Characterization Techniques of Glasses and Ceramics [1 ed.] 978-3-642-08348-8, 978-3-662-03871-0

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Characterization Techniques of Glasses and Ceramics

Springer-Verlag Berlin Heidelberg GmbH

J. Ma. Rincon

M. Romero (Eds.)

Characterization Techniques of Glasses and Ceramics

ｾｓｰｲｩｮｧ･＠

With no Figures

Prof. JESUS MA. RINCON, Ph.D. MAXIMINA ROMERO, Ph.D. The Glass-Ceramics Laboratory Instituto E. Torroja, CSIC Serrano Galvache sIn 28033 Madrid, Spain

ISBN 978-3-642-08348-8

CIP Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Characterization techniques of glasses and ceramics / J. Ma. Rincon ; M. Romero (eds.). ISBN 978-3-642-08348-8 ISBN 978-3-662-03871-0 (eBook) DOI 10.1007/978-3-662-03871-0 This work is subject to copyright. AH rights are reserved, whether the whole or part of the material is concerned, specifically of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Ouplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heide1berg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from relevant protective laws and regulations and therefore free for general use. Production: PRO EDIT GmbH, 0-69126 Heidelberg Cover Design: design & production GmbH, 0-69121 Heidelberg Typesetting: Steingraeber, 0-69126 Heidelberg SPIN: 10630302

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Preface

This book covers a wide range of lectures given at the Short Summer Course celebrated at La Laguna University about the new trends in the modern characterization methods: chemical, microscopies, thermal, X-ray, resonance and nuclear methos for ceramics, glasses and related materials. This book also looks also at the zeolite thermal characterization methods as well as the new approaches in new microscopies for the investigation of surfaces in materials. Nowadays is generally accepted in the scientific community that characterization methods must be used in research from a complementary point of view. The concious application of several characterization techniques in the same material is very useful not only for obtaining a best knowledgement of the material characteristics, but also to answer scientific and technical questions about the processing and properties of final products. Whereas the introducing chapter in chemical analysis of rare earths the several methods here described looked as complementary methods which can be used in the investigation of ceramics and glasses. The major part of the book is devoted to fundamentals and applications of the techniques with a direct style which makes the book easy to read, being particularly useful for anyone beginning in research and applications of ceramics, glasses and glass-ceramics. Each chapter include clear figures and additional references for those interested in obtaining a depth knowledgement in different techniques. The book is the consequence of the above mentioned International Summer Courses that now are being common in the summer season at the Spanish universities. The La Laguna University in Tenerife, Canary Islands celebrated this five days course focused including thirty hours lectures which were given by ten well recognized specialists that are usually investigating ceramics and glasses with the techniques here reported. Due to the importance of promoting the scientific development of the Canary Islands, the former Cancellor of La Laguna University, Prof. Marisa Tejedor, was very enthusiastic in the promotion and supporting of this course delegating as Directors in Drs. Jesus Ma. Rincon and J. Enrique Garda-Hernandez for taking care of the final programme and the organization. This course was celebrated in the Summer College in Yaiza place, small and beautiful town in Lanzarote Island. Though it was agreed to prepare a joint publication of lectures given at the course, here we have been able to select the more interesting contributions for the

VI

Preface

invited lecturers. In order to give more homogeneity for readers this monograph has been organized in four different chapters: I. II. III. IV.

Chemical analysis Microscopies: including scanning tunneling and electron microscopies. Thermal methods. X-ray, resonance and nuclear methods.

This monograph is directed not only to undergraduate (high level courses) and graduate students, but also to the researchers, professors and industrials working in Science and Technology of Glasses and Ceramics, both traditional and advanced. Also, we strongly recommend to those interested in processing and science research of inorganic materials. Head and member, respectively of The Glass-Ceramics Lab. Inst. E. Torroja de Ciencias de la Construcci6n, CSIC. Madrid, Spain (October 1998) J.Ma. Rincon and M. Romero

Table of Contents

Part I. Chemical Analysis 1. Rare Earth Elements: Applications and Determination F.J. VALLE FUENTES........................................... ....

3

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Metallurgy.......................................... ...... 3 1.1.2 Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3 Glasses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.4 Cathode Ray Tubes........................................ 5 1.1.5 Lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.6 Electric and Electronic Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1. 7 Electro-Optical Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.8 Decorated Tableware and Porcelain . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.9 Refractory Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.10 Miscellaneous Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Determination of Rare Earths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Nuclear Neutron Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Atomic Absorption Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Plasma Spectrometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.4 X Ray Fluorescence Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Determination of REE in Advanced Ceramic Materials . . . . . . . . . . . . . . 11 Part II. Microscopies: Including Scanning Tunneling and Electron Microscopies 2. Scanning Tunneling Microscopy: Applications to the Study of Ordered and Disordered Conducting Solid Surfaces L. VAZQUEZ, R.C. SALVAREZZA and A.J. ARVIA ....................... 17 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Basic Operating Principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.2 Experimental Mounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

VIII

2.2 Theoretical Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Imaging Weakly Disordered Surfaces by STM . . . . . . . . . . . . . . . . . 2.3.2 Surface Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Imaging Disordered Systems by STM . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 22 22 26 29 38

3. Basis and Applications of Convergent Beam Electron Diffraction ( CBED) for the Investigation of Phases in Ceramics and Glass-Ceramics J. MA. RINCON and M. ROMERO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Fundamentals of Electron Diffraction by CBED: Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Possibilities and Limitations of CBED for characterising ceramic powders . . . . . . . . . . . . . . . . . . 3.2 Practical Aspects of CBED: Specimen Preparation and Operation in the TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Applications of CBED for solving Problems in Ceramics: Some Examples and Application to Zirconia/Mullite Materials. . . . . . . . 3.4 Future of the CBED Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41 41 46 52 54 59 60

4. Basis and Applications of High Resolution Electron Microscopy (HREM) for the Characterization of Ceramics and Glass-Ceramics J. MA. RINCON and M. ROMERO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.1 Introduction: Fundamentals of the HREM Methods................. 4.2 Operating Procedures and Instrumental Requirements . . . . . . . . . . . . . . 4.3 Key Examples of HREM Applications on Ceramics and Glassy Materials................................ 4.3.1 Monophase Ceramics....................................... 4.3.2 Polyphase Ceramics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Interfaces and Grain Boundaries in Oxide and Non-Oxide Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Phase Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 Glass-Ceramics and Glasses Studied by HREM . . . . . . . . . . . . . . . . 4.4 Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Future Prospects on HREM: Combination with Spectroscopy, CBED and Holographic Methods . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64 65 68 68 69 69 72 74 76 76 80

Table of Contents

IX

Part III. Thermal Methods 5. Applications of Differential Scanning Calorimetry for the Study of Transformation Processes in Quenched Alloys A. VARSCHAVSKY and J. SESTAK .................................... 85 Part 1: Theoretical Basis 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Characterization of TA Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Information Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Determination of Stable and Metastable Phase Diagram Boundary . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Study of Equilibrium and Nonequilibrium Processes . . . . . . . . . . . . . . . . 5.6 Glass Transition as an Example of Highly Nonequilibrium Changes . . . . . . . . . . . . . . . . . . 5. 7 Crystallization and Transformation of Metastable Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 The Study of Reaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part II: Experimental Results of Short-Range Ordering in a-Cu-Al Alloys 5.1 Introduction and Experimental. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 DSC Thermograms for Quenched Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Kinetic Parameters and Kinetic Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Overall Kinetics for Ordering .................................... 5.5 Effect of Quenching Conditions .................................. 5.6 Vacancy Behavior .............................................. 5. 7 Concentration Dependence of the Relative Increase of the SRO Parameter .......................................... 5.8 Acknowledgements .............................................

85 86 88 89 91 92 94 94

96 97 99 100 104 104 107 110

6. Use of Thermal Analysis in Zeolite Research and Application c. COLELLA ....................................................... 112 6.1 Introduction ................................................... 6.2 Zeolite Properties and Applications ............................... 6.3 Thermal Behavior of Zeolites .................................... 6.3.1 Water Loss ............................................... 6.3.2 Decomposition and Gas Evolution ........................... 6.3.3 Order-Disorder Transformation and Phase Transition .......... 6.3.4 Structure Collapse, Recrystallization and Melting .............. 6.3.5 Changes in Electrical Properties ............................. 6.4 Evaluation of Zeolite Content in Multicomponent Mixtures .....................................

112 113 116 116 123 126 127 129 129

X

6.5 Thermal Characterization of Zeolite Catalysts ..................... 6.5.1 Adsorbate/Framework Interactions .......................... 6.5.2 Estimation of Acidity Distribution in a Zeolite Catalyst ........ 6.5.3 Modification of, and Reactant Conversion on, a Zeolite Catalyst .........................................

132 133 134 134

7. Viscous Flow of Glass Forming Liquids: Experimental Techniques for the High Viscosity Range E.D. ZANOTTO and A.R. MIGLIORE Jr ................................ 138 7.1 7.2 7.3 7.4

Introduction ................................................... The Physics of Viscous Flow ..................................... Rheological Models ............................................. Measurement Techniques ........................................ 7.4.1 Fiber Extension and Cylinder Compression ................... 7.4.2 The Beam-Bending Method ................................. 7.4.3 Indentation Techniques ..................................... 7.4.4 Parallel Plates ............................................ 7.5 Final Comments ...............................................

138 138 142 144 147 147 148 149 149

8. Diffusion Structural Analysis in the Characterization of Inorganic Materials v. BALEK

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8.1 Basic Principles of the Method ................................... 8.2 Sample Preparation for DSA Measurements ....................... 8.2.1 Diffusion Technique ........................................ 8.2.2 Sample Preparation in the Inert Gas Atmosphere .............. 8.2.3 Implantation of Accelerated Ions of Inert Gases ............... 8.2.4 Inert Gases Produced from Nuclear Reactions ................. 8.2.5 Introduction of Parent Radionuclides as a Source of Inert Gas Atoms .............................. 8.3 Mechanisms and Theories for Release of the Inert Gases from Solids ......................... 8.3.1 Cases when the Inert Gas has been Incorporated into a Solid without its Parent Nuclide(s) ..................... 8.3.2 Cases when the Parent Nuclide(s) of the Inert Gas are used for Sample Labelling ....................................... 8.4 Measurement of Inert Gas Release ................................ 8.5 Potential Use of Diffusion Structural Analysis ...................... 8.6 Examples of DSA Applications ................................... 8.6.1 Diagnostics of the Defect State .............................. 8.6.2 Assessment of Inorganic Materials Prepared by Heat Treatment ........................................ 8.6.3 Characterization of Geleous Materials ........................

151 151 151 152 152 152 152 153 154 154 155 157 158 158 158 159

Table of Contents

XI

Part IV. X-ray, Resonance and Nuclear Methods 9. Texture Determination by Using X ray Diffraction F. WAGNER .................................................... ... 169 9.1 Introduction ................................................... 9.2 Experimental Information: The Pole Figures ....................... 9.2.1 Principle of a Pole Figure Measure ........................... 9.2.2 Corrections of the Data .................................... ....................... 9.2.3 Pole Figure Representation ｾｅｸ｡ｭｰｬ･ｳ＠ 9.3 Orientation Density Function (ODF) Determination ................ 9.3.1 Orientation of a Grain ..................................... 9.3.2 The ODF (Orientation Density Function) ..................... 9.3.3 Fundamental Equation of the Texture Analysis ................ 9.3.4 Principles of the Harmonic Method for Texture Analysis ........ 9.3.5 Ambiguity in ODF Determination ........................... 9.3.6 ODF Representation and Examples .......................... 9.4 Conclusion ....................................................

169 170 170 172 175 176 176 179 179 180 181 182 184

10. Recent Advances in X-Ray Fluorescence (XRF) Analysis S. UHLIG .................................................... ...... 187 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9

Analytical Capability of XRF Analysis ........................... Simple and Rapid Sample Preparation ........................... High-Tech Instrumentation ..................................... Flexible Sample Handling ....................................... Unlimited Areas of Application .................................. Optimized Light Element Analysis ............................... Effective and Comfortable Data Evaluation ....................... Precalibrated Analytical Programs ............................... Conclusion ....................................................

187 188 190 191 192 193 193 194 198

11. Mossbauer Spectroscopy Applied to Inorganic Materials V. KOZHUKHAROV and S. V ASILEV ................................... 199 11.1 Introduction .................................................. 11.2 Fundamental Equations ........................................ 11.3 Mossbauer Isotopes and Transitions .............................. 11.4 Instrumentation ............................................... 11.5 Basic Characteristics of Mossbauer Spectra ....................... 11.5.1 Isomer Shift .............................................. 11.5.2 Quadrupole Splitting ...................................... 11.5.3 Magnetic Hyperfine Splitting ............................... 11.6 Interpretation of Mossbauer Spectra ............................. 11.7 Bonding and Structure Interpretation ............................

199 200 201 202 203 203 206 206 207 208

XII

11.8 Conclusion ................................................... 218

12. Neutron Diffraction in Amorphous Structures S. NEOV and V. KOZHUKHAROV ..................................... 220 12.1 12.2 12.3 12.4 12.5 12.6 12.7

Introduction .................................................. Diffraction Methods Review ..................................... Neutron Scattering in Amorphous Solids .......................... Nuclear Reactor as Neutron Source .............................. Neutron Detectors ............................................. Time of Flight (TOF) Neutron Diffraction ........................ Small Angle Neutron Scattering (SANS) ..........................

220 220 223 225 226 227 229

Subject Index ................................................... 231

Part I

Chemical Analysis

1. Rare Earth Elements:

Applications and Instrumental Determination F.J. VALLE FUENTES

Instituto de Cenimica y Vidrio, CSIC, E-28500 Arganda del Rey, Madrid, Spain

Abstract. The applications of rare earth elements (REE) in various technological fields are reviewed, with emphasis on the importance of the knowledge of the chemical composition of the materials used. Nuclear neutron activation (NNA), atomic absorption spectrometry (AAS), inductively coupled plasma-atomic emission spectrometry (ICP-AES), inductively coupled plasma-mass spectrometry (ICP-MS) and x ray fluorescence spectrometry (XRF) are the most frequently used analytical techniques for determining REE. Complex matrices require the prior separation of the analytes by column chromatography.

1.1 Introduction Rare earth elements (REE) have aroused growing technological interest over the past few decades [1]. In fact, these elements are frequently included in alloys, catalysts, special glasses, cathode-ray-tubes, electronic ceramics and advanced ceramics to substantially enhance their properties. As a rule, yttrium (Y) is included in the rare earth group. While its electron configuration differs from that of lanthanides, the volume contraction of the latter with increase in their atomic weight justifies inclusion of Y, the atoms of which are very similar in density and volume to those of the lanthanide series. This similarity is also reflected in nature, where REE and Y coexist in many minerals. In fact, rare earths are frequently referred to as "yttria earths". The following sections discuss the most significant technological applications of these elements. 1.1.1 Metallurgy

The main use of REE in metallurgy is in the production of steel alloys and microalloys [2]. Thus, depositing 0.5-4% of Yon the surface of chromium steel endows the material with a high resistance to increased temperatures and oxidizing gases. The addition of an appropriate amount of a mixture consisting of 60% Ce0 2, 25% La203, 10% Nd203 and 5% Pr 20 3 (Misch metal) to iron stainless steel increases its resistance to oxidation [3]. Also, the presence of small amounts of this mixture favors the formation of sphenoidal graphite in carbon steel, thereby avoiding the release of toxic fumes.

4

F.J. Valle Fuentes

Fig. 1. Use of rare earths (USA 1986)

1.1.2 Catalysis

One of the most frequent applications of REE is as catalysts. As can be seen in Fig. 1, the USA oil industry used 31 % of the worldwide production of these elements in 1986. Oil cracking catalysts contain identical concentrations of the following components: a silica-alumina refractory material, and inert substance and sodium zeolite doped with La, Nd and Pr. The presence of REE in the zeolite increases the cracking capacity of the catalyst and its thermal stability at high temperatures [4]. In smaller amounts, REE are included in catalysts used to line automobile exhaust pipes. Their presence favors the oxidation of toxic fumes and reduces the release of CO, nit rogen oxides and unburnt fuel components. 1.1.3 Glasses

The glass industry has traditionally been one of the greatest consumers of REE. In glass making, the rare earths are used individually or in mixtures , but always as oxides. La 2 0 3 , in proportions of up to 40%, is used in main optical glass (lanthanum heavy crown and heavy flint) . The presence of this oxide endows the glass with a high transparency and improves its structural properties [5]. Ce 2 0 3 is used for decolorizing glasses [6]. At a high temperature, it dissociates with release of oxygen; this increases the partial pressure of the gas in the vitrifiable mass and converts the metal to its tetravalent form , which is particularly stable. The conversion facilitates the oxidation of ferrous to ferric ion (colorless) and hence glass refining. Other rare earth oxides such as Nd 2 0 3 and Pr 2 0 3 are used for the opposite purpose, i.e. for making stained glass. Nd 2 0 3 endows glass with a beautiful ,

1. Rare Earth Elements: Applications and Instrumental Determination

5

delicate purple hue that is markedly dichroic; at high concentrations or in large thicknesses, the glass acquires a red color that turns blue in thin layers. Pr203 provides a yellowish green color similar to that given by Cr 20 3, but brighter [7]. 1.1.4 Cathode Ray Tubes TV screens and monitors have only three phosphorescent colors; the others are combinations of red, green and blue. The use of Eu-activated yttrium oxysulphide or phosphovanadate expedites red phosphorescence and results in brighter images. 1.1.5 Lasers Yttrium-aluminium garnets (YAGs) are used in constructing lasers of the short wavelengths typically employed for cutting and soldering thin metal layers (< 10 mm). Neodimium-doped YAGs increase the electrical efficiency of the laser by maintaining the wavelength. Recent research allowed the development of an Al-Sc-Gd garnets (GSAG) that emits stronger light that the typical YAG [8]. 1.1.6 Electric and Electronic Ceramics Rare earth oxides are used for manufacturing ceramic capacitors. Their presence extends the capacitor's lifetime and improves some properties such as the compensation temperature coefficient, dielectricity and magnetic permeability. Specifically, Ce, La, Pr and Nd help keep the dielectric constant of a capacitor virtually unchanged [9]. One another major application in this field is the use of Y and La as doping agents for BaTi0 3 - the main component, which preserves the positive temperature coefficient of thermistors. 1.1. 7 Electro-Optical Ceramics La203 is the main component (96%) oflead lanthanum-zirconate-titanate (PLZT) [10]. This material is highly sensitive and non-volatile at high working temperatures. Also, it possesses a high image storing capacity, so it is used in memory elements for video screens, condensation systems, light valves, modulation systems and window panes for fighter plane cockpits. 1.1.8 Decorated Tableware and Porcelain Small amounts of REE added to frit and enamel give bright, striking colors in ceramic pieces. Such is the case with Pr 20 3 which, added to Si0 2-Zr0 2-B203 frit, produces a bright yellow color. Other lanthanides such as Sm and Nd give green and red hues, respectively, to decoration transfers [11]. Ce02 gives an opal appearance to porcelain surfaces. By heat treating the material twice, the effect can be extended to the whole piece.

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F.J. Valle Fuentes

1.1.9 Refractory Materials

Yttrium oxide is used in the manufacture of ceramic materials that are to be subjected to high temperatures (e.g. furnace windows, heating microscope lenses, vacuum melting crucibles, etc.). However, the most wide application ofY 2 0 3 in this field is in the production or stabilized zirconia. Y 2 0 3 stabilizes the hightemperature cubic phase of zirconia to room temperature, thereby avoiding polymorphic changes leading to piece damage from abrupt temperature changes [12]. 1.1.10 Miscellaneous Applications

Since 1970, rare earths have been used for making permanent magnets. Sm-Co and Nd-Fe-B alloys result in more powerful magnets than those consisting of Al, Ni and Co. The increased magnetic field intensity provided by RE magnets affords smaller pieces that can be used for making clocks, radars, and TV and computer parts. Erbium and yttrium borides are used for lining solar panels. Y -Fe and Gd-Fe garnets are employed as ferritic materials in microwave devices. Fertilizers containing small amounts of REE have been found to lead to increased growth of wheat, rice and peanut crops. Highly pure lanthanum boride crystals are used for manufacturing electron microscope guns. The wide variety of existing applications of REE has, not surprisingly, aroused industrial interest in research aimed at developing analytical methods for their determination in their mineral sources (monacites, xenotimes, bastnaesites, fergusonites, allanites), mineral concentrates from beach sand and alluvial, and finished materials containing REE.

1.2 Determination of Rare Earths The earliest analytical tests for REE are described in the treatises by Kolthoff and Sandell [13], Treadwell et al. [14], Charlot and Bezier [15] and Hildebrand et al. [16], among others. These authors pointed out the difficulty of determining these elements individually owing to their similar electron configurations. Only Kolthoff and Sandell, however, proposed a systematic analytical scheme for determining Ce and Sm based on the ability of both elements to act in two different oxidation states, viz. Ce4+ and Ce3+, and Sm3+ and Sm2+. Leaving historic antecedents aside, the following sections discuss the determination of REE by instrumental techniques including nuclear neutron activation, atomic absorption spectrometry, plasma spectrometries and x ray fluorescence spectrometry. In combination, these techniques account for over 90% of all analyses for REE.

