Interaction Between Defects and Anelastic Phenomena in Solids [1 ed.] 9783038131991, 9783908451532

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Interaction between Defects and Anelastic Phenomena in Solids

Interaction between Defects and Anelastic Phenomena in Solids

Selected, peer reviewed papers from The XIth International Conference on IMPERFECTIONS INTERACTION AND ANELASTIC PHENOMENA IN SOLIDS, IIAPS XI, 24 – 28 September 2007, Tula, Russia

Edited by

Igor S. Golovin and Daniil M. Levin

TRANS TECH PUBLICATIONS LTD Switzerland • UK • USA

Copyright  2008 Trans Tech Publications Ltd, Switzerland

All rights reserved. No part of the contents of this book may be reproduced or transmitted in any form or by any means without the written permission of the publisher.

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Volume 137 of Solid State Phenomena ISSN 1012-0394 (Pt. B of Diffusion and Defect Data - Solid State Data (ISSN 0377-6883)) Full text available online at http://www.scientific.net

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Conference Chairmen

International Honory Committee

Levin D.M. Golovin I.S. Darinsky B.M.

Golovin S.A. Granato A.V. Koiwa M.

(Tula, Russia) (Tula, Russia) (Voronezh, Russia)

Local Organizing Committee Markova G.V. (Tula, Russia) Tihonova I.V. (Tula, Russia) Chukanov A.N. (Tula, Russia) International advisory committee Blanter M.S. Cantelli R. Fang Q. Lambri O.A. Magalas L.B. Mazzolai F. Nikanorov S.P. Pal-Val P.P. Rivière A. San Juan J. Schaller R. Sinning H.-R. Soifer Ya.M.

(Moscow, Russia) (Roma, Italy) (Hefei, China) (Rosario, Argentina) (Krakow, Poland) (Perugia, Italy) (St. Petersburg, Russia) (Kharkov, Ukraine) (Futuroscope, France) (Bilbao, Spain) (Lausanne, Switzerland) (Braunschweig, Germany) (Haifa, Israel)

(Tula, Russia) (Urbana, USA) (Kyoto, Japan)

Program Committee Aksenov V.L. Alekhin V.P. Alshits V.I. Botvina L.R. Feldman E.P. Glezer A.M. Golovin Yu.I. Golovinskiy P.A. Grachev S.V. Gridnev S.A. Gvozdev A.E. Kalinin Yu.E. Khonik V.A. Kondratov V.M. Kozlov E.V. Morozov B.A. Mozgovoj A.V. Nikitin A.N. Ponomarenko A.T. Sherbedinsky G.V. Shutilin Yu.F. Zuev L.B.

(Moscow, Russia) (Moscow, Russia) (Moscow, Russia) (Moscow, Russia) (Donetsk, Ukraine) (Moscow, Russia) (Tambov, Russia) (Voronezh, Russia) (Ekaterinburg, Russia) (Voronezh, Russia) (Tula, Russia) (Voronezh, Russia) (Voronezh, Russia) (Kirov, Russia) (Tomsk, Russia) (Moscow, Russia) (Vinniza, Ukraine) (Dubna, Russia) (Moscow, Russia) (Moscow, Russia) (Voronezh, Russia) (Tomsk, Russia)

Conference organizers:

D.M. Levin

B. M. Darinskij

I.S. Golovin

G.V. Markova

S. P. Nikanorov

S. Kustov

A. Rivière

P. P. Pal-Val

M.S. Blanter, L. Magalas

V.A. Semin, M.S. Blanter, P.P. Pal-Val

A. E. Gvozdev, M.A. Vibojschik, E. M. Grinberg,

S.A. Golovin, A. Rivière

I.V. Tikhonova, V.M. Zharkov

… and students

A. Rivière

L. Magalas

A. Leksowskij,

T. Ivleva, O. Sokolova, J. Göken, A. Mielczarek

A. Strahl

L. M. Bogomolov

M.S. Blanter,

B. Kardashev

L. Magalas

C. Ionascu

Presentation

Poster session

Near University

Discussion

Checking schedule

in Yasnaya Poljana

Preface This volume contains contributions to the bilingual Russian/English Eleventh Conference on “Imperfection interaction and anelastic phenomena in solids” (IIAPS-XI), held in Tula, Russia from 24 to 28 September 2007. The Russian (former Soviet Union) school of anelastic behavior of metallic materials is closely linked with the research activity of Professor B.N. Finkelstein (Moscow), who made several important contributions in the field of the physics of metals. He organized the first three conferences in the Soviet Union on relaxation effects in solids: in Moscow in 1958, in Kharkov in 1960, and in Voronezh in 1962. Later the tradition of holding All-Soviet Union conferences in the field of anelasticity was kept in Voronezh (V.S. Postnikov, B.V. Darinski) and Tula (M.A. Krishtal, S.A. Golovin). This tradition is continued in the present conference. The “Imperfection interaction and anelastic phenomena in solids” conference series in Tula was launched in 1969 at the department of Materials Science (now Physics of Metals and Materials Science), and was continued more recently in cooperation with the Physics Department. Professor G.V. Kurdjumov, especially well-known for his work in the field of martensitic transformation, played an important role in supporting these conferences in Tula. Several researchers from Poland, Czechoslovakia and Bulgaria regularly took part in these AllRussian conferences. In 2001 the conferences in Voronezh and in Tula were combined to ensure regular meetings every three years in sequence, so that the present IIAPS-XI conference is a continuation not only of IIAPS-X (Tula 2001), but also of the last “Relaxation phenomena in solids” conference which took place in Voronezh in 2004. Since 2001, research papers from Argentina, Belgium, France, Germany, Japan, Italy, Netherlands, Norway, Poland, Spain, Switzerland, UK, USA and others were presented in Tula and in Voronezh in addition to our permanent contributors from former Soviet Union countries. The main purpose of the conference series is to provide an International Meeting for researchers, scientists and engineers on defect interactions and related anelastic properties in solid materials. The Conference scope covers different aspects related to elastic energy dissipation in solids due to the presence and evolution of crystal defects, including fundamental aspects, experimental methods, technological applications, nondestructive testing and complementary techniques. The title of the conference series in Tula was translated in 1997 literally from Russian as “Imperfection interaction and anelastic phenomena in solids” (IIAPS-IX), while it sounds better in English as “Interaction between defects and anelastic phenomena in solids”. This latter title is chosen as the title of the IIAPS-XI proceedings in this volume. The editors are grateful to all authors and reviewers for their high quality work, as well as to Prof. G.V. Markova and Dr. I.V. Tikhonova for their devoted service at the Conference Secretariat. We also thank Professors S.A. Golovin, B.M. Darinski, S.P. Nikanorov, and H. Neuhäuser for their most helpful advice on the conference organisation. RFBR support (grant n. Ц 41.07 ГРФ) is gratefully acknowledged. Igor S. Golovin* and Daniil M. Levin. Corresponding author: Physics of Metals and Materials Science Department Tula State University, Lenin ave 92, 300600 Tula, Russia

Table of Contents Committees Photos Preface Computer Simulation of the Interaction of Junction Disclinations in Nanomaterials with Grain Boundary Vacancies A.A. Nazarov and R.T. Murzaev Nonlinear Correlated Interaction of Mesodefects and Transition to Macrofracturing A. Leksowskij, B.L. Baskin, A.P. Tishkin and A. Abdumanonov Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy L.B. Magalas and M. Majewski High-Temperature Mechanical Relaxation due to Dislocation Motion inside Dislocation Networks A. Rivière, M. Gerland and V. Pelosin High Temperature Mechanical Loss Spectrum of 3Y-TZP Zirconia Reinforced with Carbon Nanotubes or Silicon Carbide Whiskers C. Ionascu and R. Schaller Low Temperature Kinetics of In-Cd Solid Solution Decomposition P.P. Pal-Val, L.N. Pal-Val, A.A. Ostapovets and P. Vanek Effect of Heat Treatment on Acoustic Properties of Chromium Polycrystals at Low Temperatures P.P. Pal-Val, L.N. Pal-Val, S.B. Golovina and I.S. Golovin Analysis of Internal Friction Peaks in High Purity Molybdenum by a Viscoelastic Procedure Independent of the Relaxation Strength C.L. Matteo, O.A. Lambri, G.I. Zelada-Lambri, P.A. Sorichetti and J.A. García Structure and Anelasticity of Fe-Ge Alloys I.S. Golovin, T.V. Ivleva, S. Jäger, P. Jencus, H. Neuhäuser, S.A.T. Redfern and C. Siemers Snoek-Type and Zener Relaxation in Fe-Si-Al Alloys I.S. Golovin, S. Jäger, V.A. Semin, G.V. Serzhantova, H.R. Sinning, O.A. Sokolova, F. Stein and S.A. Golovin Room-Temperature Short-Range Ordering in Fe-Si Alloys Observed by Internal Friction F. González, D. Ruiz and Y. Houbaert Mechanical Spectroscopy and Neutron Diffraction Studies in Fe-Al-Si Alloys O.A. Lambri, J.I. Pérez-Landazábal, G.J. Cuello, J.A. Cano, V. Recarte and I.S. Golovin Mechanical Spectroscopy of the Fe-25Al-Cr Alloys in Medium Temperature Range I.S. Golovin and A. Rivière On the Formation of High Damping State in Fe-Al and Fe-Cr Alloys I.B. Chudakov, N.A. Polyakova, S.Y. Mackushev and V.A. Udovenko On the Formation of High Damping State and Optimization of Structure of Industrial Damping Steels V.A. Udovenko, I.B. Chudakov, N.M. Alexandrova, R.V. Kakabadze and N.N. Perevalov Influence of Heat Treatment on Magnetic and Damping Properties of Fe-11 at.% Al Alloys A. Mielczarek, W. Riehemann, O.A. Sokolova and I.S. Golovin Influence of Thermal Cycling and Equivalent Heat Treatment on Amplitude Dependence of Internal Friction in Cu-Al-Mn Shape Memory Alloys A. Mielczarek, M. Marczyk and W. Riehemann Mechanical and Fatigue Properties of Cu-Al-Mn Shape Memory Alloys with Influence of Mechanical Cycling on Amplitude Dependence of Internal Friction at Room Temperature A. Mielczarek, W. Riehemann, S. Vogelgesang and B. Tonn Effect of Cold Rolling on the Damping of As Cast Cu-Al-Mn Shape Memory Alloys A. Mielczarek, Y. Wöckel and W. Riehemann In Situ Neutron Diffraction Study of Internal Stresses in 60% Mn-40% Cu Alloy Introduced by Ageing S.G. Sheverev, G.V. Markova and V.V. Sumin

1 9 15 21 29 35 43 49 59 69 83 91 99 109 119 129 137 145 155 163

b

Interaction between Defects and Anelastic Phenomena in Solids

Change of Structure and Properties of 51CrV4 Shaft Caused by Thermo-Mechanical Treatment J. Göken, M. Maikranz-Valentin, K. Steinhoff, T.S. Pavlova, T.V. Ivleva and I.S. Golovin Damping in AZ31 ECAP-Processed Alloy T.V. Ivleva, J. Göken, I.S. Golovin, Z. Zuberova, M. Maikranz-Valentin and K. Steinhoff Study of PPV Polymer Layers on Si Substrates by Mechanical Spectroscopy A. Strahl, S. Schrader, S. Katholy, B. Grimm and H. Neuhäuser Do Electromagnetic Pulses Induce the Relaxation or Activation of Microcracking Rate in Loaded Rocks? L. Bogomolov and A. Zakupin Phase Heterogeneities of Lipidic Aggregates L.V. Elnikova Mechanical Spectroscopy of Oil Films on Metallic and Neutral Substrates L.B. Magalas On the History of the Russian School of Anelasticity in Solids S.A. Golovin

169 181 189 199 209 215 231

Solid State Phenomena Vol. 137 (2008) pp 1-8 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.1

Computer simulation of the interaction of junction disclinations in nanomaterials with grain boundary vacancies A. A. Nazarov1,a and R. T. Murzaev1,b 1

Institute for Metals Superplasticity Problems, Russian Academy of Sciences, 39 Khalturin street, Ufa 450001, Russia a

[email protected], [email protected]

Keywords: nanostructured metals, severe plastic deformation, nonequilibrium grain boundary, junction disclination, vacancy, atomistic simulations.

Abstract. Junction disclinations are important elements of the structure of nanostructured metals produced by severe plastic deformation (SPD). Effect of these defects on the formation energy of vacancies in grain boundaries (GBs) is studied by means of atomistic computer simulations. Estimates based on the calculations of vacancy formation energies suggest that at least two orders of magnitude increase of the GB diffusion coefficient can be expected due to junction disclinations in nanostructured metals. Introduction Experimental studies of bulk nanostructured metals and alloys fabricated by severe plastic deformation (SPD) methods show that grain boundaries (GBs) in these materials have a specific non-equilibrium structure caused by defects induced due to the deformation [1, 2]. It has been shown that disclinations at triple junctions of GBs are important elements of this structure [3]. On the other hand, SPD-nanostructured metals exhibit a GB diffusion coefficient several orders of magnitude higher than that in ordinary polycrystals or bicrystals [4, 5]. Since the GB diffusion coefficient recovers its ordinary value after mild annealing of nanostructured metals which does not affect the grain size, the enhanced GB diffusion coefficient is related to the nonequilibrium GB structure [4]. There have been several attempts to rationalize the behavior of diffusion coefficient of nonequilibrium GBs in terms of continuum theories [6-8]. In one of these approaches it has been assumed that the climb of extrinsic grain boundary dislocations to annihilate or form ordered arrays results in a decrease of the vacancy formation energy in nonequilibrium GBs [6]. It has been also suggested that gradients of elastic stresses in GBs due to junction disclinations can result in an additional driving force for the migration of vacancies that leads to an increase of the effective GB diffusion coefficient [7]. In [8], the diffusion equation with a time-dependent GB diffusion coefficient has been solved to analyze the diffusion behavior of nanostructured metals. Diffusion in the stress fields of disclinations was considered in [9] where it was shown that the disclinations could serve as effective sinks for point defects that might result in a heterogeneous nucleation of pores. Such pores are found to form in nanoparticles grown by electro-crystallization and this is explained in [10] by the absorption of vacancies by a point disclination formed in the particles at their early stages of growth. However, the effect of disclinations on the GB diffusion coefficient and the origin of enhanced GB diffusion in nanostructured metals are not well understood yet. An insight to the mechanisms and parameters of GB diffusion can be obtained by the use of atomistic computer simulations. Earlier the authors calculated the formation and migration energies of vacancies in the stress field of disclinations in special [001] tilt GBs in Ni [11]. In the present paper these data are used to estimate the effect of disclinations on the average vacancy concentration which is one of the most important factors determining the GB diffusion coefficient. Vacancy formation energies in the stress

2

Interaction between Defects and Anelastic Phenomena in Solids

fields of disclinations in a general mixed tilt and twist GB are also calculated. Implications of the data obtained to the GB diffusion coefficient are discussed. Average vacancy concentration in disclinated special tilt grain boundaries in Ni In Ref. [11] the formation energies of vacancies were calculated for a special tilt GB [001] Σ = 5 (310) in Ni containing positive and negative wedge disclinations. The disclinations were introduced along the axis of a bicrystalline cylinder with the radius R = 100 nm. As shown by earlier calculations [12], the critical strength of a negative disclination at which it initiates a crack is approximately equal to ωc ≈ 6° for this cylinder radius. Because of this, disclinations with lower strengths ω = ± 5° for the simulations of vacancies were chosen. At a site of interest of the GB an atom was removed and the system was relaxed at the zero temperature. This allowed the energy to form a vacancy at this site E f to be determined. A calculation and comparison of E f values at crystallographically equivalent sites located on different distances from the dislocation line allowed the study of the effect of disclination stress fields on the vacancy formation energy. As a reference structure, an equilibrium Σ = 5 (310) tilt GB was simulated. The atomic structure of this GB and numeration of its crystallographycally non-equivalent sites are presented in Fig. 1. The values of vacancy formation energy at these sites of the equilibrium GB, Ef0, are presented in Table 1. These will serve below as reference values for a comparison with the vacancy formation energies in non-equilibrium GBs containing disclinations.

Fig. 1. Atomic structure of Σ = 5 (310) tilt grain boundary in Ni viewed along the tilt axis [001]. Black and white circles correspond to atoms on two successive (002) planes; hC is the GB period. Numerated are nonequivalent sites for which vacancy formation energies are calculated. Table 1. Vacancy formation energies in the sites of an equilibrium Σ = 5 (310) tilt boundary. Site No.

1

2

3

4

5

Ef0, [eV]

1.51

1.32

1.31

0.98

0.80

The results of calculations of E f near the negative and positive disclinations are collected in Figs. 2 a, b. Horizontal lines on the figures denote the values of E f calculated for equilibrium GBs. As one can see from the figures, the vacancy formation energy strongly depends on a site. The stress fields of disclinations change E f significantly, particularly near the disclination core. The signs of changes near the positive and negative disclinations are opposite, although in the stress field of a particular disclination at some sites E f can increase and at the others decrease.

Solid State Phenomena Vol. 137

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At large distances from the disclination cores E f asymptotically approaches a value for the same site of an equilibrium GB, E f 0 . Due to a long-range character of the disclination stress field, the effect of the latter on E f is significant even at fairly large distances. For instance, at r = 10 hc ≈ 5.5 nm the difference is about E f − E f 0 ≈ 0.05 - 0.10 eV.

(a)

(b)

Fig. 2. The dependencies of GB vacancy formation energies on a distance from a disclination core; (a) for negative disclination ω = -5°; (b) for positive disclination ω = + 5°. - site 1, -site 3, - site 4; hC = 0.56 nm stands for the period of (310) tilt GB. Solid lines fit the simulation data obtained for the sites of a disclinated GB, while the dashed lines mark the levels corresponding to vacancy formation energies at a corresponding site in the equilibrium GB. The data presented in Figs. 2 a, b can be used for an approximate estimate of the change of vacancy concentration caused by disclinations. For this, enumerate the crystallographically nonequivalent sites of a structural unit of the GB by α (α = 1, …, m = 5). The probability of formation of a vacancy at site α at a temperature T is equal to cα = exp(− E αf / kT ) with an accuracy to a pre-

exponential factor of the order of one, where E αf is the vacancy formation energy at this site. As in an equilibrium GB all structural units are equivalent, the average vacancy concentration can be obtained by a summation of cα over m sites of one unit: m

m

< C 0 >= ∑ cα = ∑ exp( − E αf 0 / kT ) . α =1

(1)

α =1

For a GB containing a defect the averaging should be carried out oven all structural units belonging to a region of interest near the defect, since different units experience different stresses of the defect. Denote N the number of structural units belonging to a GB section of length r with the left edge on the disclination core and enumerate these units by i. Then the average vacancy concentration on the GB section of length r is equal to N

m

N

m

< C >= ∑∑ ciα = ∑∑ exp( − E ifα / kT ) . i =1 α =1

(2)

i =1 α =1

From Eqs. 1 and 2 the ratio < C > / < C0 > of the average vacancy concentrations in nonequilibrium and equilibrium GBs can be calculated.

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Interaction between Defects and Anelastic Phenomena in Solids

According to experimental data [5], a significant GB diffusion in SPD-nanostructured Ni occurs at temperatures T = 400 K and more. Hence, the ratio < C > / < C0 > was calculated for this temperature. The dependencies of < C > / < C0 > on r for a positive and negative disclination at Т = 400 К are presented in Figs. 3a, b. These figures demonstrate that on average the stress fields of a negative disclination decrease and those of a positive disclination enhance the vacancy concentration. In a section of length r = 12hC ≈ 6.7 nm the positive disclination causes an increase of average vacancy concentration by about three orders of magnitude. Basing on this result one can estimate also the effect of disclinations on the GB diffusion coefficient of SPD-nanostructured metals. Assume that the grain size is equal to d=135 nm, then the GB length is L ≈ d/2 ≈ 67 nm. Normally in a deformed polycrystals the junction disclinations are coupled into dipole configurations, i.e. disclinations of opposite signs are located on opposite junctions of a GB [13]. Let the junctions contain disclinations of the strengths ω = ± 5°. The positive disclination enhances the vacancy concentration, while the negative one decreases it. For a rough estimate one can neglect the vacancy concentration in all GB region except for the one with the length r = 6.7 nm near the positive disclination and average this over the whole GB length. This will give < C > / < C0 >≈ 10 3 r / L ≈ 102.

(a)

(b)

Fig. 3. The dependencies of the average vacancy concentrations in Σ = 5 (310) tilt GB near a negative (a) and positive (b) wedge disclination on the distance of averaging r. The circles denote calculated values, the solid line fits these data. Thus, disclinations with the strength about 5° can result in an at least two orders of magnitude increase of the average vacancy concentration in special tilt GBs in nanostructured metals with the grain size about d = 100 - 200 nm. Calculations of the activation energy for vacancy migration show that it is also affected significantly by the stress fields of disclinations [11]. Although rough estimates of the effect of this factor on the GB diffusion coefficient without detailed calculations are impossible [14], one can qualitatively expect that this can also contribute to an enhancement of the GB diffusion coefficient. Therefore, one can conclude that at least two orders of magnitude enhancement of the GB diffusion coefficient in nanostructured metals can be expected due to junction disclinations.

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Vacancy formation energies in a general tilt and twist grain boundary In real nanostructured materials GBs of general character are more common rather than special tilt GBs. Therefore, the effect of disclinations on the characteristics of vacancies in such general GBs is of interest. To study this effect, a bicrystalline cylinder containing a mixed tilt and twist GB was constructed as follows. First a Σ=5 (310) tilt GB with θtl=36.9° was constructed; then a θtw=153.4° twist was applied thus resulting in a mixed tilt and twist GB with periods H x = 1.79 nm and H z = 2.84 nm (Fig. 4). Positive and negative wedge disclinations with the strengths ω = ± 5° were introduced along the axis of a bicrystalline cylinder with radius R=100 nm containing the constructed GB by applying the displacement field of a disclination and removal or insertion of material. A system thus constructed is too large for atomistic simulations. In order to calculate the vacancy characteristics three parts of the systems containing 3rd, 5th and 7th periods of the GB located on distances 5.4, 9.0 and 12.6 nm from the cylinder axis were cut (Fig. 5). These parts were three periods of length along the GB plane and sufficiently large in the normal direction in order to simulate them as separate systems. The displacement field of the disclination characteristic for a chosen system was fixed by fixing the positions of atoms in the outer shell of these systems (Fig. 5).

Fig. 4. Computation box of a mixed tilt and twist GB on (310) plane. The GB lies on the xOz plane, z is along the tilt axis [310]. The final GB is obtained by a twist around the y axis.

Fig. 5. A schematic representation of atomic systems selected for the simulation of GB vacancies; the systems contain three periods of the GB with a period of interest in the center. The dark region inside the system denotes the region where vacancies are introduced, atoms of the outer dark region are fixed.

GB vacancies were created by removing an atom at each of 384 positions of a GB period in a layer of thickness δ = 0.8 nm in which a significant disorder of the atomic structure is observed. Relaxing each of configurations containing a vacancy the vacancy formation energies were calculated for all these sites. The statistics of the vacancy formation energies have been represented in terms of spatial distributions across the GB plane and distribution histograms. These distributions for the equilibrium GB and the third GB period from a positive and negative disclination are represented in Figs. 6 a - c and Figs. 7 a - c.

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Interaction between Defects and Anelastic Phenomena in Solids

(a)

(a)

(b)

(b)

(c)

(c)

Fig. 6. Spatial distribution of GB vacancy energies in equilibrium GB (a), in 3rd period near a positive (b) and negative (c) disclination; r is a distance from the GB central plane.

Fig. 7. Histograms of distribution of GB vacancy energies in equilibrium GB (a), in the 3rd period near a positive (b) and negative (c) disclination.

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An analysis of these distributions shows the following. First, the vacancy energy distribution is bimodal. Peaks of the distribution in the equilibrium GB occur near about 0.2 eV and 1.3 eV (Fig. 7 a). The latter is closer to the lattice vacancy formation energy E fl = 1.63 eV. As seen from the spatial distributions, both the low and high energy vacancies can exist with a nearly equal probability in the GB center and on its periphery, close to the lattice sites. The average vacancy formation energy in the equilibrium GB is equal to 0.92 eV. Near the negative disclination it is equal to 1.10 eV in the third period, 0.97 eV in the fifth and 0.92 eV in the seventh. Near the positive disclination the average vacancy energy is less than in equilibrium GB: 0.65 eV in the third, 0.84 eV in the fifth and 0.92 eV in the seventh period. Thus, a significant, up to about 0.05 - 0.07 eV difference in the average vacancy formation energy exists on a distance 9 - 11 nm from the disclination cores. This is similar to the data obtained for the special tilt GB (310) (Fig. 2). Therefore, a similar effect of the disclinations on the vacancy concentration and GB diffusion coefficient can be expected also for general GBs. As one can see from Figs. 6 b and 7 b, near the positive disclination the formation energies of low-energy vacancies become negative. This means that at all these sites the formation of a vacancy is energetically favored. Therefore, a positive disclination will absorb vacancies at these sites. Summary Calculations of grain boundary vacancy formation energies in the stress fields of wedge disclinations demonstrate that the vacancy concentration and consequently the GB diffusion coefficient is significantly effected by the disclinations. At least two orders of magnitude increase of the effective grain boundary diffusion coefficient can be expected in both special tilt and general tilt and twist GBs in bulk nanostructured materials with the grain size d ≈ 100 - 200 nm due to disclinations with the strength about ω ≈ 5°. Acknowledgments The present work was supported by the Federal Agency of Science and Innovations of Russian Federation through a government contract No. 02.513.11.3319. A partial support from the Research and Education Foundation “Intels” (Magnitogorsk, Russia) is also acknowledged. References [1]

R. Z. Valiev, A. V. Korznikov and R. R. Mulyukov: Mater. Sci. Eng. A Vol. 168 (1993), p. 141.

[2]

A. А. Nazarov and R. R. Mulyukov, in: Nanoscience, Engineering and Technology Handbook, edited by S. Lyshevski, D. Brenner, J. Iafrate and W. Goddard, CRC Press, Boca Raton, USA (2002), p. 22.

[3]

A. A. Nazarov, A. E. Romanov and R. Z.Valiev: Scripta Mater. Vol. 34 (1996), p. 729.

[4]

R. Würschum, A. Kübler, S. Gruß, P. Scharwaechter, W. Frank, R. Z. Valiev, R. R. Mulyukov and H.-E. Schaefer: Annalles de Chimie – Science des Matériaux. Vol. 21 (1996), p. 471.

[5]

Yu. R. Kolobov, G. P. Grabovetskaya, M. B. Ivanov, A. P. Zhilyaev and R.Z. Valiev: Scripta Mater. Vol. 44 (2001), p. 873.

[6]

I. A. Ovid’ko and A. B. Reizis: Phys. Solid State. Vol. 43 (2001), p. 35.

[7]

A. A. Nazarov: Philos. Mag. Lett. Vol. 80 (2000), p. 221.

[8]

A. A. Nazarov: Phys. Solid State. Vol. 45 (2003), p. 1166.

[9]

A. E. Romanov and G. G. Samsonidze: Technical Physics Lett. Vol. 14 (1988), p. 585.

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Interaction between Defects and Anelastic Phenomena in Solids

[10] I. S. Yasnikov, A. A. Vikarchuk: Technical Physics Lett. Vol. 33 (2007), p. 817. [11] R. T. Murzaev and A. A. Nazarov: Phys. Metals Metallography. Vol. 102 (2006), p. 198. [12] K. Zhou, A. A. Nazarov and M. S. Wu: Phys. Rev. B Vol. 73, Art. No 045410 (2006). [13] A. E. Romanov and V. I. Vladimirov, in: Dislocations in Solids, edited by F. R. N. Nabarro, volume 9, North-Holland, Amsterdam (1992), p. 191. [14] M. R. Sørensen, Y. Mishin and A. F. Voter: Phys. Rev. B Vol. 62 (2000), p. 3658.

Solid State Phenomena Vol. 137 (2008) pp 9-14 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.9

Nonlinear Correlated Interaction of Mesodefects and Transition to Macrofracturing A. Leksowskijа, B. L. Baskin, A. P. Tishkin, A. Abdumanonov Ioffe Physicotechnical Institute, Russian Academy of Science, Polytekhnicheskaya 26, St-Petersburg, Russia а

[email protected]

Keywords: explosion-like microcracking, discrete change of local elastic strain energy state, relaxation stress redistribution, dissipative properties, energy absorbtion capability.

Abstract. The following experimental data are presented and discussed: a) the explosion-like nucleation of micro- (meso) cracks; b) the dependence of the scale of local “microcatastrophe” on the relation between the released strain energy and the dissipative properties of the nearest environment; c) the determinative influence of the dissipative properties on the rate of redistribution of local stresses. The presented data evidence that every event of defect nucleation that takes place at either micro- or mesoscale level in the heterogeneous solid examines the energy absorbtion properties of the whole system. Future localization of the macroscopical failure is of “accidental type”, that is results from random, active formation of the ensemble of micro- and mesocracks in different localities as a consequence of the decrease of the dissipative capability of surrounding volume. Introduction It is commonly accepted [1,2] that the depletion of strength resource (longevity) is a consequence of the processes of damage accumulation not only on the level of elementary defects of crystalline lattice but also on a higher scale level, that is on the level of voids in the solid continuum, such as micro- (meso) cracks 0.1 ÷ 100 µ in size. While the physics of conversion of a cluster of elementary structural defects of dislocation type to the macroscopic crack is learned in sufficient details [3], the problem of the transformation of a microcrack to the main crack requires a thorough research. This work is to study the nucleation, evolution and interaction of individual cracks and ensembles of cracks, as well as elucidate their role in the formation of the prefailure condition of material. Methods and materials A set of complementary experimental methods was applied: in situ scanning electron microscopy (SEM); amplitude-time analysis of the acoustic emission (AE) signals with using the technique of location; fast microshooting in the polarized light; modeling of an elementary event of fracture. The samples made of hot solidified epoxy resin were shaped to a double trowel with the gauge of 10 × 6 × (0.7 ÷ 1) mm3, and they had an artificial stress concentrator (incision). In order to eliminate the surface charge, the samples were preliminary saturated by iodine. Finally, they were dark-cherrycoloured, quite brittle; their ultimate strength was about 25 ÷ 35 MPa. The sample geometry and the thermal treatment provided the stressed state close to that of plain strain type. In the case of application of the AE technique, the samples were made of a composite with the epoxy resin matrix filled by unidirectional boron, carbon, or glass fibers. The using of highmodulus fibers allows one to model successfully the practically bulk stressed state in the case of appearance of cracks resulted from breaking of a fiber possessing the great stored strain energy. In addition, the choice of the constant strain rate loading in order to reduce the effect of relaxation processes results in more severe mode of experiment as comparing with the constant stress mode.

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Interaction between Defects and Anelastic Phenomena in Solids

In situ SEM and Modeling Let us consider briefly some previously unknown features related with the nucleation and evolution of individual microcracks as well as their participation in the formation of the dynamic crack. The experiments have shown that: i) microcracks create a “processing” zone ahead of the main crack (Fig.1), however, the latter one does not propagate by means of absorption of the microcracks. The main crack grows only [4] along the plane of maximal tensile stress (see the arrow). ii) microcracks are situated in the staggered order. This fact evidences the necessity of the presence of a certain area (volume) that would collect the strain energy to produce an “elementary” microcrack (under the conditions suggested). iii) microcracks nucleate in an explosive fashion, and then their initial velocity of propagation decreases in ~ 2 orders of magnitude (Fig. 2). Finally, their velocity equalizes to the velocity of the main crack.

100

crack's diameter, µ m

crack's velocity, Vµ m/s

Fig. 1. Frames from a video film (total 53800 frames) demonstrating the development of the processing zone in the main crack tip; time resolution was 0.04 sec.

2

10

1

300 250 200 150 100

0.0

Fig.2.

0.2

0.4

0.6

time, s

50

0.8

Fig.3.

100

150

200

E"m, MPa

Fig. 2. Fast decrease of the microcrack velocity on the early (1) and late (2) stage of the main crack evolution. Fig. 3. Dependence of the diameter dcr of a crack in the model composite on the maximum modulus of mechanical losses E”m of the Rolivsan binder used as a matrix.

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The in situ SEM data and model experiment [5] confirmed the fact of the presence both of the dynamic and relaxation stages in development of newly-born (micro-) mesocracks. It is very important to note, that the explosion-like formation of a microcrack is related to a discrete change in the local strain energy with the inevitable consequent transient relaxation process. It was found [6] that the final size of a (micro-) mesocrack depends on the dissipative properties of material (see Fig. 3). 100

2

1

crack's velocity, V µ m / s

14 12 10

N

8 6 4 2

2

10

1

0

0

Fig.4.

300

600

900

time interval, µ s

1200

1500

0.0

Fig.5.

0.1

0.2

0.3

0.4

0.5

0.6

time, s

Fig. 4. Histograms of the distribution N of time intervals between acoustic emission signals for the carbon plastics based on (1) PEI-N and (2) PEI matrix [7]. Fig. 5. Variation of the propagation velocity of an “old” crack (1) of 5 µ in length caused by the nucleation of a new crack (2) of 1.5 µ in length in its neighbourhood. The data shown in fig. 4 demonstrate that the breakage of neighboring fibers in real carbon fiber reinforced plastics, CFRP, (Vf = 65 % carbon fibers) may occur in the course of the relaxation redistribution of local stresses [7]. In this case, the time interval between neighboring breaks ranges from tens of microseconds to hundreds of milliseconds. These times are much longer than the time of the redistribution of elastic stress (for the given CFRP structure, the temporal range of elastic interaction is 1 ÷ 3 µs) but they are sufficiently short to neglect any increase of the external stress in these experiments. In other words, the dissipative properties of materials affect the rate of the stress relaxation redistribution, thus delaying a break of neighboring fiber after the primary fiber rupture. This directly evidence the prevailing role of the relaxation mechanism of local stress redistribution in the competition of elastic process in microdamaging. The experiment has shown that the strain energy that releases due to the generation of microcracks in the course of the relaxation-evoked redistribution exert some effects on the surrounding volume through: i) nucleation of new microcracks (see Fig. 1); ii) short-term (but considerable) change of velocity of neighbouring “old” microcrack (see Fig.5). As the main crack grows, its velocity increases, and the latent strain energy in the processing zone increases; correspondingly, the dissipative capability of this zone decreases. (Decrease of dissipative properties at plastic deformation which is testified by transformation of dislocation substructure and internal friction is considered in [8, 9]). As a result, the explosion-like nucleation of a new crack enables (through the local energy redistribution) to stimulate, in fact, stepwise increase of the velocity the main crack propagation. The data shown in Fig. 6 demonstrate the interaction of the microcracks with the main crack during last 1.5 seconds of the entire time of sample loading (2152 sec).

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Interaction between Defects and Anelastic Phenomena in Solids

One can see that the consequent nucleation of several mesocracks (see Fig.6) (in this situation only mesocracks 3, 4, 5 and 6 of 8 µm, 6.6 µm, 8 µm and 8.5 µm in size, respectively) causes the non-stationary, dynamic propagation of the main crack.

crack's velocity, Vµ m/s

1000

6 4

10

1 61.5

Fig.6.

3

2

100

5

62.0

62.5 time, s

63.0

63.5

Fig. 6. The discrete change of main crack velocity (1) as a result of the consequent nucleation of several (3, 4, 5 and 6) mesocracks. Thus, we have considered the case of the transformation of an artificial concentrator to the main crack. AE analysis of nucleation and transformation of an ensemble of mesoscopic cracks Let us consider this problem in the exemplary case of Al – alloy -based composite strengthened by high-modulus and high-strength boron fibers of large diameter (100 and 140 µm) [10]; this material is highly sensitive to neighboring ruptures. To obtain the reliable statistics, the principal xperiments were carried out on the samples with a small content of reinforcing fibers (Vf = 2.5 %); in this case, the load is carried, mainly, by the matrix. Dimensions of the sample gauge are 2.1 × 4.3 × 22 mm3. Fibers are positioned in 4 layers in the matrix made of aluminum alloy D16T. There are approximately 30 fibers in the sample crosssection. The samples were stretched at rates 0.017, 0.118, and 0.525 mm/min. The AE signals generated by breaking fibers could be reliably separated from signals belonging to other sources. Fig. 7 shows the loading diagram and the AE activity expressed by the number of signals in a unit of time, Ń, collected during the entire period of loading at the rate 0.017 mm/min. According to the metallographic analysis, in the range 4000 - 6000 sec, the multiple breakage of fibers takes place; after this, the main load is carried by the matrix. The total number of breaks falls in the range 600 to 800. Issuing from this fact, one can estimate the critical length of fibers as equal to ~ 1 mm. In the strain scale, the multiple-breakage range occupies approximately 2.5 %. In Fig. 8, the multiplebreakage range is depicted in an extended time scale, where one can see a “fine structure” of the peak activity shown on Fig.7: the peak is decomposed into 12 - 15 sharp peaks. The number of signals in these peaks varies in limits of 25 - 100 % of the total number of fibers in the sample cross-section.

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Fig. 7. The loading diagram (P) and acoustic emission activity Ń over total loading time in Al-B (2.5 %) due to breaking of boron fibers. Fig. 8. Acoustic emission activity Ń in an extended time scale.

Fig. 9. Sharp peak acoustic emission activity Ń in an extended time scale. Fig. 10. 3D diagram of the distribution of fiber breaks (AE signals) along the sample length over loading time 4300–6800 s. The data of linear location of AE signals support the localization of breaks in limits of the peak Ń in a single cross-section of 2 ÷ 3 mm. The distance between the peaks, as recalculated for the strain, also does not depend on the rate of loading, and it is equal to 0.1 ÷ 0.2 %. However, the width of the peaks themselves is invariant now not in relation to the strain but relatively the time (see Fig. 9). This means that the multi-breakage of fibers lying in the single cross-section could be regarded as a process flowing under constant load and strain, that is as a correlated process. At the same time, this process could not be determined by the elastic stress redistribution only, since in this case, it would finish in a few microseconds with producing an AE signal of very large amplitude. Under the given, specific conditions, the AE signals would be detected as a single feature if the time interval between them is shorter than 1 msec. Taking into account that in our case the intervals between subsequent pulses are much longer, one should accept that the characteristics of correlated breaks of fibers in the sample cross-section are determined by the relaxation properties of the matrix. One can see that the process of correlated fiber breakage in a single cross-section does not lead to the failure of the sample exactly in this cross-section. Moreover, the process of this kind starts to

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Interaction between Defects and Anelastic Phenomena in Solids

develop in another cross-section; it drifts to adjacent regions, and even returns to the initially most active cross-sections. The cause of such behavior is, apparently, related with the fact that even partial accumulation of ruptures (mesoscopic defects of continuity) leads to a decrease of the local, effective elastic modulus. This causes the stress redistribution between neighboring regions thus stimulating triggering of a similar process in any “new” cross-section [11]. One can expect that in the case of high volume fraction of the boron fibers (Vf), the process of this kind, as started in any cross-section, would result in failure in exactly this cross-section. The tests performed on such samples have shown their failure really results from the sequence of ruptures of fibers, being the time intervals between them specific for relaxation-stimulated stress redistribution. At 20 °С and Vf = 18 %, this sequence consists of 3 ruptures in 11 µsec; at 300 °C the sequences cover 20 ruptures in 8.2 sec (3 % of the total loading time) and 11 ruptures in 6.4 sec (1 %) for Vf = 18 % and Vf = 43 %, respectively. Summary Every event of defect nucleation that takes place at both micro- and mesoscale level in the heterogeneous solid examines the energy absorbtion capability of the whole system. Dissipative properties of materials influence the dimension of “micro catastrophes”, the rate of the relaxationtype stress redistribution, and delayed secondary fiber break in the vicinity of the primary fiber break. Future localization of the macroscopical failure is of “accidental type”, that is results from random, active formation of the ensemble of micro- and mesocracks in different localities as a consequence of the decrease of the dissipative capability of surrounding volume. Acknowledgments We would like to thank V.E. Yudin and G.N. Gubanova ( Institute of Macromolecular Compounds, Russian Academy of Sciences) for their assistance in performing model and acoustic emission measurements. References [1] N. Morozov and Y. Petrov: Dynamics of Fracture (Springer-Verlag, Berlin-Heidelberg-New York 2000). [2] H. H. Kausch: Polymer Fracture, 2nd ed. (Springer, Heidelberg 1987; Mir, Moscow 1981). [3] V. E. Panin, V. A. Lichachev and Y. V. Grinyaev: Structural deformation levels of solids (Nauka, Novosibirsk 1985). [4] A. M. Leksowskii, B. L. Baskin et. al.: Physics of the Solid State. Vol. 25, No 5 (1983), p. 1096. [5] A. M. Leksovskii, A. Abdumanonov et. al.: Mekh. Kompoz. Mater. Vol. 6 (1984), p. 1004. [6] V. E. Yudin and A. M. Leksowskij: Physics of the Solid State, Vol. 47, No 5 (2005), p. 975. [7] A. P. Tishkin, G. N. Gubanova, A. M. Leksovskii and V. E. Yudin: J. Mater. Sci. Vol. 29 (1994), p. 632. [8] N. A. Koneva, E. V. Kozlov et. al.: Mater. Sci. Eng. A Vol. 234-236 (1997), p. 614. [9] A. N. Chukanov, D. M. Levin and L. V. Muravleva: Izvestiya of Russian Academy of Sciences, Phys., Vol. 64, No 9, (2000), p. 1714. [10] A. P. Tishkin, A. Abdumanonov and A. M. Leksowskij: Tech. Phys. Lett. Vol. 21, No 8, (1995), p. 587. [11] A. M. Leksowskij, A. V. Gavrilin and B. L. Baskin: Tech. Phys. Lett. Vol.34, No 2, (2008), p. 77.

Solid State Phenomena Vol. 137 (2008) pp 15-20 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.15

Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy L. B. Magalas, M. Majewski AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland [email protected] Keywords: Logarithmic decrement, mechanical spectroscopy, internal friction.

Abstract. The advantages of the OMI algorithm to compute the logarithmic decrement and the resonant frequency from free decaying oscillations is reported. The OMI algorithm is proved to be the best solution in the computation of the logarithmic decrement and the resonant frequency for high damping levels. Introduction In this paper we present the advantages of the OMI algorithm (Optimization in Multiple Intervals) [2 - 3] used in the computation of the logarithmic decrement δ and the resonant frequency f o for high damping levels. A comparison between the OMI algorithm and classical methods [1 - 3] is also reported. Although the results of computations depend on several parameters such as the sampling frequency f s of free-decaying signal, the signal-to-noise ratio S/N (a specific value for any particular mechanical spectrometer), the amplitude of oscillations Ai , the length of the decaying harmonic oscillations used for signal acquisition L (and in the computation of the logarithmic decrement), the absolute value of the logarithmic decrement δ to be measured, a priori defined density of experimental points, and the resonant frequency of exponentially damped harmonic oscillations f o it is clearly demonstrated that the OMI algorithm is the best solution. In all of these instances, the OMI algorithm yields stable results, the lowest dispersion of experimental points, and the lowest relative error. The scope of this paper does not cover the case of the medium and the low level logarithmic decrement ( δ below 0.01) [1, 2]. It will be also shown that the OMI algorithm yields excellent results in the computation of the resonant frequency f o (better precision and decidedly smaller scatter in experimental points) which leads to an increase in the quality of mechanical loss spectra (both the logarithmic decrement and the resonant frequency). The Logarithmic Decrement The logarithmic decrement δ can be computed from several algorithms, viz. (1) N_osc (Number of oscillations) – from the number of N oscillations to decay from amplitude A1 to An +1 (note that in this work N is the number of oscillations for given L ), (2) RA (Regression of Amplitudes) – from the height of N decaying amplitudes, (3) RS (Regression of Areas) – from the areas under a half cycle of N decaying oscillations, and (4) OMI – Optimization in Multiple Intervals. The computing algorithms used in low-frequency resonant mechanical spectroscopy are described elsewhere [1 4]. In the following sections the precision in the computation of the logarithmic decrement δ and the resonant frequency f o will be compared for the algorithms mentioned before.

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Interaction between Defects and Anelastic Phenomena in Solids

The OMI Algorithm The OMI algorithm returns the logarithmic decrement δ and the resonant frequency f o of exponentially damped pure harmonic oscillations [2, 3]. The OMI algorithm fits the following parameters A, β , f , ϕ , C of the theoretical function of damped harmonic oscillations a (t ) a (t ) = A ⋅ exp ( − β ⋅ t ) ⋅ cos ( 2 ⋅ π ⋅ f + ϕ ) + C

(1)

to the experimental data {(ti , ai ) : i = 1 ... n } . f is the frequency of harmonic oscillations,

β = δ ⋅ f , t is time, ϕ is the phase, and A , C are constants. ti and ai are time and the amplitude of the i -th sample, respectively. n denotes the total number of digital samples. The LavenbergMarquardt (L-M) method is usually used to minimize the nonlinear least-square function n

S ( A, δ , f , ϕ , C ) = ∑ [ ai − a (t i ) ] 2 .

(2)

i =1

Initial estimates of the fitting parameters Ao , β o , f o , ϕo , Co can be readily estimated. The initial values are returned to the vector of starting values [ A, β , f , ϕ , C ]. In the first step, Eq. (2) is minimized for the first cycle of damped oscillations. The fit result is returned to the vector of starting values. The second interval of experimental data contains higher number of experimental points (selection of the number of experimental points for the second interval depends on the value of the logarithmic decrement). Equation (2) is minimized for the second interval and the fit result is returned to the vector of starting values. The number of experimental data is multiplied by a parameter from the range 1.1 to 2 in the following interval, etc. The process is repeated until the last interval of experimental data contains all the experimental points {(ti , ai ) : i = 1 ... n } . When this occurs, the process has converged giving the final values for the parameters A, β , f , ϕ , C [2, 3]. It is not difficult to show, by means of the analysis of the global minimum, that the final solution is unique (the logarithmic decrement and the resonant frequency is unequivocally found). A detailed account of the OMI algorithm has been given elsewhere [2, 3]. Computation of the Logarithmic Decrement Figure 1 shows variation of the logarithmic decrement δ , the relative error γ (Fig. 1 a) and the standard deviation σ (Fig. 1 b) computed for the N_osc, RA, RS and OMI algorithms for high damping level, δ = 0.5. Computations were performed for a set of 400 measurements. The OMI algorithm shows unequivocally that its performance is superior as compared to the classical algorithms (for long and short acquisition times). The relative error and the standard deviation depends on several parameters: (1) the length of the decaying oscillations L used for signal acquisition, (2) the sampling frequency f s , the signal-to-noise ratio S/N , and the resolution of the A/D data acquisition board used for signal acquisition, and (3) amplitude of the decaying oscillations a (t ) . In this work it is tacitly assumed that exponentially damped harmonic oscillations are purely symmetrical (the ‘zero-point drift’ ZPD is negligible [4]). Figure 2 illustrates variation of the logarithmic decrement δ , the relative error γ (Figs. 2 a, 2 b) and the standard deviation σ (Fig. 2c) computed for the N_osc, RA, RS and OMI algorithms for high damping level, δ = 0.05. Computations were performed for a set of 400 measurements. Superiority of the OMI algorithm is clearly visible for short acquisition times. This is why the OMI algorithm yields lower dispersion in experimental points and higher density of experimental points. Figure 2 also illustrates how to find the best acquisition time L (see Figs. 2 a, 2 c). The point we should like to emphasize is that excellent computing result can be obtained from the OMI algorithm for a few oscillations (3 – 6 oscillations). It turns out that further increase in the acquisition time L

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OMI

OMI

5.04

OMI

OMI

OMI

OMI

0.15

OMI

OMI

(see Figs. 2 b, 2 c) does not yield substantial improvement in increasing computing precision and decreasing dispersion of experimental points. The performance of the OMI algorithm was tested for all acquisition and experimental parameters described in [2].

3.46

δ = 0.5 3.44 5.02

-1

5.00

Q x 10

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δ x 10

Relative error γ [ % ]

0.10

3.40 -0.05 4.98 3.38

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5

7

8

N_osc RA RS OMI

4.96

N_osc RA RS OMI N_osc RA RS OMI N_osc RA RS OMI N_osc RA RS OMI

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-0.10

3.36

9

L [s]

a)

δ = 0.5

N_osc RA RS OM I

0.006

Standard deviation

σ

x 10

0.008

0.004

0.002

0.000 1

2

3

4

5

6

7

8

9

10

L[s]

b) Fig. 1. (a) Variation of the logarithmic decrement δ , the relative error γ , and (b) the standard deviation σ computed according to N_osc, RA, RS and the OMI algorithm as a function of the acquisition time L . δ = 0.5, sampling frequency f s = 5 kHz, S / N = 38 dB.

Interaction between Defects and Anelastic Phenomena in Solids

5.04

1.480

δ = 0.05

1.476 1.472

5.00

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Q-1 x 102

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3

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0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0

δ x 102

γ[%]

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10

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L [s]

a) 5.04

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δ = 0.05

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N_osc RA RS OMI N_osc RA RS OMI N_osc RA RS OMI N_osc RA RS OMI

N_osc RA RS OMI N_osc RA RS OMI

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20

L [s]

x 102

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b)

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N_osc RA RS OMI

0.008 0.006 0.004 0.002 0.000 2

3

4

5

6

7

8

9

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

L[s]

c) Fig. 2. (a), (b) Variation of the logarithmic decrement δ , the relative error γ , and (c) the standard deviation σ computed according to N_osc, RA, RS and the OMI algorithm as a function of the acquisition time L . δ = 0.05, sampling frequency f s = 5 kHz, S / N = 38 dB, resonant frequency f o = 1 Hz.

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0.10

Relative error γ [ % ]

0.05

0.01

Relative error

γ

[%]

0.02

OMI ( f s = 5.0 kHz and 0.5 kHz ) Zero crossing ( f s = 5.0 kHz ) Zero crossing ( f s = 0.5 kHz )

0.00

0.00

-0.05

-0.01

-0.02 0 10 20 30 40 50 60 70 80 90 100 L[ s]

OMI ( f s = 5.0 kHz and 0.5 kHz) Zero crossing ( f s = 5.0 kHz ) Zero crossing ( f s = 0.5 kHz )

-0.10 0 5 10 15 20 25 30 35 40 45 50 L[ s]

a)

b)

2

0.20

0.10

1 Relative error γ [ % ]

Relative error γ [ % ]

0.15

OMI ( f s = 5.0 kHz and 0.5 kHz ) Zero crossing ( f s = 5.0 kHz ) Zero crossing ( f s = 0.5 kHz )

0

-1

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0 2 4 6 8 10 12 14 16 18 20 L[ s]

0 1 2 3 4 5 6 7 8 9 10 L[ s ]

c)

d)

Fig. 3. Relative error γ in the computation of the resonant frequency according to the OMI algorithm (□) and the ‘zero crossing’ method for two sampling frequencies: f s = 5 kHz (○) and f s = 0.5 kHz (∆). (a) δ = 0.0005, (b) δ = 0.005, (c) δ = 0.05, (d) δ = 0.5. Calculations were performed for a set of 400 measurements; S / N = 38 dB, resonant frequency f o = 1 Hz.

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Interaction between Defects and Anelastic Phenomena in Solids

Computation of the Resonant Frequency Figure 3 illustrates precision in the calculations of the resonant frequency ( f o from 0.5 Hz to 5 Hz) as a function of the acquisition time L obtained from the OMI algorithm and the ‘zero crossing’ method (optimized in this work) for different levels of the logarithmic decrement. The OMI algorithm yields: (1) the best estimation of the resonant frequency, (2) the lowest relative error in the estimation of the resonant frequency, (3) decidedly better results for short, average, and long acquisition times, (4) stable computing results. It is worthwhile to emphasize that the superiority of the OMI algorithm turns out to be independent of the sampling frequency ( f s from 0.1 kHz to 5 kHz). This is why the OMI algorithm can also be recommended for ‘old’ mechanical spectrometers working with low sampling frequency and/or ‘old’ A/D data acquisition boards. Although the computing parameters [2] used in this work were tailored to obtain the smallest available error the differences between the relative errors in the calculations of the resonant frequency from the OMI and the ‘zero crossing’ can be 1 - 3 orders higher for a particular mechanical spectrometer. Such differences are usually induced by the acquisition and the experimental parameters discussed in [2]. In all investigated cases the OMI algorithm yields the best results. Let us recall [2, 3] that knowing theoretical relationship between known computation error for a chosen sampling frequency in a mechanical spectrometer one can readily predict the computation error for other sampling frequency (see Fig. 3 in [2]) and the signal-to-noise ratio S / N [3]. This is why one can easily explain ‘small’ differences shown in Fig. 3. The effect of the sampling frequency and the signal-to-noise ratio is discussed in [1 - 3]. It is interesting to note that for the low and the medium damping levels the acquisition time cannot be reduced in classical algorithms. Wrong selection of the acquisition time L (or amplitudes A1 and An +1 ) leads to an increase in the computation error of f o (Fig. 3) and δ (Figs. 1, 2). For high damping levels classical algorithms generate high dispersion in experimental points for too long acquisition time (see Fig. 3 d). This aspect of mechanical spectroscopy has received scant attention to date and deserves more. It can be concluded that the OMI algorithm can be successfully used to make high-precision measurements of the logarithmic decrement and the resonant frequency in high-damping materials (HDM). Conclusions The optimal strategy in the computations of the logarithmic decrement δ and the resonant frequency f o for the high damping level is reduced to the selection of the computing algorithm. It is concluded that for the high damping level the OMI algorithm always yields the lowest relative error γ , and the lowest standard deviation σ in the computations of the δ and the f o . It also yields the smallest dispersion of experimental points as compared to the classical methods. The OMI algorithm provides better detection of fine variations in the logarithmic decrement and the resonant frequency and allows fast and precise detection of huge variations in the resonant frequency and the logarithmic decrement observed during phase transformations and other mechanical loss phenomena observed in viscoelastic, viscoplastic and anelastic materials. Acknowledgments This work was supported by Polish Ministry of Science and Higher Education under grant No.11.11.110.656. References [1] [2] [3] [4]

L. B. Magalas, T. Malinowski: Sol. St. Phen. Vol. 89 (2003), p. 247. L. B. Magalas: Sol. St. Phen. Vol. 115 (2006), p. 7. L. B. Magalas, A. Stanislawczyk: Key Eng. Mat. Vol. 217 (2006), p. 231. L. B. Magalas, A. Pilat: Sol. St. Phen. Vol. 115 (2006), p. 285.

Solid State Phenomena Vol. 137 (2008) pp 21-28 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.21

High-temperature Mechanical Relaxation due to Dislocation Motion inside Dislocation Networks A. Rivièrea, M. Gerlandb and V. Pelosinc LMPM - UMR CNRS 6617, Ecole Nationale Supérieure de Mécanique et d'Aérotechnique, BP 40109, 86961 Futuroscope, France a

[email protected], [email protected], c [email protected]

Keywords: Isothermal mechanical spectroscopy; Aluminium; Aluminium alloys; Single crystal; High temperature; Dislocations.

Abstract. Internal friction peaks observed in single or polycrystals are clearly due to a dislocation relaxation mechanism. Because a sample observed by transmission electron microscopy (TEM) often exhibits in the same time various dislocation microstructures (isolated dislocations, dislocation walls, etc.) it is very difficult to connect the observed relaxation peak with a particular dislocation microstructure. Using isothermal mechanical spectroscopy (IMS), it is easier to compare, for instance, the evolution of a relaxation peak with measurement temperature to the microstructural evolution observed by in-situ TEM at the same temperatures. IMS was used to study a relaxation peak in a 5N aluminium single crystal firstly 1% cold worked and then annealed at various temperatures. TEM experiments performed in the same material at various temperatures equal to the temperatures used for the damping experiments made possible to link this internal friction peak with a relaxation effect occurring inside dislocation walls. In two other experiments in a 4N aluminium polycrystal and in a metal matrix composite with SiC whiskers, it is shown that the observed relaxation peaks are connected to the motion of dislocations inside polygonization boundaries in the first case and in dislocation pile-ups around each whisker in the second one. Theoretical models proposed to explain such relaxation peaks due to a dislocation motion inside a dislocation wall or network are discussed. Introduction During the last 30 years, relaxation peaks have been evidenced between 0.3 and 0.7 TM (TM: melting point) in single crystals of pure metals [1 - 12] or metallic alloys [13]. These peaks are attributed to a relaxation effect associated with the dislocation microstructure. Consequently, internal friction peaks observed in polycrystals in the same temperature range can also be associated with a relaxation due to dislocation motion. However, sometimes no peak is observed in single crystals [6, 8, 14] or polycrystals [15, 16] although these samples obviously contain dispersive dislocations or dislocation networks. It was also found that a small cold work (intentionally or by handling) is necessary to make a peak to appear or to increase [6, 13, 17]. Moreover, the relaxation parameters of these peaks (limit relaxation time τ0, activation energy HA, frequency or temperature of the maximum and relaxation strength) depend on the thermal treatments carried out to the samples such as an annealing after cold work [15]. Some authors [8, 11, 18, 19] tried to characterize the dislocation microstructure of the samples studied by internal friction. In fact, the figures obtained using transmission electronic microscopy (TEM) generally displayed various kinds of dislocation microstructures (isolated dislocations, polygonization walls, deformation cells, …) and it was very difficult for these authors to link a particular microstructure to the observed relaxation peaks. Moreover the damping experiments were made at fixed frequency during continuous heating or cooling without possibility to describe with a good accuracy the evolution of the peaks with the thermal treatment. On the contrary, isothermal mechanical spectroscopy, by measuring the internal friction in a very large frequency range when the microstructure of the sample is stabilized after a temperature

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Interaction between Defects and Anelastic Phenomena in Solids

change, is a very good technique for describing the evolution of the damping spectra for instance during a heating after cold work. The comparison between the results obtained at the same temperature before and after an annealing at higher temperature is very easy. Moreover, because these experiments are carried out at very low frequencies, the relaxation peaks are evidenced at lower temperature than for measurements made, for instance, at 1 Hz or more. At least, TEM observations can be made exactly at the same temperature as the internal friction experiments. So, the change in internal friction spectra can be easily related to the microstructure change observed by TEM. This paper presents results observed in a 5N aluminium single crystal after 1% cold work and successive annealings. This specimen exhibits a relaxation peak between room temperature and 600K. TEM observations made at the same temperatures as the internal friction experiments make possible to link this peak with the dislocation networks introduced by the cold work. Other results about a metal matrix composite (2024 + SiC-whiskers) aluminium and a polycrystal strongly cold worked are presented: the observed relaxation peaks are linked with the dislocations introduced around each whisker during temperature changes for the first case and with the dislocations inside subboundaries for the second one. Experimental procedure Isothermal mechanical spectroscopy. The mechanical spectrometer used is the torsion pendulum described in detail elsewhere [20]. Measurements were conducted under vacuum below 700 K and in an inert atmosphere above 700 K. For the forced vibration technique, Q-1 is equal to tan ϕ where ϕ is the phase lag between the applied stress and the resulting strain. Each isothermal experiment began 3h after the temperature change. The vibration frequencies (f) ranged between 50 Hz and 10-4 Hz, and measurements were made at 10 discrete frequencies per decade. The internal friction was also measured at the resonance frequency of the pendulum (160 - 200 Hz depending on the rigidity of the specimen) by the free-decay method. The maximum strain amplitude εmax = 5 × 10-6 was used for all the experiments. In situ TEM study. Thin foils were prepared by the standard double-jet electrolytic technique with a solution composed of 65 % methanol, 20 % nitric acid and 15 % water, at – 10 °C and 20 V, from slices cut by spark machining and first mechanically polished to 85 µm. They were successively washed in nitric acid, water and methanol then inserted in a heating holder. Dislocation structures were observed in a Philips CM-20 electronic microscope operating at 200 kV, first at room temperature, then on a selected area, at different temperatures corresponding to the temperatures of the mechanical spectroscopy tests. A stabilisation time of ten minutes was systematically respected after each new temperature was reached before taking photography of the dislocation structures. Experimental results 2024 and 2024-SiC whiskers aluminium alloys. Metal matrix composite with 2024 aluminium alloy (Al –4.5 wt. % Cu -1.5 wt. % Mg – 0.6 wt. % Mn) and 20 % whiskers of silicon carbide (SICw) was provided by Pechiney Company. Another specimen of 2024 alloy but without SiC-whiskers was also studied. The two specimens were heat treated at 820 K under vacuum and then water quenched. The temperature was initially increased stepwise to 823 K and subsequently decreased to room temperature. Results obtained during the first heating after quench in the specimen without reinforcement have been published in [16]. After annealing in the pendulum at 823 K (in α solid solution) the Al2Cu phase precipitates inside the grain boundaries. 2024 alloy specimen cooled in this way only evidences a large exponential background as shown in Fig. 1. On the contrary, the relaxation spectrum performed in the composite specimen exhibits a relaxation peak. The two experiments described in Fig. 1 were performed at the same temperature (636K) after the high temperature annealing at 823 K. The relaxation peak shifts towards lower frequencies for experiments at lower temperatures (see Fig. 2)

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corresponding to an Arrhenius behaviour. The corresponding limit relaxation time τ0 = 3 × 10-9 s and the apparent activation energy HA = 1.05 eV. 700

500

2024 alloy + SiC-W annealed in-situ at 823 K

Measurements at 636 K after annealing at 823 K

600

Measurements at:

400 500 2024 alloy 4

671 K

-1

-1

Q x10

4

400

Q x10

752 K

300

300 2024+SiC-W alloy

200

200 576 K

100 100

0

0 -4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

Fig.1. Internal friction spectra at the same temperature (636 K) after in-situ annealing at 823 K in 2024 (uptriangles) and 2024+SiC whiskers (down triangles) alloys.

