during successive heating runs (for instance comparing curves c and d on Fig. 8I), or confirmed by the decrease of a ratio Ra/Rb between electrical resistance after every heating run (Ra) and before the first heating (Rb i.e. in amorphous state), values are listed in Table I. Table I. Estimated final temperatures (Tf) during CA and the changes of Ra/Rb ratio after successive heating runs for the Fe72V3Cu1Si16B8 (Ra is electrical resistance after every heating run and Rb is electrical resistance in amorphous state) I [A] Tf [K] Ra/Rb

First heating 0.47 710 0.975

Second heating 0.48 716 0.943

Third heating 0.51 761 0.868

Fourth heating 0.52 772 0.854

Figure 8. I) Changes of relative electrical resistance for the Fe72V3Cu1Si16B8 at the beginning of the: (a) first 0.47 A, (b) second 0.48 A, (c) third 0.51 A, and (d) fourth 0.52 A successive heating run. II) XRD patterns for the specimens in the: (a) as-cast state and current annealed by (b) 0.47 A and 0.48 A; (c) 0.47 A and 0.52 A; (d) successively 0.47 A / 0.52 A / 0.57 A and 0.61 A [12]

The X-ray diffraction patterns for the as-cast (curve a) and annealed samples (b, c and d) are given in Fig. 8II. Only broad diffuse diffraction maximum of an amorphous phase can be observed for the non-treated samples. The first crystallization event on

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current annealing is the formation of D-Fe(Si) phase (curve b, D | 15 nm; curve c, D | 25 nm). With increasing annealing current (curve d) diffraction peaks of D-Fe(Si) (D | 50 nm) and Fe2Si0.4B0.6 (D | 45 nm) emerge from the amorphous maximum. A strong decrease in the lattice parameter of the annealed samples was observed. In accordance with the literature data (shift 17˜105nm/1at.% Si [25]), the Si content in the precipitated D-Fe(Si) was estimated from the position of the (110) peaks. The increase of the Si content observed after the first two annealing runs (17.1 at.%, curve b) is followed by a saturation after the next two (higher current) treatments (18.4 at.%, curve d). Electrical resistivity measurement performed at room temperature and DSC data were used to study the increase of the volume fraction of the crystallites (p). Assuming that the total resistivity (Utot) can be obtained as the sum of the resistivity of the crystallites (Ucr) and the resistivity of the amorphous matrix (Uam ) [24], we have:

U am  U tot U am  U cr

p

1  U tot / U am 1  U cr / U am

(2)

From successive CA up to 850 K (XRD pattern on Fig. 8IId), we find that the resistivity of the almost completely crystallized sample (p | 1) normalized to the resistivity of the as-cast state (Ucr /Uam) is around 0.8. Values of p calculated from Eq. (2) are given in Fig. 9Ia. The increase of the volume fraction of the D-Fe(Si) nanocrystals can also be analysed by DSC data. The area of the exothermic peak is a measure for the enthalpy of crystallization and is expected to be proportional to the volume fraction of amorphous phase transformed into the nanocrystalline D-Fe(Si) during CA. This means that the volume fraction of the nanocrystalline phase (p) may be calculated from the equation: p

H 1  H 1 '  H 2  H 2 ' H1  H 2

(3)

where H1 and H2 are the enthalpies for the first and second stage of crystallization of the amorphous samples; H1’ and H2’ are the enthalpies for the CA samples [12] (see Fig. 9II). Figure 9Ia shows that there is a good agreement between the calculated values of the volume fraction of nanocrystals p from electrical resistivity (Eq. 2) and DSC (Eq. 3) measurements. The volume fraction of the D-Fe(Si) and Fe2Si0.4B0.6 crystals precipitated after the highest current intensity annealing is about 90%. The observed dramatic increase of the Si content in D-Fe(Si) nanocrystals after CA with low current intensity (Fig. 9Ib), was also detected by He et al. [26]. The saturation in the concentration of silicon in D-Fe crystallites to value of 19 at.% Si has been observed. As a consequence, there is a significant change in the composition of the residual amorphous phase. A calculation shows that there is only 11 weight % with the composition of Fe24Cu6V19B51. This effect of the composition changes of the residual amorphous matrix with the precipitation of D-Fe(Si) nanograins also has been observed by magnetostriction measurements [27].

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Figure 9. I) a – Volume fraction of the D-Fe(Si) nanocrystals p vs. normalized electrical resistivity Utot/Uam calculated from Eq. 2 () and Eq. 3 () and b – changes of the concentration of silicon in D-Fe crystallites for the Fe72V3Cu1Si16B8, II) DSC traces for Fe72V3Cu1Si16B8 in the: (a) as-cast state and current annealed (b) 0.47 A and 0.48 A and (c) – successively 0.47 A/0.48 A/0.51 A and 0.52 A [12]

It was pointed out by Kuzminski et al. [24] that the anisotropy of magnetoresistivity i.e. (UII  UA)/U0 in Fe-based nanocrystalline alloys can be approximated by a linear function of p. Thus, it can be presumed that both longitudinal (UII) and transverse (UA) magnetoresistivity are also proportional to p. The dependence of G U = (UII  U0)/U0 (saturated values) on the volume fraction of the crystalline phase p is shown in Fig. 10. A linear decrease of the longitudinal magnetoresistance with increase of the volume fraction of the crystallites is satisfied in the central region. The crossing point with the magnetoresistance axis was calculated to be 0.061%. This value is lower than the one measured for the as-cast state 0.096%. It can be attributed to the observed dramatic increase of the Si content in the D-Fe(Si) nanocrystals after CA with low current intensity (Fig. 9Ib).

Figure 10. Saturated values of the magnetoresistance for Fe72V3Cu1Si16B8 as a function of the volume fraction of the crystallites (p) [12]

As a consequence, the significant changes in the composition of the residual amorphous phase lead to changes in the magnetoresistance contributions originating from amorphous matrix and nanocrystals. The magnetoresistance becomes zero for a fraction of nanocrystals of about 38%. Combining this figure with the data for a commercial nanocrystalline material (p | 0.6-0.8 [28]) it can be deduced that the negative value of G U | 0.05% corresponding to the preferable crystalline content. Thus,

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magnetoresistance measurements may be used to estimate the crystalline fraction and provides an easy control of annealing procedures. 4. EFFECT OF CA ON MAGNETIC PROPERTIES Bearing in mind that the nanocrystallization of FINEMET type alloys proceeds at temperatures of about 750-800 K (first crystallization step), it is necessary to apply a relatively high current intensity I (i.e. current density j, i.e. heating power per square area PS [6, 13]). The flow of current causes a transverse magnetic field during each CA treatment (Fig. 11, right). The current of sufficiently high density, leads to induced of transverse magnetic anisotropy [2], aligning the magnetization transverse to the current and therefore to a decrease of remanence (Fig. 11, left). 4,0

4,0

as-cast

Magnetic Induction, B (T)

3,5 0.5

3,5

3,0 0.0

3,0

F.A. no field, 803K, 30 min.

2,5 0.5 -50 2,0 0.0 1,5 0.5 1,0 0.0

2,5 0

50

100

Long. field 4.5 kA/m F.A. 803K 30 min.

1,5

-50 C.A.

0 1.95 A 0,5 (estimated 770K) 0.5 5 sec. 0,0 0.0 -50

150 2,0

50

100

1,0 150 0,5

0,0

0

50

100

150

AC Driving Field, H (A/m)

Figure 11. Hysteresis curves of Fe73.5Cu1.5Nb3Si13B9 after different thermal treatments (left) and resultant domain structure under influence of the induced transverse magnetic field (right)

Figure 12. Bamboo-like domain structure in Fe-based as-cast wires and dependence of the MI-ratio in Fe73.5Cu1Nb3Si13.5B9 wires in as-cast (amorphous) and annealed (nanocrystalline) state for FA and CA samples on: I) frequency (Hmax1 = 1.35 kA/m), and II) on external magnetic field Hex (driving current frequency as a parameter, Hmax2 = 20.3 kA/m) [35]

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The one of the arising application of soft magnetic materials are the sensing devices. Alloys with very low coercivity and nearly zero magnetostriction such as amorphous Co-based and nanocrystalline Fe-based wires are most promising on materials for preparation of magneto-impedance (MI) elements [29, 30] used for magnetic field sensors. Figure 12 shows the MI ratio in Fe73.5Cu1Nb3Si13.5B9 wires after nanocrystallization performed by standard FA and dc CA multistep pulse thermal treatments [5]. The maximum change of 31% (FA at 470qC) and 12% (CA with Ian-max = 0.75 A) was obtained at a drive current frequency of 300 kHz, (Hmax1 = 1.35 kA/m). The FA sample has higher sensitivity (about 18%/kA/m) and a somewhat lower range of linearity (about 2.5 kA/m) compared with the CA sample (8%/kA/m and 4 kA/m respectively, Fig. 12II). The slightly lower sensitivity of the CA sample is due to the influence of the induced anisotropy, which leads to a bamboo-like magnetic domain structure (Fig. 12I, up).

Figure 13. I) DSC trace for Fe72Al5Ga2P11C6B4 amorphous ribbon measured at 40 K/min (the inset shows the determination of Curie temperature TC = 574 K) [33], and II) XRD patterns for as-cast, optimum CA and fully crystallized FA samples [13]

The development of multicomponent soft magnetic Fe-based amorphous alloys with a large supercooled liquid region has been a subject of an increasing attention of the scientific community in the last few years because of good soft magnetic properties combined with the possibility to prepare these alloys by direct casting in final forms for application [31, 32]. These metallic glass forming systems have an extended supercooled liquid region before crystallization defined by the temperature span between the onset temperature of glass transition (Tg) and the onset temperature of crystallization (TX), ('TX = TX -Tg e.g. 'TX = 65 K for Fe72Al5Ga2P11C6B4, Fig. 13I [33]). The alloys of the Fe-(Al, Ga)-(P, C, B, Si) amorphous systems have very promising magnetic properties for various technical purposes [31]. The existence of a large 'TX (50 to 70 K) gives the opportunity to perform annealing above Tg in the “liquid” state with efficient stress relief, i.e. an improvement of the magnetic permeability may be attained. It is therefore expected to have a decrease of the ratio (U/P) leading to a decrease of the penetration depth (Gm) and finally to an increase of the MI ratio.

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For ribbon geometry the changes of the transverse magnetic permeability (PT) are crucial for MI-effect [34]; (PT) can be modified by thermal treatments, frequency and an external static magnetic fields, i.e. PT = PT (PS, f, Hex). The resistivity (U) depends only on the annealing conditions, i.e. U = U(PS). Figure 14a shows the improvement of the MI ratio as a result of CA thermal treatments. The maximum variation occurs for PS | 5 W/cm2. In order to explore the origin of the MI increase (Fig. 14b), we analysed the changes of resistivity vs. applied heating power. The decrease in the resistivity of the sample after each treatment is rather small in comparison with other Fe-based alloys [12, 35, 36] that exhibit a giant MI effect (only 1.5% for the highest PS, see Fig.14c). Contrary to the XRD pattern of a FA-sample (773 K/20 min) which is characterized by several iron-metalloid compounds (Fig. 13IIc) no evidence of crystals was found after applying a very high PS (5.5 W/cm2, Fig. 13IIb). Therefore, it can be concluded that

Figure 14. Dependence of the MI ratio in Fe72Al5Ga2P11C6B4 ribbons in as-cast and CA state (Hmax = 20.6 kA/m): a) on frequency, b) on PS at optimum driving frequencies, and (c) variation of the resistivity of CA samples (UCA) normalized to the resistivity in the as-cast state (UO)

the highest MI response is associated with the magnetically softest state, i.e. after optimum relaxation of the amorphous structure as proved by coercivity/XRD/TEM analysis [6]. 5. CONCLUSIONS Current annealing technique is a widely applied non-conventional thermal treatment for improvement of technical properties of amorphous soft-magnetic materials. Multistep current annealing with successive increase in heating power can be successfully used to attain different degrees of structural relaxation or nanocrystallization in order to optimize magnetic and mechanical properties.