1. Rare Earth Elements: Applications and Instrumental Determination

7

1.2.1 Nuclear Neutron Activation NNA is one of the most sensitive techniques available for determining trace elements. It irradiates the target material with a thermal neutron flux from a nuclear reactor. The elements in the sample absorb the neutrons and become artificial radionuclides whose spectrum is analysed in order to calculate the proportion of each element. The greatest asset of NNA is that the detection limit can be set at will by the analyst by regulating the neutron flux and irradiation time. One additional asset is that determinations are non-destructive and involve virtually no chemical separation. Geochemists have used this technique in combination with the highly precise multicomparator method in RE determinations. Standards containing known amounts of the analyte are simultaneously irradiated with the samples and the activity induced is measured under the same conditions [17]. Matrix elements with a high absorption cross-section can give screening errors. Such is the case with Gd, which has a cross-section of 4.9 x 10 4 barns. Such a high cross-section gives rise to a neutron attenuation proportion of 1% for a Gd203 sphere 0.12p,m in diameter with a mass of 5x w- 4 g. The screening effect can be minimized either by irradiating the sample following dilution with quartz or by removing elements with a high cross-section prior to irradiation. The presence of U interferes with the determination of rare earths. This element is fissioned on neutron bombardment and produces Ce, La, Nd and Sm nuclides; as a result, these REE may be incorrectly identified as present in a sample. With very complex samples, interferences can be overcome by isolating the rare earths from the other components by successive precipitation and extraction. A typical process of this type includes the following steps: (1) Disaggregation of the sample with a mixture of Na 20 2 and NaOH in a zirconium crucible. (2) Digestion of the melt with dilute HCl. (3) Separation of Fe by extraction with di-isopropyl ether. (4) Separation of Sc by extraction with diethyl ether. (5) Separation of REE as hydroxides by precipitation with NH 4 0H. (6) Dissolution of the precipitated hydroxides with dilute HCl. This scheme can be performed prior to or after irradiation of the sample. The Sc removal step is very important since the isotopes of this element give strong x ray lines that interfere with those for REE. The isolation of individual REE by ion-exchange chromatography is discussed later in dealing with the plasma spectrometry technique. The use of Li-doped Ge detectors in NNA spectrometers affords acceptable discrimination of Y radiation from that for other lanthanides without the need for a prior chromatographic separation.

8

F.J. Valle Fuentes

1.2.2 Atomic Absorption Spectrometry Flame atomic absorption spectrometry (AAS) provides the highest detection limits for lanthanides. Its scope of application is therefore confined to samples containing high concentrations of REE (e.g. monacites, xenotimes and bastnaesites), for which the technique provides acceptable results in hydroalcoholic media containing 80% methanol. The lowest detectable contents are 0.05% referred to the solid sample [19]. Electrothermal vaporization as a sample delivery system substantially improves detection limits, which are rendered competitive with those of NNA. The lower cost of the AA spectro-meter is a decisive asset in some cases [20].

1.2.3 Plasma Spectrometries Inductively coupled plasma atomic em1sswn spectrometry (ICP-AES) is the most powerful technique for determining REE in terms of sensitivity, dynamic linear range, reproducibility and expeditiousness. Its most serious shortcoming lies in the typically large number of emission lines given by REE, which result in a myriad of spectral interferences in samples containing several elements of this group. In order to ensure correct results, the interferences must be removed by choosing appropriate lines [21]. The combined use of a plasma excitation source and a mass spectrometer (ICP-MS) has provided promising results in the determination of RE traces in geological materials in the last few years [22]. The technique is based on the resolving power of charged particles according to their charge ratio - masses are influenced by isotopic overlap and isobaric interferences. Of special significance is the effect of saline reagents from the attacks, which can decrease the signal by decreasing the ionic concentration of the analyte. The results of both ICP-AES and ICP-MS can be improved by separating REE into several groups in order to lessen interferences. Specifically, this operating mode is compulsory in ICP-MS if Pr, Tb, Ho and Tm are to be determined jointly in the same sample since each element has a single stable element that is interfered with by another resulting from the three previous components. In view of the advantages gained in isolating REE prior to analysis, let us analyze their separation from one another and from the matrix by using ionexchange column chromatography. Before we start, we must answer the following question: When must REE be subjected to concentration and subsequent separation? There are two specific occasions, namely:

(1) In petrogenetic studies, where the relative abundances of REE are used to characterize the formation environment of the rocks. The average concentrations of the elements in different chondrites (vitreous silicate meteorites consisting mostly of olivine and pyroxene of particle diameter between 100 J..tm

1. Rare Earth Elements: Applications and Instrumental Determination

9

Table 1. Average concentration of rare earths in the chondrites and detection limits of these elements by ICP-AES for 0.2 g of sample dilute at 200m! Element

Abundance in the lithosphere [ppm]

LD ICP-AES [ppm]

La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

0.33 0.87 0.12 0.63 0.20 0.077 0.28 0.052 0.34 0.076 0.23 0.032 0.22 0.034

2 10 2.5 2.5 3 0.8 1.5 2.0 1.2 0.9 1.5 1 0.8 0.6

and 1 mm, the average composition of which is representative of the earth's mantle) are used for this purpose. As can be seen in Table 1, such concentrations are lower than those detectable by ICP-AES without preliminary concentration. (2) With REE exhibiting extremely complicated spectra with many completely and partially overlapping lines, which preclude choosing appropriate, correctable working lines for each element. In both cases, the use of concentration and separation procedures, both of which can be implemented by ion-exchange column chromatography, is justified. Chromatographic Concentration and Separation. Typically, a column packed with a strongly acidic resin as the stationary phase is used for this purpose. The cations to be separated are loaded at the top of the column in a small volume (20-50 ml of a 1 N HCl solution) and retained for subsequent elution with HCl at a different concentration. As the solution flows down the column, the elements are gradually separated according to their affinity for the resin and form distinct bands. REE are the most strongly retained elements; among them, those with the lowest atomic weights are eluted the last. The smaller the resin particle size, the higher will be the ion-exchange rate since the process is mainly controlled by the resin diffusion. However, the smaller particles are more resistant to passage of the solution, so, while the exchange should theoretically be faster, in practice it is slower. The optimal column length and elution volumes and flow rates can be determined theoretically. However, the predictions are rarely fulfilled in practice. Each new column must be subjected to preliminary experiments in order to op-

F.J. Valle Fuentes

10

timize the elution conditions. The procedure for separating REE from geological materials involves loading the column with a 1 N HCl solution containing 10 mg of Al, Fe and Ca; 5 mg of Na; 2 mg of La, Ce, Nd, Gd, Er and Yb; and 1 mg of the other REE. A volume of 150 ml of 2 N HCl is needed to elute Al, Fe, Ca and Na, and 500 ml of 6 N HCl is required to elute the REE. The different RE fractions are evaporated to a volume of 5 ml. The time needed for complete separation and evaporation is about 48 h. The recoveries typically obtained in this way are given in Table 2. Element

Cone. solution [mg/1]

Recovery [%]

La Ce Pr

10 10 5 10 5 5 10 5 5 5 10 5 10 5

97 107 92 100 99 102 96 98 100 100 94 100 98 95

Nd

Sm Eu Gd

Tb Dy Ho Er Tm Yb Lu

Table 2. Analytical results of recovery of rare earths in chromatographic separation

Regarding sample dissolution, slow evaporation of the material with a mixture of HF, HN0 3 and HC10 4 is the most suitable in relation to the subsequent chromatographic separation. However, some ceramic materials require disaggregation with Na2C0 3 +Na2B407; this entails using a small amount of sample and a high proportion of sodium in the solutions which will have to be separated subsequently on the column. The chromatographic separation avoids interferences in ICP-AES and allows the most sensitive lines for the different lanthanides to be used for quantitative purposes. Table 3 shows the most frequently used lines in this respect. 1.2.4 X Ray Fluorescence Spectrometry

Like any other instrumental technique used to analyze solid samples, XRF spectrometry is subject to matrix effects and the problems derived from differences in grain size when samples are used in pellet form. Both shortcomings can be circumvented by dissolving the material and separating the lanthanides by using one of the above-described procedures. After separation, the different fractions containing the analytes are placed on solid supports for analysis [23]. This procedure is usually employed with some geological samples that are attacked by

1. Rare Earth Elements: Applications and Instrumental Determination Element

Wavelength [nm]

La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

379.478 418.660 417.939 406.109 359.260 381.967 335.862 350.917 353.170 345.600 337.271 346.220 328.937 261.542

11

Table 3. Spectral lines for rare earths determination by ICP-AES recommended

acids. Thus, 1 N HN0 3 is capable of digesting 0.5 g of geological material. The attacking solution is evaporated to dryness and the residue leached with a 1:20 mixture of 7 N HN0 3 and methanol. The extract is stored in a polyethylene flask containing 0.5 g of cationic resin in its nitric form and shaken for 5 min to facilitate the exchange. The resin is then squeezed and analyzed. Standards are also made from multi-element solutions of the lanthanides at known concentrations. The results are comparable to those provided by NNA and ICP-AES; however, the detection limits for La, Ce, Pr and Nd are somewhat worse but can be improved by using longer counting times - at the expense of increased background noise.

1.3 Determination of REE in Advanced Ceramic Materials The Glass and Ceramics Institute of the Spanish CSIC carried out an analytical study of new materials used in structural and electrical ceramics, the stoichiometries and impurity contents of which were highly interesting because of their influence on the physico-chemical properties and service response of the pieces [24]. The specific materials studied were tetragonal zirconia stabilized with ceria and yttria (Y-TZP /Ce); lead titanate modified with gadolinium and doped with manganese (Gd-PT); and lead titanate-zirconate modified with lanthanum (PLZT). The first is a structural ceramic and the other two are electrical ceramics. The three materials were analyzed for La, Ce, Nd, Sm, Gd, Er and Yb; also, Y was determined in Y-TZP /Ce. The materials were dissolved by disaggregation in a graphite crucible with Li2B404 (0.2g sample and 2g of flux) at l10°C. The melt was cast in 1:24 HN03 and made to 200 ml. No separation or concentration of REE was required.

12

F.J. Valle Fuentes

Spectral interferences were corrected by using the experimentally determined inter-elemental coefficients in the following expression:

(1) where Ci is the concentration of analyte i, Ai its apparent concentration, Cj the interferent concentration and kij the inter-elemental correction coefficient for the interference of element j with element i. The analytical lines used and the determination limits achieved are given in Tables 4 and 5, respectively. The determination limits are acceptable for the REE levels to be quantified; as expected, they were influenced by the matrix, which was not separated.

Element

La Ce Nd Sm Gd Er Yb y

Material Y-TZP/Ce

Gd-PT

PLZT

333.749 395.254 406.109 359.260 336.223 349.910 369.419 371.030

333.749 413.765 415.608 442.434 342.247 326.478 222.446

408.672 413.765 406.109 359.260 342.247 390.631 328.937

Element

Table 5. Detection limits (ngcm- 3 ) for the rare earths in advanced ceramic rnaterials

Material

Y-TZP/Ce

Gd-PT

PLZT

La Ce Nd Sm Gd Er Yb y

8.5 ND 34 39 21 11 2.9 ND

11 57 21 56 ND 9.3 36

Table 4. Analytical lines (nm) suitable for the determination of rare earths in advanced ceramic materials

ND 63 28 32 9.2 7.9 0.98

ND: Not determined due to an intermediate component

1. Rare Earth Elements: Applications and Instrumental Determination

13

References 1. Lanthanides, Tantalum and Niobium, Proceedings of a Workshop in Berlin.

(Springer Verlag. Special Public. no 7. Soc. For Geology Applied to Mineral Deposits, 1986). 2. E.C. Bain, H.\V. Paxton: Alloying elements in steel, (Handbook American Society of Metals, Park, Ohio, 1966). 3. K.A. Gschneider .Jr, B ..J. Beaudry. Mischmetal Handbook. (American Society of Metals, Park, Ohio, 1979) p. 770. 4 . .J. Scherzer, .J.L. Bas, F.D. Hunter: .J. Phys. Chern. 79, 1194 (1975). 5. A. Paul: ChemistnJ of Glasses (Chapman and Hall, London, 1982). 6. D. Uhlman, N. Kreidl: Glass Science and Technology. Vol. 1. Glass forming systems (Taylor and Francis Ltd., London, 1981). 7. F. Arnal: Bol. Soc. Esp. Ceram. 76 (1968). 8. S. Yu Zinoviev, V.A. Krizhanoskaya, V.B. Olushkova, Dokl. Akad. Nauk. SSSR 297, 6 (1987). 9. T.R.N. Kutty, P. Murugara: .J. Mater. Sci. 22, 3652 (1987). 10. P. Duran, L. del Olmo, B. Jimenez: Ferroelectrics 54 (1984). 11. H. Smyth, A ..J. Cohen: Phys. Chern. Glasses 45, 106 (1963). 12. L . .Jourdain: La technologic des products ceramiques refract aires (Gauthier-Villars, Paris, 1966). 13. I.M. Kalthoff, E. B. Sandell: Textbook of quantitative analysis (McMillan, New York, 1952). 14. F.P. Treadwell, W.D. Treadwell, C. Allue: Tratado de Quimica Analitica. Tomo II. (Manuel Marin, Barcelona 1949) 15. G. Charlot, D. Bezier: Analyse quantitative minerale (Masson, Paris, 1955). 16. W.F. Hilldebrand, G.E.F. Lundell, H.A. Bright, .J.I. .Joffman: Applied Inorganic Analysis, (.John Wiley and Sons, New York, 1953). 17. A.W. Mosen, R.A. Schmitt, .J. Vasilevskis: Anal. Chim. Acta 25, 10 (1961). 18. P. Ila, P . .Jagan, G.K. Muecke: .J. Radioanal. Chern. 79, 215 (1983). 19. W. Oghe, F. Verbeck, Anal. Chim. Acta. 73, 87 (1974). 20 . .J.G. Gupta: Talant 32, 1 (1985). 21. I. Roelandts: At. Spcctrosc. 9, 2 (1988). 22. S.R. Taylor: Geochim. Cosmochim. Acta 19, 1243 (1965).

Part II

Microscopies: Including Scanning, Tunneling and Electron Microscopies

2. Scanning Tunneling Microscopy: Applications to the Study of Ordered and Disordered Conducting Solid Surfaces 1. VAZQUEZ\ R.C. 8ALVAREZZA2 and A.J. ARVIA 2 1 2

Instituto de Ciencia de Materiales, CSIC, Campus de Ia UAM. Cantoblanco. E-28049 Madrid, Spain Instituto de Investigaciones Fisicoqufmicas Teoricas y Aplicadas, INIFTA, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina

Abstract. A brief description of the fundamentals of scanning tunneling microscopy (STM) is given, including basic principles of operation, theory, and experimental mounting. Applications of STM to characterize well ordered and disordered surfaces of conducting solids are presented. Atomic resolution of metals and semimetal single crystal faces in vacuum, air and liquids is presented and discussed. Examples of processes such as nucleation and growth of metals on single crystals are given. Recent methods developed to characterize rough solid surfaces in terms of fractal geometry based on STM image processing are described.

2.1 Introduction The invention of scanning tunneling microscopy (STM) by Binning et al. [1] has provided a powerful technique with real space imaging ability and atomic scale resolution for scrutinizing conducting surfaces under ultra high vacuum (UHV) and a variety of environments such as air and different liquids over a wide range of temperatures [2]. The STM has the ability to resolve spatially the atomic structure of surfaces. It also allows us to map energetically the electronic states at the atomic positions on the surface with energies lying a few eV on either side of the Fermi level, with a resolution of a few kT. The spatial distribution of the electronic states gives information about the atomic arrangement at the surface although the link between the electronic states and the atomic structure depends on the type of material. Thus, for metals, the electronic states generally follow the atoms on the surface so that STM provides a direct topographic image of atoms. Conversely, for semiconductors and semimetals, the electronic states are not only related to the surface atomic structure but also to the type of atom and bond and, accordingly, the interpretation of STM images becomes more complicated. STM is also widely used to study the topography of weakly disordered systems such as real single crystal faces at wavelengths greater than that corresponding to atoms. Hence, surface reconstruction processes, step and kink distributions, and surface roughness can be studied at the nanometer level. More recently, STM has been applied to the study of strongly disordered systems such as the surface of conducting materials grown far from equilibrium conditions [3]. Quantitative information about the degree of disorder and growth mechanisms

18

L. Vazquez , R.C . Salvarezza and A.J. Arvia

a

Fig. 1. a Scheme of an STM design; b scheme of the tip and sample in the J-Lm range; c scheme of the tip and sample in the nm range.

of metal deposits, porous silicon, conducting polymers and fracture surfaces can be obtained by processing STM images [3- 7]. This chapter deals with the STM application to the study of different kinds of conducting surfaces. It is shown that relevant quantitative information can be obtained either on well defined and weakly disordered systems such as stepped single crystal faces or on strongly disordered systems such as surfaces grown far from equilibrium.

2.1.1 Basic Operating Principles A schematic of the STM design is depicted in Fig. 1. It consists of a probe tip brought to within a few A of the sample surface, both the tip and the sample are conducting materials. When a voltage v; , generally in the range of few mV to 0.5 V, is applied between the tip and the sample, a tunneling current, it , is produced through the gap (vacuum, air or liquid). It has been experimentally observed that it is related to s , the tip- sample separation, according to,

(1) where k, the electron decay constant , is given by k = (2m¢/n2 ) 112 , m is the electron mass and ¢ is the local barrier height. Thus, for ¢ = 4.5 eV a change of s in 1 A results in a change of it in one order of magnitude. Scanning the

2. Scanning Tunneling Microscopy

T

p

T

19

p

SCAN

SCAN

S

A M

P

L

ｾ｟ＭＮＬﾷ ﾷ ＠

z l.___.-_,····.._·· .../_ ·"····_ ......·

E

........ ·.. . X

S

In

A M

P

L

E

'1'--·-··,..··_· -.. ..._ .... --'_ ···-··_···-·_·· '····_ .............. ._, X

Fig. 2. Scheme of the operation modes in STM: a topographic mode; b constant height mode.

sample by applying a voltage Vx and Vy to the piezoelectrics Px and Py, keeping constant the voltage Vz applied to piezo z, produces a change in it, according to the sample topography, leading to a 3D image of the surface (constant height mode) (Fig. 2b). More frequently, the STM images are taken at a constant it , by continuously adjusting the tip-sample separation by applying a voltage Vz to Pz to maintain a constant it value (topographic mode) (Fig. 2a) through a feedback loop. In the topographic mode, the tip height as a function of the lateral position provides a constant-current image of the sample surface. The scan rate is kept lower than the cut-off frequency of the feedback loop. Thus, whereas in the constant height mode the tip-sample distance s changes with tip position, in the topographic mode s is kept constant and the tip follows the surface profile. In this mode the tip acts like a profilometer but without touching the surface. The vertical resolution of STM is basically limited by the stability of the tipsample distance (0.1-0.01 A). In practice, this stability is achieved by building the microscope as compact as possible and filtering vibrations using different mechanical and electrical devices [8]. The lateral resolution depends on both the tip size and the tip-sample distance. According to Stoll [9], a, the minimum period of the corrugation of height h is proportional to:

acx

s+R)I/2 (k

'

(2)

20

L. Vazquez, R.C. Salvarezza and A.J. Arvia

where R is the tip radius. For R + s = 4 A and ¢ : : : : 4.5 eV, a results in the order of 3-4 A. It should be noted that R refers to the microscopic tip radius, as the macroscopic apex of the tip can exhibit a large number of small tips. Piezoelectric elements are important parts of STM equipments. They are usually made of ceramic and exhibit a thermal drift and creep in the order of few Amin- 1 . The drift produces a distortion of STM images, although it can be evaluated and properly corrected. To minimize drift effects, the constant height mode is frequently used as the imaging speed can be substantially increased. In the constant height mode, the feedback loop is disabled so that the tip remains at the same height (z-position) during the scan along the x- and y-directions. Obviously, this mode can be applied provided the contact between the tip and the sample can be avoided, a situation which presents only flat domains of the sample. Constant height images provide a qualitative topography as the exact dependence of it on the tip-sample separation is not known a priori.

2.1.2 Experimental Mounting STM essentially involves three different parts, namely, the STM unit including the mechanical mounting, the control electronics, and the data acquisition and image processing systems. The fundamental mechanical devices are the proper STM unit and the vibration-free mounting. The STM unit consists of the ensemble formed by the sample (sample holder), the tip and the piezoelectric element. This element can be composed of a tripod of piezoelectric ceramics with its vertex placed on the tip as shown in Fig.l (as in the early designs [10]). Another arrangement is that formed by a unique piezoelectric tube with four sectors allowing the performance of the three movements (x, y, z) with one element only. This design is more compact and increases the resonance frequency of the STM. The tip can be made of a tungsten wire prepared by electrochemical etching, or of platinum made by cutting, or of electrochemically etched Au wire. The tip can be first roughly approximated to the surface to a distance smaller than one micrometer by means of an electrostatic-step-motor, and then its position can be controlled by potentials Vx, Vy, Vz, applied to the piezoceramics. Other approaching systems have been developed, such as that called "inertial" [11] which also increases the STM stiffness. The STM unit can be operated either in an ultrahigh vacuum chamber, in contact with the atmosphere or in liquids as in the case of electrochemical cells, as well as at either very low or room temperature, depending on the operating conditions required. Vibrations can be eliminated by suspending the STM unit on soft springs to eliminate vibrations of frequencies greater than their resonance frequency. The electronics of STM consists, of a control unit made up of a logarithmic amplifier, a filter, and a proportional derivatingintegrating unit which keeps constant the tunneling current coming from the specimen, previously converted into a potential signal.