-4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

Fig.2. 2024 + SiC whiskers alloy. Internal friction spectra measured at 752 K (down triangles), 671 K (circles) and 576 K (up-triangles) after in-situ annealing at 823 K.

The microstructure difference of the samples is the dislocation network created against each SiC whisker [21-24] due to the difference of thermal expansion coefficients between the matrix and SiC. Because it appears only in composite sample, the relaxation peak is clearly linked to these dislocation pile-ups. 4N aluminium polycrystal. 4N aluminium polycrystal was annealed six hours at 870 K under vacuum and 67 % cold-rolled before the internal friction measurements. First results are described in details in [15]: between room temperature and 450 K, the internal friction spectra exhibit only a low frequency exponential background. At 460 K, a small peak superimposed to this background appears and increases with the increase in temperature of measurements. That is shown in Fig. 3 where spectra measured at 500 K and 580 K are displayed. Afterwards, measurements made at the same temperature after various higher temperatures annealings show a peak shift towards lower frequencies and the activation parameters are strongly dependent on the annealing temperatures [15]: τ0 = 10-14 s and HA = 1.5 eV after annealing at 500 K and τ0 = 10-16 s and HA = 1.7 eV after annealing at 580 K.

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Interaction between Defects and Anelastic Phenomena in Solids

2000

700

4N aluminium polycrystal 1st run after 60% coldwork

600

1500

500 measurement at 500 K

580 K

∆ Q x10

4

4

400 -1

1000

-1

Q x10

4N aluminium polycrystal 1st run after 60% coldwork

300 500 K 200

500 measurement at 580 K

100

0

0 -4

-3

-2

-1

0

1

log10 (freq./Hz)

2

3

-4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

a b Fig. 3. 4N aluminium polycrystal – Internal friction measured at 500 K (up-triangles) and 580K (down-triangles) after a 60 % cold-rolling. a: raw experiments - b: relaxation peaks after low frequency background subtraction [15]. The evolution of the disorientation of the subgrains studied by Electron Back Scattering Diffraction (EBSD) makes possible to connect the relaxation peak with the subboundaries. In fact, Fig. 4 shows the poles corresponding to different grains after annealing at 500 K (a) and at 580 K (b). In the first case, the orientations of the poles are strongly scattered for each grain. On the contrary, the disorientation is minimum after an annealing at 580 K. This corresponds to a rearrangement of the walls and to larger dislocation mobility inside the walls.

a b Fig. 4. 4N aluminium polycrystal - Orientation of the subgrains in various grains after annealing at 500 K (a) and 580 K (b). 5N aluminium single crystal. A 5N aluminium single crystal was provided by Goodfellow Company. Specimens were cut from the bar by spark machining and the surface layer was chemically removed. To introduce fresh dislocations, the specimen was 1 % cold worked by torsion. Laue X-ray diagrams of the sample were taken before mounting in the pendulum. After the experiment, Laue diagrams were taken again and macroscopic etching was made to verify that no recrystallization has occurred during the high temperature annealing.

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To study the influence of the annealing, the temperature was initially increased stepwise to 458 K and subsequently decreased to room temperature. Then the temperature was increased to 673 K and subsequently decreased. Measurements were performed at the same temperatures during heatings and successive coolings. During the first heating after cold work, the isothermal internal friction spectra exhibited a relaxation peak as shown in Fig. 5. In the experiments at successively raised temperatures, the peak shifted towards higher frequencies and became more pronounced, which is due to changes in the sample microstructure. Fig. 2 shows the Arrhenius plots of the Napierian logarithm of the peak frequencies. It turns out that the plots corresponding to the first heating are not linear. 4

5N aluminium single crystal

200

5N aluminium single crystal

st

1 heating

160

2

140

1

438 K

120

-1

Q x10

ln (freq./Hz)

3

4

180

100

1rst heating

0 -1

80 363 K

after annealing at 458 K

-2

294 K

60

-3

40 -4

-3

-2

-1

0

1

2

log10 (f/Hz)

Fig. 5. 5N aluminium single crystal. Internal friction spectra obtained at 294 (uptriangles), 363 (circles) and 438 K (down- triangles) during the first heating after cold work.

-4 3.0

2.5

2.0

1000/T(K)

Fig. 6. 5N aluminium single crystal. Napierian logarithm of peak frequencies vs inverse temperature for the relaxation peaks obtained during the first heating (up-triangles) and after annealing at 458 K (down-triangles).

The spectra measured after annealing at 458 K are shown in Fig. 7 in which the peak height was independent of the temperature. The Arrhenius plots of the peak frequencies for the experiments performed at various decreasing temperatures after annealing at 458 K are also shown in Fig. 6, which displays the Arrhenius behaviour. The relaxation parameters have been deduced from these Arrhenius plots: the limit relaxation time τ0 = 5 × 10-8 s and the apparent energy activation HA = 47 kJ/mol (≈ 0.5 eV). At 1 Hz, this peak would be located at 0.4 TM. After annealing above 673 K, this peak completely disappeared as shown in Fig. 8, which shows the internal friction spectra obtained at the same temperature (391 K) after annealing at 391, 468 and 673 K.

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Interaction between Defects and Anelastic Phenomena in Solids

240

160

5N aluminium single crystal 220

5N aluminium single crystal

annealed at 458 K

Temperature of measurement: 391 K 140

200

after annealing at: 120

180

391 K

measurement at: 160

Q x10

4

4

439 K

140

-1

-1

Q x10

458 K

100

120

80

419 K 100

60

80 40

673 K

60 391 K 40

20 -5

-4

-3

-2

-1

0

1

2

log10 (f/Hz)

Fig. 7. 5N aluminium single crystal. Internal friction spectra obtained at 391K (uptriangles), 419 K (circles) and 439 K (down-triangles) after annealing at 458 K.

-4

-3

-2

-1

0

1

2

log10 (f/Hz)

Fig. 8. 5N aluminium single crystal. Internal friction spectra obtained at 391 K after annealing at 391 K (up- triangles), 458 K (circles) and 673 K (down-triangles).

The dislocation configuration in the 5N aluminium single crystal observed by TEM are characterized by large cells more or less closed with a mean size of 6 to 8 µm and walls composed of short segments of dislocations mainly tangled. The inside of the cells is rather clear (Fig. 9a).This microstructure corresponds to the relaxation peak observed at room temperature (see Fig. 5). When temperature increases, the dislocations in the walls become less tangled and thus more mobile, and they present segments that seems pinned (Fig. 9b). A t that time, the height of the relaxation peak is maximum. Then the walls are progressively destroyed and at 673 K remaining parts are skeletonlike (Fig. 9 c). The relaxation peak has totally disappeared (see Fig. 8).

a b c Fig. 9. 5N aluminium single crystal - Dislocation wall evolution as a function of temperature: a: 294 K, b: 458 K, c: 673 K.

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Discussion Several mechanisms were proposed to explain internal friction peaks due to dislocation relaxation above room temperature: climbing of dislocations by vacancy diffusion [1,8] or dislocation sliding controlled by the climbing of jogs induced by vacancy diffusion along dislocation lines [18]. Generally these models are associated with isolated and more or less dissociated dislocations. For the three examples described in this paper, the relaxation mechanism takes place in polygonization boundaries or dislocation walls. All the possible dislocation mobility mechanisms to explain dislocation relaxation between the room temperature and 0.7 TM have been recently analysed in an excellent overview [25]. For instance, a cross-slip mechanism at the dislocation nodes as proposed in [26] is described in Fig. 10. It could be at the origin of the relaxation peak observed in 5N single crystal aluminium after 1% cold work. This mechanism requires high local stress. At low temperature (e.g. room temperature) the free dislocation segments are too small to make possible a large relaxation. With the raise of temperature, the length of the free segments increases corresponding to a larger peak and to a shift of the maximum towards lower frequency. At higher temperature the local stress relaxes and is not enough to enable the relaxation mechanism.

Fig. 10. Cross-slip mechanism at the nodes of subboundaries: bowing out of dislocation segment 2 and cross-slip of dislocation 3 [26].

Fig.11. Glide motion in P1, P2, P3 due to nucleation of a kink in the {100} plane P1 [27].

The peaks observed in metal matrix composite and strongly cold-rolled 4N polycrystal aluminium do not disappear after a high temperature annealing. These peaks can correspond to a cross-slip mechanism between different nature planes of dislocations arranged in the observed polygonization walls [27]. The gliding on a {100} plane can be thermally activated by a mechanism of a kink creation on a triple node and its diffusion on a non-compact plane as shown in Fig. 11. The activation energies calculated for the peaks in metal matrix composite (1.05 eV) and 4N polycrystals aluminium (ranged between 1.5 eV and 1.7 eV) are compatible with this model. For 5N single crystal aluminium, the experimental activation energy is low (0.5eV) which is expected for the proposed model in the case of a metal with high stacking fault energy. For a low stacking fault energy metal, higher activation energy is expected. Experiments in 5N single crystal silver are in progress to verify the proposed mechanism.

References [1] J. Woirgard, J. P. Amirault and J. de Fouquet, in: Internal friction and ultrasonic attenuation in solids, edited by D. Lenz and K. Lücke, Springer-Verlag, Berlin Vol. 1 (1973), p. 392. [2] T. Yokohama and T. Okasaki: Scripta Met. Vol. 8 (1974), p. 1201. [3] J. Woirgard: Il Nuovo Cimento. Vol. 33B (1976), p. 424. [4] E. Bonetti, E. Evangelista, P. Gondi and R. Tognato: Phys. Stat. Sol. Vol. (a) 39 (1977), p. 661.

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[5] A. Rivière, J. P. Amirault and J. Woirgard, in: Internal friction and ultrasonic attenuation in solids - Proceedings ICIFUAS 6, edited by R. Hasiguti and N. Mikoshiba, Tokyo University Press (1978), p. 749. [6] A. Rivière, J. P. Amirault and J. Woirgard: J. de Phys. Vol. 42 (1981), p. C5-439. [7] A. Rivière and J. Woirgard: Scripta Met. Vol. 17 (1983), p. 269. [8] T. S. Ke, P. Cui and C. M. Su: Phys. Stat. Sol. Vol. (a) 84 (1984), p. 157. [9] M. Weller, M. Tietze, J. Diehl and A. Seeger, in: Materials Science Monographs, 20 edited by V. Paidar and L. Lejcek, Elsevier, New York (1984), p. 215. [10] C. M. Su and T. S. Kê: J. de Phys. Vol. 46 (1985), p. C10-359. [11] J. Shi, L. D. Zhang and T. S. Kê: J de Phys. Vol. 46 (1985), p. C10-355. [12] A. Rivière, J. Woirgard and J. de Fouquet: J. de Phys. Vol. 46 (1985), p. C10-343. [13] S. Belhas, A. Rivière, J. Woirgard, J. Vergnol and J. de Fouquet: J. de Phys. Vol. 46 (1985), p. C10-367. [14] T. S. Kê: J. Mater. Sci. Technol. Vol. 14 (1998), p. 481. [15] A. Rivière and P. Gadaud: Metallurgical and Materials Trans. A Vol. 28A (1997), p. 1661. [16] A. Rivière and V. Pelosin: J. of Alloys and Compounds. Vol. 310 (2000), p. 173. [17] A. Rivière: Scripta Mat. Vol. 43 (2000), p. 991. [18] M. L. No, C. Esnouf, J. San Juan and G. Fantozzi: Acta Metallurgica. Vol. 36 (1988), p. 827. [19] M. L. No, J. San Juan and C. Esnouf: Mat. Sci. & Eng. A Vol. 113 (1989), p. 281. [20] A. Rivière, in: Mechanical Spectroscopy Q-1 2001 with Applications to Materials Science, edited by R. Schaller, G. Fantozzi and G. Gremaud, Trans Tech Publication LTD (2001), p. 635. [21] M. Vogelsand, P. J. Arsenault and R. M. Fisher: Met. Trans. Vol. 17A (1986), p. 379. [22] R. J. Arsenault and N. Shi: Mater. Sci. Eng. Vol. 81 (1986), p. 175. [23] T. Christman and S. Suresh: Acta Met. Vol. 36 (1988), p. 1691. [24] I. Dutta, D. L. Bourrel and D. Latimer: J. Comp. Mat. Vol. 22 (1988), p. 829. [25] M. L. No, in: Mechanical Spectroscopy Q-1 2001 with Applications to Materials Science, edited by R. Schaller, G. Fantozzi and G. Gremaud, Trans Tech Publication LTD (2001), p. 247. [26] D. Caillard and J.L. Martin: Acta Metall. Vol. 31 (1983), p. 813. [27] D. Caillard: Phil. Mag. A Vol. 51 (1985), p. 157.

Solid State Phenomena Vol. 137 (2008) pp 29-34 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.29

High Temperature Mechanical Loss Spectrum of 3Y-TZP Zirconia Reinforced with Carbon Nanotubes or Silicon Carbide Whiskers C. Ionascua and R. Schallerb 1

EPFL, SB, IPMC, LNNME, CH-1015 Lausanne, Switzerland a

[email protected], [email protected]

Keywords: polycrystalline zirconia; carbon nanotubes; silicon carbide whiskers, mechanical spectroscopy, internal friction.

Abstract. High temperature plasticity of fine-grained ceramics (ZrO2, Al2O3, etc) is usually associated with a grain boundary sliding process. The aim of the present research is then to improve the high-temperature mechanical strength of polycrystalline zirconia (3Y-TZP) through the insertion of multiwalled carbon nanotubes (CNTs) or silicon carbide whiskers (SiCw), which are susceptible to pin the grain boundaries. The effect of these nano-sized particles on grain boundary sliding has been studied by mechanical spectroscopy. Introduction High temperature plasticity of fine-grained ceramics is mainly due to grain boundary (GB) sliding [1 - 8]. This mechanism dissipates energy and it is then responsible for an increase in the mechanical loss, which has been observed in the high temperature range [9] and may be associated with the onset of creep in the material. In other words, a ceramic with a bad creep resistance exhibits a high level of the high temperature mechanical loss background. In order to increase its mechanical properties, as for instance creep resistance, yttria-stabilized zirconia was reinforced with CNTs or SiCw. These nanoscale reinforcements may act as pinning centers on the GB, impeding GB sliding. In such reinforced ceramics, a lower high-temperature mechanical loss background with respect to pure zirconia and a lower creep rate are expected. Experimental Procedure Commercial yttria-stabilized polycrystalline zirconia 3Y-TZP was doped with 1.5 wt. % multiwalled carbon nanotubes, 3Y-TZP/CNTs [10, 11] or with 1.5 wt. % silicon carbide whiskers 3Y-TZP/SiCw. Dense samples were obtained by powder metallurgy. The 3Y-TZP powder was first mixed either with CNTs or SiCw via attrition milling by using zirconia balls grinding media (24 h). Then the homogenized powder was cold pressed (100 MPa) and sintered in a temperature range of 1673 K – 1773 K in argon atmosphere. The density of the sintered materials was measured by Archimedes’s method in distilled water. To determine the mean grain size, bulk samples were mechanically polished, thermally etched, carbon coated and examined by SEM (Philips XL30 FEG) and HRTEM (Philips CM 30). Mechanical spectroscopy measurements were carried out in a differential inverted torsion pendulum, in which the sample (flat bars of 30 x 4 x 1 mm3) oscillates at sub-resonant frequency [8]. In this apparatus, the sample is mounted in series with a WC-Co specimen, which is used as an elastic reference. When torsion excitation is applied to the pendulum axis, the angular displacements of the sample and of the reference are converted into electrical signals through optical systems of lasers, mirrors, and linear photocells. Both signals are processed by a signal analyzer and from the phase difference and the ratio of their amplitudes; one can calculate the mechanical loss angle (tan ϕ) and the normalized elastic shear modulus (G/Gref). In this study the measurements were performed under vacuum (10-2 Pa) either as a function of temperature (300 – 1600 K) at a fixed frequency or as a function of frequency (0.001 – 10 Hz) at a fixed temperature. Creep tests were also performed on parallelepiped samples (3 x 3 x 7.5 mm3) under a compressive stress of 6 MPa at 1550 K under vacuum (1 Pa).

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Interaction between Defects and Anelastic Phenomena in Solids

Results and Discussion Composites with CNTs and SiCw were densified until 80 % of the theoretical density, i.e. 6.05 g/cm3 for 3Y-TZP, 5.90 g/cm3 for 3Y-TZP/CNTs and 4.90 g/cm3 for 3Y-TZP/SiCw. To characterize the microstructure, high resolution SEM investigations were performed on the assintered samples (Fig.1). (a)

(b)

(c)

Fig. 1. High resolution SEM images of: (a) 3Y-TZP, 3Y-TZP/CNTs and (c) 3Y-TZP/SiCw. All grades show equiaxed grains (Fig. 1 a, Fig. 1 b, Fig. 1 c). In 3Y-TZP/CNTs the grain edges seem to be sharper (Fig. 1 b) than in 3Y-TZP/SiCw, where they seem to be more rounded (Fig. 1 c). Moreover a second phase (dark spots) is observed between the zirconia grains in 3Y-TZP/SiCw (Fig. 1 c). In each sample the average grain size was determined as 1.56 times the average intercept length of the grains [12]. In all 3Y-TZP grades the mean grain size was found to be 0.30 µm. Fig. 2 a corresponds to a bright field image of a 3Y-TZP/CNTs. Important residual stress seems to be inside zirconia grains. In some cases, an amorphous layer along grain boundaries can be observed. The thickness of this layer may attempt 5 nm up to 10 nm (Fig. 2 b). (a)

(b)

Fig. 2. (a) Bright field image of 3Y-TZP/CNTs. The arrows indicate a particular bright contrast along grain boundaries. (b) HRTEM image of 3Y-TZP/CNTs. A CNTs layer situated between two zirconia grains. The presence of amorphous layer at grain boundaries in 3Y-TZP was a subject of intense discussion [13 - 15] and seems, in fact, to be strongly correlated to the cooling rate [16]. In any case, the thickness of amorphous layer is not consistent with a predicted or observed amorphous layer in 3Y-TZP [15]. It was found that the chemical composition of this layer was mainly carbon, and then it probably results from the original carbon nanotubes. Therefore, amorphous area at grain boundaries could be attributed to remainders of CNTs [17]. Fig. 3 shows a TEM micrograph of 3YTZP/SiCw which indicates that SiCw were homogeneously dispersed within 3Y-TZP matrix grains

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and/or at grain boundaries. Large pockets of glassy phase associated with porosity are often observed at the triple junctions. EDS analysis performed inside the pockets reveals that they are mainly composed of ZrO2, Si and O.

Fig. 3. TEM image of 3Y-TZP/SiCw composite. SiCw are situated within 3Y-TZP matrix grains and/or at grain boundaries. Fig. 4 shows the mechanical loss spectra of pure 3Y-TZP zirconia, 3Y-TZP/MWCNTs and 3YTZP/SiCw composites.

Fig. 4. Mechanical loss spectra of pure 3Y-TZP, 3Y-TZP/MWCNTs and 3Y-TZP/SiCw plotted as a function of temperature for an applied stress of 7 MPa and a frequency of 1 Hz. In pure zirconia, above 1200 K, the mechanical loss undergoes a monotonic increase. In both composites the 1600 K damping level is lower by 50 % in 3Y-TZP/MWCNTs and by 30 % in 3YTZP/SiCw than in zirconia. A small inflection appears at about 1450 K in the 3Y-TZP/CNTs spectrum. The mechanical loss spectrum of 3Y-TZP/SiCw exhibits a relaxation peak at 1500 K. Isothermal measurements were performed to study more in depth the high-temperature behavior of these ceramics. In Fig. 5 a the isothermal spectra of 3Y-TZP are reported. In some of the curves a peak appears superimposed to the background. The experimental curves are shifted towards lower frequencies when temperature decreases, which means that the relaxation phenomena are thermally activated. Relaxation parameters were obtained from the construction of the corresponding mastercurve (Fig. 5 b). The spectra corresponding to different temperatures have been superimposed by

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shifts along the frequency-axis. The frequency-shifts ∆(ω) = ω1 – ω2 (along x-axis) reported as function of inverse temperature ∆(1/T) = 1/T1 – 1/T2 give an Arrhenius plot (Fig. 5 b). (a)

(b)

Fig. 5. Isothermal (a) mechanical loss and (b) master curve of undoped 3Y-TZP. The activation enthalpy, deduced from the slope of the Arrhenius plot, is 679 kJ/mol and the limit relaxation time τo ~ 10-22 s. The master spectrum is composed of a peak, which turns into an exponential background at lower frequency. Similar isothermal measurements were also performed in zirconia reinforced with CNTs or SiCw. The relaxation parameters obtained by the master-curve construction are reported in Table 1 with the values obtained in pure zirconia. It is found that the activation enthalpies of composites are smaller than the one of monolithic zirconia. Table 1. Sample 3Y-TZP 3Y-TZP/CNTs 3Y-TZP/SiCw

∆Hact [kJ/mol] 659 636 626

τo [s] 10-22 10-20 10-20

Activation enthalpy and limit relaxation time as measured in pure zirconia and its composites. Creep tests in compression at low stress (6 MPa) and high temperature (1550 K) were also performed in 3Y-TZP, 3Y-TZP/CNTs and 3Y-TZP/SiCw. Fig. 6 shows that creep strain is much smaller in composites than in pure zirconia. SiCw and CNT addition increase the creep resistance of zirconia. This result is in agreement with the mechanical spectroscopy spectra (Fig. 4). A lower level of the high temperature mechanical loss is observed in the case of reinforced zirconia, and a lower level of the high temperature exponential background may be interpreted by a better resistance to creep of then material. High-temperature plastic deformation of fine-grained ceramics is generally interpreted as due to grain boundary (GB) sliding [18]. Because the CNTs were found to be located at the GBs they may limit the GB sliding process. As the high temperature exponential background in the mechanical loss spectrum of fine-grained ceramics has been interpreted as due to GB sliding, it is easy to understand that the nano-sized reinforcements lead to a decrease of the high-temperature exponential background. The decrease of the high temperature damping would be due to a limitation of GB sliding. As GB sliding is more difficult, creep is reduced. However, while the introduction of reinforcements improves the resistance to GB sliding (evidenced by a decrease in the high temperature mechanical loss and creep tests), the activation enthalpy values (Table 1) do not support the above interpretation. In fact, we expect the highest value of the activation enthalpy for the most refractory material. Here the activation enthalpy, which would be associated with GB sliding, is smaller in 3Y-TZP/CNTs than in 3Y-TZP.

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Fig. 6. Strain recorded as a function of time during compression tests at 1550 K and low stress of 6 MPa in pure, CNTs-doped and SiCw-doped 3Y-TZP. The problem here is that the activation enthalpy values obtained by the Arrhenius’s plot (Fig. 5 b) are apparent values, which are too high in all the materials of the present investigation. This assumption is supported by the values of the limit relaxation time τ0 ~ 10-20 – 10-22 s, which are much smaller than the limit value associated with the inverse of the Debye frequency (τo ~ 10-14 s). Apparent values of the activation enthalpy may be obtained in the case of a changing microstructure. If the microstructure evolves as a function of temperature leading to a decrease of the energy barrier, then high values of the activation parameters are obtained. A theoretical model has to be developed in order to correct the measured values of the activation parameters, and to use them for result interpretation. Summary Monolithic 3Y-TZP zirconia and composites 3Y-TZP reinforced with CNTs or SiCw have been processed and studied by mechanical spectroscopy with complementary observations of electron microscopy and creep tests. The high temperature mechanical loss spectrum of 3Y-TZP presents an exponential background with the superposition of a relaxation peak particularly well resolved in zirconia reinforced with SiCw whiskers. This high temperature mechanical loss spectrum may be interpreted by a mechanism of GB sliding. When GB sliding is not limited by obstacles like three point junctions or GB asperities or other defects, creep occurs and an exponential background (exponential increase with temperature) is observed in the mechanical loss spectrum. Addition of nano-sized reinforcements (CNTs and SiCw) on the GBs results in a decrease of the high temperature exponential background. This means that in these new grades GB sliding is more difficult and as a consequence a better creep resistance will be observed. As a matter of fact, 3YTZP reinforced with CNTs or SiCw exhibits a lower exponential background in the mechanical loss spectrum and a lower creep strain than pure zirconia when submitted to compressive stress at high temperature. Acknowledgments This work was financially supported by the Swiss National Science Foundation. The authors would like to thank to Dr. A. Magrez (EPFL, Switzerland) for providing them with carbon nanotubes powder and to F. Bobard (EPFL, Switzerland) for high resolution SEM images.

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Interaction between Defects and Anelastic Phenomena in Solids

References [1] A. H. Chokshi: .Mat. Sci. Vol. 25 (1990), p. 3221. [2] T. G. Langdon: Mat. Sci. and Eng. A Vol. 166 (1993), p. 67. [3] A. H. Chokshi, A. K. Mukherjee and T. G. Langdon: Mat. Sci. and Eng. R Vol. 10 (1993), p. 237. [4] D. M. Owen and A. H. Chokshi: Acta Mater. Vol. 46 (1998), p. 667. [5] D. M. Owen and A. H. Chokshi: Int. J. Plast. Vol. 17 (2001), p. 353. [6] A. H. Chokshi: Mat. Sci. and Eng. A Vol. 166 (1993), p. 119. [7] F. Wakai, S. Sakaguki and Y. Matsuno: Adv. Ceram. Mat. Vol. 1 (1986), p. 259. [8] F. Wakai, N. Kondo and Y. Shinoda: Curr. Opin. Solid. State and Mat. Sci. Vol. 4 (1999), p. 461. [9] T. Rouxel and F. Wakai: Acta Metall. et. Mater. Vol. 41 (1993), p. 3203. [10] E. Couteau, K. Hernadi, J. W. Seo, L. Thien-Nga, C. Miko, R. Gaal and L. Forro: Chem. Phys. Lett. Vol. 378 (2003), p. 9. [11] A. Magrez, J. W. Seo, C. Miko, K. Hernadt and L. Forro: J. Phys. Chem. B Vol. 109 (2005), p. 10087. [12] R. Duclos, J. Crampon and B. Amana: Acta Met. Vol. 37 (1989), p. 877. [13] Y. Ikuhara, P. Thavorniti and T. Sakuma: Acta Mater. Vol. 45 (1997), p. 5275. [14] L. Gremillard, T. Epicier, J. Chevalier and G. Fantozzi: Acta Mater. Vol. 48 (2000), p. 4647. [15] D. Clarke: J. Am. Ceram. Soc. Vol. 70 (1987), p. 15. [16] J. F. Bartolomé, I. Montera, M. Díaz., S. López-Esteban, J. S. Moya, S. Deville and L. Gremillard: J. Am. Ceram. Soc. Vol. 87 (2004), p. 2282. [17] C. Ionascu, B. Mortéele, R. Schaller and M. Daraktchiev: CIEC 9, Bardonecchia, Italy (2004), p. 150. [18] A. Lakki, R. Schaller, M. Nauer and C. Carry: Acta Metall. et. Mater. Vol. 41 (1993), p. 2845.

Solid State Phenomena Vol. 137 (2008) pp 35-42 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.35

Low Temperature Kinetics of In - Cd Solid Solution Decomposition P. P. Pal-Val1,a, L. N. Pal-Val1, A. A. Ostapovets1 and P. Vanek2 1

B.Verkin Institute for Low Temperature Physics & Engineering, National Academy of Sciences of Ukraine, Lenin Ave. 47, 61103 Kharkov, Ukraine 2

Institute of Physics, Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic a

[email protected]

Keywords: Low Temperatures, In-based Alloys, Solid Solutions, Isothermal Structure Instability, Young's Modulus, Electrical Resistivity, Phase Diagrams.

Abstract. An influence of Cd content on the kinetics of a spontaneous low-temperature structure transformation in In-rich In - Cd alloys has been investigated using acoustic, resistivity and DSCtechniques. It is established that increase of the concentration of Cd leads to an essential increase of a driving force of the transition that results in an increase of the transition rate and in decrease of the relaxation time. The low-temperature instability of acoustic, resistivity and thermal properties is caused presumably by a decomposition of the solid solution that has features of a phase transition of the 1st order. The main empirical activation parameters of the transformation are derived. The activation energy amounts to U0 = 0.43 eV, the attempt period is τ 0 =5 × 10-9 s. The probable border of the decomposition in the phase diagram of the In-Cd system is established. Introduction Mechanical spectroscopy and resistivity measurements are extremely structure sensitive experimental techniques and are widely used when studying atomic rearrangements in solids at various kinds of structure transformations and phase transitions. Elasticity measurements give us information on changes in structure of the samples tested. From the data on anelasticity we obtain information on dynamics of atoms or clusters. Resistivity is very sensitive to changes in the defect substructure of solids. Recently, a spontaneous instability and hysteretic behavior of acoustic and resistive properties of In - 4.3 at. % Cd solid solution were revealed in the temperature range 170 - 270 K [1 − 3]. When thermocycling, large closed clockwise hysteresis in the temperature dependence of the Young’s modulus E (T) and counterclockwise hysteresis in the temperature dependence of the residual resistivity ρ0 (T) were observed. Isothermal time instabilities of opposite signs took place at the lowand high-temperature hysteresis boundaries. Maximal changes in both values mounted up to 25 %. In other words, the transition led to formation of a low-temperature phase with much higher values of the Young’s modulus and much smaller values of the residual resistivity. Low-temperature phase remained stable below 250 K down to 5 K. After heating up to 310 K, the Young’s modulus and resistivity restore their initial values. A microscopic nature of the structural transformation found still remains uncleared. In - Cd substitution solid solutions with cadmium content within 4 at. % < с < 5.9 at. % on cooling undergo a martensitic structural transition, at which the high-temperature fcc α phase ( Fm3 m ) goes over to a low-temperature phase with the fct α  lattice ( I 4 / mmm ) inherited from indium. The temperature of the martensitic transition Ms is dependent on с and decreases from Ms ≈ 421 К at с = 4 at. % Cd to Ms ≈ 293 К at с = 5.9 at. % Cd. Consequently, the low-temperature structural transformation found in In - 4.3 at. % Cd occurs in the martensitic phase at temperatures far below Ms. In the present work, the investigation of low-temperature structural instability of In-Cd system has been continued. In order to obtain new experimental data on the transformation and its lowtemperature kinetics, we have carried out acoustic, resistivity and DSC measurements in samples of

36

Interaction between Defects and Anelastic Phenomena in Solids

In - 5.5 at. % Cd and In - 6.6 at. % Cd alloys in the temperature range 100 – 320 K. In the later case, concentration of Cd exceeded a solubility limit for solid solutions of this system and any martensitic transition did not precede the low-temperature transformation in this composition. Experimental The binary alloys In - c at. % Cd (c = 5.5 and 6.6) were obtained by fusion of weighed portions of 99.999 % pure indium and cadmium in air in an alundum crucible. The melt, overheated to about 20 K above the melting temperature, was poured onto the surface of a steel or ceramic slab. The polycrystalline ingot was a coarse-grained with average grain size of ~ 0.3 mm). The cadmium concentration in the ingot was determined by chemical analysis. Ingots were forged and rolled into bars of square cross section 2 × 2 mm2, from which samples of the necessary size were cut. For the acoustical measurements we used samples with dimensions of 2 × 2 × 7.5 mm3, with ends that had been lapped perpendicular to the long axis of the sample on a steel slab with a fine abrasive. The samples for the resistance measurements had dimensions of 2 × 2 × 23 mm3. A study of the morphology of the grains of the martensitic phase (in the case of c = 5.5 at. % Cd) showed that they consist of thin domains, the interfaces between which are twin boundaries. This sort of microstructure and crystallographic misorientation of the domains, as a rule, makes for a number of interesting features of the inelastic deformation of the alloy, in particular, superelasticity, high damping of mechanical vibrations, etc. The acoustical properties (the logarithmic decrement δ of vibrations and the dynamic Young's modulus E) were studied by the two-component composite vibrator technique [4] at a longitudinal standing wave frequency of ~ 75 kHz at a constant amplitude of the acoustic strain ε0 = 2 × 10-7 in the amplitude-independent region. The resistivity ρ was measured using the standard four-probe dc-method. The power dissipated in the sample did not exceed 2 × 10-5 W. To eliminate the influence of parasitic emf 's, the measurements were made for two opposite directions of the transport current. To establish the temperature boundaries of the structural instability of the alloy, we studied the temperature dependences of δ, E, and ρ which were obtained during an isochronal thermocycling in the temperature interval 320 – 100 − 320 К with an average cooling (heating) rate of 0.25 − 1 K/min. The temperature of the sample was changed by using a "standard" two-step procedure: first the temperature was lowered (raised) at a rate of 0.5 - 2 K/min, then held steady for 10 - 2.5 min; after the hold, the measurements of δ, E and ρ were made. For studying the kinetics of the transition from the high- to low-temperature structural states (“direct” transformation), we measured the isothermal time dependences of the dynamic Young's modulus and the resistivity at fixed temperatures near the low-temperature boundary of the hysteresis loop. The samples were first quenched from 320 K down to 100 K at an average rate of 20 K/min and then were heated up to one of the measurement temperatures with the same rate. To obtain new data on the structural transformation given, the differential scanning calorimetry (DSC) has been used. Samples of In - 5.5 at. % Cd and In - 6.6 at. % Cd alloys were undergone to twice repeated thermocycling in the temperature range 340 – 100 − 340 K with a cycling rate of 10 К/min. Hysteresis of acoustic properties and resistivity at isochronal thermocycling The typical temperature dependences of the dynamic Young's modulus E (T) and ρ (T) obtained on isochronal thermocycling of samples at an average rate of 0.5 K/min are shown in Fig.1 a - f. The temperature dependence of the dynamic Young's modulus E (T) exhibits a wide clockwise hysteresis with boundaries whose location is dependent on Cd concentration: the low-temperature hysteresis boundary shifts towards high temperatures when increasing c and the hysteresis loop becomes much more narrow (Fig.1 a, b, c). As in the case of In - 4.3 at. % Cd, the Young's

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modulus has higher values on heating but the maximum difference between hysteresis branches is much higher and comes to 55 % in In - 5.5 at. % Cd and more than 100 % in In - 6.6 at. % Cd. It should be noted that the transition into the low-temperature phase in the samples studied is already realized during cooling (direct measurement run) whereas in In - 4.3 at. % Cd main changes in the sample structure occurred mainly during heating (reverse measurement run). It is evidence of essential increase of the atomic rearrangements rate with increasing Cd content.

(a)

10

14

8

12 10

6

In-4.3at.%Cd

(d) (b)

12 In-5.5at.%Cd (c)

16

In-5.5 at.%Cd

10 8 6

(e)

12 10

12 8

4 12

ρ, µΩ cm

E, GPa

16

8

In-4.3 at.%Cd

In-6.6 at.%Cd

8 In-6.6at.%Cd

6

(f)

4 150

200

T, K

250

300

150

200

250

300

T, K

Fig. 1. Temperature dependence of the dynamic Young's modulus E (T) (a, b, c) and the resistivity ρ (T) (d, e, f) for a single isochronal thermocycling at an average rate of 0.5 K/min. Open circles on cooling (direct measurement run), filled symbols are data measured on heating (reverse run). A more detailed study of the reversible structural transformation observed was done by a resistometric method. The resistivity is one of the most sensitive indicators of the structure state of conducting materials [5]. It is seen in Fig.1 d, e, f that for all the alloys studied the dependences ρ (T) exhibit a counterclockwise hysteresis loops with temperature boundaries somewhat narrower than in the case of the dynamic elastic modulus. In the central part of the hysteresis loop the resistance is of ~ 10 % lower on heating than that on cooling and the effect grows slowly with increase of Cd content. In other respects, the temperature dependences of resistivity have the features similar to temperature dependences of elastic modulus: transition into the low-temperature phase in the samples studied is realized during direct measurement run (in contrast with In - 4.3 at. % Cd alloy); the transition rate essentially increases; within an experimental error, the hysteresis loops on E (T) and ρ (T) are reproducible when the samples are heated up to T ≈330 K and the thermocycling is repeated.

38

Interaction between Defects and Anelastic Phenomena in Solids

heat flow, a.u.

To obtain new data on the hysteretic behavior of the structural transformation given, the differential scanning calorimetry (DSC) has been used. In - 5.5 at. % Cd and In - 6.6 at. % Cd alloys were undergone to twice repeated thermocycling in the temperature range 340 - 100 - 340 K with the thermocycling rate of 10 К/min (Fig. 2 a, b, c). There were the exothermic and endothermic extrema found in the DSC-curves. Locations of the extrema well correspond to the low- and hightemperature boundaries of the hysteresis of the acoustic and resistivity properties of the alloys. Let mention briefly some important features of the DSC-curves obtained during two 30 (a) In-5.5 at.%Cd successive thermocycling. Because of rather 28 1st cycle high thermocycling rate (in comparison with the acoustic and resistivity measurements), a 26 transition depth during first cooling of the 24 samples In - 5.5 at. % Cd is rather small and main atomic rearrangements occur during subsequent heating (Fig.2 a). In In - 6.6 at. % Cd (b) In-6.6 at.%Cd 28 the transition rate increases and a much greater 1st cycle part of the transition takes place during first cooling (Fig.2 b). Moreover, it is established 26 that in both alloys the most part of the transition (or even the whole transition) occurs during 24 second cooling of the samples (Fig.2 c). In other words, some preconditions for acceleration of (c) In-6.6 at.%Cd 28 the atomic rearrangements at subsequent 2nd cycle thermocycling are created during preceding 26 thermocycling. It is also shown that the reverse transition 24 10 K/min from the low-temperature into the high22 temperature state has in both alloys two-stage 100 150 200 250 300 350 character. It can be seen in Fig. 2 that there two endothermic maxima are observed in the DSCT, K curves in all the cases and this effect becomes Fig. 2. Exothermic minima and endothermic more pronounced with increase of Cd content. maxima in DSC-curves obtained during Occurrence of the extrema in the DSC-curves two subsequent measurements in In - 5.5 testifies that the low−temperature structural at. % Cd (a) and In - 6.6 at. % Cd (b, c) transformation found has features of the first samples. Cycling rate is 10 K/min. order phase transition. Quenched samples An important information on properties of high-temperature phase at relatively low temperatures was obtained when studying the samples quenched from the temperature T = 320 K down to 100 K and subsequent isochronal heating. The quenching rate was about 20 K/min, the average heating rate amount to 0.5 K/min. The behavior of the dynamic Young’s modulus E and resistivity ρ in quenched samples is shown in Fig. 3 a - f. At low temperatures, values of E in the quenched samples are lower (Fig. 3 a - c) and values of ρ are higher (Fig. 3 d - f) than in the slowly cooled samples and the dependences E (T) and ρ (T) are, in fact, the prolongations of the corresponding temperature dependences of the Young’s modulus and the resistivity received in the high-temperature region. At T > 180 K, a rapid increase of E and a decrease of ρ take place and measured values approach to the values corresponding to the low-temperature structural state. This temperature is practically insensitive to the concentration of Cd in the alloys. At further heating, the dependence E (T) and ρ (T) coincide practically with the

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ρ, µΩ cm

curves received at slow thermocycling of the sample including the reverse transition into the hightemperature structural state. (a) 14 12

In-4.3at.%Cd

In-4.3at.%Cd

8 6 (d)

4 2

In-5.5at.%Cd

2

12

10 δ

(b)

ρ, µΩ cm

10

E, GPa

10

4 12 10

In-5.5at.%Cd

8 6

8

(e)

0 12

ρ, µΩ cm

(c)

12 8 In-6.6at.%Cd

10

In-6.6at.%Cd

8 6

(f)

4 150

200

250

300

T, K

150

200

250

300

T, K

Fig. 3. Changes in the dynamic Young’s modulus E (a - c), logarithmic decrement δ (b) and resistivity ρ (d - f) during isochronal heating of samples with a different Cd content after quenching from 320 K down to100 K with the rate 20 K/min. The average heating rate amounts to 0.5 K/min. It should be noted two important features in the dependences studied. Firstly, the transition into the low-temperature phase does almost not accompanied by any inelastic effect. Only small violation of a monotonic increase of the decrement δ is observed in the temperature dependence δ (Τ) in this temperature range (Fig. 3 b). It is an evidence of the fact that, relative to the vibration frequencies used in the experiment, the transformation process is essentially quasistatic. Secondly, a magnitude of the Young’s modulus E in the high-temperature phase rapidly decreases with increasing Cd content. At the same time, E decreases much slower in the low-temperature phase. Obviously, that is the main reason of the huge increase of the elastic modulus at the transition from the high to low-temperature phase. Kinetics of the low-temperature structure transformation As it has been mentioned, an essential instability of acoustic and resistivity properties was observed in the vicinity of the hysteresis boundaries. To obtain kinetic parameters of this instability, we have measured isothermal time dependences of the dynamic modulus and the resistivity at selected temperatures near the low-temperature hysteresis boundary. The samples were first quenched from 320 K down to 100 K at an average rate of 20 K/min and then were heated up to one of the measurement temperatures with the same rate. As an example, the time dependences of the relative changes in the Young’s modulus and resistivity measured at the

40

Interaction between Defects and Anelastic Phenomena in Solids

20

In - 4.3 at.% Cd

10

(a) (a)

0

(ρ/ρ0-1)*100 %

0

transition rate, ppm/s

(E/E0-1)*100 %

constant temperature T = 190 K are shown in Fig. 4. All the kinetic curves are sigmoidal (Sshaped) and cannot be described by a first-order reaction equation. The kinetic curves may be approximated rather well by a simple expression proposed by Avrami for describing the kinetics of isothermal transformations governed by processes of nucleation and growth of the particles of the new phase [6]:    t n   ∆E/E = (∆E/E)max 1 - exp −     , (1a) 50    τ    In 5.5 at.% Cd 40    t n   ∆ ρ / ρ = (∆ ρ / ρ ) 1 exp (1b) max  −     , 30    τ   

(b)

190 K -5

In - 4.3 at.% Cd -10 In - 5.5 at.% Cd -15

0

2

4

6

8

10

t, h Fig. 4. Time dependences of the spontaneous isothermal relative changes of the dynamic Young’s modulus (a) and resistivity (b) in In - 4.3 at. % Cd (●) and In - 5.5 at. % Cd (▲) alloys at the transition to the low-temperature structural state at T = 190 K. The solid curves show the approximating functions according to Eq. 1 a and Eq. 1 b.

200

190 K 5.5

100 4.3 0 4.3 5.5

-100 10

100

1000

(b) 10000

t, s Fig. 5. Time dependences of the transformation rates at T = 190 K taken as the time derivatives of the functions approximating the experimental data on relative changes of the dynamic Young’s modulus (a) and resistivity (b) from Fig. 4. Figures denote the Cd concentration in at. %.

where (∆E/E)max and (∆ρ/ρ)max are maximal changes of the corresponding measured values, τ is the effective relaxation time at the temperature given, n is an exponent that varies in the range 1.2 1.6 (the lower values of n are typical for the changes in the elastic modulus and higher values are typical for the resistivity changes). It can be seen that at all temperatures the transformation begins slowly, then it speeds up, the rate reaches a maximum value and after that gradually declines (Fig. 5). The maximal transformation rates in In - 5.5 at. % Cd and In - 6.6 at. % Cd alloys are approximately an order of magnitude higher than in In - 4.3 at. % Cd whereas the corresponding relaxation times are as much lower. From the kinetic curves we have obtained values of the relaxation time τ at different temperatures. The temperature dependences of the relaxation time τ (T) in the Arrhenius coordinates for the resistivity measurements are shown in Fig. 6. In contrast to the almost symmetric non-monotonic curve with a minimum at T = 200 K obtained for In - 4.3 at. % Cd, the temperature dependences of τ in In - 5.5 at. % Cd and In - 6.6 at. % Cd in the Arrhenius coordinates

Solid State Phenomena Vol. 137

41

may be well approximated by a straight line. Using the expression for the relaxation time τ for the thermoactivated processes: τ = τ0 exp(U0/kT),

(2)

we can derive the main empirical activation parameters of the transformation: the activation energy U0 = 0.43 eV and the attempt period τ0 = 5×10-9 s.

T, K

10

5

10

4

10

3

10

2

240

200

400

4.3 at.%Cd 5.5 at.%Cd 6.6 at.%Cd

4.0

4.5

5.0

5.5

6.0

-1

1000/T, K

Fig. 6. Arrhenius plot for the relaxation times derived from the isothermal time dependences of the resistivity measured at selected temperatures in the vicinity of the low-temperature hysteresis boundary.

αK

αT

300

1

10 3.5

160

T, K

τ, s

280

200

In-Cd decomposition of αT

100 0

5

10

15

c, at.% Cd Fig. 7. In-rich side of the In-Cd phase diagram. The dotted line passes through a hysteresis midpoints corresponding to 3; 4.3; 5.5; 6.6 at. % Cd and may be regarded as the solid solution decomposition boundary.

Low-temperature part of the In-rich side of the In - Cd phase diagram Let us consider a possible connection between the structural instability observed and the In-Cd phase diagram. As far as we know, the phase diagram of this binary alloy has not yet been studied below a room temperature, and a phase boundary of possible decomposition of solid solution in the literature is absent [7]. Presumably, as the temperature is lowered, the tetragonal phase αT undergo a decomposition, with the formation of a small amount of cadmium-enriched clusters in the matrix of the αT phase, and the temperature of the decomposition decreases with decreasing Cd content. If the decomposition is the microscopic mechanism of the low-temperature instability of the αT phase studied, the phase boundary should pass between the low- and high-temperature boundaries of the hysteresis (see Fig. 7). In this case, one would expect manifestations of instability of the acoustical properties and resistivity in the alloys with smaller concentrations of Cd at even lower temperatures. Actually, we have observed a wide hysteresis only in the temperature dependences of the dynamic Young's modulus (but not of the resistivity) in In - 3 at. % Cd [2]. The absence of anomalies in the alloys with a smaller Cd concentration may be due to an essential decrease of the transformation driving force when decreasing Cd content and/or due to a significant decrease of the rate of thermally activated processes at the temperatures expected. A conclusive explanation of the nature of the observed effects will require further study preferably by the direct methods of structural analysis. The close values of the scattering

42

Interaction between Defects and Anelastic Phenomena in Solids

factors of the In and Cd atoms makes it difficult to study this alloy using x-ray diffraction methods. The high plasticity and low melting point of the samples make it practically impossible to use the high-voltage transmission electron microscopy. It seems, the most suitable method in this case is the neutron diffraction. Summary In this work, an influence of Cd content on the kinetics of a spontaneous low-temperature structure transformation in In-rich In-Cd alloys has been investigated by means of acoustic, resistometry and calorimetry methods. It is established that increase of the concentration of Cd leads to essential increase of the transition rate and to decrease of the relaxation time of the corresponding atomic rearrangements in alloys. It may be evidence of the increase of the driving force of the transition studied. The observed instability of acoustic, resistivity and thermal properties of the alloys investigated may be caused by a thermally activated decomposition of the solid solution that has the features of a phase transition of the 1st order. Presumably, it can be a clusterization of Cd atoms inside of the αΤ solid solution. The main empirical activation parameters of the transformation are obtained. The activation energy amounts to U0 = 0.43 eV, the attempt period is τ 0 =5 × 10-9 s. The probable border of the decomposition in the phase diagram of the In-Cd system is established. Further study, mainly by methods of direct structural analysis, is needed to explain the detailed microscopic picture of this structural transformation. References [1]

S. V. Lubenets, V. D. Natsik, P. P. Pal-Val, L. N. Pal-Val and L. S. Fomenko: Mater. Sci. Eng. A Vol. 256 (1998), p. 1.

[2]

S. V. Lubenets, V. D. Natsik, P. P. Pal-Val, L. N. Pal-Val and L. S. Fomenko: Izv. RAN, Fizika (in Russian), Vol. 64 (2000), p. 1718.

[3]

S. V. Lubenets, V. D. Natsik, L. N. Pal-Val, P. P. Pal-Val and L. S. Fomenko: Low Temp. Phys. Vol. 28 (2002), p. 465.

[4]

V. D. Natsik, P. P. Pal-Val and S. N. Smirnov: Acoust. Phys. Vol. 44 (1998), p. 553.

[5]

G. T. Meaden: Electrical Resistivity of Metals (Plenum Press, New York 1965).

[6]

J. W. Christian: The Theory of Transformations in Metals and Alloys (Pergamon Press, Oxford 1975).

[7]

T. B. Massalski (ed.): Binary Alloy Phase Diagrams, 2nd ed. Vol. 2, ASM International, Materials Park, Ohio 44073, USA (1990).

Solid State Phenomena Vol. 137 (2008) pp 43-48 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.43

Effect of heat treatment on acoustic properties of chromium polycrystals at low temperatures P. P. Pal-Val1,a, L. N. Pal-Val1, S. B. Golovina2 and I. S. Golovin3 1

B. Verkin Institute for Low Temperature Physics & Engineering, National Academy of Sciences of Ukraine, Lenin Ave. 47, 61103 Kharkov, Ukraine 2

Technical University of Braunschweig, Institute for Materials, Braunschweig, Germany 3

Tula State University, Lenin Ave. 92, 300600 Tula, Russia a

[email protected]

Keywords: Chromium, Magnetic Phase Transition, Antiferromagnetism, Néel Point, Spin Density Wave, Spin-Flip Transition, Elastic Moduli, Internal Friction, Low Temperatures.

Abstract. Acoustic properties of polycrystalline Cr samples of 99.99 % purity are investigated at frequencies of longitudinal vibrations f ~ 75 kHz and of bending vibrations at 0.6 < f < 1.5 kHz when thermocycling within the temperature interval 5 − 330 K. Special attention is paid to the acoustic anomalies in the vicinity of the magnetic phase transitions: the Néel point and the spin-flip transition. In the as-received samples, a significant hysteresis of the acoustic properties has been found for the first time. The effect of heat treatments on internal friction and elastic properties of chromium polycrystals is also investigated. The data obtained are compared with the effect of small preliminary deformation and а long-time ageing at room temperature on the ultrasound anomalies in Cr single crystal. The observed behavior of the acoustic properties may be caused by changes in the antiferromagnetic domain structure in Cr polycrystals under the action of thermoelastic stresses arising from quenching, preliminary plastic deformation or thermocycling. Introduction At low temperatures in chromium with the electronic configuration 3d54s1, two magnetic phase transitions are observed [1], which are accompanied by structural transformations of the first order. At the Néel point TN ≈ 309 К, the paramagnetic-to-antiferromagnetic (PM to AFM) transition takes place with the formation of the transversal spin density wave (TSDW). The paramagnetic chromium has the bcc lattice that below ТN turns into the orthorhombic one at cooling. At the temperature of the spin-flip transition, TSF ≈ 124 K, the transversal polarization of the spin density waves changes to the longitudinal polarization (LSDW), and the chromium lattice transforms into the tetragonal modification. Earlier, the temperature dependences of the decrement δ (T) and the dynamic Young’s modulus E (T) in Cr single crystals were investigated at the vibration frequencies of f ~ 89 kHz, and new acoustic effects were revealed in the vicinity of the magnetic phase transitions [2 − 4]. Along with the known and expected anomalies connected directly with the phase transitions, a strong amplitude dependence was revealed for the first time in the temperature interval TSF ≤ T ≤ TN. It was also established that preliminary plastic deformation leads to smearing and splitting of the acoustic anomalies (i.e. in the dependences δ (Т) and Е (Т)) near TN and also to a displacement of the average value of TN towards higher temperatures. Ageing of the samples at room temperature for a long time led to a partial recovery of the parameters of the anomalies mentioned. Some important aspects of elastic and anelastic behavior of chromium crystals at low temperatures appeared, which were beyond the goals of the works [2 − 4]. In particular, no investigations have been made to determine the influence of thermal treatments on the internal friction and the elastic moduli of chromium in the vicinity of the magnetic phase transitions. In addition, all the measurements were made on Cr single crystals. Therefore, possible grain boundary effects have not been studied. In this work, we have investigated the elastic and inelastic properties

44

Interaction between Defects and Anelastic Phenomena in Solids

of as-received and annealed polycrystalline Cr samples to establish whether there was an influence of the crystal microstructure on the parameters of the magnetic phase transitions. The measurements were carried out in a wide range of vibration frequencies when thermocycling the samples in the temperature interval from 340 K down to liquid helium temperatures. The results obtained are discussed together with the earlier ones obtained with the single crystals. Experimental The acoustic properties of as-received polycrystalline Cr samples of 99.99 % purity with 0.01 % (C+N) content were investigated at frequencies of the forced longitudinal vibrations f ~ 75 kHz (the two-component composite vibrator technique [5]) and of the forced bending vibrations [6] at frequencies 0.6 < f < 1.5 kHz when thermocycling within a temperature interval 330 − 5 − 330 K. The Young's modulus E was determined from the sample resonant frequency f taking into account the temperature changes of the sample length and density. At high frequencies, the measurements were made in the amplitude independent region and the strain amplitude was ε0 ≈ 8·10-8. At low frequencies, the strain amplitude was two order of magnitude higher ε0 ≈ 1×10-5 and in some cases corresponded to the amplitude dependent regions of the δ (ε0) and E (ε0) dependences. The temperatures were measured with an absolute accuracy of ± 0.2 K using copper-constantan or Ni-NiCr (Thermocoax LKI 05/50) thermocouples in the temperature range Т > 30 К and with an absolute accuracy ± 0.05 К using GaAs thermoresistor at temperatures below 30 К. The temperatures were stabilized with a relative accuracy better than ± 10-4 over the entire temperature range by means of the electronic control device. Thermocycling was carried out at heating-cooling rates varying from 0.1 to 2 K/min depending on the measurement temperature. 320 cooling heating

Results and discussion

315 Cr 99.99 polycrystal 75 kHz

310

E, GPa

Hysteresis of acoustical properties of polycrystals. In [2 − 4] the acoustic properties of pure single crystals of two different orientations were investigated at frequencies of 90 kHz. To establish an influence of grain boundaries on the elastic and inelastic properties, it was interesting to receive analogous data on chromium polycrystals of technical purity using the same experimental technique. As earlier, the main attention was paid to the temperature regions close to the magnetic phase transitions. The results related to the temperature changes in the dynamic Young’s modulus Е in as-received polycrystalline sample are shown in Fig. 1 and

(a)

305 355

Cr RRR=33 90 kHz -8 ε0=2*10

350

345 (b) 0

50

100

T, K

150

Fig. 1. Temperature dependences of the dynamic Young's modulus measured in the vicinity of the spin-flip transition in the Cr polycrystal (a) and single crystal (b) (see [2]) during thermocycling at a rate of 0.1 K/min.

Solid State Phenomena Vol. 137

295 (a)

E, GPa

290 Cr 99.99 polycrystal 75 kHz 285 330 Cr RRR=33 90 kHz -8 ε0=2*10

320 310

cooling heating

(b) 300 300

310

320

330

T, K Fig. 2. Acoustic anomalies on the temperature dependences E(T) near the Néel point in the Cr polycrystal (a) and single crystal (b) [2] at thermocycling with a heating-cooling rate 0.1 K/min.

Cr 99.99 polycrystal 90 kHz -8 ε0=8×10

4

Fig. 2 together with the corresponding data obtained on single crystals. It can be seen that the temperature dependences Е (T) obtained with the polycrystals agree qualitatively with those obtained with the single crystals. However, there are also some distinctions. The most interesting effect, that was not observed earlier, is a significant counterclockwise hysteresis of the acoustic properties that takes place when thermocycling the as-received polycrystalline samples. On cooling, the values of the dynamic Young's modulus are appreciably higher than at heating. Hysteretic behavior is observed over the whole temperature range studied. The hysteresis loop closes itself at temperatures about 330 K; this effect is reversible and can be observed again during repeated termocycling. The critical points of the acoustic anomalies near ТN and TSF are somewhat lower on cooling than on heating. In the single crystals, hysteretic behavior was observed only near the phase transition points and appeared as a shift of the anomaly temperatures. In all cases the anomalies are more pronounced in single crystals than in polycrystals.

cooling heating

3

10 δ

6

45

2

0

TN

TSF 0

100

200

300

T, K Fig. 3. Hysteresis in the temperature dependence of the decrement δ (T) in a polycrystalline sample measured at a frequency of 90 kHz: ○ – cooling, ● – heating. Temperature dependences of the decrement δ(T) at high-frequencies exhibited several distinctive features. In particular, no internal friction peak was found at the Néel point ТN at 90 kHz for polycrystals whereas it was observed for single crystals. On the other hand, hysteretic behavior in the dependences δ (T) is more complicated (see Fig 3). At a temperature of 160 K, an inversion of

46

Interaction between Defects and Anelastic Phenomena in Solids

the effect is observed. At temperatures above 160 K, the counterclockwise hysteresis turns into a clockwise one. As in the case of the dynamic Young's modulus, the hysteresis loop closes on heating to 330 K. The behavior of the observed acoustic properties may be caused by changes in the AFM domain structure of the Cr polycrystals which may occur under the action of thermoelastic stresses originated from the anisotropy of the thermal expansion of quasirandomly oriented crystallites of orthorhombic and tetragonal phases of Cr. Significant accommodation stresses may appear in а polydomain structure of the Cr crystal due to the pronounced anisotropy of the lattice parameter at T < TSF. The appearance of stretched and compressed zones with a complicated distribution of internal stresses should result in a specific distribution of domains with different orientations of the spin density wave vectors that differs from a distribution in unstressed crystals [7 − 9]. Influence of heat treatments. To clarify a role of the defect structure on the acoustic anomalies, the effect of the quenching temperature and subsequent annealing of the polycrystalline samples has been studied at the frequencies 0.6 < f < 1.5 kHz. After quenching from 1173 to 1373 K, at temperatures just below the Néel point a bimodal peak of internal friction was observed (Fig. 4 gives example for quenching from 1273 K, circles). Location of the peak did not appreciably depend either on the quenching temperature or on the vibration frequency. After annealing, the peak height increased and in most cases the peak took an unimodal shape (up triangles). Unimodal shape of the peak was also observed after quenching from 1523 K.

3

10 δ

6

4

Cr 99.99 polycrystal 650 Hz -5 ε0=1*10

280

270

260

heating rate 0.3 K/min

2 120

E, GPa

290

130

308

310

312

T, K Fig. 4. Effect of heat treatments on the behavior of the decrement and the Young's modulus near the Néel point and variation of the low-frequency acoustic properties in the vicinity of the spin-flip transition: ● – after quenching from 1273 K, + − after quenching from 1523 K, ∆ - after quenching from 1273 K and subsequent annealing at 733 K for 2 hours. The effect of quenching and annealing of the polycrystalline samples correlates rather well with the results obtained on the plastically deformed and aged Cr single crystals of different orientations. Small preliminary plastic deformation of the samples (up to 1 %) led to broadening and splitting of the acoustic anomalies in the dependences δ (Т) and E (T) in the vicinity of the Néel point (see Fig. 5). The anomalies shifted towards higher temperatures. Near the spin-flip temperature ТSF, splitting of the anomalies due to plastic deformation did not occur although the dip-like anomaly in the E (T) curve becomes less pronounced.

Solid State Phenomena Vol. 137

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Ageing of the samples for one year at room temperature restores the width of the peak at the Néel point, but bimodality and the new average location temperature of the anomalies still remain.