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INTERPRETATION OF THE GLASS TRANSITION TEMPERATURE FROM THE POINT OF VIEW OF MOLECULAR MOBILITY V.I. DIMITROV Department of Physics, Iúık University Büyükdere Cad., 80670 Maslak-Istanbul, Turkey Corresponding author: V.I. Dimitrov, e-mail: [email protected] Abstract:

Glass transition has been one of the biggest challenges in condensed matter physics during the last century: in spite of significant progress we still cannot explain the sudden solidification of undercooled liquids on the atomic scale. The liquid state itself is one of the less developed branches of condensed matter physics. The theoretical concepts of atomic mobility, diffusion and viscosity in liquids are not in good agreement with experiments. In the present paper we attempt to answer this challenge by describing the thermal motion of the native molecules of the liquid as Brownian motion. On the basis of this theory we have derived general expressions for the atomic mobility, P, self-diffusion, D, and viscosity, K for liquids. In dependence on a reduced temperature t , the mobility is expressed as P = P0 m(t ) for t t 0 and P = 0 for t d 0 where P0 is the mobility at the jamming point of the liquid, and m(t) is defined by t = m/(1 – e–m). The reduced temperature t = J2T/Jc2Tc is determined by a quantity J accounting for the anharmonicity of interparticle interactions in the liquid state. At the special values Jc and Tc the mobility becomes zero, i.e. the equilibrium glass transition occurs when the reduced temperature becomes equal to 1.

1. INTRODUCTION In the late 1820s the British botanist Robert Brown discovered that a tiny pollen grain suspended in water undergoes erratic, unceasing and puzzling movements – now called Brownian motion. The cause of Brownian motion was understood much later. Theoretical foundations were only laid at the beginning of the 20th century by Albert Einstein, Marian Smoluchowski and Paul Langevin. The main results of this theory were soon confirmed experimentally by Jean Perrin. There were a number of attempts to describe the atomic motion in liquids by reformulating the theory of the classical Brownian motion in order to describe 345 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 345–352. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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adequately the motion of the particles of the liquid itself. In spite of some understanding of the thermal molecular motion and relaxation processes in undercooled liquids, the development of a coherent theory describing all aspects of the glass transition remains a challenge. Basically the challenge is due to the absence of a molecular theory of liquids. Among a number of models, the mode coupling theory (MCT) proved to be one of the most successful [1, 2]. Although MCT was formulated originally for simple (monatomic) fluids only, and its predictions have been tested in simple liquids and essentially above the glass transition temperature, it is believed to be of much wider applicability, and nowadays is widely used for quantitative analysis of different experiments with undercooled liquids and glasses [3]. However, despite all the achievements of modern experiments and theory of liquids we still do not understand what distinguishes a fluid from a glass – thus we should look for a new approach to the theory of liquids. In the present work, we develop an alternative approach to describing thermal motion in condensed matter which can be considered an attempt to create a kinetic theory of liquids. 2. THEORY Any atom in condensed matter is surrounded by a number of neighbouring atoms which form a very good “cage”. If we neglect vacancy-like motions, any atom of a solid is a “prisoner for ever” in its own cage built by its neighbours, and endlessly oscillates within its cage. However, as experiment shows, the situation is quite different in liquids. In spite of the fact that the cages should be almost the same (the density of the liquid state is almost the same as that of the solid state) atoms of a liquid travel around quite freely (the self-diffusion and atomic mobility are many orders larger than in solids, even near the glass transition temperature). After a certain time an atom may be situated in a totally new cage, i.e. simultaneously with its displacement the atom changes its neighbours. What is the mechanism of this behaviour? How can it be described? These are the questions we answer in this paper. For simplicity we consider a monatomic liquid only in the following. At a given instant any atom is in a certain “cage” formed by its neighbours. Because of the structural disorder the potential wells of the cages cannot be simply parabolic. I.e. if we consider a certain direction, say along the x-axis, the potential energy of the atom in the well as a function of its displacement from the bottom of the well, x, can be presented in the form: U ( x) U (0)  1 / 2 fx 2  1 / 3 gx 3  

(1)

where g and f are parameters of the potential well. f is positive, and g may have positive or negative values with equal probability. The latter statement follows from the absence of a macroscopic anisotropy in the liquid state (any direction in the liquid must be equivalent). In this potential well the atom oscillates due to the thermal excitation of the system. Parameter f accounts for harmonic interactions of the central atom with its neighbours and g for the anharmonicity of interactions. We should note from the very beginning a few points. First, since the liquid state is well above the Debye temperature, there is no need of quantum mechanical considera-

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tion of atomic motion. Second, barring exceptional fluctuations, the high mobility of the oscillating atom permits it to adjust its mean position to the center of the bottom of the potential well, otherwise there would be a force acting on the atom, which in turn would pull it back to the center of the bottom. In other words, atoms self-organize their oscillations around the center of their potential wells unless special fluctuations occur. According to classical statistics the mean energy of an oscillating atom is equal to kBT per degree of translational motion, where kB is the Boltzmann constant and T the temperature. The energy of an atom is not a constant; it fluctuates around its mean value. The energy fluctuations of atoms may occur in two distinctive ways: first, fluctuations caused by direct energy redistribution within the “cage” subsystems, and second fluctuations caused by the energy redistribution between different modes of oscillation in the system as a whole, e.g. by phonon-phonon interactions. For our aim however, the exact mechanism of fluctuation of the energy of atoms is not important. However, it is important that the energy redistribution and energy fluctuations are cooperative phenomena and, most importantly, the mechanism of energy redistribution involves atomic rearrangements within very short distances only, if any. Let us now see what happens with an atom, subject to energy fluctuation with value 'H . Due to fluctuations the mean position of the oscillating atom will change by an amount 'x

x  xm

J 'H ,

(2)

where J g f 2 , xm xm (0) 0 is the initial equilibrium position of the atom and x is the new position. The displacement is caused by the asymmetry of the potential well of the cage, an effect similar to the linear expansion of solids. Because of the displacement from the equilibrium position a net force F  wE p (r; rn ) wr starts acting on the considered atom, where Ep is the potential energy of the atom in the field of its neighbours, r is the current position of the atom, and rn is a set of the position vectors of its neighbours. This force, however, is compensated by the fluctuating forces on the atom. Since the displacements are small, the above force can be represented by its linear term



F





D x  x m (t ) ,



(3)

where D w 2 E p (r 0; rn ) w x 2 is a certain force constant which depends on the inter atomic interactions. In Eq. (3) we assume that the direction of displacement is along the x-axis. In accordance with the third law of mechanics conjugate forces act on the neighbouring atoms. Their vector sum is equal to –F. In this way the peripheral part of the subsystem is subject to a force F, and because of their mobility the neighbouring atoms will rearrange their positions (relax). As a result the equilibrium position of the “cage” potential well will migrate in the direction of the displacement of the atom undergoing such a fluctuation. Instead of describing the atomic rearrangement in the cage it is more convenient to consider the motion of the central atom with respect to the center of mass of the surrounding atoms in the cage subsystem. This motion can be considered as that of a particle in a medium with friction. The mean velocity of the moving particle can be quite generally expressed by the well-known equation

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u P F , where F is the force acting on the particle and P is the atomic mobility. Therefore, in our case

dxm dt

 P D x  xm ,

(4)

where dxm dt is the drift velocity of the center of the cage, and F  D x  xm . The solution of Eq. (4) is

J 'H 1  exp D P t .

xm (t )

(5)

Then, within the average duration W f , of the fluctuation, the new average position of the atom undergoing the fluctuation will shift by the distance

[

xm (W f )

[ 0 1  exp D P W f ,

(6)

where [0 = J 'H is the maximum possible “jump” of the equilibrium position for the fluctuated particle. What is the result after the fluctuation? First the cage subsystem has been rearranged. After repeated rearrangements of the cage related to one central atom, the central atom may partially or even totally (depending on time of observation) renew its list of its neighbours. Secondly and of great importance for our aim, the central atom, which has initially jumped by a distance [0 due to the energy fluctuation, does not return back to its initial position after a rearrangement of its neighbours. Rather, its position is shifted by distance [ [ 0 1  exp  D P W f with respect to its initial position. In this way, the ensemble average of [0 for a perfect random walk process in the liquid yields a “jump” distance [ [ 0 r modified by the mobility correlation factor r 1  exp( P / P 0 ), where P 0 1/(D W f ) . The frequency of atomic “jumps” can be found from the probability of the fluctuations Z exp('H /(k BT )) W f W | W 0 W , where W is the average time between two consecutive fluctuations of an atom; IJf is average duration of the fluctuation, being of order the period of atomic oscillations IJ0 – (usually 10-13 s), i.e.



W

§ 'H · ¸¸ . © k BT ¹

W 0 exp¨¨





(7)

This equation was first proposed by Frenkel [4] and has been confirmed by many computer simulations [5]. Having obtained the length and frequency of jumps, a further development of the theory of thermal motion for liquids relies on simple mathematics, presented below. At high temperatures P !! P 0 , then r o 1 , i.e. the drift thermal motion in this case is highly cooperative, the neighbourhood of an atom rearranges correspondingly and completely during its fluctuating motions, thus the atoms diffuses in a way similar to that in gases. In the opposite limit, when P  P 0 then r o 0, thus the fluctuating atom, after dissipating its “excess” energy, returns back to its mean position – the system behaves like a solid. This situation occurs at temperatures approaching the equilibrium glass transition temperature Tc.

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The average of g in the potential energy Eq. (1) over different atoms indeed is zero because the liquid is isotropic; as a result [ 0 as well. This means that half of the particles of the liquid jump along say the x-axis and the other half in opposite direction, i.e. atoms perform a random walk like a classical Brownian particle in a liquid. However, if an external force F is applied, the potential wells of atoms are inclined towards the direction of the applied force, and the energy change of a fluctuating atom consists of two terms: the energy of the fluctuation itself and the energy due to the work done by the applied external force, 'H  F[ 0 , where F is the applied external force. Consequently, the relation [ 0 J 'H becomes [ 0 J 'H  F[ 0 and together with Eq. (6) we find

[





'H J  J 2 F  J 3 F 2  ... >1  exp( P / P 0 )@ .

(8)

Thus, if we observe the motion of a particle, its position xn + 1 after the (n+1)th displacement will be xn1 xn  [ . Then the drift velocity of the particles in the system can be calculated by the standard equation u

x n 1  x n

[

6W

6W

.

(9)

Considering that J takes on positive and negative values with equal probability, from Eqs. (8-9) we obtain u P F , where 'HJ 2 >1  exp( P / P 0 )@

P



6W 1  J 2 F 2

(10)



is the atomic mobility. Taking F = 0 we obtain the inherent atomic mobility of the liquid

P

'HJ 2 >1  exp( P / P 0 )@ . 6W

Using the well-known fact that 'H

(11)

k BT , Eq. (11) is further specified §

§

P P 0 ©

J 2 k B T ¨¨1  exp¨¨  ©

P

6W

·· ¸¸ ¸¸ ¹¹

.