2. Scanning Thnneling Microscopy

21

The programmed amplification of the signal from the control unit operates the movement of the z-piezoceramic. The same signal goes to an analog recorder and is fed into the computer through an analog-digital converter. The software consists of data acquisition in real time and its further analysis. Finally, through image processing it is possible to obtain a noise-filtered real image, as well as the corresponding depth level profiles.

2.2 Theoretical Outline The tunnel current given by (1) measures the overlap of the electronic wave functions of the tip and the sample at the gap distance. The tip wave functions probe the sample wave functions as schematically shown in Fig. 1c. According to Bardeen [12] }t, the tunnel current density, takes the following form,

. Jt

21re'"' =---,; L.J (E,J [1- f

(Ev- V)] J(EJL- ｅｶＩｉｍｾｴｬ＠

2

,

(3)

where,

(4) where f(E) is the Fermi-Dirac occupation factor at the energy E, V is the applied voltage, and Mpv is the matrix element between the tip state '1/JJL and the sample state '1/Jv· EJL is the energy of the JL-state and the 2::: is taken over all tip and sample states. The matrix element is evaluated over any surface lying entirely within the gap region. According to Tersoff and Hamann [13], let us now consider a 1D problem, neglecting the electric field in the tip-sample region and all barrier rounding effects, and the same work function, ¢>, for both the tip and the sample. The wave functions decay exponentially with z according to,

(5) (6) By introducing (5) and (6) into (4) we obtain, m Mpv = 2fi2

J (

ds 2k '1/JJL0)* '1/Jv0 exp( -ks) ,

(7)

and by combining (3) and (7),

Jt

ex

L ｉＧＯｊｾ

Ｒ

ＱＧＯｊ･ｬ

Ｒ

･Ｍ

Ｒ

ｫｳＬ＠

(8)

where 2::: stands for the sum of all energy states participating in the tunneling process. It should be noted that (8) derived from this simple model leads to the experimentally observed dependence of }t on s.

22

L. Vazquez, R.C. Salvarezza and A.J. Arvia

To evaluate ]t, it is necessary to know explicitly the wave functions of the tip and the sample. Unfortunately, the geometry and the structure of the tip at the atomic level are generally poorly defined so that accurate calculations of the tip wave functions are not feasible. This problem can be solved through a different approach proposed by Tersoff and Hamann [14]. This model considers an ideal tip with the smallest dimension compatible with the highest resolution and it intends to measure· the properties of the sample surface instead of the properties of tip-sample system. Thus, the tip on the limit R ---+ 0, is replaced by a point located at the distance r 0 perpendicular to the surface sample. For small vt and T, Jt is given by

(9) Thus, the tunneling current is a measure of the local density of states (LDOS) r 0 should be assigned to the tip radius of curvature. More realistic models [15] lead to the same results, i.e. STM images represent closely p(r 0 , EF) at the sample surface. Thus, the tip "maps" profiles of constant LDOS at the Fermi level.

(p) at the Fermi level at the tip position. For a real tip,

2.3 Applications 2.3.1 Imaging Weakly Disordered Surfaces by STM Real single crystals at room temperature and atmospheric pressure exhibit weakly disordered surfaces when these crystals are scrutinized by STM at high resolution. Under these conditions, the images usually depict smooth, defect-free surface domains. Atomic resolution for a variety of metals, semiconductors and semimetals has been obtained under UHV conditions [16]. The 34 x 34 A2 STM image of Al( 111) in UHV with atomic resolution is shown in Fig. 3. Atomic resolution in air can be obtained for low reactive metals such as Pt or Au or for highly oriented pyrolitic graphite due to the low reactivity of the C(OOOl) basal plane. Typical20x20 A2 images ofPt(111) and C(OOOl) in air with atomic resolution are shown in Fig. 4. Pt(111) (Fig. 4a) exhibits the hexagonal array of atoms with an interatomic distance, d = 2.8 ± 0.2 A as expected for Pt. For more reactive surfaces, 0-adsorption or other impurities promote surface reconstruction so that atomic resolution of the unreconstructed metal surface can be only obtained in UHV. In intermediate cases, the situation should be more complicated. In the case of Ag, the 0-adsorption, to form Ag 2 0 depends on the exposure time to the atmosphere. For times shorter than 6 h the interatomic distance results d ｾ＠ 2.9 A, i.e. close to that expected for Ag [17]. On the other hand, after prolonged exposure to the atmosphere the value d = 4 A is obtained, a figure which is close to that expected for Ag 2 0 [18]. Single crystal faces have also been imaged in electrochemical cells [16]. In electrochemical systems, since both the tip and the substrate are immersed in

2. Scanning Tunneling Microscopy

23

[A] 30

20

10

0 0

20

30

[A]

Fig. 3. 34 x 34A 2 STM image (top view) with atomic resolution of Al(lll) obtained in UHV (from [16], with the permission of the American Physical Society)

the electrolyte solution, electrochemical reactions (Faradaic processes) can occur at both the tip and the substrate. Therefore, the current is the sum of the tunneling and the Faradaic currents. By using an independent control of the STM unit for the sample, and trying to minimize the Faradaic current at the tip (lower than 10 pA), flat terraces with monoatomic steps and pits have been resolved. STMs for operating in electrochemical systems have been improved and atomic resolution of different metal single crystals in electrolyte solutions have been reported [19- 21]. As mentioned above, for metal surfaces, the profile of electron states density closely represents the profile of atoms in the surface, making, in principle, the interpretation of the STM images easy. However, according to theoretical calculations, the resolution of individual atoms for most of the metal surfaces is not feasible as for many metals the atomic corrugation is negligible for just 2 A away from the surface. The physical origin of the atomic corrugation at metal surfaces is still a matter of investigations. It has been argued that the atomic resolution was due to the existence of surface states near the Fermi energy level [22]. Also tip-induced elastic deformations have been proposed as being responsible for the lateral resolution obtained on single crystal metal surfaces [23, 24]. The possible role of localized p and d states instead of spherical s-states at tip atoms has been proposed to explain the increase in the lateral resolution and, accordingly, the resolution of individual atoms on closely packed metal surfaces [2].

24

L. Vazquez, R.C. Salvarezza and A.J . Arvia

b Fig. 4. 3D STM images obtained in air with atomic resolution: a 21.4 x 21.4 A2 image of Pt(111) ; b 21 x 21 A2 image of highly oriented pyrolytic graphite (HOPG)

2. Scanning Tunneling Microscopy

25

For semiconductors and semimetals surfaces such as C(OOOl), the situation becomes more complicated. The hexagonal array of atoms shown in Fig. 4b exhibit d = 2.4 ± 0.2 A far from d = 1.2 A as expected for carbon. It is well known that bulk graphite has a layered structure with a weak interlayer coupling. Since the atomic positions in the consecutive layers are shifted, two different sites can be distinguished in the (0001) plane, A-sites which involve C atoms with a C atom directly below in the next layer, in contrast to B-sites which have no C atoms below them. The symmetry lowering due to the shift in the atomic positions and the weak layer interactions yield only three protrusions rather than six in the surface hexagons. It has been suggested [25] that the three atomic sites (B-sites) which do not have atoms directly below and for which the electronic density is significant are more likely imaged. Also, a sort of mechanical interaction between tip and graphite has been suggested to account for the giant corrugations detected when imaging this surface and for the 2.4A structure [26]. In each layer, sites A and B form an hexagonal array that could explain the hexagonal structure with d = 2.4A seen on the C(OOOl) surface. However, experimental results for the deposition of only one monolayer of C on Pt yield the d = 2.4 A instead of d = 1.2 A, in contrast with the expectations of this model [27]. The case of C(OOOl) is a clear example showing that for semimetals and semiconductors the density of electron states at the Fermi energy level differs from the total surface charge density. On many metal surfaces, whether clean or covered by adsorbates, reconstruction occurs leading to superstructures which result in a corrugation with a longer wavelength than that of the atomic lattice. Thus, clean surfaces of different metals reconstruct leading to corrugations in the order of 0.2 A-0.3 A. This corrugation is due to the misfit between the substrate and the topmost layer which produces a slight vertical displacement of surface atoms. Thus, STM images of Au(lOO) single crystals show large terraces separated by monoatomic steps. The corrugation on the terraces is due to surface reconstruction [28]. The corrugation details reveal different types of reconstruction processes. Similarly, the surface of a Pt(lOO) single crystal shows an irreversible reconstruction after heating at T > 420 K into a 5 x 25 structure (hexagonal), which after annealing at T > 1100 K changes into an inverse hexagonal structure. No reconstruction occurs if a molecule such as CO, NO or ethylene is adsorbed on the metal surface. Surface reconstruction has also been observed for clean Au(110) and Pt(llO) [29, 30]. When the STM resolution is lowered, defects such as steps and kinks are observed. The local distribution and orientation of steps, as the predominant type of defect, can be easily determined through STM imaging in contrast to the average information provided by LEED. The STM image of a polyfacetted Au single crystal surface at the [111] pole (Fig. 5) exhibits flat terraces and monoatomic steps which dominate the surface topography. The steps extend linearly over thousands of angstroms and their intersection determines 60° angles. Pits of monoatomic depth are also frequently imaged at the surface of metal single

26

L. Vazquez, R.C. Salvarezza and A.J. Arvia

Fig. 5. 8250 x 8250 A2 STM image (top view) of a Au single crystal at the (111) pole

crystal surfaces [31]. For soft metal surfaces, such as Au , the time dependence of the pit radii has been used to estimate the surface diffusion coefficient, D , of the metal atoms. The values of D for Au in electrolyte solutions are close to 10- 15 cm 2 s- 1 , in agreement with those obtained by other macroscopic methods such as roughness relaxation measurements [32, 33] . From the preceding description, it is evident that the surface of single crystals can be described as weakly disordered rather than smooth. Also , the STM has proven its applicability to the study of diamond films grown by microwave assisted chemical vapor deposition (MWCVD) from a gas mixture of methane and hydrogen [34] . In principle, STM should not be suitable for this kind of analysis as diamond is an insulator. However, due to the slight graphitic film content together with the low tunnel current and high bias used, images such as those of Fig. 6 can be obtained. The films are polycrystalline with predominantly {111} and {100} faces. The latter are flatter than the former, supporting the 2 x {100} 1 reconstruction during growth. Atomic resolution images have been obtained in air showing this sort of reconstruction [35]. 2.3.2 Surface Reactions

Single crystals are suitable substrates for studying adsorption processes and the early stages of phase formation. Surface reactions produce chemical and structural modifications of substrates or adsorbates. In this respect, STM gives information at the atomic level about very early stages of surface processes, surface local reactivity and the extent of the reaction , for instance, when a new phase is produced on the surface. An interesting example on the STM capability for the study of surface reactions is the Ag electrodeposition on C(0001). In this case, at low cathodic potentials, the Ag ion deposition takes place mainly at substrate defects (Fig. 7). Initially, small 3D Ag nuclei (100-200A size) following the C(0001) directions are formed (Figs. 7, 8).

2. Scanning Tunneling Microscopy

27

Fig. 6. 25 000 x 25 000 A2 3D STM image of a diamond film grown from a mixture of methane and hydrogen

Fig. 7. 9835 x 9835 A2 3D STM image showing electrodeposited Ag at HOPG substrate defects (from [17], with permission of the American Chemical Society)

28

L. Vazquez , R.C . Salvarezza and A.J. Arvia

Fig. 8. a 3000 x 3000 A2 3D STM image of an incomplete Ag crystallite; b cross-section of the crystallite showing the 3D Ag nuclei at the crystal edges and the flat terrace (from [17], with permission of the American Chemical Society)

Due to the high mobility of Ag surface atoms at room temperature, the Ag atoms move from 3D Ag nuclei to uncovered C(OOOl) areas, so that domains of C(OOOl) are covered by a first Ag atom layer. The position of these atoms is revealed through STM imaging at a step ｾ＠ 3 A in height close to small 3D nuclei (Fig. 9). Two different interatomic distances can be measured for the hexagonal arrays of atoms shown at the right hand side and the left hand side of Fig. lOa, respectively. The hexagonal array of atoms at the right hand side exhibit d = 2.4 ± 0.2A, i.e. the value corresponding to the C(OOOl) substrate when imaged by STM. Conversely, the d = 3.3 ± 0.03 A value at the left hand side can be

2. Scanning Tunneling Microscopy

29

Fig. 9. 823 x 823 A2 3D STM image. An Ag crystal growing at a step edge is shown. Arrow indicates the step at which the image showed in Fig. 10 was taken (from [17], with permission of the American Chemical Society)

related to the first layer of Ag on HOPG . It can be observed that the Ag adlayer is rotated with respect to the C(OOOl) substrate. The d value and the rotation angle are compatible with a (7 /2) 112 x (7 /2) 112 R19° structure (Fig.10b). The growth of the adlayer by addition of Ag atoms on top of the first layer results in the formation of flat and triangular crystallites (Fig. 11) with d = 2.9 ± 0.2 A (Fig. 12) as expected for Ag [17]. The formation of ordered crystals from small 3D nuclei is also observed for Pt electrodeposition on C(0001) in H 2 PtCl 6 +ClH solutions (Fig. 13). In this case, 3D Pt nuclei with 10-20 A size form rows which agglomerate following well defined directions. These agglomerates act as the precursors of large and geometrical crystallites observed at advanced stages of growth. 2.3.3 Imaging Disordered Systems by STM

Surface disorder and random roughness can play a determining role in the physicochemical properties of surfaces and interfaces. Roughness is a common characteristic of solid materials as found in nature and used by man. The description and properties of rough surfaces at present is far from being understood. For polycrystalline, amorphous, or inhomogeneous surfaces, the experimental methods available with sufficiently high lateral resolution and vertical sensitivity are limited. STM can also be used to study these disordered systems.

30

L. Vazquez, R.C. Salvarezza and A.J . Arvia

Fig. 10. a 73 x 73 A2 STM image (top view) with atomic resolution taken at the step indicated by the arrow in Fig. 9 (from [17], with permission of the American Chemical Society); b The (7 /2) 112 x (7 /2) 112 Rl9° structure for the first layer of Ag on HOPG . Open circles and filled circles correspond to C and Ag atoms, respectively. The unit cell is drawn on the schematic (from [17], with permission of the American Chemical Society) a

b

The surfaces of vapor deposited Au on glass, electrodeposited Au on Au wire cathodes and poly(o-toluidine) grown on a gold single crystal are shown in Fig. 14 [4, 6, 36]. In all cases, the deposited surfaces were grown far from equilibrium conditions, leading to an open structure formed by rounded elements with branched voids between them. Despite their difference in growth mechanism, substrate, and the nature of deposited material itself, these deposits look very similar. It appears that different systems evolve spontaneously into common patterns. In fact, both theoretical considerations and experimental results indicate that surfaces grown under nonequilibrium conditions reach a steady state characterized by universal self-affine fractal properties [37] . The dynamic scaling theory provides a useful approach to characterize this type of disordered surface.

2. Scanning Tunneling Microscopy

31

Fig. 11. 4100x4100A 2 STM image (top view) of fiat triangular Ag crystallites and small 3D nuclei grown by electrodeposition on HOPG (from [17], with permission of the American Chemical Society)

Fig. 12.31 x 31A 2 STM image (top view) with atomic resolution of the fiat triangular crystallite shown in Fig. 11 (from [17], with permission of the American Chemical Society)

Theoretical Considerations and STM Applications to Rough Surfaces. The dynamic scaling theory [38] considers the development of a rough surface on a flat 1D surface of size L at timet = 0 (Fig. 15). It is assumed that the growth of the rough surface takes place in a well defined direction so that the instantaneous surface height can be described by the function h(x , t). The surface width in the i-direction, ｾｩ＠ (L, t), taken as a measure of the surface roughness, is defined by the root mean square of the height fluctuations , (10)

where h(x;) is the deposit height measured in the i-direction at the x position and h is the average height of the surface profile. Initially, increases with time due to the build up of random fluctuations, according to,

e

ｾ［＠

(L, t

--7

0) ex: tf3 ,

(11)

where the exponent (3 describes the growth of the correlations with time along the growth direction.

32

L. Vazquez, R.C. Salvarezza and A.J . Arvia

Fig. 13. 2931 x 2931 A2 3D STM image of electrodeposited Pt on C(0001) from H2PtCI5+CIH aqueous solution

STM images (Fig. 16) of the surface evolution of a vapor deposited Au film on smooth glass with the film thickness, 8, (or time) clearly reveal the development of random fluctuations as 8 increases due to the competition among small growing columns (20 nm size) . The value of ｾｩ＠ for each Au film measured from the STM images increases with 8 (time), fulfilling (11) (Fig. 17) , but after a certain time (or thickness) has been attained, the surface reaches a steady state which is characterized by, ｾｩ＠

(L , t--+ oo)

1.2

0.8 • 0.4 0.0

!------------------'

200

0

400 ｾＨｮｭＩ＠

600

800

1000

Fig. 17. Ctm vs t5 plot for vapor deposited Au films on glass, (from [3], with permission of the American Physical Society)

at incident angles nearly normal to the substrate plane without surface restructuring (a = 1/3) [43, 44]. In principle our experimental data are in reasonable agreement with the Halpin-Healey predictions for interface growth [38]:

5-d

(15) 6 where d is the space dimension. However, these results have also received different interpretatoins [45, 46]. Besides, the (3 values obtained recently (0.25 and 0.45 for L < L 8 and L > L 8 , respectively [47]) suggest that new theoretical efforts should be made for a complete description of real systems since some of these sets of values cannot be explained at present. This example shows the ability of the STM to characterize in a quantitative way the surface of strongly disordered systems. Relevant information concerning growth mechanism and degree of surface disorder at the nanometer level can be obtained by STM observations and image processing. a=-

2.4 Conclusions From the results presented in this Chapter it is clear that STM is a suitable technique to study different problems posed in the field of surface science such as nucleation and first stages of growth which are of great interest in many experimental systems. In this case, STM can reveal the structure of the deposit and its relationship with that of the substrate. This kind of study can be performed in UHV, air, and liquids. In the same way, STM, supported by other

L. Vazquez, R.C. Salvarezza and A.J. Arvia

38

Cll

exp

0.8

,

Q4

•' . .

,, 0 ＧＭｾｌ 0

,

., , ,

,

,

,

,

• . . ,

,.

,

,

,,

,i

,

Fig. 18. The 1Xexp VS plot, (from [41], with permission of Elsevier Science Publishers)

IXth

04

08 cx.th

UHV techniques, aids the resolution of the surface structure of different metals and surface reconstructions at the atomic level. However, as we have shown in Sect. 3 working at nonatomic resolution conditions, quantitative information concerning surface evolution during growth and the fractal character of the interfaces on the nanometer scale can be obtained. This small scale, which is not easily reached with other techniques, is of interest in order to be able to compare the experimental data with the results obtained from computer simulations of theoretical growth models. Thus, the STM reveals itself as a powerful structural technique to be added to already standard ones routinely in use in the different research fields. The same can be stated for the Atomic Force Microscopy (AFM) as it has proved the same capabilities to study either conducting or insulating disordered surfaces [48]. Finally, it should be noted that STM also presents capabilities to analyze the electronic structure of the surface and to modify the surface. These applications have not been considered in this text but the main principles and examples can be found in the literature [2, 16].

2. Scanning Tunneling Microscopy

--s

0.4

c: .._...