I

3

I 1 2

3

10 δ

3

2

310 I

Cr single crystal RRR=33 90 kHz

300 2 3 2

1

1

I

2

I

I

290

E, GPa

4

3

3

0

1

1

120

130

308

310

280 312

T, K Fig. 5. Effect of plastic deformation on the dependences δ (T) (curves 1 to 3) and E (T) (curves 1' to 3') in the vicinity of the Néel point and the spin-flip transition: ○ – undeformed specimen, ▲− after a plastic deformation, εpl = 1 %, at room temperature, □ - after plastic deformation, εpl = 1 %, and subsequent ageing at room temperature for 1 year. Taking into account that most of the physical properties are sensitive to the presence of lattice defects, it is naturally to expect that an increase in the density of the crystal defects takes place during plastic deformation would entail significant changes in these properties. Both in the case of quenching and preliminary deformation, a considerable number of deformation defects should be produced in the samples. Dislocations and deformation point defects are the main types of defects produced during plastic deformation. Internal stresses associated with deformation defects may essentially change the Cr thermodynamic properties in the vicinity of the magnetic phase transitions. Conditions for the formation of ordered regions in disordered crystal containing dislocations at temperatures slightly above the critical point have been discussed in [10]. It has been shown that such pre-ordered regions could form a randomly spaced skeleton penetrating the entire crystal but occupying only а small fraction of its volume. When decreasing temperature, the thickness of the ordered skeleton branches increases and the phase transition spreads gradually over the entire crystal volume. This should lead to smearing of a phase transition and to its shift towards higher temperatures. For dislocation densities of about 109 cm-2, this smearing should be of 0.3 K. In [7] a semiquantitative analysis of the influence of dislocations on the Néel point TN in chromium has been done. The authors pointed out that the increase in the temperature and width of the transition is determined by the components of the internal stresses coincided with the vectors of the spin density waves. Estimations made in [11] have shown that for dislocation densities between 107 and 109 cm-2, the increase in TN should vary from 0.2 to 0.5 К. The estimations mentioned above are of the same order of magnitude as the increase in TN and the broadening of the acoustic anomalies obtained experimentally in this work. The bimodal shape of the peak at the Néel point may indicate that a bimodal distribution of internal stresses takes place in the crystals. It is interesting to note that the temperature separation of the peak components is almost the same in polycrystals and in single crystals. It does not practically depend (or slightly depend in a non-systematic way) on the vibration frequency, on the vibration

48

Interaction between Defects and Anelastic Phenomena in Solids

amplitude, on the amount of the preliminary plastic deformation, on the quenching temperature, and seems to be some sort of fundamental parameter whose microscopic nature is to date unknown. To gain a better insight into this problem, detailed data on the domain structure of the quenched and deformed samples should be required. Summary In conclusion, low temperature dynamic elastic and anelastic properties of polycrystalline Cr of 99.99 % purity have been investigated in the kHz range during thermocycling within the temperature interval 5 < T < 330 K. In as-received samples, a significant hysteresis of the acoustic properties was found for the first time when termocycling below the temperature of the spin-flip transition TSF. The hysteresis loop closes at temperatures about 330 K and the effect is almost completely reversible and can be observed again during repeated termocycling. The effect of heat treatments on the acoustic anomalies in the vicinity of the magnetic phase transitions in chromium polycrystals has also been investigated. The data obtained in the present work correlate rather well with the data on the influence of small preliminary deformation and longtime ageing at room temperature on the acoustic anomalies in Cr single crystals obtained earlier. The observed behavior of the acoustic properties may be caused by transformations in the antiferromagnetic domain structure in tetragonal and orthorhombic phases under the action of stresses due to thermocycling, quenching or plastic deforming the Cr samples. References [1]

В. Fawcett: Rev. Mod. Phys., Vol. 60 (1988), p. 209.

[2]

L. N. Pal-Val, P. P. Pal-Val, V. Ya. Platkov and V. K. Sulzhenko: Fiz. tverd. tela. Vol. 28 (1986), p. 3577.

[3]

P. P. Pal-Val and L. N. Pal-Val, in: Proc. ICIFUAS-9, edited by T. S. Kê, Int. Acad. Publishers & Pergamon Press, Beijing (1989), p. 609.

[4]

P. P. Pal-Val, L. N. Pal-Val and V. K. Sulzhenko: Fiz. met. Metalloved. Vol. 67 (1989), p. 103.

[5]

V. D. Natsik, P. P. Pal-Val and S. N. Smirnov: Acoust. Phys. Vol. 44 (1998), p. 553.

[6]

U. Harms, L. Kempen and H. Neuhäuser: Rev. Sci. Instrum. Vol. 70 (1999), p. 1751.

[7]

J. S. Williams and R. Street: Phil. Mag. B Vol. 43, part 2 (1981), p. 955.

[8]

V. S. Golovkin, V. N. Bykov and V. Yu. Panchenko: Fiz. tverd. tela. Vol. 27 (1985), p. 2881.

[9]

E. Fawcett, D. Feder, W. C. Мuіr and C. Vettier: J. Phys. F, Met. Phys. Vol. 14 (1984), p. 1261.

[10] I. M. Dubrovskii and M. A. Krivoglaz: Zh.E.T.F. Vol. 77 (1979), p. 1017. [11] J. S. Williams, E. S. R. Gopal and R. Street: J. Phys. F, Metal. Phys. Vol. 9 (1979), p. 431.

Solid State Phenomena Vol. 137 (2008) pp 49-58 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.49

Analysis of Internal Friction Peaks in High Purity Molybdenum by a Viscoelastic Procedure Independent of the Relaxation Strength C. L. Matteo1,a, O. A. Lambri2,b, G. I. Zelada-Lambri2,c, P. A. Sorichetti1,d J. A. García3,e 1

Depto. de Física, Facultad de Ingeniería, Universidad de Buenos Aires, Buenos Aires, Argentina

2

Laboratorio de Materiales, Instituto de Física Rosario (CONICET), Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina 3

Depto. de Física Aplicada II, Facultad de Ciencias, Universidad del País Vasco, Bilbao, País Vasco, España a

[email protected], [email protected], [email protected], d [email protected], [email protected]

Keywords: Distribution Function of Relaxation Times, Internal Friction, Molybdenum, Dislocations, Vacancies.

Abstract. In this work we present a novel procedure, involving linear viscoelastic analysis, to discriminate the two possible contributions of the observed damping peak which appears around 840 K – 1050 K in mechanically deformed high purity single-crystalline molybdenum. An interesting feature of the procedure is that, for low damping samples, it can efficiently resolve experimental peaks that result from the superposition of different processes independently of the ratio between their relaxation strengths. This allows us to confirm that two different relaxation processes appear in molybdenum in the temperature range about 0.3 Tm, one around 840 K, and the other one near 1050 K. These can be related to diffusion and to a coupled mechanism involving creation and diffusion of vacancies, respectively. Introduction Molybdenum, a group VI transition metal has a melting point of 2883 K, high specific heat, and good corrosion and creep resistance. Among the metals useful for high-temperature applications, the melting point of molybdenum is exceeded only by tungsten and tantalum. Molybdenum is ductile at room temperature, with a brittle-ductile transition temperature significantly lower than that of tungsten. Molybdenum has also good strength at high temperatures, being lighter than tungsten and tantalum [1, 2]. These qualities make molybdenum attractive for the use in the nuclear industry [3 - 7]. Mechanical spectroscopy, referred to also as the internal friction method, is a non-destructive technique and is a fundamental tool for studying the movement of dislocations and their interaction with point defects [8, 9]. It involves the simultaneous measurement of the damping or internal friction, Q-1, and the elastic modulus as a function of temperature. We have reported recently that molybdenum exhibits a damping peak at about 840 K – 1050 K, which is developed in deformed samples after annealing at temperatures above that of the vacancy migration [10, 11]. The intensity of the damping peak depended on the degree of plastic deformation at room temperature, but it was not affected by a bias stress. Moreover, the peak temperature and activation energy of this relaxation process increased with the temperature of the previous annealing of the sample; and it was independent of the crystal orientation. For instance, the activation energy increases from 1.6 eV for peak temperature at around 840 K to 2.7 eV for a peak at 1000 K. Also, the shape of the peak when it appears at temperatures around 1000 K is markedly asymmetrical. It has been proposed that the vacancy-dislocation interaction mechanism controls this peak [10, 11]. The Modified Relaxation Time (MRT) function and its applications, derived from a general linear viscoelastic formalism, are a very useful tool to determine if more than one overlapping

50

Interaction between Defects and Anelastic Phenomena in Solids

relaxation processes are taking place. In fact, it is well known that relaxation processes involving dislocations and non-dilute concentration of point defects originate damping peaks that are wider in comparison with the Debye model. Also, in most cases the observed peaks are asymmetrical. The MRT function clearly describes the width and symmetry characteristics of relaxation processes, as it will be later shown. In this work, the MRT is applied to the study of the relaxation damping peaks at high temperatures in deformed and deformed plus irradiated molybdenum. The dependence with temperature of experimental data from these relaxation processes is adequately described by a Havriliak-Negami (HN) function, and the MRT makes possible to find a relation between the parameters of the HN function and the activation energy of the process. The analysis allows us to relate the relaxation peak appearing at temperatures below 900 K, to a physical mechanism involving vacancy-diffusion-controlled movement of dislocations. In contrast, when the peak appears at temperatures higher than 900 K, the damping is controlled by a coupled mechanism of diffusion and creation plus diffusion of vacancies in the dislocation line. Theoretical Background The dynamical response of a linear viscoelastic material is usually described in terms of the complex modulus G* (or the complex compliance J*) as functions of the circular frequency ω and the temperature T. The complex modulus is generally presented in terms of its real and imaginary parts, that is, G* (T, ω) = G’(T, ω) + i G”(T, ω), where G’ is the storage modulus, G” is the loss modulus and i is the imaginary unit [12]. The internal friction (or loss tangent) Q-1 is defined as the quotient between the imaginary and real part of the complex modulus. Q −1 (T , ω ) =

G" (T , ω ) . G ' (T , ω )

(1)

It is useful to define a dimensionless magnitude ∆, usually called the relaxation strength, in terms of the characteristic parameters of the modulus: ∆(T ) =

δG (T ) Gr (T )

=

Gu (T ) − Gr (T ) , Gr (T )

(2)

where the zero-frequency limit Gr(T) = G*(T, ω = 0) is the called relaxed modulus, and the highfrequency limit Gu(T) = G*(T, ω → ∞) is the unrelaxed modulus. The Debye function, a process characterized by an single relaxation time, τD (T), is often employed to describe relaxation processes; due to its conceptual simplicity. In this case, the internal friction is written as

Q −1 (T , ω ) =

ωτ D (T ) ∆(T ) . 1 + ∆(T ) 1 + (ωτ D (T )) 2

(3)

On the other hand, if the process cannot be represented by a single relaxation time, different approaches have been developed for analyzing the problem [9, 12]. This work presents a different, novel way to represent the loss tangent and, therefore, re-analyze the magnitude and its characteristic parameters. The Modified Relaxation Time (MRT) function. The internal friction represented by Eq. 3 can be written in a different manner. In previous works [13, 14] it has been rigorously demonstrated that the dependence of Q-1 on T and ω can be expressed in terms of two functions, Λ(T) and τt(T, ω) as follows:

Q −1 (T , ω ) = Λ(T )

ω τ t (T , ω ) , 2 1 + [ω τ t (T , ω )]

(4)

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where Λ (T) is the envelope function and τt(T, ω) is the modified relaxation time function (MRT function), formerly called the integrated distribution function in [13, 14]. The function τt represents a local perturbation of the Debye process in the (T, ω) domain, and its frequency dependence is critically related to the existence of multiple relaxation processes, that is, a relaxation times distribution function. For the case of only one relaxation time, the MRT function is reduced to τD T) and the envelope function is the pre-factor in Eq. 3. In a measurement of internal friction as a function of frequency, at constant temperature, which usually gives a single-peaked function, Λ (T) represents simply the double of the peak value, since the loss tangent takes its maximum value at the frequency ωm where ωmτt(T, ωm) = 1. On the other hand, in a measurement of internal friction as a function of temperature at constant frequency, Λ(T) represents the envelope of the family of Q-1 vs. T curves, since Q −1 (T , ω ) ≤ Λ (T ) / 2 for all ω [13]. Analysis of Thermally Activated Processes Using the MRT The MRT function can be used to analyse the relaxation distribution involved in thermally activated processes. Usually, the shift of the peak temperature in the internal friction peaks with frequency has been widely used to determine the activation energy in this kind of processes [8, 9]. In fact, assuming that the characteristic relaxation time of the present distribution function depends exponentially on temperature as

τ (T ) = τ 0 exp( H / kT )

(5)

and at the peak temperature is such that ωτ (T ) = 1 , the mean activation energy, H, can be obtained from a linear regression between the measurement frequency at the peak temperature and the peak temperature. This is the so called Arrhenius plot [8, 9]. In Eq. (5) k is the Boltzmann constant and τ0 is the mean pre-exponential factor. However, this procedure does not give any information about the distribution function that describes the internal friction peak, and in particular, whether there are or not several closely spaced relaxation times around the principal one. In order to show the advantages of the MRT formalism the Havriliak-Negami (HN) parametrical expression for dynamical modulus will be used. They are defined by [15, 16] G * (T , ω ) = Gu (T ) −

δG (T )

[1 + (iω τ (T )) ]

α (T ) β (T )

.

(6)

This function has been used to generate different Q-1 vs. T curves, for several frequencies and relaxation strength values. The values of α and β are the characteristic parameters of HN function, while relaxation time τ (T ) has been simulated by using Eq. (5) for different values of H. α and β are phenomenological parameters that describe the symmetrical and asymmetrical broadening of the peak, respectively. In fact, these behaviours are related to the loss modulus (the imaginary part), which could lead to slightly differences in Q-1. For simplicity, α, β and ∆ will be considered independent of temperature in the following discussion. In addition, it is convenient to mention that α and β are introduced as phenomenological parameters to describe the broadening of the relaxation peak (in comparison to the Debye model) and in consequence do not have, up to the present, a clear physical interpretation. Fig. 1 shows a few typical examples of internal friction peaks and the corresponding MRT functions vs. temperature curves. In all cases, even though the relaxation strength, ∆ , varies over three orders of magnitude, it is evident that the MRT functions are independent of ∆.

52

Interaction between Defects and Anelastic Phenomena in Solids

Fig. 1. Internal friction peaks (full symbols) and MRT functions (empty symbols) for the case of a HN function, with different relaxation strengths. Also, it is important to note that the MRT functions show a linear behaviour on both sides of the peak, but the slopes of the linear sections on each side of the peak have a different dependence on the activation energy and on the parameters of the HN function. On the high temperature side, the slope of the MRT function, SH is found to be very close to

SH = α H

(7)

and therefore it is independent of the value of β. In addition, on the low temperature side, the slope SL is found to be nearly equal to

SL = α β H

(8)

Eqs. 7 and 8 have been verified through extensive numerical computations spanning all the physically meaningful range of the variables α, β, ∆ and H. This remarkable, novel result

Solid State Phenomena Vol. 137

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highlights the usefulness of the MRT formalism for the analysis of experimental data of relaxation processes. When β is different from 1, there is a change in the slope of the MRT function, and the quotient between SL and SH is directly the value of the parameter β. Moreover, both slopes are proportional to the activation energy H. In the Debye case, that is, when α = 1 and β = 1, the function is a straight line and its slope is directly the value of H, as it could be expected. It should be emphasized that in the novel procedure described above for the analysis of relaxation processes, the Modified Relaxation Time (MRT) function depends only on the relaxation times distribution function, and in consequence it is independent of the relaxation strength and the relaxed modulus. Moreover, for processes described by the Havriliak-Negami function, the slope of the MRT, as a function of temperature at a given frequency, is proportional to the shape parameters, α and β, and the activation energy H. Therefore, the graphical representation of the MRT makes much easier identify the characteristic parameters related to the shape and symmetry of the distribution function of relaxation times involved in the process. Experimental Samples. The single crystals used in this work were prepared from zone refined single-crystal rods of molybdenum in A.E.R.E., Harwell, UK. The residual resistivity, RR, of the samples was about 8000, the main residual impurity being tungsten. Samples with crystallographic tensile axis were annealed and then deformed in extension, followed by torsion at room temperature. Two types of deformed samples were studied: type I (elongation: 5 %, torsion: 1 %) and type II (elongation: 3 %, torsion: 1 %). Further experimental details are given in Ref. [11]. After the room temperature deformation some samples of type II were neutron irradiated. Low flux neutron irradiation were performed at room temperature, at the Siemens SUR 100 nuclear reactor, RA-4, of the National University of Rosario and National Atomic Energy Commission of Argentina. The RA-4 was operated at 0.7 W. The thermal- and fast-neutron fluxes were about 5.2 x 107 n/cm2s, and their energies were of 0.025 eV and 10 Mev, respectively. Samples were irradiated at two different doses, 64 Gy and 127 Gy, and in this work are indicated as samples b and c, respectively. A more detailed description of the neutron irradiation procedure is given elsewhere [17]. Mechanical Spectroscopy Measurements. Damping and natural frequency were measured in an inverted torsion pendulum, under a vacuum of about 10-5 Pa. The equipment can also apply a bias stress or “in situ” deformation. The maximum strain on the surface of the sample was 5 x 10-5 and the measurement frequency was around 1 Hz, except for the determination of the frequency dependence of the peak temperature. The heating and cooling rates employed in the test were 1 K/minute. A heating ramp and its corresponding cooling run will be called hereafter a thermal cycle. There was no hold time once the maximum temperature had been achieved [11]. Results and Discussion Fig. 2 shows the damping peaks for the samples of type I and II, after background subtraction [18]. Curves A, B and C correspond to damping peaks obtained from a stabilised damping spectrum measured in a type II sample at a natural frequency of about 0.2 Hz, for thermal cycles with maximum temperatures of 1040 K, 1100 K and 1155 K, respectively; see reference [11]. The resulting peak temperatures were around 900K, 940 K and 960 K, respectively. Peaks labelled D and E correspond to the sample of type I after stabilization during thermal cycles up to temperatures of 1050 K and 1230 K, respectively. The resulting peak temperatures were 817 K and 949 K, respectively. In this figure the relaxation peaks measured in samples have been summarized, in order to study the response of the MRT formalism, see for more details Ref. [18]. The calculated curves of the logarithm of the MRT as a function of 1/kT (that is, ln(τt(ω,T)) vs. 1/kT), corresponding to peaks in Fig. 2 are given in Fig. 3. For the sake of clarity, only part of the

54

Interaction between Defects and Anelastic Phenomena in Solids

points calculated with the MRT function have been plotted. For the same reason the curve corresponding to the peak B has not been included, but it has a similar behaviour to the plotted curves, E and C. Vertical arrows in the figure indicate the temperature Tp corresponding to the maximum value of damping (Qp-1). SH and SL indicate the slope at high temperature and low temperature of the fitted straight lines (full lines), as defined in Eqs. 7 and 8. It has to be remarked that for curves A and D two linear zones with the same slope were found in the MRT plot, in spite of the scatter of the calculated data. For temperatures far from the peak temperature the linearity is lost, as it could be expected due to the uncertainties introduced in the data by the background subtraction procedure. It was shown in the theoretical background section that the distribution function of relaxation times should be symmetrical for this kind of behaviour of the MRT. In contrast, for spectra B (not shown in Fig. 3), C and E two clearly linear zones with different slopes were found. The behaviour of the MRT function indicates that these relaxation peaks should be asymmetrical, in agreement with the experimental results. Therefore, for these peaks it can be proposed that at least two overlapped relaxations occur; where each one can be described through its corresponding distribution function of relaxation times. It should be emphasized that, as it was indicated in the theoretical background section, no assumptions or restrictions were made about the shape of the distribution function of relaxation times for the calculation of the MRT curves plotted in Fig. 3.

Fig. 2. Internal friction peaks after background Fig. 3. Natural logarithm of MRT as a function of 1/kT for the peaks plotted in Fig. 2. subtraction (symbols) for the Vertical arrows indicate the position of molybdenum samples. Spectra A, B and the peaks on the 1/kT axis. Full lines, SH C: type II. Spectra D and E: type I. and SL are defined in the text. Full lines represent the numerical fitted peaks. From the slopes of the straight segments fitted to the ln(MRT) vs. 1/kT curves (full lines in Fig. 3), the parameters of the HN distribution function can be obtained by means of Eqs. 7 and 8. Table 1 gives the calculated parameters for the HN function together with relevant experimental information related to each damping peak. The damping peaks calculated theoretically by means of Eqs. 1 and 6 using the fitted parameters of the HN function are also shown in Fig. 2 by means of full lines. The activation energy for the calculation of Eq. 6, using Eq. 5, is the value that we obtained previously from the usual Arrhenius procedure, see ref. [11] and Table 1. The use of this value of the activation energy for the HN function is supported by the fact that, even if there is a distribution of relaxation times, the experimentally measured τ (T) (Eq. 5) corresponds to the mean value of the distribution function. The peak temperature and peak height for the calculated relaxations are also listed in Table 1.

Solid State Phenomena Vol. 137

55

Table 1. AT: annealing temperature. Qp-1: damping value at the maximum. Tp: temperature for the Qp-1. α and β: parameters of the HN function. H: activation energy, taken from Ref. [11]. Peak name / AT (K) Tp (K) Qp-1x103 H [eV] α sample type A / II 1040 880 10.3 1.8 0.58 B / II 1100 940 3.0 2.0 →1 C / II 1155 960 1.7 2.75 →1 D/I 1040 817 9.5 1.6 0.6 E/I 1230 949 9.8 2.1 →1 A / b (irradiated 973 615 4.5 1.6 (*) 0.33 64 Gy) B / b (irradiated 1230 972 2.8 2 (*) →1 64 Gy) A / c (irradiated 973 695 3.6 1.7 (*) 0.39 127 Gy) B / c (irradiated 1230 842 3.7 1.7 (*) 0.50 127 Gy) 929 3.7 C / c (irradiated 1230 1067 1.7 3 (*) →1 127 Gy) (*) calculated value from the fitting of the HN function (see the text).

β →1 0.3 0.12 →1 0.25 →1

Calculated Tp (K) Qp-1x103 880 10.7 935 3.2 960 1.9 817 9.6 949 9.8 615 4.5

0.31

980

2.5

→1

695

3.6

0.54

872

3.7

0.32

1060

1.6

As it can be seen from Fig. 2, the agreement between the experimental and calculated peaks is good, indicating that the calculated parameters of the HN function (α and β) are appropriate for describing the relaxation peaks in molybdenum at temperatures about 0.3 Tm. Therefore, from the study of the behaviour of α and β parameters as a function of temperature valuable information can be obtained about the physical process controlling the relaxation peaks. As it can be noted from Table 1 the peaks A and D were mainly symmetrical (β → 1) but broader (α < 1) than a Debye peak, in agreement with previous works [10, 11], where the half-width of the peaks was evaluated by means of the traditional analysis [8, 9]. Indeed, the peaks which appear at temperatures well below 900 K, obtained during annealing up to temperatures smaller than about 1100 K, can be described by a symmetrical distribution function of relaxation times, with an average activation energy represented by the value obtained from the Arrhenius plot. In addition, a good agreement was also found for relaxation peaks during thermal cycles up to 973 K in type I samples with a Qp-1 of about 20 x 10-3. This indicates that the same physical mechanism occurs when the sample is heated below 1100 K [18]. For peaks B, C and E (with Tp > 900 K), which correspond to samples heated above 1100 K, the α and β parameters are: β < 1 and α → 1, revealing that the peaks are asymmetrically broadened. This means that there is an overlapping of relaxation processes leading to an asymmetrical broadening of the peak. It must be remembered that α and β are the phenomenological parameters that describe the symmetrical and asymmetrical broadening of the peak, respectively, and in consequence, if β ≠ 1, the limit α → 1 does not lead to a Debye peak. Moreover, C and E peaks, which have close peak temperature (≈ 950 K) and very different relaxation intensities (by a factor about 5), exhibit similar α and β parameters, indicating an effect only on the relaxation strength, in agreement with the explanation given above for the peak at lower temperature. However, the physical mechanism controlling these asymmetrical peaks at higher temperatures is different to the physical mechanism giving rise to the symmetrical peaks found at lower temperatures. The change in the α and β parameters, depending of the peak temperature, (see Table 1) leads to the conclusion that there exist two relaxation processes in molybdenum in the temperature range of 0.3Tm. The first relaxation process is related to the symmetrical peak which

56

Interaction between Defects and Anelastic Phenomena in Solids

appears between 820 K - 900 K, and the other to the asymmetrical peak which appears at higher temperatures, above 950 K [18]. The behaviour of the damping peaks and the MRT curves measured in irradiated samples are in good agreement with the analysis given above. Figures 4 and 5 show the damping peaks for samples (b) and (c) after background subtraction, after some thermal cycles up to 973 K. In this case, during the cooling part of the first thermal cycle ,after heating to 973 K, the damping peaks appear at lower temperature and have smaller intensity than the one for non-irradiated samples, as a consequence of the excess of vacancies, out of thermodynamic equilibrium, promoted by the neutron irradiation [17]. Successive thermal cycles up to 973 K did not modify the peak temperature and intensity of the peaks (see spectra A in the Figures). After the first thermal cycle up to 1230 K a wide peak appears within the temperature interval 600 K – 1100 K, which is composed by more than one elementary peak. This situation is shown in the spectrum B for the sample (c) in Fig. 5. Indeed, the extra amount of vacancies produced by irradiation in the deformed samples makes it possible, at least once, to observe the two relaxations in the same spectrum [17]. Subsequent thermal cycles up to 1230 K lead to a strong shift in the peak temperature and to a decrease in the peak height, in a similar fashion as the non-irradiated sample (see peak marked B in Fig. 4 and peak C in Fig. 5).

Fig. 4. Internal friction peaks after background subtraction (symbols) for molybdenum (b) samples (deformed and irradiated 64 Gy). A: After thermal cycles up to 973K. B: After several thermal cycles up to 1230K. Full lines represent the numerically fitted peaks.

Fig. 5. Internal friction peaks after background subtraction (symbols) for the molybdenum (c) samples (deformed and irradiated 127 Gy). A: After a thermal cycles up to 973K. B: After first heating up to 1230K. C: After several thermal cycles up to 1230K. Full lines represent the numerically fitted peaks.

The behaviour of the calculated MRT values for the peaks plotted in Figures 4 and 5 is shown in Figures 6 and 7. As it can be inferred from these Figures, MRT results are in agreement with experimental data. This clearly shows that, for peaks measured after annealing at temperatures higher than 1100 K, the relaxation process must be described by more than a single relaxation time; see also Table 1. In fact, curves B for sample (b) (Figure 6) and curves B and C for sample (c) (Figure 7) have two linear zones, indicated as above by SL and SH, with markedly different slopes. In contrast, peaks obtained from thermal cycles performed up to temperatures lower than 1100 K exhibited the same slope in the straight lines SL and SH.

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57

It should be also mentioned that in irradiated samples the activation energy values given in Table 1, were also determined from the numerical procedure of fitting the HN function. Despite the scatter in the obtained values, the agreement is fairly good. Finally, full lines in Figures 4 and 5 are the calculated peaks using the parameters determined through the MRT function, as it was done above for deformed samples. The agreement between experimental and theoretical results is good.

Fig. 6. Natural logarithm of MRT as a function of 1/kT for the peaks plotted in Fig.4. Full lines, SH and SL are defined in the text.

Fig. 7. Natural logarithm of MRT as a function of 1/kT for the peaks plotted in Fig.5. Full lines, SH and SL are defined in the text.

In order to relate the information obtained from the MRT function with the physical driving force which gives rise to the damping peaks discussed above, the following facts must be taken into account. The low temperature peak is developed both in deformed and deformed plus irradiated samples after annealing at temperatures above that of vacancy diffusion, and the higher temperature peak appears at temperatures near to 0.3 Tm [10, 11, 17, 18]. In addition, the measured activation energy for the lower temperature peak is 1.6 eV [11]. Therefore, this peak can be related to the dragging of vacancies by the dislocation line controlled by a diffusion mechanism. In contrast, when the peak appears at higher temperature, results show that it is controlled by another mechanism. This mechanism is consistent with the creation and diffusion of vacancies in the dislocation line, in agreement with the activation energy measured for the high temperature peak (2.7 eV). In addition, it has been proposed that the high temperature peak is involving both diffusion and creation plus diffusion of vacancies in the dislocation line [17, 18]. Conclusions A novel method has been presented to analyze relaxation processes in terms of the Modified Relaxation Time function (MRT). The slope of the MRT when applied to processes described by the Havriliak-Negami function, as a function of temperature, is shown to be proportional to the shape parameters, α and β and the activation energy H. Also, the MRT is independent of the relaxation strength and the unrelaxed modulus. The Modified Relaxation Time function procedure was applied to a Havriliak-Negami fit of experimental results from mechanical spectroscopy in high purity single-crystalline molybdenum, with good results. The analysis indicates that the distribution of relaxation times is symmetrical for peaks below 900K and asymmetrical at higher temperatures. The lower temperature relaxation was related to vacancy-diffusion-controlled movement of dislocations and the higher temperature peak was related to a process controlled by both the diffusion and the creation plus diffusion of vacancies in the dislocation line.

58

Interaction between Defects and Anelastic Phenomena in Solids

Acknowledgements We acknowledge to Prof. J. N. Lomer for the interest in the present work and for the single crystal samples. This work was partially supported in part by the Collaboration Agreement between the Universidad del País Vasco and the Universidad Nacional de Rosario Res. CS.788/88 - 1792/2003 UPV224.310-14553/02 and Res. CS. 3469/2007, Projects PID-UNR 2005-2007, and CONICETPIP Nos. 5665 and 6465. References [1]

S. Nemat–Nasser, W. Guo and M. Liu: Scripta Mat. Vol. 40 (1999), p. 859 - 872.

[2]

E. R. Braithwaite and J. Haber: Molybdenum: An Outline of Its Chemistry and Uses (Elsevier, New York 1994).

[3]

M. S. El-Genk and J. M. Tournier: J. of Nucl. Mat. Vol. 340 (2005), p. 93 - 112.

[4]

B. V. Cockeram, J. L. Hollembeck and L. L. Snead: J. of Nucl. Mat. Vol. 324 (2004), p. 77 89.

[5]

A. A. Ivanov, M. V. Kollegov, V. V. Kolmogorov, E. A. Kuper, A. S. Medveko and A. N. Shukaev: 8th International Conference on Accelerator and Large Experimental Physics Control Systems, San José, California, TUAP017 (2001).

[6]

D. J. Mazey and C. A. English: J. of Less Comm. Metals. Vol. 100 (1984), p. 385 - 427.

[7]

B. V. Cockeram, J. L. Hollembeck and L. L. Snead: J. of Nucl. Mat. Vol. 336 (2005), p 299 313.

[8]

R. Schaller, G. Fantozzi and G. Gremaud (eds.): Mechanical Spectroscopy 2001 (Trans. Tech. Publications, Uetikon-Zuerich, Switzerland, 2001).

[9]

A. S. Nowick and B. S. Berry: Anelastic Relaxation in Crystalline Solids (Academic Press, New York 1972).

[10] O. A. Lambri, G. I Zelada-Lambri, L. M. Salvatierra, J. A. García and J. N. Lomer: Mat. Sci. and Eng. A Vol. 370 (2004), p. 222 - 224. [11] G. I. Zelada-Lambri, O. A. Lambri and J. A. García: J. of Nucl. Mat. Vol. 353 (2006), p. 127 134. [12] N. W. Tschoegl: The phenomenological theory of linear viscoelastic behavior (Springer Verlag, Berlin 1989). [13] F. Povolo, and C. L. Matteo: Materials Transactions, JIM Vol. 33 (1992), p. 824 - 833. [14] C. L. Matteo: Rheol. Acta. Vol. 35 (1996), p. 308 - 314. [15] S. Havriliak Jr. and S. Negami: J. Polym. Sci. C Vol.14 (1966), p. 99. [16] S. Havriliak Jr. and S. Negami: Polymer Vol. 8 (1967), p. 161. [17] O. A. Lambri, G. I. Zelada-Lambri, P. B. Bozzano, J. A. García, and C. A. Celauro: submitted to Acta Mat. (2007). [18] C. L. Matteo, O. A. Lambri, G. I. Zelada-Lambri, P. A. Sorichetti and J. A. García: submitted to J. of Nucl. Mat. (2007).

Solid State Phenomena Vol. 137 (2008) pp 59-68 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.59

Structure and anelasticity of Fe - Ge alloys I. S. Golovin1,a, T. V. Ivleva1, S. Jäger2, P. Jencus2, H. Neuhäuser3, S. A. T. Redfern4, C. Siemers3 1

Physics of Metals and Materials Science Department, Tula State University, Tula, Russia 2

Institute for Materials, Technical University of Braunschweig, Braunschweig, Germany

3

Institute of Condensed Matter Physics, Technical University of Braunschweig, Germany 4

Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, UK a

[email protected]

Keywords: Fe - Ge alloys, internal friction, structure, phase transformations, DSC, XRD.

Abstract. Several ternary Fe – Ge - C alloys with Ge contents ranging between 3 and 27 at. % have been studied. The structure, anelastic, thermodynamic and kinetic phenomena in Fe - 3, - 12, 19/21 and – 27 Ge have been examined by X-ray diffraction (XRD), heat flow (DSC), vibrating sample magnetometry (VSM), optical-light and scanning electron microscopy, and internal friction (IF) methods. The Fe - 3Ge and Fe - 12Ge alloys form b.c.c. solid solutions. A Snoek-type internal friction (P1) peak is recorded in the Fe - 3Ge alloy with parameters similar to those for α-Fe: Н = 0.86 eV, Δ = 0.015, β = 0.72 and τ0 = 2 × 10-15 s, showing that Ge atoms have little influence on the diffusivity of carbon in iron. The Fe - 12Ge alloy, with a Curie point around 1008 K, has several IF peaks: a broad Snoek-type (P1 and P2), the P3 peak caused by structural changes in as quenched specimens during annealing, and a P4 (Zener) peak at higher temperature (Tm ≈ 773 K at f = 2 Hz, β ≈ 0.7). The Fe - 21Ge alloy has bcc or bcc plus hexagonal structure depending on heat treatment. The structure of the Fe3Ge-type alloy (Fe - 27Ge) consists mainly of hexagonal phases, i.e. hexagonal ε (D019), β (B81), and cubic ε′ (L12), and exhibits corresponding magnetic ordering transitions below 873 K which are not well-reflected in the common Fe - Ge phase diagrams. In particular a high stability of the hexagonal ε phase at room temperature is noted. A broad internal friction relaxation peak with Δ = 0.0036, H ≈ 1.8 eV and τ0 = 2 ⋅ 10-17 s is found in Fe – 27 Ge and is classified as a double Zener peak in the ε and β two-phase mixture. Introduction Unicertainties still exist over the Fe - Ge phase diagram, especially in the low temperature range. As in the Fe - Al and Fe - Si systems, which are also known by their strong tendency to order the substitutional atoms, the Fe - Ge system shows a range of magnetic transformations which are either not indicated in the phase diagram [1] or are given for selected areas only [2, 3]. Contrary to Fe - Al and Fe - Si systems, very few results on anelasticity in Fe - Ge alloys can be found in literature [4, 5 - 8]. One of the reasons for this is the brittleness of Fe - Ge alloys [5], which hinders specimen preparation. There is considerable interest in the Fe - Ge alloy system as a model system [9] involving several phase transformations including structural ordering [10] and variation of ferromagnetic properties [11, 12], as shown, e.g. by X-ray and neutron diffraction studies [13] and by Mössbauer spectroscopy [9, 11, 13 - 16]. Recently, using rapidly solidified alloys [3] or mechanically alloyed material [14], valuable information on the phase selection during heat treatments has been provided for the various, sometimes metastable phases. Further interest arises from observation of dislocations on octahedral and cube planes in connection with anomalous temperature dependence of the flow stress [17 – 19].

60

Interaction between Defects and Anelastic Phenomena in Solids

Materials and Methods Three Fe – Ge - C alloys with nominal compositions: Fe - 3.5 Ge, Fe - 12, and Fe – 27 Ge (all compositions in at. %) have been studied. In addition, a few preliminary tests were done with Fe19/21Ge alloys. All alloys were produced by induction melting of 99.98 % Fe and 99.99 % Ge under argon atmosphere, with a small amount of carbon (0.01 to 0.04 at. %) added in order to check the appearance of the Snoek peak. Nevertheless, for reason of simplicity the indication of carbon is omitted everywhere below. The positions of the present alloys are indicated in the Fe - Ge phase diagram in Fig. 1. In addition to EDX analyses, the heat flow tests (see below) confirm the alloy compositions; the measured phase transformation temperatures are added to the diagram in Fig. 1. Damping Q-1 and modulus change (shear modulus G or Young’s modulus E, both are ∼ f2, where

Fig. 1. Phase Fe - Ge diagrams according to Kubashewski [2] and Massalsky [3] with indicated compositions of the studied alloys as well as their observed structural transitions. f is the resonance frequency for torsion or flexural vibrations, respectively) were measured as a function of temperature (from room temperature to 873 K) at an amplitude of γ0 ≈ 5 ⋅ 10-5, in (1) an inverted torsion pendulum (0.5…3 Hz) [20] and (2) vibrating-reed set-ups (150…3000 Hz) [21, 22], usually applying a heating rate of 1 K/min up to a chosen temperature, followed by cooling down with nearly the same, less controlled rate. For the characterization of the alloys additional methods were applied (see [23]): (1) optical microscopy, (2) EDX, (3) X-ray diffraction (XRD), (4) vibrating-sample magnetometry with a heating rate of 0.5 K/min from room temperature to 950 K and with 3 K/min from liquid helium (4 K) to room temperature and in an external magnetic field of 16 up to 950 kA/m, and (5) differential scanning calorimetry (DSC) with a heating and cooling rate of 10 K/min between room temperature and 1650 K.

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61

Results The bcc Fe – 3 % Ge alloy. The specimen was characterised by DSC and magnetometry, which yield a Curie point TC ~ 770 oC / 1043 K (heating), 762 oC / 1035 K (cooling), the α - γ transition temperatures 1075 oC / 1348 K (heating), 1035 oC / 1308 K (cooling), and γ - α transition at 1301 oC / 1574 K (heating), 1279 oC / 1552 K (cooling) (Fig. 2). These points are added to the diagram in Fig. 1 (for ease of comparison the temperatures in Fig. 2 are also given in °C as in Fig. 1), and appear to be in reasonable agreement with literature data. XRD after water quenching from 1000 K (5 hrs) shows the bcc lattice with the lattice parameter 2.87579 ± 0.00044 Å. An IF (P1) peak practically at the same temperature as the carbon Snoek peak in “pure” α-Fe occurs in Fe - 3.6 Ge - 0.03 C (denoted below as “Fe – 3 Ge”) (Fig. 3). The peak position depends on measurement frequency corresponding to activation parameters of the peak using an Arrhenius plot as: H = 0.86 eV and τ0 = 2 × 10–15 s [4]. Based on these values of the activation energy and relaxation time, we can classify this peak as the carbon Snoek-type peak. The procedure of the peak analysis is given in detail in [23, 26]. The peak is slightly wider than a Debye peak with a relaxation time distribution of 0.4 6 at. %. The Zener peak relaxation strength is much lower in ternary alloys than in the binary ones probably due to mutual compensation of elastic distortions in presence of Al and Si atoms which are bigger and smaller, respectively, than Fe atoms. Introduction Alloying elements in iron affect carbon atom diffusion and distribution in the solid solution and between solid solution and carbides. By studying the height and shape of the C-related Snoek peak [1], these parameters can be estimated; the peak height is proportional to the C content in solid solution while the peak shape gives information on C – substitute atom interaction. Fe – Si and Fe – Si – Al alloys are magnetically soft materials which are used in the production of electric motors and transformers. An investigation of the shape of the Snoek peak for a systematic study of carbon atom distribution in the Fe solid solution of transformer steels (~ 3 wt. % Si, 0.03 wt. % C) was performed for the first time by Krishtal [2]. An increase of the quenching temperature to 900 °С leads to an increase of the peak height. The Snoek peak consists of two components which correspond to C atom jumps (diffusion) in areas where it is surrounded by Fe atoms only (Fe - C - Fe) and in presence of Si atoms (Fe – C - Si). The main aim of the present study is twofold: firstly, the influence of Al and Si atoms on the carbon Snoek relaxation is systematically studied, and the origin of this effect is analysed by decomposing the experimental curves of temperature-dependent internal friction (TDIF)

70

Interaction between Defects and Anelastic Phenomena in Solids

experiments into single IF peaks. The second part of this study deals with the analysis of Zener relaxation [3] in ternary Fe – Si – Al alloys. Materials and Methods We have studied binary Fe – Al, Fe – Si and several ternary Fe – Si – Al alloys with Si + Al contents of up to 25 % (all contents are given in at.% throughout this paper if not stated otherwise) and varying relative amount of Si/Al. Most alloys were prepared by induction melting of high purity components (99.98 % Fe, 99.999 % Al, and 99.9995 % Si); carbon (C) was additionally introduced in amounts sufficient to form a Snoek peak (0.01 – 0.02 at. %) using a Balzers induction furnace in an argon atmosphere at the Institute of Condensed Matter, Technical University of Braunschweig, Germany. Several induction-melted binary and ternary alloys were produced at the Max-PlanckInstitut für Eisenforschung in Düsseldorf, Germany. Heat treatments of the alloys were performed for 5 h at 1000 K, 1 h at 1173 K, or 20 min at 1273 K in argon with subsequent quenching in water (290 K). For the heat treatments, the samples were encapsulated in quartz ampoules which were evacuated and back-filled with argon. For the characterization of the alloys, several methods were applied: (1) light-optical microscopy (digital video-microscope VHX-100 (KEYENCE) with attachment VH-Z450, after etching of the polished specimen surface), (2) EDX (Thermo NORAN VANTAGE), (3) X-ray diffraction (XRD) using GE XRD 3003 PTS and Oxford diffractometers (room temperature, Cu Kα1 with a wavelength of λ = 1.5406 Å, in a 2Θ range from 10 to 120°, or to 140°, respectively), (4) Vickers hardness (HV 30s/10N) and (5) transmission electron microscopy (TEM) using a Philips CM12 electron microscope at an accelerating voltage of 120 kV. Damping Q-1 and modulus change (shear modulus G or Young’s modulus E, both are ∼ f2, where f is the resonance frequency for torsional or flexural vibrations, respectively) were measured with 1) an inverted torsion pendulum (0.5…3 Hz) at Tula State University [4] as a function of temperature (from room temperature to 873 K) at an amplitude of γ0 ≈ 5⋅10-5, and 2) vibrating-reed set-ups (150…3000 Hz) at Technical University of Braunschweig with optical detection of the vibrations [5]. Temperature dependent internal friction (TDIF) measurements were performed with a heating rate of 1 K/min up to a chosen temperature and cooling with nearly the same rate. TDIF Curve Fitting Procedure The mechanical loss peak ( Q −1 ) in case of a relaxation effect with a single relaxation time is described by the Debye equation: Q −1 = ∆ ⋅

ωτ , 1 + (ωτ ) 2

(1)

where ∆ is the relaxation strength (discussed later), ω = 2πf . In practice, values of Q −1 are often measured as a function of temperature ( T ). The jumps of atoms are the elementary steps of most relaxation processes and their temperature dependence is described by the Arrhenius equation: τ −1 = τ 0 −1 exp(− H / kT ) , with H being the activation energy and τ the relaxation time. For a fixed

frequency and a single relaxation time, the temperature dependence of Q −1 is described by San Juan [6]: H 1 1   −1  , Q −1 (T ) = Qmax cosh −1   −  k T T max   

(2)

Solid State Phenomena Vol. 137

71

where k is the Boltzmann constant. A variety of particular distribution functions were developed for the description of different alloys. The most widely used one is the Gaussian distribution of a variable z = ln (τ τ 0 ) : z exp(−( ) 2 )

β β π

Φ( z ) =

,

(3)

where β is a parameter characterising the width of the relaxation time distribution. −1 Introducing the distribution function into Eq. (1) and considering ∆ = 2Qmax , the damping Q −1 can be written as ∞

−1 Q −1 = 2Qmax ∫ Φ( z ) −∞

ωτ dz 1 + (ωτ ) 2

(4)

or ∞ −1 Q −1 = 2Qmax

exp(ln (ωτ 0 ) + z ) dz = 2 0 ) + z )]

∫ Φ( z ) 1 + [exp(ln (ωτ

−∞

z exp(−( ) 2 )

−1 ∞ max

2Q

β π

∫ exp(−(ln (ωτ

−∞

β

0

) + z )) + exp(ln (ωτ 0 ) + z )

(5)

dz.

Using the abbreviation x = ln(ωτ 0 ) Eq. (5) can be rewritten as

Q −1 =

−1 ∞ max

2Q

β π

z exp(−( ) 2 )

β

∫ exp(−( x + z)) + exp( x + z )

−∞

dz =

−1 Qmax

β π

∞

z

∫ exp(−( β ) ) cosh 2

-1

( x + z ) dz .

(6)

−∞

Results Light-Optical Microscopy. The macrostructure of selected specimens was studied by light-optical microscopy (etching solution: 100 cm³ hydrochloric acid - HCl, 10 cm³ nitric acid - HNO3, 100 cm³ water - H2O). Some examples for Fe – Si and Fe – Si – Al alloys are shown in Fig. 1 and 2, respectively. The Fe – Si alloys have homogeneous grain structures with equiaxed grains of about 1 mm in diameter. In the outer region often elongated, radially inwards grown grains are observed. In the ternary Fe – Si – Al alloys with low Al + Si content, large, elongated crystals dominate the structure (Fig. 2 a, b). The alloys with higher Si + Al content show again predominantly equiaxed grains (Fig. 2c, d). In order to avoid texture effects, all specimens for mechanical properties testing were cut from the central area with equiaxed grains.

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Interaction between Defects and Anelastic Phenomena in Solids

a) Fe-6.7Si

b) Fe-8.6Si

c) Fe-10.4Si

d) Fe-12.2Si

Fig. 1. Macrostructure of Fe – Si alloys after heat treatment for 5 h at 1000 K and subsequent water quenching: Fe – 6.7 Si (a), Fe – 8.6 Si (b), Fe – 10.4 Si (c) and Fe – 12.2 Si (d).

a) Fe-2.5Si-3Al

b) Fe-3Si-3.5Al

c) Fe-2Si-4.5Al

d) Fe-1Si-9.5Al

Fig. 2. Macrostructure of Fe – Si – Al alloys after heat treatment for 5 h at 1000 K and subsequent water quenching: Fe – 2.5 Si – 3 Al (a), Fe – 3 Si – 3.5 Al (b), Fe – 2 Si – 4.5 Al (c), and Fe – 1 Si – 9.5 Al (d).

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X-Ray Diffraction. No effect of ordering was observed by XRD in binary Fe – Si alloys with compositions below Fe – 12.2 Si. In this latter alloy, 100 h annealing at 670 K after water quenching from 1000 K leads to B2 ordering (no order was observed in the as-quenched state). D03 ordering was found in Fe – 14 Si and Fe – 25 Si, and several Fe – Si – Al alloys. Fig. 3 shows the lattice parameter in dependence on the Si content and the Si / Al ratio. As expected, Si decreases and Al increases the lattice parameter of α-Fe. In the ternary alloys it is lower than in α-Fe if Si / Al > 1 and vice versa.

Fe-Si 2,86

2.90

Fe-Si-Al

a, A

Fe

1.8/17.7

2/4

2.88

5,80

Fe3(SixAl1-x)

0/25

7/8

Fe

5,75

a, A

12.9/12.4

6/3

2.86

a, A

9/6

2,84

5,70 2.84

25/0

D03

14/0

A2 2,82

[a]

0

5

D03 10

15

at.% Si

20

25

5,65

2.82 0

[b]

5

10

15

at.%(Si+Al)

20

25

[c]

0

5

10

15

20

25

at.%Si

Fig. 3. Lattice parameter of studied alloys in dependence on a) Si content, b) Si + Al content in Fe (numbers near experimental points indicate Si/Al contents in at. %., in case of D03 ordered alloys, a was halved), and c) Si in D03 Fe3(Si, Al) alloys. Transmission Electron Microscopy. In agreement with the X-ray results, D03 ordering was detected by TEM in Fe – 9 Si – 6 Al, Fe – 13 Si – 12 Al and Fe – 5 Si – 20 Al after water quenching from 1173 K followed by 100 h annealing at 750 K (Fig. 4). As TEM is a local method in contrast to XRD, it is much more sensitive for the detection of ordered regions. Indications of D03 ordering were found in Fe – 12.2 Si and – very weakly – also in Fe – 10.4 Si. No carbides were found in our TEM studies of Fe – Si and Fe – Si – Al alloys.

Fig. 4. TEM pictures of the D03 order in the alloys Fe – 9 Si – 6 Al (a), Fe – 13 Si – 12 Al (b) and Fe – 5 Si – 20 Al (c) after 100 h annealing at 750 K ([110](111)).

74

Interaction between Defects and Anelastic Phenomena in Solids

Vickers Hardness. An increase in Si content increases the Vickers hardness (HV 30s/10N) of the Fe – Si alloys (Fig. 5 a). Al results in an additional increase of the hardness of the Fe – Si alloys (Fig. 5 b). However, the effect of Al on the hardness increase in Fe – Si – Al alloys is weaker than that of Si. Substitution of Si by Al in stoichiometric Fe3(Si, Al) results in a decrease of the hardness (Fig. 5 c). HV

HV

HV

500

5.5/6.8

300

1.8/17.7 0/25

1.9/6.9

500

400 250

4.7/5.9

300

400

200

1.9/6.9

200

0

[a]

5

10

15

at.% Si

20

5

25

[b]

Si/Al, at.%

2/4

150

100

10

15

20

at.% Si + Al

300 0

25

[c]

5

10

15

20

25

at.% Si, (Al+Si)=25%

Fig. 5. Hardness as a function of composition in (a) Fe – Si, (b) Fe – Si – Al, and (c) Fe3(Si, Al) alloys. Numbers near experimental points in (b) indicate Si/Al content in at. %. Internal Friction Snoek-type Relaxation. The Snoek-type relaxation has been observed in several Fe – Al alloys [7, 8] and explained in terms of two main components, namely an ordinary Fe - C - Fe peak (C atom jumps with C surrounded by Fe atoms only) and an Fe – C – Al peak (C atom jumps in the iron lattice in presence of substitute atoms). In order to check the reliability of the experimental setups used in this study, Snoek peaks in unalloyed iron in a wide range of vibration frequencies, i.e., of peak temperatures were measured as a first step. The Arrhenius plot for the carbon Snoek peak in αFe quenched from 1000 K yields an activation energy H = 0.84 ± 0.02 eV and a value for the preexponential factor in the Arrhenius plot of the relaxation time τ0 ≈ 4.7 × 10–15 s. These parameters of carbon Snoek relaxation in α-Fe coincide with those commonly accepted and confirm the reliability of the measurements performed. It is seen that an increase of the Al content dissolved in α-Fe leads to a redistribution of C in the solid solution. This can be concluded from the appearance and regular growth of a second IF peak, an Fe – C - Al peak caused by diffusion jumps of C atoms that interact with Al atoms (Fig. 6). The activation energy of this peak, according to the Tm [K] = 362 × H [eV] [9] dependence, is higher by approximately 0.21 eV than that of the “main” (Fe – C – Fe) peak. The Fe-C-Fe and Fe – C – Al peaks were fitted according to the method described above. The temperature dependence of damping and resonance frequency for three Fe – Si alloys with 2, 5.5 and 10.4 at. % Si is shown in Fig. 7. The difference between first heating and cooling curve (or second heating curve) shows the effect of annealing. At heating the peak is double-headed similar to the case of Fe – Al. Peak positions are roughly indicated by dotted lines, the temperatures of the peak maxima depend on the frequency of the vibrations. The height of the second peak, which is denoted as the Fe – C - Si peak, increases with increase in Si content in iron.

Solid State Phenomena Vol. 137

-1

0.005

Q -Qb

-1

Fe-3Al

-1

Q -Qb

experiment single peaks theor. curve

0.004

-1

0.008

75

Fe-6Al

0.005

experiment single peak theor. curve

0.004

0.003

0.006

0.003

0.002

0.004

0.002

0.001

0.002

0.001

0.000 300

400

T, K 500

0.000 300

600

400

T, K 500

-1

Q -Qb

-1

0.000 300

600

Fe-10Al experiment single peak theor. curve

400

T, K 500

600

a b c Fig. 6. TDIF curves for binary Fe–Al alloys (3, 6, and 10 at. % Al) water-quenched from 1000 K (the dotted curves show the deconvoluted peaks) [8]. Q

-1

Fe-2%Si 1 run 2 run

0.003

f,Hz

0.003

405

-1

0.002

0.002

820

400 0.001

810

0.001 500

410

830

390

T, K

f, Hz 0.003

395

400

Fe-10.4Si 420

-1

Q

~2 Hz

0.001

300

f, Hz 840

Q

400 0.002

Fe-5,5Si

0.000 300

600

400

T, K

500

300

600

400

T, K

500

600

390

a b c Fig. 7. Damping Q-1 (left-hand scale) and resonance frequency f (right-hand scale) from TDIF measurements for binary Fe – Si alloys with 2, 5.5 and 10.4 at. % Si. All specimens were water-quenched from 1000 K. After heating to 550 K and higher, the peak at higher temperature (Fe – C - Si) is no longer observed during cooling or/and second heating, while the main Fe - C - Fe component of the peak remains visible. Examples are given in Fig. 7 a and b. In case of Fig. 7 c, the specimen was measured in the first run up to ~ 850 K resulting in a very smooth cooling curve without indication of a peak. Heating for a second time gives a peak broadened to the high-temperature range with a maximum at ~ 500 K. This maximum may have another origin than the carbon Snoek-type peak. The experimental data presented in Fig. 7 a and b were fitted by Debye peaks, the results are shown in Fig. 8. Q

-1

0.002

experim. Fe-C-Fe Fe-C-Me sim.sum.

Fe-2Si 400 Hz

0.001

0.000 0.0021

Q

-1

experim. Fe-C-Fe Fe-C-Me sim.sum.

Fe-5.5Si 500 Hz

0.002

0.001

0.0024

0.0027

1/T, K

-1

0.0030

0.000

0.0020

0.0024

0.0028

1/T, K

-1

0.0032

a b Fig. 8. Deconvolution of the TDIF peaks of the binary Fe–Si alloys shown in Fig. 7 a and b. Similar to Fe – Al alloys, the TDIF peak of the Fe – Si alloys can be decomposed into two peaks, a Fe – C - Fe and probably a Fe – C – Si peak. It is notable that for equal concentrations of substitutional atoms the second peak is higher in case of the Fe – Al alloys as compared with the Fe – Si alloys.

76

Interaction between Defects and Anelastic Phenomena in Solids

Finally, several ternary Fe – Si – Al alloys were studied. Similar to both Fe – Al and Fe – Si alloys at least two peaks can be distinguished in the TDIF curves (Fig. 9). In this paper we focus on alloys with (Si + Al) contents below 10 at. %. The Snoek relaxation in more complex IF spectra of alloys with (Si + Al) > 10 at. % (see e.g. the appearance of a third peak in the TDIF curves of Fe – 10.4 Si (Fig. 7 c)) will be discussed in another paper. Q

-1

Fe-1.6Al-3Si f = 500 and 300 Hz

0.006

510

f, Hz 500

0.004

Fe-3Al-3Si f, Hz

0.006

Q

wq1000K wq1173K wq1273K

-1

-1

Q

Fe-4Al-2Si f, Hz w.q. 1173K 192

0.009

500 490

0.004

0.006

188

480

490

0.002 f ~300 Hz

300

400

0.002

470

308

T, K

500

303 600

300

400

500

T, K

0.003

600

184

300

400 T, K 500

600

a b c Fig. 9. TDIF curves for three ternary Fe – Si – Al alloys (Fe – 3 Si – 1.6 Al was water-quenched from 1000 K and measured at two different frequencies, see right scale; specimens of the Fe – 3 Si – 3 Al alloy were also quenched from 1173 and 1273 K; the Fe – 4 Al – 2 Si specimen was quenched from 1173 K). The following conclusions can be drawn from these figures: (i) The observed peak is indeed a relaxation peak as its position shifts with changing the frequency, see e.g. Fig. 7 b and 9 a; (ii) the temperature of annealing prior to quenching influences the relative height of the Fe – C - Fe and Fe – C - Si peaks (Fig. 9 b). The specimens presented in Fig. 10 all contain about 6 at. % of (Si + Al), but the Si/Al varies from ~ 1/2 to 2. This allows the third conclusion that the substitution of Si by Al leads to an increase of the relative height of the Fe – C - (Si, Al) peak. The same conclusion can be drawn from Fig. 6 and 7 comparing, e.g., the peak heights for Fe – 6 Al and Fe – 5.5 Si. Q

-1

0.0050

experim. Fe-C-Fe Fe-C-Me sum.sim

Fe-1.6Al-3Si 500Hz

Q

-1

experim. Fe-C-Fe Fe-C-Me sum.sim.

Fe-3Al-3Si 500Hz

0.0010

0.0075

Q

-1

experim. Fe-C-Fe Fe-C-Me peak sum.sim

Fe-4Al-2Si 200Hz

0.0050

0.0025

0.0005 0.0025

0.0000 0.0020

0.0000 0.0024

0.0028 -1

1/T [K ]

0.0032

0.0020

0.0024

0.0028 -1

1/T [K ]

0.0032

0.0000

0.0020

0.0024

0.0028

0.0032

-1

1/T [K ]

a b c Fig.10. Deconvolution of TDIF curves for ternary Fe – Si - Al alloys: a) 3 Si - 2 Al, b) 3 Si – 3 Al, c) 2 Si – 4 Al. Measurements of TDIF curves with step-by-step increase of the highest temperature (i.e. stepby-step ageing of quenched specimens) show that the height of the complete Snoek peak monotonously decreases (Fig. 11). An additional observation is that the decrease of the height of the Fe – C - Me peak component is faster than that of the Fe – C - Fe component. After heating to ~ 670K the inverse effect takes place: some increase of the Snoek-type peak is observed. Additionally a new peak at 550 - 600 K appears. In order to check changes of the dislocation pinning at a certain stage of ageing, we carried out amplitude-dependent IF (ADIF) tests at different temperatures. In Fig. 12 a, an ADIF curve at room temperature for Fe – 3 Al – 3 Si is shown. There is a pronounced difference between measurements with and without a magnetic field. Damping consists of two components: magnetomechanical damping which can be suppressed be external magnetic fields and non-magnetic, dislocation-related

Solid State Phenomena Vol. 137

77

-1

Q , 10

-4

damping. The critical level of damping capacity of Ψ = 10 %, above which materials are defined as high damping materials, is included in the figure [10] indicating a potential application of Fe - Al Si alloys. Fe-3Al-3Si w.q. 720C 293-403K

60

f, Hz

Q

Fe-3Al-3Si 720°С, 500Hz experim. Fe-C-Fe Fe-C-Me sim.sum.

-1

n.1

470

0.004

50 468

40

466

30 20

0.002

464

10 462

-1

Q , 10

-4

300

325

350

T, K

375

400

0.0021

0.0024

0.0027

0.0030

-1

1/T [K ]

293-453K

70

0.000

60

-1

-1

f, Hz

Q

468

0.004

0.004

0.002

0.002

n.2/1

Q

n.2/2

50 40

464

30 460

20 10

456 300

325

350

375

400

425

450

0.000

60

0.000 0.0021

T, K

0.0024

0.0027

0.0030

0.0021

-1

293-478K

f, Hz

0.0027

0.0030

1/T [K ]

-1

Q

-1

Q

n.3/1

n.3/2

50

0.003

468

-1

Q , 10

-4

0.004

0.0024

-1

1/T [K ]

40

0.002

464

0.002

30

0.001

460 20

10 300

456 350

40

T, K

0.000

0.000 0.0021

450

0.0024

0.0027

0.0021

0.0030

0.0027

0.0030

-1

1/T [K ]

35

0.0024

1/T [K ]

-1

293-503 K

-4 -1

Q , 10

400

-1

-1

f, Hz

Q

468

0.002

0.002

0.001

0.001

Q

n.4/1

n.4/2

30 464 25 20

460

15 456 350

400

T, K

30

450

0.000 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032

500

293-533 K

-1

Q , 10

-4

10 300

0.000 0.0021

-1

1/T [K ]

f, Hz 468

-1

0.0027

0.0030

-1

1/T [K ]

0.0015

Q

0.0024

0.0015

n.5/1

Q

-1

n.5/2

25 0.0010

0.0010

0.0005

0.0005

464 20 460 15

10 300

456

452 350

400

450

T, K

500

0.0000

0.0000 0.0021

0.0024

0.0027 -1

1/T [K ]

0.0030

0.0021

0.0024

0.0027 -1

1/T [K ]

0.0030

Interaction between Defects and Anelastic Phenomena in Solids

27

293-572 K / 60 min

-1

Q , 10

-4

78

f, Hz

0.0015

468

Q

464

0.0010

0.0010

0.0005

0.0005

-1

0.0015

n.6/1

Q

-1

n.6/2

24

21

460 456

18

452 15 448 300

350

400

450

500

0.0000

0.0000 0.0021

550

0.0030

0.0021

f, Hz

-4

470

40

-1

0.0027

0.0030

-1

1/T [K ]

0.0015

0.0015

Q

0.0024

n.7/1

Q

-1

n.7/2

-1

Q , 10

0.0027

1/T [K ]

293-693 K / 60 min

45

0.0024

-1

T, K

35

460

0.0010

0.0010

0.0005

0.0005

30 25

450

20 15

440

10 300

400

500

600

700

0.0021

-4

0.0027

0.0021

0.0030

Q

f, Hz

0.002

0.0027

0.0030

1/T [K ]

-1

470

0.0024

-1

1/T [K ]

-1

Q

n.8/1

0.002

n.8/2

-1

Q , 10

0.0024

-1

293-693 K / 60 min n.2

45

0.0000

0.0000

T, K

40 460 35 30

0.001

0.001

450 25 20 440 0.000

15 400

500

T, K

50

600

-1

0.000 0.0021

700

293-573 K

Q , 10

-4

300

0.0024

0.0027

0.0030

0.0021

-1

Q

f, Hz

0.002

0.0027

0.0030

1/T [K ]

-1

470

0.0024

-1

1/T [K ]

Q

n.9/1

-1

0.002

n.9/2

465 40 460 30

455

0.001

0.001

450 20 445 300

350

400

450

T, K

500

550

0.000

0.000 0.0021

0.0024

0.0027 -1

1/T [K ]

0.0030

0.0021

0.0024

0.0027

0.0030

-1

1/T [K ]

Fig. 11. Influence of increasing ageing temperature on the profile of TDIF curves: left column – experimental data (water quenched from 1000 K Fe – 3 Si – 3 Al specimen, step by step heating to 1) 403, 2) 453, 3) 478, 4) 503, 5) 533, 6) 573, 7) 693, 8) again to 693, and 9) 573 K), and simulations: middle column with fixed parameters for the Fe-C-Fe peak (Н1 = 0.84 eV and β1 = 0.7) – index 1, and right column – with free parameters for both peaks, index -2. With increase in temperature, tg αADIF, i.e. the slope of the dislocation-related amplitudedependent damping increases (Fig. 12 b). The sharp increase of this value at ~ 670 K for Fe – 3 Al – 3 Si corresponds to temperature of interstitial atoms condensation at dislocations [11]: at this temperature the configuration entropy due to relocation of interstitial atoms from solid solution to dislocations (∆S) becomes equal to binding energy between interstitials and dislocations (∆H). Above this temperature pinning points atmospheres at dislocations starts to dissolve. This is the same temperatures range, where we also observed the increase in the Snoek-type peak and the appearance of a new peak at ~ 600 K. In view of the ADIF data (possible unpinning of dislocation) and the increase in C content in solid solution (increase in the Snoek peak height), this new peak at 550 – 600 K can be suggested to be the Snoek-Köster peak.