(12)

Eq. (12) has a unique non-zero solution only if T > Tc, where the critical temperature Tc is the solution of the equation (J 2 k BT ) (6WP 0 ) 1 , i.e. Tc

6WP 0 , J c2 k B

(13)

where J c J Tc is the quantity J near Tc. Using Tc, Eq. (12) can be written in more symmetric form

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P P0

§ ·· § ¨1  exp¨  P ¸ ¸ . ¨ P ¸¸ ¨ 0 ¹¹ © ©

J 2T J c2Tc

(14)

The solution of Eq. (14) is ­P 0 m(t ), t t 1 , ® t 1 ¯0,

P where t

(15)

J 2T J c2Tc . m(t ) is described by the function m . 1  em

t

(16)

We call m(t ) the mobility function. For m !! 1 we have m | t . At low mobility m  1 , m | 2t  1 . The case t 1 corresponds to zero mobility. Thus, m 1 (or P P 0 ) is a characteristic mobility which indicates the onset of the “self-jamming” of liquid state. The corresponding “self-jamming” temperature is t j 1 (1  e 1 ) | 1.582. Therefore, we call P0 the jamming mobility, and the temperature Tj is the jamming temperature given by the solution of equation 1 J c2Tc . 1  e 1

TJ 2

(17)

Below Tj the system starts to‘prepare’ itself for a transition into the glassy state. Using the standard expression for diffusion in random walk processes, D [ 2 6W , we obtain from Eq. (8) with F = 0 and using Eq. (12) D

§ ¨ ©

§

P P 0 ©

Pk B T ¨1  exp¨¨ 

·· ¸¸ , ¸¸ ¹¹

(18)

which obviously is a generalization of the Einstein equation D Pk BT . Shear viscosity (or simply viscosity) depends on the inverse of the atomic mobility. One of the most popular expressions for viscosity is obtained from Stokes law, F 6SK Ru , and the definition of mobility, u P F , where F is the force acting on a particles of radius R, Kis the viscosity, and u is the relative velocity between the particle and liquid. Thus K 1  6S R P . Various researchers have calculated many other types of flow around particles of different shapes, thus obtaining different values for the geometrical factor 6S R but usually these values are quite close to each other, therefore the viscosity can be presented in a more general form as

K

1 , cP

(19)

where c is a constant having dimension of length which accounts for the geometry of the moving particle. Equation (19) can be written as

K K 0 n(t ) ,

(20)

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where K 0 1 c P 0 may be called the jamming viscosity, and n (t ) 1 m(t ) the viscosity function. From Eqs. (18-19) it follows that D

§ P ·· k BT §¨ ¸¸ ¸ . 1  exp¨¨  ¨ ¸ 6S rK © © P0 ¹¹

(21)

Approximately, when P ! 4 P 0 Eq. (21) reduces to the well-known Einstein-Stokes equation D = (kBT)/6SRK. In the temperature interval 1.582  t  4 the Einstein-Stokes equation is observed approximately, but below this interval it fails totally which is known as the breakdown of the Einstein-Stokes law in supercooled liquids. In this way Eq. (21) can be considered as generalization of the Einstein-Stokes equation which is valid up to the liquid-gas critical temperature and down to the glass transition temperature. One should keep in mind that we do not consider the “solid-like” contribution to the atomic mobility. This is a subject for a separate investigation. 3. DISCUSSION The basic conclusion of this paper is that the particles of a liquid perform a specific Brownian motion caused by the energy fluctuations and a disordered atomic structure of the liquid. While the energy fluctuations are inherent for any state of matter (gasses, liquids and solids), the anharmonicity of the potential wells, which is caused by the locally disordered atomic structure, is characteristic only for liquid and amorphous condensed matter. So, the cause for Brownian motion of the particles forming a molecular liquid themselves is different from that for the classical Brownian motion of suspended “foreign” particles, which is the density fluctuation of the liquid. However, the local energy, short-range order, and density fluctuations are closely related to each other: the local short-range order determines the local density, and energy fluctuations may cause a rearrangement of the local atomic structure. For this reason it is not an accidental result that the mechanism of classical Brownian motion approximately describes the thermal motion of the particles of the liquid as well. However, at low temperatures, and therefore at low mobility, the efficiency r 1  exp( P P 0 ) of the “driving force” of Brownian motion, namely the energy fluctuation, may become much less than unity. Moreover, when temperature tends to the glass transition point this efficiency becomes zero, and the random walk of the atoms of the liquid stops. Mathematically the “self-solidification” near the glass transition temperature results in the relation K v Tc (J 2 / J c2 )(T  Tc ) , where J 2 J c2 is a smooth function of temperature, since the atomic structure of the liquid changes smoothly with temperature even when temperature approaches the glass transition point. Therefore J 2 J c2 o 1 with T o Tc . Thus, the divergence of viscosity near the glass temperature is controlled by the expression K v Tg T  Tc : the viscosity increases by many orders for temperature changes of just one Kelvin. The present theory of thermal molecular motion in liquids predicts and explains the glass transition temperature of supercooled liquids. It can be extended to create an “exact” theory of the liquid state by taking into account the “variable behaviour” of the translational degree of thermal motion trough the factor r 1  expm .





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It is instructive to compare some of the results of present theory with results from previous theories. One example we have already considered – the generalization of the Einstein and Einstein-Stokes relations. Another example is the “structural arrest”, or transition from ergodic T ! Tc* to nonergodic T  Tc* behaviour predicted by MCT. * Analyses of experiments show that Tc in fact is in a range of temperature * approximately around Tc | 1.2Tg for a number of liquids where Tg is the empirical glass transition temperature (defined as the temperature where the viscosity of the undercooled liquid takes on a value characteristic for normal crystalline solids, K T Tg 1013 P ). Below Tg the “solid-like” atomic mobility is higher than the “liquidlike”, which smoothly becomes zero at the “equilibrium glass-transition temperature” Tc. Most probably Tc corresponds to the empirical parameter T0 in the modified VogelFulcher-Tamman equation [6], K (T ) A expBT0 T  T0 , where T0, A, and B are constants of the model. Parameter T0 is approximately equal to the so-called Kauzmann temperature TK [3], where the extrapolated excess entropy of the undercooled liquids over the entropy of the counterpart crystal becomes equal to zero. Therefore, this temperature should correspond to our critical temperature of “equilibrium glass transition” Tc, where the excess degree of Brownian motion disappears. Analysis of the experimental data shows that for a majority of glass forming liquids the following relations hold [7] Tg | 2 / 3Tm and T0 | 1 / 2 Tm , where Tm is the melting temperature. For the same class of materials the radial distribution function varies very slowly with the temperature, consequently quantity Ȗ should have a similar behaviour, thus t | T / Tc , and the beginning of the jamming of the glass-forming liquids can be approximated as T j | Tc 1  e 1 | 1.6 Tc . Taking into account that Tc and T0 are the same quantities we obtain Tc | 3 / 4T g and T j | 1.2 Tg . Consequently our jamming temperature corresponds to the critical temperature of the MCT. Further analysis and application of the present theory is a subject of new and detailed investigations, which will be published soon.

















REFERENCES 1. Bengtzelius, U., Götze, W., and Sjölander, A., (1984) Dynamics of supercooled liquids and the glass-transition, Journal of Chemical Physics 17, 5915-5934. 2. Götze, W., (1989) Liquids, freezing and the glass transition, in: J. Hansen, D. Levesque, J. Zinn-Justin (eds.), Liquids, Freezing and Glass Transition, New York, Plenum, 287-503. 3. Binder, K., Baschnagel, J., and Paul, W., (2003) Glass transition of polymer melts: test of theoretical concepts by computer simulation, Progress in Polymer Science 28, 115-172. 4. Frenkel, J., (1946) Kinetic Theory of Liquids, Oxford University Press, Oxford. 5. Slutsker, A.I., Mihailin, A.I., and Slutsker, I.A., (1994) Microscopics of fluctuations of the energy of atoms in solids, Physics-Uspekhi 37, 335-344. 6. Angell, A.C., (1996) The glass transition, Current Opinion in Solid State & Materials Science 1, 578-585. 7. Gutzow, I. and Schmelzer, J., (1995) The Vitreous State, Springer, Berlin.

THE EFFECT OF THERMAL RELAXATION ON THE SHORT-RANGE ORDER IN MELT-QUENCHED Zr-Co AND Zr-Ni ALLOYS I. KOKANOVIû and A. TONEJC Department of Physics, Faculty of Science, University of Zagreb P.O. Box 331, Zagreb, Croatia Corresponding author: I. Kokanoviü, e-mail: [email protected] Abstract:

The Zr803d20 (3d = Co, Ni) metallic glasses and the partially crystalline Zr76Ni24 metallic glass were prepared by melt spinning. The effect of thermal relaxation on the short-range order in melt-quenched the Zr803d20 (3d = Co, Ni) metallic glasses and the partially crystalline Zr76Ni24 metallic glass during heat treatment at different heating rates has been investigated by means of the differential scanning calorimeter (DSC) and the X-ray powder diffraction (XRD) measurements in temperature interval from 300 K to 823 K. According to the XRD results, for the partially crystalline Zr76Ni24 metallic glass, melt-quenched alloy consists of a fraction of metastable Zr3Ni crystalline phase and an amorphous phase. The estimated volume of the fraction of the Zr3Ni crystalline phase was | 9.6%. The crystalline peaks of the Zr3Ni crystalline phase were fitted to the orthorhombic structure type. The Zr3Ni crystallite size was estimated using the Sherrer formula to be from 15 nm to 30 nm. Crystallization studies have shown that the existence of the orthorhombic Zr3Ni crystalline phase does not change the thermal stability of the amorphous phase against further crystallization and remains unchanged during the annealing of the samples up to 823 K. On the basis of the DSC and XRD obtained data it was possible to identify the phases which occur in the heat treatment of the Zr803d20 (3d = Co, Ni) metallic glasses and of the partially crystalline Zr76Ni24 metallic glass up to 823 K. The average crystallite sizes of these nanocrystalline phases were from 10 nm to 24 nm.

1. INTRODUCTION

Rapid solidification from the melt is a widely spread method in producing metallic glasses. However, during rapid quenching the atoms do not have time to relax from a high temperature atomic configuration to a low temperature configuration and therefore the quenched metallic glass exists in a metastable state with respect to the relaxed, more stable glassy state as well as to the crystalline state. Thus, a metallic glass obtained by rapid solidification can be regarded as a metallic solid with a frozen-in melt structure 353 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 353–362. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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which lacks the three-dimensional atomic periodicity. On the other hand, by varying the quenching rate during melt spinning or the crystallization procedure of some metallic glasses it is possible to produce partially crystalline and nanocrystalline alloys. Recently, nanocrystalline alloys have attracted a lot of attention because of their potential applications [1, 2] due to the fact that the structure consists of a nanocrystalline phase embedded in the remaining amorphous matrix. The nanocrystalline phase is often in a non-equilibrium state and grows with a highly faulted morphology. Eventually, the quenched-in crystals can destabilize the remaining amorphous matrix in different ways. They can simply grow at a lower temperature than required for homogeneous nucleation and growth of crystals in glassy matrix or/and can act as heterogeneous sites [3, 4]. Also, the lower quenching rate required to produce a partially crystalline metallic glass may lead to a higher population of quenched-in nuclei and therefore facilitate subsequent crystallization. However, Toloui et al. have shown that the presence of the quenched-in D-Zr crystals within the glassy matrix of the Zr76Ni24 metallic glass increases the stability of the matrix against further crystallization [5]. The metastable state of metallic glass and partially crystalline metallic glass can relax structurally to a more stable state whenever the atoms attain an appreciable mobility upon annealing. This structural relaxation is a fundamental characteristic of metallic glasses. Associated with the structural relaxation, many physical properties, such as magnetic, electrical and superconducting ones, can change, some drastically and others only slightly. Furthermore, the properties of metallic glasses are also highly sensitive to small amounts of a crystalline phase embedded in the amorphous matrix and in some cases the introduction of a controlled amount of the crystalline phase into the amorphous matrix can enhance their properties. For example, soft magnetic properties are extremely sensitive to the number of quenched-in crystallites within the glassy matrix [1, 2]. Also, the physical properties of nanocrystalline materials often differ in comparison to the crystalline or amorphous ones and the difference has been attributed to the presence of a fraction of nano-grains and longer specific surface area between grains [6]. Zr-3d (3d = Co, Ni) metallic glasses have been formed over the continuous ranges, (20-50 and 88-93 at.% Co) and (20-70 at.% Ni) [3, 7, 8] and although they have only small differences in the atomic structures, their properties differ appreciably. These metallic glasses are especially interesting because of the low-temperature configuration changes from superconductivity through enhanced paramagnetism to ferromagnetism with increasing 3-d concentration. Zr-based metallic glasses are used in a number of applications because of their mechanical properties. On the other hand, high numbers of tetrahedral coordinated sites for interstitial hydrogen make these alloys a good candidate for a hydrogen storage application. In this paper we have studied the effect of thermal relaxation on the short-range order in melt-quenched the Zr803d20 (3d = Co, Ni) metallic glasses and the partially crystalline Zr76Ni24 metallic glass obtained during heat treatment at different heating rates by means of the DSC and the XRD measurements in a temperature interval from 300 K to 823 K. These alloys are characterized by high room-temperature resistivity, they are paramagnetic [9] and become superconducting at temperatures below 3.5 K [10, 11].