5

"'VoJ'" .._...

cw 0

39

i i

0 .0 ]

......l

-0.4

- 0 .1\

0'::: 0 .7 1

i

-l.2l., ＱＭｲｬＢｔＧｾＮＬ＠ - 0 .2

0.2

I

0 .6

1.0

1.4

I

1.0

I

I

I

I

2 .2

I

I

I

I

2.6

I

I II

3 .0

LoO'(l.( nm)) Fig. 19. The log.;:tm vs log£ plot of a 5070 x 5070A2 STM image (inset) of a 8500A ass (from [ 41), with permission of Elsevier Science thick vapor deposited Au film o n gl Publishers)

R eferences 1. G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel: Appl. Phys. Lett. 40 , 178 (1982). 2. Scanning Tunneling Microscopy and Related Methods (Kiuwer Academic Publishers, 1990). 3. P. Herrasti, P. Oc6n, L. Vazquez, R . Salvarezza, J .M. Vara, A. Arvia: Phys. Rev. A 45, 7440 (1992). 4. R. Salvarezza, L. Vazquez, P. Herrasti, P . Oc6n, J.M. Vara, A. Arvia: Europhys. Lett. 20 , 717 (1992). 5. M.W. Mitchell, D.A. Bonnell: J. Mater. Res. 5 , 2244 (1990) . 6. L Vazquez, J.M . Alb ella, R.C. Salvarezza, A.J. Arvia, R.A. Levy and D. P erese: Appl. Phys. Lett . 68, 1285 (1996) . 7. S. Miller , R. Reifenberger : J . Vac. Sci. Techno!. B J . Dev.10 , 1203 (1992) . 8. D. Pohl: IBM Res. Develop. 30, 417 (1986) . 9. E. Stoll: Surf. Sci. 143, L411 (1984). 10. L. Vazquez, A. Bartolome, R. Garcia, A. Buendia, A. Bar6: Rev. Sci. Instrum. 59, 1286 (1988) . 11. J.W. Lyding, S. Skala, J.S. Hubaceck, R. Brockenbrough , G . Gammie: J . Microscopy 152, 371 (1988). 12. J. Bardeen : Phys. Rev. Lett. 6 , 57 (1961). 13. J . Tersoff, D.R. Hamann: Phys. Rev. Lett. 50, 1998 (1983). 14. J. Tersoff, D.R . Hamann: Phys. Rev . B 31, 143 (1984) . 15. N.D. Lang: Phys. Rev . Lett. 56, 1164 (1986) .

40

L. Vazquez, R.C. Salvarezza and A.J. Arvia

16. Proceedings of the Sixth International Conference on STM, Interlaken, Switzerland, 1991. Ultramicroscopy pp. 42-44 (1992). 17. L. Vazquez, A. Hernandez Creus, P. Carro, P. Oc6n, P. Herrasti, C. Palacio, J.M. Vara, R. Salvarezza, A. Arvia: J. Phys. Chern. 96, 10454 (1992). 18. W. Obretenov, M. HoSpfner, W.J. Lorenz, E. Budevski, G. Staikov, H. Siegenthaler: Surf. Sci. 271, 199 (1992). 19. O.M. Magnussen, J. Hotlos, R.J. Nichols, D.M. Kolb, R.J. Behm: Phys. Rev. Lett. 64, 2929 (1990). 20. W.J. Lorenz, L. Gassa, U. Schmidt, W. Obretenov, G. Staikov, V. Bostanov, E. Budevski: Electrochim. Acta. 37, 2173 (1992). 21. S.L. Yau, C.M. Vitus, B.C. Schard: J. Am. Chern. Soc. 112, 3677 (1990). 22. V.M. Hallmark, S. Chiang, J.F. Rabolt, J.D. Swalen, R.J. Wilson: Phys. Rev. Lett. 59, 2879 (1987). 23. J. Wintterlin, J. Wiechers, H. Brune, T. Gritsch, H. Hofer, R.J. Behm: Phys. Rev. Lett. 62, 59 (1989). 24. J. Wintterlin: Ph. D. Thesis, University of Berlin (1989). 25. S. Ciraci: in Scanning Tunneling Microscopy and Related Methods (Kluwer Academic Publishers, 1990). 26. J.M. Soler, A. Bar6, N. Garcia, H. Rohrer: Phys. Rev. Lett. 57, 444 (1986). 27. T.A. Land, T. Michely, R.J. Behm, J.C. Hemminger, G. Cosma: Surf. Sci. 264, 261 (1992). 28. Y. Kuk, P.J. Silverman, F.M. Chua: J. Microsc. 152, 449 (1988). 29. G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel: Surf. Sci. 131, L379 (1983). 30. W. Roesler: Ber. Bunsenges. Phys. Chern. 90, 205 (1986). 31. D.J. Trevor, C.E.D. Chidsey, D.N. Loiacono: Phys. Rev. Lett. 62, 929 (1989). 32. C. Alonso, R.C. Salvarezza, J.M. Vara, A.J. Arvia, L. Vazquez, A. Bartolome, A.M. Bar6: J. Electrochem. Soc. 137, 2161 (1990). 33. C. Alonso, R.C. Salvarezza, J.M. Vara, A.J. Arvia: Electrochim. Acta 35, 1331 (1990). 34. H.G. Bussmann, H. Sprang, I.V. Hertel, W. Zimmermann-Edling, H.J. Giintherodt: Appl. Phys. Lett. 59, 295 (1991). 35. W. Zimmermann-Edling, H.G. Busmann, H. Sprang LV. Hertel: Ultramicrosc. 42-44, 1366 (1992). 36. J.M. G6mez-Rodriguez, L. Vazquez, A. Bar6, R. Salvarezza, J.M. Vara, A.J. Arvia: J. Phys. Chern. 96, 347 (1992). 37. F. Family, T. Vicsek: J. Phys. A 18, L75 (1985). 38. F. Family: Physica A 168, 561 (1990). 39. B.B. Mandelbrot: The Fractal Geometry of Nature (Freeman, New York, 1982). 40. R.F. Voss, Fundamental Algorithms in Computer Graphics (Springer-Verlag, Berlin, 1985). 41. L. Vazquez, R. Salvarezza, P. Herrasti, P. Oc6n, J.M. Vara, A. Arvia: Appl. Surf. Sci. 70/71, 413 (1993). 42. T. Vicsek: Fractal Growth Phenomena, (World Scientific, Singapore, 1989). 43. P. Meakin, P. Ramanlal, L.M. Sander, R.C. Ball: Phys. Rev. A 34, 509 (1986) 509; J. Krug P. Meakin, Phys. Rev. A 43, 900 (1991). 44. J. Krug, P. Meakin: Europhys. Lett. 11, 7 (1990). 45. A. Barabasi and E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York, 1995). 46. M. Marsili, A. Maritan, F. Toigo and J.P. Banavar: Europhys. Lett. 35, 171 (1996). 47. L. Vazquez, R.C. Salvarezza, P. Herrasti, P. Oc6n, J.M. Vara and A.J. Arvia: Surf. Sci. 345, 17 (1996). 48. L. Vazquez, R.C. Salvarezza and A.J. Arvia: Phys. Rev. Lett. 79, 709 (1997).

3. Basis and Applications of Convergent Beam Electron Diffraction ( CBED) for the Investigation of Phases in Ceramics and Glass-Ceramics J. MA. RINCON and M. RoMERO The Glass-Ceramics Lab., Instituto. E. Torroja de C.C. Construcci6n, CSIC, c/Serrano Galvache s/n, Madrid-28033, Spain Abstract. The convergent beam electron diffraction (CBED) technique, as well as the electron microdiffraction methods are currently used in analytical electron microscopy for materials characterization. These diffraction methods allow the identification of very small crystalline phases and tri-dimensional crystallographic analysis with high spatial resolution through the application of a very thin electron beam and wide diffraction angle through the specimen in a transmission electron microscope (TEM). Despite the wide range of analytical possibilities, its use in the characterization of ceramics, glass-ceramics and their raw materials has been scarce. Therefore, in this chapter are shown the basic principles of CBED as well as microdiffraction for the crystallographic analysis of ceramics both from our own research and by reviewing some examples of applications from the literature.

3.1 Introduction 3.1.1 Fundamentals of Electron Diffraction by CBED: Basic Principles Convergent beam electron diffraction (CBED) strictly refers to diffraction using an electron probe in a TEM with very large convergence angle. When this convergence angle becomes small the conditions are similar to the spot pattern obtained with parallel illumination in the conventional Selected Area Diffraction Patterns (SADP) as is shown in Fig. 1. This type of small angle patterns are termed as microdiffraction patterns (MDP). In practice, the convergence of the probe usually is controlled by the second condenser aperture [1, 2]. Table 1 gives the comparison between both diffraction procedures, SADP and CBED. In 1939 Kassel and Mollenstedt demonstrated the possibility of obtaining CBED patterns from crystals with more information than obtained from the more conventional focused patterns for special beam directions. Later, in 1940, it was demonstrated that the intensity of a reflection is a function of the excitation ･ｲｯＬｾＧ＠ and the thickness, t, of a plane parallel crystal slab [3]. Lately, more advances in CBED became possible with the introduction of field emission guns and scanning TEM (STEM) techniques. Thus, the STEM instrument has electron optics similar to CBED for obtaining diffraction results from areas as small

42

J. Ma. Rincon and M. Romero

a·I

a i> 6Bragg

...)L

)8( J

(

Fig. 1. The different ways in which a beam of electrons focused onto the sample gives different diffraction methods which can be used by transmission electron microscopy (TEM) , from Willia ms [2]

Table 1. Comparison between microdiffraction methods and the conventional selected area diffraction

Spatial resolution Limiting factors Angular resolution Limiting factors 3D information Thickness information Lattice parameters determination Others

SADP

CBED

ｾ＠

ｾ＠ 1nm Probe size and thickness of specimen 10- 3 - 10- 4 rads Second condenser Yes size aperture Yes 1:10 3 -10 4

0.5JLm

Aperture size a nd objective lens Mx ｾ＠ 10- 4 rads Photographic No plate resolution No 1:102

More sensitivity for symmetry changes (HOLZ changes)

as 2 nm in diameter. The most important difference between the CBED patterns and the SADP is the reduced degree of angular resolution. The calculation of ai from a CBED pa tterns is simple. The convergent beam which subtends an angle of 2ai produces a main beam and several diffracted rays that are focused as disks in the back focal plane of the objective lens. Thus, the distance between the main beam and any of the diffracted beams is proportional to 28 B: y

X

(1)

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

43

where X is the horizontal distance between the center of disks and Y the diameter of disks. By this simple calculation the degree of convergence can be computed directly from a CBED or microdiffraction pattern [4]. There are three variants of the CBED method [3] a) Defocused CBED shadow imaging, b) Wide or large CBED, and c) Grigson scanning CBED. When the lenses are defocused, so that a small crossover is formed before or after the specimen, the central spot of the CBED pattern will become a bright-field shadow image of the specimen and each diffraction spot will become a dark- field shadow image showing the variation of intensity within the illuminated zone, this is the afore mentioned a) variant. In the b) variant the convergence angle is increased by using a very large limiting aperture or none. Thus, the individual round diffraction spots produce large overlap and superimposed black and white lines are obtained, similar to the Kossel or the Kikuchi lines formed from electrons diffusely scattered in thick crystals. The separation of these line pairs can be used as a measure of crystal curvature. In the c) variant the diffraction is scanned over a single detector of small aperture using deflection coils after the thin foil. The advantage in this case is the possibility of measuring the diffraction pattern intensity in the form of an electronic signal. However, the time to record the diffraction pattern (DP) is long and the radiation damage and contamination of the small zone illuminated may be strong. Both the electron microdiffraction and the CBED diffraction methods give a large amount of information concerning the structure of small regions of materials and powders [5]. This includes: -

Two-dimensional symmetry, Three-dimeusional symmetry, Crystal symmetry, Poly-type determination, Disordered systems, Strain identification.

The 2D symmetry yields information of the projected crystal potential, giving identification of the crystalline phases present in a material or powder. The special characteristics of this method make it possible to use the CBED patterns as fingerprints for identification of phases [6]. The primitive cell volumes can be deduced easily from CBED unindexed patterns, as was shown by Carpenter and Page in [7]. By combining the measurements from the ZOLZ, (zero order Laue zones, which appear in the center of the CBED pattern) and the HOLZ (higher order Laue zone, which appears as rings around the ZOLZ pattern) it is possible to calculate the primitive cell

44

J. Ma. Rincon and M. Romero

volume, Vc. Defining g 1 and g 2 as two primitive vectors in the ZOLZ the volume of the primitive reciprocal cell is:

(2) where H is the reciprocal interplanar spacing calculated from the diameter ( s) of the HOLZ ring(s). The inverse of Vc* is the volume of the primitive cell, v;,, which is easily compared with data of possible phases. The primitive cell parameters from single CBED patterns also have been determined by using a computer programme simplifies the diffraction experiment considerably and which allows automated on-line analysis. The 3D diffraction is the most important in the CBED method. Within the disks of the ZOLZ plane is valuable information about the crystal symmetry and the lattice parameters. The determination of glide planes and screw dislocation axes is also possible. On the other hand, the HOLZ planes contain additional information about the dispersion of the surface geometry, crystal space group, point and planar defects. The identification of polytypes or layered structures is also a useful capability of the convergent beam electron diffraction. Finally, CBED has a special ability to make qualitative or comparative identification of localised strains which is very important in toughening mechanisms in materials, as reported by Bielicki [8] in the case of an alumina grain neighboring a transformed tetragonal zirconia grain and the lattice distortion measured in a Mn-Zn ferrite as a function of temperature by CBED. The CBED method in a TEM has a wide range of advantages over the more normal diffraction analysis methods: -Analysis by electron diffraction of smaller areas: 10-lOOnm. - Information about symmetry, allowing identification of phases. - More sensitivity in the determination of lattice parameters. - More sensitivity to the crystalline symmetry changes. - Thickness determination of specimen. The spacing between the reciprocal lattice layer, H, can be calculated easily from the radius of the FOLZ (first order Laue zone) ring (Fig. 2); G, as described by Steeds [9]:

G2>.

H=2

(3)

where G(A -l) = R/CL, R being the radius of the FOLZ ring in em, CL is the camera constant in em, and >.(A) is the wavelength of electrons. H- 1 (A) is the real space correspondence of the reciprocal lattice layer spacing, H [1]. The diffraction information revealed by the FOLZ is valuable since certain reflections, which are kinematically forbidden in the ZOLZ, are allowed in the FOLZ. In fact, some additional reflections can occur as a result of the modifications introduced by the third dimension and allowed by the structure factor.

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

45

e- beam

A

Atomic Planes

!

t

1

11111111

-.a ...

Ewald Sphere

B

c

Reciprocal Lattice

lid

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Second layer

H t • · · · · · · · · · · · • · · · · • +-First layer • • • • • • • • • • • • • • • • • • ' Zero layer

. .......... ... . ZOLZ

ｾＺ＠

i;

• :: ·: •::: •: •: :::

..

.....

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• : : : : :•

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Fig. 2. Intersection of the Ewald sphere with the reciprocal lattice showing the scattering angle for ZOLZ and HOLZ reflections in the case of a short camera length DP and schematic projection of a corresponding CBED pattern

46

J. Ma. Rincon and M. Romero

The characteristic geometry of HOLZ diffraction and the relative position of deficiency lines inside the central disk are very sensitive to changes in the lattice parameters. The application of CBED depends of the same properties of the material examined. The g vectors in the diffraction process imply an increase of the Debye-Waller factor, giving very weak intensities in the HOLZ lines in some materials, but by using liquid N 2 or He temperatures these can be overcome. The HOLZ can be weakened in materials with a high degree of "frozen" disorder, that is to say, point defects. Therefore, some materials show weak effects in particular orientations in the HOLZ due to the large spacing along some directions [10]. The spatial resolution of the method is related to the condition of minimum thickness for the HOLZ lines where the extinction distances are very large (about 100 nm). The beam widening due to difussion phenomena inside this distance can increase the analyzed area by several orders depending of the atomic number. The small probes give rise to lower current producing very fine CBED patterns

[11]. 3.1.2 Possibilities and limitations of CBED for characterising ceramic powders Despite the advantages of using CBED in powder characterization, due to the non-uniform thickness scattering effects can be produced which affect the diffraction patterns. The most frequent example is the information obtained from finely dispersed particles. As an example, the case of 10-50 nm YAG cubic particles of a YA10 3 perovskite oxide, YAP, in a strengthened alloy can be seen in [1]. Determination of foil thickness. Among other capabilities, the CBED provides the possible determination of specimen thickness. There are two methods: The Ackerman method and the Kelly method, where both depend on two-beam dynamic theory, which relates the minimum intensity oscillation in the diffracted beam to the thickness [13, 14, 18]. For determination of thickness the distances between the Kossel-Mollestedt fringes are used as is shown in Fig. 3. The distance (BB) from the symmetric and the asymmetric images is considered, as well as the distances of maximum intensity from the center of the symmetric image (L1Bi)· Thus, the Bragg deviation (si) is:

(4) while both of the more usual methods for thickness determination use the following expressions. In the Ackerman-Rez method is represented versus ni being an integer, according to the following equation:

sr

(sre+ 1) t

2- 2 -ni

nr,

(5)

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

47

Maximum Intensity

ｾ＠

Asymmetric image

Symmetric image

Fig. 3. Model of the Kossel-Mollestedt fringes showing the useful lines for the thickness determination

In the Kelly method the equation for determination of thickness is:

(6)

sr

where k = i + j and j is an integer < ｾ Ｙ ＯｴＮ＠ Plotting against gives from the slope and ｾ＠ from the intercept with the coordinate; alternatively, plotting (si/nk) 2 against 1/n% gives t as intercept with the ordinate. In both cases, the correct starting number nk of the first minimum has to be known. For a foil and (m + ＱＩｾ＠ the appropriate value is nk = m + 1. thickness between ｭｾ＠

Crystal symmetry determination. The determination of crystal group and space group in phases which constitute the ceramics and powders by CBED gives information about: -

Identification of unknown phases. Microstructure determination. Phase transition analysis. Atomic displacement locations.

From the CBED patterns, high symmetry axes can be rapidly and easily determined, with a little experience [15]. Thus, 17 of the 32 possible point groups can be identified from a single pattern. The remaining can be identified by carrying out at least two patterns at the same zone axis. The main starting step for point group determination is the obtention of a good high symmetry pattern. For this first step it is necessary to tilt the specimen until clear zone axes or Kikuchi bands are located and then to study the details at low camera length looking for the mirror lines. If, after rotating the specimen through 90° and recentering the eucentric tilt axis, no mirror lines are located the crystal is almost triclinic [16]. When a high symmetry zone axis is obtained the next step is to use the published tables, which are shown in Table 2 from Buxton et al. [17].

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Fig. 4. Mullite (001) orientation showing dark extinctions in vertical and horizontal reflections corresponding to glide planes

The relation between the diffraction groups and the crystal point groups can be seen in Table 3. For the space group determination it is necessary to use the information given by the lines of absent intensity (named "dynamic absences", "Gjonnes Moodie" lines or "black crosses") [18] in the reflections which would be completely absent in the weak scattering. In order to distinguish these lines, the following recommendations must be followed: -

They only appear along the principal axes of a ZAP. Alternate reflections along a line show the characteristic line of absence. These lines are narrower as the specimen thickness increases. They occur at any operational voltage and thickness. A second absence line is observed orthogonal to the first ( "black cross").

Figure 4, taken from Bielicki [8], shows a glide plane for the lines of dynamic absences in a mullite crystal. A bright field mirror line parallel to a line of dynamic absence indicates that there is a glide plane parallel to the incident beam while one orthogonal shows a 21 screw axis perpendicular to the mirror line. Sometimes, when the crystal is thin enough, the absence is broad enough to fill the whole Bragg disk. In this case, a different method must be used for locating the absent reflections: that is, the observation of the wide angle or large angle CBED (LACBED) or Tanaka patterns [19] . Usually, for the standard method of crystal point group and space group determination four types of pattern are required: whole, bright field , dark field

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

49

Table 2. CBED patterns symmetries (from Buxton et al. [17])

Diffraction group

Bright field

Whole pattern

General

Dark Field = G Special General

1 1R 2 2R 21R

1 2 2 1 2 m m 2mm 2mm 2mm m 2mm 4 4 4 4mm 4mm 4mm 4mm 3 6 3m 3m 6mm 6 3 6 6mm 6mm 3m 6mm

1 1 2 1 2 1 m m 2 2mm m 2mm 4 2 4 4 4mm 2mm 4mm 3 3 3 3m 3m 6 3 6 6 6mm 3m 6mm

1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 2 1 1 2 1 1 1 2

none none none none none m m 2mm m m m 2mm none none none m m m 2mm none none m m 2mm none none none m m m 2mm

fiR

m m1R 2mRffiR

2mm 2RffiffiR 2mm1R 4 4R

41R 4mRffiR

4mm 4RffiffiR 4mm1R 3 31R 3mR

3m 3m1R 6 6R

61R 6mRffiR

6mm 6RffiffiR 6mm1R

1 1 2 2R 21R 1 1 1 2 2 2R 21R 2 2 21R 2 2 2 21R 1 1 1 1 1 2 2R 21R 2 2 2R 21R

Special

Projection diffraction group

none none none none none

1R 1R 21R 21R 21R m1R m1R m1R 2mm1R 2mm1R 2mm1R 2mm1R 41R 41R 41R 4mm1R 4mm1R 4mm1R 4mm1R 31R 31R 3m1R 3m1R 3m1R 61R 61R 61R 6mm1R 6mm1R 6mm1R 6mm1R

fiR

m m1R

none none none

none none fiR

m m1R none none none

The symbol R denotes the special rotation when top and bottom surfaces are equivalent in a 180° rotation about a point in each of the Bragg reflections.

and ±g dark field patterns, but Tanaka and Tareuchi [20] have developed a method that allows the four patterns to be taken simultaneously in a plate and in 100 nm diameter specimen area by adjusting the objective exciting current interlocking to the intermediate exciting lens. They perform this method by removing the condenser aperture from the optical axis. The excitation of the objective lens is increased by 0.5% from that for the ordinary method, causing the elevation of the focused position of the incident beam receiving defocused illumination. The image is formed above the selector aperture, which is inserted into the optical axis so that the neighboring diffraction disks do not overlap each

J. Ma. Rincon and M. Romero

50

Table 3. Relation between diffraction groups and crystal point groups (from Buxton et al. [17]) Diffraction Groups

6mm!R 3m!, 6mm

X X X

Ｖｭｒｾ＠

X

6JR 3JR 6

X X X

ｾｭ＠

X

X

3m 3mR 6R 3 4mml,

X

X X

X X

X X

X IX

X

ｾｭ＠

X

X

4mm

X

Ｔｾｭｒ＠

X

X Ｔｾ＠

X

4, 4 2mm!R ｾＱ＠ 2mm

X X X X

X

X X

X

X

ＲｭＬｾ＠

X

miR m m, 21, 2,

X X XX

X X X X

X

2 X

·-

ｾ｣＠

X XX XX XX X

XX X

X

X

X

X X

X X X

X

XX

XX

XX X

X

X XX

Ｍｉｾ＠

N

X

X

XX XX XX X

X X XX

X

X X

E N E a a EN -N N a Na NN ｾ＠ aa .... 1'1" ..§..... .......... .......... "' .....