Solid State Phenomena Vol. 137

79

Zener Relaxation. The Fe – Al and Fe – Si alloys exhibit not only Snoek relaxation but also Zener relaxation due to the reorientation of pairs of substitute atoms Al - Al and Si - Si. The relaxation strength of the Zener relaxation ∆ = 2Qmax-1 in disordered alloys is proportional to both the amount of substitute atoms and the relaxation strength per atom pair. As Al atoms are bigger and Si atoms smaller than Fe atoms, both Al - Al as well as Si - Si pairs give rise to an increase of the Zener peak height due to changes of the local lattice parameter. Selected data from literature (results of Tanaka [12] – open triangles and our results – closed triangles) are shown in Fig. 13 demonstrating the increase in the peak height with both Si and Al content until ordering takes place at ~ 11 at. % Si or > 20 at. % Al in binary alloys. 4

tgαADIF

Q

Fe-3Si-3Al

-1

0,02

test at room temperature after annealing at indicated temperatures

~670K 3

Ψ = 10% 2

Т = 295K without magnetic field 4 in: H=2x10 А/m

0,01

0,00 0,0000

0,0001

0,0002

1

0,0003

γ

0 0,0010

0,0015

0,0020

0,0025

0,0030 1/T,

K

-1

a b Fig. 12. Fe – 3 Al – 3 Si alloy: a) ADIF curve for quenched measured with and without magnetic field, b) tan αADIF at room temperature as a function of the inverse ageing temperature. 150

∆

Ternary: Si+Al (Si/Al)

Binary: Si Tanaka Si present Al Tanaka Al present

∆

100

4/9 6/8

12/13 and 20/5

10/5

5/6 50

150

2/6

100

50

5/20

Ternary: Si+Al (Si)

Binary: Si Tanaka Si present Al Tanaka Al present

5 2 20

10

5

6

2/18

4 12

0

2

0

5

10

15

20

at. %

25

30

5

10

15

at. %

20

25

30

a b Fig. 13. The relaxation strength of the Zener peak (∆) in binary Fe - Si and Fe - Al and in ternary Fe – Si - Al alloys. Some data for binary alloys were added from [12] (open triangles: up – for Si, down – for Al). Data for ternary alloys are shown by circles: a) ∆ is given as a function of the total amount of Si + Al in at. % and the respective Si and Al contents are indicated at the experimental point as Si/Al; b) ∆ for ternary alloys is given as a function of the Al content and the amount of Si in at. % is indicated at the experimental points. In ternary alloys, the occurrence of Si - Al pairs may reduce the contribution to the Zener relaxation compared to the binary alloys. The double-headed Zener peak in Fe – Si - Al alloys was already discussed earlier in [13]. In the present paper we give only a short overview of the relaxation strength in ternary Fe – Si - Al alloys and their comparison with binary systems. Indeed the Zener relaxation in all ternary alloys is significantly lower than in binary alloys. This can be seen in the plot of the peak height as a function of the total amount of substitute atoms (Fig. 13 a).

80

Interaction between Defects and Anelastic Phenomena in Solids

There are at least two reasons for that. Firstly, ordering, which leads to a decrease in the Zener peak height, starts at lower alloying element concentrations in Fe - Si - Al alloys than in Fe - Al alloys. The second and more important reason is that Al and Si atoms in iron at least partly compensate the elastic distortions produced by each species. This effect can be seen in Fig. 13 b: For a constant Al content, the addition of Si strongly reduces the Zener peak height (the alloy Fe - 9.6 Si - 5.4 Al seems to be an exception; the reason for that is not clear in the moment). Conclusions Several C-containing Fe – Si and Fe – Si – Al alloys were studied with respect to their macro-, microstructure and temperature- and amplitude-dependent anelastic behaviour (internal friction). The following conclusions can be drawn: Snoek-type relaxation was observed in all studied alloys, Zener relaxation was observed only in alloys with concentration of substitute atoms higher than 5 at. %. Si decreases and Al increases the lattice parameter in binary alloys, in ternary Fe – Si – Al alloys the lattice parameter depends on the ratio Si/Al. As a rule of thumb, Zener relaxation in such ternary alloys is significantly lower than in binary alloys, because Al and Si partially compensate their contributions to the creation of elastic distortions of the Fe lattice. In contrast to C-containing Fe – Ge and Fe – Co [7, also this conference] alloys, the Snoek peak observed in the present alloys consists of two components: a peak whose parameters correspond to those of the Snoek peak in pure Fe (Fe – C – Fe: H ≈ 0.84 eV), and a second peak whose parameters are determined by an additional interaction between C and substitute atoms. The broadening of the C-related Snoek-type relaxation in both Fe – Si and Fe – Al alloys reflects the existence of a set of energetically different positions for the C atoms depending on their distance from the substitute atom or atoms. At comparable concentrations of Al and Si in the Fe – Si – Al alloys with Al and Si content < 5 at. %, Al exerts a greater effect on the TDIF profiles in the region of Snoek relaxation, which is explained by its more efficient contribution to the long-range elastic interaction with C atoms. An increase of the heating temperature for quenching leads to an increase in the Fe – C – Fe component at the expense of the Fe – C – Me component of the Snoek peak. Ageing up to 670 K leads to a monotonous decrease of the Snoek peak height with increase of ageing temperature. Short time ageing at higher temperatures T > 670 K leads in several alloys (e.g., Fe – 3 Si – 3 Al, Fe – 3 Si – 1.5 Al, Fe – 2 Si – 4 Al) to some increase in the Snoek peak height and appearance of another, probably Snoek-Köster peak due to increasing mobility of unpinned dislocations (C atoms leave dislocations and go back to solid solution). An increase in Si and Al + Si content in Fe – Si or Fe – Si – Al alloys leads to the occurrence of an additional peak at the high-temperature side of the Snoek peak. This peak is observed only in those as-quenched alloys which are inclined to ordering at low temperature heating and may be caused by correlated vacancy and substitute atom short range diffusion. Acknowledgements. The authors are grateful to H. Neuhäuser and U. Brust for producing the alloys, and to S. B. Golovina, Chr. Grusewski and M. Maikranz-Valentin for help with experiments. References [1]

J. Snoek: Physica. Vol. 8 (1941), p. 711.

[2]

Yu. A. Krishtal: Phys.Met.Metallogr. Vol. 19 (1965), p. 111.

[3]

C. Zener: Elasticity and Anelasticity of Metals (University of Chicago Press, Chicago, Illinois, USA 1948).

[4]

S. A. Golovin, S. I. Arkhangelskij: Problemi Prochnosti (in Russian). Vol. 5 (1971), p. 120.

[5]

K. Bothe, H. Neuhäuser: Scr.Metall.Mater. Vol. 16 (1982), p. 1053.

Solid State Phenomena Vol. 137

81

[6]

J. San Juan, in: Mechanical Spectroscopy Q-1 2001, edited by R. Schaller, G. Fantozzi and G. Gremaud, Trans Tech Publications, Uetikon- Zuerich, Switzerland (2001), p. 32.

[7]

I. S. Golovin, S. B.Golovina: Phys. Met. Metallogr. Vol. 102 (2006), p. 636.

[8]

D. Ruiz, J. L. Rivera-Tovar, D. Segers, R. E. Vandenberghe and Y. Houbaert: Mater. Sci. Eng. A Vol. 442 (2006), p. 462.

[9]

M. Weller: J. Phys. (Paris) Vol. 46, C10 (1985), p. 711.

[10] I. S. Golovin: Key Eng. Mater. Vol. 319 (2006), p. 225. [11] A. H. Cottrell: Dislocations and Plastic Flow in Crystals. (Clarendon Press, Oxford 1953). [12] K. Tanaka: Trans. Jpn. Inst. Met. Vol. 16 (1975), p. 199. [13] T. S. Pavlova, I. S. Golovin, H.-R. Sinning, S. A. Golovin, C. Siemers: Intermetallics. Vol. 14 (2006), p. 1238.

Solid State Phenomena Vol. 137 (2008) pp 83-90 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.83

Room-Temperature Short-Range Ordering in Fe - Si Alloys Observed by Internal Friction Fernando González1,а, Daniel Ruiz2,b , Yvan Houbaert1,c 1

Ghent University, Dep. Metallurgy and Material Science, Ghent, Belgium

2

ArcelorMittal Research Industry Gent, JF. Kennedylaan 3, B-9060 Zelzate, Belgium a

[email protected],[email protected] c

[email protected]

Keywords: Silicon steel; Zener peak; isothermal internal friction, room temperature ageing.

Abstract. Research performed at Ghent University, regarding new production methods for electrical steel, has shown that high silicon steel suffers an ageing phenomenon at room temperature. Recent studies carried out by the same group using different analysis techniques (Mossbauer spectroscopy, neutron diffraction, etc) brought to light a probable process of ordering towards the D03-structure, which is responsible for the observed low ductility during cold rolling and makes the processing of steel extremely difficult. In addition, the Si-steels become more brittle as the delay time between hot and cold rolling is increased. Frequency dependent internal friction (FDIF) studies were performed on different Fe - Si alloys with a Si content varying from 3.73 at. % to 8.7 at. % immediately after several thermal treatments and compared with ultra-low carbon steel. The evolution of relaxation peaks during the IF measurements, performed at constant room temperature, helps to understand the ageing mechanisms. Three processes have been observed: firstly, as expected, addition of Si reduces the carbon Snoek peak. Secondly, a peak associated to C - Si is formed. Thirdly, a low frequency peak associated with Zener relaxation (Si atom pairs) appears for a content of approximately 3.77 wt. % Si. The two latter peaks decrease with ageing time and in the case of the Zener peak there is a notable displacement to higher frequencies with a small increase of the Si content. The reduction of the peaks during the ageing after annealing is more noticeable in quenched specimens than in air cooled ones, and in furnace cooled specimens the reduction is even smaller, indicating that the process is really an ageing phenomenon. Room temperature short-range ordering might explain both the lowering of the Zener peak and the observed macroscopic embrittlement. Introduction Electrical steel is used for generators, electric motors, etc. Alloying with silicon constitutes the basis for all the high electrical steel grades, but using a conventional industrial process (hot and cold rolling) it is possible to reach only 3.5wt.% Si due to an appearing very poor cold workability. This content is far from the ideal 6.5 wt. % Si, which reach the compromise between very low energy loss with very high permeability and a still large enough polarization. Using special thermomechanical routes [1], studied at Ghent University, it is possible to obtain steel of 6.3 wt. % Si. Two parameters were important: the time of cooling after the hot rolling and, surprisingly, the time of delay between the hot and the cold rolling. This ageing phenomenon at room temperature, which caused embrittlement, made the cold rolling very difficult to perform. First studies [2, 3, 4] using Mossbauer spectroscopy, neutron diffraction, positron annihilation and frequency-dependant internal friction pointed out an ordering to D03 structure to be the main cause for this embrittlement. It is well known that short-range ordering phenomena in alloys are source of hardening [5], and neutron diffraction studies confirm this ordering in our alloys. Increasing the concentration of Si leads to a rise of the degree of order [5]. The probable mechanism

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that causes this ordering is a orientation of pair of Si atoms, rising thus a Zener peak when the concentration of Si is around 3.5 wt. % (around 7 at. %). The background in these preliminary studies was too high. More studies were performed, and are presented in this text, to understand the development of the peaks depending on compositions. Experimental The forced pendulum method was used for the internal friction measurements. We measure the damping caused by the movement of defects when a stress is applied (Internal Friction, Q-1), or more specifically, the tangent of the phase lag between an applied torsional stress and the response of the material. The temperature was not changed (room temperature) and thanks to that, in-situ phenomena were avoided (which may change the metallurgical state of the sample). The torsion in the sample was measured with a laser and an optical detector. The strain amplitude is 1.5 × 10-5. The pendulum consists in a forced torsion pendulum activated by a magnetic coiling. The resonance frequency was 200 Hz. Each cycle consists in 61 measurements of Q-1 in a range of frequencies from 10 to 0.0005 or 0.001 Hz. Frequencies under 0.0005 presented a large scattering. No magnetic field was applied to eliminate magnetomechanical damping due to lack of this device in the machine (coiling under development), but it was modelled using an exponential function. Preparation of Samples. Samples were obtained by laboratory casting and their composition was obtained by spark spectroscopy. Analisys of nitrogen content in high silicon samples was performed by melt extraction. Compositions of samples are listed in Table 1, where ULC stands for Ultra Low Carbon steel. They were cut by spark erosion in strips of 58.0 × 3.0 × 0.8 mm3. After the measurement of Q-1 in the as-cast state, samples were sealed in silicon capsules (air removed with vacuum pump and argon) to be heat treated under protective atmosphere. The heat treatments consisted in heating up the sample to 900 °C and then: - Furnace Cooling: maintaining 900 °C for 12 hours and slow cooling in the oven for 12 hours to room temperature. - Quenching: maintaining 900 °C for 1/2 hour, and quench in water (breaking the ampoule inside the water to minimize oxidation). Table 1. Chemical compositions of samples. Sample ULC FeSi - 3 FeSi - 7 FeSi - 8

Si (wt. %) < 0.005 1.91 3.77 4.61

Si (at. %) < 0.01 3.73 7.23 8.77

Al (wt. %) 0.0348 0.05 0.007 0.004

C (wt. %) 0.004 0.002 0.002 0.002

N (wt. %) 0.006 0.004 0.0035 0.0058

Measurements. It consisted on several cycles, each cycle takes between 2 and 4 hours depending on the range of frequencies used. At least three cycles were measured using the as-cast state samples, because the first cycle of measurements presented always high background. This effect is probably due to internal stresses induced during the manipulation and mounting of the sample before the measurement. Immediately after heat treatment, Q-1 was measured (with a delay of 10 minutes after quenching for removing superficial oxidation). Around 30 cycles were measured in order to detect any ageing phenomenon.

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Analysis of Results In forced-vibration torsional pendulum, we can assume that the tangent of the phase lag is the internal friction, so: Q-1 = ∆ ⋅

ϖ ⋅τ 2 1 + (ϖ ⋅ τ )

∆ denotes the maximum value of the peak, the angular frequency of the stress sequence is ω and the relaxation time is τ. The program used for the fittings is Origin 7.0. This program automatically fits the desired equations and gives the error. Depending if one, two or three peaks are used, the fitting equation would have five, seven or nine parameters. Peaks were fitted using this Debye model superimposed to an exponential background: 1/Qb = A + B e-c f with f the frequency of measurements. Background was fitted together with the rest of the curves, and the error given by Origin was optimized to be always less than 6 % in the ‘B’ parameter (4.2 % in FeSi - 7, 5.4 % in FeSi - 8) and less than 15 % in the decay ‘c’ parameter (11.5 % in FeSi - 7, 14.4 % in FeSi - 8). This background may be due to dislocations or, more likely, to the movement of magnetic domains. Other theories considering electrical components of the device are being under research. A Snoek peak at 0.18 Hz (Fig 1.) is found in the ULC sample, agreeing with literature [6]. An ageing phenomenon is seen with time, which can be related to diffusion of C-atoms. Furnace cooled samples normally show a smaller quantity of carbon in solution and little ageing, in comparison with the present quenched sample. No nitrogen peak is found because only nitrogen in solution would rise a Snoek peak (N - Fe peak), and according to computer simulation (Leslie model, [7]), in ULC steel most of the nitrogen content is forming AlN precipitates at 900 °C. If a N peak is added (at around 1 Hz) the height of it is less than 0.0005, so it is completely overlapped by Fe - C Snoek peak, and it would decrease also during ageing. As we can see in Fig. 3, there is a decrease of Snoek carbon peak when the content of Si increases, so a nitrogen peak (around 1 Hz, at 20 °C, in good agreement with literature [8]) has to be added, but the height is smaller than the carbon peak because, as said before, the quantity of nitrogen in solution after an annealing at 900 °C is small. A peak related with a substitutional-interstitial interaction (Si - C) appears at lower frequency with respect the C-Snoek peak, so the interaction between C and Si should be positive [9]. For higher concentrations of Si (Fig. 4, quenched sample) the Snoek peak of carbon decreases, in agreement with literature [2, 9]. The only C peak remaining is the one related to the substitutional-interstitial couples (Si - C). The N - Fe peak is very small in this case, if it exists at all, due to a decreasing in the solubility of nitrogen: the quantity of nitrogen is small and the quatity of aluminium is higher compared with the rest of the samples.

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Fig. 1. Internal friction spectra of quenched ULC sample. The Snoek peak decreases because of ageing at room temperature: the measurements shown in the graph were performed after 6 hours, 75 hours and around 4.5 months after quenching, where a small amount of C in solution is still appreciable.

Fig. 2. Computer simulation of solubility of N for our compositions. Annealings were done at 900 °C, where nitrogen in solution is very low.

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Fig. 3. Internal friction spectrum of a FeSi - 3 quenched sample. Three peaks were needed to fit the experimental curve, each of one identified with a relaxation. At very low frequencies there is a curvature not explained by the exponential background we are using. It is assigned to a slope of a possible Si - Si pair peak; although at these very low frequencies the scattering of the experimental points is substantial. The fitting was done using three peaks, considering the effect of the relaxation of nitrogen, and it was done also using only two peaks, being identified as the C - Si and the believed Zener peak at low frequencies. These two peaks appear approximately at the same frequency, no matter which fitting is used, although due to the high scattering it was difficult to obtain any regularity. When using two peaks we can see qualitatively some ageing effect, which can be explained by atomic migration to defects (Si - C peak) and ordering phenomena (Si-Si peak, short-range ordering). The more ordering, the lesser the Zener peak [10], because mobility of Si pairs decrease when the ordered superstructure is formed. Thus, the ageing phenomenon can be related to ordering. Calculations made with activation energy and time constant found in literature [11], calculated for 400 °C - 700 °C , show that the Zener peak should be at much lower frequency and thus there would be no overlap with the Snoek C - Si peak, so basing on the activation energy we can not confirm that it is a Zener peak. Previous studies of alloys up to 8.7 at. % Si reveal the ageing phenomena at room temperature in a quenched specimen [2]. We repeated the study for a furnace cooled sample, obtaining the peaks at the same frequencies. There is a general decrease of the background, but the peaks do not show a dramatic change (Fig. 5) as expected, and the N-Snoek peak only appears in the first measurements. Best fitting is obtained with two peaks, identified by the substitutional-intersitial pair and another peak at lower frequencies, probably the same that began to show in the FeSi - 7 sample with the frequency shifted to higher values. Frequencies at which we have the maximum Q-1 for each peak are shown in Table 2. We could not notice if the low frequency Z-peak in FeSi - 8 increased with respect the FeSi - 7 due to higher concentration of Si [10], but as we see in Table 2 the frequency of maximum Q-1 is shifted to higher values. This could be explained as a decrease of activation energy when the Si concentration increases. The appearance of the Z-peak in the FeSi - 7 sample is only estimated, due to the high scattering and background for these low frequencies.

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Fig. 4. Quenched FeSi - 7. The fitting was done using two peaks (Z-peak and C - Si interaction). If N peak is added, position and height of this two peaks present almost no variation. Background is always exponential.

Fig. 5. FeSi - 8 furnace cooled sample. Peaks do not evolve significantly, the general background decreases. Nitrogen peak appears only in the first measurements and it is too small so it can be disregarded.

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Table 2. Frequency at which peaks have the maximum internal friction in isothermal conditions (Room Temperature Frequency-Dependent Relaxations). Sample C-Snoek C - Si ULC 0.13 Hz FeSi - 3 0.14 Hz 0.017 Hz FeSi - 7 ≈ 0.01 Hz FeSi - 8 0.012 Hz *Nitrogen peak present only in first measurements

Low freq. Z-peak < 0.0005 Hz 0.0013 Hz

N-Snoek 0.77 Hz (0.8 Hz)*

The peak decays were fitted using an exponential model: Q-1 = Q0 -1 + A e-t/τ Results are given in Table 3 for each peak. The low frequency Z-peak height is not measured in the case of the FeSi-7 sample because the frequency at which the maximum is reached is not a reliable data. The calculation of decay of the FeSi-7 sample was based on the two-peak fitting. Table 3. Exponential decay (in hours) of first order is used to model the decreasing of peaks. Within hours the decrease of alloys concentration in solution is noticeable. Peak C-Snoek N-Snoek Si-C Low freq. Z-peak

ULC 46.5 -

FeSi - 3 5.2 3.2 5.3 -

FeSi - 7 1.9 No applicable

FeSi - 8 slow cooling No decay No decay

The decrease of peaks is due to migration of interstitial atoms (C, N) to crystal defects like vacancies or dislocations. In FeSi-3 sample the decays for Si-C and C peaks are similar probably because both ageing processes are caused by the migration of C to defects. We can notice also that peaks do not change in the furnace cooled sample, as expected. Conclusions High silicon steel suffers embrittlement at room temperature. Substitutional-interstitial pairs are formed, and when the content of silicon increases over 7at.% , short-range phenomena appear and substitutional silicon atoms tend to interact by pairing and increasing the degree of order. This explains the embrittlement observed before cold rolling. There is also the possibility that the activation energy of the Z-peak depends on the concentration of the alloying element, raising the characteristic frequency of the relaxation. The explanation of this Z peak as a Si-Si interaction (Zener peak) is not confirmed by calculations made with the energy of activation. Acknowledgments We wish to thank Professor I.S. Golovin for the information and ideas shared about the FDIF technique and its applications, and also Professor L.B. Magalas, for his assistance, help in upgrading the device and technical support, without which this work would have been almost impossible.

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References [1] T. Ros-Yáñez, Y. Houbaert, O. Fischer and J. Schneider: Mat. Science Forum. Vols. 373-376 (2001), p. 773-776. [2] D. Ruiz, J. L. Tovar, D. Segers, R. E. Vandenberghe, Y. Houbaert: Mat. Sci. Eng. A Vol. 442 (2006), p. 462-465. [3] M. Agundez, D. Ruiz, S.Van Petegem, J. Baerdemaeker, K. W. Chou, D. Segers, Y. Houbaert: Phys. Stat. Sol. Vol. (a) 202, No. 9 (2005), p. 1751-1757. [4] D. Ruiz, T. Ros-Yáñez, E. De Grave, R. E. Vanderberghe, Y. Houbaert: Journal of Magnetism and Magnetic Materials. Vols. 272-276 (2004), p. e1663-e1665. [5] H. Seifert, M. Jurisch, J. Tobisch, C. G. Oertel: Mat. Sci. and Engineering. A Vol. 133 (1991), p. 292-296. [6] A. S. Nowick, B. S. Berry: Anelastic relaxation in crystalline solids (Academic Press, New York 1972). [7] W. C. Leslie et al.: Trans. ASM. Vol. 46 (1951), p. 1470. [8] J. D. Fast and M. B. Verrijp: Journal of the iron and steel institute, January (1954), p. 24-27. [9] D. A. Leak, W. R. Thomas, G. M. Leak: Acta Metallurgical. Vol. 3 (1955), p. 501-507. [10] I. S. Golovin, A. Riviere: Intermetallics. Vol. 14 (2006), p. 570-577. [11] I. R. Boesono, G. J. Ernst, M. C. Lemmens, M. J. van Langen, G.De Vries, Phys. Stat. Sol. Vol. 19 (1967), p. 107.

Solid State Phenomena Vol. 137 (2008) pp 91-98 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.91

MECHANICAL SPECTROSCOPY and NEUTRON DIFFRACTION STUDIES in Fe – Al - Si ALLOYS O. A. Lambri1,a, J. I. Pérez-Landazábal2,b, G. J. Cuello3,c, J. A. Cano1,d, V. Recarte2,e, I. S. Golovin4,f 1

Laboratorio de Materiales, Instituto de Física Rosario (CONICET), Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina. 2

Departamento de Física, Universidad Pública de Navarra, Pamplona, Spain. 3

Institut Laue-Langevin, Grenoble, France.

4

Physics of Metals and Materials Science Department, Tula State University, Tula, Russia

a

[email protected], [email protected], [email protected], [email protected], e [email protected], [email protected]

Keywords: Mechanical spectroscopy, Neutron diffraction, Fe – Al - Si alloys, Order degree.

Abstract. Mechanical spectroscopy and neutron diffraction studies were performed on several samples with compositions Fe - 25 at. % (Al + Si) and Fe - 15 at. % (Al + Si). It was found that the solute grain boundary relaxation is strongly dependent on the degree of order in the sample. A decrease in the orderdegree allows the development of a relaxation peak at around 1000 K during cooling from 1200 K. In contrast, if the order degree is not decreased, the grain boundaries remain locked and consequently the relaxation peak does not appear. The magnetic response both in the asquenched and after thermal treatment states was also explored and correlated to the microstructural state. Introduction The mechanical spectroscopy (MS) technique, involving usually damping and modulus measurements versus temperature, is very sensitive to the microstructure of the sample and it is suitable for the study of defects and their interaction processes in materials [1, 2]. Several damping peaks at temperatures smaller than about 800 K (at 1 Hz) were observed in Fe Al binary alloys: Due to (i) interstitial atoms (the Snoek-type peak), (ii) vacancies (the so-called X peak), and (iii) substitute atoms (the Zener peak) [3 - 5]. These peaks were also observed in several ternary iron-aluminium-based alloys [6]. Additionally, a study of the grain boundary (GB) relaxation in binary Fe-Si alloys has been reported in Refs. [7 - 9]. In these works the behaviour of the characteristic grain boundary relaxation in iron and the grain boundary peak related to the presence of solute atoms in the iron matrix [1] was studied in order to correlate the behaviour of these peaks to the recrystallization and order degree. In contrast, very scarce information is available in the literature concerning the grain boundary relaxation in ternary Fe – Al - Si alloys. In this work, the analysis of the damping and elastic modulus behaviour in the temperature range between 800 K and 1200 K, in four different samples with composition Fe - 25 at. % (Al + Si) and Fe - 15 at. % (Al + Si) is carried out. In order to explain the MS results, neutron diffraction (ND) studies as a function of temperature were performed. Hysteresis loops of induction against applied magnetic field measurements were also performed. Experimental Procedure Samples: Alloys were produced by induction melting of 99.98 % Fe, 99.999 % Al and 99.99 % Si [10].

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The following samples were studied Fe – 12 Al – 12 Si, Fe – 5 Al – 20 Si, Fe – 6 Al – 9 Si, Fe – 7 Al – 7 Si (all compositions in at. %), which will be called hereafter A, B, C and D, respectively. Samples were annealed at 1323 K during 1 hour under high vacuum (10-5 Pa), followed by quenching into room temperature (RT) water. Measurements MS measurements were performed in an inverted torsion pendulum at natural frequencies, f, close to 1 Hz for free decaying vibrations. Measurements have been performed under vacuum (about 10-5 Pa). The employed samples were bars of rectangular section 1 × 2.2 × 20 mm3. The maximum strain on the surface of the sample was 5 × 10-5. Damping and frequency squared (∝ elastic modulus), were measured with an error less than 2 %. The measurements were carried out during subsequent heating and cooling runs on the same specimen. Heating and its cooling run is hereafter called a thermal cycle. Thermal cycles were performed up to three different maximum temperatures, 973 K, 1130 K and 1200 K. The heating rate was 2 K/minute. ND studies were performed at the D1B powder diffractometer in the Institut Laue Langevin, Grenoble, France. The employed neutron wavelength was λ = 1.28 Å. Spectra were obtained under high vacuum (10-2 Pa) in situ during heating. The heating rate was 3 K/minute. The used samples were parallelepipeds of 2 × 4 × 20 mm3. Hysteresis loops of induction against applied magnetic field were performed at RT using a conventional induction system with sinusoidal wave excitation at a frequency of 50 Hz. Samples were checked in two states: as-quenched and thermally treated. The thermal treatments, in previously annealed and quenched samples, were performed at a heating rate of 2 K/min up to 1200 K followed by cooling at the same rate, under high vacuum (10-4 Pa). Results and Discussion The damping spectra measured for the A sample, during thermal cycles up to two different final temperatures, 1130 K and 1200 K are shown in Fig. 1 by means of diamonds. The damping spectra increase monotonously with the temperature increase and no relaxation peaks have been found during the thermal cycles up to 1130 K (full diamonds). The heating and cooling runs are similar with a small thermal hysteresis. Thermal cycles measured up to 973 K neither show differences between heating and cooling runs. However, increasing the temperature above 1200 K during the heating process leads to the appearance of a damping peak during the subsequent cooling at around 1100 K (empty diamonds). The same kind of behaviour in the damping spectra has been found for B samples. In fact, thermal cycles up to 973 K and 1130 K show similar damping spectra both during the heating and cooling runs. However, a relaxation peak appears during cooling after a previous heating up to 1200 K, see inverted triangles in Fig. 1. Fig. 2 shows the damping spectra measured for Fe - 15 at. % (Al + Si) samples. A thermal cycle up to 1130 K is shown for the C sample, by means of empty triangles. The internal friction change below 950 K is small (Q-1 ~ 2 × 10-3) but the damping increases strongly up to values Q-1 of about 110 x 10-3 for higher temperatures. During the subsequent cooling run a damping peak develops. A thermal hysteresis in the damping of about 100 K appears in the temperature interval 850 K – 1050 K. The same behaviour of damping was measured also during the subsequent thermal cycles. In addition, increasing the final temperature of the thermal cycles up to 1200 K did not modify the damping behaviour. The behaviour of damping measured for a D sample for thermal cycles up to about 1200 K is also shown in the Figure by means of full circles. The damping values are almost constant (about 4 × 10-3) during the heating runs up to about 900 K. Subsequently, the damping increases up to

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values of about 80 × 10-3. During cooling, down to 950 K, the shape of the damping spectra is rather similar to the one measured during heating. However, a hysteresis between heating and cooling of about 50 K can be seen within the temperature interval 850 K – 950 K. On the other hand, it should be mentioned that the S and X peaks [3] are clearly observable in C and D samples at around 400 K and 600 K (at around 1 Hz), respectively; during the first heating. However, in samples A and B only the S peak, at around 400 K, was clearly resolved during the first warming. Regarding to the Zener peak, so called Z peak in Ref. [3], we have found a peak at around 800 K, which is explained as the Zener peak in these ternary samples by one of coauthors of present paper [6, 10]. Nevertheless, all these peaks are beyond the scope of this paper. The behaviour of the elastic shear modulus, G (T) (~ f2), is shown in Fig. 3 where the ratio G(T)/G(RT) (G (RT) is the shear modulus at room temperature) is plotted as a function of temperature. Full inverted and empty triangles correspond to samples A and C, respectively; during thermal cycles up to 1200 K. After heating up to 1200 K a clear thermal hysteresis appears in the moduli curves, which is in agreement with the development of the damping peak during cooling. In fact, the hysteresis behaviour in the modulus appears only when hysteresis appears in the damping spectrum. As it can be also seen from the Figure, the modulus values during cooling were smaller than in the heating run [11]. In addition, the hysteresis in the modulus between heating and cooling run during thermal cycles below 1130 K resulted very small.

Fig. 1. Damping spectra for Fe - 25 at. % (Al + Si) samples. Diamonds: A sample, Inverted triangles: B sample.

Fig. 2. Damping spectra for Fe - 15 at. % (Al + Si) samples. Triangles: C sample, Circles: D sample.

Fig. 3. Behaviour of the elastic shear modulus as a funtion of temperature for A and C samples.

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The diffraction pattern measured at room temperature for the A sample (empty circles), the Rietveld refinement (full line) [12] and the difference between measured and calculated profiles are shown in Fig. 4. The sample exhibits D03 order. The small differences between the fitted pattern (full lines) and the experimental points are due to preferential orientation (texture effects) of the grains. Fig. 5 shows the evolution of the relative integrated intensity of (111)/(220) and (200)/(220) reflections as a function of temperature. In contrast, during cooling of the sample the order degree is restored. The (200)/(220) intensity ratio shows an increase below ~ 800 K that can be attributed to an initial increase of the B2 nearest neighbours order. The as quenched sample recovers the B2 order degree since the B2 - A2 transition is well above the measured temperature range. On the other side, the D03 order evolves mainly near the equilibrium value of the D03 order parameter since the D03 - B2 transition is at a lower temperature. The C sample after the annelealing treatment exhibited at RT the appearance of D03 order, Fig. 6. Above 983 K the order disappears, as shown by the disappearance of the (111) and (200) reflections related to the D03 structure. In addition, during cooling, after a previous heating up to 1150 K, the order is restored approximately at the same temperature (983 K). In addition, in the D sample only a disordered bcc phase was found in the whole temperature range. The monotonous increase of damping as a function of temperature without the appearance of a damping peak during the thermal cycles up to 1130 K for Fe - 25 at. % (Al + Si) samples and the further appearance of the damping peak during cooling after heating up to 1200 K (Fig. 1), can be explained by considering the evolution of the degree of order and the defect configuration in the sample as a function of temperature (see Fig. 5).

Fig. 4. Rietveld refinement of the sample A at room temperature. The fitting was performed according to a D03 structure.

Fig. 5. Evolution of the relative integrated intensity of the (111)/(220) and (200)/(220) reflection as a function of temperature for the A sample.

In fact, it has been reported for Fe - 10 at. % Si (Fe - 6 wt. % Si) alloy that the intensity of the characteristic grain boundary relaxation peak of iron is controlled by the order degree (B2 order) and the defect configuration of the sample [7]. A higher degree of order accompanied by a grain boundary blocking led to a smaller damping peak height.

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Fig. 6. The evolution of the D03 order temperature for the C sample. The decrease of the order degree by heating the sample above 1223 K enhances the dislocations and grain boundaries mobility making easier the recovery of the as-quenched-dislocations. This leads to a rearrangement of grain boundary dislocations revealed through the increase in the GB peak intensity [7]. Therefore, the absence of the GB relaxation peaks during heating up to 1130 K in Fe – 25 at. % (Al + Si) can be produced by a reduced dislocation and grain boundary mobility owing to the appearance of the D03 ordered state. In fact, dislocations should move in pairs in the ordered lattice, which leads to a decrease in their mobility. In addition grain boundary movement in ordered lattices is also reduced [13]. In contrast, the appearance of the damping peak at around 1100 K during cooling after the pre-heating to 1200 K can be related to the increase in the capability of movement of grain boundaries and dislocations due to the decrease in the order degree with increase in temperature. The decrease in the order degree, as it was shown by the ND studies, allows to the microstructure to re-arrange recovering quenched-in dislocations and defects, which operate as obstacles. The restoring of the order degree during cooling is in agreement with the reproducibility of mechanical spectroscopy spectra during successive thermal cycles up to 1200 K. In addition, the decrease in the moduli values during cooling, after heating up to 1200 K (see Fig. 3), is produced by both the recovery of the structure and by a smaller order degree, as it was mentioned above. The temperature of appearance of the damping peak is not too far from the solute grain boundary peak for iron [1, 9]. Therefore, the observed IF peak during cooling could be related to the solute GB damping peak, which could be composed by the overlapping of the aluminium solute peak and the silicon solute peak [11]. Therefore, it can be concluded than in Fe - 25 at. % (Al + Si), the development of the damping peak during cooling is related to the decrease in the D03 order degree obtained during heating which allows a rearrangement of the defect configuration. If the order is not decreased the grain boundary relaxation does not appear, since the grain boundary arrangement remains locked. The influence of the order degree on the mechanical spectroscopy spectra in Fe – Al - Si alloys is also highlighted in C samples, Fig. 2. The damping behaviour exhibits a large hysteresis between heating and cooling during the thermal cycles up to 1130 K (similarly in thermal cycles up-to 1200 K). Indeed, the C sample is D03 ordered at room temperature, Fig. 6. However, at temperatures close to 983 K, the D03 structure changes to the bcc in agreement with the ternary phase diagram [11]. This temperature is close to the one where the damping starts to increase strongly (980 K). Moreover, the temperature where the strong increase in the damping appears does not shift towards higher temperatures when the vibration frequency is increased. This kind of behaviour is the usual one for a phase transition process, in agreement with the ND results and

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phase diagram. After the D03 → bcc transition, the order degree is reduced and then the mobility of dislocations and grain boundaries is enhanced, leading to a recovery of the microstructure. Consequently, again the GB relaxation peak appears during the cooling process. The temperature of this peak is also close to the solute GB peak for iron. The peak in C samples appears during cooling at smaller temperatures than in A samples. This difference can be produced by either a larger order degree or by larger quantity of substitutional atoms in the A sample. In contrast, the smaller peak height in the A sample, even if it has a larger solute concentration, could be controlled by the larger order degree than in C samples. This is shown in Figs. 4 and 6 where the reflections corresponding to the D03 order are much more evidenced in the A samples indicating a higher order degree. For C samples lower values of the modulus also appear during the cooling in agreement with both, a smaller order degree and the recovery of quenched-in defects, assisted by the order decrease at temperatures higher than the D03 → bcc transition (around 983 K). The behaviour of the MS spectra for D samples does not exhibit large changes between heating and cooling runs, Fig. 2. This is in agreement with the neutron diffraction results, which show that the sample is disordered, and also with the phase diagram [11]. In fact, the sample is in a disordered state and consequently the damping peak at 1000 K appears both on the heating and in the cooling runs, since the absence of order is not reducing the mobility of grain boundaries and dislocations, as it was already mentioned above. At 900 K a new peak appears which shows a hysteretic behaviour that could be attributed to the solvent grain boundaries which undergoes the same mobility sequence linked to the mobility of the same defects (see Fig. 2) [11]. In addition for sample A, a small peak at around 960 K can be resolved during the cooling from 1200 K, but this peak is not discussed in the present paper. The behaviour of the induction (B) against applied magnetic field (H) hysteresis loops for the sample C in the as-quenched state and after a subsequent thermal treatment up to 1200 K is shown in Fig. 7. Sample C and D after the thermal treatment up to 1200 K exhibit a larger value of the induction of saturation, Bs, and a smaller coercive force, Hc. The increase in Bs for samples C and D was about 20 % and 30 %, respectively; and the reduction in the coercive force was about 27 % for both kinds of samples, see Table 1. However, for samples Fe – 25 at. % (Al + Si) clear changes in the magnetic loops after the thermal treatment cannot be found. Table 1 summarises the results from magnetic measurements.

Fig. 7. B vs. H in arbitrary units (AU) for C sample, measured at RT.

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Table 1. Summary of the magnetic measurements in Fe – Al - Si alloys. SAMPLE Fe – 12 Al – 12 Si (A) Fe – 5 Al – 20 Si (B) Fe – 6 Al – 9 Si (C) Fe – 7 Al – 7 Si (D)

STATE Annealed After heat treatment Annealed After heat treatment Annealed After heat treatment Annealed After heat treatment

Hc (AU) 15 ± 1 15 ± 1 15 ± 1 16 ± 1 17 ± 1 13 ± 1 31 ± 1 23 ± 1

Bs (AU) at H = 300 (AU) 170 ± 2 180 ± 2 150 ± 2 160 ± 2 180 ± 2 215 ± 2 140 ± 2 190 ± 2

The magnetic behaviour for the C sample indicates that, even if the order is restored at RT, after the thermal treatment, the structure has recovered and then the magnetic behaviour is improved. It is in agreement both with the one expressed above and with the behaviour shown by the D sample (disordered). Nevertheless, in Fe – 25 at. % (Al + Si), where the order is larger than for the C sample, an improvement of the magnetic behaviour after the thermal treatment cannot be found. It can be explained considering the followings points: (a) the recovery degree of the structure at RT after the thermal treatment is not enough for improving the magnetic behaviour and (b) the larger order degree in A and B samples than in C sample is controlling the magnetic response. In fact, it has been reported recently that the defects configuration and internal stresses are playing a key-role in the magnetic behaviour of Fe - 10 at. % Si (6 wt. % Si) alloy [14]. The increase of order is related to the deterioration of soft magnetic properties in Fe - Si alloys [15, 16]. However, in fully ordered Fe - Si alloy an improvement of magnetic quality was found when the quantity of defects decreased by thermal recovery [14]. Consequently, more effort must be paid for resolving the effect of the competition between order and defects configuration on the magnetic behaviour in ternary Fe – Al - Si alloys. Conclusion In Fe - Al - Si alloys exhibiting D03 order at room temperature, the mechanical spectroscopy response at elevated temperatures is controlled by the degree of order of the sample. A decrease in the order degree, after heating up to 1200 K, allows a damping peak to appear during cooling, which could be related to the solute grain boundary relaxation of aluminum and silicon atoms. The temperature of this peak depends on the order degree of the alloy. The lower is the D03 orderdisorder transition temperature, the lower is the peak temperature. The dislocation structure and solute atoms interaction with grain boundaries, is the mechanism that controls the damping spectrum. The non- appearance of relaxation peaks during heating is due to a reduced dislocation and grain boundary mobility in the D03 structure. References [1] R. Schaller, G. Fantozzi and G. Gremaud: Mechanical Spectroscopy (Trans Tech. Publ. Ltd, Switzerland 2001). [2] M. S. Blanter, I. S. Golovin, H. Neuhäuser, H.-R. Sinning: Internal Friction in Metallic Materials (Handbook, Springer, Germany 2007). [3] I. S. Golovin, H. Neuhäuser, A. Rivière, A. Strahl: Intermetallics. Vol. 12 (2004), p. 125. [4] I. S. Golovin, S. V. Divinski, J. Čížek, I. Procházka, F. Stein: Acta Mat. Vol. 53, No 9 (2005), p. 2581.

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Interaction between Defects and Anelastic Phenomena in Solids

[5] A. Strahl, I. S. Golovin, H. Neuhäuser, S. B. Golovina, H.-R. Sinning: Mat. Sci. Eng. A Vol. 442, (2006), p. 128. [6] I. S. Golovin: Mat. Sci. Eng. A Vol. 442 (2006), p. 92. [7] O. A. Lambri, J. I. Pérez-Landazabal, J. A. Cano, V. Recarte: Mat. Sci. Eng. A Vol. 370 (2004), p. 459. [8] O. A. Lambri, J. I. Pérez-Landazábal, L. M. Salvatierra, L. M. Milani, C. Gómez-Polo, V. Recarte: J. Non-Cryst. Solids Vol. 287 (2001), p. 70. [9] O. A. Lambri, E. D. Bulejes, P. R. Gorria, J. Tinivella: J. Mater. Sci. Vol. 35 (2000), p. 79. [10] T. S. Pavlova, I. S. Golovin, H.-R. Sinning, S. A. Golovin, C. Siemers: Intermetallics. Vol. 14/10-11 (2006), p. 1238. [11] O. A. Lambri, J. I. Pérez-Landazábal, G. J. Cuello, J. A. Cano, V. Recarte, C. Siemers, I. S. Golovin: submitted to Journal Alloys and Compounds (2007). [12] The Rietveld Method, Edited by R. A. Young, International Union of Crystallography, Oxford University Press, Great Britain (1993). [13] F. J. Humphreys and M. Hatherly: Recrystallization and Related Annealing Phenomena (Pergamon, Elsevier Science Ltd., Netherlands 2002). [14] J. A. Cano, O. A. Lambri, I. Pérez-Landazábal, V. Recarte, in: 12º Encuentro Regional Iberoamericano del CIGRÉ, Comisión Técnica Transformadores, Foz Do Iguazú, Brasil (2007). [15] B. Viala, J. Degauque, M. Baricco, E. Ferrara, M. Pasquale, F. Fiorillo: J. Mag. Mag. Mat. Vol. 160 (1996), p. 315. [16] B. Viala, J. Degauque, M. Fagot, M. Baricco, E. Ferrara, F. Fiorillo, Mater. Sci. Eng. A Vol. 212 (1996), p. 62.

Solid State Phenomena Vol. 137 (2008) pp 99-108 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.99

Mechanical spectroscopy of the Fe - 25 Al - Cr alloys in medium temperature range I. S. Golovin1,a, A. Rivière2,b .

1

Physics of Metals and Materials Science Department, Tula State University, Lenin ave. 92, Tula 300600 Russia

2

LMPM ENSMA, UMR CNRS 6617, F-86961 Futuroscope Chasseneuil Cedex, France a

[email protected], [email protected]

Key words: iron aluminides, (Fe,Cr)3Al alloys, order-disorder transformation, damping.

Abstracts. Fe3Al intermetallic compounds and several (Fe,Cr)3Al alloys with Cr content from 3 to 25 % have been studied using isothermal mechanical spectroscopy. The Zener relaxation caused by reorientation of pairs of substitute atoms in Fe is observed in all studied alloys and used to evaluate the activation parameters of Al (Cr) atom jumps in Fe. The second internal friction peak at higher temperatures was observed only in Cr containing alloys. Isothermal mechanical spectroscopy (employed frequency from 10-4 to 102 Hz) gives some advantages as compared with ordinary techniques, i.e. study of anelasticity as a function of temperature. It allows to avoid transient effects and to measure materials in a state close to equilibrium. This allows to distinguish clearly between Al atom diffusion in Fe3Al in B2 and D03 states (activation energies for Fe – 26 Al in the B2 range the HB2 ≈ 235 kJ/mol, and in the D03 ordered range the HD03 ≈ 286 kJ/mol). Effect of chromium on the Zener relaxation is analysed. Introduction Anelastic effects in Fe - Al alloys were reviewed in Ref. [1], and in Fe – Al - Me (where Me = Cr, Si, Ge, Mo, Co, Ti, Zr) alloys – in [2]. In binary and ternary alloys both the following relaxation peaks were found: the dislocation and deformation related peaks-family [3], the carbon Snoek-type relaxation [4, 5], the vacancy-and-carbon related relaxation [4, 5], the Zener relaxation and the grain boundary (GB) relaxation. The Zener peak in ternary Fe – Al - Cr alloys is the subject of this paper. The Zener relaxation [6] in Fe - Al alloys was first reported in 1960 by Shyne and Sinnot [7] and then by different authors using temperature dependent internal friction (TDIF) tests [8 - 10], i.e. in all these papers Zener relaxation was considered in non equilibrium conditions. Study of the Zener relaxation in several binary Fe - Al alloys in equilibrium conditions was for the first time performed in [11] using frequency dependent IF (FDIF) for a fixed temperatures. The effect of Si in Fe - Al alloys on both Snoek and Zener relaxation is reported in [12] using TDIF tests. In this paper we also use the isothermal mechanical spectroscopy technique [13] to study the high temperature relaxation both in Fe - Al binary and Fe - Al - Cr ternary alloys. It is well-known that a mechanical loss peak in case of a relaxation effect with a single relaxation time can be described by a Debye equation: ωτ Q −1 = ∆ ⋅ , (1) 1 + (ωτ) 2 where τ is the relaxation time, ∆ is the relaxation strength (in case of the Zener relaxation it is denoted in this paper as ∆Z), ω = 2πf with f - the frequency of the mechanical vibrations. The relaxation strength of the Zener relaxation (∆Z) depends on the degree of order, i.e. on the order parameter (η) which was varied in our experiments by varying the temperature of the FDIF measurements. The theory of the Zener relaxation [6, 14] proposes that for concentrated (in our case Fe - Al) alloys the relaxation magnitude (δJ ~ ∆Z) is:

100

Interaction between Defects and Anelastic Phenomena in Solids

δJ = {f(χo,CAl)×(CAl2(1-CAl2))/kBT}×βa2(dUp/dap),

(2)

where T is temperature, kB is Boltzmann’s constant, the term CAl2(1-CAl2) exhibits the concentration dependence of δJ: CAl is the atomic concentration of Al in iron; the function f (χo, CAl) reflects the effect of order of Al atoms on δJ: χo is a parameter of short range order in absence of external stress, f (χo,CAl) = 1 for the disordered state and f(χo,CAl) = 0 for the complete ordered state (this means the Zener relaxation is impossible in 100 % ordered alloy); β is a dimensionless geometrical parameter, a is the interatomic spacing, ap – the same in the direction “p”, Up is the ordering energy in the direction “p”, p is a direction of applied stress. Additions of Cr (3 – 5 %) increases plasticity of Fe3Al intermetallic compounds. At the same time further increase in Cr content in Fe - 25 at. % Al is less studied and should have an influence on several transition temperatures: e.g. D03 – to - B2 transition, Curie point, and also on Zener phenomena by adding to Al - Al pairs Cr - Cr and possible Al - Cr pairs. By varying the temperature of the isothermal FDIF tests the Zener peak can be measured in different ranges of the equilibrium phase diagram, thus the activation parameters of this effect can be studied with respect to the type of order in Fe - Al alloys. Experimental procedure Mechanical spectroscopy techniques. Beyond standard methods of structural characterisation (DSC, TEM, X-ray), a forced torsion pendulum under a vacuum of 10-3 Pa and specimens with 64 mm in length and 0.5 × 4 mm2 cross section was used. In forced vibration, Q-1 is equal to tan (ϕ), where ϕ is the phase lag between the applied cyclic stress and the resulting strain. The measurement frequencies were varied between 50 Hz and 10-4 Hz, ten discrete frequencies per decade were used (for more details see [12]). The internal friction was also measured at the resonance frequency of the system (300 Hz) using the free-decay method. The maximal vibration amplitude was γ0 = 5 × 10-6, which can be considered as the amplitude independent range even with respect to magnetomechanical damping in specimens with low Al content. Materials and regimes of the FDIF tests. Compositions of the studied alloys are given in the Table 1. For better visualisation reason alloy compositions are shown in a ternary diagram in Fig. 1. According to TEM and X-ray examination all studied alloys were ordered. Heat flow tests of as quenched specimens are used to determine the D03 - to - B2 (TO) temperature, vibrating sample magnetometry – to determine the Curie point (TC). These results, as well as the average grain size (D) are also included in Table 1. Table 1. Chemical composition of the specimens (at. %) and temperatures for the D03-to-B2 (TO) and the ferro-to-paramagnetic (TC) transitions. n 1

Nominal composition Fe - 26Al

(Fe3Al)

Al

Cr

TO, K

TC, K

25.9

-

822

780-800

D, µm #

2

Fe – 28 Al – 3 Cr

no data

2.67

806

no data

3

Fe – 26 Al – 8 Cr

27.01

8.4

825

~ 560

∼ 180

4

Fe – 25 Al – 15 Cr

25.0

14.7

793

~ 425

∼ 180

5

Fe – 25 Al – 25 Cr

25.0

25.0

740

~ 410

∼ 130

# TC in D03 phase; * according to EDAX analyses.

*

,D 0, 3 D 0+ 3 B 2

Solid State Phenomena Vol. 137

All the specimens were homogenized at 1273 K in a quartz ampoule and annealed at 750 K during 100 hrs to eliminate relaxation effects caused by interstitial atoms and thermal vacancies in solid solution. Two series of experiments were made using each sample. During the first run, the samples have been progressively heated step by step. At each temperature the specimens were annealed for 24 hours, which leads to nearly equilibrium condition of the specimens for each temperature used. In a second stage the specimens were measured at the same temperatures as for heating but after annealing at higher temperatures. Average grain size in all specimens after FDIF test was measured and included into Table 1.

Al

0.5 0.5

0.6

,A 2+ D0

3

0.4

0.7

bc cA 2, K

1

0.3

0.8

0.2

0.9

1.0 0.0

Fe

0.1

0.1

0.2

0.3

0.4

bcc A2, decomposition, σ - phase

0.5

101

0.0

Cr

Fig. 1. Composition of studied specimens. Results and discussion

Two IF peaks are recorded in Fe – Al - Cr alloys: the Zener peak denoted as P1 peak and second peak at lower frequency, which is equivalent to a higher temperature at TDIF tests as the P2 peak. The results are presented in Fig. 2 a after background subtraction, the procedure of background subtraction is shown in Fig. 2.b for only one alloy (Fe - 25 Al - 15 Cr). One can see from the Fig. 2 a that there is only peak P1 in Fe – 25 Al and Fe – 28 Al – 3 Cr while in alloys with higher Cr content there are two peaks. In Fig 2.a, all the results were obtained at 823 K during the first run, i.e. during step by step tests with increasing temperatures of isothermal test for specimen annealed 100 h at 750 K. Fig. 2.b shows result for Fe – 25 Al – 15 Cr obtained also at 823 K but after annealing of the specimen at 928 K. The difference between the two curves corresponding to the Fe – 25 Al – 15 Cr is due to the evolution of the peaks during the high temperture annealing. 100

25Al-15Cr

Fe-25Al-15Cr

823 K

200 4

annealed at 928K

T = 823 K

Q x10

-1

-1

∆Q x10

4

25Al-25Cr 75

26Al

25Al-9Cr

estimated background

150

as measured 50

100

P2

25

0

P1 28Al-3Cr

-4

-3

-2

-1

P2

50

0

1

log10 (freq./Hz)

2

0

3

P1

after background subtraction -4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

Fig. 2. Overview of two IF peaks in Fe – Al - Cr alloys after low frequency background subtraction (a), procedure of low frequency background subtraction (Fe – 25 Al – 15 Cr).

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Interaction between Defects and Anelastic Phenomena in Solids

DSC, mW/mg

The main attention in this paper is paid to the P1 (Zener) peak while analyses of the P2 peak will be reported elsewhere. For the characterization of the alloys we used (1) transmission electron microscopy (TEM) using a Philips CM12 electron microscope at an accelerating voltage of 120 kV, (2) X-ray diffraction (XRD) using GE XRD 3003 PTS and Oxford diffractometers (room temperature, Cu Kα1 with a wave length of λ = 1.5406 Å, in the range of 2Θ from 10 to 120°, or to 140° correspondingly); (3) EDX (Thermo NORAN VANTAGE); (4) differential scanning calorimetry (Netzsch DSC 404, with a heating and cooling rate of 10 K/min between room temperature and 1473 K), and (5) vibratingsample magnetometry (Foner magnetometer Oxford, heating rate 0.5 K/min for measurements from room temperature to 950 K and 3 K/min for measurements from liquid helium (4 K) to room temperature, H from 16 up to 950 kA/m). Heat flow in studied alloys is shown in Fig. 3. In this figure we also include ranges of existence of D03 phase which was controlled by X-ray and TEM (Fig. 4). The up triangles in Fig. 3 show temperature at which the specimens were annealed before FDIF tests (except Fe – 26 Al alloy which was also studied at lower temperatures (these results are not included into this paper)). The grey bar along the temperature scale shows roughly the range in which the Zener peak is studied. 0.14 0.12 0.10

DSC, mW/mg

DSC, mW/mg

0.08 400 0.15

D03 600

B2

800

1000

0.12 0.09 400 0.15

1200

Fe-26Al-8Cr

135.9 mg 10 K/min

D03 600

B2

800

1000

a

b

c

d

1200

Fe-25Al-15Cr

73.4 mg 10 K/min

0.12

D03 B2

0.09 400

DSC, mW/mg

Fe-26Al

106.5 mg 10 K/min

0.12

600

800

0.08 400

1200

Fe-25Al-25Cr

84.4 mg 10 K/min

0.10

1000

B2

D03 600

800

T, K

1000

1200

Fig. 3. Heat flow in the Fe – Al - Cr samples. The D03 structure was detected in all alloys after annealing at 750K. At the same time the B2 order is detected by X-ray studies in Fe – 25 Al – 25 Cr alloy: the D03 – to - B2 transition in this composition is close to the annealing temperature (see Table 1).

Fig. 4. TEM micrographs showing the D03 structure (dark field, [110](111)) in Fe 26 Al quenched from 1270 K and annealed 48 h at 673 K (a), Fe – 25 Al – 8 Cr quenched from 1120 K and annealed 48 h at 750K (b), Fe – 25 Al – 15 Cr, quenched from 1170 K and annealed 100 h at 750 K (c), and Fe – 25 Al – 25 Cr quenched from 1170 K and annealed 48 hrs at 750K (d).

Solid State Phenomena Vol. 137

103

Hardness of the alloys after annealing for 48 h at 750K: HV = 308 (Fe – 26 Al), 280 (26 Al - 8 Cr) 284 (25 Al – 15 Cr), and 361 (25 Al -25 Al). In all D03 ordered alloys the superdislocations were observed by TEM. The Fe – 26 Al alloy. The Zener peak and corresponding defect of modulus have been recorded between 660 and 850 K in the frequency range from ~ 10-4 to ~ 102 Hz. The peak is symmetric, only slightly broader than a Debye peak (the peak width is characterised by relaxation time distribution β [14]). The peak increases with increase in temperature of measurements (Fig. 5 a). Increase of the peak height takes place from about 100 K below the D03 to B2 transition and continues above this transition. The peak P1 parameters for different temperatures are summarised in Table 2. Incompleted curves for 856 and 882 K were approximated by a symmetrical Gauss peak (dotted lines). The Zener peak height at temperatures below 710 K, i.e. in the D03 phase, is practically the same or even has very weak opposite tendency: some decrease in ∆Z with increase in temperature, which is predicted by the theory (∆Z ~ T-1) for alloys where the effect of ordering does not play any role. In case of Fe - 26 Al the slope of the Arrhenius curve also changes but at higher temperatures around ~ 800 K (Fig. 5 b), which is close to the D03 to B2 transition (820 K). Below this temperature the HD03 value is about 290 kJ/mol, above (HB2) and also on cooling the activation energy is about 238 kJ/mol. The P2 peak as it can be seen in Fig. 2 a is practically absent in this alloy. 100

Fe-26Al

882 856

P1

4

833

80

2

-1

753 738

783

0

ln (freq./Hz)

Q x10

4

809

60

Fe-26Al

768

723 708 692

40 668

cooling

-2

D03

-4

B2

-6 20

1st heating

-8

-3

-2

-1

0

1

log10 (freq./Hz)

2

-10

1.6

1.5

1.4

1.3

1.2

1.1

1000/T (K)

a b Fig. 5. The Fe – 26 Al alloy: a) overview of Zener peaks measured at different temperatures, b) Arrhenius plot: up triangles – first step by step heating (1/2 filled in up triangles for Fe 26 Al – result of approximation, see Fig. 4 b), down triangles – after heating step by step cooling (isothermal technique), stars – from TDIF tests. The Fe – 28 Al – 3 Cr alloy. The T0 transition in this alloy takes place according to DSC tests at lower temperature as compared with Fe – 26 Al T0 = 806 K mainly because of a higher Al content. Thus the Zener peak is mainly recorded in the D03 range of the phase diagram except the test at 824 K (Fig. 6). Magnetic properties were studied in this alloy. The P2 peak was not observed in this alloy. The Fe - 28 Al - 3 Cr alloy was measured as yet only in a limited temperature range close to the

104

Interaction between Defects and Anelastic Phenomena in Solids

D03 to B2 transition (see Table 2) and values H = 276 kJ/mol, and τ0 =2.8 × 10-19 s were found. Only one point belongs to the B2 range (824 K), which makes to think that the D03 structure dominates in the structure of this alloy in the range of our tests. T = 746 K

Fe-28Al-3Cr

2.71

Fe-28Al-3Cr

-1

785

Modulus arb. units

20

804

-1

2.70

∆Q x10

Q x10

4

30

824 K

P1

4

60

40

2.69

766 746

2.68

20

10

707 2.67

P1 0

0 -3

-2

-1

0

1

2

-4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

log10 (freq./Hz)

a

b

Fig. 6. The Fe – 28 Al – 3 Cr alloy: a) experimental data, isothermal tests at 746 K: IF and relative modulus supplied with exponential background, and IF peak after the background subtraction, and b) overview of the Zener peaks measured at different temperatures.