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2. EXPERIMENTAL TECHNIQUES Ribbons of the Zr803d20 (Co, Ni) metallic glasses and of the partially crystalline Zr76Ni24 metallic glass were prepared by rapid melt solidification on a single-roll spinning wheel in the argon atmosphere. The thermal stability of these metallic glasses was studied by means of a calibrated Perkin-Elmer DSC-4 differential scanning calorimeter using an atmosphere of purified argon gas. The crystallization activation energy was determined from the isochronal measurements made at different heating rates. The samples were packed tightly in sealed aluminum cans and an empty aluminum can was used as the reference. The temperature and heat flow axes were calibrated using the zinc solid-liquid transition recorded with the same heating rate. The heating rates of 10 K/min and 60 K/min up to temperatures between 563 K and 823 K were used in the experiments. The structures of the samples before and after the heating were investigated by XRD using a PHILIPS PW 1820 powder diffractometer with Cu KD radiation. The diffraction intensity was registered in the angular range 10o < 2D (inset in Fig. 6b) represents the value of the Curie temperature of the amorphous alloy. Experimental errors in the determination of Af and plotted against the temperature of measurement Tm. The inset in Fig. 6b shows the determination of Curie temperature from the derivative of (mm/s)

0.74 0.72 0.70 0.68 a.q.

300

400

o

ta ( C)

Figure 7. Room temperature Mössbauer spectra of Fe76Mo8Cu1B15 alloy taken from a sample in the as-quenched state (dashed line) and after annealing at 410oC/1h (solid line)

Figure 8. Parameters of Mössbauer spectra (non-magnetic component) of Fe76Mo8Cu1B15 alloy: (a) standard deviation V and (b) average value of quadrupole splitting are plotted as a function of the temperature of annealing ta. The standard deviation V can serve as a quantitative measure of topological SRO and permits one to estimate the degree of structural (dis)order. A high V means that the structure is rather chaotic, whereas its decrease indicates a tendency toward closer packing. Deviations in chemical SRO are recognized by variations in -value in Fig. 8b which was remarkably different from that of the asquenched sample. The reason why we do not see any traces of a narrow spectral component in the room temperature Mössbauer spectrum (solid line in Fig. 9a) is the thermal fluctuation of magnetic moments associated with nanograins. It effectively smears out the signal due to a very small contribution of nanocrystalites and, even more, their separation by a paramagnetic amorphous residual phase. Microstructure and magnetic structure of nanocrystalline alloys. Varying the temperature of annealing we are able to control the amount of nanocrystallites. Magnetic states of iron atoms are significantly affected already by a small crystalline fraction. This phenomenon can be explained by Mössbauer spectra in Fig. 10 and their respective parameters which are plotted in Fig. 11 as a function of the annealing temperature. For the sake of comparison we use Mössbauer spectra of the original as-quenched alloy (dotted lines in Fig. 10) superimposed over the spectra of the 460oC annealed sample. At room temperature, a remarkable broadening of the central part of Mössbauer spectra, with respect to the as-quenched state was observed in Fig. 10a around the velocity of ±2 mm/s when nanocrystallites had emerged. It originated from the ferromagnetic interactions among the grains penetrating the amorphous residue [16] and strengthening the magnetic hyperfine fields within the amorphous retained matrix. An increase in Bhf of the amorphous phase in Fig. 11b which starts from ta = 450o C, i.e. after the onset of crystallization, supports this conclusion. The initial decrease of Bhf (AM) is caused by a structural rearrangement which is taking place after the annealing at moderate temperatures as described in Section 3.3.1. The results of liquid nitrogen temperature measurements show the opposite behaviour. Mössbauer spectra of nanocrystalline specimens in Fig. 10b are narrowed relative to the as-quenched state and Bhf (AM)-values in Fig. 11b slightly decrease with ta, i.e. higher crystalline fractions. This can be explained by changes in the chemical SRO of the retained amorphous phase which are a consequence of the segregation of Fe atoms into nanocrystalline grains. The concentration of Fe atoms in the amorphous rest is effectively decreased and the number of (mainly) Mo and B nearest neighbours increased, initiating a fall of magnetic hyperfine fields of the resonant atoms. At the same time, the polarization of paramagnetic regions inside the amorphous matrix introduced by exchange and dipolar interactions among the nanocrystalline bcc-grains acts in the opposite direction. Both effects are, of course, temperature dependent. Nevertheless, at the temperature of liquid nitrogen, which is well below the Curie temperature of the investigated amorphous alloy (TC § 310 K), the majority of originally paramagnetic regions is converted into ferromagnetic ones. As a consequence, the overall average hyperfine field of the retained amorphous matrix is notably higher than at room temperature (see Fig. 11b). As far as crystalline and interface phases are concerned, their features strongly depend upon the temperature of measurement. At a low temperature, hyperfine magnetic fields Bhf of both phases do not change with ta as demonstrated in Fig. 11b. The results of room temperature measurements show lower values of Bhf(CR) for ta = 460 and 470oC and for ta = 450oC it was not possible to determine the hyperfine

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Figure 10. Mössbauer spectra of nanocrystalline Fe76Mo8Cu1B15 alloy taken at (a) room temperature and at (b) liquid nitrogen temperature from samples annealed at the indicated temperatures. The dotted spectra correspond to the as-quenched alloy

field at all. A similar situation was also observed for Bhf-values of interface regions. To explain these finding we have to consider a small amount of the crystalline phase (and of the interface as well) in the early stages of the crystallization process of the order of 5-7% and the effect of temperature. At room temperature, thermal fluctuations of magnetic moments cause dynamic effects that significantly broaden the respective Mössbauer lines and/or decrease the average hyperfine field value depending on the amount of nanograins which are well separated from one another (see Fig. 3). Regarding the relative fractions of the structural components, two remarks should be made: (i) Figure 11a presents a development of spectral line areas rather than a relative amount of the crystalline and amorphous phases within the samples and the differences observed for room and liquid nitrogen temperature measurements originate from the temperature dependent probability of the Mössbauer effect (equal recoil free

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Figure 11. Parameters of Mössbauer spectra of amorphous and nanocrystalline Fe76Mo8Cu1B15 alloy: (a) relative fraction Af and (b) average value of hyperfine field Bhf plotted against the temperature of annealing ta for amorphous residual phase (squares), crystalline (circles), and interface (triangles) phases as obtained from room temperature (open symbols) and liquid nitrogen temperature (solid symbols) measurements

fractions are assumed). (ii) The data for the crystalline component plotted in Fig. 11a represent the contributions from the spectral components assigned to the crystalline phase and to the interface zone. Topography of hyperfine fields. Applying Mössbauer spectroscopy, we can investigate the hyperfine interactions associated with all resonant atoms contained in the samples studied. It is important to note that in the case of a disordered structural arrangement, the pieces of information on individual atomic sites and their corresponding hyperfine interactions are not directly related to each other. Since they cannot be unambiguously correlated, the results from other techniques should be looked for to support the proposed interpretation of the Mössbauer spectra. Alternatively, Mössbauer effect measurements should be carried out under different conditions (e.g., temperature of measurement, external magnetic field) in order to reveal the trends in the evolution of particular spectral parameters, which can be subsequently compared to those of similar (amorphous) systems [18]. To allow a thorough view on the evolution of hyperfine interactions within the nanocrystalline material, corresponding hyperfine field distributions P(B) are derived from the spectral component assigned to the retained amorphous matrix. When arranged into 3D mappings with respect to the investigated parameter, e.g. the temperature of annealing ta which determines the amount of nanocrystalline phase created the topography of hyperfine interactions can be visualized. Figure 12 illustrates a modification of hyperfine interactions with the temperature of measurement. At room temperature, prevailing electric quadrupole interactions (paramagnetic regions) tend to disappear on account of an increased contribution of magnetic interactions resulting from the formation of nanocrystalline grains and enhanced exchange coupling among them. This can be seen in Fig. 12a as a decrease in intensity

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of the main hump positioned at low B-values and progressive appearance of higher field humps in the range of 15-30T after the onset of crystallization (beyond ta = 460oC). (a)

(b)

Figure 12. 3D mappings of hyperfine magnetic field distributions P(B) derived from Mössbauer spectra of amorphous and nanocrystalline Fe76Mo8Cu1B15 alloy recorded at: (a) room temperature and (b) liquid nitrogen temperature and stacked according to the temperature of annealing ta

3D P(B) mappings in Fig. 12b derived from Mössbauer spectra taken at liquid nitrogen temperature exhibit a dominating contribution of magnetic regions in the samples by humps positioned at higher B-values (B > 20 T). Nevertheless, as already mentioned above, the segregation of Fe atoms into crystalline grains depletes the residual amorphous matrix in the iron thus altering its composition. Consequently, several distinct humps which can be assigned to regions with different compositions can be distinguished toward the higher crystalline contents (higher ta). Originally bimodal P(B) feature a multiple peak structure in the nanocrystalline state. Thus, by employing hyperfine field distribution (and their 3D representations), we are able to distinguish among different structural arrangements in nanocrystalline alloys. At the same time, hyperfine interactions describe structural positions from the point of view of their magnetic states [18, 19]. It should be noted that low B-values up to about 5 T actually represent electric quadrupole interactions and that is why the corresponding resonant atoms are located in paramagnetic regions. A non-negligible contribution of structural arrangements which exhibit non-magnetic and weak magnetic character is documented by well resolved humps located at about 5 and 10 T, respectively, (Fig. 12b) for ta > 460oC. 3.3.3. Modification of surface by laser treatment Conversion electrons provide information from the depth of about 150 nm for most iron rich alloys [20, 21]. Thus, surface effects can be effectively studied by means of Conversion Electron Mössbauer Spectroscopy (CEMS). The surface crystallization was studied by CEMS for FeZr(Cu)B [22, 23] and for FeMCuB-type nanocrystalline alloys [24]. Both the quantitative and qualitative distinctions between the surface and the bulk are apparent. The former are depicted by a more rapid progress of the crystal formation on the surface whereas the latter are documented by deviations in the magnetic micro-

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structure with the help of hyperfine field distributions. We employed this technique as a principal method for the investigation of surface modifications induced by the pulsed excimer laser irradiation (55 ns, 308 nm) of the Fe76Mo8Cu1B15 alloy.