XX X

XX

E E

0

X X

X

X

X

X XX

p., ;: ::;"'

X X

X X

X

IR l

X X

X

X

X

XX

E

N

E

a

MM M

..§

N N

a a NE-a ｾｳ＠

S

\0 l\0 " ' " ' \ 0

"'"'

N

a ...,a

.......... E ..........

other. Thus, the neighboring disks are not in contact with each other; then, the excitation of the objective lens must be readjusted to bring the disks in contact. According to these authors in some sense this method is an extension of the more traditional SADP. Figure 5 shows an example from [20] obtained by this method. The bright field disk and six surrounding 220 dark field disks still contain enough HOLZ lines. Thus, the central disk shows the BF symmetry 3m. The exact 220 Bragg positions exist at the centers of the corresponding DF disks. Each of these disks shows the DF mR symmetry due to a horizontal two-fold axis. A pair of the 220 and 220 disks, which exhibits the ±g DF symmetry shows the translational symmetry or 2R. The disks, as a whole, form the whole-pattern symmetry 3m

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

51

Fig. 5. CBED pattern from Si in orientation (111) using the Tanaka method [20] in a field emission gun at accelerating voltage of 60 k V. The angular size of the disks is the Bragg angle of the 220 reflection, 1 x 10- 2 rad and the exact Bragg position is at the center of the disk (reproduced with permission of JEOL Co, Japan)

with respect the center of the BF disk. From these symmetries appearing in one photograph, the diffraction group of the specimen (in this case Si, (111) pattern) is identified as 6R mmR· The present method, as well as the LACBED method, does not use the condenser aperture, but uses the selected area aperture to determine the angular disk size, whereas the ordinary method and the many-beam LACBED method use the condenser aperture. Therefore, this method allows the observation of the specimen with less contamination even in specimens which are not sufficiently clean. Despite the possibilities of the CBED method, there are some disadvantages or problems which arise when this method is used in the characterization of ceramics and their powders: - Due to radiation damage, the most sensitive specimens are difficult to analyse, in particular with high beam currents applied to very small areas. - The contamination effects can mask the details of the CBED pattern with diffusion of dispersed intensities. - The CBED method requires time for obtaining good results and a well trained operator. Limitations for materials and powders characterization can result from the extreme sensitivity of CBED to alterations in the specimens, such as:

52

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J. Ma. Rincon and M. Romero

Weak strains from internal defects, Dislocations or surface contaminants, Roughness of surfaces, Non-uniformity of thickness of specimens, ｂｾ｡ｭ＠ spreading, Beam heating.

All these effects are important, but beam spreading due to large thicknesses of some samples is the chief factor limiting the spatial resolution of the CBED and which frequently makes it difficult to obtain good results. Similarly, thermal conductivity of specimens, such as poor thermal conductors can increase the temperature to above 300°C for larger beam currents [21].

3.2 Practical Aspects of CBED: Specimen Preparation and Operation in the TEM The normal procedures for obtaining CBED patterns are described in [21-23] and here are summarized in the following steps: 1. After focusing the beam and correcting the astigmatism, obtain an image in a TEM of the area of interest at higher magnifications setting the specimen height and the eucentric point. 2. Insert the selected area diffraction aperture, focus the image and switch the diffraction mode. Thus, a conventional SADP is obtained as starting point for the next operations. 3. Focus the pattern by using the intermediate lens and C 2 lens control and remove the selected area and objective apertures. Return to the image mode. 4. Insert a small C 2 condenser aperture and focus the shadow image of the aperture with the objective lens; the image will then go out of focus. 5. Adjust the specimen height until the image is in focus in the plane of the condenser aperture image. 6. Switch to the diffraction mode and observe the microdiffraction pattern. 7. The sizes of the diffraction disks are controlled by the condenser aperture in order to obtain no overlapping of disks (Kossel-Mollensted diagram) or by using a larger aperture for obtaining a diagram showing overlapping of disks (Kossel diagram). 8. The beam convergence must be adjusted with the second condenser by focusing the image over a selected small zone or edge of the specimen. Then, the beam is overfocused and underfocused until the selected zone is inverted (in the central disk the "ghost image" is observed which inverts in this focusing operation). This image vanishes in the "crossover" condition. 9. The main objective is to obtain a CBED diagram perfectly oriented throughout displacement of the condenser aperture or when operating with dark field deflectors.

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

53

10. As final recommendations the specimen must be cooled in liquid N2 and several photographic plates in different conditions of apertures and camera length should be obtained. With respect to step 9, the best procedure for obtaining a good zone axis pattern (ZAP) is to be helped by the presence of Kikuchi lines, as recommended by Eades [24]. The Kikuchi lines are generally clearer in CBED than in the SADP, because the convergent beam is obtained in a very small area of specimen. For tilting the specimen to a high symmetry low index zone axis, we can tilt and looking the diagram for both the narrowest Kikuchi bands available and the orientation at which they intersect. If the diffraction is degraded during operation in the TEM, due to radiation damage or contamination, it is essential to obtain the necessary information as fast as possible. Another frequent problem can be the small drifting of the specimen during the operation if adequate beam illumination is not used. Different areas and slices to be explored are a function of the condenser aperture size and the demagnification of the upper objective polepiece. Camera length can be modified as is usual in any TEM instrument for obtaining the external rings. Specimen preparation. The specimen preparation is always a very important problem in any method used in TEM. As stated by Steeds [25], for CBED the specimen preparation is more or less demanding depending in the considered objective. The crystallographic information is easily disturbed by artefacts, defects or interfaces with other phases. The carbon extraction replica technique has proved to be successful for CBED, in this sense this technique is good for examining powdered particles when they are separated from other phases. Another advantage of the extraction is that strain from the matrix is released. The ion-thinning specimen preparation procedure is the most usual for ceramics observation by TEM, but is time consuming and costly, and can produce stresses, phase transformations or alterations in the multiphase specimens. Heating produced by ion bombardment can lead to such specimen alterations. Even Ar implantation can be possible in some phases in ceramics, as has been observed by Rincon in 1985 (own results not yet published). Otherwise, selective removal of atoms can lead to the formation of an amorphous skin on the surface of ceramic materials, degrading the quality of CBED. Another very simple method in the case of ceramic powders is to grind the sample and, as is usual for clays and minerals, spread it directly over a carbon foil supported over the TEM grid. When particles are of sufficiently small size this method is simple and can give good CBED patterns. The embedding of powder samples in stable and hard polymer matrices sometimes can be a useful method before the ion-thinning.

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J. Ma. Rincon and M. Romero

3.3 Applications of CBED for solving Problems m Ceramics: Some Examples and Application to Zirconia/Mullite Materials There are not too many cases in the literature of applications of CBED to ceramics and their powders. Azough et al. [26], for example, have investigated dielectric ceramics prepared by the mixed-oxide route in the BaO-Pr 2 03-TiOz composition system. They identify a compound with formula Ba4.5Pr9 Ti 18 0 5 4 with orthorhombic symmetry and space group identified by CBED as Pnam. The obtained powders after drying, were pressed into discs, sintered in air at 16481723K and cooled at 120Kh- 1 . In this case the obtention of CBED patterns was performed at 300kV. The first observation of defects in crystals by CBED was carried out by Johnson [27] in a graphite crystal. An example of identification of lattice defects by CBED in a silicon specimen can be seen in the excellent work of Tanaka and Kaneyama [28]. They demonstrated the capability of this method for analyzing stacking faults and dislocations. The method is based on using HOLZ reflections, because the lines from a faulted area are simple and easy to distinguish compared with those from a perfect region. The plural lines enable determination of the displacement vector R and whether the defect is intrinsic or extrinsic. The method is based in the dynamic diffraction effects. On the other hand, when the beam illuminates a small area around a dislocation, only the effect of local strain of the dislocation is observed. Similarly, defocus illumination or LACBED allows observation ofthe whole strained area and identifies the Burgers vector on dislocations. The pattern gives the intensity profile of a reflection as a function of the distance from a dislocation and of excitation error. Such patterns show n nodes at the crossing region between a dislocation line and a reflection line when g · b = n. An application of residual stresses determination by CBED can be seen in the work of Kim et al. [29], where such types of stresses have been determined in B4C-Al cermets, which are characterized by high toughness properties. The possible strengthening mechanism may be the residual stresses that are created from the differential contraction in the metal and ceramic phase during cooling after the high temperature infiltration processing. Thus, the shifts in the positions of the HOLZ lines were determined in various zone axis orientations and compared with B4C and AI standards. The results indicate that the residual stresses in the aluminum phase range from 24 to 340 MPa and similarly, residual compressive stresses from -137 to -314 MPa exist in the boron carbide phase which is consistent with the thermal expansion differences. Similarly, Sarikaya et al. [30] have determined the relative change of cell parameters in a stainless steel by CBED. Since past few decades the zirconia, Zr0 2 , has been considered as one of the ceramic materials with higher scientific and technological interest. It is well known that this is due to the capabilities for retention at ambient temperatures

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

55

of the high temperature cubic or tetragonal phases, giving rise to high toughness materials. The more interesting materials developed thus far have been: - Partly stabilised zirconia (PSZ), - Polycrystal tetragonal zirconia doped with 2.3% Y 2 0 3 (TZP), - Composites of zirconia/alumina, zirconiajmullite, zirconia/mullitejalumina, etc. This type of material usually contains 15-17 wt% of tetragonal zirconia in a ceramic matrix [31]. Other kinds of composites are being investigating such as zirconia/NAl, zirconia/NZr, zirconia/SiC fibers, zirconia/stC'atite. In all cases, the general microstructures are Zr0 2 grains between the matrix crystals with 1-3 J-tm size and Zr0 2 (intragranular) rounded crystals (0.1-0.3 J-tm size) trapped in the ceramic crystals matrix. The formation of new phases and the order-disorder phenomena in the tetragonal phase or solid solution effects can be investigated through CBED [11]. In the case of advanced ceramics and powders of nanometric size, the use of the classical selected area diffraction Patterns (SADP) by using different apertures in the electron path in the TEM is very short. In these cases and similarly for Zr02/mullite materials, the very small size of intragranular zirconia formed in the reaction sintered process inside the matrix, reaching 50-300 nm sizes, makes it fully necessary to use higher resolution in the electron diffraction analysis. The microstructure of zirconia grains is observed by TEM and analyzed by CBED (Fig. 6). The large intergranular grain is transformed and the twin domains and a microcrack formed in the mullite matrix due to the different expansion coefficient after transformation are visible. In this case, the intragranular tetragonal zirconia particles show only a small concentric stress field around them. The CBED allows determination not only of the orientation of crystals, but also of solid solution or phase transformations in relation to solid solution effects and stress fields generated in the grain boundaries, as can be seen in Fig. 7. It can be seen how the grains in certain orientations depict undulated contrast lines in the bright field image. Otherwise, the presence of small glassy phase areas between the grain joins can be confirmed directly by CBED without the necessity of using the well known dark field methods as will be discussed later. Figure 8 shows an intragranular rounded Zr0 2 grain with a size larger than the critical size for transformation, being clearly transformed in a twinned monoclinic crystal. The corresponding CBED shows the ZOLZ diffraction and several rings of the HOLZ from which is possible to deduce the expansion in these types of transformed crystals and possible solid solution effects. The thin foils were prepared in this case by argon ion-thinning in a dual ion-milling, Gatan equipment, after coating with a carbon conducting layer. The observations were carried out by TEM, Philips analytical EM-420 equipped with a Si(Li) EDAX detector. The CBED diagrams have been obtained at 120 kV with a beam size of 40 nm.

56

J. Ma. Rincon and M. Romero

Fig. 6. Zirconia grains with different degree of transformation observed by TEM in zirconia/mullite specimen and corresponding CBED patterns

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

57

Fig. 7. Bright field images of a zirconia grain observed in different orientations with respect to the electronic beam and the corresponding CBED patterns. The high stress field around the particle can be seen in certain orientations

58

J. Ma. Rincon and M. Romero

Fig. 8. Monoclinic zirconia grain, with a size larger than that critical for phase transformation, showing the twinned domains and the corresponding CBED pattern

In Fig. 8 can be seen in the centered disks the deficiency intersections of the high order Laue zones (HOLZ). As was demonstrated previously by Sarikaya et al. [30] in austenitic steels in the central disks with deficiency lines, they are very sensitive to the crystal lattice parameters when the diagrams are obtained in the same excitation conditions. The first results obtained in mullite/zirconia are in this sense promising. There is also the additional advantage for analyzing through energy dispersion by x-rays (EDX) the composition of boundaries, showing the existence of Zr02 in the mullite and Si0 2 and Al 20 3 in the zirconia grains. Due to the

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

59

problems of microanalytical resolution limitations in grain boundaries this solid solution effect could only be detected by deficiency lines in electron diffraction analysis. Therefore, the CBED patterns have allowed: - Frequent observations of reflections in the cubic and tetragonal Zr0 2 which are forbidden, - Sometimes the spacing of reflections appears to be divided in one direction - The dark field (DF) images can give information of altered zones, - Sometimes, the spacing along some directions is 1/4 of a normal measurement, revealing also "domains" at higher magnifications. The possible explanations are the formation of new phases or the existence of ordering effects due to electrostatic forces between the additives (Y, Ca, Mg etc.) and oxygen vacancies.

3.4 Future of the CBED Method The hollow-cone beam method which was suggested some time ago by Riecke to improve the contrast of the dark field images has not been sufficiently developed. It is based on the introduction of an annular aperture and an electrical method which revolved the beam around the optical axis to the Bragg angle. The advantage of this method is that it can easily find three-dimensional symmetries about a zone axis since it eliminates the strong intensities due to the ZOLZ reflections or due to two-dimensional interaction. Otherwise, it can observe the different HOLZ lines separately. When a zone axis pattern is compared with the patterns from this method, an inversion center can be identified allowing the observation of a vertical glide plane with a vertical translation [19]. The recently incorporated imaging filter is an attachment to a TEM that produces energy-filtered electron images and CBED patterns and which allows the contrast of images and diffraction patterns to be improved by removing the inelastic scattering contribution. This energy filter (EF) has similar behavior to adding an objective aperture to a TEM. The contamination limitations can be overcome by using this energy filtering Microscopy (EFTEM) and the greatest contrast is obtained at small angles, where the inelastic scattering dominates. Thus, the filter allows the use of a much greater thickness for CBED, showing many more fringes with more detailed information. Examples of this improvement attachment are given in [33]. The lattice strain built up at the interface of anAl/SiC composite due to different thermal expansion coefficients has been quantitatively determined by Deininger and Meyer [34]. Structure factor determinations on the (220) reflection of Si have been also carried out. Recent research in CBED is allowing advanced measurements of ionicity in crystals by measurements of structure factor phases in MgO non-centrosymmetric crystals [35]. This can be possible through automation of the process of comparing elastically filtered intensities with Bloch-wave

60

J. Ma. Rincon and M. Romero

and dynamically corrected kinematic computations by combining them with the "Simplex" east-squares refinement algorithm, as used in the Rietveld method [36]. Thus, the dynamic equation for a HOLZ line has been deduced. Likewise, the low order CBED reflections in the non-centrosymmetric BeO structure has been determined. The high spatial resolution CBED (HSCBED) is nowadays possible by using the new generation of TEM operating at higher voltages and with coherent sources. As stated by Steeds [37], there are possibilities for quantitative work of very high accuracy. The treatment of absorption effects in the calculations of Bloch waves of electron diffraction has been improved. Therefore, now it is possible to make accurate structure determinations, determinations of charge, redistributions and measurements of thermal parameters. The higher quality data may be obtained from very small areas of larger particles. The patterns obtained in very small focused areas with small ai (microdiffraction patterns) resemble the SADP, making visible the HOLZ diffraction allowing accurate zone axis alignment. By this method it was possible to identify epidote tracks in muscovite micas as a result of a phase transformation [37]. The LACBED is being enhanced by the use of coherent sources, even allowing atomic resolution in the shadow image of a specimen in the overlap region of adjoining disks. The coherent CBED is another more recent possibility as reported in the case of polytype 6H of SiC. Lastly, the detection of subtle phase changes, even the existence of local electric or magnetic fields has been pointed out by Steeds [38]. Recently, computer program calculation software were developed for facilitating the identification of reflections in the CBED patterns [39]. Finally, in spite of the capabilities for determining the amorphous halo on the residual glassy phase in glass-ceramics, the application of CBED to glassceramics has not been sufficiently developed. As is well known, glass-ceramics are materials obtained from the controlled nucleation and crystallization process of an original glass, giving materials with a wide range of scientific and technological applications [40]. As can be seen as an example, in Fig. 9 the CBED is able to detect small areas of glassy phase pockets in a mullite/zirconia ceramic, the amorphous contrast of which could be conveniently analyzed by the radial distribution function. Therefore, the resolution of this diffraction methods will allow not only the direct recognition of very small glassy or residual glassy phase areas without using the well known methods of dark field contrast, but also amorphous characterization.

3.5 Conclusion The electron diffraction analysis carried out by TEM is a very useful method for the crystallographic characterization of materials and powders. Although much progress has been made in the last decade, in particular in ceramic materials, there is yet much research to be done with this technique in characterization of phases that constitute the glass-ceramics and advanced ceramics. High toughness

3. Basis and Applications of Convergent Beam Electron Diffraction (CBED)

61

Fig. 9. Observation by BF and DF of a glassy pocket in a mullite ceramics and CBED pattern of this very small glass zone showing the amorphous halo

materials, thanks to the martensitic transformation of tetragonal to monoclinic zirconia inside mullite matrices can be efficiently analyzed by CBED. The small size of intragranular Zr0 2 inside a mullite matrix (0.1- 0.3 p,m) does not allow the use of selected area electron diffraction. However, the convergent beam method is capable of carrying out crystallographic analysis of this type of particles. The CBED has a great potential not only for the identification of phases and ceramic powders but also for crystallographic analysis of imperfect crystals. Therefore, it is hoped that much effort can be developed by researchers in electron microscopy during the coming years for extracting more complementary and new information in ceramics, powders for advanced ceramics and glass-ceramics. Acknowledgements. Many thanks are due to Prof. Moya from the Instituto de Ciencia de Materiales, CSIC, Madrid and G. Thomas, University of California, Berkeley for purchasing some of the materials and facilities for electron microscopy investigations. The collaboration for CBED study at higher voltage from Philips Electron Optics Lab. in Eindhoven are also much appreciated.