Activation parameters for the P1 and P2 peaks were found as follows: The P1 peak: H = 290 kJ/m, τ0 = 5 × 10-20 s. The P2 peak (experimental data at step by step cooling from 928 K are used): H = 282 kJ/m, τ0 = 10-17 s. The P1 peak width and height at different temperatures are collected in Table 2.

experimental curve

250

200

after background subtraction

4 -1

Similarly to the Fe - 26 Al alloy the P1 (Zener) peak height increases in Fe – 26 Al – 8 Cr with increase in temperature if the temperature of the isothermal test is more than 720 K. The same is also true for the P2 peak (Fig. 8). The P1 peak height below 720 K does not change pronouncedly.

Fe-26Al-8Cr T = 838 K

300

Q x10

The Fe – 26 Al – 8 Cr alloy. The T0 transition (825 K) in this alloy takes place according to DSC tests at practically the same temperature as in Fe – 26 Al, while the Curie point is about 200 K lower. Both the P1 (Zener) and P2 peaks are overviewed in Fig. 7. The P1 peak - in both the D03 (paramagnetic) and B2 ranges, the P2 peak - above D03 – to - B2 transition.

150

estimated background

P1

100

50

0

P2 -4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

Fig. 7. The Fe – 26 Al – 8 Cr alloy, experimental data, isothermal tests: FDIF in the range of the P1 (Zener relaxation) and P2 peaks at 838 K.

Solid State Phenomena Vol. 137

105

200

100

P1

P2

867K 853K

1st run

927K

1st run 898K 150

838K

883K

-1

-1

Q x10

Q x10

4

4

75

808K

100

50

853K

763K 748K 673K 718K 25

823K

50

793K 0

0

-4

-3

-2

-1

0

1

2

3

-4

-3

log10 (freq./Hz)

-2

-1

0

1

2

3

log10 (freq./Hz)

a

b

Fig. 8. The Fe – 26 Al – 8 Cr alloy: P1 (Zener) (a) and P2 (b) peaks measured at different temperatures. Table 2. The P1 peak parameters for several selected temperatures ♣. n

Alloy

1

Fe – 26 Al

2

3

4

5

The Peak1 parameters at different temperatures T, K Qm-1

Fe – 28 Al – 3 Cr

β T, K Qm-1

Fe – 26 Al – 8 Cr

β T, K Qm-1

Fe – 25 Al – 15 Cr

β T, K Qm-1

Fe – 25 Al – 25 Cr

β T, K Qm-1 β

♣

692 20 1.4 688 12 688 24 1.2 703 35 1.5

708 20 1.4 707 14 1.2 718 24 1.38 718 38 1.55

723 29 1.22 746 21 1.2 733 28 1.39 733 42 1.4 763 73 2.1

738 32 1.25 766 33 1.4 748 31 1.34 748 45 1.4 778 68 2.3

753 37 1.39 785 41 1.33 763 38 1.39 763 53 1.41 793 51 1.7

768 44 1.39 804 50 1.5 793 41 1.35 808 67 1.37 808 67 1.7

783 49 1.42 824 57 1.5 838 77 1.38 823 82 1.6 823 78 1.9

809 833 66 78 1.42 1.42

853 867 87 94 1.36 1.45 839 853 86 92 1.7 1.9 838 853 68 66 1.6 1.7

Peaks measured in the D03 range are typed in normal font on the grey background, peaks measured in the B2 range are typed in italic.

106

Interaction between Defects and Anelastic Phenomena in Solids

The Fe – 25 Al – 15 Cr alloy. The T0 transition (793 K) in this alloy is 25 – 30 K lower as compared with the Fe – 26 Al alloy, Curie point is at about 425 K. After 100 h annealing at 748 K followed by water quenching it has the D03 structure with lattice parameter 5.7907(70) and after 100 h annealing at 898 K – the B2 structure with lattice parameter 2.8968(25). Both the P1 (Zener) and P2 peaks are recorded. The P1 peak - in both the D03 (paramagnetic) and B2 ranges, the P2 peak - above D03 - to - B2 transition. The P2 peak height is slightly lower than that is in Fe - 26 Al 8 Cr alloy. We do not present figures for this alloy as some curves are included in Fig. 2 and the peak parameters are summarised in Table 2. Activation parameters for the P1 and P2 peaks were found as following: for P1 the H = 285 kJ/m (2.9 eV), τ0 = 4.10-20 s in cooling, and for P2 peak: H = 290 kJ/m (3 eV), τ0 = 1.3 × 10-17 s (after annealing at 928 K). The Fe – 25 Al – 25 Cr alloy. In contrast with other Fe – Al - Cr alloys only one peak is recorded in this alloy in the studied temperature range. Furthermore, the peak is broader (in all tests β > 1.5), and its height does not have such a clear dependence on temperature of measurements (Fig. 9 a). The activation energy of the peak τ0 = 10-19 s and H = 288 kJ/mol. In several tests (not in all) asymmetry of the peak can be clearly seen (Fig 9 b). 110 100

100

after ann. at 823 K experiments at:

90

823 K

90

808 K 70

ann. at 778 K

793 K

4

Q x10

4

70

-1

ann. at 823 K

80

80

60

-1

Q x10

T. experiments: 763 K

60 50

50

40

40

30

30

748 K 763 K

20

20

778 K

10

10 -4

-3

-2

-1

0

1

2

log10 (freq./Hz)

ann. at 763 K

0 -4

-3

-2

-1

0

1

2

log10 (freq./Hz)

Fig. 9. The Fe – 25 Al – 25 Cr alloy: the peaks measured at different temperatures after annealing at 823 K (a) and the influence of different annealing prior to tests at 763 K (b). Effect of a high temperature annealing Experiments were made in Fe - 26 Al - 8 Cr and Fe – 25 Al – 15 Cr alloys after annealing in-situ at 928 K at the same temperatures as during the heating. The height, width and frequency of the P1 peak are the same after and before the annealing for the Fe – 25 Al – 15 Cr alloy. It is the same for the Fe - 26 Al - 8 Cr alloy: the frequency of P1 peak is always the same but the height is increased for about 18 × 10-4 and the β factor decreases until 1.17 on average. For P2 peak, the behaviour is the same for both the alloys. The height increases (∼ 35 to 40 × 10-4) and the peak shifts towards lower frequency after annealing for measurements at the same temperature.

Solid State Phenomena Vol. 137

107

Discussion and conclusions -1

4

In all alloys except Fe – 25 Al – 25 Cr composition an increase in the P1 peak height with temperature of measurements is observed. Increase in the peak height with temperature might be a result of several reasons and one of them is decreased in order in the alloy. The influence of temperature on β is not well pronounced in contrast to the influence of Cr content: increase in Cr content in Fe – 25 Al Cr alloys increases the value of β. This means that Cr increases the relaxation time distribution. Nevertheless, we did not observe double headed Zener peak as it might be expected in case two types of pairs: Al - Al and Al - Cr contribute independently to the Zener effect.

Qm x 10

As it concerns the P2 peak which is not discussed in this paper in details, it is possible to give the following information: in spite its higher temperature (or lower frequency) location of its activation energy is lower than that is for the P1 peak in the same alloy, values of β are higher, and it was not observed neither in Fe - 26 Al nor in Fe – 25 Al – 25 Cr composition.

0

100

-1

β

Qm

25Al-25Cr

2.0

50 0 100 50 0 100 50 0 100 50

100 50 0

β 2.5 1.5

700

750

800

850

25Al-15Cr

2.5 2.0 1.5

700

750

800

850

26Al-8Cr

2.5 2.0 1.5

700

750

800

850

28Al-3Cr

2.5 2.0 1.5

700

750

800

850

26Al

2.5 2.0 1.5

700

750

800

850

T, K Fig. 10. Overview of the P1 peak height (Qm-1, left scale) and width (β, right scale) as a function of temperature of isothermal measurements for all alloys studied.

Table 3. Activation parameters for the Zener (P1) peak in Fe – Al - Cr alloys. Alloy

H, kJ/mol

τ0 , s

Comments (e.g. heating/cooling)

Fe – 26 Al

231

1.5 × 10-17

in D03 range, cooling

Fe – 28 Al – 3 Cr

276

2.8 × 10-19

heating

Fe – 26 Al – 8 Cr

290 204

5 × 10-20 1.6 × 10-15

heating cooling

Fe – 25 Al – 15 Cr

285

3.6 × 10-20

cooling

Fe – 25 Al – 25 / 35 Cr

288

10-19

heating

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Interaction between Defects and Anelastic Phenomena in Solids

References [1] I. S. Golovin, H. Neuhäuser, A. Rivière, A. Strahl: Intermetallics. Vol. 12 (2004), 125. [2] I. S. Golovin, A. Strahl, H. Neuhäuser: International Journal of Materials Research (formelly Z. Metallkd.) Vol. 42 (2006), p. 1078-1092. [3] I. S. Golovin, T. S. Pavlova, S. B. Golovina, H.-R. Sinning, S. A. Golovin: Mat. Sci. Eng. A Vol. 442/1-2 (2006), p. 165-169. [4] I. S. Golovin, S. B. Golovina, A. Strahl, H. Neuhäuser, T. S. Pavlova, S. A. Golovin, R. Schaller: Scr. Mater. Vol. 50 (2004), p. 1187. [5] I. S. Golovin, S. V. Divinski, J. Čížek, I. Procházka, F. Stein: Acta Mater Vol. 53 (2005), p. 2581-2594. [6] C. Zener: Elasticity and Anelasticity of Metals (The Univ. of Chicago Press, 1948). [7] J. C. Shyne, M. J. Sinnott: Trans AIME. Vol. 218 (1960), p. 861-865. [8] J. A. Hren: Phys. Stat. Sol. Vol. 3 (1963), p. 1603-1618. [9] K. Tanaka, K. Sahashi: Trans. JIM. Vol. 3 (1971), p. 130-135. [10] K. Tanaka: Trans. JIM. Vol.16, No 4 (1975), p. 199-205. [11] I. S. Golovin, A. Rivière: Intermetallics. Vol. 14, No 5 (2006), p. 570-577; and Mat. Sci. Eng. A Vol. 442/1-2 (2006), p. 86-91. [12] I. S. Golovin, S. Jäger, V. A. Semin et al.: This conference (Snoek-type and Zener relaxation in Fe – Si – Al alloys). [13] A. Rivière, in: Mechanical Spectroscopy Q-1 2001 with Applications to Materials Science edtied by R. Schaller, G. Fantozzi, G. Gremaud, chapter 9.1, Trans tech Publication LTD (2001), p. 635-651. [14] A. S. Nowick, B. S. Berry: Anelastic Relaxation in Crystalline Solids (Academic Press, New York, 1972).

Solid State Phenomena Vol. 137 (2008) pp 109-118 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.109

On the Formation of High Damping State in Fe - Al and Fe - Cr Alloys I. B. Chudakov1,a, N. A. Polyakova1,b, S. Yu. Mackushev1,c, V. A. Udovenko1 1

I. P.Bardin Central Research Institute for Ferrous Metallurgy, Moscow, 105005, Russia a

[email protected], [email protected], [email protected]

Keywords: Fe - Cr alloys, Fe - Al alloys, damping capacity, magnetostriction, electron microscopy, heat treatment.

Abstract. High damping Fe - Cr and Fe - Al alloys have been studied in two different states: in the high damping state and in the suppressed damping capacity state. It has been shown that magnetic domain structures of Fe - Cr and Fe - Al alloys are fundamentally different in the high damping state and in the state with the suppressed damping. Magnetic domain structure corresponding to the high damping state can be characterized by an enhanced volume fraction of the easy movable 90o-domain walls, but the state with the suppressed damping capacity can be characterized by the enhanced volume fraction of the 180o-domain boundaries. Introduction It is known that the high-purity Fe - Cr [1 - 3] and Fe - Al alloys [4 - 6] are able to exhibit very high level of magnetomechanical damping. A very high damping capacity allows an effective application of high damping Fe - Cr and Fe - Al alloys in industry for the reduction of noise and vibration levels in various engineering devices [1]. In addition to the practical importance, the structure of ferromagnetic materials with a very high level of magnetomechanical damping can be considered as a very interesting object for the investigation since the properties of these materials appear to be very sensitive to the variety of external factors, including heat treatment and the preparation procedure. In addition to the high damping state, a low damping state can be also fixed in Fe - Cr and Fe - Al alloys (as well as various intermediate states), providing an opportunity to adjust the level of properties according to different experimental (or practical) purposes. In the present research magnetic domain structure and magnetic properties of high damping Fe Cr and Fe - Al alloys have been studied in two different states: in the high damping state and in the state with suppressed damping capacity. Industrial high damping steels (high damping Fe - Al alloys, produced using factory metallurgical equipment) have been studied as well. Materials and Experimental Methods High damping alloys on the base of the Fe - Cr metallic system have been prepared in the vacuum induction furnaces from the pure raw materials, melting was followed by the standard metallurgical processing including forging, machine grinding, hot rolling, pickling and cold rolling. Impurities and non-metallic inclusions content did not exceed 0.01 C; 0.013 N; 0.13 Si; 0.04 Mn; 0.02 Ni; 0.003 S; 0.003 P (mass. % everywhere) in the studied Fe - Cr alloys. High-purity damping alloys on the base of the Fe-Al metallic system were prepared in the open-air induction furnaces under protecting slag. Ingots grinding was followed by the standard metallurgical processing including forging, grinding of billets, hot rolling, pickling, cold-rolling. Impurities and non-metallic inclusions content did not exceed 0.01 C; 0.02 Ni; 0.01 Cr; 0.01 Cu; 0.01 Mo; 0.01 Co; 0.003 S; 0.005 P in the studied Fe - Al alloys. Samples from the industrial high-damping steels (grade 01Ю5T) were cut from the commercial hot-rolled sheets (thickness t = 3 or 6mm) [7]. To obtain the cold-rolled materials, the hot-rolled sheets were additionally cold rolled using the pilot-plant equipment. After mechanical treatment all samples were heat-treated in the vacuum furnaces; samples quenching was performed directly from

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Interaction between Defects and Anelastic Phenomena in Solids

the braked quartz vacuum tube. To obtain comparable grain sizes for each tested material, during all heat treatments the high temperature annealing was performed by using the uniform conditions (1000 oC for 40 minutes), however the cooling rates were quite different. An amplitude-dependent internal friction (ADIF) of the samples was studied by the inverted bending pendulum method in the relative strain range of ε = ∆l/l = (4 ~ 130) x 10-5 (frequency f ≈ 40 Hz) at the room temperature. Values of the logarithmic decrement (or specific damping capacity ψ) were obtained by computer analysis of amplitudes of the free decaying oscillations. Images of the magnetic domain structure were obtained by the displaced aperture method with the help of the transmission electron microscope Tesla BS-540 (accelerating voltage 120 kV), the traditional Lorentz electron microscopy has been used as well. The magnetic hysteresis loops were obtained in the fields of 0.5, 2.4, 24 kA/m (frequency ~ 0.1 Hz), quasi-static test regime has been used. Samples in the shape of thin rectangular strips were tested using the quasi-closed magnetic circuit (permeameter). Ring-shaped samples were also studied. Thin rectangular strips (0.3 x 10 x 100 mm3) were used for the investigation of longitudinal magnetostriction under condition of ac-excitation (f = 50 Hz). All tests were performed at the room temperature. Experimental Results and Discussion The properties of the high damping Fe - Cr and Fe - Al alloys are very sensitive to the variations in the heat treatment regime. Figure 1 presents typical amplitude dependencies of the logarithmic decrement for the Fe – 16 % Cr - 0.2 % Nb and Fe - 5.5 % Al alloys after the furnace cooling from T = 1000 oC (annealing time 40 minutes), after the air-cooling from 1000 oC and after the water quenching from the same temperature. It can be seen that annealing at T = 1000 oC (40 min) followed by the furnace cooling or air-cooling causes the realization of the high damping state. In the same time quenching of the samples results in a serious suppression of the damping capacity and the level of the logarithmic decrement is substantially lower (approximately 5 - 7 times lower) than in the high damping state. The similar modifications of the damping properties with the heat treatment were observed for all investigated Fe - Cr and Fe - Al alloys (see also [4, 6, 8, 9]). In the present research, the alloys were tested after the water quenching, air-cooling or furnace-cooling.

Fig. 1. Amplitude dependencies of the logarithmic decrement for the alloys Fe - 5.5 % Al (a) and Fe – 16 % Cr - 0.2 % Nb (b) after quenching (1), air-cooling (2) and furnace cooling (3). The magnetic hysteresis loops recorded in the maximum field of 2.4 kA/m for the Fe - 15.5 % Cr alloy are presented in Fig. 2. It can be seen that the coercive force of the alloy is larger in the high damping state (HC ≅ 180 A/m after furnace cooling and HC ≅ 120 A/m after quenching). The residual magnetization is also higher in the high damping state (as compared with the quenched state). Analysis of the shape of magnetic hysteresis loops allows one to assume that irreversible

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magnetization processes take place in the alloys in the region of small and high (~ 2.4 kA/m) applied fields. It can be seen from Fig. 2, that the total core losses are higher in the high damping state. The results of the studies of the shape of magnetic hysteresis loops in high damping Fe - Al alloys after different heat treatments [8] were quite similar to the described above. However, the changes in the coercive force were found to be much smaller in the Fe - Al alloys, than in the Fe Cr alloys. In the same time differences in the shape of the magnetic hysteresis loops were found to be larger and the residual magnetization is much smaller in the quenched Fe - Al alloys (as compared with the furnace-cooled alloys), [8].

Fig. 2. Magnetic hysteresis loops for quenched (a) and furnace-cooled (b) alloy Fe - 15.5 % Cr. It is reasonable to consider the magnetic hysteresis loops of the alloys along with the results of magnetostriction testing, since investigation of magnetostriction is one of the direct methods providing quantitative information on the magnetic domain structure of polycrystalline materials [10]. Analysis of magnetostriction data is very informative for polycrystalline materials (such as Fe-Si alloys with Si content C ≤ 4.5 % Si, Fe - Al alloys with Al content C ≤ 9 %Al, Fe Cr alloys possessing 12 ~ 19 % Cr) that are characterized by high magnetocrystalline anisotropy, by 3 easy magnetization axes and by high magnetostriction characteristics. The results of longitudinal ac-magnetostriction testing for high damping Fe - Cr alloys are presented in Table 1. It shows that the magnetostriction is lower in the quenched state, and the decrease of the cooling rate during heat treatment leads to the increase of the longitudinal magnetostriction. It can be assumed that in the quenched samples the volume fraction of magnetic domains oriented along the longitudinal direction of the sample (or domains with the small disorientation angles with the longitudinal axis) is significantly larger than the volume fraction of such domains in the alloy after furnace cooling or air cooling, where the longitudinal magnetostriction was found to be high. The preferred orientation of the magnetic domains along the longitudinal direction is equivalent to the increase of the volume fraction of 180o-domain walls oriented along the longitudinal axis (noticeable increase of the average size of magnetic domains is not considered here as a possibility). Let us mention here that the major contribution to the magnetomechanical damping comes from the irreversible motion of

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Interaction between Defects and Anelastic Phenomena in Solids

asymmetrical 90o-domain walls [1, 11 - 13], and the contribution from the motion of 180o-domain boundaries to the overall magnetomechanical damping is below 10% [13]. Table 1. Longitudinal ac-magnetostriction (λ||) of the alloy Fe – 16 % Cr - 0.2 % Nb, (x 106) Hmax , kA/m quenching air-cooling

0.8 < 0.5 1.2

1.6 1.2 3.6

2.4 2.4 6.0

3.2 5.0 7.5

4.8 7.5 10.1

6.4 8.6 12.0

The formation of the magnetic domain structure with the enhanced volume fraction of 180o-domain walls during quenching can be interpreted as follows: during the plunge of the elongated magnetostriction sample (l = 100 mm) into the water, the material is under the strong gradients of internal stresses caused by the temperature gradients. The interaction between the local magnetostrictive distortions of the crystalline lattice and the oriented gradients of the internal stresses caused by quenching, results in the formation of the preferred axis and in the preferred orientation of magnetic domains along the direction of the maximum temperature gradients during quenching. An experimental verification of the above assumption has been made with the help of a special test. During this experiment, the elongated magnetostriction sample (0.3 x 10 x 100 mm3) was quenched from T = 1000 oC into the water by using two different procedures (illustrated by Fig. 3). According to the procedure No I the magnetostriction sample, fixed between two thin-walled non-magnetic clamps, was plunged into the water with the longitudinal direction of the sample being perpendicular to the surface of the water. According to the procedure No II, the sample has been plunged into the water using such orientation where the longitudinal direction of the sample was parallel to the water surface, but the plane of the sample was perpendicular to the surface of the water. In this case the directions of the maximum temperature gradients during quenching were mutually orthogonal for the procedures No II and I. The results of the longitudinal magnetostriction testing for the Fe – 16 % Cr - 0.2 % Nb alloy are presented in Table 2. It shows that the magnetostriction λ|| is much lower after quenching in the accordance with the procedure No I. It can be assumed that after quenching (procedure No II), the preferred orientation of the magnetic domains along the transversal direction is realized, and the magnetization rotation from the transversal direction to the longitudinal direction provides noticeable increase of the longitudinal magnetostriction in the range of high fields. Let us mention that quenching of the samples for the damping capacity testing by using quenching conditions similar to the procedures No II and I, resulted in almost the same suppression of the damping capacity. Table 2. λ|| after quenching (x 106). Hmax, kA/m

Fig. 3. Schematic diagram, illustrating sample quenching with the help of two different procedures: a- procedure No I; b- procedure No II; 1- magnetostriction sample; 2- water.

Procedure Procedure No I No II

2.4

2.4

5.0

3.2

5.0

7.5

4.8

7.5

15.0

6.4

8.6

20.0

8.0

10.1

22.5

In the present research the magnetic domain structure of the high-damping alloys and high-damping industrial steels was studied by using TEM with the help of Lorentz electron

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microscopy and with the help of the displaced aperture method. In case of Lorentz electron microscopy [10], a pronounced linear modulation of intensity (caused by 180o-domain wall) can be observed quite easy when 180o-domain wall is parallel to the electron beam. It happens since electrons (passing through two neighboring domains having opposite spontaneous magnetization vectors) are deflected in the opposite directions due to the Lorentz force. As a result of the change of the trajectory of electrons, sharp linear modulation of the intensity is formed, displaying the position of the 180o-domain wall, parallel to the electron beam. The analysis shows however, that the visualization of the 90o-domain walls in the same manner is quite questionable. The direct contrast caused my magnetic domains (i.e. uniform spontaneous magnetization areas) can be observed by using the displaced aperture method [14]. When the electron beam passes through magnetic domains with the different directions of spontaneous magnetization vectors, it splits into several parts depending on the orientation of the magnetization vectors within the electron-beam illuminating area and the split can be seen in the diffraction pattern recorded in the back focal plane of the microscope (both for the direct electron beam and for diffracted electron beam). By displacing the objective aperture, the splitted beam can be partially cut off and it causes the decrease of the brightness of magnetic domain, which beam has been cut off (or partially cut off) by the aperture. The TEM studies of the high damping alloys and the high damping industrial steels show that the specific strip contrast can be observed on the electron-microscope images of the samples where the level of damping capacity is very high. The specific strip contrast appears when the aperture of the microscope is specially displaced and this contrast can be characterized by the boundaries direction, aligned along . It should be specially mentioned that the specific strip contrast has been never observed for the investigated Fe - Cr and Fe - Al alloys with the low level of damping capacity or where high damping properties of the alloy were suppressed (by specific heat treatment, deformation, strong magnetic field or so). Figure 4 a presents the TEM image, obtained from the high-damping alloy Fe – 16 % Cr – 0.2 % Nb in the high damping state (i.e. after annealing at T = 1000 oC within 40 minutes with subsequent furnace cooling), where the maximum value of δ reaches 28 %. The plane of the foil was parallel to {110}. The analysis shows that the contrast, observed on Fig. 4 a, is caused by the ferromagnetic domains with the 90o-orientation of the magnetization vectors in the neighboring magnetic domains. Additional minor modulation of intensity, caused by extinction banding contours, can be observed as well (this makes the specific contrast more visible). The conclusion regarding the magnetic character of the specific strip contrast is supported by the split of the direct electron beam that is caused by the influence of spontaneous magnetization of observed domains on the trajectory of electrons. The diffraction pattern (Fig. 4 b) and the TEM image (Fig. 4 a) were obtained from the same foil area. Let us specially mention, that we were able to observe the abovementioned specific strip contrast by studying those alloys and steels, where the level of damping was very high. If high damping properties of the samples were suppressed (for instance, using sample water quenching from T = 1000 0C or so [6 - 9]), we were unable to obtain the strip contrast for all studied alloys and steels. However, a lot of partially bent 180o-domain walls have been observed in water-quenched alloys (both for the alloys of the Fe - Cr and Fe - Al systems) with the help of Lorentz electron microscopy (see Fig. 5). Bending of the 180o-domain walls can be considered as an indication that quenched samples are characterized by serious gradients of the internal stresses in the alloy. Areas where 180o-domain walls were observed have been studied with the help of the electrons diffraction. It has been found that the split of the direct electron beam can be easily detected in the diffraction pattern, and this split is much wider than the split presented on Fig. 4 b, so the two beams are almost completely separated on the electron-diffraction pattern (the pattern is very similar to one presented in [10] for classic 180odomains structure with the 180o-domain walls). Twice as wide split of the electron beam is an indication that the magnetic domain structure presented on Fig. 5 is characterized by much more serious disorientation angles between spontaneous magnetization vectors of the observed magnetic domains (as compared with the domains presented on Fig. 4 a).

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Interaction between Defects and Anelastic Phenomena in Solids

Fig. 4. Electron-microscope image illustrating the structure of magnetic domains in high damping alloy Fe - 16 % Cr - 0.2 % Nb after furnace cooling from T = 1000 oC (a), and the split of the direct electron beam in the diffraction pattern (b).

Fig. 5. TEM image of 180o-domain walls in the high damping alloy Fe - 16 % Cr - 0.2 % Nb after water quenching from T = 1000oC; foil plane {100}. × 20000. Let us mention, that the magnetic domain structure, corresponding to the high damping state and presented on the Fig. 4 a, is very sensitive to the external factors and the pattern is movable along the foil inside the microscope - the picture observed in Fig. 4 a can be modified by moving the irradiating beam along the foil. It takes place due to modification of gradients of internal stresses due to heating of the irradiating area by the electron beam. When the electron beam has been displaced along the foil, the authors were able to observe bending of the domain walls followed by the Barkhausen jump of the wall between the places of local pinning. The described regularities of the magnetic domain structure of high-damping Fe - Cr alloys have been observed in the high-damping Fe - Al alloys as well. In the same time the specific domains dimensions were found to be a little larger in the Fe - Al alloys as compared with the studied Fe - Cr alloys. Figure 6 presents TEM image of the magnetic domain structure of the high damping steel (Fe - Al type, grade 01Ю5T, experimental heat, production of the AO “Supermetall” steelworks, Moscow) after annealing at T = 1000 oC within 40 minutes followed by the furnace cooling of the samples (maximum value of the logarithmic decrement after this heat treatment was found to reach δm = 31 %). The specific strip contrast that represents the structure of the magnetic domains with the 90o-mutual orientation is clearly visible on the image, and it is characterized by the

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boundaries direction, aligned along . The observed images are very similar to the ones observed for high damping Fe - Cr alloys. It is necessary to mention, that magnetic domain structures are very sensitive to the influence of the scale factor, so specific dimensions of magnetic domains, observed in thin TEM foils, should be strongly different from characteristic domain dimensions, observed in the bulk samples.

Fig. 6. TEM image illustrating the structure of magnetic domains in high damping steel 01Ю5T (experimental heat: Fe - 5.5 % Al - 0.02 % Ti) after furnace cooling from T = 1000 oC; foil plane {110}. The formation of the specific magnetic domain structure with enhanced fraction of easy movable 90 -domain walls in thin electron-microscopy foils can be considered as a preposition for arrangement of the analogous domain structure in the bulk materials (including samples for damping capacity testing with the thickness t = 2.5 mm). The abovementioned magnetic domain structure of bulk polycrystalline materials, in addition to the enhanced volume fraction of 90o-domain walls, can be characterized by the intensive internal closure of magnetic flow. The magnetic domain structures of Fe - Cr and Fe - Al high damping alloys in bulk polycrystalline samples (thickness t≤6mm) were investigated earlier with the help of the thermal neutrons refraction technique and the experimental results were described in the earlier works of the authors [8, 15]. The experiments were undertaken by using an ultra-SAS spectrometer at the EWA research reactor of the Institute of Atomic Energy, Poland. It is important, that the neutrons refraction method allows one to estimate the average dimensions of the magnetic domains in thick polycrystalline materials (more exactly, average dimensions along the direction of neutrons beam). Let us briefly discuss the summary of the earlier works in connection with the present experimental data. It has been shown in [8, 15], that for high damping Fe - Cr and Fe - Al alloys, the change in the damping state (from the high damping state to the state with the suppressed damping, obtained using water quenching) results in the noticeable decrease of the average dimensions of magnetic domains. In case of Fe - Cr alloys [15], the average size of magnetic domains hd was found to decrease from hd ~ 10 µm in the quenched state to hd ~ 8 µm in the high damping state (similar results were obtained for binary Fe - Cr alloys and for additionally alloyed high-purity Fe - Cr alloys). In case of Fe - Al alloys [8], the average size of magnetic domains decreases from hd ~ 12 µm in the quenched state to hd ~ 10 µm in the high damping state. Brief analysis of these experimental data can be made on the basis of the model of domain structure for cubic crystals [10], where average domain dimension depends on the domain wall energy as hd ~ γ (where γ is the specific energy of domain wall). Considering that the specific energy of the 90o-domain wall γ90 is almost twice lower, than the energy of the 180o-domain wall, the results of the neutrons refraction experiments can be easily explained by the increase of the volume fraction of 90o-domain walls in the structure of the studied alloys. Let us mention that magnetic domain structures with the o

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Interaction between Defects and Anelastic Phenomena in Solids

enhanced fraction of the 90o-domain walls have been experimentally observed in the studied alloys using the TEM methods (Fig. 4 and Fig. 6). Consequently, all experimental data discussed above indicate a significant rearrangement of the magnetic domain structure, accompanying the change of the damping state of the material (from the high damping state to the state with the suppressed damping). The magnetic domain structure, corresponding to the high damping state, can be characterized by enhanced volume fraction of easy movable 90o-domain walls. The formation of the specific magnetic domain structure with the enhanced volume fraction of 90o-domain boundaries can be explained by the minimization of the overall elastic energy, accumulated by the system of magnetic domains in the alloy with high magnetostriction characteristics. It can be assumed that the condition of maximum accommodation of the magnetostrictive deformations and compliance of the magnetic flow on the boundaries of neighboring crystallites in the polycrystalline material with high magnetocrystalline anisotropy and 3 easy magnetization axes and, simultaneously, with high magnetostriction characteristics, may cause the formation of the specific magnetic domain structure with the enhanced internal closure of the magnetic flow (by analogy with observed in [16, 17] for single-crystalline materials) and, consequently, with the enhanced volume fraction of 90o-domain walls. The increase of the volume fraction of the asymmetrical 90o-domain walls in the magnetic domain structure of the material can be considered as a factor that favors an increase of the magnetomechanical damping because the total losses (caused by the irreversible motion of the domain walls) are obtained by additive combination of the local losses produced by individual domain walls. In this case, if the mobility of the individual domain walls is not suppressed, magnetomechanical damping is directly dependent on the volume fraction of the 90o-domain walls (both for the existing 90o-domain walls and the 90o-domain walls, generated by the external stress). It can be assumed that the character of the initial magnetic domain structure of the material (before application of the external magnetic field) is very important for the magnetomechanical damping since the rearrangement of this domain structure under small external applied stress (i.e. irreversible displacements of already existing domain walls) provides the major contribution to the damping capacity in the range of small external loadings (this range is very important for practical application of high damping alloys).

Fig. 7. Model, illustrating rearrangement of fundamentally different magnetic domain structures under external stress for the material possessing high positive magnetostriction.

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Fig. 7 presents a model, illustrating rearrangement of two fundamentally different magnetic domain structures under external compressive and tensile stress. The domain structures in the initial state (σ = 0) are not imaginary – these domain patterns of real 3-axis ferromagnetic materials were taken from the classical work [10]. It was assumed that the observed domain boundaries are easy movable. It can be seen, that the application of the external stress causes a serious rearrangement of the magnetic domain structure, characterised by the enhanced fraction of the 90o-domain walls. In contrast magnetic domain structure, characterised by the abundance of 180o-domain walls, is subjected to the minor modifications under external elastic stress and this structure is unable to absorb considerable elastic energy under the alternating external elastic loading. It is very important to mention here, that not only fundamental rearrangement of the magnetic domain structure of the high damping Fe - Cr and Fe - Al alloys takes place when the heat treatment regime is principally changed. It is accompanied by the serious changes in the fine crystalline structure of the alloys affecting their damping capacity. However these changes were specially placed beyond the framework of the present research. Obtained experimental results show, that at least for the Fe - Cr and Fe - Al alloys, exhibiting very high level of magnetomechanical damping, it is reasonable to consider modifications in the crystalline structure along with the modifications in the magnetic domain structure of the materials. Conclusions 1. Obtained experimental results show that magnetic domain structures of high damping Fe - Cr and Fe - Al alloys are fundamentally different in the high damping state and in the state with suppressed damping capacity. 2. It has been shown that magnetic domain structure corresponding to the high damping state in Fe - Al and Fe - Cr alloys can be characterized by the enhanced volume fraction of an easy movable 90o-domain walls. The magnetic domain structure corresponding to the state with suppressed damping capacity can be characterized by the enhanced volume fraction of 180o-domain walls. 3. The formation of the specific magnetic domain structure with the enhanced volume fraction of 90o-domain boundaries can be explained by taking into account the compliance of the magnetic flow and the minimization of the overall elastic energy accumulated by the system of magnetic domains in polycrystalline material with the high magnetostriction characteristics and high magnetocrystalline anysotropy. It can be assumed that the condition of maximum accommodation of the magnetostrictive deformations and compliance of magnetic flow on the boundaries of the neighboring crystallites in the polycrystalline material with the high magnetocrystalline anisotropy and 3 easy magnetization axes and, simultaneously, with high magnetostriction characteristics, may cause the formation of specific magnetic domain structure with the enhanced internal closure of the magnetic flow and, consequently, with the enhanced volume fraction of 90o-domain walls. Acknowledgments The authors are grateful to A. N. Savvin, I. G. Yastrebov and L. P. Babichev (Principal Researchers of the I.P.Bardin Institute) for invaluable help in the studies of magnetic hysteresis loops or magnetostriction and for fruitful discussions. The authors are grateful to Drs. K. Mikke and J. J. Milczarek (the Institute of Atomic Energy, Swierk, Poland) for very efficient joint work in the field of neutrons refraction study of high damping alloys and for fruitful discussions. References [1] Yu. K. Favstov: Phys. Met. Heat Treat (in Russian). Vol. 18 (1984), p. 98. [2] I. S. Golovin: Met. Trans. A Vol. 25 (1994), p. 111. [3] D. W. James: Mat. Sci. Eng. Vol. 8 (1969), p. 4.

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[4] V. A. Udovenko, S. I. Tishaev, I. B. Chudakov: Physics Doklady, Vol. 38 (1993), p. 168. [5] T. Yamada, T. Takamura, S. Hashizume, T. Odake, T. Omori, K. Hattori: NKK Technical Review, Vol. 65 (1992), p. 21. [6] V. A. Udovenko, S. I. Tishaev, I. B. Chudakov: Russian Metallurgy (Metalli, 1994), p. 98. [7] V. A. Udovenko, I. B. Chudakov: Solid St. Phenomena. Vol. 115 (2006), p. 57. [8] V. A. Udovenko, I. B. Chudakov, N. A. Polyakova, in: Mechanics and Mechanisms of Material Damping, ASTM STP 1304, edtied by A. Wolfenden and V. Kinra, ASTM, Philadelphia, (1997), p. 204. [9] I. B. Chudakov, I. S. Golovin: ASTM STP 1304, Vol. 1304 (1997), p. 162. [10] S. Chikasumi: Physics of Ferromagnetism. Magnetic Characteristics and Engineering Applications. (Syokabo, Tokyo 1984). [11] A. Cochardt, in: Magnetic Properties of Metals and Alloys (ASTM, 1959), p. 251. [12] I. B. Kekalo, S. B Villems, L. P. Smirnova, V. L. Stoliarov, I. M. Ivanov: Phys. Met. & Met. Vol. 30 (1970), p. 566. [13] S. I. Ilyin, F. N. Dounaev, G. P. Yakovlev, in: Internal Friction in Metals and Inorganic Materials (in Russian), (Nauka Publications, Moscow 1982), p. 113. [14] P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, M. J. Whelan: Electron Microscopy of Thin Crystals (Butterworth, London 1965). [15] V. A. Udovenko, N. A. Polyakova, I. B. Chudakov, J. J. Milczarek, K. Mikke: Acta Physica Plonica A Vol. 96 (1999), p. 303. [16] S. Sh. Shilstein, V. A. Somenkov: J.Magn.Magn.Mater. Vol. 42 (1984), p. 193. [17] K. M. Podurets, D. V. Sokolski, R. R. Chistyakov, S. Sh. Shilstein: Sol. State Phys. (in Russian), Vol. 33 (1991), p. 2954.

Solid State Phenomena Vol. 137 (2008) pp 119-128 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.119

On the Formation of High Damping State and Optimization of Structure of Industrial Damping Steels V. A. Udovenko1, I. B. Chudakov1,a, N. M. Alexandrova1,b, R. V. Kakabadze2,c, N. N. Perevalov2 1

I. P. Bardin Central Research Institute for Ferrous Metallurgy, Moscow, 105005, Russia 2

Moscow Steelworks “Serp & Molot” , Moscow, 109033, Russia

a

b

c

[email protected], [email protected], [email protected]

Keywords: Fe - Al alloys, damping capacity, crystalline structure, deformation, heat treatment.

Abstract. Industrial high damping steels based on the Fe - Al metallic system have been studied. The optimization of the crystalline structure of the industrial damping steels has been shown to be very important for the achievement of high mechanical properties including high fatigue resistance. In the same time the achievement of high damping properties strongly depends on the magnetic domain structure of the material and, consequently, on the heat treatment procedure. Introduction It is well known that an application of the high-damping alloys (HDAs) allows reduction of noise and vibration levels in various engineering devices [1 - 6]. The highly efficient high-damping alloys application can be explained by considering a very high level of the damping capacity in modern high damping alloys (the level of the specific damping capacity ψ of modern HDAs reaches 40 50 %, so up to ~ 40 ~ 50 % of the vibration energy can be absorbed by the damping material within a single cycle of oscillation). In addition to the very high damping capacity modern HDAs are characterized by really high mechanical properties that are comparable to the properties of the widely used steels. The Fe-based high damping alloys are characterized by the high level of the elastic modulus E (180 – 200 x 103 MPa). In this case the high damping Fe - based alloys with the high elastic modulus and relatively high mechanical properties can directly replace the low-carbon steels in the already operating technical devices. However the replacement of the low-carbon steels by very expensive high damping alloys is absolutely unreasonable economically (although the use of HDAs allows reduction of the level of noise and vibration). This is the main reason, why the real practical application of HDAs in 1970-s, 1980-s and 1990-s was strongly restricted (HDAs were used in very special technical devices or specific military applications). Recently in the most industrialized countries the level of noise and vibration has been strictly limited by the legislation (especially within the urban areas), which resulted in the significant growth of the overall production of conventional damping materials. Nowadays the vibrations damping steel sheets (two steel sheets banded together with a special viscoelastic core) are produced by metallurgical companies in the very large industrial volumes in all industrialized countries. This class of materials is widely used in the automotive industry, civil engineering, home appliances, washing machines etc. In the same time the use of the organic viscoelastic materials for the core of the damping steel sheets is the origin of the very strict temperature limits for an application of damping steel sheets in the engineering devices. Damping sheets are also limited by the product thickness and by the absorbed elastic energy. As a consequence, engineers have focused on the high damping alloys, free from the above limitations. But the relatively high price of conventional HDAs has been considered as the main obstacle for the wide application of the damping alloys in industry [4 - 8]. The development of the new Fe – Al - Si and Fe - Al based HDAs in Japan [4, 12, 13] and in Russia [9 - 11] provided an opportunity for improving the situation. It was shown that the full-scale

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industrial metallurgical equipment can be used to fabricate Fe - Al - Si or Fe - Al based HDAs and it resulted in the development of the high damping steels “Serena”, “Intellial” (Japan) [4, 12, 13] and 01Ю5T (Russia) [7, 14]. The use of the full-scale industrial equipment reduces the cost of manufacturing of these steels, providing an opportunity for a widespread practical application of the high damping steels. In fact, these steels can be considered as the high-purity Fe - Al or Fe – Al - Si alloys, produced with the help of modern (Hi-Tech) industrial metallurgical equipment. The present paper describes the structure and the properties of several high damping industrial steels. A special focus is on the optimization of the crystalline structure of damping steels (that is required for the achievement of high mechanical properties including high relative elongation and high fatigue resistance). Materials and Experimental Methods All specimens were cut from high damping industrial steels, specially produced to obtain industrial material possessing high damping capacity. 3 industrial damping steels (representing the steel grade 01Ю5T) were selected for the present research (it was important to select steels, that slightly differed in metallurgical technologies). However, after full metallurgical processing all 3 final products were found to satisfy (within limited deviations) the chemical composition requirements, mechanical and damping properties requirements, size and flatness requirements. All materials can be considered to be 3 variations of 01Ю5T steel. To avoid confusion with our previous paper [7], selected steels are the same as in [7]. In Table 1 these steels are specified as ‘Steel No 1’, ‘Steel No 2’, ‘Steel No 3’. Steel No 1 was produced in 1993 by “Zlatoust Metallurgical Works” in 1-ton open induction furnace under protecting slag. Steel No 2 was produced in 1996 by Moscow Steelworks “Serp & Molot” in an industrial 10-ton furnace with the subsequent refinement in the ladle. Steel No 3 was produced by Moscow Steelworks “Serp & Molot” using 1-ton open furnace. Chemical compositions of the studied materials are listed in the Table 1. Other steels (not listed in the Table 1) were studied as well (they will be briefly described below). Table 1. Chemical composition of the studied steels [ mass. %]. Material

Al

Si

C

Mn + Cu Ni + Cr + Co Σ (V + Nb + W + Mo + Ti + Zr)

P+S

No 1

5.6

0.13 < 0.01

0.04

0.05

0.15

< 0.02

No 2

5.3

0.4 < 0.02

0.4

0.45

0.2

< 0.03

No 3

6.0

0.03 < 0.01

0.25

0.1

0.2

< 0.02

Specimens were cut at different stages of treatment. The majority of specimens were cut from commercial hot-rolled sheets (thickness t = 3; 4 and 6 mm), samples were mechanically processed and heat-treated in vacuum furnaces with different heat treatment conditions. Cold-rolled samples were obtained by additional rolling of the hot-rolled sheets with the help of the pilot-plant equipment. An amplitude-dependent internal friction of samples was studied by the inverted bending pendulum method in the relative strain range of ε = ∆l/l = (4 ~ 130) x 10-5 at room temperature. Values of the logarithmic decrement δ (as well as the specific damping capacity ψ) were obtained by computer analysis of amplitudes of free decaying oscillations. The mechanical properties of the samples have been studied using Instron and ZD10/90 universal testing machines (deformation 0.5 mm/min). Analysis of macrostructure has been performed in accordance with the recommendations presented in [15]. X-ray diffraction study has been made with the help of the diffractometer DRON-

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3.0 (Fe Kα radiation has been used). Investigation of microstructure has been performed using transmission electron microscopes Tesla BS-540 and JEM-200CX (JEOL). Experimental Results and Discussion The initial goal of high-damping steel’s metallurgical processing was to obtain hot-rolled sheets with the high damping capacity, high flatness, thickness t = 3.2 and 4.0 mm and given level of mechanical properties including high relative elongation (in order to make final device sustainable against unexpected mechanical overloading). It is well known that the final steel structure strongly depends on the initial (as-cast) structure, so the detailed metallurgical processing should be designed after the analysis of the special structural features and the properties of the initial material. Since melting and casting technologies are not discussed in the present work we analyze the industrial damping steels starting from as-cast materials. For different damping steels (including not mentioned in the Table 1), round-shaped ingots were prepared (maximum diameter of the cross-section D = 380 mm); ingots with the maximum cross-section as
350 x 350 mm were used as well. Since this steel is subjected to the lowest degree of hot plastic deformation during the treatment, the as-cast slab’s structure (cross-section 140 x 420 mm) is the most important for the properties of hot-rolled sheets with the final dimensions of the product as t = 4.0 mm or t = 3.2 mm. The macrostructure of the as-cast slab 140 x 420 mm (high damping steel No 3) is presented in Fig. 1 (in order to improve the visibility of details, only a half of the structure is presented in the figure).

Fig. 1. The macrostructure of the as-cast material. Steel No 3 (cross-section 140 x 420 mm). Fig. 1 shows small almost equiaxial crystals in the vicinity of the ingot’s surface. With the increase of the depth, the elongated dendrite crystals appear and large dendrites are dominant in the central part of the ingot. It is important to mention that equiaxial crystals are not dominant in the center of the ingot. The observed structure is quite typical for the as-cast materials. However the average grain size in the as-cast damping steel is larger than the one observed in the well-known steels (this can be explained by the general tendency of the Fe - Al alloys to exhibit structures with an enlarged grain size). Analysis of the structure presented in Fig. 1 shows that the pronounced porosity of the ingot is not observed and the internal cracking of the ingot is not realized. In the same time the large grain size indicates that the distribution of the non-metallic inclusions is highly important for the mechanical properties of the material. A sulfur print obtained from the as-cast slab 140 x 420 mm (steel No 3) is presented in Fig. 2.

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Fig. 2. Sulfur print, representing a distribution of non-metallic inclusions in the as-cast material. Fig. 2 shows that fortunately, the distribution of non-metallic inclusions on the base of S is quite uniform across the section of the as-cast industrial slab. There are no large conglomerations of particles. It can be assumed that hot plastic deformation will make the distribution of nonmetallic inclusions more uniform (in case of carefully designed treatment). It is necessary to consider a drastic grain size reduction during hot deformation (since recrystallization and growth of the average grain size are unavoidable during the final heat treatment when high damping properties are being formed). In the present work hot plastic deformation of the industrial high damping steels was produced in several stages. A high dislocation density was observed on the TEM-images of the samples after final hot rolling. At the same time the distribution of the dislocations within the grain is not uniform. A well-developed sub-grain structure with bright sub-grain boundaries and dislocations walls can be seen in the TEM-images (Fig. 3). The sub-grain boundaries can be described as the areas of the very high dislocations density. The sub-grain boundaries can be considered as the origin of a strong pinning of magnetic domain walls. Consequently these dislocation structures in the hot-rolled samples causes a strong suppression of the magnetomechanical damping due to the strong suppression of the mobility of the 90o-domain walls and due to the decrease of the volume fraction of the 90o-domain boundaries under a strong field of the long-range internal stresses produced by the sub-grain boundaries. It has been shown in our previous works [9 - 11], that the formation of the specific magnetic domain structure with an enhanced volume fraction of the easy-movable 90o-magnetic domain boundaries is required to form a high damping state in the binary and additionally alloyed Fe - Al alloys with the Al content C = 3.5 ~ 6.5 % Al (mass. %). It is known [1, 16], that the major contribution to the magnetomechanical damping in the ferromagnetic materials with 3 easy magnetization axes and with pronounced magnetocrystalline anisotropy comes from the irreversible motion of the asymmetrical 90o-domain walls. The contribution from the motion of the 180o-domain boundaries to the overall magnetomechanical damping [16] is below 10 %. Consequently the crystalline structure, formed during the hot rolling procedure and characterized by well-developed sub-grain substructure, doesn’t favor the formation of the high level of magnetomechanical damping due to a strong pinning of the 90o-domain walls and due to formation of the long-range fields of the internal stresses produced by the sub-grain boundaries and dislocation walls. The details on the interaction between domain walls and dislocations in the

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high-purity iron can be found in [17, 18]. Modification of the described structure of hot-rolled steels with additional heat treatment seems to be the most interesting question.

Fig. 3. TEM images, illustrating microstructure of steel No1 after the final hot rolling at T = 1200 °C (a- hot-rolled sheets t = 3.2 mm; b- hot-rolled sheets t = 6.0 mm). × 30000. Fig. 4 presents the modification of the maximum logarithmic decrement δmax (maximum value of δ in it’s amplitude dependence) with the increase of the annealing temperature for steel No 1. A hot-rolled sample (steel No 1, t = 3.2 mm) has been annealed step-by-step at T = 600, 700, 800, 900 and 1000 oC. Each time, the sample was annealed for 60 minutes in the furnace with subsequent cooling by air. Each step of annealing was followed by testing of the specimen’s damping capacity and by annealing at the higher temperature. All heat treatments were performed in a high vacuum furnace. Tanneal = 25 oC (Fig. 4) represents the properties of the as-rolled damping steel.

Fig. 4. The effect of annealing temperature on the logarithmic decrement of the hot-rolled steel. Fig. 4 shows, that the maximum value of the logarithmic decrement increases with the increase of the annealing temperature and the damping capacity reaches its maximum after annealing at T = 1000 oC. In the same time, damping capacity visible decreases after annealing at T = 600 oC. It is well known [19] that the microstructure of hot-rolled low-carbon steels (characterized by well-developed sub-grain structure with well-developed sub-grain boundaries and dislocations walls) is very stable and remains almost unchanged after low-temperature annealing. It can be assumed that annealing of the hot-rolled damping steels at T = 600 oC causes stabilization of positions of sub-grain boundaries (by analogy with processes described in [19]). Consequently, low-temperature annealing causes additional decrease of magnetic domain walls mobility. Bright-field and dark-field electron-microscope images obtained from hot-rolled steel No 1 after

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Interaction between Defects and Anelastic Phenomena in Solids

additional annealing at T = 600 oC (for 1 hr) are presented in the Fig. 5. Well-developed sub-grain structure can be seen at the electron-microscope images. It can be assumed that this type of crystalline structure strongly influences the magnetic domain structure and asymmetrical 90o-domain boundaries.

Fig. 5. Bright-field (a) and dark-field (b) TEM-images, illustrating microstructure of the steel No 1 (thickness t = 6.0 mm) after hot-rolling and additional annealing at T = 600 oC (within 1 hr). × 12000. In contrast with annealing of the hot-rolled damping steel, annealing of the cold-rolled steel causes continuous increase of damping capacity of the material, and high values of the logarithmic decrement can be observed already at Tanneal = 900 oC (Fig. 6). However, initial damping capacity of the material in the cold-rolled state is lower, than that in the hot-rolled state (Fig. 6 and Fig. 4).

Fig. 6. Effect of annealing temperature on the logarithmic decrement for cold-rolled material. The difference in the hot-rolled and cold-rolled materials behavior can be explained by taking into consideration the differences in the structure of cold-rolled and hot-rolled materials. It can be seen from Fig. 7 that microstructure of the cold-rolled damping steel can be characterized by very high dislocations density. Dispersed, labyrinth magnetic domain structure can be observed in the cold-rolled materials and this structure is characterized by very low damping capacity.

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Fig. 7. Bright-field TEM-image, illustrating dislocations structure of the cold-rolled steel (after cold rolling from t = 3.0 mm to t = 0.6 mm). × 80000. Electron-microscope investigation of the cold-rolled and hot-rolled samples after annealing at T = 1000 oC shows that both samples can be characterized by low dislocations density and the uniform dislocations distribution. TEM-images illustrating microstructure of damping steel after annealing at T = 1000 oC are presented at the Fig. 8 with uniform distribution of dislocations clearly visible. The type of dislocations structure (Fig. 8) allows one to assume that this crystalline structure can’t provide enough obstacles (first of all, long-range fields of internal elastic stresses) to form the specific magnetic domain structure during heat treatment (specific magnetic domain structure with an enhanced volume fraction of the 90o-domain walls). Consequently, the discussed structure favors the high-damping state formation.

Fig. 8. TEM-images illustrating dislocations structure of high damping steel in the high damping state (after annealing at T = 1000 oC for 1hr and subsequent air-cooling). × 30000 (a); × 50000 (b). It can be assumed also that the microstructure observed in the annealed cold-rolled and hot-rolled steels is favorable for the achievement of high plasticity of the material. Measurements of mechanical properties of the samples show that value of relative elongation of the annealed materials can reach 25 – 30 %. It should be mentioned that similar results were obtained in our previous works [7, 9 - 11, 14] for the samples annealed at T = 1000 oC (within the previous works, single-step annealing has been used). Impact tests show that the studied damping steels are characterized by relatively high energy dissipated during impact testing at room temperature (25 - 40 J/cm2 obtained using U-type samples

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Interaction between Defects and Anelastic Phenomena in Solids

cut). It is important that high damping steels do not exhibit very sharp embrittlement at a specific temperature. These steels show quite smooth decrease of the impact energy with the reduction of T and even in the range of liquid nitrogen temperatures the impact test doesn’t go lower than 2 4 J/cm2. These results can be explained by the low content of impurities and non-metallic inclusions in the tested steels and by the uniform structure of the material. High content of Al in the high damping steels favors the achievement of high mechanical properties at the elevated temperatures. Figure 9 presents the dependence of mechanical properties of the damping steels on the test temperature (before testing, all samples were annealed at T = 1000 oC for 40 minutes). It can be seen from Fig. 9 that at the room temperature, tensile strength of conventional low-carbon steel is almost equal to the value σB for the high damping steel. At the temperatures above T = 350 – 400 oC σB value for the low-carbon steel intensively decreases, and in the temperature range T = 500 - 650 oC mechanical properties of the high damping steels are substantially higher, than the properties of low-carbon steels (Fig. 9).

Fig. 9. Mechanical properties of the damping steel (steel No 2 in the high damping state) and conventional low-carbon steel (0.17 % C) at the elevated temperatures: 1, 3 –yield strength σ0.2; 2, 4 - tensile strength σB. Combination of the relatively high mechanical properties and high relative elongation in the high damping state can be considered as a preposition for a wide application of high damping steels in various engineering devices. However, for a variety of practical applications engineering steels are used under condition of alternating external elastic loading and in many cases the total number of loading cycles is extremely high. It was reasonable to verify whether high damping steels are able to sustain multi-cycle elastic loading or not (it was necessary to check it because high damping steels are characterized by the enlarged average grain size in the high damping state). Figure 10 presents the fatigue resistance curve for the steel No 1 (thickness t = 3.2 mm) in the high damping state (after annealing at T = 980 oC for 40 min). Testing has been made at the room temperature.

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Fig. 10. Fatigue resistance of the steel No 1 in the high damping state. It can be seen from Fig. 10, that the fatigue limit for steel No 1 can be estimated as ~ 280 MPa (based on N = 107 cycles). This value is quite high and it allows the application of the high damping steels (grade 01Ю5T) in a variety of engineering devices without serious risk of the material damage within the long-term exploitation period. It can be assumed that the chemical composition, steel production technology and metallurgical processing were carefully designed. Obtained experimental results allow one to assume that crystalline structure and properties of high damping engineering steels based on the Fe - Al metallic system can be optimized for each practical application. Special engineering steel with the required combination of damping and mechanical properties can be mass-produced with the help of industrial metallurgical equipment. Conclusions 1. High damping steels based on the Fe - Al metallic system can be produced on a large manufacturing scale. The use of the full-scale industrial metallurgical equipment allows one to achieve low manufacturing cost. 2. Industrial high damping steels (grade 01Ю5T) are characterized by a proper combination of high damping capacity and relatively high mechanical properties including high relative elongation, high fatigue resistance, high impact test results. These steels can be used at the elevated temperatures. High purity of industrial damping steels along with the favorable crystalline structure optimized during metallurgical processing and heat treatment are the major contributors to the high level of properties. 3. In order to achieve the best combination of properties and to optimize the structure of damping steels, strict technological control should be provided at all stages of metallurgical processing. Acknowledgments The authors are grateful to the specialists and administration of the I. P.Bardin Institute, Zlatoust Metallurgical Works (Zlatoust city, Ural Region) and Moscow steelworks “Serp & Molot”, who contributed their efforts and specific knowledge to the development of high damping industrial steels. Special gratitude should be expressed to S. I. Tishaev, M. G. Isakov, E. Z. Vintaikin, B. V. Molotilov, V. E. Sukhanov, A. M. Glezer, N. A. Polyakova, S. Yu. Mackushev, I. I. Nikitina, D.

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F. Litvin, V. I. Trakhimovich, V. A. Pogonchenkov, V. P. Pavlov, S. L. Parenkov, V. I. Bragin, G. B. Koulikov, E. V. Sinev, V. L. Troshin, A. N. Sergeev, G. N. Korneev, B. P. Koloskov. References [1] Yu. K. Favstov: Phys. Met. Heat Treat (in Russian). Vol. 18 (1984), p. 98. [2] D. W. James: Mat. Sci. Eng. Vol. 8 (1969), p. 4. [3] I. G. Ritchie, Z. L.Pan: Met. Trans. A Vol. 22 (a) (1991), p. 607. [4] T. Yamada, T. Takamura, S. Hashizume, T. Odake, T. Omori, K. Hattori: NKK Technical Review (in English). Vol. 65 (1992), p. 21. [5] N. Igata: Key Engineering Materials. Vol. 319 (2006), p. 209. [6] K. Kawahara: Key Engineering Materials. Vol. 319 (2006), p. 217. [7] V. A. Udovenko, I. B. Chudakov: Solid State Phenomena. Vol. 115 (2006), p. 57. [8] N. Igata, K. Nishiyama, K. Ota, Y. Yin, W. Wuttig, I. S. Golovin, J. V. Vanhumbeeck, J. San Juan: Journal of Alloys and Compounds. Vol. 335 (2003), p. 230. [9] V. A. Udovenko, S. I. Tishaev, I. B. Chudakov: Physics Doklady (in English). Vol. 38 (1993), p. 168. [10] V. A. Udovenko, S. I. Tishaev, I. B. Chudakov: Russian Metallurgy (Metalli, 1994), p. 98. [11] V. A. Udovenko, I. B. Chudakov, N. A. Polyakova, in: Mechanics and Mechanisms of Material Damping, edtied by A. Wolfenden and V. Kinra, volume 1304 of ASTM STP 1304, ASTM, Philadelphia (1997), p. 204. [12] I. Aaltio, K. Ullakko: Smart Materials and Structures, Vol. 6 (1997), p. 616. [13] M. Sugioka, M. Fukusumi, Y. Okanda: Science and Industry (ISSN: 0368-5918) (in Japanese). Vol. 77 (2003), p. 143. [14] V. A. Udovenko, T. A. Turmambekov, I. B. Chudakov, S. Yu. Mackushev: Steel in Translation (ISSN: 0967-0912) (in English). Vol. 29, No11 (1999), p. 81. [15] M. Beckert, H. Klemm: Handbuch der Metallografischen Ätzverfahren, (Veb Deutshcher Verlag fur Grindestoffindustrie, Leipzig, 1976). [16] S. I. Ilyin, F. N. Dounaev, G. P. Yakovlev, in: Internal Friction in Metals and Inorganic Materials (in Russian) (Nauka Publications, Moscow 1982), p. 113. [17] K. A. Taylor, J. P. Jakubovi, B. Astie, J. Degauque: J. Magn. Magn. Mat. Vol. 31 (1983), p. 970. [18] B. Astie, J. Degauque: J. Physique, Vol. 42(C5) (1981), p. 627. [19] N. L. Bernstein: Structure of Deformed Alloys (in Russian) (Metallurgia Publ., Moscow 1977).

Solid State Phenomena Vol. 137 (2008) pp 129-136 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.129

Influence of Heat Treatment on Magnetic and Damping Properties of Fe – 11 at. % Al alloys Agnieszka Mielczarek1, Werner Riehemann1,a, Olga A. Sokolova2, and Igor S. Golovin2 1

Institute of Materials Engineering and Technology, Clausthal University of Technology, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany 2

Physics of Metals and Materials Science Department, Tula State University, Lenin ave. 92, Tula, 300600 Russia a

[email protected]

Keywords: Fe - Al alloys, magneto-mechanical damping, magnetostriction, coercivity.