Figure 13. Room temperature Mössbauer spectra of nanocrystalline Fe76Mo8Cu1B15 alloys taken in (a) transmission mode and (b) CEMS before and after laser treatment

Transmissions and CEMS Mössbauer spectra of the 490 and 510oC annealed Fe76Mo8Cu1B15 alloy after laser treatment with one pulse of the energy density of 0.2 J/cm2 are shown in Fig. 13. A laser treatment was performed in the atmosphere of nitrogen. Transmission spectra do not show any qualitative changes after laser irradiation. In CEMS spectra, however, a notable decrease in the crystalline components is observed. This effect is more pronounced for the 490oC annealed sample with a lower crystalline fraction. The dependence of structural phases as a function of the energy density of the irradiation laser pulse H are plotted in Fig. 14 as derived from CEMS and transmission Mössbauer spectra. As for the latter, no appreciable changes are observed in the whole range of the laser irradiation in Fig. 14a.

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Figure 14. Relative fractions: (a) of amorphous and crystalline phases ATMS derived from transmission Mössbauer spectra of nanocrystalline Fe76Mo8Cu1B15 alloy, (b) of crystallites ACR comprising contributions from the crystalline phase and interface zone, and (c) of amorphous residual phase AAM with non-magnetic and magnetic components as derived from CEMS Mössbauer spectra plotted against the energy density of a laser pulse H

A gradual decrease in the crystalline component is observed on the surface as a function of the laser’s energy density H as depicted in Fig. 14b. Surface melting caused by the laser beam and subsequent rapid quenching due to the thermal contact with neighbouring regions of the sample’s material have lead to complete reamorphization after the irradiation with H = 0.75 Jcm–2. This is demonstrated by an increase of AAM in Fig. 14c. However, the magnetic regions of the retained amorphous phase (comprising in this case 100% of the surface) have vanished entirely and only contribution from paramagnetic regions is recognized. 4. CONCLUSIONS At room temperature the investigated amorphous Fe76Mo8Cu1B15 alloy exhibits combined electric quadrupole and magnetic dipole interactions. These interactions correspond to the non-magnetic and magnetic regions inside the amorphous phase, respectively. Annealing, even at moderate temperatures, well below the onset of crystallization, has unveiled a structural rearrangement accompanied by changes in the magnetic microstructure as evidenced by Mössbauer and DSC measurements. From

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temperature dependence of Mössbauer spectra, the Curie temperature of the original amorphous precursor was determined to be of 310 K. During the first crystallization stage, bcc-Fe nanocrystallites up to 10 nm in size were created. They were identified by XRD, TEM, high resolution TEM as well as by Mössbauer effect measurements. The latter pointed out significant variations of the magnetic microstructure within the amorphous residual phase. Using 3D mappings of the distributions of hyperfine fields, possible sources comprising compositional changes resulting from the segregation of Fe atoms into bcc-grains and the exchange coupling among them were discussed. The number of nanocrystallites affects strongly the evolution of hyperfine interactions. Employing the transmission Mössbauer spectrometry at liquid nitrogen temperature, it was shown that the onset of crystallization in the bulk of the studied alloy starts already at 450oC whereas Tx1 was obtained from DSC at about 480oC. Surface effects were studied using the conversion electron Mössbauer spectrometry after irradiation with an eximer laser. While no changes were observed in the bulk, the reamorphization of surface crystallites took place after laser treatment of sufficiently high energy density (0.75 Jcm–2). Laser irradiation of lower energy affected only the relative ratio of the crystalline-to-amorphous phase contents. ACKNOWLEDGEMENTS This work was supported by SGA 1/1014/04, DAAD 8/2003 projects, and by bm: bwk GZ 45.529/2-VI/B/7a/2002.

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MICROSTRUCTURE – MAGNETIC PROPERTIES RELATIONSHIP IN NANO-CLUSTERED GLASSY MAGNETS High-Coercivity Nd-Fe-Al Glassy Magnets

N. LUPU* and H. CHIRIAC National Institute of Research and Development for Technical Physics 47 Mangeron Blvd., P.O. 3, P.O. Box 833, 700050 Iasi, Romania *

Present address: IFCAM Project – Institute for Materials Research, Tohoku University 980-8577Sendai, Japan; EURONANO – LTPCM-CNRS, Institut National Politechnique de Grenoble, 38402 Saint-Martin d’Heres, France

Corresponding author: N. Lupu, e-mail: [email protected] Abstract:

Structures with atomic medium-range order (MRO) of 2-4 nm are observed in NdFeAl “amorphous” melt-spun ribbons and cast rods by high resolution transmission electron microscopy (HRTEM). The volume fraction and size of the MRO regions increases as the cooling rate decreases, leading to the increase in the coercive field from 80 kA/m to about 350 kA/m when the ribbon thickness increases from 25 to 120 micrometers. The huge increase in the coercive field up to 4 MA/m in the maximum applied field of 7.2 MA/m as temperature decreases below room temperature is ascribed to the competition between exchange interactions and local anisotropies. The role of the MRO regions as pinning centres is discussed.

1. INTRODUCTION The interest in glass-forming alloys, which vitrify at relatively low cooling rates from the molten state, compared with conventional rapidly quenched metallic glasses has grown in the last years. Owing to their resistance to crystallization, these easy-glass forming alloys can be cast in bulk shape with dimensions of millimetres [1-4]. Recently, it has been found that Nd-Fe-(Al,Si) ternary amorphous alloys are formed in a wide range of compositions by melt spinning and mould casting techniques and exhibit large coercive fields at room temperature [5-10]. Their magnetic behaviour indicates that they are structurally glasses but magnetically granular with coercive fields as high as 8.4 T at low temperatures in an applied field of 30 T [11]. These results are in contradiction to those found in conventional Nd2Fe14B ternary amorphous alloys, in 437 B. Idzikowski et al. (eds.), Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, 437–446. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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which the amorphous microstructure gives rise to soft magnetic characteristics with negligible coercivities, but they are in agreement with the high coercivities obtained in the past for Nd-Fe binary amorphous alloys [12, 13]. This paper focuses on the understanding of the relationship between the microstructure and magnetic properties in nano-clustered Nd50Fe40Al10 glassy magnets as melt-spun ribbons with different thicknesses and cast rods with diameters up to 2 mm. A wide variety of structural and magnetic methods are used for sample characterization. Additionally, the topological/magnetic structure is modelled using the neutron diffraction data by means of the Reverse Monte Carlo (RMC) method.

2. EXPERIMENTAL PROCEDURE The rapidly and slowly quenched samples were prepared by first arc melting commercially available components: Nd (99.9%), Fe (99.97%), Al (99.9%), in Cu crucibles and then melt-spinning or suction casting under an Ar atmosphere. Nd50Fe40Al10 melt-spun ribbons with thicknesses between 25 and 120 Pm and width of 2-4 mm and cast rods with diameters up to 2 mm were investigated structurally and magnetically. X-ray diffraction (XRD) investigations confirmed that most of the samples were nominally amorphous. Neutron diffraction measurements were carried out using the Studsvik Liquids and Amorphous Materials Diffractometer (SLAD) at the R2 reactor, Studsvik Neutron Research Laboratory, Sweden. The melt-spun ribbons, about 3-4 g each, were packed tightly and sealed inside a standard vanadium container, whereas the cast rods 4 cm long were stuck together to fill out the container. The data collected between 15 and 800 K were corrected and normalized to an absolute scale [14]. The data were. The systems containing 2000-2500 particles were used in the RMC simulations. The input experimental data was S(Q). The experimental number density, U, was 0.0055 nm–3. Closest-approach distances were determined on the basis of the corresponding experimental data. All calculations were started from hard spheres random configurations. To reach the equilibrium (the closest fit to the experiment), 6.5-8.5 u 106 accepted moves had to be completed. Deeper atomic investigations were carried out by high resolution transmission electron microscopy (HRTEM), after the previous preparation of the investigated surfaces. dc-magnetic measurements at room temperature and above, but not exceeding 1100 K, in applied fields limited to 640 kAm–1, were carried out using a homemade vibrating sample magnetometer (VSM). The variation of both the magnetization and coercive field at low temperatures was investigated using a SQUID MPMS2 magnetometer (maximum field 800 kAm–1) and an Oxford MagLab VSM (maximum field 7.2 MAm–1). ac-susceptibility in the temperature range 4.2-300 K was measured by using a very sensitive susceptometer in ac-magnetic fields between 160 and 1600 Am–1 and frequencies ranging from 29.1 to 291 Hz. The magnetic field was applied in the axial direction of the samples.

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Mössbauer measurements were performed between 77 and 500 K in transmission geometry with a constant acceleration spectrometer, using a 57Co source in a rhodium matrix. The ribbons were oriented perpendicularly to the J-beam. 3.

RESULTS AND DISCUSSION

3.1. Local atomic structure Figure 1 presents the neutron diffraction patterns taken at room temperature for two melt-spun ribbons with thicknesses of 25 and 120 Pm as well as for a cast rod 1 mm in diameter and nominal composition Nd50Fe40Al10. The split of the first peak and the pronounced structure at higher angles are features not present in the patterns for the other amorphous alloys with dense random packed atomic structures but they were observed in Nd-Fe binary amorphous alloys [15]. The split is more pronounced for the thicker ribbon than for the thin ones or cast rods. We suppose this behaviour being related to the more heterogeneous disordered structure developed in the thick ribbons due to the intermediary values of the cooling rate of 103-104 Ks–1 in comparison with 105-106 Ks–1 for thin melt-spun ribbons and 101-102 Ks–1 for cast rods. The reduced radial distribution functions, G(r), (Fig. 2) obtained by Fourier transform of the total structure factor, S(Q), show first neighbours peaks at 0.254, 0.285, and 0.336 nm. The peak at 0.254 nm is at the position expected for the nearest neighbour Fe atoms in the dense random packing (DRP) model; the other peaks cannot be correlated to combinations of the radii of Nd (0.182 nm), Al (0.143 nm) or Fe (0.127 nm) atoms as predicted by the DRP model. This disagreement, which is particular to the case of the present light rare-earth–Fe alloys, could be ascribed to the development of a new type of disordered structure, in which few Fe atoms form clusters randomly distributed, whereas Nd and Al atoms are distributed randomly between these clusters.

Figure 1. Neutron diffraction patterns as a function of wave-vector, Q 4S sin T /O , for Nd50Fe40Al10 bulk amorphous alloys

Figure 2. Reduced radial distribution function, G ( r ) 4S r 2U ( r ), for Nd50Fe40Al10 amorphous ribbons and cast-rods

Topological structures simulated by RMC for 2 ribbons with thicknesses of 25 and 120 Pm and for a cast rod 1 mm in diameter having nominal composition Nd50Fe40Al10, are presented in Fig. 3. There are no significant differences between the topological

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structures as a function of samples thickness and the preparation method. The most disordered structure seems to be developed in bulk cast rods, due to the low cooling rate of 101-102 K/sec that allow small relaxations of the atoms in their equilibrium position in the supercooled liquid region. The heterogeneous structure observed for thick amorphous ribbon, 120 Pm in thickness, could explain the largest values observed for the coercive field because of the larger dimensions of the magnetic clusters [16].