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References 1. M. Raghavan, J. Y. Koo, P. Luton: J. Met. june, 44 (1983). 2. D. B. Williams: Practical Analytical Electron Microscopy in Materials Science. (Philips Electron Optics Publishing Group, New Jersey, 1984) 300 pp. 3. J. M. Cowley: Advances in Electronics and Electron Physics, 46, 1 (1978). 4. J. B. Warren: Practical Analytical Electron Microscopy in Materials Science (Philips Electron Optics Publishing Group, New Jersey, 1984) 369 pp. 5. J. W. Steeds, K. K. Fung: Norelco Reporter 26, 28 (1979). 6. The Bristol Group: Convergent Beam Diffraction of Alloys Phases (Adam Hilger, UK, 1984). 7. G. J. C. Carpenter, Y. LePage: Proc. of the 5dh Annual Meeting of EMSA (San Francisco Press, 1992), 1444 pp. 8. T. A. Bielicki: Processing of Advanced Ceramics, (Soc. Esp. Ceram. Vidr., Madrid, 1987) 170 pp. 9. J. W. Steeds: Introduction to Analytical Electron Microscopy (Plenum Press, New York, 1979) 387 pp. 10. G. Thomas: J. Electron Microsc. Techno!. 3, 95 (1986). 11. G. Thomas: First Beijing Conf. On Instrum. Anal. , China 1985, (Lawrence Berkeley Lab. LBL-20224 Report,1985). 12. I. Ackerman: Ann. Der Phys. 6, 19 (1948). 13. P. M. Kelly et al.: Phys. Status Solidi 31, 771 (1975). 14. C. H Mac Gillavry: Physica 7, 329 (1940). 15. L. M. Brown, J. A. Eades, J. W. Steeds, M. Rackmam: Philos. Trans. R. Soc. Lond. A 281, 353 (1976). 16. J. A. Eades, M. J. Kauffman, H. L. Fraser: Materials Problems Solved with TEM in Mater. Res. Soc. Symp. Proc. 62 (Materials Research Soc. 1986) 143 pp. 17. B. F. Buxton, J. A Eades, J. W. Steeds, G. M. Rackman: Philos. Trans. R. Soc. Lond. A 28, 171 (1976). 18. J. Gjonnes, A. F. Moodie: Acta Crystallogr. 19, 65 (1965). 19. M. Tanaka: Jeol News 23E, 2, (1985). 20. M. Tanaka, M. Terauchi: Jeol News 25E, 2 (1987). 21. J. W. Steeds: Electron Crystallography in Quantitative Electron Microscopy, 25 Scottish Univ. Summer School in Physics (1983). 22. R. J. Vincent: Electron Microsc. Techno!. 13, 40 (1989). 23. A. R. Landa, L. Otero: Cristalografia, (CSIC, Madrid, 1995) 265 pp. 24. J. A. Eades: Philips Electron Optics Bulletin 123, 22 (1985). 25. J. W. Steeds: Analytical Electron Microscopy (San Francisco Press, 1981) 124 pp. 26. F. Azough, P. E Champness, R. J. Freer: Appl. Crystallogr. 28, 577 (1995). 27. A. W. Johnson: Acta Crystallogr. A 28, 89 (1972). 28. M. Tanaka, T Kaneyama: Jeol News 27E, 40 (1989). 29. G. H. Kim, M Sarikaya, I. A. Aksay: Proc. 5dh Annual Meeting EMSA, (San Francisco Press, 1992) 154 pp. 30. M. Sarikaya, W. Steed, G. Thomas: Proc. 41st Annual Meeting of the EMSA (, San Francisco. Press, 1983). 31. J. Ma. Rincon, T. Dinger, G. Thomas, J. S. Moya: Acta Metallogr. 11, 751 (1986). 32. J. Ma. Rincon: Microscopia Electr6nica en Inorganica (Univ. de Salamanca, 1986) 67 pp. 33. J. Mayer, J. C Spence, G. Mabus: Proceedings of the 49th Annual Meeting of the EMSA, (San Francisco Press, 1991) 786 pp. 34. C. Deininger, J. Mayer: Electron Microscopy 1994, Procs. 13th Intern. Congress on Electron Microscopy (Les Editions de Physique, Paris, 1994) 842 pp.

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35. M Saunders, P. A. Midgley, R. Vincent: Electron Microscopy 1994, Procs. 13th Intern. Congress on Electron Microscopy (Les Editions de Physique, Paris, 1994) 839 pp. 36. J. C. H Spence, J. M. Zuo: ICEM, Paris, 1994, 837 p. 37. J. W., Steeds: Proc. 50th Annual Meeting of the EMSA, (San Francisco Press, 1992) 1152 pp. 38. J. C. H. Spence, J. M. Zuo: Proceedings of the 50th Annual Meeting of the EMSA (San Francisco Press, 1992) 1172 pp. 39. J. F. Morniroli, J. W. Steeds: Ultramicroscopy 45, 219 (1992). 40. J. Ma. Rincon, G.C. Pellacani and T. Manfredini: Glass ceramics: Fundamentals, Processing and Applications, (Mucchi Editori, Modena, 1997).

4. Basis and Applications of High Resolution Electron Microscopy (HREM) for the Characterization of Ceramics and Glass-Ceramics J. MA.

RINCON

and M. ROMERO

The Glass-Ceramic Lab., Instituto E. Torroja de C.C. Construcci6n, CSIC, c/Serrano Galvache s/n, Madrid-28033, Spain

Abstract. The microstructure characterization of ceramics, traditional and advanced, as well as glass-ceramics can be nowadays investigated by modern transmission electron microscopes which allow high resolution microstructure views of the crystalline phase details that constitute these materials to be obtained. From the lattice fringes to the network images very valuable information can be obtained by the use of the two or multi-beam electron illuminations giving direct information from crystalline structures, ordering effects, internal defects, twinning, transformation of phases, interfaces etc. After a summary reviewing the fundamentals of this type of electron microscopy, several examples are shown, as well as problems that can be afforded by HREM in ceramics and glass-ceramics.

4.1 Introduction: Fundamentals of the HREM Methods The evolution of capabilities of transmission electron microscopy (TEM) in parallel with the great advance produced in ceramics in the last few years in materials constituted by smaller size phases has opened a continuous development of the applications of high resolution imaging electron microscopy methods in ceramics and glassy Materials Science. With this method direct symmetry evidence and full crystallographic information from crystalline structures can be obtained and visualization of: -

Perfect crystals; Imperfect crystals; Clusters of atoms; Single atoms; Amorphous or pseudo-amorphous materials.

The complete diffraction diagram, which appears at the back focal plane of an electronic objective lens, is actually a mapping of the Fourier transform of the specimen [1, 2]. An object point usually is displaced from its true conjugate point by an amount due to defocus (Llz) and the spherical aberration coefficient (Cs) giving rise to a total displacement on the TEM image of:

6 ］ｇｩｬｾ＠

+ Llz() .

(1)

Due to the finite aperture size and phase of lens aberrations the distribution of intensity at the back focal plane in the real optical system of a TEM introduces modifications, or phase distortion, given by the expression:

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

65

CONDENSER LENS CONVERGENT ANGLE Current density (J) Specimen C5 , Cc (and c.. )aberration coefficients DEPTII DEFOCUS (Z)

Bragg Difraction Angle

OBJECTIVE LENS (Fourier transform)

BACKFOCAL PLANE F (u, v)= P [f(x,y)]

IMAGEPLANE \V(x,y)= P [f(u,v)] Fig. 1. Beam illumination related to the transfer of information from the important parameters in high resolution transmission electron microscopy

(2) where Cs is the spherical aberration coefficient and Llz is the defocus magnitude of the objective for a given wave electron length (A). Thus, the variation in the phase factor exp(ix(g)) on the reciprocal space, which is known as the contrast transfer function (CTF) gives directly the information of the capability of objective lens for TEM normal operation [3]. Figure 1 shows the beam illumination related to the transfer of information from the more important parameters in high resolution transmission electron microscopy and in Fig. 2 can be similarly seen a schematic diagram depicting the different function shapes along the electron beam in the TEM. Similarly, Fig. 3 shows an example of the contrast transfer function for the case of a TEM working at 1000 kV acceleration voltage.

4.2 Operating Procedures and Instrumental Requirements There are two basic methods for working in HREM imaging (3]: - Fringes imaging; - Lattice imaging.

66

J. Ma. Rincon and M. Romero

ａｾｍ＠

Specimen

ｾｏ｢ｪ･｣ｴｩｶ＠

lens

0

Diffraction pattern

0

Transmission Function Fourier Transform (FT)

ｾ＠

1 DIFFRACTED INTENSITY

MANv

Contrast Transfer Function (CFT) Inverse Transform (1/CFT)

....Image

J\MN

1 IMAGE INTENSITY

｟ｾ＠

Fig. 2. Schematic diagram depicting the different function shapes along the electron beam in the TEM

For the high resolution electron fringes imaging (HREFI) the "tilted illumination" procedure is the more usual, allowing the obtention of fringes of less than 0.1 nm spacing to be resolved. The operation requires thin specimens strongly oriented in the Bragg conditions and with beams symmetrically situated with respect to the optical axis. After accomplishing these conditions the beams are surrounded by an objective aperture and the image is recorded by using a through-focus series of photographs. The high resolution electron lattice imaging (HRELI) requires exploration in the thinnest specimen areas at magnifications x 250 000 or higher. The steps for operation are, after search and tilt of the adequate orientation and alignment of the beam: 1) Center the objective aperture on the optical axis. 2) Set the condenser for optimum balance of brightness; check for coherence and image stability. 3) Preliminary focusing of upper surface of specimen and set of magnification. 4) Correct astigmatism and fine focusing . 5) Through focal series of micrographs. (This is the operation which differs most from conventional TEM and additional information for this operation will be discussed later.) 6) Process of negatives for optimum contrast and selection of the most adequate pictures.

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

67

.\

I d

-0.85

_,

Fig. 3. Representation of a contrast transfer function showing the variation of cos x versus space frequency d at optimum defocus, ilf = 108.5 nm for Cs = 10 mm in a TEM at 1000 kV. Due to chromatic aberration and electrical instabilities the function is X value decreasing for large frequency [4]

The requirements from the electron microscope in order to carry out the structure image observation must be: a) The lattice fringes with spacing of at least 0.2 nm must be resolved under axial illumination at high accelerating voltage. b) A goniometer stage with a tilting angle of 35° in all azimuths must be available in order to orient the specimen crystal exactly at a zone-axis orientation. c) The spherical aberration coefficient must be about 10 mm and with chromatic aberration as low as possible. d) Maximum magnifications greater than 300 000 times. e) Very small spot size on the specimen in order to minimize the electron damage. f) The vacuum must be high and clean. g) The intrinsic astigmatism of the objective lens must be small. It has been established for some time that high resolution conditions only can be reached in a special optical condition of defocus [5, 6] (Fig. 4). For selecting the optimum defocus to obtain the highest resolution, the following formula can be used, which is known as Scherzer Defocus:

(3) from which is possible to determine the also named Scherzer resolution limit:

dsch

= 0.7c_;I 4 .X 3 14 .

(4)

J. Ma. Rincon and M. Romero

68

e- Beam -Specimen (thin foil)

-Defocus E =

Plane of objective focus

Extintion distance

Fig. 4. Relation of diffracted beam, defocus and Bragg angle with respect the specimen in the HREM conditions

Therefore, this simple calculation allows us to approximate the operation in the microscope to the ideal conditions, but this does not eliminate the need for taking through focus series of micrographs. including the amorphous edge detail that will help in the determination of the optical diffractogram power spectrum transferred by the lens, as the more practical and direct method for obtaining HREM information [7, 8].

4.3 Key Examples of HREM. Applications on Ceramics and Glassy Materials In the last 25 years the combination of electron diffraction and HREM images has played an important role in the characterization of inorganic compounds [6, 8], obtaining valuable information about order, disorder, thinning and intergrowth of crystalline phases. Therefore, in the case of ceramic and glass-ceramics these characterization methods are essential for investigating these materials. However, not much work has been done in such multi-phase materials to obtain a general view of capabilities some examples are given for different types of inorganic materials. 4.3.1 Monophase Ceramics Since the first structure image was obtained from a complex oxide crystal (Ti 2 Nb 10 0 29 ) in 1971, the lattice image method in zone-axis orientation has been widely used [9]. Oxides are materials more usually considered by HREM

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

69

studies, good examples are those carried out by Horiuchi and Hovmoller from Thus, in ion conductive /)-A)z03 Japanese and Swedish research groups ｛ＱＰｾＲ｝Ｎ＠ lattice images have been obtained since 1977 visualizing the blocks of spineltype structure. Defect structures have been observed which are responsible for bridges under prodecreasing conductivity and destruction of the ｾａｬｏ＠ longed electron irradiation [14, 15]. Many beam lattice images obtained at 200 kV from thin regions (5 nm) in V 2 0 3 crystals for showing the importance of the defocus value and crystal thickness to interpret the images in crystals of relatively small unit cells (two molecule rhomboedral cell with aR = 5.473nm and a= 53.79°). This crystal depicts also a metal-semiconductor phase transition at about 150 K, which can be easily observed by HREM [16]. The position of interstitial oxygen created during oxidation of inorganic compounds can be identified as well as the point defects situation. Thus, images of mNb20s · n W0 3 and Nb 22 0 54 have been taken by HREM showing the stages of reduction in the former mixed oxide with microdomain regions (Fig. 5). By comparing the lattice images from the initial Nb 22 0 54 oxide with the same heat treatment at 200 oc for 27 h, the change or ordering and clustering of domains has been obtained. Irregularities are seen in several areas of the heated oxide, which correspond with weak streaks along the C* direction in the electron diffraction patterns [11]. 4.3.2 Polyphase Ceramics Ceramics used as refractories have usually strong chemical covalent bonding giving rise to very good mechanical properties at high temperatures. This is the case of SiC and Si 3N 4 materials. To facilitate the sintering of these products the original powders are doped with sintering aids which give rise to formation of amorphous and/or glassy phases, which can be identified in HREM due to the lack or ordering in very small areas. Horiuchi [17] has examined Si 3 N 4 .Y 2 0 3 materials with tetragonal symmetry where the interphase crystal/amorphous phase is parallel to (110) and steps are observed with atomic scale height in several parts. Niobate materials such as KNb0 3-Nb 2 0 5 - Nb0 2 F, termed tetragonal-tungsten bronzes, depicting several potassium fluor niobate phases and U0 2 -Mo0 2 -Mo03 system phase determinations by HREM combined with electron diffraction are good examples of simple applications for structure characterization [18]. 4.3.3 Interfaces and Grain Boundaries in Oxide and Non-Oxide Ceramics Commensurable interfaces with a small repeated unit constitute an important example of the application of HREM for grain boundary investigation. Ernst and Hoffman [19] used the following procedure for obtaining 2D coordinates of atomic columns in grain boundaries.

J . Ma. Rincon and M. Romero

70

150A

Fig. 5. HREM image obtained at 1000 kV from the mixed compound of 4Nb205.9-W03 (taken from Horiuchi [11])

They digitize the experimental image and reduce the noise by spatial averaging or adaptive Fourier filtering. Then, they cross-correlate the image with the pattern of one atomic column yielding to a preliminary set of column coordinates. Finally, they refine these initial coordinates in a straightforward and iterative procedure, simulating the corresponding HREM image and comparing it quantitatively with the experimental image. From the mathematical point of view, the image is a vector with as many components as there are pixels in the image. Therefore, the discrepancy between two images A and B is given by the normalized Euclidean distance: D(A , B) =

lA - Bl/ v iAl - IBI .

(5)

Another example is an interface of spinel/olivine produced by internal oxidation of an olivine matrix and spinel/NiO interfaces where a cubic arrangement from spinel gives a very clear line with the olivine ordering [20]. Metal-ceramic interfaces are essential for the overall mechanical properties of ceramic (CMC) and metal matrix ceramic composites (MMC). The combined use of parallel electron energy loss spectroscopy (TEM/ PEELS) and HREM imaging allows the direct determination of the arrangement of atoms along the interfaces from the Fe and/or Ni/ Al 2 0 3 composites processed by hot pressing

[21] .

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

71

Fig. 6. Lattice images of transformation interface on SiC showing fringes parallel to (0001) and spacing of 1.52 nm on hexagonal phase. The cubic phase does not show fringes in this orientation (taken from [6])

In the Fe composite HREM imaging has shown that alumina (012) is amorphous close to the interface (5- 10 nm), due probably to the random vacancies within the aluminum cation sublattice close to the interface. The energy loss near-edge structure (ELNES) calculations suggest that its shape corresponds to a tetrahedral Al0 3 Fe arrangement. Elemental line profiles across the interphase suggested a change in the oxygen and possibly aluminum concentrations from the alumina matrix. Similar results are obtained from a Ni composite where the (012) fringes are also amorphous and the ELNES suggest that Ni at the interface is reduced. Again the reduction in AI coordination from octahedral to a tetrahedral Al0 3 Ni arrangement has been determined by molecular scattering calculations. Therefore, by HREM it is possible to obtain from interfaces the following information: -

Coherency or incoherency; Periodicity of symmetry; Presence of steps and facets; Dislocations;

72

J. Ma. Rincon and M . Romero

Fig. 7. HREM on zirconia/mullite ceramic obtained by reaction sintering, a at lower magnification showing two mullite and a black contrasted zirconia crystal, b and c lattice fringes of mullite and [001 J axis zone of monoclinic zirconia [25]

- Texture of grains. Quantitative information from this useful method associated with numerical atomic relaxation results enable us to determine the atomic positions at grain boundaries [22]. The local measurements of lattice parameter permits, by HREM, local strains to be determined and a test of Vegard 's law for solid solutions, giving chemical information. This can be also very useful in multilayer materials. Thus, in Zr/Dy multilayers it has been confirmed that the two materials are slightly intermixed and a measure of the local displacement between columns of atoms has been obtained. Pattern analyse made from HREM are possible when the local patterns around the main maximum varies in a linear way with the chemical composition over a range of thickness and defocus. 4.3.4 Phase Thansformations Silicon Carbide Ceramics. Silicon carbide ceramics have been demonstrated to be an adequate high-temperature engineering material. This compound shows polytypism from the cubic stacking form , beta, which is stable at temperatures lower than 1800 °C, to the hexagonal or rhombohedral , a. The ;3-SiC is compounded of long lath shaped grains with can be distinguished by HREM from the a-SiC by lattice fringe images of intergrowth. As is shown in Fig. 6, the irregular interface between both phases is stepped with steps one fringe high , suggesting advance of successive unit cells. Due to the imaging conditions, only the regions with the alpha (a) stacking display lattice fringes. The terminations of the fringes show the mophology of

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

(a)

73

MULLITE

A

(b)

Fig. 8. Regular blocks of mullite lattice fringes inside the zirconia grain interphase, (end of the triangles that are arrowed). Therefore, the HREM method can support, in this case, the idea of solid solubility of mullite inside the zirconia boundary [25]

the glissile interface, suggesting the advance of the interface during the phase transformation.

The Zirconia/Mullite Case. It has been demonstrated that zirconia additions to ceramic matrices increase the toughness of ceramic materials either by transformation toughening or by grain boundary solid solution mechanisms. Several ceramic composites from the mullite/zirconia system have been developed by sintering processing from ZrSi0 4 and alumina with additions, in some cases, of sintering aids such as CaO , MgO and Ti0 2 [23, 24]. With the CaO additions has been obtained a ceramic of mullite + zirconia +anorthite showing K 1c values of 4.5MPam 112 in which HREM has been carried out [25] . The observation by conventional TEM depicts twinned crystals in both zirconia grains and anorthite precipitated from the glassy phase produced via reaction sintering. There are two types of zirconia composing the microstructure of these ceramics, viz: intergranular with 1- 3 J.Lm size located between the mullite crystals and intragranular with very small (0.1-0.5 J.Lm size) rounded crystals. At higher magnifications in HREM, the mullite lattice fringes (d(llO) = 0.55 nm) corresponding to the periodicity of (110) planes have been observed (Fig. 7) . Similarly, the cross fringes of 0.508 nm corresponding to (010) planes of the monoclinic zirconia are shown in Fig. 7.

74

J. Ma. Rincon and M. Romero

Fig. 9. HREM images of metal particles over amorphous substrates: a gold over silicon,b silver over carbon, c and d colloidal copper on different orientations showing twins and hexagonal packing. (All particles were observed under [110] zone axis. Taken from [28] .)

The zirconia/mullite interphase has been examined indicating a coherent relation between both types of crystals, as is shown in Fig. 8. Only the A labeled grain shows this coherency; while the B grain oriented with respect to the other does not show this effect. Therefore, the HREM allows us to distinguish the critical orientations of crystals at interphases. Domains of closure interpenetrating into the zirconia are visible at the boundary [25].

4.3.5 Glass-Ceramics and Glasses Studied by HREM Although structure of ordering in glassy and/or amorphous phases and/or materials is not directly visualized by HREM due to amorphous haloes in electron diffraction, these structures can be comparatively distinguished with respect to the ordered areas at high resolution. Zarcycki [26, 27] has explained that amorphous structures are obtained in practice by using x-ray and neutron diffraction methods. The radial distribution function (RDF) analysis allows the determination of short, medium and large range ordering, it is now also possible to apply this determination for electron diffraction diagrams. The high resolution capability of lattice and fringes imaging has not been sufficiently used for the investigation of nucleation and crystallization of glasses and microstructure of final glass-ceramics products. Thus, the HREM may allow us to obtain lattice images from platinum and gold metals, when they are used as nucleating agents for crystallization. There are some examples of this imaging, in oxidized polycrystalline silicon, of metal impurities and in an interphase of

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

75

ｳｾﾷＭＧＷ＠ Dill,.dioo ponem •

.

I

,.. .. • I .. \

1.(\1 I •

\

ＧＭｾ＠

• •

. ｾ＠

•

＠ｾ •• /..;.-,

',/

.

/_/

\. ..•

OiHuse ring""'-

.,....-.-....

I

I

e \

\ X ,•

•

• ·

ｾＭＯＮ＠

Objective aperture !Very ｷ･｡ｾ＠ area of scattering)

Lattice imaging

• •

•

Dark field

e

Main beam

X Optic axis

Fig. 10. a Representation of the HR bright field and DF imaging from grain boundaries containing residual amorphous phases (taken from [3]) , b schematic representation of the aperture position for obtaining DF imaging from amorphous areas

76

J. Ma. Rincon and M. Romero

Si/Si0 2 • Gold crystallites have been imaged with (111) orientation on the surface of Ce0 2 [8]. Similarly, pyramids of wiistite FeO growing at the surface of spinel ZnCrFe04 crystals under the influence of the electron beam are formed.