Abstract. The influence of heat treatment on the amplitude dependence of internal friction in Fe 11 at. % Al alloys with carbon contents in the range 0.005 - 0.2 at. % has been studied using an inverted torsion pendulum in the temperature range 300 – 950 K and a vibrating reed apparatus at room temperature. The specimens were annealed at 1273 K in vacuum and cooled down with different cooling rates in order to obtain different degrees of order. It was found that ordering is hardly avoidable in Fe - Al alloys with Al contents > 11 at. %. Ordered alloys are characterised by lower damping capacity due to higher coercivity caused by additional pinning of magnetic domain walls by antiphase boundaries. X-ray diffraction investigations indicate that water-cooling suppresses ordering in Fe - 11 at. % Al alloys while cooling in air or in furnace provokes D03–type ordering. Slowly cooled specimens are characterised by higher damping capacity due to lower coercivity than water cooled or plastically deformed specimens. The amplitude dependent magneto-mechanical damping was determined as the difference between amplitude dependent damping without and with saturating magnetic field (~ 20 kA/m). Magneto-mechanical damping was found to be proportional to the strain where the amplitude dependent damping is maximum and reciprocal to the coercivity and saturation polarisation. Cold rolling increases the coercivity and therefore decreases the magneto-mechanical damping. An increase of the grain size in the investigated samples by heat treatment leads to a qualitatively expected decrease of coercivity and therefore to an increase of magneto-mechanical damping. Introduction Fe - Al alloys are characterized by good mechanic, magnetic and dissipative properties. As compared with pure iron these alloys have higher strength, lower density and much better resistance against oxidation at elevated temperatures [1, 2]. The strength of Fe – Al - C-alloys depends on their carbon content. For low carbon contents hardness and yield strength increase with increasing carbon content. The mechanical properties of these alloys are reported in refs. [2 - 4]. Very high damping capacity [5] of these ferromagnetic alloys can be explained by magnetomechanical hysteretic losses. Magneto-elastic damping is caused by stress-induced motion of magnetic 90° domain walls [5 - 8]. If the ferromagnetic material is subjected to cyclic stress, 90°domain walls dissipate mechanical energy by irreversible Barkhausen jumps via Eddy currents [9]. The saturation magnetostriction λS of the alloys as an intrinsic property depends on the aluminium composition and the degree of order. The magneto-elastic damping can be suppressed by magnetically saturating the material using a strong external magnetic field [9 - 10]. The maximum damping level strongly depends on the coercivity and saturation magnetostriction of the material. An improvement of the damping properties can be achieved by decreasing the coercivity and increasing the magnetostriction. In the present article the correlations between magnetic and damping properties derived from a simple model are to be revised for the investigated Fe - Al

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Interaction between Defects and Anelastic Phenomena in Solids

alloys in order to investigate the potential for an optimisation of the damping properties by chemical composition and heat treatment. Experimental Alloys and heat treatments The investigated alloys were prepared in a vacuum induction furnace in the Institute of the Physics of Metals of the Central Research Institute for Iron and Steel Industry in Moscow (Russia). The compositions with different content of aluminium (10 - 11 at. %) and carbon (0 - 0.2 at. %) are listed in table 1. The magnetic and damping measurements were performed after different heattreatments. All alloys were heat treated at 1273 K for 20 minutes under argon-gas atmosphere with subsequent air-cooling, furnace cooling or water quenching. Water-cooling suppresses ordering in Fe – 11 at. % Al alloys while air-cooling or furnace cooling provokes D03–type ordering. Ordered specimens were additionally cold rolled by 2 or 4 %. Table 1. Chemical composition and heat- or cold rolling treatment of the investigated specimens. Coercivity (Hc), saturation polarisation (Js), saturation magnetostriction (λs) measured in the longitudinal sample direction and grain size (d) were determined at room temperature. Alloy composition [at. %] Fe - 10.7 Al - 0.005 C

Fe - 10.4 Al - 0.006 C

Fe - 10.4 Al - 0.19 C

Fe - 10.0 Al - 0.2 C

Heat and cold rolling treatment 1273K/20 min and water quenching 1273K/20 min and air-cooling 1273K/20 min and furnacecooling 1273K/20 min and water quenching 1273K/20 min and air-cooling 1273K/20 min and furnacecooling 1273K/20 min and water quenching 1273K/20 min and air-cooling 1273K/20 min and furnacecooling 1273K/20 min and water quenching 1273K/20 min and air-cooling 1273K/20 min and furnacecooling 1273K/20 min and furnacecooling plus 2 % cold rolling 1273K/20 min and furnacecooling plus 4 % cold rolling

HC [A/m] 29.4

JS [T] 1.48

10 4.3

d [µm] -

20.0 17.1

1.48 1.21

8.6 1.6

-

28.4

1.63

6.5

-

14.2 13.9

1.6 1.13

5.8 2.3

270 440

36.3

-

9.8

-

23.7 14.3

-

9.5 2.6

337 544

32.1

1.7

4.2

230

23.5 13.1

1.7 1.7

4.2 3.5

250 380

103

1.9

-

420

142

1.9

-

450

λs

-6

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Damping measurements Amplitude dependent damping was measured using an inverted torsion pendulum (in Tula, Russia [11, 12]) and a vibrating reed (bending) apparatus (in Clausthal, Germany [13]). The free decay inverted torsion pendulum (frequencies 1 - 2 Hz) allows damping measurements in the temperature range 300 – 950 K under vacuum (3 Pa) and under maximum magnetic field of 40 kA/m. Damping in this case is obtained as a function of the maximum elastic shear deformation γ. The bending set-up allows to measure the logarithmic decrement of free decaying bending vibrations of a single side clamped vibrating beam as function of maximum bending strain amplitude at room temperature under vacuum (30 Pa) according to

δ =

A 1 ln i , n Ai + n

(1)

where Ai and Ai+n are the amplitudes of the i-th and (i + n)-th cycle, respectively. The investigated strain range was 10-6 – 10-3. For the present investigation a sensitive Lock-In-Amplifier with 20 measurements per second has been used instead of the digital voltmeter, described in [13]. Therefore for a typical vibration frequency of 40 Hz n in eq. (1) equals 2. Magnetic measurements Saturation polarisation JS has been determined using a computer controlled AC-digital hysteresis recorder with air-flux compensating coil system. The specimens (1 × 1 × 50 mm3) were sticked onto a plane wood specimen holder and centered in the pick-up coil of 10 mm diameter. A schematic description of this apparatus is given in [14, 15]. Coercivity HC was measured by compensating the stray field of the sample with an external magnetic field being the coercivity. The stray field was measured using a Förster Magnetometer (Magnetoscop 1.068), the external field was produced by a coil with 350 mm length 10 mm diameter and 3500 windings and a tuneable precision DC-current supply. Saturation magnetostriction λS was measured as the relative change of the longest specimen length by application of saturating field of 40 kA/m. The length change was measured by a high-sensitive inductive displacement transducer (Hottinger Baldwin KWS-6A5). XRD X-ray diffraction analysis was made with the help of a Siemens (Cu Kα1, λ = 1.5406Å) and an Oxford diffractometer (Co Kα1, λ = 1.789Å) at the room temperature in the range 2Θ = 10° - 140°. Results and Discussion The measured magnetic properties and grain sizes of the investigated samples are listed in Table 1. It was ensured that the maximum applied magnetic field of 20 - 40 kA/m, depending on the investigation method, allows magnetic saturation of the specimens. The lowest coercivities were found after cooling in the furnace. The high coercivities for cold rolled materials can be explained with the high dislocation densities. The results for JS and λS measured in the sample length direction are shown in the table 1 as well. Experimental results obtained for the Fe - 10.7 Al - 0.005 C alloy after heat treatment at 1273 K for 20 min and subsequent furnace cooling are shown in figures 1, 2 and 3. Damping properties (see fig. 1) were obtained at the temperatures 300, 500, 600, 700, 800 and 900 K. For all adjusted temperatures, a maximum was found in the amplitude dependent damping curve which disappears under saturating external magnetic field. In soft ferromagnetic metals the strain amplitude (ε denotes here tensile (ε) as well as shear strain (γ)) and magnetic field dependent logarithmic decrement δ (ε, H) can be divided into three parts, the logarithmic decrement due to dislocation bowing between weak pinning points δD,0 [16], other anelastic contributions neglected here, the logarithmic decrement due to break-away of dislocations from weak pinning points (mostly solid solutes) δD,h (ε), and the logarithmic decrement due to irreversible motion of the 90°-domain walls δME(ε, H)

132

Interaction between Defects and Anelastic Phenomena in Solids

δ(ε, H) = δD,0 + δD,h(ε) + δME(ε, H)

(2)

The δME (ε, H) curves exhibit a maximum at εC. For all studied samples a magneto-elastically caused maximum was found. The δME (ε, H) component disappears, if the damping of the material is measured in a strong external magnetic field (H >> HC) which annihilates or fixes the domain walls. For strains smaller than εC magneto-mechanical damping is proportional to the strain. This dependence was found in all ferromagnetic materials in the Rayleigh-range [8, 17]

δ = tg(αME) ε for ε < εC ,

(3)

where tg (αME) is the slope of the δME versus ε curve below εC. For higher strains the energy, which is dissipated within one cycle, will saturate because the domain walls become more and more immobile. For magneto-mechanical coupling the coupling constant is the magnetostriction and for square shaped hysteresis loops the magnetic energy density will be approximately equal to the mechanical energy density: HcJs ≈ λsEεc .

(4)

So, the magneto-mechanical damping δME (ε, H = 0) for strains higher than the critical strain εC can be written as:

δ ME (ε , H = 0) =

0,05

H=0A/m 300K

0,04

500K 600K 700K

δ

0,03

0,02

0,01

4 FH λs ε c

ε

4

2

H=2x10 A/m

=

B

ε2

for ε > εC ,

(5) where FH characterizes the form of the “J-H” hysteresis loop. For square hysteresis loops (FH=1) the maximum of magneto-elastic damping δm can be calculated from eq. (4) and (5) to be

δ ME max ≅

800K 900K

4λ2s E Hc Js

(6)

and the slope of δME(ε,H=0) versus ε for ε < εC equals tgα ME =

δ ME max 4λ3s E 2 = εc (H c J s ) 2

(7)

The temperature dependence of the damping versus shear amplitude is 0,00 -5 -4 -3 10 10 10 shown in fig. 1. It can be seen that γ shear strain at maximum damping shifts to higher values and maximum Fig. 1. Amplitude dependent damping of Fe - 10.7 Al - damping shifts to lower damping with 0.005 C after 20 min annealing at 1273 K and increasing temperature. This can also subsequent furnace cooling at various temperatures be seen in fig. 2 where fig. 1 is evaluated and strain at maximum measured with (20 kA/m) and without magnetic field. damping and maximum damping are plotted versus temperature. The decrease of magneto-elastically caused damping with increasing temperature is reasonable because δME will vanish at the Curie temperature. This behaviour can be explained mainly by a decrease of the saturation magnetostriction which enters eq. (6) with the second power, if it is assumed that the change of coercivity with temperature is low and the decrease of the saturation polarization with temperature is not higher than the decrease of the saturation magnetostriction. Using eq. 4 the increase of the shear strain at maximum damping suggests that the decrease of λsE is stronger than the decrease of HcJs with increasing temperature.

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But nevertheless these are assumptions and have to be verified by future temperature dependent measurement of these alloys’ magnetic properties.

δME

γC

With the increase of temperature the dislocation damping δD,0 increases. This can be seen in fig. 1and more evaluated in fig. 3 where the slope of δD,h (ε) versus ε 0,0003 0,012 (tg αD = δD,h (ε) / dε) is plotted versus the inverse temperature. 0,010 The observed behaviour can be 0,0002 explained by different mechanisms 0,008 of dislocation motion under applied alternating stress. At lower 0,006 0,0001 temperatures dislocations are pinned εC by foreign, presumably mainly inter0,004 δME stitial, atoms and the slope is practically temperature independent. 0,0000 0,002 With increasing temperature, the 300 400 500 600 700 800 900 diffusion of interstitial atoms increaT in °C ses and above a critical (condensation) temperature of about 580 K Fig. 2. Critical torsion angle and maximum damping for (see fig. 3), interstitials begin to different temperatures. evaporate from the dislocations and increase their mobility. Therefore 580 K is an estimate for the 15 temperature of carbon atom condensation at dislocations in Fe Al. This condensation temperature is 10 higher in Fe - Cr-alloys [18].

tg α D

Water quenching suppresses the formation of ordered structures, and slower cooling favours the formation 5 of ordered structures since the time at higher temperatures available for atomic diffusion is longer. XRD 0 measurements of the (Fe - 10.4 Al -3 -3 -3 -3 10 2x10 3x10 4x10 0.006 C)-specimens after 20 min -1 -1 annealing at 1273 K with subsequent T in K furnace cooling showed a (110)-peak for all used wavelengths. Additional -1 Fig. 3. Dependence of the slope tg αD on T for peaks from D03 structure were found Fe - 10.7 Al - 0.005 C alloy after heat treatment at as well using Co Kα1 radiation. XRD tests in the Cu Kα1 radiation revealed 1273 K for 20 min and furnace cooling. (110) small-intensity peaks in the aircooled specimens, while this result was not confirmed using Co Kα1 radiation. Additionally cues for texture were found. The influence of the cooling rate on strain amplitude dependent damping with and without magnetic field is shown in fig. 4. It can be seen that the cooling rate influences significantly magneto-mechanical damping while dislocation damping is mainly unchanged.

134

Interaction between Defects and Anelastic Phenomena in Solids

δME

δ

In heat treated Fe – 11 % Al alloys the more ordered samples have also lower coercivity due to less internal 0,12 H=0A/m H=4000A/m stresses or lower dislocation density furnace cooling 0,10 (see table 1). This correlates with cooling on air higher magneto-elastic damping. In water cooling 0,08 contrast, water quenching causes a higher level of internal stresses and, 0,06 therefore, an increase in coercivity and a decrease in damping [19]. 0,04 The strain dependencies of δME for samples of variously cooled alloy Fe – 0,02 10 Al - 0.2 C are shown in fig. 5. The highest magneto-elastic damping was 0,00 -5 -4 -3 found after heat treatment at 1273 K 10 10 10 and subsequent cooling in furnace. ε The damping capacity of cold rolled specimens was found to be at least Fig. 4. ADIF at T = 300 K for the Fe - 10.4 Al - 0.006 C one order lower than the damping alloy after 1273 K/20 min followed by different capacity of furnace cooled specimen. types of cooling, under the magnetic field and Tenfold increase of the coercivity of without the field. the alloys after cold rolling (see table 1) provides reasonable explanation of this experimental fact. This also explains the shift of εc to higher strains and the broadening of the -1 maximum. The magneto-elastic 10 damping curves (fig. 5) were found to fit eq. 3 and 5 obtaining the parameters tg αME (eq. 3) for ε < εC -2 and B (eq. 5) for ε>εC, as shown in 10 fig. 5. water cooling In fig. 6 tg (αME) is plotted versus cooling in air furnace cooling (HcJs)-2 for all investigated specimens. -3 10 εp=2% A great slope tends to be observed for samples with high carbon contents εp=4% and a lower slope for samples with -5 -4 -3 10 10 10 lower carbon contents. Following eq. ε 7, the difference between the slopes can only be due to different saturation Fig. 5. Influence of heat treatment and additional cold magnetostrictions of the according rolling on the amplitude dependent magneto samples. The magnetostrictions of the mechanical damping for the alloy Fe – 10 Al - samples listed in table 1 can not 0.2 C: tg αME = 0.002 B = 1.72 x 10-9 represent support this point of view. This fact is not surprising because these saturation the fitted curves. magnetostrictions were measured in longitudinal direction and depend seriously on the texture of the individual sample [9] because saturation magnetostriction is well known as a very anisotropic property becoming extreme in special crystallographic directions like [100] or [111]. But only the according extreme values for the saturation magnetostriction (which could not be obtained in this investigation) and the domain wall configuration are relevant for the magneto-elastic effect and therefore also for the amount of magneto-elastic damping.

Solid State Phenomena Vol. 137

Fe-10Al-0.2C Fe-10.4Al-0.19C furnace cooling furnace cooling cooling in air cooling in air water quenching

135

Fe-10.4Al-0.006C furnace cooling cooling in air water quenching

Fe-10.7Al-0.005C furnace cooling water quenching

-8

3000

1,0x10

B

tg αME

2000 -9

5,0x10

1000

0,0

0 0,0

-3

0

2,0x10 -2

3 -2

(HcJs) in (J/m )

20

40

60

HcJs in J/m

3

Fig. 6. Slope tg (αME) of the magneto-elastic damping curve for strains smaller than the critical strain against reciprocal square of HcJs. Constant B of the damping curve for strains higher than the critical strain against HcJs. There is moderate but slightly better correlation between the parameter B and HcJs for all carbon contents also shown in fig. 6. From eqs. 4 and 5 a proportionality between B and HcJs can be expected. The better correlation can be explained by the lower role of the saturation magnetostriction in case of B. The correlation is only moderate because the equations do not include the individual domain wall configuration. An increase of the grain size in the investigated heat treated samples leads to a qualitatively expected decrease of coercivity (see table 1) and therefore to an increase of magneto-mechanical damping. The coercivity caused by grains is reciprocal to the grain size. If HC0 is the coercivity of the single crystal and C is a constant [8, 10 and 20], equation (8) holds:

H c= H c 0 +

C d

(8)

Additional factors like dislocation density and internal stresses, affect the coercivity of the alloys, as well. These factors prevail in case of cold rolled specimen. Moreover other unknown micro-structural factors like small precipitates and ordered domains in the order of domain wall thickness increase the coercivity. Conclusions The results confirm that water cooling suppresses ordering in Fe – 11 % Al alloys while cooling in air or in the furnace provokes D03–type ordering. More slowly cooled specimens are characterised by higher damping capacity and these specimens are magnetically softer compared with the water-quenched or plastically deformed ones. The dependence of magneto-elastic damping on temperature is mainly governed by the temperature dependence of the saturation magnetostriction.

136

Interaction between Defects and Anelastic Phenomena in Solids

Correlation between magnetic properties and magneto-elastic damping expected by a very simple model could only partially be confirmed. Improvement of the model by considering anisotropy and domain wall configuration is necessary. Acknowledgement The authors are grateful to Dr. I. B. Chudakov for the studied specimens and discussions. References [1]

O. Kubaschewski: Iron – binary phase diagramm (Springer Verlag, Berlin 1982).

[2]

R. G. Baligidad, U. Prakash, V. Ramakrishna, P. K. Rao, N. B. Ballal: ISIJ. Vol. 36 (1996), p. 1453.

[3]

L. Falat, A. Schneider, G. Sauthoff, G. Frommeyer: Intermetallics. Vol. 13 (2005), p. 1256.

[4]

A. Schneider, L. Falat, G. Sauthoff, G. Frommeyer: Intermmetallics. Vol. 13 (2005), p. 1322.

[5]

V. A. Udovenko, I. B. Chudakov: ASTM Spec. Tech. Publ. Vol. 1304 (1997), p. 204.

[6]

I. S Golovin: Key Eng. Mat. Vol. 319 (2006), p. 225.

[7]

M. S Blanter, I. S. Golovin, H. Neuhäuser, H.-R. Sinning: Internal Friction in Metallic Materials. Handbook (Springer, 2007).

[8]

W. Riehemann: Metallische Werkstoffe mit extremer innerer Reibung und deren Messeung (Papierflieger, Clausthal-Zellerfeld 1994).

[9]

B. D. Cullity: Introduction to magnetic materials (Addison-Wesley, 1972).

[10] R. D. Adams: J. Phys. D Vol. 5 (1972), p. 1877. [11] S. A. Golovin, S. I. Arkhangelskij: Problemi Prochnosti (in Russian). Vol. 5 (1971), p. 120. [12] I. S. Golovin, T. V. Pozdova, S. A. Golovin: Met. Sci. Heat Treatm (in Russian). Vol. 40 (1998), p. 134. [13] J. Göken, W. Riehemann: Technisches Messen. Vol. 68 (2001), p. 535. [14] M. Pott-Langemeyer, W. Riehemann, W. Heye: Anales de Fisica. B Vol. 86 (1990), p. 232. [15] D. Ramin and W. Riehemann: TM, Vol. 3 (2001), p.116. [16] A. V. Granato, K. Lücke: J. Appl. Phys. Vol. 27 (1956), p. 583. [17] F. Förster, W. Köster: Naturwiss. Vol. 25, (1937), p. 436. [18] I. S. Golovin: Met. Mat. Trans. A Vol. 25A (1994), p. 111. [19] X. Young-Gang, L. Ning, S. Bao-Luo, H. Hong-Xin: Mat. Sci. Eng. A Vol. 447 (2007), p. 163. [20] L. J. Dijkstra: Advanced Semiconductor Materials (Cleveland, Ohio 1954), p. 20.

Solid State Phenomena Vol. 137 (2008) pp 137-144 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.137

Influence of thermal cycling and equivalent heat treatment on amplitude dependence of internal friction in Cu – Al - Mn shape memory alloys Agnieszka Mielczareka, Marcin Marczyk, and Werner Riehemannb Institute of Materials Science and Technology, Clausthal University of Technology, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany a [email protected], [email protected]

Dedicated to Prof. Trojanová on the occasion of her life jubilee Keywords: Thermal fatigue, Cu – Al - Mn, Shape memory alloys, thermal cracks.

Abstract. The influence of thermal cycling between - 196 °C and 200 °C and equivalent heat treatment at 200 °C on the amplitude dependence of internal friction at room temperature has been studied in as cast Cu – Al - Mn shape memory alloys with different chemical compositions. Using X-ray diffraction one composition was found to be austenitic and two others martensitic with two martensite types (2H and 18R) at room temperature. All specimens were thermally cycled for 100 times. During one thermal cycle the specimen underwent altogether two phase transformations one in each direction. Thermal cycling causes microstructural changes in the specimens due to atomic reordering, thermal stresses, which are generated in the martensitic state due to the anisotropy of thermal expansion, or due to the nucleation and propagation of interphase cracks in parent phase. During repeated thermal cycling the transition peaks obtained in mechanical spectroscopy became narrower due to an enduring change of the microstructure and annealing effect at 200 °C. To compare between the effects of thermal cycling and heat treatment one martensitic specimen was annealed at 200 °C. For selected cycle numbers and heat treatment times the amplitude dependence of damping was measured at room temperature. The influence of thermal cycling of martensitic specimens on the damping level was found to be similar to the influence of heat treatment at 200 °C. It is most likely that the highest heat treatment temperature is more important for the amplitude dependence of damping than the temperature change during thermal cycling. Cracks due to thermal cycling were found in all cycled specimens. They have no significant effect on the amplitude dependence of damping of the martensitic samples, whereas some small influence could be observed in austenitic samples at room temperature. Introduction Cu – Al – Mn alloys can be developed as high damping metals making use of the shape memory effect, i.e. a stress induced thermoelastic martensitic transformation. It was already shown, that the damping of these shape memory alloys in as cast condition can be much higher in the technical relevant strain amplitude range than damping of commonly available high damping metals [1]. Future industrial application of high damping Cu – Al – Mn alloys is very probable because many mechanical problems can be solved by the passive damping of mechanical vibrations. Easy castability under air [2] and good mechanical properties make Cu – Al – Mn alloys very attractive for industrial applications, too. Depending on Al content and phase at testing temperatures the tensile strength is approximately 600 – 650 MPa, the yield strength 250 – 300 MPa, and the fracture strain can be adjusted to 7 % - 18 %. In this paper the influence of thermal cycling and of equivalent heat treatment on the amplitude dependence of damping at RT is described. Thermal and mechanical stability of shape memory alloys are important factors for technical damping applications. Below approximately 500 °C Cu – Al – Mn alloys have the order structure L21 (bcc), which transforms martensitically

138

Interaction between Defects and Anelastic Phenomena in Solids

to α’1 (3R - fcc), β’1 (18R-small martensite plates) or γ’1 (2H-large martensite plates) [3, 4] structures. In the Ramsdel notations [5] the numbers denote the number of the basal plane layers (planes distorted from austenite {110} type plane) in one period. R denotes rhombohedral and H hexagonal symmetry. The range of martensite phase existence depends on the average number of conduction electrons per atom (e/a ratio), being in the range of 1.4 - 1.5 for the investigated alloys. In this e/a range β’1 (18R), and γ’1 (2H) martensites are expected [3]. During the transition from martensite to austenite, the lattice transforms from hexagonal or rhombohedral symmetry (depending on the Mn composition) to body centred cubic crystal structure [6, 7]. These transformations involve a change in the packing density and cause microstructural changes in the material. Experimental procedures The investigated alloys were melt at 1150 °C Table 1. Chemical composition, e/a-ratio and transition under air at normal pressure, followed by temperatures of the investigated as cast alloys. casting in metallic mould preheated to 300 Name of alloy A MP1 MP2 °C, subsequently the alloys were cooled in Cu 81.4 83.8 80.4 air [8]. Fe was added for grain refinement. Chemical composition in wt. % Al The alloy was investigated in as cast 8.5 12.1 11.2 condition due to reasons of technical Mn 10.1 4.1 6.4 application of huge mechanical components Fe 2 which can not be homogenized before Valence electron’s e/a 1.4 1.49 1.46 application. After casting and thermal concentration/atom cycling the transition temperatures Mf, As, Transition Measuring Number of Ms and Af (M and A for martensite and temperatures method cycles N Af in °C DSC 0 22 96 90 austenite and indexes s and f for start and finish, respectively) were determined by Ms in °C DSC 0 6 43 43 differential scanning calorimetry DSC As in °C DSC 0 -4 40 40 (DSC2920, TA Instruments, New Castle, Mf in °C DSC 0 -59 30 22 cooling and heating rate 5 K/min). Changes in internal friction spectra during thermal cycling were measured with dynamic mechanical analysis DMA (DMA2980, TA Instruments, New Castle, heating and cooling rates 2 K/min). The applied temperature range was - 100 °C to 200 °C. The samples with dimensions of 17 x 10 x 2 mm3 were single clamped at one end, and cantilevered in the DMA instrument, the measuring frequency was 1 Hz. The amplitude at the free end of the cantilever was adjusted to 5 µm resulting in a maximum strain amplitude of 2.4 x 10-4. In Table 1 the chemical compositions, e/a ratios and the transition temperatures of the investigated as cast alloys are listed. The names are given according to the major phases of the alloys at room temperature. “A” means austenitic and “MP” means multiple phase. X-ray analyses were made with Siemens diffractometer (Co tube, λ (Co Kα1) = 1.789 Å). X-ray measurements were done at room temperature in the range 2Θ = 10° to 140°. The alloy A was found to be austenitic with bcc phase, whereas in alloys MP1 and MP2 two types of martensite (2H and 18R) and small amounts of bcc phase were found at RT. Alloys A, MP1 and MP2 were thermally cycled for all together 100 times. The specimens were thermally cycled in the range from – 196 °C to 200 °C (see Fig. 1). One thermal cycle means that the specimen had been cooled from room temperature (RT) to - 196°, was held there for 5 min, then subsequently was heated to 200 °C (being lower than the recrystallization temperature), was held there for 5 min, and cooled to RT again. Two specimens of alloy MP2 were used: MP2A and MP2B. MP2A was thermally cycled and MP2B was heat treated at 200 °C for all together 500 minutes being also the collective time at 200 °C for the cycled specimen MP2A. The amplitude dependence of the damping was always measured at RT after the finished cycle. The amplitude dependence of the

Solid State Phenomena Vol. 137

139

T in °C

T in °C

damping δ (ε) is a sum of the damping background δ0 and δH (ε), which is due to hysteretic effects. Internal friction versus maximum strain amplitude was measured at RT in vacuum (10 Pa) as the logarithmic decrement δ of free decaying vibrations of a single clamped vibrating beam. The samples with a vibrating kept for 5min length of 97 mm, a width of 10 mm, a) 200 and a thickness of 2 mm were clamped into the damping apparatus 100 damping measuerement and excited to resonant bending 0 vibrations with resonant frequencies -100 in the range 38 - 63 Hz depending on -200 the mass at the end of the bending 1 cycle time b) 80min 75min 100min 80min 165min beams. After that, the excitation was 200 stopped, the decaying amplitudes 100 were measured and the strain amplitude dependence of damping 0 was calculated. The investigated damping measuerement time strain amplitude range was 10-6 - 10-3. More details about the used damping Fig. 1. Schematic diagrams of the a) thermal cycling apparatus are given in refs. [9, 10]. and b) heat treatment. Light optical micrographs of the cycled alloys in various conditions 0,20 were produced by conventional peaks during peaks during cooling metallographic techniques. heating

tan φ

0,15

0

10 1 10 2 10

Results and discussion

Fig. 2 shows the changes of the transition peaks during thermal cycling obtained by DMA for 0,05 specimen MP2A. With increasing number of thermal cycles the 0,00 transformation peaks during heating -40 0 40 80 120 160 200 and cooling in one thermal cycle T in °C became narrower and converged. The direct transformation temperatures are Fig. 2 Changes of the internal friction spectra for selected essentially unchanged, or at least thermal cycles determined by DMA with 2 K/min much less affected by thermocycling heating/cooling rate, max strain amplitude than the reverse ones. This behaviour 2.4 x 10-4, vibration frequency 1Hz. was found in DSC measurements as well which is contrary to the results of Wang et al. [11], who measured the effect of thermal cycling in CuAl11.9Mn2.5 (wt. %) alloy and found out, that the transition temperatures did not change with increasing numbers of thermal cycles. The changes can be explained with the fact, that the specimens of Wang were homogenized, whereas specimens in present specimens are as cast. Thermocycling might affect the structure both due to the variations of the temperature (thermal stresses are generated in the martensitic state due to the anisotropy of thermal expansion), and due to the martensitic transformation itself. Fig.3 a shows the amplitude dependence of damping for austenitic alloy A after different numbers of thermal cycles N. The basic effect of thermal cycling demonstrated by Fig. 3 a is due to the amplitude-independent background δ0. Except of some very small maxima δH (ε) is essentially unchanged. Due to the cycling treatment up to 40 cycles a decrease of the logarithmic decrement for 0,10

140

Interaction between Defects and Anelastic Phenomena in Solids

all strain amplitudes was found. This can be explained by the cumulative blocking of dislocations by other dislocations due to their small irreversible movement during thermal cycling [11, 12]. For N > 40 the damping increases again in the whole strain amplitude region and some small maxima develop which is presumably caused by cracks. Similar effects were found for other bulk and foam materials, for example in [14]. On the damping curve for N = 100 a distinct maximum develops at a strain amplitude 2 x 10-5. This maximum could be also due to the nucleation, opening and growth of cracks in the material during thermal cycling and be explained like it has been done in ref. [13]. This interpretation could be supported by the fact, that cracks were found in the thermally cycled material (Fig. 3b). With increasing number of cycles damping can increase due to the propagation of old or the nucleation of new cracks [13 - 15]. In Fig. 4 a the strain dependence of the damping δ (ε) of specimen MP1 after different numbers of thermal cycles is shown. Already after the first thermal cycle a maximum at strain amplitude of about 10-4 has developed [1]. The oscillatory movement of phase and twin boundaries [1], here mostly intermartensite boundaries, is presumably the reason for the high damping. Therefore, at the critical strain amplitude (εc ), where the damping steeply increases, stress controlled energy 0,005

0,25 0,20

0,004

δ 0,002

0,001

-5

10

-4

10

-3

10

0,15

δ

N=0 N =1 N=7 N=20 N =40 N =60 N =100

0,003

N=0 N=1 N=7 N = 20 N = 40 N = 100

0,10 0,05 0,00

-5

-4

10

ε

10

10

-3

ε

Fig. 3 a. Amplitude dependence of damping of Fig. 4 a. Amplitude dependence of damping of the alloy A after different numbers of the alloy MP1 after different numbers thermal cycles N. of thermal cycles N.

as cast

N=100

Fig. 3 b. Microstructures of alloy A in as cast state and after 100 thermal cycles.

as cast

N=100

Fig. 4 b. Microstructures of alloy MP1 in as cast state and after 100 thermal cycles.

consuming oscillatory phase transition between martensites or austenite and martensite begins. A maximum in δ (ε) appears due to the smaller increase of the mechanical energy ∆W dissipated in one cycle, being proportional to the displacement of twin and phase boundaries, compared with the increase of the total energy W for higher strain amplitudes. The microstructural changes of specimen MP1 due to thermal cycling are shown in Fig. 4 b. Before cycling the specimen is prevailing martensitic. Mf was measured to be 38 °C by stress free

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DSC. However in this specimen two types of martensite (2H and 18R) were found by X-ray analysis, so intermartensite boundaries are available for damping of mechanical vibrations, too. After 100 thermal cycles interphase cracks have developed in the austenite during thermal cycling and are well visible in the microstructure. During one thermal cycle the highest temperature was 200 °C for 5 minutes. To distinguish between the effects of thermal cycling and annealing heat treatment another martensitic specimen MP2B was heat treated at 200 °C for various times as schematically shown in Fig. 1 b. So the specimen MP2B had been heat treated for all together 500 minutes, corresponding to the heat treatment time of 100 thermal cycles. The results are shown in the Fig. 5. It can be seen, that already after 80 minutes (corresponding to 16 thermal cycles) a maximum develops. The δ (ε) curves for specimens MP1 and MP2B look similar to the ones measured after homogenisation heat treatment (850 °C, 1h) [1]. The critical strain amplitudes and the maxima in logarithmic decrement, which were obtained during thermal cycling and heat treatment are compared in Fig. 6. The curves of critical strain amplitude against number of thermal cycles for MP1 and of critical strain against heat treatment time for MP2 are similar. Except of the first 10 thermal cycles or 50 minutes, respectively, which have not been measured, obtained differences are only small. Therefore it can be concluded that the heat treatment at 200 °C affects the amplitude dependence of damping much more than the repeated phase transformations due to thermal cycling for the investigated number of cycling range. The effect of decreasing critical strain amplitude and increasing maximum damping is opposite to the effects observed in Cu – Al – Mn alloys during ageing at room temperature after homogenization heat treatment (at 850 °C for 1 hour with subsequent water quenching) [1], where the critical strain amplitude shifts to smaller strains after homogenization and increased with increasing ageing time. The experimental results indicate that the stress induced transformation of martensite variants could lead to a similarly high or even higher damping than the austenitemartensite transformations, which were presented in ref. [1]. t in min

0,35

0,15

300

400

1

εc δmax

εc δmax

0,15

500

thermal cycling

0,10

0,10

0,1

δmax

δ

0,20

200

3

0,25

100 heat treatment

εc x 10

0,30

0,20

0 min 80 min 155 min 320 min 420 min 500 min

0

0,05

0,05 0,00

0,00 -5

-4

10

10

-3

10

0,01 0

20

40

60

80

100

number of cycles

ε

Fig. 5. Amplitude dependence of damping of alloy MP2 after different times of heat treatment at 200 °C.

Fig. 6. Critical strain amplitude and maximum damping versus number of thermal cycles for sample MP1 and versus time of heat treatment at 200 °C for sample MP2.

Cracks, which are visible in the micrographs shown in Figure 3 b and 4 b can propagate either during thermal cycling due to martensitic transformation, or during the damping measurements due to mechanical fatigue. On the other hand no cracks have been found in the only heat treated sample (MP2B). This leads to the conclusion that only thermal cycling due to repeated forwards and reverse martensitic phase transformations is responsible for the found cracks. Hornbogen stated in ref. [16]

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Interaction between Defects and Anelastic Phenomena in Solids

that not only mechanical cycling but also lattice transformations can be considered as an early state of fatigue, and can cause nucleation and propagation of cracks. In martensite state the cracks can be easily nucleated but they can not propagate fast, because they interact shielding between themselves [16, 17]. Cracks can propagate much easier in austenite or during reordering of atoms i.e. martensitic transformation. Conclusions The direct transformation temperatures are essentially unchanged, or at least much less affected by thermal cycling than the reverse ones. The small damping of austenitic samples at room temperature is only slightly changed by thermal cycling. The small decrease of damping until 40 thermal cycles can be explained by dislocation blocking - an effect which is known as training in fatigue experiments. The increase of damping associated with the formation of small maxima following with further increasing number of thermal cycles can be explained with the opening or propagation of old or the nucleation of new cracks. The same thermal cycling treatment increases damping in the region of martensite variants (T < Mf) for low cycling numbers up to 40. This effect is much stronger than the cracks influence which therefore can not be detected during damping measurements in the martensite variant range. The increase of damping in this case is mainly due to the associated heat treatment and not the repeated phase transformations during thermal cycling. Acknowledgements The authors are very grateful to Prof. Babette Tonn and Dipl.-Ing. Sönke Vogelgesang (IMet, Technical University Clausthal, Germany) for casting of the investigated alloys. This work is supported by Deutsche Forschungsgemeinschaft (DFG). References [1]

A. Mielczarek, W. Riehemann, S. Vogelgesang, H. Zak, B. Tonn: Key Engineering Materials. Vol. 319 (2006), p. 45.

[2]

G. Zak, A.C. Kneissl, G. Zatulskij: Script. Mat. Vol. 34 (1996), p. 363.

[3]

R. Kainuma, S. Takahashi, K. Ishida: J. Phys. IV Vol. 5 (2001), p. C8-961.

[4]

J. Dutkiewicz, H. Kato, S. Miura, U. Messerschmidt, M. Bartsch: Acta Mater. Vol. 44 (1996), p. 4597.

[5]

X. Gao, M. Huang, L.C. Brinson: Int. J.Plast. Vol. 16 (2000), p. 1345.

[6]

Y. Sutou, T. Omori, T. Okamoto, R. Kainuma, K. Ishida: J. Phys. IV Vol. 11 (2001), p. Pr8185.

[7]

R. Kainuma, S. Takahashi, K. Ishida: Met. Mat. Trans. Vol. 27A (1996), p. 2187.

[8]

S. Vogelgesang, H. Zak, B. Tonn, A. Mielczarek, W. Riehemann: Int. Found. Res. Giessereiforschung. Vol. 59 (2007), p.2.

[9]

J. Göken, W. Riehemann: Technisches Messen. Vol. 68 (2001), p. 535.

[10] A. Mielczarek: Werkstoffe mit Maxima in ihrer isothermen dehnungsabhängigen Dämpfung, PhD thesis (Papier Flieger, Clausthal-Zellefeld 2007). [11] Q. Z. Wang, F. S. Han, Q. Wang: phys.stat.sol. Vol. (a) 201 (2004), p. 2910. [12] J. Font, J.Muntasell, J. Pons, E. Cesari: J. Mater. Res. Vol. 12 (1997), p. 2288. [14] J. Göken, W. Riehemann: Mater. Sci. Engn. A Vol. 370 (2004), p. 417.

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[13] Z. Trojanova, A. Mielczarek, W. Riehemann, P. Lukac: Comp. Sci. Tech. Vol. 66 (2006), p. 585. [15] J. Kiehn, K. U. Kainer, P. Vostrý, I. Stulíková: phys. Stat. Sol. Vol. (a) 161 (1997), p. 85. [16] E. Hornbogen: Legierungen mit Formgedächtnis (Westdeutscher Verlag, Opladen 1991). [17] E. Hornbogen: Fatigue Fracture Mat. Structure. Vol. 25 (2002), p. 785.

Solid State Phenomena Vol. 137 (2008) pp 145-154 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.145

Mechanical and fatigue properties of Cu - Al - Mn shape memory alloys with influence of mechanical cycling on amplitude dependence of internal friction at room temperature Agnieszka Mielczarek1,a, Werner Riehemann1,b, Sönke Vogelgesang2,c, Babette Tonn2,d 1

Institute of Materials Engineering and Technology, Clausthal University of Technology, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany 2

Institute of Metallurgy, Clausthal University of Technology, Robert-Koch-Str. 42, D-38678 Clausthal-Zellerfeld, Germany a

[email protected], [email protected], c

d

[email protected], [email protected]

Keywords: Cu – Al - Mn, High Damping Materials, Shape memory alloys, mechanical and fatigue properties.

Abstract. The mechanical and fatigue properties of Cu - Al - Mn shape memory alloys with different phase fractions at room temperature were investigated. The specimens with different chemical compositions (Al: 8.9 - 12.5 wt. % and Mn: 3.3 - 9.3 wt. %) were tensile loaded with 10-3 s-1 tensile strain rate. Austenitic specimens have the highest tensile strength and fracture strain. Yield strength, tensile strength and elongation of martensitic alloys were lower compared with austenitic alloys. Fracture strain of martensitic alloys depend only little on the chemical composition. Specimens of martensitic, austenitic and three different multiple phase specimens were tested in the high cycle fatigue range at room temperature. The Woehler curves for multiple specimens depend on the phase fraction at testing temperatures. Different elements as Co, Ni, Fe and Si were alloyed to CuAl11.6Mn5. All decreased the ductility of the specimens, and their fatigue properties. Maxima could be detected in the strain amplitude dependence of damping for multiple phase specimen. These maximum are shifted to lower damping and to higher strains with increasing number of mechanical cycles, compared to the as cast condition for not cycled specimen. The strain amplitude dependence of damping in martensitic and austenitic Cu – Al – Mn shape memory alloys does not change much during mechanical cycling. Introduction Damping in materials can increase strongly, when fatigue cracks are present and propagate [1 - 4]. Strain amplitude dependence of internal friction of materials with cracks is similar to damping, which is measured during stress induced martensitic transformation or during the motion of phaseand twin boundaries in shape memory alloys [4 - 7]. In both cases a maximum appears in the strain amplitude dependence of damping δ(ε) [1, 4, 5]. Therefore, it is interesting, how the fatigue affects damping (δ (ε)) and Young’s modulus of shape memory alloys. High life times are expected for most of the high damping SMA [8]. Defects, which are caused by mechanical cycling, can change the transition temperatures, and therefore the damping level, as well. Corresponding literature about the influence of mechanical cycling is rare and could not be found for Cu – Al - Mn shape memory alloys at all. Fatigue properties of pseudo elastic Cu – Al - Mn alloys were detected for single crystals, for which the periodic cycling increases the critical strain εc amplitude (or critical stress amplitude σc) where the stress induced phase transition starts [9]. The advantages of the Cu – Al - Mn shape memory alloys (SMA), compared with common

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Interaction between Defects and Anelastic Phenomena in Solids

metals, are good strength, very high damping and shape memory effects. Cu - Al - Mn are cheaper to produce comparing to widely used TiNi shape memory alloys, because there is no need to vacuum cast. The transition temperatures can be adjusted from - 180 °C until 230 °C [10 - 11] by the alloying contents, the casting conditions or subsequent heat treatment. For low aluminum contents the alloys are ductile and can be cold worked [12]. Additionally the Mn-rich Cu – Al - Mn alloys have better castability, due to their lower melting temperatures [13]. The lattice transition between martensite and austenite can be caused by temperature changes or by stress loading i.e. shape memory alloys can be fatigued by thermal and mechanical cycling. Cracks due to thermal cycling were found in all cycled specimens as is reported in another paper of this volume. Cracks have no significant effect on the amplitude dependence of damping of the martensitic samples, whereas some small influence could be observed in austenitic samples at room temperature. For this paper the mechanical and fatigue properties and the influence of mechanical cycling on the amplitude dependence of damping δ (ε) were investigated. Experimental The investigated alloys were obtained by melting copper (99.99 wt. %), aluminium (99.7 wt. %) and manganese (99.85 wt. %) in a mid-frequency induction furnace in normal atmosphere, followed by casting in metallic moulds preheated to 300 °C, subsequently the alloys were cooled in air. The chemical compositions of the alloys were determined by inductively coupled plasma spectroscopy (ICP) [14]. In the Table 1 the chemical Table 1. Chemical composition, phases at RT and transition temperatures obtained by DSC of the investigated compositions, phases at room alloys. Relevant transition temperatures for the phases temperature and the transition present at RT after casting are martensite finish MF temperatures of the investigated alloys are listed. After casting the and martensite start MS. specimens were cooled, so MF MS AS AF Alloy composition Phases martensite start (MS) and in wt. % at RT* in °C in °C in °C in °C martensite finish temperature CuAl11.6Mn5 M 20 45 55 90 (MF) determine the phases present Cu11.3Mn6.4Fe2 M 20 43 40 90 at room temperature. Austenite CuAl12.5Mn3 M 80 140 120 200 start temperature (AS) and CuAl11.5Mn4.8 MA1 0 42 62 100 austenite finish temperature (AF) CuAl12.7Mn3,3 MA1 6 28 26 45 are relevant for the phases present CuAl11.7Mn4.6 MA2 -10 18 41 60 at room temperature after heating CuAl10.9Mn6.7 MA2 -20 20 0 136 from lower temperatures. CuAl11.9Mn4.3 MA3 < - 20 15 11 50 After casting the transition CuAl12.1Mn4.9 A -50 -27 -35 -8 temperatures MF, MS, AS and AF, CuAl8.2Mn10 A -20 which are listed in table 1, were CuAl8,9Mn9,3 A -10 18 measured by differential scanning CuAl9.4Mn5.7Ni4 A -25 calorimetry (DSC) using a DSC 2920 (TA Instruments, New *M martensite; MA1 multiple phase: MF 0.02) is not very reliable. Nevertheless, it is clear that the peak shifts to higher temperature with increase in frequency, which makes hypothesis about recrystallization related mechanism of the IF peak untenable. -1

Q 0,03

f ~ 1 Hz f ~ 180 Hz f ~ 430 Hz

0,02 0,01 0,00

50

100

150

200 T, oC

Fig. 2. The TDIF for AZ31 alloy after ECAP-1 at different frequencies. Since calculation of the activation energy by the frequency – temperature shift (Arrhenius plot) is not possible due to lack of reliable data, the activation energy (H) of the mechanism controlling this peak was estimated by Wert-Marx equation [13] as H = 1.25 eV

H = RTmax ln

kTmax + Tmax ∆S , hf max

where Tmax is the peak temperature; f max is the frequency at Tmax ; k is the Boltzmann constant; h is the Plank constant; ∆S is the entropy; R is the universal gas constant. This value of activation energy is only rough estimation. Nevertheless, the value obtained is close to the activation energy of

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Interaction between Defects and Anelastic Phenomena in Solids

the self-diffusion for Mg, which is 1.39 eV [14]) and also to values of activation energy of GB relaxation in non deformed Mg-based alloys: The GB peak in pure Mg (99.98 %) was obtained at 185 °C at 2 Hz with H = 1.38 eV [15]. For the AZ91 magnesium alloy aged at 200 °C for 80 h the IF peak at 165 °C at 1 Hz was referred to the GB sliding [16]. The activation energy of this peak could be determined as H =1.31 eV. Investigations of AZ91 in homogenized and as-cast state show a GB peak at ~ 150 °C at 1 Hz with H = 1.14 eV [14]. Therefore, the peak presented in Fig. 2 for AZ31 alloy is caused by grain boundary relaxation, too. Nevertheless, the effect of superposition with the IF background cannot completely excluded. The high-temperature IF background may be influenced by dynamic recrystallisation of ECAPed specimen during TDIF measurements which will decrease the high-temperature IF background. To check this influence, the time dependent IF of AZ31 alloy after 1 and 4 passes of ECAP was measured during 160 min at 120 °C and during 260 min at 140 °C, respectively (Fig. 3). In both cases the value of IF was not changed during isothermal annealing. Consequently, the effect of dynamical recrystallisation at 120 - 140 °C does not play significant role.

-1

Q

enter -70text

0

70

140

τ, s

-1

Q

-1

Q

0,015

-200 âì-100 ëäæðî 0

100 200 τ, s

-1

Q

0,032

0,032

0,024

0,024

0,016

0,016

0,008

0,008

0,015

0,010

0,010

0,005

0,005

0,000

ãíïòíå ã

50

o 100 T,150 C 200

250

0,000

50

100

o 150 T, 200 C 250

b a o Fig. 3. TDIF at 120 and 140 C (~ 1 Hz) for AZ31 alloy after 1 (a) and 4 passes (b) of ECAP. -1

-1

Q -Qb

0,03

1 pass of ECAP (1) o (1) + 340 C (2) o (2) + 420 C, 20 min

-1

b

0,06

f ~ 1 Hz 4 passes of ECAP (1) o (1) + 200 C, 1 h (2) o (2) + 400 C, 1 h

0,04

0,02

0,02

0,01

100 Fig.

-1

Q -Q

f ~ 180 Hz

200

300

o

0,00

T, C

4. TDIF (after background (Qb-1) subtraction) in three subsequent runs after ECAP-1 (frequency ~ 180 Hz).

Fig.

5.

50

100

150

o

200 T, C

TDIF (after background (Qb-1) subtraction) in three subsequent runs after ECAP-4 (frequency ~ 1 Hz).

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Fig. 4 and 5 shows TDIF in three subsequent runs after one and four ECAP processes, respectively. It is seen that the influence of annealing temperature on the IF high-temperature background takes place at higher temperatures: the background decreases with increase in the annealing temperature as the result of decrease in dislocation density and grain growth. To find out contribution of recrystallisation to this process microstructures were studied. Microstructure The AZ31 specimens were annealed 1 h at 250 °C and at 400 °C in a furnace with argon inert atmosphere and quenched in water of ambient temperature afterwards. After annealing of ECAP-1 specimen (the mean grain size is 4.8 ± 4.1 µm) for 1 h at 250 °C an average grain size of 6.5 ± 3.6 µm is measured (Fig. 6 a). Some grains are deformed and shear bands have evolved, but also areas with equiaxed and round grains exist whereas the rounded grains can be observed at the junctions of larger grains which is in agreement with literature [17]. Annealing at 250 °C affects the initial microstructure after ECAP-1 only slightly which was also observed by IF (Fig. 5). a)

25 µm

b)

25 µm

Fig. 6. Micrographs of ECAPped-1 AZ31 after annealing at a) 250 °C and b) 400 °C. Micrographs were taken in ECAP direction.

number of grains

After annealing at 400 °C (Fig. 6 b) a homogeneous microstructure is obtained with a mean grain size of 9.7 ± 6.3 µm. In contrast with the before mentioned micrographs some twins are observable. Appearance of twins is limited to temperatures lower than 200 °C [18]: these twins should already be seen after ECAP which is not obvious from Fig. 1. The graphical analysis of the grain size distribution after ECAP-1 (Fig. 7) confirms the broad grain size distribution by recrystallisation. ECAP-1 50 When an annealing at 250 °C is performed all fitted data grains seem to grow uniformly. After a heat 1h at 250°C 40 treatment of 400°C a broad grain size distribution fitted data is received which is explicable by a stronger 1h at 400°C 30 growth of small grains at this temperature. fitted data After ECAP-4 a fine grained microstructure 20 with a mean grain size of 2.7 ± 1.9 µm can be observed (Fig. 1 d). The microstructure is 10 crossed by bands of very small grains of about 1 µm. This leads to an irregular grain growth after heat treatment at 250 °C which is visible in 0 5 10 15 20 Fig. 8 a. The mean grain size in this case is 3.3 ± grain size in µm 2.6 µm. The inhomogeneous microstructure also occurs when the sample is exposed to a Fig. 7. Grain size distribution in AZ31 after temperature of 400 °C (Fig. 8 b): a mean grain ECAP-1 and annealing at 250 °C and 400 °C. size is 6.7 ± 3.9 µm.

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Interaction between Defects and Anelastic Phenomena in Solids

a)

b)

25 µm

25 µm

Fig. 8. Micrographs of AZ31 alloy in ECAP-4 after heat treatment at a) 250 °C and b) 400 °C. Micrographs were taken in ECAP direction. The graphical analysis of the grain size distribution after ECAP-4 (Fig. 9) verifies that very small grains in the microstructure developed by forming. In case of annealing at 250 °C the small grains have grown but areas with small grains still exist. After annealing at 400 °C a more intensive grain growth sets in which is dominated by the growth of especially small grains leading finally to an increasing homogeneity of the microstructure as shown in Fig. 8 b. as received fitted data 1h at 250°C fitted data 1h at 400°C fitted data

100 80 60

210 hardness HV1

number of grains

120

40 20 0

180

initial 250°C 400°C

ECAP 1 250°C 400°C

ECAP 4 250°C 400°C

150 120 90 60 30

5

10

15

20

0

grain size in µm Fig. 9. Grain size distribution after ECAP-4 and Fig. 10. Hardness development of AZ31 alloy annealing at 250 °C and 400 °C. by ECAP and following annealing. The evolution of the microstructure during ECAP can be explained by continuous recovery, recrystrallisation and growth which are active during multiple ECAP process [18]. In Fig. 10 the hardness of the specimens after ECAP and annealing, respectively, is plotted. It shows that a significant increase of the hardness by ECAP to grain size reduction is observable in agreement with [19]. After ECAP-4 the hardness is higher than after ECAP-1. While the annealing of the sample in pre-deformed state is negligible, it leads to a reduction of the hardness in all other cases. The hardness of the ECAPed samples after annealing at 400 °C is similar to that received for the undeformed one. Summary An internal friction peak with the activation energy ~ 1.25 eV (170 oC at ~ 1 Hz) was found in AZ31 alloy subjected to ECAP. It is proved that this peak is the relaxation, most probably, the grain

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boundary peak while the change of high-temperature background is strongly affected by recrystallization process. Acknowledgement The author’s whish to thank Prof. J. Estrin for studied materials and Mr. A. Schabacker for help in metallographic work. Parts of this paper are based on investigations of the collaborative research center SFB/TR TRR 30 which is kindly supported by the Deutsche Forschungsgemeinschaft (DFG). References [1] B. Q. Han, E. J. Lavernia, F. A. Mohamed: Metall. Mater. Trans. A Vol. 35A (2004), p. 13431350. [2] I. S. Golovin, in: Internal friction method in material science researches (in Russian), edited by M. S. Blanter, and Y. V. Piguzov (Metallurgizdat, Moscow 1991), p. 133-146. [3] I. S. Golovin, S. A. Golovin: High damping alloys, a review (in Russian). Ferrous Metallurgy. Vol. 5 (1989), p. 7-30. [4] J. Göken, J. Swiostek, D. Letzig, K. U. Kainer: Mater. Sci. Forum. Vol. 482 (2005), p. 387-390. [5] A. Bussiba, A. Ben Artzy, A. Shtechman, S. Ifergan, M. Kupiec: Mater. Sci. Eng. A Vol. 302 (2001), p. 56-62. [6] J. Zhang, R. J. Perez, C. R. Wong, E. J. Lavernia: Mater. Sci. Eng. R Vol. 13, No. 8 (1994), p. 325-389. [7] T. S. Kê: Phys. Rev. Vol. 71 (1947), p. 533. [8] M. A. Krishtal, Y. V. Pigusov, S. A. Golovin: Internal friction in metals and alloys (Metallurgizdat, Moscow 1964). [9] M. S. Blanter, I. S. Golovin, H. Neuhäuser, H. R. Sinning: Internal friction in metallic materials. A Handbook (Springer, 2007). [10] I. N. Fridliander, O. G. Senatorova, O. E. Osintzev (Eds.): Non-ferrous metals and alloys. Composition metallic material. Vol. II-3 (2001). [11] S. A. Golovin, S. I. Arkhangelskij: Strength of Materials (in Russian). Vol. 5 (1971), p. 120124. [12] K. Bothe, H. Neuhäuser: Scr. Metall. Mater. Vol. 16 (1982), p. 1053. [13] A. S. Nowick, B. S. Berry: Anelastic relaxation in crystalline solids (Academic Press, New York 1972). [14] O. A. Lambri et al.: Scripta Materialia Vol. 45 (2001), p. 1365-1371; Phys. Stat. Sol. Vol. (a) 204 (2007), p. 1077-1092. [15] C. C. Smith, G. M. Leak: Internal friction and ultrasonic attenuation in crystal solids. Proc. 5th International conference. 1973. Aachen. Vol. 1. (1975), p. 383-391. [16] G. L. Hao, F. S. Han, Q. Z. Wang, J. Wu: Science Direct, Phisica B Vol. 391 (2007), p. 186192. [17] C. W. Su, L. Lu, M. O. Lai: Mater. Sci. Eng. A Vol. 434 (2006), p. 227-236. [18] K. Máthis, F. Chmelik, Z. Trojanová, P. Lukáč, J. Lendvai: Mater. Sci. Eng. A Vols. 387-389 (2004), p. 331-335. [19] K. Xia, J. T. Wang, X. Wu, G. Chen, M. Gurvan: Mater. Sci. Eng. A Vols. 410-411 (2005), p. 324-327.

Solid State Phenomena Vol. 137 (2008) pp 189-198 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.189

Study of PPV polymer layers on Si substrates by mechanical spectroscopy A. Strahl1,a, S. Schrader2,b, S. Katholy3, B. Grimm2, H. Neuhäuser4,c 1 2

Faculty of Engineering, Dept. of Engineering Physics, University of Applied Scienes Wildau 3

4

Institute of Didactics of Sciences, Dept. Physics, Techn.Univ. Braunschweig

Institute of Physics, Department of Condensed Matter Physics, University of Potsdam

Institute of Physics of Condensed Matter, Technical University of Braunschweig, Germany a

[email protected], [email protected], [email protected]

Keywords: OLED, PPV, polymer, thin films, structural relaxation, damping peaks.

Abstract. Thin layers of the OLED related polyphenylene-vinylene (PPV) deposited by a precursor on micro-fabricated Si cantilevers were studied by applying the vibrating-reed technique during repeated temperature cycling between 100 and 520 K. By means of the Langmuir-Blodgett method for film production, the dependence of damping and elastic modulus on well defined values of film thickness (16 to 69 nm) was determined. Simultaneous measurements of these quantities showed four damping peaks during heating around 130 K (called γ), 250 K (β), 350 K (β’), and 400 K (called C). Three of them (γ, β’, C) disappeared after heating to the highest temperature (520 K) indicating their presence in the precursor only. The activation parameters of the relaxation peaks (γ, β, β’) were estimated and assigned to specific atomic movements in the molecule. Peak C occurs during the conversion process of precursor to polymer. Earlier results are essentially substantiated, indicating only slight differences to those for layers produced previously by spin coating. The observed thickness dependence of damping for the γ and β peaks suggests a weaker contribution of molecules in the surface region than of those in the bulk, while the β’ peak is supposed to result from molecules in the interface region between layer and substrate. Introduction PPV (poly(1, 4-phenylene-vinylene)) is one of the semiconducting and electro-luminescent polymers that have gained much interest as operating material in organic light emitting diodes (OLEDs) in the form of thin films [1 - 4]. Their mechanical properties have not yet been widely studied although they will be important in applications, e.g. in flexible displays. The method of mechanical spectroscopy (classical name: internal friction [5, 6]) can be used to study with high resolution the elastic properties (Young’s modulus) and mechanical loss (damping of oscillations), as well as structural transformations during heating and long time annealing, i.e. during normal or accidental use of the material. Structural relaxations and transformations have been investigated by this method [7, 8] and by dielectric measurements in many kinds of polymers and are classified as types α, β, γ, and δ, where α is due to the glass transition (e.g., [9 - 12]), i.e. involves co-operative motion of chain segments of the polymer chain, while the others result from activated motion of smaller molecular units modulated by rotational or translational potential wells: β is due to a reversible motion of molecular groups like side chains or subgroups of the main chain [9 - 13], γ and δ result from the motion of small molecular moieties like end groups, additives, plasticizers etc. [9 - 12]. In addition, the present material shows a chemical reaction during its conversion from the soluble precursor poly {[1, 4-phenylene]-[1-(n-octylsulfinyl)ethylene]} to the insoluble PPV polymer poly (p-phenylenevinylene) via the following reaction, where the 1(oxidosulfanyl) octane molecule represents the volatile outgoing group:

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Interaction between Defects and Anelastic Phenomena in Solids

CH3 (H2C)7 S

O

O

T

+

n

n

n

S

(CH2)7 CH3

H

The present work continues an earlier study [14] mainly by investigating the dependence on PPV layer thickness and the influence of the film production method. Contrary to the spin coating method used in [14], the Langmuir-Blodgett method [15] is applied here to achieve rather well defined thickness variations of the film deposited onto Silicon substrates, which are selectively etched to produce single-ended fixed micro-cantilevers [16]. The behavior of the variation of their resonance frequency in flexural (or torsion) vibrations is followed for the Si substrate and for the coated Si specimens during heating/cooling programs; the variation of the resonance frequency is a sensitive measure of changes of Young’s modulus, and the simultaneously measured damping is used to determine the characteristic mechanical losses accompanying relaxation and transformation processes. Experimental details

Several cantilever resonators (thickness 30 µm) of different geometry, designed for flexural (and torsion) oscillations (typical basic frequencies 100 to 500 Hz, harmonics up to 20 kHz) and fixed to the outer wafer frame (25 x 25 mm2) of (001) oriented Silicon wafers (0.5 mm thickness) [14, 17], were produced by selective etching [16] with beam axis along [110]. Details about methods (electrostatic excitation, optical detection of vibrations by a laser beam reflected at the specimen surface) and data evaluation are described in [14, 17, 18]. The damping of the composite system (index c) and the background damping by the substrate (index s) are determined from the free decay of the amplitude to yield the damping, characterized by the loss angle Φ of the film (index f) according to [7, 19] for the case of film with thickness df on both sides of the substrate: E tan Φ f =  S' E  f

 d  S  6d f 

 (tan Φ c − tan Φ S ) + tan Φ c .  