(a)

(b)

(c)

Figure 3. Reverse Monte Carlo (RMC) modelled structures for Nd50Fe40Al10 amorphous samples: (a) ribbon 25 Pm; (b) ribbon 120 Pm; (c) rod 1 mm; (Nd atoms – light grey spheres, Fe atoms – black spheres, Al atoms – dark grey spheres)

12 K

150 K

220 K

295 K

373 K

423 K

473 K

523 K

623 K

673 K

723 K

773 K

Figure 4. Topological structure vs. temperature for Nd50Fe40Al10 amorphous melt-spun ribbon 25 Pm; (Nd atoms – larger grey spheres, Fe atoms – smaller grey spheres, Al atoms – light grey spheres)

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The topological structure is changing with temperature as shown in Fig. 4, and the explanation of these changes is not clearly understood yet. Despite of that, it is clear from Fig. 4 that below 220 K there are no significant modifications in the topological structure, even if the magnetic properties suffer important changes as will be shown below. The topological disorder increases with the increase of the temperature, the maximum being reached in the temperature range 290-375 K. The continuous increase of the temperature up to crystallization temperature (about 715 K) leads to the increase of the structural order of each magnetic species, i.e. Nd and Fe atoms, whereas the magnetic properties remain unchanged, as we will see below. The disappearance of the amorphous phase and the isolation of the Fe atoms between the Nd-rich columnar structures (at 773 K) result in the weak ferromagnetic behaviour. Figures 5(a) and 5(b) show HRTEM images taken from very small area of Nd50Fe40Al10 melt-spun ribbons of 25 and 120 Pm, respectively. Medium-range ordered (MRO) regions of about 2-3 nm having mainly fcc-structures, the nominal composition Fe77.2Nd22.8, and the lattice fringe spacing of about 0.25 nm frequently appear in thin ribbons of 25 Pm and, in addition, the fringe geometries are randomly distributed within the amorphous matrix and cross each other sometimes.

(a)

(b)

Figure 5. Bright-field electron micrograph of the as-cast Nd50Fe40Al10 melt-spun ribbons: (a) 25 Pm, and (b) 120 Pm thickness

The structure is different for the thick ribbons of 120 Pm showing over the whole area a modulated contrast consisting of fringes with a size of about 0.5 nm typical for the relaxed amorphous structure [17]. The difference between the 2 images is predictable, as being caused by the decrease of the cooling rate during the melt-spun amorphous ribbons preparation process. The average size and the volume fraction of the fccMRO clusters increases as the quenching rate decreases, i.e. the ribbons thickness increases, leading to a higher percolation limit.

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3.2. Magnetic properties Neutron diffraction and HRTEM investigations on Nd50Fe40Al10 amorphous meltspun ribbons and cast rods revealed a new type of disordered structure consisting in a dense random packing of nanometre-sized atomic clusters, whose size is dependent on the samples thickness, i.e. the preparation conditions. Consequently, one expects complex magnetic behaviour dependent on the thickness and the composition. Figure 6 shows the magnetization and the coercive field for Nd50Fe40Al10 melt-spun amorphous ribbon 25 and 120 Pm subjected to different external fields, taken between 5 and 280 K after the sample had been cooled in zero-field from room temperature to 5 K.

Figure 6. Magnetization and coercive field vs. temperature for amorphous melt-spun ribbons Nd50Fe40Al10

For comparison, in Fig. 7 is presented the magnetic behaviour of the cast amorphous rod, 1 mm in diameter. All amorphous samples exhibit almost the same behaviour. The larger the applied field the smaller the temperature at which the maximum of the coercive field is attained. If the applied field is not enough to rotate the magnetic moments along its direction, the response of the system will be different and consequently the different magnetization behaviour observed at low temperatures as a function of applied field. The multiphase transitions inferred from the low temperature ac-susceptibility measurements can be seen in Fig. 8. A slight dependence on temperature appears with the increase in the sample’s thickness and probably is due to the changes of the micro-

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structure depending on the cooling rate. The imaginary part (F '') clearly shows differences between ribbons and bulk amorphous rod being related to the more relaxed amorphous structure existent in bulk samples. The peak in F ' at around 10 K seems to be the Néel temperature of the main Nd-rich antiferromagnetic phase or the freezing temperature below which Nd magnetic moments will be locked to their local easy axis. It is also interesting to note the existence of one step on the real part around 100 K for amorphous samples, just before F ' starts to increase, which corresponds to the pronounced increase of the coercive field obtained by the dc-magnetic measurements. Above 70 K, the Nd-rich matrix and Fe-based magnetic clusters are magnetically uncoupled and the response of the system is weakly ferromagnetic. The strong increase of the susceptibility with the temperature above 70 K represents the response of the ferromagnetic clusters that cannot be saturated by the available applied fields.

Figure 7. Magnetization and coercive field vs. temperature for Nd50Fe40Al10 amorphous cast rod

Figure 8. Real part (F ') and imaginary part (F '') (inset) of the ac-susceptibility for Nd50Fe40Al10 amorphous melt-spun ribbons and cast rods

The hysteresis loop at room temperature is the response of the magnetic clusters phase, because the Nd-rich phase is paramagnetic and has no contribution. The annealing at temperatures lower than crystallization temperature (Tx # 440ºC), as shown in

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Fig. 9, leaves almost unchanged the magnetic properties, which we suggest is due to the thermal stability of the amorphous alloys. The onset of the crystallization leads to the formation of a few metastable phases, which have larger coercive fields but smaller 40 as-cast 0 10' / 100 C 0 10' / 150 C 0 10' / 200 C

V (Wb·m/kg)

20

Figure 9. Hysteresis loops as a function of annealing temperature for Nd50Fe40Al10 amorphous ribbon 25 Pm thickness

0 0

10' / 350 C 0 10' / 400 C 0 10' / 450 C 0 10' / 500 C

-20

-40

-640 -480 -320 -160

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160

320

480

640

Applied Field (kA/m)

magnetizations in comparison with the amorphous phase. These metastable phases disappear after annealing at 500ºC in agreement with XRD and neutron diffraction results, above this temperature the sample being paramagnetic.

3.3. Mössbauer effect results At high temperatures (around room temperature) the magnetic Fe atoms participate in the reversible magnetization along with some paramagnetic contribution. Mössbauer effect data are consistent with this (Fig. 10). 250

200 80 Hyperfine field over the whole system Hyperfine field over the magnetic contribution

60

150

100 40 50

20 0

Hyperfine field (kOe)

Paramagnetic Fraction (%)

100

Figure 10. Hyperfine fields and the evolution of the paramagnetic fraction vs. temperature as resulted from Mössbauer effect data

0 0

100

200

300

400

500

Temperature (K)

The Nd atoms in the Fe-rich region (fcc-patches in Fig. 5), may order spero-magnetically and have no magnetic contribution. As the temperature is lowered the thermal effects are weaker and the coercive field increases (Figs. 6 and 7). At a critical temperature, ranging from 30 to 210 K depending on the external field value, some Fe atoms within the MRO regions become pinned so strongly in orientation that the available applied field cannot reorient them along the field direction. Thus as the temperature is lowered, more and more Fe moments become frozen and they have

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no contribution to the magnetization processes. Since the material has a paramagnetic contribution to the magnetization, the value of the magnetization is small and positive when temperature is below the critical temperature. Above room temperature the paramagnetic fraction corresponding to the Nd-rich matrix increases and the magnetic moment of the Fe atoms decrease due to the frustration of the ferromagnetic exchange interactions by the thermal effects, as shown in Fig. 9. 4. CONCLUDING REMARKS PROSPECTS From the data presented here, it can be concluded that the high coercive fields obtained for Nd50Fe40Al10 amorphous alloys at room temperature as well as their dependence on the quenching conditions and temperature, result from the development of very small Fe-based atomic clusters distributed isotropically in the Nd-rich amorphous matrix, in agreement with the atomic configurations obtained by RMC modelling and HRTEM results. From the reduced radial distribution function, G(r), we calculated the nearest neighbour pairs, the results indicating that in Nd-Fe-based amorphous alloys with large glass-forming ability, a structure consisting in a packing of nanometre-sized clusters is developed. Despite the considerable progress achieved in recent years concerning the knowledge of the atomic structure of amorphous alloys and the understanding of their basic magnetic properties, there are still many questions related to the microstructure of NdFe-based high coercivity bulk amorphous alloys and its interplay with magnetic properties. The magnetic ground states of Nd-Fe-based clustered amorphous alloys and noncollinear structures existent in these materials are far from being fully characterized. These problems and others make the study of the magnetic properties of these bulk amorphous alloys a fascinating field of research. Although the high-coercivity Nd-Febased bulk amorphous alloys are currently more suitable for fundamental research, they could be in the future successful candidates for different applications as magnetic recording media, magnetostrictive materials or low temperature permanent magnets.

ACKNOWLEDGEMENTS Access to facilities at the Studsvik Neutron Research Laboratory was supported by the Access to the Research Infrastructures activity, Improving Human Potential Programme, of the European Commission under contract HPRI-CT-1999-00061. We are also grateful to Prof. H. Pattyn from IKS, KUL, Leuven, Belgium and Prof. K.V. Rao from Royal Institute of Technology, Stockholm, Sweden for helpful discussions on the magnetic characterization of the materials as well as to Dr. J.M. Greneche from Laboratoire de Physique de L’Etat Condensé, UMR CNRS 6087, Université du Maine, France for the Mössbauer effect measurements and for helpful discussions concerning the interpretation of the results. HRTEM Images were taken at LME/LNLS (Brazil) by Juliano Casagrande Denardin. This work was supported in part by the Romanian Ministry of Education and Research – Department of Research under Contract CERES2/15.10.2001.

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REFERENCES 1. He, Y., Poon, S.J., and Shiflet G.J. (1988) Synthesis and properties of metallic glasses that contain aluminium, Science 241, 1640-1642. 2. Schwarz R.B. and He Y. (1997) Formation and properties of bulk amorphous Pd-Ni-P alloys, Materials Science Forum 235, 231-240. 3. Inoue A. (1988) Bulk Amorphous Alloys: Preparation and Fundamental Characterization, Trans Tech Publications Ltd., Switzerland. 4. Johnson W.L. (1999) Bulk glass-forming metallic alloys: science and technology, Materials Research Bulletin 24(10), 42-57. 5. He Y., Price C.E., Poon S.J., and Shiflet G.J. (1994) Formation of bulk metallic glasses in neodymium-based alloys, Philosophical Magazine Letters 70, 371-377. 6. Inoue A., Zhang T., Zhang W., and Takeuchi A. (1996) Bulk Nd-Fe-Al amorphous alloys with hard magnetic properties, Materials Transactions, JIM 37, 99-108. 7. Chiriac H. and Lupu N. (1999) Magnetic properties of (Nd,Ce,Pr)-Fe-(Si,Al) bulk amorphous materials, Journal of Magnetism and Magnetic Materials 196-197, 235-237. 8. Wang X.Z., Li Y., Ding J., Si L., and Kong H.Z. (1999) Structure and magnetic characterization of amorphous and crystalline Nd-Fe-Al alloys, Journal of Alloys and Compounds 290, 209-215. 9. Fan G.J., Löser W., Roth S., Eckert J., and Schultz L. (1999) Magnetic properties of cast Nd60-xFe20Al10Co10Cux alloys, Applied Physics Letters 75, 2984-2986. 10. Kramer M.J., O’Connor A.S., Dennis K.W., McCallum R.W., Lewis L.H., Tung L.D., and Duong N.P. (2001) Origins of coercivity in the amorphous alloy Nd-Fe-Al, IEEE Transactions on Magnetics 37(4), 2497-2499. 11. Ortega-Hertogs R.J., Inoue A., and Rao K.V. (2001) Evolution from random-axis Ising to Stoner-Wohlfarth type of hysteresis loops of the cluster glass Fe3Nd phase in bulk glassy Nd60Fe30Al10 hard magnets, Scripta Materialia 44, 1333-1336. 12. Croat J.J. (1981) Crystallization and magnetic properties of melt-spun neodymium-iron alloys, Journal of Magnetism and Magnetic Materials 24, 125-131. 13. Croat J.J. (1981) Magnetic-properties of melt-spun Pr-Fe alloys, J. Appl. Phys. 52, 25092511. 14. http://www.studsvik.uu.se. 15. Alperin H.A., Gillmor W.R., Pickart S.J., and Rhyne J.J. (1979) Magnetization and neutron scattering measurements on amorphous NdFe2, Journal of Applied Physics 50, 1958-1960. 16. Chiriac H., Lupu N., Rao K.V., and Vandenberghe R.E. (2001) Magnetic behaviour of Nd50Fe40Al10 bulk amorphous alloys, IEEE Transactions on Magnetics 37(4) 2509-2511. 17. Hirotsu Y. (1994) High resolution electron microscopy o medium-range order in amorphous alloys, Materials Science and Engineering A179/A180, 97-101.