Dark Field in Amorphous Areas and HREM. Although the bright field lattice imaging has demonstrated the direct observation of glassy grain boundaries, the misfit in tilting of grain boundaries can obscure extremely narrow residual glassy phases between crystalline phases in ceramics and glass-ceramics. This effect can be seen in through focus series in the grain boundary of a silicon nitride material [3]. As is shown in Fig. lOa, the dark field (DF) imaging can identify the glassy area quite clearly. Thus, DF gives the following advantages: defocus and specimen tilt are less critical and large areas of material can be examined simultaneously, allowing the recognition of residual glassy phases in glass-ceramics, as has been demonstrated in sialon glass-ceramics [3]. Figure lOb shows the schematic representation of the objective aperture position with respect to the diffuse ring and planes diffracted.

4.4 Computation It is now possible to carry out the processing of HREM images and diffraction patterns on an ordinary computer (PC). Programs are available [29] where the processing takes only ten minutes with demonstrated capability to perform crystallographic analysis from minerals and materials. Otherwise, the quantification of the intensities of electron diffraction spots is also available for solving structures and a precision of 0.01 nm can be reached by calculation without using any previous information about the crystal structure. Thus, reconstruction of superstructures from multioxides is nowadays readily available. Computerizing of image processing has allowed the determination of atomic coordinates in the projection of metal atoms in thin inorganic crystals to an accuracy of 0.01 nm, through averaging over many identical unit cells in Ks-xNb16-x W 12+x080 . A pentagonal arrangement is clearly visible from the HREM and calculations indicate that the structure is built-up of pentagonal Me0 7 bipyramids and Me0 6 octahedra (Me = Nb or W) where each bipyramid is linked by equatorial edge-sharing to five octahedra forming a shaped cluster of polyhedra [13] (Fig. 11).

4.5 Future Prospects on HREM: Combination with Spectroscopy, CBED and Holographic Methods Although more progress is necessary in specimen preparation techniques for ceramics, glasses and glass-ceramics allowing improvement in observations, the

4. Basis and Applications of High Resolution Electron Microscopy (HREM)

77

Fig. 11. High resolution image of a Ks-xNbl6 -x WI2+xOso crystal obtained with a defocus of -63 nm with inserted computerized area. Atom positions correspond to the dark areas. The scale bar is 5 nm (taken from [13])

use of more coherent sources as field emission guns (FETEM) and/or superconducting lenses will allow the improvement of the lower voltage microscopes and hence of capabilities for HREM imaging. Recent progress in HREM has allowed us to obtain atomic resolution imaging (ARM), that is the "direct" imaging of atom positions in a crystal. Thus, the imaging of modulated microstructures in alloys has been directly revealed by lattice imaging [2] and the possibility to determine the wavelength of spinodally decomposed materials in some alloys has been realized. As is well known, feldspars and some glasses also show the spinodal decomposition phenomena, which could be investigated by following

78

J. Ma. Rincon and M. Romero

Fig. 12. a Lattice image of CdTe by using the converging of a beam, b CBED pattern from a perfect area, c lattice image by converging the beam at the imperfect area, and d corresponding CBED pattern [30] similar methods to those applied to alloys. Modulated structures often produce typical diffuse scattering, which gives valuable information. From this point of view the application of high voltage HREM is useful because it is possible to obtain structure images from a wide range of thick areas on specimens. Atomic resolution has been made from Zr0 2 cubic crystals showing the fcc array of Zr with 0 in all the tetrahedral interactions by Gronsky and Thomas [5]. They imaged a-Si 3 N4 crystals at voltages higher than 400kV in an ultrahigh voltage ARM instrument with 0.16 nm point resolution [5]. The combination of different capabilities of modern TEM instruments with HREM has not been sufficiently exploded for optimizing the interpretation of high resolution images. Thus , although the combined use of CBED was reported some time ago [30], there has not been a more extended application of this combination of methods for ceramics. The CBED pattern, as can be seen in [31], enabled us to reveal the symmetry of the area and the characteristics of defects in a specific area. By observing the [llO]lattice image from CdTe with a stacking fault and an edge dislocation and switching to the CBED diffraction mode, the symmetry appearing between the disks is that expected for a perfect crystal. If the pattern of the fault and its edge is taken with a slightly defocused illumination by changing the excitation of the third condenser lens (or brightness), the image of the fault can be observed in the disks, except for the (111) disks. The shift vector of the stacking fault can be obtained from these patterns.

Elect ron Micro scopy (HRE M) 4. Basis and Applicatio ns of High Resol ution

79

fi eld emis s ion gu n

(a)

obje ct obj ectiv e lens

bipr ism

holo grom

ｾ＠ 1NM transm ission micro scopy by mean s of an Fig. 13. a "Off-a xis" electr on holographi c waves are super impo sed (take n from [32)), electr on bipris m , the image and the refere nce fringes modu lated accor ding to ampl itude b electr on holog ram exam ple with 0.075 nm and phase of the wave for Nb20 5

nsion al view chan ging in perThe holog rams allow us to see a t hree- dime giving the idea of 3D images. The spect ive from the stand poin t of the observer to prop ose the idea of carry ing out inven tor of holography, Gabo r, was the first by superimp osing a cohe rent refholog raphi c images in electr on microscopy [32], at the objec t and recovering, in a erence wave with the elect ron wave scatt ered wave. copy secon d step, the holog ram as a light optic al

80

J. Ma. Rincon and M. Romero

HREM STRUClURE OF CRYSTALLINE PHASES

DEFECTS INTRINSIC MICROSTRUCTURJ::

L ｾｐｌａｎｒ＠

PARTICLES INCLUSION FINE DEFECTS (DISLOCATIONS) DEFECTS

INTF.RFACF.S(COHERENCY)

AMORPHOUS INTERFACES IT.CHNOI.i (8mi)r = (8M)T , n

(5)

i=l

where

Xi

is the fractional content of the i-th hydrated component of the mixture,

(8mi)T is the isothermal weight loss of the i-th hydrated component at temperature T, (8M)r is the isothermal weight loss of the mixture at temperature T, n is the number of the hydrated components in the mixture. Provided the single components of the mixture are known and available, their contents in the mixture may be calculated solving n simultaneous equations, like (5), obtained for

6. Use of Thermal Analysis in Zeolite Research and Application

131

n different temperatures, and bearing in mind that: n

m

i=l

j=l

:L:>i +

(6)

LYj = 1 '

where Yj is the fractional content of the j-th non-hydrated and thermally-inert component of the mixture and m is the number of the non-hydrated components in the mixture, the total contents of which may be obtained by difference. In order to make the method accurate, it is advisable that each isothermal treatment temperature, T, is selected in such a way as to maximize (or minimize, if the sign is negative) the difference between the weight loss of the i-th component and the sum of the weight losses of the other (n -1) hydrated components. This method, which can be applied also on the basis of DTG data, appears particularly suitable when n = 2, one of which is, for instance, a zeolite, such as clinoptilolite, and the other one a clay mineral, such as montmorillonite [52]. A rather complex mixture is that constituted by the Italian tuffs [8, 53, 54], which contain various hydrated phases, namely three zeolites (phillipsite, chabazite and analcime, Table 1), unreacted glass (pumice, glass fragments, scoriae), hydrated ferric oxides and an X ray amorphous gel-like alumino-silicate, in addition to some non-hydrated phases, such as sanidine and biotite crystals. The most concentrated phases are phillipsite and chabazite, the total content of which usually amounts to 50% or more. Since Italian tuffs, simply because of the elevated contents of the above zeolites, are gaining a pre-eminent position in many industrial, agricultural and environmental applications, it is of great interest to have a rapid and reliable method available for evaluating zeolite content in the rock. A proposed methodology, based on TG measurements of water loss/gain in dehydration/rehydration cycles [55], takes advantage of two effects: i) analcime and all the non-zeolitic hydrated phases fully dehydrate at 513 K, with no evident rehydration after cooling to room temperature within the successive fourteen hours; ii) phillipsite, in contrast with chabazite, breaks down at 623 K during dehydration and consequently does not regain any water on rehydration at room temperature. This allows a five-step treatment cycle to be set up, summarized in Fig. 10, during which, through a thermobalance, it is possible to perform four key weighings w 1 -w4 , the meaning of which is the following: w 1 = initial weight of the tuff sample; w 2 = weight of the sample, cleaned of the water amount connected to analcime and the other hydrated non-zeolitic phases; w 3 = weight of the sample, cleaned of the water amount connected to phillipsite; w 4 = weight of the fully dehydrated sample. Accordingly, the weight per cent phillipsite and chabazite contents in the tuff, P% and C%, respectively, can be calculated through the following formulae: P%

=

100 (w2- w3) , W1Wp

C%

=

100 (w3- w4) ,

( 7)

W1Wc

where Wp and We are per cent water contents of the pure phillipsite and chabazite, respectively.

132

C. Colella

recorded

w,

weights I

I I I

I I

-----------r------------------------------Lr-;

1173

I I

I I

T, K

1000

I I I I I I

623 Ｍｮｾ＠

513

rl

500

1

r. m. 15

24

20 time, h

Fig. 10. Five-step dehydration/rehydration cycle, employed for evaluating through a thermobalance phillipsite and chabazite content in zeolitic tuff samples (see the text for details)

The presence of organic matter in highly-siliceous zeolites (for instance TPA in zeolite ZSM-5) and the awareness that its content is proportional to the zeolite amount may be used for the determination of the zeolite content in a mixture containing either zeolite crystals or parent amorphous phase, overcoming also the fact that some organic matter is occluded in the precursor alumino-silicate gel [25]. Figure 11 illustrates the adopted procedure, based on simultaneous TG and DTA. The mass changes in TG, useful for the estimation of zeolite content, are related to: a) dehydration, b) oxidative decomposition of the occluded organic matter (confirmed by the exotherm in DTA), the amount of which is proportional to the sum: zeolite + gel, c) adsorption of dry nitrogen at room temperature by the calcined zeolite, the extent of which is obviously proportional to the zeolite content in the mixture.

6.5 Thermal Characterization of Zeolite Catalysts Apart from the above described usual characterization (Sects. 6.3.1-6.3.4), with particular emphasis to thermal stability, the thermal investigation of a zeolite

6. Use of Thermal Analysis in Zeolite Research and Application

l ｾ＠

TG ENDO

133

...c:...

I

I ｍｬｾＭ＠

1

I

I

I

973

ｾＭ

1 I I

f

I I

I

I

I

.....-

I

I I

I

I

I

I I

Ｍｾｊ＠

293

2

0

3

time, h Fig. 11. DTA and TG curves showing the oxidative decomposition of the zeolite (Na, TPA)-ZSM-5. a loss of water; b loss of TPA; c adsorption of dry nitrogen by the calcined zeolite. (Reproduced by permission from [25])

catalyst is essentially focused on the surface features with the aim of understanding the sorbate/sorbent interactions and obtaining indications for a correct use in catalysis. In the following sections the most usual techniques useful to the thermal characterizazion of zeolite catalists will be described.

6.5.1 Adsorbate/Framework Interactions As previously mentioned (Sect. 6.3.1), TPD is a thermal technique which has been gaining growing importance in the last few years as a tool for investigating the interaction of the sorbate with the sorbent. Much research has been carried out on the majority of zeolite catalysts (essentially Linde X andY, ZSM-5 and analogs, mordenite) tested with numerous organic and inorganic gases and vapors: hydrocarbons [56, 57], alcohols [58], hydrogen sulfide [59], ammonia [60, 61]. TPD thermograms provide good opportunities to study either kinetics or energetics of the desorption. As far as desorption kinetics are concerned, efforts have been made particularly to find solutions to the equation: - d() = A()

dT

{3

exp

[-__£] RT '

(8)

derived from (2), considering that n = 1 and T = T 0 + {3t where {3 is the linear heating rate. The difficulty arises from the fact that in the equation:

134

C. Colella

{el- d() = .::!. {Tl exp

lea

()

f3

lro

[-E] RT

dT'

(9)

obtained by rearranging (8) and integrating, the temperature integral has no exact solutions. Approximate solutions of the integral and suitable functions taking into consideration the dependence of A and E on () allow satisfactory values for A, E and desorption entropies for several sorbate/framework pairs to be obtained from TPD data [56, 60, 61]. Values of heats adsorption may also be derived from a TPD curve, since a relationship between the temperature corresponding to the peak maximum (TM ), and heating rate, involving also LJ.H for adsorption, has been worked out, and applied in particular to the system: ZSM-5/aromatic hydrocarbons [57]. The correct estimation of TM can depend on the selection of a suitable linear or nonlinear temperature program [62].

6.5.2 Estimation of Acidity Distribution in a Zeolite Catalyst Acidity is the main property required of a zeolite catalyst, especially when used in a cracking process. Decationation, attained, as previously mentioned (Sect. 6.2) via cation-exchange with NHt and successive deammoniation, increases the concentration of acid sites. Since only the strong acidic sites are catalytically effective, it is of extreme interest to obtain information on the abundance and distribution of such sites. This may be done by several techniques, such as IR spectroscopy [63] or calorimetry [64], but also thermal procedures may be applied. In this case the preactivated zeolite catalyst is allowed to absorb a weak base, such as an amine or more often ammonia, and then is subjected to thermal analysis (TPD, DSC), in order to record the thermal profile of the desorption. Figure 12 shows a typical chromatogram concerning NH 3 desorption from zeolite ZSM-5, previously transformed through thermal treatment in acid form (see Sect. 6.3.2). Here, the low-temperature peak refers to the weaker acidic sites, the other obviously to the strong acidic sites, in agreement with the lower or higher acid-base binding energy. The peak area is proportional to the amount of the specific acidic site, while the peak-maximum-temperature gives informations about its acid-strength and the NH 3 heat of desorption [20]. Analogous information may be obtained through a DSC analysis [65].

6.5.3 Modification of, and Reactant Conversion on, a Zeolite Catalyst The combined use of several thermal analysis techniques (TG, DTA, DTG), complemented by other physico-chemical diagnostic methods, has proved to be useful for investigating various events affecting the zeolite catalyst reactivity, such as change in porosity or in channel tortuosity, due to incorporation of metals or substances within the pore volume [25].

6. Use of Thermal Analysis in Zeolite Research and Application

135

w z:

(I)

C) Cl.. (I)

w

ct::

ct:: C)

1ｾ＠

w

1-

w

Cl

/

400

600

BOO

K

1000

Fig. 12. TPD chromatogram of ammonia from zeolite ZSM-5

The conversion of simple organic molecules (e.g. methanol, ethanol or ethylene) can also be monitored by the use of combined TG-DTA. For instance such an analysis, applied to ethylene conversion on the acid form of ZSM-5, enabled the transformation to be interpreted in terms of five different reaction steps [25]. Another example of thermal analysis application to the study of the development of a catalyzed reaction is the use of isothermal TG for investigating the kinetics of coke deposition in inner or external zeolitic sites and its subsequent removal by oxidation in air [25].

References 1. D. W. Breck: Zeolite Molecular Sieves. Structure, Chemistry and Use (John Wiley & Sons, New York 1974), 771 pp. 2. H. van Bekkum, E. M. Flanigen, J. C. Hansen (Eds.): Introduction to Zeolite Science and Practice (Elsevier, Amsterdam,1991), 754 pp. 3. D. B. Hawkins: In Zeo-Agriculture. Use of Natural Zeolites in Agriculture and Aquaculture (W.G. Pond and F.A. Mumpton Eds., Westview Press, Boulder, Colorado, 1984), pp. 69-78. 4. R. M. Barrer: Hydrothermal Chemistry of Zeolites (Academic Press, London, 1982), 360 pp. 5. R. Szostak: Molecular Sieves. Principles of Synthesis and Identification (Van Nostrand Reinhold, New York, 1989), 524 pp. 6. W. M. Meier, D. H. Olson, C. Baerlocher: Atlas of Zeolite Structure Types, Zeolites 17, 1-230 (1996). 7. M. M. Dubinin, A. A. Fomkin, I. I. Seliverstova, V. V. Serpinski: In Proc. 5th Int. Conf. on Zeolites ( L. V. C. Rees, Heyden, London, 1980), pp. 468-475. 8. M. de' Gennaro, C. Colella, E. Franco, R. Aiello: Industrial Minerals 186, 47-53 (1983). 9. A. Yamazaki, R. Otsuka, H. Nishido: Thermochim. Acta 109, 237-242 (1986). 10. G. Gottardi, E. Galli: Natural Zeolites (Springer-Verlag, Berlin, 1985), 409 pp. 11. A. Dyer, M. J. Wilson: Thermochim. Acta 10, 299-304 (1974). 12. A. Dyer, M. J. Wilson: Thermochim. Acta 11, 55-64 (1975).

136

C. Colella

13. C. Colella, R. Aiello: Thermochim. Acta 27, 253-260 (1978). 14. V. Vucelic, V. Dondur, P. Djurdjevic, D. Vucelic, Thermochim. Acta 14, 341-347 (1976). 15. V. Dondur, V. Vucelic, D. Vucelic, M. Susie, Thermochim. Acta 14, 349-356 (1976). 16. V. Dondur, D. Vucelic: Thermochim. Acta 68, 91-99 (1983). 17. V. Dondur, D. Vucelic: Thermochim. Acta 68, 101-111 (1983). 18. V. Dondur, D. Vucelic: Thermochim. Acta 68, 113-119 (1983). 19. V. Satava, J. Sestak: Anal. Chern. 45, 154-159 (1973). 20. R. J. Cvetanovic, Y. Amenomiya: Catal. Rev. 6, 21-48 (1972). 21. E. Dima, L. V. C. Rees: Zeolites 7, 219-227 (1987). 22. N. Petranovic, M. Susie: Thermochim. Acta 31, 211-219 (1979). 23. A. B. Halgeri, M. H. Joshipura, T. S. R. Prasada Rao: Thermochim. Acta 34, 325-330 (1979). 24. C. Colella, R. Aiello, A. Nastro: Annali di Chimica 72, 407-414 (1982). 25. z. Gabelica, J. B. Nagy, E. G. Derouane, J.P. Gilson: Clay Minerals 19, 803-824 (1984). 26. R. J. Argauer, G. R. Landolt: U.S. Patent 3, 702 886, 1972. 27. J. L. Guth, H. Kessler, R. Wey: In New Developments in Zeolite Science and Technology (Y. Murakami, A. Iijima and J. W. Ward Eds., Kodanska, Tokyo, and Elsevier, Amsterdam, 1986), pp. 121-128. 28. L. M. Parker, D. M. Bibby, J. E. Patterson: Zeolites 4, 168-174 (1984). 29. M. Soulard, S. Bilger, H. Kessler, J. L. Guth: Thermochim. Acta 204, 167-178 (1992). 30. M. Soulard, S. Bilger, H. Kessler, J. L. Guth: Zeolites 7, 463-470 (1987). 31. A. Nastro, z. Gabelica, P. Bodart, J. B. Nagy: Calorim. Anal. Therm. 15, 206-213 (1984). 32. A. Nastro, Z. Gabelica, P. Bodart, J. B. Nagy: Stud. Surf. Sci. Catal. 19, 131-137 (1984). 33. A. Dyer, M.A. Saghal: Thermochim. Acta 195, 105-111 (1992). 34. F. Testa, F. Crea, A. Nastro, R. Aiello, J. B. Nagy: Zeolites 11, 705-709 1991). 35. A. Dyer: An Introduction to Zeolite Molecular Sieves (J. Wiley & Sons, Chichester, U.K., 1988), pp. 107-108. 36. A. Alietti: Am. Mineral. 57, 1448-1462 (1972). 37. J. R. Boles: Am. Mineral. 57, 1463-1493 (1972). 38. V. A. Drebushchak: Thermochim. Acta 159, 377-381 (1990). 39. A. Alberti, G. Vezzalini: In Proc. 6th Int. Zeolite Conf. (D. Olson and A. Bisio Eds., Butterworths, Guildford, U.K., 1984), pp. 834-841. 40. M. H. Simonot-Grange: Clays Clay Minerals 27, 423-428 (1979). 41. L. P. van Reeuwijk: Am. Mineral. 57, 499-510 (1972). 42. T. Rayment, J. M. Thomas: Zeolites 3, 2-4 (1983). 43. B. Belbeoch, M. Roulliay, R. Kahn, E. Cohen de Lara: Zeolites 3, 99-101 (1983). 44. M. B. Sayed, M. E. Kassem, I. !'vi. Al-Emadi: Thermochim. Acta 188, 143-150 (1991). 45. G. T. Kerr: In Molecular Sieves, Advances in Chemistry Series 121 (R. F. Gould Ed., Washington, 1973), pp. 219-229. 46. A. Langella, M. de' Gennaro, C. Colella, M. Pansini: In Proc. J. Med. CAT-93 (Mediterranean Symp. on Calorimetry and Thermal Analysis), Corte (France) 1993, pp. 229-232. 47. D. W. Breck, E. M. Flanigen: In Molecular Sieves (Society of Chemical Industry, London, 1968), pp. 47-60. 48. E. Alsdorf, M. Feist, H. Fichtner-Schmittler, H. H. Jerschkewitz, U. Lohse, B. Parlitz: J. Therm. Anal. 33, 691-698 (1988).