(1)

where Es is Young’s modulus of the substrate, Ef’ is a modified Young’s modulus of the film assumed to stick firmly to the substrate (thickness ds) and therefore to deform according to the substrate’s Poisson ratio νs rather than to the film’s Poisson ratio νf [7]. Accounting for the transverse stress component, the relation to the true film modulus Ef is [19] E 'f = E f

(1 − 2ν f v s + v s2 ) 1 − v 2f

.

(2)The modified Young’s modulus E ’ can be determined from the eigen-frequencies f , f of comf c s posite and substrate, respectively, in free decay (or from the resonance frequencies) [20]  ρf d f 2−f 2 E 'f = E S  + s c 2 s fs  3 ρ s 6d f

   

with

 ρ   l 4 E S = 12 2s  ⋅   ω S2 d  z  s 

,

(3)

as the sample geometry and applied amplitudes justify the Euler-Bernoulli beam approximation (with obstructed transverse strain). Here ρ is the density of substrate (s) and film (f), respectively, l is the length of the vibrating reed, and z is a numerical factor characterizing the vibration mode (e.g., z = 1.8751 for the basic flexural frequency, z = 4.6941 for the first harmonic, z = 7.8648 for the second harmonic [5]).

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The PPV polymer with its luminescent properties is insoluble due to strong interactions of its π electrons. For production of thin films the starting material is a precursor with an appropriate side chain allowing the material to be dissolved in chloroform, toluene or other organic solvents. Contrary to the spin coating method used in [14], in the present work the PPV layers were produced by the Langmuir-Blodgett (LB) technique [15]: A LB trough filled with extremely clean water on whose surface a monolayer of PPV precursor has been deposited by spreading a few drops of the PPV precursor dissolved in chloroform. At a certain surface pressure, determined from the surface pressure isotherm of this monolayer, thin films of molecularly controlled thickness have been prepared by repeated dipping of the substrate into the LB trough, whereby monolayers have been deposited onto the substrates at every dipping cycle, and the surface pressure during layer deposition has been kept constant by a feedback system. So a deposition of 9 monolayers results in a film thickness of df = 16.6 nm, as measured by ellipsometry; 39 times dipping leads to a thickness of df = 33.6 nm, and 79 times dipping yields a film of df = 69 nm thickness (Tab. 1). Table 1. Results of layer thickness of the precursor phase and of the converted PPV film as measured by ellipsometry prior and after vibrating-reed measurements, i.e. prior and after the heat treatments. Specimen no.

Number of LB dips

409 408 418 407

9 39 39 79

Thickness precursor [nm] 16.5 – 16.8 33.5 – 33.6 35.2 – 36 69

Thickness conv. PPV [nm] 11.3 18.6

Decrease of thickness by conversion and anneal

29.9

56 % (Tmax = 530K)

32 % (Tmax = 450K) 46 % (Tmax = 530 K)

Scanning force microscopy (AFM) showed that during the conversion reaction which is starting near 400 K, the wavelength of surface roughness decreases, while its amplitude increases. The values for the precursor phase approach that of the Si substrate (wavelength several µm, amplitude about 2 nm), while the converted PPV layer exhibits a doubled roughness amplitude (2 – 4 nm) with distinctly smaller wavelength (0.1 – 0.3 µm). Nevertheless it can be considered as sufficiently smooth in view of the film thickness (16 – 69 nm). The vibrating-reed measurements have been performed in a vacuum chamber (< 10-5 mbar) where the specimen (micro-etched Si wafer substrate with resonator cantilevers without and with coating) is positioned inside of a furnace on a specimen holder which can be cooled down to 100 K by flowing liquid nitrogen through a channel inside the grip and is slowly heated at a fixed rate of 1 K/min from 100 K up to 520 K [14, 17, 18]. The cooling rate is usually around 1.5 K/min. Several heating and cooling cycles are performed, sometimes with increasing maximum temperature, without removing the specimen, in order to check the changes of the film in successive temperature intervals. The decrease of film thickness during conversion and during annealing is shown in Tab.1 and in one example of thermogravimetric measurements in Fig.1 (note the higher rate of temperature rise (10 K/min) in these measurements, which shifts the effects to higher temperature compared to the vibrating-reed measurements (1 K/min)). For further characterization of the PPV film properties, measurements by differential scanning calorimetry (DSC 121 – Setaram) [21] were performed using PPV precursor material (without Si substrate) placed in a closed aluminium sample pan avoiding loss of material during the measurements. For each heating rate a new PPV precursor specimen has to be used. Heating rates of 2, 5, 10.

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Interaction between Defects and Anelastic Phenomena in Solids

100 95

2. heating

Weight [%]

90

1. heating

85 80 75 70

Fig. 1. Example of thermogravimetric measurements of PPV precursor material (heating rate 10 K/min), showing the mass loss during the conversion reaction. The first heating was finished at 460 K; the second heating cycle up to 640 K (without removing the sample) indicates that the loss is not yet finished by conversion.

65 60 55 50 45

300

350

400

450

500

550

600

T [K] and 20 K/min are applied to perform a Kissinger analysis [22, 23], where the maximum temperature (about 650 K) certainly exceeds the conversion temperature. Results Vibrating-reed measurements: Young’s modulus and loss factor. Fig. 2 shows a typical course of the variation of the relative change of Young’s modulus Ef of a 35 nm PPV film according to eqs.(2, 3), with νs = 0.064 and νf assumed to be 0.33. We restrict ourselves here to relative values of the modulus, because absolute values of Ef are uncertain within up to ± 40 % mainly due to the uncertainty in film thickness and cantilever geometry, while changes of Ef can already be recognized within less than ± 0.1 % in the course of heating and cooling cycles. The numbers and arrows in Fig. 2 indicate the succession of measurements and direction of temperature changes, respectively. The most prominent change is the increase of Ef during the conversion reaction (called “C”) in the range of 350 to 425 K, which is in part due to the mass loss (evaporation of C8H18OS side chain material, as will be discussed below in sect. 4) rising the eigen-frequency of the system. The other peculiarities are discussed with the simultaneously measured damping behavior shown in Fig. 3. Starting at room temperature, during cooling first the β peak (around 250 K) and later the γ peak (around 130 K) is observed for the precursor phase. In this condition the peaks are also seen during 2,2

35 nm PPV

Ef(T) / Ef(300K)

2,0



β

1,8 1,6

γ



1,4 1,2 1,0 0,8




C 



β'

β



0,6 0,4 100 150 200 250 300 350 400 450 500 550

T [K]

Fig. 2. Relative change of Young’s modulus from the change of eigenfrequency in free decay, according to eqs.(2, 3) of the PPV precursor film of 35 nm thickness, measured during several heating/cooling cycles simultaneously with damping (loss factor) shown in Fig. 3. The temperatures of the γ, β, β’ maxima and of the C process are given in Fig. 3 and Tab.2. The modulus is normalized to its value at room temperature Ef(300K) = 40.88 GPa. Cantilever length 9.5 mm, thickness 30 µm, second harmonic vibration, f ≈ 8 kHz.

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Fig. 3. Damping (tan Φf loss factor, Φf loss angle) of the PPV film (eq. (1), contribution from the silicon substrate is negligible) measured simultaneously with Fig. 2 (same numbers and arrows indicate the succession of temperature changes).

35 nm PPV - 8214 Hz

tan(φf) [10-6]

100

C 75

β' 

50 25

γ

0






193



β 

100 150 200 250 300 350 400 450 500 550

T [K] successive heating back to room temperature. Further heating reveals a peak (called β’) around 350 K which is superimposed to the shoulder of the big C peak (conversion reaction) starting around 340 K. The resulting polymer structure has now changed to the insoluble semiconducting PPV, which shows still the β peak after conversion, but with reduced magnitude, while the disappearance of the C, β’, and γ peaks on cooling indicates that they are coupled to the molecular structure of the precursor polymer. This information helps to assign specific mechanisms to the peaks (section 1 and 4). The related modulus effects are marked in the Young’s modulus curves (Fig. 2) accordingly with γ, β, β’, and C. The variation of the temperature positions of the peaks (Tp ) at different exciting frequencies f can be used to estimate the activation enthalpy H of the underlying relaxation process, if the relaxation time τ is represented by a simple Arrhenius law with a single activation enthalpy H: τ = τo exp (H/kT). The expected peak shifts [5] could be observed for the γ, β, and β’ peak, indicating their relaxation nature, while the C peak does not shift with frequency and, therefore, appears to correspond to an irreversible structural transformation (i.e. the conversion reaction). The resulting Arrhenius plots (Fig. 4) indicate rather wide ranges of activation parameters as shown in Tab. 2. They compare reasonably well with those determined earlier 10000

f [Hz]

f [Hz]

10000

35 nm 62 nm

1000

0,0075

1000

35 nm β' 62 nm β' 0,0080

1/Tp [1/K]

0,0085

35 nm β

100 0,0028

0,0030 0,0040

0,0042

0,0044

1/Tp [1/K]

Fig. 4. Arrhenius plots for the shift of peak maximum temperature (Tp) with varying freuency f for the relaxation peaks a) γ, and b) β, and β’, for estimating the effective activation enthalpy H and pre-exponential factor τ0 of relaxation time (see Tab. 2). The associated processes are discussed in section 4.

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Interaction between Defects and Anelastic Phenomena in Solids

Table 2. Peak positions Tp on the temperature scale (at a frequency of about 103 Hz) and estimated activation enthalpies (H) for the relaxation processes (relaxation times τ = τo exp(H/kT) ) involved in the peaks γ, β, and β’; in comparison with earlier results (df = 25 nm, spin coated films) in [14]. The associated processes are discussed in sect.4 and explained in sect.1. H H Tp [14] H [14] τo [14] τo τo [eV] [K] [eV] [eV] [s-1] [s-1] [s-1] df = 35nm df = 62nm df = 25nm -15 130 0.1…0.5 10-(8...22) 0.1…0.4 10-(9…22) 130 0.25±0.1 6.5⋅10 -(15…39) 250 0.5…1.6 10 260 0.6±0.1 5⋅10-17 -(15…35) -30 350 0.6…2 10 ≈1.7 ≈3⋅10 (∼ 350) 340-425 340-380 -

Peak

Tp [K]

γ β β’ C

[14] for spin-coated films (Tab. 2) and are rough estimates, as the Arrhenius plots do not show well straight but rather curved lines, suggesting spectra of activation enthalpies typical for cooperative motion rather than single values which occur for activated motion over fixed potential barriers. This explains also some unreasonably low values of the pre-exponential relaxation times τo (cf. [24]). Finally, in Fig. 5 the peak heights of the γ and β damping maximum as well as those for β’ and C are shown for varying film thickness. Except for the behavior at very low thickness, a linear increase is observed for γ and β peaks, although the increase of damping with the volume of deformed film material on the substrate should be removed by division with df in Eq.(1). On the contrary, for C a definite decrease of peak height occurs with increasing film thickness, while the β’ peak heights do not change distinctly. The loss contribution by the silicon substrate itself (tan Φs < 5⋅10-6) can be neglected in all cases, cf. [18].

30 25

b)

γ LB-coating γ Spin-coating [14] linear fit of γ LB-coating β LB-coating β Spin-coating [14] linear fit of β LB-coating

β ' LB-coating

150

C LB-coating

-6

-6

tan(φf) - tan(φbg) [10 ]

35

tan(φf) - tan(φbg) [10 ]

a)

20 15 10 5

125 100 75 50 25 0

0 0

15

30

45

Thickness [nm]

60

0

15

30

45

60

Thickness [nm]

Fig. 5. a) Variation of the heights of the peak maxima (background tan Φbg subtracted) with film thickness df for Langmuir-Blodgett-produced layers (
) and for an earlier result [14] with films prepared by spin coating (), a) for the γ and peaks, and b) for the β‘ and C peaks. (Note that the Si resonators are coated at both sides by the LB method, while the spin coated layer covers only one side of the specimen). DSC heat flux measurements. A few runs were performed with differential scanning calorimetry (DSC) using the precursor material to find characteristic temperatures due to endo- or exothermic reactions. Fig. 6 shows a typical measurement of heating and cooling cycles (indicated by arrows) for a temperature variation rate of 10 K/min. Three exothermic peaks can be observed in the heating curve, i.e. around 414 K (peak 1), 491 K (peak 2), and 556 K (peak 3). However, peak 2 may also be considered as an endothermic peak around 530 K. In the successive cooling run, only the second peak remains (around 490 K), while peak 1 and 3 have disappeared after conversion of the precur-

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Heat Flow (exothermal) [mW]

sor to the PPV polymer. For the first maximum around 414 K, which shifts with the imposed heating rate, the activation energy was determined by means of the Kissinger method [22,23], resulting in 1.08 eV. The other peaks (2, 3) do not produce linear Kissinger plots, although they shift in the same sense as peak 1.

Fig. 6. DSC heating and cooling curves (indicated by arrows) for PPV precursor material, measured with a heating/cooling rate of 10 K/min.

8 6 4

2 3

2 2

0 1

-2 -4 -6 300

350

400

450

500

550

600

T [K]

Discussion Young’s modulus. The strong increase of the value of Young’s modulus (Fig. 2) during the conversion reaction from Ef,precursor ≈ 36 GPa (at 353 K, with density ρprecursor = 1.1030 ± 0.0051 g/cm3 and thickness df = 35 nm) up to Ef,PPV ≈ 65 GPa (at 423 K, with ρPPV = 1.1530 ± 0.00061 g/cm3, df = 18 nm) reflects the strengthening of the material during conversion. In spite of their considerable uncertainty (up to 40 %) the absolute modulus values exceed by far those found in common tables on properties of bulk polymers, e.g., polyamide (ca. 3 GPa), polycarbonate (ca. 2.7 GPa) or polyethylene (ca. < 1 GPa). The reason for this is not quite clear. The difference may be due to the anelastic strain occurring in quasistatic stress-strain measurements on which the literature data of elastic moduli are mostly based, contrary to our values for 8 kHz. It may also be related to a high degree of order in the LB layers or to some restriction of molecule mobility in the thin layer fixed to the substrate, if the thickness is in the order or less than the molecule length. This should, however, be proven by additional investigations, e.g. by means of x-ray techniques. Relaxation processes in precursor and PPV film. The estimated activation enthalpies (Tab. 2) and peak positions on the temperature scale, as well as the behavior of the peaks (disappearance or persistence during annealing) support the assignment of mechanisms to the relaxations as proposed already in [14], in accord with information from literature (e.g. [8 - 13] on similar polymer structures, as indicated in section 1, γ : motion of small molecular groups in the precursor, β : reversible motion of molecular groups in the main chain of the precursor and of the converted polymer, β’: similar motions in the side chains of the precursor (as β’ disappears together with γ after conversion, contrary to β). The relaxation strength (proportional to tan Φf, determined according to eq. (1)) as a material property should be independent of material thickness. The observed linear increase of the peak height of the relaxation peaks γ and β with film thickness (Fig. 5 a) indicates different contributions of the material in the surface region and in the interior of the film: The dependence in Fig. 5 a shows that the bulk contribution to the relaxation processes exceeds that of the material situated at

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Interaction between Defects and Anelastic Phenomena in Solids

the surface, probably because for the latter the back forces are weaker than in the bulk. This is in accordance with the observation that peak β is absent (or no longer resolved) in the layers with smallest thickness (< 16 nm). It might be expected that the molecular relaxations are modified in the interface region between film and substrate [8]. The lack of thickness dependence for the β’ peak suggests that it results from molecules situated in the interface region. The restriction of their mobility seems to shift the peak temperature to higher values in comparison to the β peak for the bulk. The glass transition (α) is not clearly observed in the present mechanical measurements; it might be superimposed for the precursor by the conversion reaction C, i.e. the material converts already at temperatures lower than the glass transition temperature Tg (cf. next section). Conversion reaction and DSC results. Contrary to the thickness dependence of the peak height of relaxation processes (Fig. 5 a), the loss peak height of the conversion transformation decreases with increasing film thickness df (Fig. 5 b). This can be explained as a consequence of the removal of the side chains during conversion: The side chain material evaporates more readily from the surface region than from the bulk, where evaporation is retarded by the surface layer. This implies that the conversion peak C is expected to be sharp and high for thin layers, while for thicker layers lower and broader peaks should occur, as it was observed but is not shown here for brevity. The connection of the relaxation and transformation peaks to those observed in DSC measurements (Fig. 6) is not straightforward and still very uncertain. The higher heating rate for DSC (10 K/min) than for vibrating-reed measurements (1 K/min) shifts the characteristic temperatures to higher values. The DSC peak 1 (around 414 K, which disappears together with peak 3 around 556 K after conversion) is supposed to correspond to the conversion reaction (activation enthalpy 1.08 eV, which is a reasonable value for the elimination reaction), while the peak 2, if considered as endothermic during heating (around 530 K) may be connected with an internal phase transition, seen as an exothermic peak during cooling, even after heating to a higher temperature. Peak 3 (556 K) can be assigned to a second step of the conversion reaction (cf. Fig. 1) leading to more complete elimination of the outgoing groups from the bulk material. It should be mentioned that the degradation of the converted polymer occurs at considerably higher temperatures above 800 K. Conclusions Vibrating-reed measurements on Si cantilevers coated with precursor and converted PPV polymer, respectively, have shown that Young’s modulus increases considerably with conversion to the polymer. In addition to a distinct mechanical loss at this conversion process, three relaxation peaks could be observed and identified with γ, β, and β’ processes, i.e. characteristic movements of atom groups in the precursor and in the PPV molecule, respectively. The observed dependences of modulus and damping on film thickness indicate different relaxation behavior of molecules situated at the surface, in the interior of the film, and in the interface region between film and substrate. Acknowledgements The authors express their sincere thanks to Dr. I. Behrens, Priv.-Doz. Dr. E. Peiner and Prof. Dr. A. Schlachetzki, Institute of Semiconductor Technology, Technical University of Braunschweig, for producing the Silicon cantilever specimens by selective etching, to O. Zelesnik, Fraunhofer Institute for Thin Film Technology, Braunschweig, for his help with ellipsometry in film thickness measurements, to Mrs. U. Baronick for her help with DSC measurements, and to Prof. H.-R. Sinning for fruitful discussions.

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References [1]

J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friench, P. L. Burns, A. B. Holmes: Nature Vol. 347 (1990), p. 539-541.

[2] S. A. Van Slyke, C. H. Chen, C. W. Tang: Appl. Phys. Lett. Vol. 69 (1996), p. 2160-2162. [3]

M. S. Weaver, D. G. Lidzey, T. A. Fisher, M. A. Pate, D. O’Brien, A. Bleyer, A. Tajbaksh, D. D. C. Bradley, M. S. Skolnick, G. Hill: Thin Solid Films. Vol. 273 (1996), p. 39-47.

[4] S. Schrader, W. Rieß, H. Vestweber: SPIE. Vol. 3476 (1998), p. 188-194. [5]

A. S. Nowick, B. S. Berry: Anelastic Relaxation in Crystalline Solids (Acad. Press, New York 1972).

[6]

M. S. Blanter, I. S. Golovin, H. Neuhäuser, H.-R. Sinning: Internal Friction in Metallic Materials. A Handbook (Springer, Berlin 2007).

[7]

B. S. Berry, W. C. Pritchet: J. Physique 42 Suppl. Vol. 10 (1981), p. C5-1111-1122.

[8]

H. Lacombe, B. M. J. Kellner: Nature Vol. 289 (1981), p. 661-662.

[9]

N. G. McCrum, B. E. Read, G. Williams: Anelastic and Dielectric Effects in Polymer Solids (Wiley, London 1967).

[10] R. F. Boyer, in: Polymeric Materials: Relationships between Structure and Mechanical Behavior, Amer. Soc. Metals, Metals Park, Ohio (1975), p.277-368. [11] S. Havriliak, Jr., S. J. Havriliak: Dielectric and Mechanical Relaxation in Materials Analysis, Interpretation and Application to Polymers (Hanser Publ., Munich, Vienna, New York 1997). [12] J. P. Punt, J. J. Fitzgerald (Eds.): Dielectric Spectroscopy of Polymeric Materials, Fundamentals and Applications, Amer. Chem. Soc., Washington DC (1997). [13] T. Nicholson: Modelling of solid state relaxations in polymer science and technology, http://www.irc.leeds.ac.uk/~phy6tmn/-research/relax.html, (2001). [14] A. Nagy, A. Strahl, H. Neuhäuser, S. Schrader, I. Behrens, E. Peiner, A. Schlachetzki: Mater. Sci. Eng. A Vol. 370 (2004), p. 311-315. [15] G. G. Roberts: Contemporary Physics, Vol. 25 (2) (1984) p. 109 – 128; M.C. Petty: LangmuirBlodgett Films - An Introduction, Cambridge University Press (1996). [16] E. Peiner, D. Scholz, A. Schlachetzki, P. Hauptmann: Sensors and Actuators A Vol. 65 (1998), p. 23-29; I. Behrens, E. Peiner, K. Fricke, A. Bakin, A. Schlachetzki: Proc. 14th Europ. Conf. Solid-State Transducers (Eurosensors XIV), Copenhagen (2000), p.511-514. [17] U. Harms, L. Kempen, H. Neuhäuser: Thin Solid Films Vol. 323 (1998), p. 153-157. [18] U. Harms, L. Kempen, H. Neuhäuser: Rev. Scient. Instr. Vol. 70 (1999), p. 1751-1756. [19] U. Harms: Dissertation, Technical University of Braunschweig (1999). [20] B. S. Berry, W. C. Pritchet: J. Appl. Phys. Vol. 67 (1990), p. 3661-3668. [21] W.F. Hemminger, H.K. Cammenga: Methoden der thermischen Analyse (Springer, Berlin 1989). [22] H. E. Kissinger: Analyt.Chem. Vol. 39 (1957), p. 1702. [23] F. S. Scholz, E. Woldt: http://www.tu-bs.de/institute/ifw/ifw/deutsch/forschung/ physik_mess/transformation/kalorimetrie/, (2000). [24] P. Krueger, Th. Stucky, M. Böwe, H. Neuhäuser: phys. stat. sol. Vol. (a) 135 (1993), p. 467475.

Solid State Phenomena Vol. 137 (2008) pp 199-208 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.199

Do Electromagnetic Pulses Induce the Relaxation or Activation of Microcracking Rate in Loaded Rocks? /acoustic emission based study/ Leonid Bogomolova and Alexander Zakupinb Research Station of the Russian Academy of Sciences (RS RAS) in Bishkek city, Kyrgyzstan a

[email protected], [email protected]

Keywords: Rock specimen, compression load, microcracking, acoustic emission (AE) activity, electromagnetic (EM) field pulses, defects accumulation, triggering.

Abstract. The work is devoted to the problem of role of ambient factors (external electromagnetic field, in particular) in the process of ageing of mechanically burden nonmetallic solids (rocks). A specific research point is the effect of temporary activation of Acoustic Emission (AE) of rocks specimens during action of EM field pulses applied externally. Extended experimental studies of responses of AE have been conducted to evince the changes in defects accumulation process in loaded specimens due to external power impacts (EPI). The experiments have been held on noiseless rheological machines available at Bishkek Geodynamic Research Center - RS RAS. We have tested a number of specimens made of different materials and analyzed the temporal dependence of AE activity during exposure in electric field and crossed electric and magnetic fields; the compressive load being constant. The effect of AE stimulation by power pulses (triggering) has been verified. The obtained results allow to distinguish two kinds of AE activation. The first kind involves simultaneous well correlated growth of numbers of minor and major AEs (so-called selfconsistency of temporal plots of activity of different range acoustic events). The second kind represents dissimilar variations: the increment of activity of minor energy AEs, but the decrement of those of major energy. The first kind of solids material responses to EPI is prevailing when the compressive loads is under 0,85 of fracturing value. The episodes of dissimilar AE responses may signify that electromagnetic control of defects accumulation process inside rocks is possible, in principle. Introduction It is well-known that strong enough electric and magnetic fields have an influence on plastic straining of nonmetallic solids (particularly on the plasticity of alkali-halogenic crystals, [1 - 4]). According to these and other works some increment of plasticity occurs when the strength of electric field, E, is of order of 10 - 100 kV/m (at least, [1, 3]), or when the magnetic inductance, B, exceeds 0.1 T [4]. One can assume that electromagnetic (EM) field of such minor values of E or B components may contribute to inelastic straining (microfracture) which are evolving on micro- and meso-scales of length. Acoustic Emission (AE) is a good indicator of inelastic straining processes and microfracture inside specimens of semi-brittle materials loaded up to near critical point [5, 6]. AE method allows detection of any (even very weak) change in straining/microcracking rate in solids made of semi-brittle materials. So, temporal variations of AE activity may be considered as signatures of effects of physical fields applied externally and induced (or triggered) changes in a rate of accumulation of structural defects, microcracks in particular. Actually, numerous experiments with pristine rocks samples and artificial solids (such as concretes and water-containing ceramics, to simulate terrestrial materials) subjected to compressive load and to additional action of EM field have revealed AE activation as a response to external power impacts (EPI), [7 - 9]. Our previous works [9 - 11] specified that the increment of AE activity due to EM field pulses occurs providing that the fixed compressive load over tested rock specimen is from 0.75 to 0.95 of maximal value (fracture of given specimen). We tested a number

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Interaction between Defects and Anelastic Phenomena in Solids

of specimens, made of materials with different elastic and piezoelectric properties: granodiorite, quartzite, granite, halite, and zirconium oxide ceramic. We argued that the effect of AEs electrostimulation is related to anelasticity of terrestrial materials under stressed-strained conditions corresponding to dilatancy rather than to structural defects clustering or formation of main crack. But the physical mechanism of electromagnetic influence is not clear completely. The excitation of microvibrations and acoustic waves during EPI is the most serious candidate to explain the responses of AE, since the effect of vibrations (even very small) on microcrack growth has been already proved [9]. It should be noted that piezoelectric effect can not be responsible for this electric to acoustic transformation because the values of piezoelectric modulus of rocks studied in [7 - 11] are too low. An idea of F. Freund [12] that overstress before break can generate electric currents in some igneous rocks, which normally are good insulators, may be used as a starting point for more realistic approach to EM field effect over stressed-strained rocks. Shortly, F. Freund has deduced in [12] that rocks may become “p-type” semiconductors. This means that they contain mobile positive charges which can conduct some electrical charge. The crystals within such rock of abyssal origin contain some paired oxygen atoms, called peroxy groups, which can snap under stress. F. Freund speculates that once a peroxy group is snapped, a negative oxygen ion will remain trapped in the lattice of the rock, while a positive charge – or hole – will be free to flow outwards. He has proposed the model of charge transfer to natural geologic media (Earth crust) as well as to tested rock specimens [12]. Surprisingly, this model also involves such aspect as possible mechanism of interaction, of free carriers of electric charge, with an EM field externally applied to a tested rock. The density of released positive charges should oscillate due to EM field pulses. The oscillation of charge carriers will be delivered to the main frame of the loaded body (i.e. to the crystal lattice in the simplest case). The triggering effect of the vibrations is well-known, including the case of very weak vibrations whose amplitude of oscillating pressure is close to 10-6 of main compression stress [6]. The aforementioned interaction of the EM field with charges generated according to [12] is therefore a hypothesis for mechanism of electromagnetic triggering effect. Alternative approach concerns only wetted heterogeneous rocks containing bound water or free water or its vapor in cracks and porous cavities. Authors of [13] appealed to electrokinetical phenomena in systems with solid and liquid phases. They remarked that numerous phase contacts inside heterogeneous material may be equivalent to a media with anomalous averaged polarization; the dispersion of dielectric permittivity being strong. Simplifying the consideration of [13], one can draw an analogy between vibrations occurrence in such media under electromagnetic pulses and oscillation of dielectric liquid near edge of plane capacitor biased by high frequency alternative voltage (alternative ponderomotive force acting along the gradient of electric strength will result in liquid sucking up pulsation). Similar simplified picture was sketched by T. Chelidze [14, 15] who studied the effect of EM field on slippage of contacting blocks. No proposed model is able to evince the aspect as follows - do defects of minor or major size mostly contribute to AE activity increment under electromagnetic action? Meanwhile this issue is of great significance from viewpoint of geophysical and seismological applications of noted above effect of microcracking stimulation by EPI. The problem of the most relevance is that how to estimate a hazard of seismicity induced by man-made factors without sufficient knowledge of physics of earthquakes nucleation or reliable algorithms to predict natural events. One can regard the acoustic emission as a model of real seismisity due to well-known self-similarity property of which in a wide range of scales [6, 8, 9, 16]. Extra argumentation for the validity of such modeling is that the materials of the tested specimens are the same as for embedded rock massifs and that the typical value of compression stress during creep tests on press is close to those at depths of shallow earthquakes source-sites (5 - 15 km). Motivated partially by above we developed investigations of AEs of rock specimens which being tested by constant uniaxial compression (so called creep test) and additional action of EM pulses. A new set of experiments under axial loading using the spring rheological press with the strength up to 100 tons was carried out. Some experiments were conducted with the help of lever loading machine

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UDI-L providing compressive load up to 35 tons. The aim was to study AE in rocks specimens influenced by pulses of EM fields with parameters never been used before. Also we compared the parameters of AE responses to external impacts with that caused by trial stepwise increment of compressive load. The main results have been described below. Experimental set-up and procedure The work on electromagnetic- acoustic effects mentioned above involves the creep test of specimens of rocks and of artificial heterogeneous materials burden by uniaxial compression. The Fig.1 shows the rheological machines used to test rocks in noiseless conditions. We have described in details in our previous works [9, 11] the technique of long- term experiments on spring rheological press UDI (designed by A. Stavrogin, [17]) with application of external power actions. Recently, we have constructed lever machine UDI-L of 35 tons on the base of load-carrying components of UDI press. Both: spring and lever machines have been used to test solids in noiseless conditions in relevance to the problem of EM fields influence. Fig.1 shows both rheological machines. It is worth to emphasize that a lever press provides noiseless conditions at all the time of the test, including sessions of fixed compressive loads and load increments by making up the weight on a longer side of the lever. This allows continuous AE recording during stepwise change in main load, meanwhile a spring press is actually noiseless only during constant loads sessions, after clamping the displacement of compressed working spring by a screw and nuts. Besides, we remark that the effects of weak external factors cannot be studied on a usual hydraulic press because its drive produces a host of noise inevitably. Fig.1. General views on: a) spring press UDI, b) lever machine UDI-L, c) specimen installed for tests. Denoted elements: 1- loading platen, 2 – specimen, 3 – cross-arm, 4- spring, 5- clumping nut, 6- supporting rod, 7hydraulic jack, 8- lever units, 9 – AE sensors, 10electrode. Using the merits of lever and spring presses we tested rocks specimen and recorded the variations of AE signals flow during trial increment of compressive load as well as during the sessions with action of electromagnetic pulses applied externally. During last series experiments we tested 5 intact samples (granodiorite-1, granite-2, gabbro-1, and rock salt- 1) with the help of lever machine UDI-L. The total number of specimens tested on spring press with additional action of EM field was 38 (26 of them are pristine rocks). Tested specimen was located on the lower platen with built-in AE sensors integrated constructively with cable amplifiers. The spherical joint, integrated with lower platen, assures the parallel alignment of specimen and compression axis. In most cases, single noise-immune sensors were used for recording flow of AE signals. These sensors applied to the side surface of specimen. Signals from the one of the side sensors (SE2MEG, DECI Inc.) after amplification and filtration were used to perform the triggering of recording equipment – ADC (CAMAC standard). AE signals were recorded on wide frequency region 80 kHZ - 2 MHz. This allowed signals waveform control. The measuring system operated in a waiting mode. This means that the recording starts every time when the signal magnitude exceeds threshold. Inherent noise of AE channel set a value of threshold. The value of threshold was equal nearly 1.5 times more than root-mean-square of the noise to avoid a false triggering.

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Additional electric power impacts, produced by external sources, took place during a deformation session with constant level of compressive load. It took place in some time of sample exposure just after load increment but before measuring session to avoid the bias of unsteady processes caused by non-uniformity of load ramping up and edge effects (surface microchipping etc.) Permanent registration of AE started when the manifestations of transition processes (low frequency fluctuations) became of order of natural noise. During experiments the following sources of additional power action were used: square-wave generator G5-54 giving square-wave pulses, whose amplitude was close to 50 V and duration was of order of 5 - 50 µs; the frequency varied from 1 to 50 kHz. The capacitor discharges, that supplied electric pulses, had the following parameters: time of voltage ramp about 1 µs and peak voltage of order of 1 kV. Other sources were used to reveal the significance of such factors as voltage amplitude, rate of pulse rise, and pulses repetition rate for AE activation considered. Also, we performed AE measurements during trial session with crossed electric and magnetic fields impacts. A magnetic coil supplied by AC sinusoidal current (G3-112) was the source of additional magnetic field with near 0.004 T maximal amplitude of inductance. The coil was placed near lateral surface of a rectangular specimen so that the induced magnetic field was approximately orthogonal to electric field (G5-54), produced by electrodes fasten to other (transversal) facets (Fig. 2 a). Alternative magnetic field was used to avoid negative bias of ferromagnetic elements of press. Phases of generators to electric and magnetic supply were synchronized with the help of triggering unit. The unit produced a triggering signal to start G5-54 generator when the current in magnetic coil reached the maximum. Just after the end of electric pulse of G5-54 the triggering unit allowed no new pulse during specified dead time (nearly half period of AC sinusoidal current of magnetic coil supply). So, the frequency of electric field induced in the specimen was two times less than that of magnetic field (Fig. 2 b). It should be emphasized that the direction of dynamical force and the vector of energy flow remained the same during the session with action of crossed E and B fields. Fig.2. Experiment with loaded specimen in crossed EM field: a) the geometry: directions of main compression (vertical), electric field E, and magnetic inductance B are orthogonal, b) synchronization of periodical electrical pulses (G5-54) with AC generator supply to magnetic coil. In addition to computation of usual AE activity (the based informative parameter) we determined the rate of accumulation of AE events of major and minor magnitudes. For this purpose we separated the flow of AE signals on 2 groups called “strong” and “weak”. AE signals with amplitudes above the given discrimination level were considered as “strong”, other signals - as “weak”. The program of numerical discriminator working with recorded waveform of AE signals was used. We prescribed the level of discriminator so that the numbers of strong and weak AEs per second (the selective activity parameters) were comparable, say the difference between their trends should be less than 50 %. As a result, we get information closely related to kinetics of structural defects of various sizes. Results and discussion Previous experiments performed with different kinds of rocks under creep test in presence of electromagnetic field [6, 8, 9] revealed the effect of energy release increase (relaxation). These fundamental results were obtained by means of AE activity parameter. In the experimental series held at RS RAS [10, 11] AE activity responses with time profiles as shown on Fig. 3, and with

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considerable increments of AE (exceeding triple level of AE root-mean-square over steady background) have occurred in 22 cases from 26 sessions. The responses have been observed when the value of main compression stress was from 0.7 to 0.95 of fracturing for given specimen. Temporary activation of AE (Fig. 3) and correspondent growth of accumulated energy release are followed by partial relaxation of specimen material. By other words, some zones of stress concentration (source sites of AEs) are to unload themselves after triggered emissions. It should be highlighted that in experiments such as described in [9] dynamical stress due to electric ponderomotive force is about 7 orders of magnitude less than the main compression stress. It is worth to remark that a delayed increment of AE activity after EPI is a realization of triggering which is quite similar to the activation of weak seismicity after powerful electric discharges supplied by geophysical MHD generators [18]. The similarity of emission responses on various scales of geological medium is to denote that electrostimulation effect is definitely fundamental for overstress unloading in Earth Crust and adaptation of its material to stressed-strained state. Potentially, this effect could allow the controlled release of overstress. Fig. 3 a demonstrates an example of the effect of AE activity stimulation by powerful electric impacts produced by capacitor discharges, Fig. 3 b by periodical electrical pulses by G5-54 generator and Fig. 3 c by combined action of crossed electric and magnetic fields. As a whole, these examples of various AE responses are an expression of general features of electromagnetic effect in rocks.

Fig.3. Plots of AE activity ( N& ), versus time (t): a) gabbro, action of capacitor discharges; b) gabbro, periodical pulses of generator G5-54; c) granite Westerly, session with crossed E × B fields power on. To get some information about evolution of energy release (peculiar relaxation) we considered separately the flow of AE signals of major and minor magnitude and calculated the selective AE activity for each group. The data obtained on granodiorite specimen under action of EM field have been processed, the results are shown on Fig. 4 a - c. According to our previous investigations electromagnetic pulses are working effectively to stimulate AE when the normalized load is high enough, typically exceeding the level 0.8 of fracturing value. So, we focused our attention on three sessions with EPI during which the values of compressive load were equal 179, 188, and 198 MPa. These compression stresses were near critical, because the ratios of these loads to fracturing value for given specimen (KNL) were as follows 0.86; 0.91; 0.95. The periods of electric pulses supply lasted an hour (denoted by black bars on Fig. 4). A square waveform generator G5-54 was used. Each case of Fig. 4 demonstrates two temporal dependencies, and the dark line denotes the activity of strong AE signals (of major magnitude) and the grey line the activity of weak AEs (minor magnitude).

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Fig. 4. Temporal plots of N& of granodiorite specimen at three fixed loads (a - KNL = 0.86; b – 0.91; c – 0.95); d) the same plot of AE activity of gabbro (KNL = 0.87). In the first case (Fig. 4 a) the temporal dependencies of activity of major and minor AEs are practically identical, and electromagnetic action does not affect the similarity of trends of curves. But this is not the case when the main load has increased and the background level of AE activity becomes higher (Fig. 4 b). One can see that some growth of minor AEs simultaneous with slight fall of major ones occur just in the beginning of square waveform electric pulses supply (interval I on Fig.4b). Meanwhile, the response of total AE activity arrives later than the dissimilar variation in interval I. Dissimilar variations of activity of major and minor AEs have been observed also in interval II, simultaneously with the maximal increment of total AE activity. The distinction of curves is more apparent compared to that in interval I. This notes that under considered load of 180 MPa (KNL = 0.91) AE signals of minor magnitude provide the most part of total activation. During the last session for given specimen a spontaneous spike of AE activity has occurred before start of EPI. This fluctuation is to mitigate AE increase stimulated by electric pulses, since a number of metastable zones (ready to emit acoustic energy while weak actions) is less after the spike. It is of interest that only marginal difference between trends of minor and major AE plots has been observed in the period of spontaneous activation. In contrast to the “prehistory” up to 3600 s, three episodes of obviously dissimilar or even antipodal variations of both selective AE plots take place during action of electric pulses. Intervals I- III on Fig.4c denote these episodes in the period of EPI. The first dissimilar variation has arisen just after the start of electric action, similarly to that at previous stage of loading (case of Fig. 4 b). Beside data on granodiorite specimen we have processed primarily data and analyzed the results of the experiment with other rock specimen, namely gabbro. AE measurements have been performed during a session when the compressive load is 0.87 of maximal for given specimen. G554 generator has been used as a source of EPI, the period of electric action is shown by a bar on Fig. 4 d (in the same manner as I the cases a - c). One can see on Fig. 4 d that AE activity response consists of two successive spikes. Before external action both activity plots: for strong and weak AE signals temporal dependencies, have practically the same trends. Fluctuations of activity, which are correspondent to near random character of AE sources occurrence, give no statistically valid deviation on averaged plot. But during the session with electric pulses, two intervals are to attract attention, when the growth of weak events flow takes place while steady or even decreasing flow of strong events. The first interval is in the beginning of period of EPI, actually it coincides with the transition period before the front of activation. The second interval of dissimilar variation is correspondent to a burst of activity. The length of these two intervals is about 850 s, or near one quarter of EPI period and less than 0.1 of total time of the session.

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The results of analysis of selective activity of AE have demonstrated that the concept of selfsimilarity (proportional each to other change in accumulation of major and minor defects) is fulfilled during the most time, but in some episodes the deviations like dissimilar mode of responses may take place, due to action of EM field. Such results are typical for sub-critical loads. They probably look like peculiar relaxation after EPI in superimposed on rock materials in stressedstrained state, when the compressive load is close to fracture. Comparison of responses to trial load and electric pulses. Some extra experiments were performed as a topical development of above noted studies. The aim was to compare the characteristics of AE responses (spikes or raised plateau intervals at temporal plots of AE activity) due to electric pulses with those caused by trial relatively small increments of compression load. Specimens of both kinds of material: semi-brittle rocks (granites) and pseudo plastic ones (rock salt) were used. The experimental technique for specimens test by compression load and electric pulses and the measuring system were the same as in previous experiments [9 - 11]. The only modification involved a new modulus for AE signals filtering, which allowed continuous measurements of AE even during trial load increments. The Fig. 5 a demonstrated the results of measurements of AE from a granite specimen (Sary-Jaz deposit, Kyrgyzstan). In the given measuring session with the specimen under compression stress of 100 MPA value (near 0.85 of fracturing) the level of AE activity was steady (near 4 events per second). In the middle of the session the load was increased up to new steady value 107 MPA. The correspondent increment of axial strain was about 3.5 ⋅10-4, and the trial energy input (work of deformation during trial loading) was approximately equal to 5 J. This extra loading resulted in sharp rise of AE activity (Fig. 5 a) which was followed by drops of AE events flow similarly to Omori law [19]. The relaxation lasted near 180 s. During this period approximately 4100 AE events were recorded. One can evaluate the number of stimulated events by subtracting the contribution of background activity (defined in prehistory and extrapolated to activation interval) from total AE accumulation. So, approximately 3400 events seemed to be triggered by additional compressive load. Thereafter, with some time lag the source of electric pulses (square waveform generator) was powered on. The specimen was biased by unipolar pulses; the amplitude of electric strength was about 400 V/m, the frequency was equal 50 kHz. The amount of energy absorbed by specimen during electric field action may be roughly estimated as 2 ⋅ 10-2 J (only the order of magnitude is of significance). This evaluation is based on the parameters of electric pulses, geometry of supplying electrodes and the value of dielectric loss tangent for the material of tested specimen. The response to electric pulses (EPI case on Fig. 5 a) exceeded that in “pure mechanic” case (TL-spike on Fig. 5 a) by the duration and magnitude of AE activity increment. The number of events triggered in 300 s period of electric biasing was estimated as to be near 7100 ± 50 (the accuracy was limited by near 0.5 s uncertainty in time of electric source start). It should be noted that 5700 ± 50 electrically stimulated events occurred in first 180 s of biasing, this is 1.7 times more than under previous “TLactivation”. The ratio determined for a granitic specimen exceeded unity, meanwhile energy supplied externally in the first case (trial loading) was much more than in the second. Similar results were obtained on specimen of pseudo plastic material (rock-salt). The specimen of such creeping material was tested on lever-gravitational loading machine for which no specimen decompression can take place due to its shortening (in contrast to spring press). Fig. 5 b represented the temporal dependence of AE activity of rock salt specimen under uniaxial compression stress of 30 MPa value (0.85 of fracture by cracking). The background activity of AE was about 4 events per second (close to the case of granitic specimen), but with slight decreasing trend. Again, trial loading was undertaken firstly in the measuring session. The increment of stress was about 0.5 MPa, the correspondent change in axial strain was of order of (1 - 2) ⋅10-4. The energy input to the specimen may be estimated as a product of mean acting load by specimen shortening caused by stress increment. The value of energy input was between 1 to 2 J. The trial loading caused the response of AE activity of 4700 s duration. Then AE activity relaxed to a new steady level. The number of triggered events during the spike interval was 5050 ± 50.

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Fig.5. Plots of AE activity ( N& ), versus time (t): a)granite; b)rock salt; c)granite, anywhere KNL =0, 87 The second abrupt activation of AE (see plot on Fig.5b) was stimulated by electric pulses produced by the same square waveform generator. This time the amplitude of electric strength was about 103 V/m, the frequency – 2.2 kHz. The amount of absorbed electric energy was nearly 0.05 J. The spike of AE activity (the response to electric pulses, by other words) became with rather long delay after start (near 4000 s). The duration of the second spike on Fig.5b was 3300 s. In the spike interval nearly 4100 AE events were recorded, and 2500 of them were above accumulation due to part of “unchanged”, background level activity and may be considered as stimulated. Meanwhile, in the case of response to trial loading more than 4200 events occurred in first 3300 s after TLmoment (Fig. 5 b). We regarded these events as triggered because the level of AE activity was too low before load increment (so, it cannot explain the accumulation of 4200 events during 3300 s interval). A ratio of number of AE events induced in the case of EPI (second spike on the Fig. 5 b) to similar number of those in the case of first spike can describe a potential of electric pulses to activate AE. For the rock salt specimen this ratio appears to be equal 2500/4200 ≈ 0.6. An important result was obtained on the specimen of another sort of granite than that of Fig. 5 a. The specimen was tested on lever-gravitational loading machine also as rock salt specimen. Fig. 5 c represented the temporal dependence of AE activity of granite specimen under uniaxial compression stress of 198 MPa (0.85 of level of fracture by cracking). The background activity of AE was about 1.4 events per second, but with stable trend (unlike to previous experiments). Stability of background values (values of AE activity before any external action) was estimated as constant level with error of 5 - 8 % due to a considerable fluctuation which occurred before trial loading, or before interval of E × B pulses (as evident from Fig. 5 c). Following our overall technique we undertook the trial loading at first. The increment of stress was about 0.4 MPa, the correspondent change in axial strain was of order of 10-4, and the energy input to specimen was about 0.5 J (estimated by work done, in the same manner as before). The trial loading caused the response of AE activity of 120 s duration. Then AE activity relaxed to a new steady level of 3 events per second. The number of triggered events during the spike interval was 2790 ± 20. Activation of AE (see Fig. 5 c) due to the external action produced by crossed E × B field began just after the start of the action. Only one minute delay was required to achieve the maximal level of AE response in this case. This time the amplitude of electric strength was about 400 V/m, the frequency – 3 kHz. The pulse frequency produced by the generator G3-112 (magnetic field) was 6 kHz. The amount of absorbed energy due to power influx of crossed E × B fields was nearly 0.1 J (this estimation based on values of the Pointing vector and total duration of all E × B pulses, sketched on Fig. 2). The duration of the AE response (Fig. 5 c) is 1765 s. During the response nearly 10800 AE events were recorded; and 5990 of them were triggered by external fields. Meanwhile, the response to trial loading (first spike on the Fig. 5 c) involved more than 2790 induced AE events. Given estimate resulted from the difference between actual accumulation of AEs and extrapolation of previous level of AE activity to period after TL-moment. For the same length of observation (1765 s) the ratio of electric- to trial loading stimulation was ~ 2, which was similar to the data obtained from the previous experiment with granite sample. Such value of the ratio allowed to remark speculatively that the stimulation of AE source sites by electromagnetic pulses may be effective so as that by increment of mechanical load.

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To summarize and compare results for semi-brittle and pseudo plastic specimens we calculated the ratio of energy input to relevant number of triggered events. The values of energy per unit triggering (EUT) were placed in Table 1, for sessions with trial loadings and electric actions. In the case of trial loadings the specific increment of strain (per triggered event) was calculated as well. Table 1. Absolute and specific values of parameters describing triggerability of additional trial loading (TL), external power impacts (EPI) and action of crossed electric and magnetic fields (E × B). Specimen

Action

Granite #1

TL EPI TL EPI TL E×B

Rock salt Granite #2

Strain increment 3.5⋅10-4 (1-2)⋅10-4 10-4

Number of triggered events 3400 Not applicable 5050 Not applicable 2790 Not applicable

Specific increment of strain 10-7 (2-4)⋅10-8 3.5⋅10-8

Energy input, [J] 5 0.02 1-2 0.05 2.5 0.1

Number of triggered events 3400 7100 5050 2500 2790 5990

Value of EUT, [J] 1.5⋅10-3 3⋅10-6 (1-2)⋅104 2⋅10-5 10-3 2⋅10-5

Table 1 denotes a great difference in values of EUT for electrically triggered AEs of granitic and rock salt specimens (more than 3 orders of magnitude). Regarding the activations due to trial loadings, the values of specific strain increment and EUT for these two specimens differ from each other less than an order. It is a surprising result that from the viewpoint of AE (microcracks growth) triggering the distinction of rheological properties of semi-brittle granitic specimen and pseudo plastic rock salt one plays no serious role. AE stimulation by electric pulses of generator G5-54 appears to be the most effective for granitic specimen, since in this case the energy price for one extra AE event is minimal as compared to trial loading stimulation and in comparison with rock salt specimen under electric impacts as well. However, the most effective way to trigger the energy release is the combined action of magnetic field with synchronized periodical electrical pulses. This crossed E × B fields action give rise to AE activation with the minimal delay, and the accumulation of the most number of triggered events. Summary The experimental results have demonstrated that the effect of EM fields applied externally is of potential to modify the process of defects accumulation in rocks under near critical loading conditions. The prevalent reaction of rocks materials to electromagnetic pulses is the temporary increase of microcracking rate. During the induced activation the proportion of major and minor sizes defects is without change, in accordance with observed self similar activation of AE. Stimulated release of extra energy is seemingly followed by relaxation of stress distribution nonheterogeneity. The dissimilar AE activation with preferred formation and growth of defects of minor sizes can be triggered under specific conditions, in particular, on compressive loads of value 0.9 – 0.95 of fracture, providing the microcracking process (average AE activity) is still steady. This is a non-trivial resource for relaxation and inelastic strengthening. The analysis of energy per unit triggering has proved that electromagnetic pulses (impacts of crossed electric and magnetic field and other EPI with optimized parameters) may stimulate AE similarly to small (few percents) increment of load. A suggestion that EM pulses affect the softened domains on the background of quasi uniform distributed mechanical stress could explain the low value of EUT in comparison with trial loading. Acknowledgement Given research has been partially supported by the grant of RFBR # 07-05-00687a.

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References [1] L. B. Zuev: Physics of Electroplasticity of Alkali-halogenic Crystals (Nauka, Novosibirsk, 1990). [2] Yu. I. Golovin: Physics of the Solid State Vol.46 (2004), p. 769. [3] A. A.Urusovskaya, V. I.Alshitz, N. N. Bekkenbauer and A. E. Smirnov: Ibid. Vol. 42 (2000), p. 267. [4] V. I. Alshitz, A. A.Urusovskaya, A. E. Smirnov and N. N. Bekkenbauer: Ibid. Vol. 42 (2000), p. 271. [5] M. Canneli, R. Cantelli and F. Cordero: Phys. Rev. Lett. No 70 (1993), p. 3923. [6] L. M. Bogomolov, B. Ts.Manzhikov, Yu. A Trapeznikov, et al: Russian Geology and Geophysics. Vol. 42 (2001), p. 1593. [7] G. A. Sobolev, A. V. Ponomarev, A. A. Avagimov and V. A. Zeigarnik, in: Proc. of 27-th General Assembly Europ. Seismological Soc. (ESC), Lissabon, Portugal (2000), p. 17. [8] G. A. Sobolev and A. V. Ponomarev: Physics of earthquakes and precursors. (Nauka, Moscow 2003). [9] L. M. Bogomolov, P. V. Il’ichev, A. S. Zakupin, et al: Annals of Geophysics. Vol. 47 (2004), p. 65. [10] A. S. Zakupin, A. A. Avagimov and L. M. Bogomolov: Izvestiya, Physics of the Solid Earth (Fizika Zemli). Vol.43 (2006), p. 830. [11] A. S. Zakupin, A. V. Alad’ev, L. M. Bogomolov et. al.: J. Volcanology and Seismology (in Russian). Vol. 28 (2006), p. 22. [12] F. Freund: J. Geophys. Res. Vol. 105, B5 (2000), p. 11001. [13] A. A. Avagimov, V. A. Zeigarnik, V. A. Novikov, in: Physical grounds for prediction of rocks fracture (in Russian), edited by V.A.Mansurov/ Krasnoyarsk (2002), p. 138. [14] T. Chelidze, N. Varamashvili, M. Devidze et. al.: Annals of Geophysics. Vol. 45 (2002), p. 587. [15] T. Chelidze and O. Lursmanashvili: Nonlinear Processes in Geophysics. Vol. 10 (2003), p. 557. [16] P. Diodati, F. Marchesoni and S. Piazza: Phys. Rev. Lett. No 67 (1991), p. 2239. [17] A. N. Stavrogin and A. G. Protosenya: The strength of rocks and stability of mines (Nedra, Moscow 1985). [18] N. T. Tarasov and N. V. Tarasova: Annals of Geophysics. Vol. 47 (2004), p. 199. [19] T. Utsu: Geophysical Magazine. Vol. 30 (1961), p. 521.

Solid State Phenomena Vol. 137 (2008) pp 209-214 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.209

Phase heterogeneities of lipidic aggregates L. V. El’nikova A. I. Alikhanov Institute for Theoretical and Experimental Physics, 25, B. Cheremushkinskaya street, 117218 Moscow, Russia [email protected] Keywords: lipids, Kibble-Zurek mechanism, topological defects, Monte Carlo.

Abstract. We propose a model for explanation the “domain-wall” type configuration states in binary lipid mixtures of cationic and neutral lipids, associated with observed relaxation effects in their aggregates. We apply the analogy with formation of Kibble-Zurek topological defects, which we suppose connected with structural dynamics of the lipid phases. In frames of the proposed model, the density of kink-type defects and the energy of the configurations are calculated. Introduction A number of applications for lipids and their mixtures in the biomaterial technology, therapy and industry cause the necessity of careful theoretical predictions of their phase transformations. Lipidic aggregates, as well as lyotropic systems at all, are ideal substances demonstrating the quantum topological phase transitions ([1, 2] and references therein). Some experiments on polar fluids [3, 4] reveal new interesting phenomena of their self-organization [5]. For concentrated suspensions, pastes, emulsions, foams, and associative polymers, the mechanism of structure relaxation in soft solids, which is based on the mechanical anelastic spectroscopy in rheological frequencies, was proposed by Wyss and coworkers [3]. Amplitudedependent measurements have shown, that when the strain rate becomes large, it can itself drive the slow structural relaxation process at the time scale of the imposed strain rate [3]. Also, under an applied strain, the observations of high-frequency shifts cause to interpret the enigmatical slow relaxation dynamics in a principally new way. While, the authors [3] seek an explanation of their measurements in analogous phenomena in supercooled fluids [4]. From the other side, the recent anelastic spectroscopy studies [5] of dynamical processes on neutral DMPC (dimyristoil phosphatidylcholine), DOPE (di-oleoyl phosphotiylethanolamine) lipids, cationic DDAB (dimethyldioctadecylammonium), DOTAP (di-oleoyl trimethyl-ammonium) lipids, and their DOTAP/DOPE and DOTAP/DMPC mixtures brought out the hypothesis of new micro- and nanoscale structure heterogeneities in the lipid membranes [5], which look like onto domain walls. These observations have been carried out in a wide temperature range starting with the supercooled state, and at wide-range excitation frequencies (102 − 104 Hz), with the lipids deposited on a solid substrate. Weak frequency-dependent shifts in the elastic modulus are observed at these cryogenic temperatures; peaks on the relaxation curves at the low-dynamics regime are closed by the typical “smooth” relaxation, so, the observations evidence collective short-range motions of the lipids [5]. Also, one may indirectly compare these data with neutron scattering [6] and atomic-force microscopy (AFM) [7] on some neutral and cationic lipids and their mixtures. Hence, a number of soft matter phenomena can be described in the common interdisciplinary modeling associated with a mechanism of forming of topological defects, such as domain walls, or vortex strings. Formation of topological defects Generally, in the cases specified above, the phase transitions are continuous. The Kibble-Zurek (KZ) mechanism of formation of the domain-wall type defects in an adiabatic regime is convenient

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for a description of dynamics of these transitions [8, 9]. As topological defects, domain walls are broadly known in their universality [10, 11], from cosmological models to the theory of condensed matter [1, 12]. The initial Landau-Zener (LZ) Hamiltonian [13] of a two-level system expresses the dynamical processes at classical phase transitions. Afterward, the LZ Hamiltonian has been generalized onto quantum phase transitions. Here, we identify the domain-wall defect formation with the some quantum phase transition at the last (“adiabatic”) stage of the LZ-type evolution, which includes three regimes in general [8]. Then, one may apply a formalism of adiabatic quantum computations, or Quantum Annealing (AQC-QA), with the KZ approach [12] in absence of frustrations. This modeling enables us to estimate a density of kinks and a residual energy, corresponding to the one-dimensional quantum Ising system with the time-dependent term of a transverse field, the Hamiltonian of which is [12]: H (t ) = −∑ J iσ iz σ iz+1 − Γ(t )∑ hiσ ix , i

i

(1)

here, σiz, σix are the Pauli matrices for the i-th spin of the chain. Ji denote random couplings between neighboring spins, and hi is a random transverse field. The function of time Γ(t) serves for rescaling a transverse field hi at an annealing rate τ-1 : t Γ(t ) = − ,τ ∈ (−∞,0] .

(2)

τ

One should note, that following the KZ scenario, in the end of the ordering into a nonequilibrium state, the transition time τQ and the average finite ordered domain size ξˆ are connected by

ξˆ ≅ τ Qν /( zν +1) ,

(3)

where z and ν are critical exponents [14]. The LZ Hamiltonian describes the evolution of a system in time t:  t  ~ 1 τQ H= 2 1  

 1   t . −  τQ 

(4)

In the adiabatic-impulse approach, with the evolution of a system in time t from –∞ to 0, after completion of the transition, the density of kinks equals [15]: n = lim

N = +∞

1 2N

n = N −1

∑ (1 − σ

z n

σ nz +1 ) .

(5)

n =1

In other words, dynamics in a system can be exactly described by a series of uncoupled LZ systems [15, 16]. The authors of [12] have analyzed the fermionic Hamiltonian received by applying the JordanWigner transformation to the Hamiltonian (1). To treat the question of dynamics, they have solved a system of linear differential equations received from the fermionic Bogoliubov’s equations by means of the known ansatz. So, in agreement with [14], at a finite τ and at LZ factor, scaled by the Bogoliubov–de Gennes transformation, the density of kinks and the residual energy, reduced to the total lattice size L, can be estimated respectively by the next relations [12]:

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1 [ Π −1 (ε )]2 ≥ , Lε (τ ) log2 (γτ )

ρ k (τ ) ~ ~

1  E res   L  ~ log ξ (γτ ) .  

211

(6)

(7)

The ζ parameter has been found numerically, ζ ≈ 3.4 ± 0.2 [12]. γ are the Bogoliubov operators diagonalizing H(t); Π is the universal function, and Π −1 denotes the inverse function of Π [12]; the characteristics g is defined by the equality g = − log(− ∆1 ) / L . ∆1 = 2(ε 1 + ε 2 ) is the excitation energy of single-particle eigenvalues ε i , ε 1 ≤ ε 2 ≤ ... ≤ ε L . Eres = Et - Ecl, here, Et denotes the time~ evolved state energy, and Ecl is the classical ground state energy; L is the lattice size, and Lε (τ ) is a length of the defect-free region upon annealing. The critical point probability (ibid) is ∞

P cr (τ , L) ≈ Π ( g c ) ≡ ∫ dgP ( g ) . gc

(8) gc denotes the characteristics g in the critical point. The exact chain's probability P depending on concentration is known [15]. In principle, we know the classical 2D Ising simulation with Glauber dynamics [9] (the heat bath algorithm) for a non-equilibrium system under the KZ mechanism. The continual version of the Hamiltonian with pure relaxation time is given there. It seems useful for our goal, because, in such model, the "domain walls" are always annihilating [9]. However, we can not follow it directly by virtue of the reasons shown below. Numerical modeling and results

According to the hypothesis of displacing lipids motion [5], we carry out the numerical experiments in the spirit of the quantum model of [12] and references therein, but for a 3D Ising lattice allowing frustrations. To involve “concentration” in this modeling, we have to keep a number of particles during simulations. At free field parameters, let us assume that the Hamiltonian (1) is a bosonized Hamiltonian of our particles, so that we operate with the spin variables σ = ± 1. Then, above the critical point [17], at the periodical boundary conditions on the bcc-lattice of 48 × 48 × 48 and 60 × 60 × 60 sizes, we calculate this energy (Fig. 1) and the kink density (Fig. 2). For the Hamiltonian (1), we have performed a typical Monte Carlo (MC) algorithm, in which the probability of states is exp (-∆H/kBT), where T is absolute temperature, kB is the Boltzmann factor, and ∆H is the energy difference between neighboring states. A number of MC running steps equals 106, and the thermalization is carried out in 105 steps. Discussion

At the adiabatic regime (Fig. 1), the average residual energy behaves in agreement with the KZ mechanism (see, for instance, [12]). These data allow us to discuss, how far the LZ theory is satisfied to the hypothesis, following from the experiment [5], where a density of kinks could be measured hereafter. The lattice models for lipids are widely known [18]; in their frames, an aggregation scale and a lattice size are comparable. Thus, it will be possible to construct a structure parameter of fluid aggregates and lipidic mixtures in terms of quantum Ising models [8]. Some interesting 3D calculations [19] are known for vortex strings in the He isotopes, which qualitatively agree with our results (Fig. 2).

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However, our approach encloses the next problem. The KZ-type models contain a concentration dependence, an absence of which was emphasized especially for the cryogenic experiments [5] on the lipid mixtures. Sometimes [15, 16], at the calculations of domain wall sizes in the onedimensional case, this question is imperceptible, but is not solved for different types of soft solids [3, 5].