INDEX OF AUTHORS

ANGELAKERIS, M. 249 AUDEBERT, F. 301 363 BABIû, E. BALOGH, J. 385 BARANDIARAN, J.M. 35 209 BARMIN, YU.V. BATARONOV, I.L. 209 BATTEZZATI, L. 267, 279 249 BERGER, L. BLÁZQUEZ, J.S. 111 BONDAREV, A.V. 209 CHIRIAC, H. 165, 437 CONDE, A. 111 CONDE, C.F. 111 CRISAN, A.D. 249 CRISAN, O. 253 DEANKO, M. 69 DEGMOVÁ, J. 219, 421 DIMITROV, H. 313 DIMITROV, V.I. 345 DJUKIC, S. 331 ECKERT, J. 199, 331 FAZAKAS, E. 321 FECHOVÁ, E. 147 FERENC, J. 47 FLEVARIS, N.K. 249 FÜZER, J. 147 GERCSI, Z. 135 GRENECHE, J.-M. 219, 249, 373 HAESENDONCK, C. VAN 385 HAFNER, J. 289 HAIDER, F. 229 HASEGAWA, R. 189 HERZER, G. 15 IDZIKOWSKI, B. 177 ILLEKOVÁ, E. 79, 421 289 JAHNÁTEK, M. JALNIN, B.V. 59, 99 JANIýKOVIý, D. 69, 421 59, 99 KAEVITSER, E.V. KALOSHKIN, S.D. 59, 99 KAĕUCH, T. 421 385 KAPTÁS, D. KAVEýANSKÝ, V. 147 KEMÉNY, T. 385 385 KISS, L.F.

353 KOKANOVIû, I. KOLANO-BURIAN, A. 47 147 KOLLÁR, P. KONý, M. 147 KOPCEWICZ, M. 395 KOSTYRYA, S.A. 91 KOVÁý, J. 147 KOWALCZYK, M. 313 289 KRAJýÍ, M. KULIK, T. 47, 313, 321 KUSÝ, M. 267, 279 LABAYE, Y. 249 LATUCH, J. 313 LE BRETON, J.M. 249 LUPU, N. 165, 437 MAROHNIû, Ž. 363 MAZALEYRAT, F. 135, 157 MIGLIERINI, M. 421 MITROVIC, N. 331 MÜLLER, D. 69 OBRUCHEVA, E.V. 59 PALUMBO, M. 267 PETROVIý, P. 147 RASSOLOV, S.G. 91 RISTIû, R. 363 RONTO, V. 267, 279 ROTH, S. 199, 331 SAAGE, G. 199 SCHMOOL, D.S. 409 SCHULTZ, L. 199 SEBERÍNI, M. 229 SEDLAýKOVÁ, K. 229 SITEK, J. 219, 229 ŠKORVÁNEK, I. 69 SUZUKI, K. 1 ŠVEC, P. 69, 421 123 ĝLAWSKA-WANIEWSKA, A. TCHERDYNTSEV, V.V. 59 TEMST, K. 385 91 TKATCH, V.I. TONEJC, A. 353 VARGA, L.K. 135, 157, 321 385 VINCZE, I. WOJCIECHOWSKI, K.W. 241 XU, J. 99

447

INDEX OF SUBJECTS

activation energy, 35, 41, 72, 99, 181, 206, 268, 274, 323, 355 Al-based amorphous alloy, 267, 313, 321 amorphous: - precursors, 1, 48, 92, 177, 331, 385, 393, 406, 421 - residual phase, 111, 254, 9, 435 - wires and microwires, 65, 107, 165, 170, 341 - binary amorphous alloys, 209, 438, 439 anisotropy: - field, 136, 139, 171, 182, 395, 411 - magnetocrystalline, 1, 11, 49, 126, 130, 150, 178, 374, 411 - shape, 139, 141, 157, 162, 374, 390 - surface, 130, 254, 260, 262, 375 aperiodic solid, 241, 246 Arrhenius activation energy, 72 atomic mobility, 268, 274, 345 atomic structure, 15, 102, 209, 254, 289, 298, 351, 439 Avrami exponent/equation/index, 35, 40, 71, 115, 179, 310, 321 Avrami/Arrhenius-type equations, 73

- nanocrystallization, 10, 35, 47, 59, 69, 85, 99, 107, 111, 141, 180, 324, 331, 340, 409, 415 - nucleation, 7, 60, 70, 80, 91. 114, 179, 268, 275, 291, 303, 325 - partial, 112, 147, 157, 178, 320 - primary, 4, 35, 49, 62, 79, 91, 111, 179, 219, 260, 275, 279, 321, 374 - secondary, 113, 116 Curie temperature, 10, 47, 50, 60, 99, 123, 132, 144, 157, 167, 196, 226, 254, 332, 341, 373, 388, 410, 429, 435 current annealing, 36, 331, 335, 338, 342 devitrification, 47, 79, 88, 112, 123, 178, 267, 279, 284, 377, 409 differential scanning calorimetry, 39, 59, 79, 91, 99, 113, 179, 332, 421 diffusion: - coefficient, 6, 41, 271 - controlled crystallization, 6, 72, 85, 91, 115. 157, 179, 206, 283, 325 dipolar ferromagnetism, 159, 163 elastic/magnetoelastic: - anisotropy, 24, 47 - constant, 246, 295 - properties, 2, 35, 243, 182, 375, 295 electron microscopy: - transmission electron microscopy (TEM), 5, 51, 70, 80, 116, 180, 200, 229, 235, 280, 301, 377, 388, 421 - high resolution transmission electron microscopy (HRTEM), 437 enthalpy, 40, 59, 79, 95, 114, 118, 180, 243, 338 equilibrium phase, 177 exchange interaction, 15, 28, 49, 62, 70, 123, 158, 178, 183, 215, 255, 365, 375, 437, 445 exchange softening, 157, 160 exchange stiffness, 11, 16, 123, 133, 158, 410

bcc-Fe, bcc-Fe(Si), 3, 37, 138, 178, 230, 306, 386, 399, 429 cluster formation/clustered state, 69, 303 cluster glass, 123, 131 coercivity, 437, 445 compaction process/parameters, 313, 315, 328 composition fluctuations, 59, 67 corrosion, 79, 165, 229 corrosion resistance, 165, 229 crystallization: - crystallite sizes, 353 - grain boundary, 3, 47, 75, 112, 153, 385, 397 - Johnson-Mehl-Avrami (JMA) kinetics/model, 41, 80, 115, 323 449

450 extended X-ray absorption fine structure (EXAFS), 35, 231, 327 ferromagnetic: - domain, 219 - material, 15, 396, 409, 418 - ordering, 63, 123, 159 - resonance (FMR), 409 FINEMET, 1, 7, 35, 47, 60, 73, 79, 83, 112, 135, 147, 150, 187, 219, 226, 230, 253, 331, 340, 373, 409 finite size effects, 253, 260 fractal dimensionality, 209, 214, 217 free energy curve, 267, 276 glass forming ability, 166, 169, 306, 311, 321, 326, 445 glass transition, 136, 143, 166, 170, 267, 281, 327, 341, 345 glassy alloys, 363 (see: amorphous alloys) glass formers, 199, 267, 321 grain size: - determination, 149, 231, 237 - distribution, 20, 77, 117, 392 - grain size average, 1, 16, 27, 35, 111, 418 heat treatment, 2, 35, 48, 61, 64, 87, 105, 133, 162, 177, 181, 185, 199, 274, 302, 353, 361, 378, 386, 410, 423, 425 HITPERM, 10, 47, 73, 79, 111, 136, 187, 373, 381 hyperfine field, 59, 66, 116, 183, 187, 220, 233, 256, 377, 385, 396, 401, 429, 444 icosahedral phase/short range order, 301, 311, 313 infrared radiation, 331 interatomic bonding, 69, 289 intergranular phase, 28, 33, 124, 152, 255, 373, 422 intermediate range order, 38, 389 intermetallic compounds, 267, 276, 279, 301 isolated nanoparticles, 124, 253, 264

magnetic behaviour: - antiferro, 443 - ferro, 10, 15, 65, 100, 114, 162, 175, 262, 369, 396, 409, 441 - hard, 4, 23, 123, 131, 197, 395 - paramagnetic, 33, 62, 123, 354, 391, 444 - soft, 1, 15, 47, 70, 111, 123, 159, 164, 177, 189, 199, 255, 331, 409, 422 - superparamagnetic, 123, 151, 158, 182, 233, 255, 373, 376, 385, 393 magnetic multilayer, 275, 385, 409, 412 magnetic permeability, 165, 196, 341, 373 magnetic susceptibility, 215, 257, 363 magnetoimpedance, giant magnetoimpedance (GMI), 171, 331, 336 magnetoresistance, 331, 336, 339, 364, 370, 393 magnetostriction, 2, 8, 38, 47, 102, 107, 136, 142, 167, 170, 182, 196, 204, 254, 338, 375, 395, 422 mechanical alloying, 3, 148 mechanical properties, 91, 165, 197, 241, 279, 289, 302, 313, 320, 321, 354, melting point, 267, 271 melt spinning, 3, 92, 147, 159, 166, 170, 199, 280, 301, 313, 353, 361, 364, 437 metastable crystalline phase, 177, 268, 279, 302, 444 microhardness, 313, 316, 319 molecular dynamics simulation, 209 Monte Carlo simulation, 131, 241, 253, 263 Mössbauer effect: - magnetic hyperfine splitting, 396, 403 (see: Zeeman sextet) - quadrupole doublet, 153, 180, 223, 306, 378, 396, 402 - rf-collapse, 182, 395, 388, 406 - rf-sidebands, 395, 399 Mössbauer spectrometry: - conversion electron (CEMS), 177, 299, 421, 432 - rf-technique, 182, 395, 406 nanocomposite, 163, 385 nanocrystal formation, 79