10

- 1

3 60

3 /L

3 48 10

- 2

10

- 3

100

τ

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Fig. 1. Average residual energy per site as a function of the annealing rate τ.

8E- 5

n

6E- 5

4E- 5

L in e ar f it o f d at a 2E- 5 500

1000

τ

Fig. 2. Density of kinks as a function of the annealing rate τ for the 60 × 60 × 60 size lattice. Conclusion So, in contrast to lipidic phases without defects, where phase transformations may be characterized in classical Ising models [20], the case of unexplored low-temperature phase transitions compels us to involve the quantum lattice model with a random transverse field. If the domain walls are annihilating and/or generating a new phase, then it is reasonable to continue the experiments in a wide amplitude and frequency range. The discussed model can be tested also in neutron diffraction experiments on similar lipidic membranes [6].

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In the case of AFM, and in general in the presence of a substrate [7, 21], the observable relaxation peaks have to be separately specified. Acknowledgement The author thanks Prof. F. Tokumasu and Prof. R. Cantelli for useful discussions, and Prof. I. S. Golovin for help in data processing. For the simulations, the FORTRAN programs composed jointly with Prof. V. A. Kashurnikov, were adapted. References [1] M. Kleman and O. D. Lavrentovich: Philosophical Magazine. Vol. 86 (2006), p. 4117. [2] L. V. Elnikova: E-print archives, cond-mat/0601651. [3] H. M. Wyss, K. Miyazaki, J. Mattsson, Z. Hu, D. R. Reichman and D. A. Weitz: Phys. Rev. Lett. Vol. 98 (2007), p. 238303. [4] K. Miyazaki, H. M. Wyss, D. A. Weitz and D. R. Reichman: Europhys. Lett. Vol. 75 (2006), p. 915. [5] C. Castellano, J. Generosi, D. Pozzi and R. Cantelli: Mater. Sci. And Eng. A Vol. 442 (2006), p. 375. [6] J. Zbytovska, M. A. Kiselev, S. S. Funari, V. M. Garamus, S. Wartewig and R. Neubert: Chem. and Phys. of Lipids. Vol. 38 (2005), p. 69. [7] F. Tokumasu, A. J. Jin, G. W. Feigenson and J. A. Dvorak: Biophys. J. Vol. 84 (2003), p. 2609. [8] W. H. Zurek, U. Dorner and P. Zoller: Phys. Rev. Lett. Vol. 95 (2005), p. 105701. [9] J. Dziarmaga: Acta. Physica. Polonika. B Vol. 35 (2004), p. 2205. [10] A. Seidel and D.-H. Lee: Phys. Rev. B Vol. 76 (2007), p. 155101. [11] R. Auzzi, M. Shifman and A. Yung: Phys. Rev. D. Vol. 72 (2006), p. 025002. [12] T. Caneva, R. Fazio and G. E. Santoro: E-print archives, cond-mat/0706.1832. [13] C. Zener: Proc. Roy. Soc. London Vol. 137 (1932), p. 696. [14] J. Dziarmaga: Phys. Rev. B. Vol. 74 (2006), p. 064416. [15] B. Damski and W. H. Zurek: Phys. Rev. A. Vol. 73 (2006), p. 063405. [16] J. Dziarmaga: Phys. Rev. Lett. Vol. 95 (2005), p. 245701. [17] P. Laguna and W. H. Zurek: Phys. Rev. Lett. Vol. 78 (1996), p. 2519. [18] Z. Zhang, M. Laradji, H. Guo, O. G. Mouritsen and M. J. Zuckermann: Phys. Rev. A Vol. 45 (1992), p. 7560. [19] N. D. Antunes, L. M. A. Bettencourt, and W. H. Zurek: Phys. Rev. Lett. Vol. 82 (1999), p. 2824. [20] H. L. Schott: Phys. Rev. A Vol. 37 (1988), p. 263. [21] K.-I. Akabori, K. Tanaka, A. Takahara, T. Kajiyama and T. Nagamura: Eur. Phys. J. Special Topics. Vol. 141 (2007), p. 173.

Solid State Phenomena Vol. 137 (2008) pp 215-230 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.215

Mechanical Spectroscopy of Oil Films on Metallic and Neutral Substrates L. B. Magalas AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland [email protected] Keywords: Mechanical spectroscopy, internal friction, thin films, arachis oil, cold-rolled steel sheets, substrate.

Abstract. Characteristic low-temperature mechanical loss peaks are reported in cold-rolled steel sheets. Similar mechanical loss peaks are observed in both metallic and paper substrates covered with thin oil films. The surface induced origin of these peaks is elucidated through direct comparison of mechanical loss peaks observed in the as-received, cold-rolled samples with loss peaks observed in metallic and paper substrates covered with thin films of the arachis oils. In all of these instances, similar low-temperature mechanical loss peaks are observed in the temperature range from 180 K up to 300 K in both low-frequency resonant and low-frequency sub-resonant mechanical spectrometers. It is concluded that low-temperature mechanical loss peaks are generated by surface induced effects that arise from the oil film itself. Introduction Industrially produced steel sheets are normally investigated from a metallurgical point of view, that is, mechanical properties of steel sheets are the primary subject of the investigation. In this work, however, the bulk properties of steel sheets are neglected, and instead we focus on surface related issues. This is especially important for steel sheets that are subjected to secondary operations, such as surface coating. In this case, the condition of the sheet’s surface is critical. It is demonstrated that mechanical spectroscopy can be successfully used to detect fine, microscopic-size traces of oil debris present on the surface of steel sheets. The results obtained from cold-rolled steel sheets and from laboratory-cleaned steel samples covered with an arachis oil film containing different amounts of sulphur are similar. In addition similar results are obtained on different substrates covered with the same oil films. It is clearly shown that low-temperature mechanical loss spectra described in this work are generated by surface induced effects that take place in the oil film itself. We shall not address a detailed interpretation for each constituent peak present in the complex low-temperature mechanical loss spectra. We will, however, present selected experimental results that can be repeatedly reproduced under strictly controlled experimental conditions. It is concluded that the complex mechanical loss spectra observed in the temperature range between 180 K and 300 K are due to the presence of microscopic oil debris retained on steel sheets after industrial coldrolling and industrial cleaning. Experimental procedure Three types of samples were investigated in this study: (1) samples taken from ferritic steel sheets after cold-rolling, (2) samples prepared from ordinary paper and (3) metallic and paper samples covered with a thin film of different types of oil. In the proceeding sections, the paper samples will be referred to as the neutral substrate and the metallic samples as the metallic substrate. The oils used for oil-film deposition on metallic and neutral substrates were supplied by a steel plant. The oils are used as rolling oil, a cooling/lubricating media used during cold rolling of steel sheets [1, 3 - 5]. Figure 1 shows that all oils used in this study can be identified as the arachis oil as

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6,0 5,5

0.40 %S 0.41 %S

5,0 4,5

0.70 %S 0.74 %S

4,0 3,5

I

3,0 2,5 2,0 1,5 1,0 0,5 0,0 4000

3500

3000

2500

2000

1500

1000

500

ν~ [cm −1 ]

Fig. 1. Infrared spectroscopy of rolling oils under examination. Oils contained various amounts of sulphur: 0.40 %, 0.41 %, 0.70 %, and 0.74 % [1]. based on results obtained from infrared spectroscopy utilizing a Perkin-Elmer DSC7 IR spectrometer [1]. The oils used by a steel plant possess similar physico-chemical properties regardless of the oil producer. Chemical analysis of these oils, however, revealed that the oils contain the following sulphur levels: 0.40 %, 0.41 %, 0.70 %, and 0.74 %. It should be mentioned that the investigated oils were delivered from different producers at different times. The oils used in this study were based on the arachis oil doped with various amounts of sulphur. These oils were also used in the laboratory scale to cover metallic and neutral substrates with oil-films. Metallic Substrate Mechanical loss measurements of metallic specimens were carried out in an inverted torsion pendulum in the resonant mode. The logarithmic decrement δ was determined from free decaying exponentially damped harmonic oscillations at the resonant frequency around 1.3 Hz [6, 7]. The experiments were performed on several grades of cold-rolled steel sheets [1, 3, 4]. Typical chemical composition of investigated steel sheets was: 0.01 - 0.04 % C, 0.20 - 0.24 % Mn, 0.02 % Si, 0.006 0.009 % P, 0.010 - 0.012 % S, 0.02 - 0.04 % Cr, 0.035 - 0.043 % Al, 0.0037 - 0.0055 % N2 and 0.02-0.03% Cu. The metallic samples used in mechanical loss experiments were prepared in the form of platelets 0.22 × 2.0 × 90.0 mm3. The platelets were excised from steel sheets at the same angle in relation to the rolling direction. An axial magnetic field of 140 Oe was applied during mechanical loss measurements to suppress magnetomechanical damping that occurs in ferromagnetic samples. Investigated samples were analyzed in three states: (1) Samples in the as- received state: The samples were excised from steel sheets in the as-received condition, i.e. after cold rolling followed by an industrial cleaning in the rolling line. Samples were not yet subjected to the annealing procedure in an industrial furnace. (2) Laboratory-cleaned samples: The samples in the as-received state were subjected to a laboratory cleaning procedure comprised of cleanning and chemically etching away the surface layer (removal of a surface layer 0.02 - 0.04 mm thick).

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(3) Samples after oil-film deposition: Laboratory-cleaned samples were covered with thin films of the arachis oils. Low-frequency mechanical spectroscopy was used to study the effect of oil films deposited on different substrates. In the case of oil-film deposition on laboratory-cleaned metallic substrates, the experimental set-up was monitored and executed under reliable and repeatable controls with the condition of the substrate, surface of the substrate and parameters of the liquid oil precisely controlled. By contrast, the surface condition of the metallic samples excised from cold-rolled steel sheets was subject to the actual industrial process comprised of cold rolling and industrial cleaning during production. The surface quality of cold-rolled steel sheets in the as-received state was verified by light video-microscopy, light microscopy, scanning electron microscopy, Barkhausen noise, and electric resistivity. The upper and lower sides of the steel sheets were identified by IBN, Identified Barkhausen Noise Analysis [7]. This procedure enabled reliable control of all the samples in the as-received state. Nonetheless, the experimental techniques used in this study to control the surface quality were not able to detect the presence of fine oil debris retained on the surface of industrially cleaned cold-rolled steel sheets. That is why mechanical spectroscopy is successfully used in this work as a new technique to determine the surface quality of cold-rolled steel sheets. Mechanical loss spectra reported in this paper are obtained in cold-rolled steel sheets for different surface conditions: (1) following the industrial cleaning procedure (as-received samples), (2) following the thorough surface laboratory-cleaning procedure, (3) following the covering of a clean sample with thin films of the arachis oils with various sulphur content, (4) following the covering of a clean sample with oil films showing different oil consistency (oil films deposited at room temperature and oil films heated up to 340 - 343 K followed by film deposition on steel surface) and (5) following the covering of a clean sample with thin oil films collected from different fractions of the arachis oil. Paper Substrate Mechanical loss measurements were also carried out in a low-frequency sub-resonant mechanical spectrometer on paper samples. The paper was utilized in this study as a neutral substrate for oil films. The paper substrates were 0.09 mm thick. The sub-resonant mechanical loss measurements on neutral substrates were carried out incrementally at two pre-selected, constant frequencies of forced oscillations: 0.10 Hz and 0.31 Hz. These two consecutive frequencies of forced oscillations were used in nearly parallel sequence during linear heating and/or cooling in the temperature range from 175 K to 300 K. Experimental Results Mechanical Spectroscopy of Steel Sheets in the As-received State Figure 2 shows typical mechanical loss spectra (internal friction curves), Q-1 = δ /π = f (T), obtained for the as-received steel sheets during the first run-up, (Fig. 2 a), and during the second run-up, (Fig. 2 b), which follows in-situ annealing in the spectrometer during the temperature ramp up to 473 K. Characteristic low-temperature mechanical loss peaks occur in the temperature range from 150 K up to 300 K. Two significant peaks are discernable near 220 K and 275 K [5]. Figure 3 clearly demonstrates that the characteristic low-temperature mechanical loss spectra disappear after precise laboratory cleaning of the metallic samples [1, 2, 5]. Laboratory cleaning of the surface not only eliminates the low-temperature spectra but also decreases the background, thereby reducing the height of the Snoek-Köster (SK) peak (see Fig. 3, curve 2).

Interaction between Defects and Anelastic Phenomena in Solids

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45 40 35 30

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25 20 15 10

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f 2Q [ 1× /10 s2 ]

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1,75

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-1

× 10

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Fig. 2. (a) Typical mechanical loss spectra of cold-rolled ferritic steel sheets after industrial cleaning, i.e. in the as-received state. The first run-up, Q-1 = f (T). (b) The second run-up, Q-1 = f (T), i.e. after annealing of the sample during the first run-up completed at 473 K. The arachis oil film contained 0.40 % of sulphur. Frequency of free decaying oscillations f ≈ 1.3 Hz [5]. 55 50 45 40 35 30 25 20 15 10 5 0

1 SK

2

150

200

250

300

350

400

450 500 T [K ]

Fig. 3. Mechanical loss spectra of cold-rolled steel sheet. Curve 1 – as-received state, i.e. after cold rolling and industrial cleaning, curve 2 – after thorough surface laboratory - cleaning procedure [1]. The relaxation phenomena that occur in cold-rolled steel sheets are not addressed in this work. It should be mentioned, however, that carbon and nitrogen Snoek peaks were not observed in the asreceived samples. The loss peak that occurs between 270 and 295 K (Figs. 2, 3) should not be misinterpreted as the nitrogen Snoek peak. A well developed SK peak [8 - 13] was observed around 420 K in the as-received samples (see Figs. 2 a, 3) [1]. The SK peak decreases in magnitude and shifts towards lower temperatures in the second run-up (Fig. 2 b) [12, 13]. This behavior occurs because the sample is inevitably annealed in the spectrometer (inverted torsion pendulum) during mechanical loss measurement in the first run-up as the temperature reaches 473 K (Fig. 2 a) followed by a slow cool to room temperature. For completeness it should be mentioned that the SK

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peak does not occur after the batch annealing of steel sheets, an operation that normally follows cold-rolling and industrial cleaning. It should be emphasized that the shape and the height of the low-temperature spectra are hardly reproducible in steel sheets in the as-received state.

55 50 SK

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Q -1 x 10 4

40 35 30 25 20 15 10 5 0 100

200

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400 500 T [K]

Fig. 4. The Snoek-Köster peak and the low-temperature mechanical loss peaks observed in coldrolled steel sheets in the as-received state, f ≈ 1.35 Hz. Sulphur content in the rolling oil was 0.40 %. Figure 4 illustrates a small, irregular increase on the low-temperature side of the SK peak. These small peaks occur in the temperature range 180 K – 300 K and are still similar to those shown in Fig. 2. Figure 5 shows mechanical loss spectra obtained for the laboratory-cleaned steel sample covered with oil films containing various amounts of sulphur, 0.41 % (curve 1), 0.70 % (curve 2) and 0.74 % (curve 3) (note the different scale between curve 1 and curves 2, 3). Figure 5 proves that an oil film deposited on clean steel surface generates low-temperature mechanical loss spectra that are not observed in samples with a clean surface (compare Fig. 3, curve 2). An increase in the sulphur content of the deposited oil substantially decreases the height of the low-temperature peaks, but their temperature location is unaffected. The shape of the low-temperature mechanical loss peaks can be used to distinguish different oil films.

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600 1

60

0.41 %S

50

1 × 10 4

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2 30

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Fig. 5. Mechanical loss spectra of laboratory-cleaned cold-rolled steel sheets covered with a film of arachis oils containing various amounts of sulphur. Curve 1 − 0.41 % S, curve 2 − 0.70 % S, curve 3 − 0.74 % S [1]. Figure 6 shows typical mechanical loss spectra, Q-1 = f (T), obtained for the laboratory-cleaned steel samples covered with the arachis oil films containing 0.40 % (Fig. 6 a) and 0.70 % (Fig. 6 b) sulphur. The low-temperature peaks are higher and more discernable as compared to the as-received samples (see Figs. 2, 4). Figure 6 confirms that an oil film deposited on a clean-surface steel sample generates the characteristic low-temperature mechanical loss spectra [1, 5]. It can be concluded, therefore, that the low-temperature mechanical loss spectra observed in the as-received steel sheets (Figs. 2 - 4) are very similar to the loss spectra shown in Fig. 6 that were obtained after deposition of arachis oils containing different amounts of sulphur. The low-temperature mechanical loss spectra shown in Fig. 6 were obtained after oil deposition at room temperature. Figure 7 illustrates the impact of oil film temperature during deposition on the loss spectra. Here, the mechanical loss spectra observed in the second run-up (Fig. 7, curve 2) are analogous to the loss spectra observed in a sample coated with a thin film of the oil heated to 340 343 K (Fig. 7, curve 1) prior to deposition. It can be concluded, therefore, that the oil temperature during deposition (oil consistency/density) influences the shape and the amplitude of the mechanical loss spectra measured in the low-temperature range from 150 K up to 300 K. In each experimental scenario, however, the shape of the characteristic low-temperature mechanical loss spectra remains consistent (Figs. 2 - 7). The above oil-film deposition was done with the use of: (1) oil liquid thoroughly mixed at room temperature to obtain a homogeneous liquid (Figs. 5, 6) and (2) oil heated to an elevated temperature (Fig. 7) that simulates the working conditions in the rolling gap during cold-rolling of steel sheets.

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T [K] b) Fig. 6. Mechanical loss spectra of laboratory cleaned cold-rolled steel sheets covered with a thin film of arachis oils containing various amounts of sulphur: (a) 0.40 % S and (b) 0.70 % S. The samples were subjected to laboratory-cleaning procedure prior to oil film deposition [5].

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40

1

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0 100

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500 T [K]

Fig. 7. The low-temperature mechanical loss spectra observed in cold-rolled steel sheets after direct contact of steel sheets with the arachis oil containing 0.40 % S. Curve 1 – the first run-up, Q-1 = f (T), in a cold-rolled steel sheet after the laboratorycleaning procedure and covering the sample with a film of the arachis oil containing 0.41 % S. Temperature of the arachis oil during deposition was approximately 340 - 343 K. Curve 2 – the second run-up, Q-1 = f (T), in a cold-rolled steel sheet after industrial cleaning (as-received state) and after annealing at 473 K (see Fig. 2 b). Frequency of free decaying oscillations f ≈ 1.3 Hz. If careful attention is not taken when mixing the oil or if the oil is allowed to stand for extended time periods, the liquid will separate. As a result, the density of the liquid in the upper portion of the container will be less than the density of the liquid in the bottom portion. And further, both of these densities will be distinct from the density of the mixed liquid. To distinguish between these conditions, we will refer to the lower density liquid as upper fraction, the higher density liquid as bottom fraction and the thoroughly mixed liquid as mixed fraction. With that in mind, let us now consider the effect of these oil fractions on the characteristic low-temperature mechanical loss spectra. Figure 8 shows the low-temperature mechanical loss spectra observed after deposition of the three different fractions of the arachis oil containing 0.40 % S. The impact of the mixed fraction deposited on the steel surface is shown in Fig. 8a, and these spectra are similar to those in Fig. 6a. It is interesting to note that the upper and the bottom oil fractions deposited on the steel surface yield different spectra as shown in Fig. 8 b and Fig. 8 c, respectively. Although annealing at 473 K suppresses mechanical loss spectra below 220 K (Fig. 8, curves 1’, 2’, 3’), it does not suppress the loss peak around 270 K (Fig. 8a, curve 1’) as effectively. Thus, it can be concluded that the lowtemperature mechanical loss spectra are not only sensitive to the oil fraction, but also to its density/consistency and the annealing temperature.

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F2a 40

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c) Fig. 8. Mechanical loss spectra of laboratory cleaned cold-rolled steel sheets covered with a thin film of the arachis oil containing 0.40 % of sulphur. (a) Oil film with mixed oil fractions. (b) Oil film from the upper oil fraction. (c) Oil film from the bottom oil fraction. Curves 1, 2, 3 – the first run-up, Q-1 = f (T). Curves 1’, 2’, 3’ – the second run-up, that is, after annealing at 473 K [5]. It was hypothesized that the mechanical loss peak observed around 270 K originates from a phase transformation of the arachis oil from the solid into liquid phase (i.e. melting) that takes place within the film [1 - 5]. That is why the presence of fine oil debris on the surface of steel samples is sufficient to induce the mechanical loss peak generated by the oil phase transformation around 270 K [1, 5]. Extra care, therefore, must be exercised to keep the surface of metallic samples (e.g. cold-rolled steel sheets) investigated by mechanical spectroscopy perfectly clean; otherwise, mechanical loss spectra may be highly susceptible to the presence of oil debris on the surface. Further experimental and theoretical study is required to better comprehend the behavior of the characteristic low-temperature mechanical loss peaks induced by the presence of organic oil films on the surface of steel sheets and other substrates.

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Mechanical Spectroscopy of Metallic Covered with Oil Films Figure 6 shows typical mechanical loss spectra, Q-1 = f (T), obtained for the laboratory-cleaned steel samples covered with the arachis oil films containing 0.40 % (Fig. 6 a) and 0.70 % (Fig. 6 b) sulphur. The low-temperature peaks are higher and more discernable as compared to the as-received samples (see Figs. 2, 4). Figure 6 confirms that an oil film deposited on a clean-surface steel sample generates the characteristic low-temperature mechanical loss spectra [1, 5]. It can be concluded, therefore, that the low-temperature mechanical loss spectra observed in the as-received steel sheets (Figs. 2 - 4) are very similar to the loss spectra shown in Fig. 6 that were obtained after deposition of arachis oils containing different amounts of sulphur. The low-temperature mechanical loss spectra shown in Fig. 6 were obtained after oil deposition at room temperature. Figure 7 illustrates the impact of oil film temperature during deposition on the loss spectra. Here, the mechanical loss spectra observed in the second run-up (Fig. 7, curve 2) are analogous to the loss spectra observed in a sample coated with a thin film of the oil heated to 340 343 K (Fig. 7, curve 1) prior to deposition. It can be concluded, therefore, that the oil temperature during deposition (oil consistency/density) influences the shape and the amplitude of the mechanical loss spectra measured in the low-temperature range from 150 K up to 300 K. In each experimental scenario, however, the shape of the characteristic low-temperature mechanical loss spectra remains consistent (Figs. 2 - 7). The above oil-film deposition was done with the use of: (1) oil liquid thoroughly mixed at room temperature to obtain a homogeneous liquid (Figs. 5, 6) and (2) oil heated to an elevated temperature (Fig. 7) that simulates the working conditions in the rolling gap during cold-rolling of steel sheets. If careful attention is not taken when mixing the oil or if the oil is allowed to stand for extended time periods, the liquid will separate. As a result, the density of the liquid in the upper portion of the container will be less than the density of the liquid in the bottom portion. And further, both of these densities will be distinct from the density of the mixed liquid. To distinguish between these conditions, we will refer to the lower density liquid as upper fraction, the higher density liquid as bottom fraction and the thoroughly mixed liquid as mixed fraction. With that in mind, let us now consider the effect of these oil fractions on the characteristic low-temperature mechanical loss spectra. Figure 8 shows the low-temperature mechanical loss spectra observed after deposition of the three different fractions of the arachis oil containing 0.40 % S. The impact of the mixed fraction deposited on the steel surface is shown in Fig. 8 a, and these spectra are similar to those in Fig. 6a. It is interesting to note that the upper and the bottom oil fractions deposited on the steel surface yield different spectra as shown in Fig. 8 b and Fig. 8 c, respectively. Although annealing at 473 K suppresses mechanical loss spectra below 220 K (Fig. 8, curves 1’, 2’, 3’), it does not suppress the loss peak around 270 K (Fig. 8a, curve 1’) as effectively. Thus, it can be concluded that the lowtemperature mechanical loss spectra are not only sensitive to the oil fraction, but also to its density/consistency and the annealing temperature. It was hypothesized that the mechanical loss peak observed around 270 K originates from a phase transformation of the arachis oil from the solid into liquid phase (i.e. melting) that takes place within the film [1 - 5]. That is why the presence of fine oil debris on the surface of steel samples is sufficient to induce the mechanical loss peak generated by the oil phase transformation around 270 K [1, 5]. Extra care, therefore, must be exercised to keep the surface of metallic samples (e.g. coldrolled steel sheets) investigated by mechanical spectroscopy perfectly clean; otherwise, mechanical loss spectra may be highly susceptible to the presence of oil debris on the surface. Further experimental and theoretical study is required to better comprehend the behavior of the characteristic low-temperature mechanical loss peaks induced by the presence of organic oil films on the surface of steel sheets and other substrates.

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Sub-resonant Mechanical Spectroscopy of Paper Substrate Covered with Oil Films Figure 9 shows typical temperature dependence of the mechanical loss angle measured at two constant frequencies, 0.10 Hz and 0.31 Hz, for the paper neutral substrate covered with the oil film containing 0.40 % S. 300

2.5 tg ϕ ,

G ’ - 0, 31 Hz

tg ϕ ,

G ’ - 0, 10 Hz

2.0

200 1.5 150 1.0 100

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Fig. 9. Mechanical loss angle versus temperature for a neutral paper substrate covered with the oil film containing 0.40 % of sulphur. Forced oscillations at 0.10 Hz and 0.31 Hz. Low-frequency sub-resonant mechanical spectroscopy readily resolves the characteristic lowtemperature mechanical loss spectra observed in the as-received steel sheets and in steel substrates covered with different oil films into three distinct peaks. These peaks are situated near 188 K, 215 K, and 270 K [1, 3 - 5]. The effect of the oscillation frequency on the shape of the 270 K peak is clearly demonstrated in Fig. 9 b. The 270 K peak is sharp and asymmetrical. The asymmetry increases with the increase in frequency. The high-temperature side of the 270 K peak does not dependent on the frequency of forced oscillations. This peak represents typical features of a mechanical loss peak induced by the phase transformation from the solid into liquid state [1]. The 270 K peak can arise from a phase transformation of the arachis oil from the solid into liquid phase within the oil film during mechanical loss measurement. Figure 10 shows the 270 K peak measured at 0.10 Hz and 0.31 Hz for the paper neutral substrate covered with the arachis oil films containing various amounts of sulphur: 0.40 % S (Fig. 10 a), 0.70 % S (Fig. 10 b) and 0.74 % S (Fig. 10 c). Measurements of the mechanical loss angle were

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carried out during cooling from room temperature. In all investigated cases the 270 K peak exhibits the same behavior characteristic for phase transformation from the solid into liquid state. The hightemperature side of the 270 K peak shown in Figs. 9 and 10 does not depend on the frequency. 300

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Fig. 10. The 270 K peak observed at two consecutive frequencies 0.10 Hz and 0.31 Hz in neutral paper substrate covered with a thin film of the arachis oil containing various amounts of sulphur: (a) 0.40 % S, (b) 0.70 % S and (c) 0.74 % S. Mechanical loss measurements were carried out during cooling from room temperature. Mechanical Spectroscopy of Metallic and Neutral Substrates Covered with Arachis Oil Films Figure 11 illustrates several similarities, which can be deduced from mechanical loss spectra obtained with metallic and paper substrates covered with the same oil film containing 0.40 % S. Let us recall that resonant and sub-resonant techniques were employed to study temperature variation of the mechanical loss in oil-covered metallic and neutral substrates, respectively.

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Fig. 11. Mechanical loss spectra obtained in the resonant mode for laboratory-cleaned steel sheets covered with a film of the arachis oil containing 0.40% of sulphur (curve 2 – Q-1 = f (T), frequency of free decaying oscillations f ≈ 1.3 Hz) and in the subresonant mode for a paper neutral substrate covered with a film of the same oil (curve 1 – tg ϕ = f (T), frequency of forced oscillations = 0.31 Hz) [1]. The narrow 180 K peak in the paper substrate covered with the oil (Fig. 11, curve 1) resembles a relaxation peak. The peak temperature occurs at a similar temperature in both oil film-covered metallic and paper substrates. However, the complex shape of the low-temperature mechanical loss peaks in metallic substrates (Fig. 11, curve 2) does not yield any information about the existence of a narrow 180 K peak as readily observed in neutral substrates (Fig. 11, curve 1). The 270 K peak also occurs at the same temperature in both oil-covered metallic and paper substrates (Figs. 9 - 11). The skew asymmetry of the high temperature side of the 270 K peak is similar for both substrates. The peak temperature, its shape and asymmetry all coincide in paper and metallic substrates regardless of sulphur concentration in the oil. The use of a neutral substrate covered with oil films enabled us to detect a well-defined peak located between the 180 K peak and the 270 K peak. It should be emphasized, therefore, that the low-temperature mechanical loss spectra of metallic and neutral paper substrates with identical oil depositions overlap regardless of the substrate. The mechanical loss spectra shown in Figs. 2 - 8 demonstrate that low-frequency resonant mechanical spectroscopy of oil-covered metallic substrates yields the characteristic low-temperature mechanical loss spectra that are complex and extremely difficult to resolve and interpret. By contrast, the low-frequency sub-resonant mechanical spectroscopy obtained with oil-covered neutral substrates provides superior resolution of the spectra into three distinct peaks located at 188 K, 215 K, and around 270 K (see Figs. 9, 11). It can be concluded that similar in shape, mechanical loss spectra were obtained for oil films deposited on both the paper and metallic substrates. Discussion and Conclusions It has been suggested [14 - 17] that the low-temperature mechanical loss peaks observed in metallic and ceramic substrates [17] coated with films of synthetic oil or synthetic grease can be interpreted in terms of hydrogen-induced relaxation effects occurring in a metallic substrate. In our opinion, any interaction between an oil film and a metallic substrate that might influence the origin of the

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characteristic low-temperature mechanical loss peaks can be ruled out. The characteristic lowtemperature mechanical loss spectra observed in metallic substrates (cold-rolled steel sheets and clean metallic substrates covered with oil films) are consistent with the sub-resonant mechanical loss spectra, tg ϕ = f (T), observed in neutral substrates covered with the same oil films [1 - 5]. Moreover, sub-resonant mechanical spectroscopy readily resolves the characteristic lowtemperature mechanical spectra into three constituent peaks located at 188 K, 215 K, and approximately 270 K [1]. It is also concluded that the mechanical loss spectra induced by the presence of the arachis oil are similar regardless of the nature of the substrate (steel or a paper, copper or brass) [1 - 5]. For the reasons outlined above, we propose that the observed mechanical loss peaks arise in the oil film itself. In other words, the interaction between the oil film and the metallic substrate is negligible. Mechanical spectroscopy can definitively reveal the presence of extremely fine oil debris present on the surface of cold-rolled steel sheets and other metallic substrates and the presence of oil films deposited on the surface of metallic and neutral substrates. Resonant and sub-resonant mechanical loss spectra reveal the presence of an asymmetrical peak around 270 K whose origin is the phase transformation of the solid to liquid phase within the oil film during heating or cooling. The lowtemperature constituent mechanical loss peaks (188 K, 215 K, and approximately 270 K) are more distinct in sub-resonant mechanical spectroscopy as compared to resonant mechanical spectroscopy. Mechanical spectroscopy can be successfully used to study organic materials and organic thin films. Acknowledgements This work was supported by Polish Ministry of Science and Higher Education under grant No.11.11.110.656. References [1]

L. B. Magalas, S. Etienne, L. David, T. Malinowski: Sol. St. Phen., Vol. 89 (2003), p. 326.

[2]

L. B. Magalas, Q. F. Fang: Acta Metall. Sin., Vol. 39 (2003), p. 1228.

[3]

L. B. Magalas, T. Malinowski, S. Etienne, L. David, J. Kostro: Proc. Conf. XXIX KKBN, on Non-destructive Testing, SIMP, Warsaw, Poland, Vol. 5 (2000), p. 223.

[4]

L. B. Magalas, S. Etienne, D. Laurent: Proc. Conf. XXXI KKBN on Non-destructive Testing, SIMP, Warsaw, Poland, Vol. 7 (2002), p. 257.

[5]

L. B. Magalas, S. Etienne: Sol. St. Phen., Vol. 115 (2006), p. 157.

[6]

L. B. Magalas, T. Malinowski: Sol. St. Phen., Vol. 89 (2003), p. 247.

[7]

L. B. Magalas: J. Alloy Compd., Vol. 310 (2002), p. 269.

[8]

L. B. Magalas: Acta Metall. Sin., Vol. 39 (2003), p. 1145.

[9]

T. O. Ogurtani, M. R. Gungor, E. E. Oren: Sol. St. Phen., Vol. 89 (2003), p. 141.

[10] L. Sun, Y. Wang, M. Gu: Proc. the 9th Int. Conf. on Internal Friction and Ultrasonic Attenuation in Solids, edtied by T. S. Kê International Academic Publishers, Beijing (1990), p. 61. [11] K. L. Ngai, Y.-N. Wang, L. B. Magalas: J. Alloy Compd., Vol. 211 (1994), p. 327. [12] L. B. Magalas: J. Phys. IV, Vol. 6 (1996), p.163. [13] L. B. Magalas, K. L. Ngai, in: Mechanics and Mechanisms of Material Damping, ASTM STP 1304 (1997), p. 189.

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[14] D. Samatowicz, E. Łunarska: Proc. IX Int. Conf. Imperfections Interaction and Anelasticity Phenomena in Solids, Izv. Akad. Nauk – Physics (in Russian), Vol. 62 (1998), p. 1317. [15] D. Samatowicz, A. Zieliński: Proc. Int. Conf. on Engineering Materials Environmental Degradation, EDEM 1999, Gdańsk - Jurata, Poland (1999), p. 381. [16] D. Samatowicz: J. Alloy Compd. Vol. 310 (2000), p. 457. [17] D. Samatowicz, O. Olszewski: Ceramics International. Vol. 22 (1996), p. 187.

Solid State Phenomena Vol. 137 (2008) pp 231-236 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.137.231

On the history of the Russian School of Anelasticity in Solids S. A. Golovin Physics of Metals and Materials Science Department, Tula State University, Tula, Russia

Abstract. A brief historical review of scientific research in the field of anelasticity in solids carried out during the last 50-70 years in the USSR, Russia and states of CIS is given. The XI International Conference “Impurities Interaction and Anelastic Phenomena in Solids” (IIAPS-XI) took place at the Tula State University, Russia in September 24-28, 2007 after two other conferences in Voronezh “Relaxation Phenomena in Solids” (2004) and Vinnica “Structural Relaxation in Solids” (2006). Thus the recent conference continues the long running research activity in Russia in the field of interaction between defects and anelastic phenomena in solids∗. The hysteresis phenomena in different materials and mechanical systems subjected to oscillations were studied already in the 1930s in Russia. The basis of this studies was the theory of nonlinear mechanics introduced by Krylov N.M and Bogolyubov N.N., and by works by Davidenkov N.N. in the field of nonlinear mechanics of materials [1]. Nearly at the same time Clarence Zener formulated the physical basis of anelasticity in solids in his famous book and papers [2, 3]. This was translated in Russia only in 1956. That is why for a long time (1930-1960) two different approaches and terms have been used for the description of energy absorption in solids in Russia or, more general, in the Soviet Union: relative dispersion of energy of the mechanical oscillations (or damping) and internal friction. The Russian scientific school on relaxation phenomena in solids was created due to the scientific and organizing activity of the leading soviet solid state physicists Professor Finkelstein B.N. (Moscow Institute of Steel and Alloys (MISiS), Moscow). He was one co-author of the effect of couple relaxation of interstitial atoms in the face-centered cubic lattice (Finkelstein-Rozin effect, 1953 [4]), which was observed later by Kê and Tsien, [5]. He was the first to observe an oxygen peak in steel and solved many other problems of the physics of metals. He has organized the first three All-Union Conferences on the relaxation phenomena in solids. The last conferences in Voronezh, Vinnica and Tula, which took place already in the XXIst century, have confirmed that in 1950s there were created several research centers on the problems of anelastisity in the materials; apart of the above mentioned places, big research groups were created in St.-Petersburg (Leningrad), Kharkov, Moscow, Ekaterinburg (Sverdlovsk), Tomsk, Perm, Viatka (Kirov), Kiev, Donetzk, Tbilisi, Erevan etc. The first set up for internal friction (IF) tests in the Soviet Union, often also called ‘relaxator’, was a direct torsional pendulum constructed in 1951 in MISiS by Postnikov V.S., Piguzov Yu.V., and Finkelstein B.N. The works of post graduate students and research assistances at the Moscow Institute of Steel and Alloys have obtained wide recognition in the field of studies of different relaxation mechanisms in metals and alloys (Verner V.D., Ashmarin G.M.), in semiconducting and non-metallic materials (Schaskolskaya M.P., Vekilov Yu.Kh., Naimi E.K.), magnetic and magneto∗

Editor’s remark: Professor S.A. Golovin. began internal friction studies in the Tula Polytechnical Institute (now Tula State University) in 1955. In 1956-1957 he worked in the Moscow Institute of Steel and Alloys in the Physics Department, the Head of the Department was Prof. Finkelstein B.N. Since 1958 he works at Tula State University having thirty years experience as a Head of the Physics of Metals and Materials Science Department and Head of Internal Friction Lab. Most recently Prof. S.A. Golovin was elected as an Honorary Chairmen of the consortium for three regular conferences: ‘Relaxation Phenomena in Solids’ (Voronezh) ‘Impurities Interaction and Anelastic Phenomena in Solids’ (Tula), and ‘Structural Relaxation in Solids’ (Vinnica), with Profs. S.P. Nikanorov and V.V. Pal-Val as co-chairs.

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elastic relaxation and hysteresis (Livshits B.G., Kekalo I.B.) and others. In the early 1960s Piguzov Yu.V. became head of the construction bureau at MISiS and assembled several relaxators. The scientific teams working on IF were organized in several Moscow institutes: at the Moscow State University (acousto-plastic, photo-acoustic and surface effects in ion crystals – Tyapunina N.A. et al.), in the Institute of Crystallography and in the Institute of Solid State Physics of the Academy of Science of the USSR (theories of dislocation, phonon and electron relaxations – Indenbom V.L., Chernov V.M., Alshits V.I., Nadgornij E.M., Soifer Ya.M.), in the Central Research Institute of Ferrous Metals (impurity and magnetic relaxations in structural inhomogeneous materials – Lyubov B.Ya., mechanisms of microplasticity and of IF – Sarrak V.I. and Suvorova S.O., high damping alloys – Vintajkin E.Z., Udovenko V.A., Volynova T.F.), computer simulation and analysis of atomic relaxation mechanisms – Blanter M.S., in the Moscow State Pedagogical Institute (relaxation mechanisms in polymers – Barten’ev G.M.), in the Moscow Institute of Chemical Engineering (substructure-ordered states of metals – Gordienko L.K.), nonferrous alloys – Piguzov Yu.V. and others. In the 1960-70s the first Russian books on internal friction were published [6, 7]. Later on the translation of the famous Nowik A. and Berry B. book (1972) [8] in Russian was done by Nadgornij E.M., Soifer Ya.M. (1975). These books played a remarkable role in the expansion of the investigations on the problem of relaxation in the USSR. In 1960s Prof. Postnikov V.S. relocated to Voronezh, and Voronezh became one of the main centers for studies of relaxation processes in Russia. Research groups of physicists involved in the investigation of IF were established at the Voronezh State Technical University, at the Voronezh State Pedagogical University and at the Voronezh State Academy on Chemistry and Technology. The research work at the Voronezh State Technical University covered a wide range of anelastic phenomena, methods of relaxation peak interpretations, theoretical models for diffusion, dislocation, grain boundaries, domain relaxation mechanisms of IF in amorphous alloys, phase transitions of the Ist and Iind kind in solids (Shermergor T.D., Darinskij B.M. et al.). Experimental studies of IF were carried out for a wide range of materials of different classes: in pure metals and alloys (Usanov V.A., Razumov V.M.), in semiconductors (Rembeza S.I., Mitrokhin V.I.,), in dielectrics and ferroelectrics (Gridnev S.A., Pavlov V.S.), in whiskers and films (Zolotukhin I.V., Kosilov A.M.), in silicate glasses (Balashov Yu.S., Makarov V.N.), in amorphous and nanocrystal metals (Kalinin Yu.E., Kondusov V.A.), in metal alloys with shape memory (Kosilov A.T., Vasilenko A.Yu.), on the non-diffusive phase adsorption in metals (Sharshakov I.M., Belko V.N.) and on the superconducting transition (Miloshenko V.E., Shunin G.E.) and martensitic transformation (Belko, Darinskij): paper [9] gave the idea about IF peak in alloys with thermoelastic martensite developed later in many research papers by Delorme, Dejonghe, Gremaud, Stoiber et al. Experimental studies of IF in crystalline semiconductors have been carried out (Kapustin Yu.A.), in matrix samples containing inclusions with low-melting point (Maslennikov E.M.) and in metals (Gorshkov G.A.). At the Voronezh State Pedagogical University studies of IF in metals during their plastic deformation and after coating of their surface with moistening liquids (El’kin Yu.M., Karataev E.N.) and metallic glasses including bulk glasses (Khonik V.A.) have been carried out. In 1960s the Department of Materials Science and Heat Treatment of Metals in the Tula Polytechnical Institute became another research center (Kristal M.A. - 1960-1972 and Golovin S.A. - 1960-2007) of relaxation and hysteretic anelasticity in Russia. Under their supervision different equipment was created: low-frequency pendula for different applications; kilohertz ranged resonance set-up; ultrasonic set-ups with composite vibrator. The elastic modulus and damping of many steels and alloys were certificated in this Lab and the first Russian automated database was created. Temperature spectra for different anelastic phenomena caused by diffusion, dislocationimpurities interaction, the Snoek, Snoek-Köster, Finkelstein-Rozin effects were studied in a big variety of metallic materials with different structure: in solid solutions and in tetragonal martensite

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of tempered iron based alloys (Baranova V.I., Belkin K.N., Ageev B.S.). The kinetics of decomposition of oversaturated solid solutions was studied (Vlasov V.M., Tikhonova I.V.); dislocation and microdeformation characteristics in metals with bcc, fcc, hcp crystals and in the systems with low stacking fault energy (Levin D.M., Arkhangelskii S.I., Chukanov A.N.), mechanisms of isothermal, athermal and thermo-elastic martensite transformation of invar type, martensite-aged steels and alloys with shape memory (Markova G.V., Golovin I.S.), relaxation phenomena in different ordered alloys (Golovin I.S.) were studied. Deformation fields of structural inhomogeneous systems like cast iron and different composites (Golovin S.A, Arkhipov I.K., Petrushin G.D. et al.), and cellular metals (Golovin I.S.) were studied experimentally and theoretically. New types of alloys with high damping were elaborated for industry based on these experimental and theoretical results. On the basis of an agreement between Ministries of Russia and Czechoslovakia there was organized a Soviet-Czechoslovak Laboratory “Elastic and Anelastic Properties of Metals” (scientific heads – Golovin S.A. and Pušhkar A.) in 1980-1990. The main trend of the laboratory was the problem of mechanical spectroscopy of fatigue processes. Other research centers were developed in Saint-Petersburg and in Kharkov. At the end of 1930s Davidenkov N.N. started investigations in the Physical-Technical Institute after A.I. Ioffe of the Russian Academy of Science in Leningrad (Saint-Petersburg). Since the end of the 1950s this research continued in the Laboratory of Physics of Crystals under the supervision of Stepanov A.V. Investigations of IF in ionic crystals were added by studying effect of electrical polarization caused by the movement of charged edge dislocations. Based on the analysis of the character of dislocation interaction with point defects resulting from impurities and radiation, and correlations of microplastic effects during the oscillation of the samples (acoustic experiments) in the initial stage of plastic deformation were carried out. During the last several decades the study of anelasticity in Saint-Petersburg has been carried out under the general supervision of Nikanorov S.P. by Kardashev B.K., Lebedev A.B., Kustov S.B. et al. They study semiconductors, metals and alloys (in particular alloys of the system V-Ti-Cr that can be used in thermonuclear reactor, shape memory Cu-Al-based alloys), materials with effect of the shape memory, composites and ceramic materials (including biomorphous ceramics SiC/Si) etc. According to the data of an acoustic study of microplasticity it turned out that in some cases it is possible to forecast the behavior of plastic characteristics of material. Some brittle materials have evident microplasticity that confirms the hypothesis of Stepanov A.V.: plastic deformation precedes brittle failure. In Kharkov the investigations have developed mainly in the Physical-Technical Institute of Low Temperatures after Verkin B.I. of the Ukrainian Academy of Science, in the Kharkov PhysicalTechnical Institute and at the Kharkov State University. In 1961 in the Department of Physics of Real Crystals in the Physical-Technical Institute of Low Temperatures Startsev V.I. started the investigation of acoustic properties of crystals with different defect structure. At that time the research group studying internal friction was conducted by Platkov V.Ya., and later by Pal-Val P.P. Natzik V.D., Semerenko Yu.A., Beloshapka V.Ya., Roschupkin A.M. et al. working in neighbouring areas have often taken part in the investigations of internal. The following studies were carried out: for the alkaline-halide single crystals data were obtained about the dynamic characteristics of dislocations in the range of low temperatures; the effect of abnormal “nondamping” separation of dislocations from the pinning centers at temperatures below T ≈ 30 K was found, and the effect of “dymanic annealing” in deformed single crystals in strong ultrasonic fields at liquid helium temperatures was determined; the thermally activated character of the dislocation separation from pinning obstacles in semimetals and in highly pure single crystals with bcc lattice was found; for type II superconductors it was found that the superconducting properties change locally nearby dislocations; the dynamics of cyclc movement of dislocations under different damping conditions was discussed; the evolution of low-temperature relaxation spectra of the ceramic Yba2Cu3Ox with decreasing of oxygen content was observed for the first time.

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It was determined that the low-energy relaxation peaks of ultrasound absorption in Nb and CsI in the range of helium temperature are caused by the relaxation of geometric dislocation kinks, which is controlled by the thermally activated formation of kink pair on the dislocation. A spontaneous low-temperature structural transformation of the hysteretic type in the alloy In-4.3 at.%Cd was found. The effect of fast cooling of Nb samples induced by the n-s transition on the modulus defect (increase of the elastic modulus in the s-state) was found. The research group directed by Bengus V.Z. and Lavrent’ev F.F., started in 1968-1974 and was concerned with the strain relaxation in alkaline-halide crystals, with the deformation of zink single crystals, and calcite singly crystals with different twin size. Internal friction studies in the Kharkov Physical-Technical Institute were started in 1958. Garber R.I. and Mogilnikova T.T. proposed a method of highly precise determination of the physical limit of elasticity by measurements of IF in metals and alloys during monotonous strain increase. Later on Gindin I.A. et al. have studied by methods of low-frequency IF: the low-temperature polymorphism in lithium, phase transformations in iron, the structural phase instability of superconducting Nb-Ti alloys in the range of cryogen temperatures; the influence of magnetic and temperature fields on the elastic and dissipative properties of HTSC (Y and Bi ceramics). The role of boundaries (including twin layers) and small additives in pure, constructive, super-conducting and radiatiated materials has been studied. Shapoval B.I. et al. have studied the phase transitions in superconducting alloys and grain boundary effects on IF. The second conference on the internal friction was organized in 1960 at the Kharkov State University: the chairman was Professor Pines B.Ya., the successor of Professor Ioffe A.F. In 195659 he together with his post-graduate student Den Ge Sen investigated internal friction in metalceramics produced by using powders of pure metals Cu, Ni, Fe, binary mixtures of Cu-Ni, Cu-Fe and ternary alloys Cu-Ni-Fe. Internal friction effects connected with the contacts of grains of different elements were found at the first time in mixtures of Cu-Ni, Cu-Fe. Startzev V.I. and Karmazin A.A. studied the temperature dependencies of high-temperature background of IF in the samples of pure metals with large grains at different frequencies in the infrasonic range of frequencies (1967-1971). The researchers have given the analytical solution for these dependencies as Q-1 = K{ω.exp(U0/kT)}-n and determined the value of n for the different metals. At the same time the peak connected with grain boundaries containing a segregation of insoluble impurities was found, and its mechanism as the sliding of grain boundary dislocations blocked by the segregated impurities was proposed. Evidences of dislocation structure of large edge grain boundaries were obtained from the IF data. Startsev V.I. et al. have studied a high frequency IF and on its basis they determined the rules of the dynamical drag of dislocations in some alkaline halide crystals (NaCl, KCl, LiF) and in some metals (Zn, Cu, Pb, Al). In 1960s Andronov V.M. began the investigation of copper whiskers by IF. It was found the nonlinear behavior of whiskers in the regime of forced oscillations (asymmetric resonance maximum), the mechanisms of plastic deformation on the stage of light sliding (microplasticity) etc. Sirenko A.F., Rokhmanov N.Ya. et al. determined the contribution of the magnetic component of IF in transition metals during plastic deformation, the character of the amplitude dependence of supersaturated solid solutions Al-Mg, Al-Cu during continuous decomposition, low frequency IF in over-eutectic alloys Fe-C near the Curie point of iron carbide. By extraction of cementite and studying its thermal expansion it was shown that IF near the Curie point of cementite is connected with thermal fluctuations of interfacial friction having magnetic nature. The problem of anelasticity in materials has widely reflected the geography of the USSR. A group of gifted researchers was organized in 1964-1966 in Georgia at the Institute of Metallurgy of the Georgian Academy of Science under supervision of Professor Tavadze F.N.: Bairamashvili I.A., Badzoshvili V.I., Zoidze N.A. et al. They were involved in studies of relaxation spectra in pure iron, boron and its influence on the IF in iron; the structure of Snoek and Cottrell atmospheres in tetragonal martensite; the mechanisms of bainite transformation and the interaction of dispersed particles in the iron matrix and many others. In Armenia at the Yerevan University research a team under supervision of Professor Durgarian A.A. has carried out a systematic study of the influence of

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ultrasonic irradiation on the internal friction of crystals and has provided the original classification of ultrasound absorption in metals. Several research teams have been organized in the Ukraine besides Kharkov: in Kiev, Donetsk, Chernovtsy, Vinnica. In 1960s in the Institute of Metal Physics of the Ukrainian Academy of Science Polotskii I.G. started investigations of the influence of crystal structure imperfections on the elastic and anelastic properties of metals, mobility of dislocations in Mo and W (Golub T.V.), ultrasound in monocrystals (Morduk V.S.), IF in metal-ceramic alloys Cu-Mg (Chuistov K.V.), oxygen in Nb, Ni, Co and rhenium in Mo (Kushnareva N.P.), IF in doped martensite Fe-C (Gavriluk V.G.), grain boundary IF in pure metals and alloys (Yagodzinskyy Y.I.) etc. At the Kiev State University Maksimiuk P.A. at al. have studied the IF of antimony, bismuth, silicon and some alloys with amorphous and microcrystalline structure, the effects of interactions of dislocations and impurity atoms. At the beginning of 1980s Rabukhin V.B. in the Kharkov Road-Transport Institute investigated the internal friction of fibers with coatings, whiskers and thin films. Theoretical and experimental aspects of anelasticity were studied at the Donetsk PhysicalTechnical Institute of the Ukrainian Academy of Science in 1970s-1980s (Zilberman L.A., Beloshenko V.A. et al.): internal friction of pure nickel, of aluminium with large grain size and of cobalt, the mechanism of Köster peaks at large deformations, the Simpson-Sosin effect at ultrasound, absorption of ultrasound during dislocation movement in the Peierls relief, the “peak effect” in ultrasound absorption, the background of IF at hydrostatic compression and the brittleductile transition and some others. In 1970s Strongin B.G. organized a research group at the Chernovtsy University (Strongin B.G., Varvus I.A.) involved with investigations of materials with coatings, non-equilibrium systems and beryllium in the contact with liquid materials. Polygonal structures of alloys and fiber composites were studied in the Vinnitsa State Pedagogical Institute (Zuziak P.M., Mozgovoi A.V.). At the Perm State University – relaxation mechanisms in metal-hydrogen systems were studied (Spivak L.V.); at the Ekaterinburg State Technical University and in the Ural Institute Physics of Metal (Academy of Science) - structural relaxation, elasticity and internal friction in martensiteaged, martensite-austenite and ferrite alloys (Grachev S.V., Schastlivtsev V.M. et al.); at the Tomsk State University and in the Institute Physics of Strength and Material Science of the Russian Academy of Science – dislocation microplasticity in metals and alloys (Panin V.E., Dudarev E.F. et al.) and acoustic properties of metals (Zuev L.B.); in the Gorki Physical-Technical Institute – the IF in martensite in nickel- and aluminum containing steels (Bogatyrieva G.P.); in the Kostroma Technical Institute – IF in alkaline halide crystals (Belozerova E.P.); at the Altai State University (Barnaul) – acoustic emission in the thermally activated processes and relaxation spectra in porous metals (Plotnikov V.A.); in the Institute of Metals Superplasticity Problems of the Russian Academy of Science (Ufa, Muliukov R.R.) and in Nizhnij Novgorod (Chuvildeed, Griaznov) – IF in submicrocrystalline Cu, Mg-based alloys; at the Kursk State Technical University – IF of electroacoustic coatings (Gadalov V.N.) and in many others research and academical institutes and universities. This report concerns the research activities in Russia mainly in the field of relaxation phenomena. The investigations of hysteretic damping in materials have been reported in the Materials of All-Union and All-Russian Conferences in the Institute Problems of Strength of the Ukrainian Academy of Science (“Energy Dissipation During the Oscillations of Elastic Systems”, 1960-1990 – Academic Pisarenko G.S.), at the Tula State University (since 1969 “Defects Interaction and Metals and Alloys Properties” – Prof. Golovin S.A.) and at the Viatka State Technical University (“Damping Metallic Materials” since 1988 – Prof. Kondratov V.M.). The Author realizes that in this short review it is not possible neither to specify the all studies nor to name all names of researchers involved in the development of the Russian scientific school on anelasticity, and apologizes on this behalf.

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References [1] N. N. Davidenkov: A review on energy dissipation during cycling deformation. Journal of Technical Physics (Zhurnal tekhicheskoi fiziki) (in Russian). Vol. VIII, No 6 (1938), p. 247263. [2] C. M. Zener: Phys Rev. Vol. 52 (1937), p. 230-235; Phys Rev. Vol. 53 (1938), p. 90-99, 10101013. [3] C. M. Zener: Elasticity and anelasticity of metals (University of Chicago Press, Chicago, Illinois 1948). [4] K. M. Rosin, B. N. Finkelshtein: Dok. Akad. Nauk SSSR Vol. 91 (1953), p. 811-814. [5] T. S. Kê, C. T. Tsien: Scientia Sinica. Vol. 5 (1956), p. 625; Fizika Metallov i Metallovedenie. Vol. 4 (1957), p. 291-305. [6] M. A. Krishtal, Yu. V. Pigusov, S. A. Golovin: Internal friction in metals and alloys (in Russian) (Metallurgizdat, Moscow 1964). [7] V. S. Piguzov: Internal friction in metals (in Russian) (Metallurgia, Moscow 1972). [8] A. S. Nowick, B. S. Berry: Anelastic relaxation in crystalline solids (Academic Press, New York 1972) (translation to Russian: Atomizdat, Moscow 1975). [9] V. N. Belko, I. M. Sharshakov, V. S. Postnikov: Fizika Metallov i Metallovedenie (in Russian). Vol. 27, No 4 (1969), p. 749-750; Phys of Metals and Metallography Vol. 27, No 4 (1969), p. 180-181.

Keywords Index (Fe,Cr)3Al Alloys

99

A Acoustic Emission (AE) Activity Aluminum (Al) Aluminum Alloy Antiferromagnetism Arachis Oil Atomistic Simulation AZ31 Alloy

199 21 21 43 215 1 181

C Carbon Nanotube (CN) Carbon Snoek Peaks Chromium Coercivity Cold-Rolled Steel Sheet Cold Rolling Compression Load Crystal Structure Cu-Al-Mn

29 69 43 129 215 155 199 119 137, 145, 155

99 109, 119 189 199 119 59 9 21, 49 99 9 49

9

Fatigue Property Fe-Al Alloy Fe-Al-Si Alloys Fe-Cr Alloy Fe-Ge Alloys Fe–Si–Al Steel Functionally Graded Material (FGM)

145 109, 119, 129 91 109 59 69 169

H Hardness Heat Treatment High Damping Materials High-Temperature

181 109, 119 145 21

I

Iron Aluminide Isothermal Internal Friction Isothermal Mechanical Spectroscopy Isothermal Structure Instability

35 15, 29, 43, 49, 59, 69, 169, 181, 215 99 83 21 35

J Junction Disclination

1

K Kibble-Zurek Mechanism

209

L

E Elastic Modulus Electrical Resistivity Electromagnetic (EM) Field Pulses Electron Microscopy Energy Absorbtion Capability

181

F

In-Based Alloys Internal Friction

D Damping Damping Capacity Damping Peaks Defects Accumulation Deformation Differential Scanning Calorimetry (DSC) Discrete Change of Local Elastic Strain Energy state Dislocation Disorder Transformation Dissipative Properties Distribution Function of Relaxation Times

Equal-Channel Angular Pressing (ECAP) Explosion-Like Microcracking

43 35 199 109 9

Lipid Logarithmic Decrement Low-Temperature

209 15 35, 43

M Magnetic Phase Transition

43

238

Interaction between Defects and Anelastic Phenomena in Solids

Magnetomechanical Damping Magnetostriction Manganese-Copper Alloys Mechanical Properties Mechanical Spectroscopy Microcracking Molybdenum Monte-Carlo

129 109, 129 163 145 15, 29, 91, 215 199 49 209

N Nanostructured Metals Néel Point Neutron Diffraction Nonequilibrium Grain Boundary

1 43 91 1

91 99 189

35 59 29 189 189

9 199 83

S Severe Plastic Deformation (SPD) Shape Memory Alloy Actuator Silicon Carbide Whiskers Silicon Steel Single Crystal Snoek-Köster Peaks Solid Solution Spin Density Wave Spin-Flip Transition Steel Stress Induced Martensite Structural Relaxation Structure

Thermal Cracks Thermal Fatigue Thermoelastic Martensitic Transformation Thin Film Third Type Stresses Topological Defects Triggering

137 137 163 189, 215 163 209 199

V Vacancy

1

X-Ray Diffraction (XRD)

59

Y 35

Z

R Relaxation Stress Redistribution Rock Specimen Room Temperature Ageing

T

Young's Modulus

P Phase Diagram Phase Transformation Polycrystalline Zirconia Polymer PPV

215

X

O Order Degree Order Transformation Organic Light-Emitting Devices (OLEDs)

Substrate

1 137, 145, 155 29 83 21 169 35 43 43 169 155 189 59

Zener Peaks

69, 83

Authors Index A Abdumanonov, A. Alexandrova, N.M.

9 119

L Lambri, O.A. Leksowskij, A.

49, 91 9

B Baskin, B.L. Bogomolov, L.

9 199

C Cano, J.A. Chudakov, I.B. Cuello, G.J.

91 109, 119 91

E Elnikova, L.V.

209

Golovin, S.A. Golovina, S.B. González, F. Grimm, B.

49 21 169, 181 43, 59, 69, 91, 99, 129, 169, 181 69, 231 43 83 189

H Houbaert, Y.

83

I Ionascu, C. Ivleva, T.V.

29 59, 169, 181

J Jäger, S. Jencus, P.

Mackushev, S.Y. Magalas, L.B. Maikranz-Valentin, M. Majewski, M. Marczyk, M. Markova, G.V. Matteo, C.L. Mielczarek, A. Murzaev, R.T.

109 15, 215 169, 181 15 137 163 49 129, 137, 145, 155 1

N

G García, J.A. Gerland, M. Göken, J. Golovin, I.S.

M

59, 69 59

Nazarov, A.A. Neuhäuser, H.

1 59, 189

O Ostapovets, A.A.

35

P Pal-Val, L.N. Pal-Val, P.P. Pavlova, T.S. Pelosin, V. Perevalov, N.N. Pérez-Landazábal, J.I. Polyakova, N.A.

35, 43 35, 43 169 21 119 91 109

R Recarte, V. Redfern, S.A.T. Riehemann, W. Rivière, A. Ruiz, D.

91 59 129, 137, 145, 155 21, 99 83

K Kakabadze, R.V. Katholy, S.

119 189

S Schaller, R.

29

240

Interaction between Defects and Anelastic Phenomena in Solids

Schrader, S. Semin, V.A. Serzhantova, G.V. Sheverev, S.G. Siemers, C. Sinning, H.R. Sokolova, O.A. Sorichetti, P.A. Stein, F. Steinhoff, K. Strahl, A. Sumin, V.V.

189 69 69 163 59 69 69, 129 49 69 169, 181 189 163

T Tishkin, A.P. Tonn, B.

9 145

U Udovenko, V.A.

109, 119

V Vanek, P. Vogelgesang, S.

35 145

W Wöckel, Y.

155

Z Zakupin, A. Zelada-Lambri, G.I. Zuberova, Z.

199 49 181