451 nanocrystalline materials, 3, 16, 27, 47, 77, 123, 135, 178, 192, 220, 230, 253, 354, 385, 409, 418 nanocrystalline phase/state/structure, 40, 69, 75, 83, 88, 92, 97, 99, 109, 147, 178, 230, 377, 404 nanocrystallization kinetic, 36, 111 NANOPERM, 1, 3, 35, 50, 53, 73, 79, 112, 136, 141, 159, 182, 219, 230, 253, 373, 402, 421, 427 nanophase composites, 91, 321, 328 nanowire arrays, 165, 174 neutron irradiation, 219, 226 Pauli susceptibility, 363 particles: - fine/ultrafine, 87, 88, 177, 230, 375 - isolated, 62, 129, 253, 263, 415 - multi particle system, 19, 29 - nanoparticles, 60, 123, 144, 157, 253, 390 penetrating fields, 253, 255, 261, 263 percolation, 209, 242, 246, 391, 441 periodic crystals, 241, 249 phase transitions, 126, 157, 214, 241, 246, 297 planar flow casting, 229 Poisson ratio: - definition, 243 - negative, 241, 246, 250 pressure negative, 241 radial distribution function (RDF), 37, 209, 352, 359, 439, 445 random anisotropy, 3, 11, 15, 111, 141, 143, 158, 178, 256 rapid quenching/solidification, 69, 148, 200, 267, 276, 279, 301, 314, 321, 353, 357, 434 (see: melt spinning) relaxation: - activation energy, 99, 104, 107 - structural, 60, 67, 82, 99, 105, 331, 342 - paramagnetic, 182, 388 - thermal/temperature, 99, 105, 353 - time, 104, 369, 395

resistivity, 35, 73, 75, 77, 81, 167, 171, 220, 331, 354, 364, 368 Scherrer formula/equation, 231, 233, 305, 356, 359 short range order (SRO), 74, 102, 132, 141, 215, 220, 255, 274, 276, 301, 351, 353, 375, 426 solid solution, 3, 91, 301, 303, 307 specific heat, 63, 67, 257, 269, 276, 363, 366 spinodal decomposition, 61 Stokes-Einstein equation, 267, 271, 277 Stoner enhancement factor, 363, 365 structure thermal stability, 185 stress tensile, 135, 137 superconducting transition, 363, 366, 369 supercooled liquid, 136, 166, 270, 327, 331, 341, 351, 440 surface spin disorder, 253, 257, 262 Surinach curve/plot, 80, 81, 88 thermodynamic properties, 257, 267 thermogravimetry, 199 thermokinetic extraction process, 199, 204 transport properties, 368 two phase model, 409, 411 undercooled liquid/melt, 69, 268, 271, 274, 345, 352 viscosity: - liquid state, 267, 345 - undercooled liquid, 352 X-ray diffraction (XRD), 55, 80, 116, 138, 177, 200, 229, 262, 280, 301, 309, 313, 321, 335, 353, 386, 392, 421, 435, 444 Zeeman sextet, 184, 396

LIST OF PARTICIPANTS of the NATO Advanced Research Workshop “Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors (PROSIZE)” June 8-14, 2003, Budmerice, Slovakia FERNANDO AUDEBERT, e-mail: [email protected] Dept. of Materials, University of Oxford, Parks Road Oxford OX1 3PH, United Kingdom ANTON ANDRONIC, e-mail: [email protected] Institute for Physics and Nuclear Engineering IPNE P.O. Box MG6, R-76900 Bucuresti-Magurele, Romania JUDITH BALOGH, e-mail: [email protected] Research Institute for Solid State Physics and Optics, Konkoly Thege ut 29-33, P.O. Box 49, 1525 Budapest, Hungary JOSE MANUEL BARANDIARAN, e-mail: [email protected] Dpto de Electricidad y Electronica, Universidad del Pais Vasco (UPVEHU) P.O. Box 644, E-48080 Bilbao, Spain YURI V. BARMIN, e-mail: [email protected] Voronezh State Technical University Moskovski Prospekt 14, 394026 Voronezh, Russia LIVIO BATTEZZATI, e-mail: [email protected] Dipartimento di Chimica IFM, Università di Torino Via Giuria 9, 10125 Torino, Italy ALEXEY V. BONDAREV, e-mail: [email protected] Voronezh State Technical University Moskovski Prospekt 14, 394026 Voronezh, Russia SVEN BOSSUYT, e-mail: [email protected] Dept. of Materials Science & Metallurgy, University of Cambridge Pembroke St., Cambridge CB2 3QZ, United Kingdom HORIA CHIRIAC, e-mail: [email protected] National Institute of Research and Development for Technical Physics 47 Mangeron Blvd., 700050 Iasi, P.O. Box 833, Romania CLARA CONDE, e-mail: [email protected] Departamento de Fisica de la Materia Condensada, Universidad de Sevilla Apartado 1065, 41080 Sevilla, Spain OVIDIU CRISAN, e-mail: [email protected] National Institute for Materials Physics, P.O. Box MG-7 76900 Bucharest, Romania JARMILA DEGMOVA, e-mail: [email protected] Dept. of Nuclear Physics and Technology, Slovak University of Technology Ilkoviþova 3, 812 19 Bratislava, Slovakia 453

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VENTSISLAV DIMITROV, e-mail: [email protected] Dept. of Physics, Iúik University Büyükdere Cad., 80670 Maslak-Istanbul, Turkey EVA FAZAKAS, e-mail: [email protected] RISSPO, Hungary Academy of Sciences Konkoly Thege ut 29-33, P.O. Box 49, 1525 Budapest, Hungary JEAN-MARC GRENECHE, e-mail: [email protected] Lab. de Phys. de l’Etat Condensé, UMR CNRS 6087, Université du Maine F72085 Le Mans Cedex 9, France RYUSUKE HASEGAWA, e-mail: [email protected] Metglas, Inc, 440 Allied Drive, Conway, SC 29526, USA GISELHER HERZER, e-mail: [email protected] Rapid Solidification Technology, Vacuumschmelze GmbH & Co. KG D-63450 Hanau, Germany KAZUHIRO HONO, e-mail: [email protected] Metallic Nanostructure Group, National Institute for Materials Science 1-2-1 Sengen, Tsukuba 305-0047, Japan BOGDAN IDZIKOWSKI, e-mail: [email protected] Institute of Molecular Physics, Polish Academy of Sciences M. Smoluchowskiego 17, 60-179 PoznaĔ, Poland EMILIA ILLEKOVA, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia BORIS JALNIN, e-mail: [email protected] Moscow State Institute of Steel and Alloys Leninsky prosp., 4, Moscow, 119049, Russia DUSAN JANIýKOVIý, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia SERGEY D. KALOSHKIN, e-mail: [email protected] Moscow State Institute of Steel and Alloys Leninsky prosp., 4, Moscow, 119049, Russia IRINA YU. KHMELEVSKAYA, e-mail: [email protected] Moscow State Institute of Steel and Alloys Leninsky prosp., 4, Moscow, 119049, Russia IVAN KOKANOVIC, e-mail: [email protected] Dept. of Physics, Faculty of Science, University of Zagreb P.O. Box 331, Bijenicka cesta 32, Zagreb, Croatia PETER KOLLÁR, e-mail: [email protected] Institute of Physics, Faculty of Sciences, P. J. Šafárik University Park Angelinum 9, 041 54 Košice, Slovakia MICHAL KOPCEWICZ, e-mail: [email protected] Institute of Electronic Materials Technology Wólczynska 133, 01-919 Warsaw, Poland

455

MACIEJ KOWALCZYK, e-mail: [email protected] Faculty of Materials Science and Engineering, Warsaw University of Technology Woáoska 14, 02-507 Warsaw, Poland MARIAN KRAJýI, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia TIBOR KRENICKY, e-mail: [email protected] Institute of Experimental Physics Slovak Academy of Sciences, Watsonova 49, 043 53 Košice, Slovakia PETR KUBECKA, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia TADEUSZ KULIK, e-mail: [email protected] Faculty of Materials Science and Engineering, Warsaw University of Technology Woáoska 14, 02-507 Warsaw, Poland MARTIN KUSÝ, e-mail: [email protected] Università di Torino, Dipartimento di Chimica IFM P. Giuria 9, 10125 Torino, Italy NICOLETA LUPU, e-mail: [email protected] National Institute of Research and Development for Technical Physics 47 Mangeron Blvd., P.O. Box 833, 700050 Iasi, Romania FREDERIC MAZALEYRAT, e-mail: [email protected] SATIE – ENS de Cachan 61 Av. du Prés. Wilson, 94235 Cedex, France MARCEL MIGLIERINI, e-mail: [email protected] Dept. of Nuclear Physics and Technology, Slovak University of Technology Ilkoviþova 3, 812 19 Bratislava, Slovakia NEBOJSA MITROVIC, e-mail: [email protected] Joint Laboratory for Advanced Materials, Technological Faculty ýaþak Svetog Save 65, 32 000 ýaþak, Serbia DUSAN MÜLLER, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia KATARINA MÜLLEROVA, e-mail: [email protected] Institute of Materials and Machine Mechanics, Slovak Academy of Sciences Raþianska 75, 831 02 Bratislava, Slovakia MAURO PALUMBO, e-mail: [email protected] Dipartimento di Chimica IFM, Università di Torino via Giuria 9, 10125 Torino, Italy MAREK PEKALA, e-mail: [email protected] Dept. of Chemistry, Warsaw University, al. wirki i Wigury 101, 02-089 Warsaw, Poland KATARZYNA RACKA, e-mail: ifpan.edu.pl Institute of Physics, Polish Academy of Sciences al. Lotnikow 32/46, 02-668 Warsaw, Poland

456

NIRINA RANDRIANANTOANDRO, e-mail: [email protected] Lab. de Phys. de l’Etat Condensé, UPRESA CNRS 6087, Universite du Maine F72085 Le Mans, France SERGEY RASSOLOV, e-mail: [email protected] Physics & Engineering Institute of NAS of Ukraine 72 R. Luxemburg Street, Donetsk, 83114, Ukraine RAMIR RISTIC, e-mail: [email protected] Faculty of Education P. O. Box 144, HR-31000 Osijek, Croatia VIKTORIA RONTO, e-mail: [email protected] Dipartimento di Chimica IFM, Universita di Torino Via Giuria 9, 10125 Torino, Italy STEPHAN ROTH, e-mail: [email protected] IFW Dresden, Institute for Metallic Materials P.O. Box 270116, D-01171 Dresden, Germany JACOB SCHIOTZ, e-mail: [email protected] Center for Atomic-scale Materials Physics, Dept. of Physics Technical University of Denmark, DK-2800 Kogens Lyngby, Denmark DAVID SCHMOOL, e-mail: [email protected] Departamento de Fisica, Faculdade de Ciências, Universidade do Porto Rua do Campo Alegre 687, 4169-007 Porto, Portugal KATARINA SEDLAýKOVÁ, e-mail: [email protected] Dept. of Nuclear Physics and Technology, Slovak University of Technology Ilkoviþova 3, 812 19 Bratislava, Slovakia IVAN SKORVÁNEK, e-mail: [email protected] Institute of Experimental Physics, Slovak Academy of Sciences Watsonova 49, 043 53 Košice, Slovakia KIYONORI SUZUKI, e-mail: [email protected] School of Physics and Materials Engineering P.O. Box 69M, Monash University, Clayton, Victoria 3800, Australia PETER ŠVEC, e-mail: [email protected] Institute of Physics, Slovak Academy of Sciences Dubravska cesta 9, 845 11 Bratislava, Slovakia ANNA ĝLAWSKA-WANIEWSKA, e-mail: [email protected] Institute of Physics, Polish Academy of Sciences al. Lotnikow 32/46, 02-668 Warsaw, Poland MARILENA TOMUT, e-mail: [email protected] National Institute for Materials Physics, Atomistilor 105 bis P.O. Box MG7, 77125 Bucuresti-Magurele, Romania LAJOS K. VARGA, e-mail: [email protected] RISPO, Hungarian Academy of Sciences Konkoly Thege ut 29-33, P.O. Box 49, 1525 Budapest, Hungary KRZYSZTOF WOJCIECHOWSKI, e-mail: [email protected] Institute of Molecular Physics, Polish Academy of Sciences M. Smoluchowskiego 17, 60-179 PoznaĔ, Poland