6. Use of Thermal Analysis in Zeolite Research and Application 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

137

N. Juranic, D. Karaulic, D. Vucelic: J. Therm. Anal. 7, 119-124 (1975). A. Montes, R. Roque-Malherbe, E. D. Shchukin: J. Therm. Anal. 31, 41-47 (1986). R. Roque-Malherbe, A. Montes: J. Therm. Anal. 31, 517-521 (1986). E. N. Shlyapkina: J. Therm. Anal. 13, 553-560 (1978). M. de' Gennaro, C. Colella, R. Aiello, E. Franco, Industrial Minerals 204, 97-109 (1984). R. Sersale: In Natural Zeolites. Occurrence, Properties, Use (L. B. Sand and F. A. Mumpton Eds., Pergamon Press, Elmsford, N.Y., 1978), pp. 285-302. M. de' Gennaro, C. Colella, Thermochim. Acta 154, 345-353 (1989). R. E. Richards, L. V. C. Rees: Zeolites 6, 17-25 (1986). V. R. Choudhary, K. R. Srinivasan, A. P. Singh: Zeolites 10, 16-20 (1990). C. Li-feng, T. Wacker, L. V. C. Rees: J. Chern. Soc. Faraday Trans. I 85, 33-45 (1989). I. Ferino, R. Monaci, E. Rombi, V. Solinas, L. Burlamacchi: Thermochim. Acta 199, 45-55 (1992). K. Hashimoto, T. Masuda, T. Mori: In New Developments in Zeolite Science and Technology (Y. Murakami, A. Iijima and J. W. Ward Eds., Kodanska, Tokyo and Elsevier, Amsterdam, 1986) pp. 503-510. E. Dima, L. V. C. Rees: Zeolites 10, 8-15 (1990). B. Hunger: J. Therm. Anal. 35, 107-112 (1989). B. M. Lok, B. K. Marcus, C. L. Angell: Zeolites 6, 185-194 (1986). A. Auroux, P. C. Gravelle, J. C. Vedrine: In Proc. 5th Int. Conf. on Zeolites (L. V. C. Rees Ed., Heyden, London, 1980) pp. 433-439. A. K. Aboul-Gheit: Thermochim. Acta 191, 233-240 (1991).

7. Viscous Flow of Glasses Forming Liquids: Experimental Techniques for the High Viscosity Range E.D. ZANOTTO and A.R. MIGLIORE Jr. Department of Materials Engineering- DEMA, Federal University of Sao Carlos, 13565-905 Sao Carlos - SP, Brazil

Abstract. The viscosity is a physical parameter which controls not only the melting and fining of melts, but also the stress relaxation and the nucleation and crystallization phenomena. Here the basis of viscous flow is presented and discussed. Rheological models and some measurement methods: fiber extension, beam bending and indentation are described.

7.1 Introduction Viscous flow governs melting, homogenization, fining, the forming operations (pressing, casting, blowing, injection molding, extrusion, etc.), and the annealing behavior of glasses and polymers. It also regulates the crystallization kinetics and consequently the thermal stability of these materials. The viscosity reflects the intrinsic resistance to atomic or molecular translations in the liquid and, for good glass forming liquids, varies over several orders of magnitude when the temperature drops from the "liquidus" to the glass transition temperature. In this chapter we summarize the viscous flow behavior of glass forming liquids and discuss the main experimental techniques for viscosity determinations in the upper range.

7.2 The Physics of Viscous Flow The viscosities for a number of representative glass types are shown in Fig. 1. We stress here the great variety of glasses, ionic/covalent (Si02, B 20 3 ), ionic (BeF2), metallic (Pd-Au-Si), and molecular (o-Terphenyl). An important feature ofthe log(ry) vs 1/T plots is that some of them are curved while others are straight lines (Arrhenian). Arrhenian viscosities have only been reported for a few network (fully polymerized) inorganic glasses: silica, germania, phosphorus pentoxide, albite

7. Viscous Flow of Glass Forming Liquids

139

Table 1. Some properties of Arrhenian network liquids [1, 2]. Glass

Hn [kJjmol]

Tm [K]

1og7J(Tm), [Pas]

Si02 Ge02 P205 NaAlSi30s BeF2

520-710 290-340 200 400 240

1996 1387 853 1380 685

5.1-6.7 3.0-5.0 5.7 6.9 5.7

Table 2. Properties on non-Arrhenian liquids. Glass

T [K]

Hn (Tg), [kJjmol]

Hn (Tm) [kJjmol]

B203 Pd-Au-Si o-terphenyl

546 620 242

395 1100 490

85 710 65

(NaAlSi30 8 ) and beryllium fluoride, although there may be some slight curvature for germania and BeF 2 . In all these glasses the higher-charged cations are tetrahedrally co-ordinated by the anions, and the anions are two-fold coordinated by the cations. The tetrahedra are thus linked at the vertices to form a three-dimensional continuous network. In albite the alkalis reside in holes near the aluminum ions to conserve the local charge. The constant activation enthalpies (given by the slopes of the straight lines) indicate that the structure of the (unknown) flow units of these glasses does not change appreciable with temperature. Table 1 shows the activation enthalphies (Hn) for viscous flow and the viscosities at the melting points (Tm) for these glasses [1, 2]. It should be emphasized, however, that for other network liquids such as B 2 0 3, anorthite (CaO·Ab03·2Si02) and ZnCb the viscosity is not Arrhenian. As far as we know, Arrhenian viscosities have never been reported for polymers and metallic glasses. For these liquids the viscosities at the melting points (of the equilibrium crystal phases) are much greater than for most liquids (log7](H 2 0) = -3; log 7] (honey) = + 1). This is one of the reasons why the materials of Table 1 are so resistant to crystallization and thus are good glass formers. For all other oxide, fluoride, chalcogenide, metallic, polymer and molecular glasses, for which viscosity data is available in wide temperature ranges, log(77) vs 1/T plots have a negative curvature and thus the apparent values of Hn decrease with temperature. The activation enthalphy for flow can vary by almost an order of magnitude between the melting point and the glass transition, as shown in Table 2 [1]. A formula often used to fit viscosity vs temperature data for inorganic glasses is the Vogel-Fulcher-Tamman (VFT) equation, log7]

B

=A+--, T-To

(1)

E.D. Zanotto and A.R. Migliore Jr.

140

OOOo ogoo It) 0 It) (\IC\1 ..... ....

0 0

0

0 It)

It)

I

0- Terphenyl

14 en

It)

0

ｾＲ＠

d Q.

.

F

0 t11""'

E

10

8 6 4

2 0

-2 5

0 103

T

( ｋｾＩ＠

Fig. 1. Viscosities of some good glass-forming liquids (MP

=

melting point).

where A, B and T0 are empirical parameters and T is the temperature. Typical values of these constants for stoichiometric oxide glasses were collected by Zanotto [2] and are listed in Table 3. Thus, at a reduced temperature (T0 /Tm) of approximately 0.45 the viscosity of non-Arrhenian oxide liquids tend to infinity. Caillot et al. [3] have also shown that the viscosity of a variety of liquids diverge at a reduced temperature of 0.5. This behavior is predicted by both free-volume and entropy theories of glass transition [1]. (WLF) Polymer scientists make extensive use of the ｗｩｬ｡ｭｳｾｌｮ､ｵｆ･ｲｹ＠ equation,

7. Viscous Flow of Glass Forming Liquids

141

Table 3. Viscosity parameters for oxide glasses (ry, Pas)

A

Glass Na20·2Ca0·3Si02 Lb0·2Si02 Ba0·2Si02 CaO·Ab03·2Si02 Na20·2Si02 Li20·P20s B203

C1T

log 'fJ

-4.86 +1.81 +1.83 -5.85 -0.64 -4.10 -5.02

= C2 + T - Tg '

B

To [KJ

To/Tm

4893 1347 1702 6750 2315 2000 3665

547 595 795 738 541 462 333

0.35 0.46 0.47 0.40 0.47 0.50 0.46

(2)

where C 1 = 17.2 kJ /mol and C2 = 56.1 K are universal constants, supposedly valid between Tg and Tg + 50°C for all polymers. Several authors hypothesize that the temperature dependence of the activation enthalpy for viscous flow is due to the cooperative motion that must accompany structural changes. This means that the activation enthalpy is not representative of the hopping of single atoms. As the temperature is lowered and the atomic motions become more cooperative, an increasing number of atoms will be involved in flow, and the activation enthalpy will increase. Alternatively, it can be envisaged that the molecular flow units change with temperature thus changing the activation enthalpy. Indications of structural changes with temperature are only available for a few glasses. For B 2 0 3 there is experimental evidence for breaking up of the boroxyl rings with increasing temperature (Walrafen et al. [1]). High temperature, X ray data and molecular dynamics simulations also indicate that melt fragility can be correlated to increasing Si-0 and Al-0 lengths and decreasing Si-0-Si and Al-0-Al angles with temperature, while these parameters are equal for silica glass and liquid, which display Arrhenian behavior. Finally, it should be stressed that it is not possible to correlate the viscosity activation enthalphy with bond strength. For instance, the energy of vaporization of o-terphenyl is about 75 kJ /mol, whereas Hn at Tg is 490 kJ /mol and Hn at Tm is 65 kJ /mol. The heat of vaporization of BeF 2 is 170 kJ /mol but the activation enthalpy for flow is 240kJ/mol. For Si0 2 , Hn = 520-710kJ/mol while the Si-0 bond energy is about 440 kJ /mol. The activation enthalphy for oxygen diffusion is about 300 kJ /mol in this same glass.

E.D. Zanotto and A.R. Migliore Jr.

142

DILATANT

BINGHAM

(/) (/)

ILl

a:

..... (/) a: c:(

ILl J: (/)

SHEAR RATE

a)

log

t

b)

Fig. 2. Rheological behavior of liquids.

7.3 Rheological Models In a simplified way the rheological behavior of liquids can be represented schematically by Fig. 2. While polymers are typically pseudoplastic, most oxide glasses are Newtonian, at least for the typical (low) strain rates employed in common forming operations. For a Newtonian liquid confined between two parallel plates, the lower one of which is stationary whilst the upper moves at a constant velocity v 0 , the distance between them remaining constant, the liquid velocity is zero at the surface of the lower plate and varies linearly with distance between the plates. A shear stress T must be supplied to the upper plate to maintain this motion and the coefficient of shear viscosity TJ, or simply viscosity, is the relation between the applied stress and the velocity gradient dv / dy, T

TJ

= (dvjdy) ·

(3)

In more detail, the flow of glass is more complex due to the combined elastic and viscous response to any type of applied stress, known as viscoelasticity. Several models have been proposed to describe viscoelasticity. Among them, Burger's model has been shown to characterize reasonably well the behavior of inorganic glasses [5]. In this version, illustrated in Fig. 3a, viscous (TJd and elastic (E 1 ) elements are combined in series with a Kelvin solid, where two other elements (TJ2,E2) are arranged in parallel and reflect the slow elastic properties. The rate of deformation under constant tensile stress a and zero initial deformation is made up from the rate of Newton's viscous deformation,

a T/1

and the rate of deformation of the Kelvin solid

(4)

7. Viscous Flow of Glass Forming Liquids

143

E-1

,2

a)

b)

Fig. 3. a) Burger's model, b) three-parameter model.

(5) Since IJ

eK = E 2 {[1- exp ( -tE2/172)]}

(6)

for any time

de = !!.._ [l + 171 exp ( -tE2)] (7) dt 171 172 172 ' where e =eN+ eK. The external stress IJ and the equilibrium elastic deformation of the whole solid e 1 are associated by Hooke's law,

(8) where E is the elastic modulus of the glass. Thus, when t -+ oo (in practice when t » 172/ E 2) corresponding to Newtonian flow,

de dt

Ee1 17

e1

""F '

where t* is the relaxation time.

(9)

144

E.D. Zanotto and A.R. Migliore Jr.

An interesting three-parameter model (the Burger model has four parameters) was proposed by Hsueh [6] and is shown in Fig. 3b. He demonstrated that for a Hookean elastic element (EI) in series with a Kelvin solid (E 2 ,ry), the stress-strain rate relations for constant strain rate and constant stress creep tests are,

2 - 17 a (t) = ( E E 12 ) 7JE 1 [1 - exp (-Et)] where, E

1 (

t

a exp (- E2 t / 7J) = ----'------'-....:..:...

)

+ E1E2tc' E

(10)

(11)

7J

and,

(12) It should be emphasized that a constant stress can be achieved only when

E2 -+ 0 and t-+ oo. Note also that the three-parameter model dictates a decreasing strain rate during the constant-stress creep test. To avoid the long loading time required for the conventional creep test and the elaborate instrumentation for the constant stress test, Hsueh [6] suggested an experimental procedure to determine the parameters E 1 , E 2 and the viscosity ry. Hsueh's technique is appropriate for measuring high viscosities, where elastic effects are more important. In the following section we describe some simpler, more usual methods for viscosity determinations.

7.4 Measurement Techniques The determination of viscosity is based on the analogy proposed by Trouton [7] between elastic and viscous deformations, where the shear modulus G is substituted by the viscosity coefficient 17 and the elongation u is replaced by the elongation rate u' = dujdt. The analogy can be appreciated if we refer to the distortion of a rectangular block subjected to a shearing stress (Fig. 4). The relationship between the applied stress T and the angle of shear 'Y is T = G"(. If 'Y is small, 'Y = dujdy and, T

= Gdu dy

(13)

where u is the displacement of a point in the direction of the applied stress. This has the same form as (3), which defines the viscosity. It should be emphasized here that

G=

ＲＨＱｾｶＩ＠

(14)

For incompressible liquids, v = 0.5 and thus G = E /3. The range of viscosity of interest in the manufacture and use of glasses and polymers is very wide, varying from 10° to 10 13 Pas, and thus one has to use more

7. Viscous Flow of Glass Forming Liquids

145

I

I

y

k1

I I I I Fig. 4. Solid block under shear stress.

than one method to make measurements over the whole of this range. Hence it is convenient to describe the methods by dividing them into two groups, one group is used for relatively low viscosities (log 17 < 5) and the other for 14 < log 17 < 5. Table 4 summarizes the typical viscosity range screened by each method. The actual range measured depends on the instrumental details and can vary by one or two orders of magnitude. Many other techniques exist to determine the melt viscosity (Iog17 < 5) and are extensively used by polymer scientists: sliding plate, poiseuille, rotational plates, dynamic shear, couette, cone-plate, uniaxial flow, etc. These were thoroughly reviewed in several rheology textbooks, see for instance [8] and will not be detailed here. In this chapter we will describe only the main techniques used to determine viscosities in the upper range (14 < log 17 < 5) which have received much less coverage in the literature. We will demonstrate in the following section that the viscosity can be determined by taking well known equations for the deformation of elastic solids under load and replacing in these equations G or E /3 by 17 to obtain corresponding relations for the rate of elongation of a viscous liquid under load.

Method

Log TJ [Pas]

Beam-bending Fiber extension Cylinder compression Penetration Parallel plates Rotating cylinder Counter sphere

7-13 8-12 8-12 6-12 4-8 1-7 1-3

Table 4. Typical viscosity range measured by each method [Pas].

146

E.D. Zanotto and A.R. Migliore Jr.

p p

SPECIMEN

Cl)

d)

c)

e)

Fig. 5. Schematic diagram for: a) fiber elongation, b) beam-bending, c) spherical indentation, d) cylindrical indentation and e) parallel plates.

7. Viscous Flow of Glass Forming Liquids

147

7.4.1 Fiber Extension and Cylinder Compression The technique of fiber extension was first proposed by Lillie and is now an ASTM standard [9, 10]. Let us assume the geometry depicted in Fig. 5a, i.e a fiber of cross-sectional area A and initial length L, subjected to a uniform force P. If we assume that A does not change significantly for a small elongation and that the mass of the specimen is negligible compared to the external load, the elastic elongation u, is given by, U=

PL EA.

(15)

Thus, by using Trouton's analogy for viscous flow, one has

PL 2(1+v)A17.

du dt

If we assume that v

(16)

= 0.5 and u' = du/ dt,

PL 17

(17)

= 3Au'

Therefore, to determine the viscosity at a given temperature it is only necessary to know the applied force P, the fiber radius (and thus A) and to measure the elongation rate u'. Thus, one only needs a good furnace with a stable and uniform temperature profile along the fiber length equipped with a LVDT or some other device for measuring deformations. However, it is not trivial to obtain uniform fibers in the laboratory scale. Actually, it is very difficult to obtain fibers of certain materials. Exactly the same solution is found for the case of compression of cylinders. Hence, one can use commercial dilatometers or thermo-mechanical analyzers to measure the viscosity of cylindrical specimens.

7.4.2 The Beam-Bending Method The beam-bending method was describes by Jones [11] and Hagy [12] and is now an ASTM standard [13]. A schematic drawing of the experimental arrangement is shown in Fig. 5b, where a specimen of length L and inertia I is symmetrically bent under a weight P. From elasticity theory, the elastic elongation is,

p£3 48EI

u =

5qL4

+ 384EI

( 18 )

where P = mg and q = pAg and I = bh 3 /12. Here, m is the mass, g the gravity, p the specimen density and b and h its lateral dimensions. With the appropriate substitutions into (18) we arrive at,

u

=

ｾＭ＠

gL 3 (m

+ 5pAL/8)

48EI By analogy, for viscous flow one has,

(19)

E.D. Zanotto and A.R. Migliore Jr.

148

7] =

gL 3 (m + 5pAL/8) 96 ( 1 + v) I u'

(20)

Hence, if one knows the specimen geometry and density, the applied load and the deflection rate u', the determination of viscosity is straightforward.

7.4.3 Indentation Techniques Spherical Indenters. If two elastic spheres of radius R are pressed against each other, it can be shown [14] that the stretching u at a distance r from the center of the contact area (Fig. 5c) is given by u(r)

= [nP0

(2a 2

Ｍｲ

Ｒ

Ｉ｝ Ｔ ｾ＿ＬＩ＠

+ ＨｾＩＧ＠

(21)

where P0 = 3P/2na 2 is the maximum pressure, a the radius of the contact circle and P the applied force. If one of the spheres is much more rigid than the other (this is the case for a metallic indentor on a hot glass, as depicted in Fig. 5c), E 1 E

»

E 2 and the term ( Ｑ ｾｩＩ＠

= 2G(l + v), for r

vanishes. With the well known relation

-t 0, (21) becomes

_ 3P (l- v) . G u (0 ) 8a

(22)

Thus, using Trouton's analogy [7], one obtains 7]

=

3P (l- v) ; 8au'

(23)

where u' is the penetration rate. The radius of indentation a is related to the penetration depth, u(r = 0), by a 2 = u(2R- u). Since a = RcosB and u = R(1 - sin B), integration of (23) gives 7]=

9P(l-v)t 16 (2R) 1 / 2 F (u)

( 24 )

where

F(u) = (2R) 312 (n-2B-sinB)

(25)

() = arcsin [1 - (u/ R)] in rad .

(26)

and For small penetrations, u « 2R and F(u) -t u 3 12 . However, for small penetration (short times) elastic deformations may still be important and thus flow is not Newtonian and should be described by the more complex equations of Sect. 7.3. Therefore, it is more correct (although more time-consuming) to measure the penetration as a function of time and to compute the value of F( u) to obtain the viscosity rather than using u 312 .

7. Viscous Flow of Glass Forming Liquids

149

Cylindrical Indenters. The elastic stretching u produced by a rigid planar indenter in a semi-infinite plate was deduced by Streicher [15]: u

=

c (1- v 2 ) P 7rl/2 ER

'

(27)

where R is the radius of the cylindrical indenter and c = 0.96. Using the Trouton analogy, one has

ry=

c(1-v)P 21r 1 / 2 Ru'

(28)

A schematic drawing of indentation by a cylinder is shown in Fig. 5d. This method is interesting because it is capable of covering the widest viscosity range (13 < log ry < 6) among all the techniques, the specimen geometry is very simple (cylinders or cubes, the only requirement is that their dimensions must be ｾ＠ 5 times larger than the indenter diameter) and the same specimen can be used for several measurements. Finally, commercially available thermo-mechanical analyzers can be used. On the other hand, as far as we know, the indentation techniques are not recognized by the ASTM or any other standardization organization.

7.4.4 Parallel Plates The parallel-plate technique is schematically represented in Fig. 5e. It is an important method because it covers the intermediate viscosity range, 8 < log ry < 4 (Pas). The equation which relates the viscosity to the deformation is 'T/

= Ｓｖｾ＠

21rmh 5

(27rh3

+ V)

'

(29)

where m is the applied load, h is the specimen thickness and V is the specimen volume.

7.5 Final Comments In measuring the viscosity of glass forming liquids, especially in the region of high viscosities where the viscosity varies rapidly with temperature, it is important to pay careful attention to the measurement of temperature. The thermocouple should be placed as close to the specimen as possible and ideally should be in thermal contact with it. The viscometer furnace must be carefully designed so that the entire sample is in a zone of constant temperature. An adequate time should be given at each temperature of measurement to ensure that the specimen has reached an equilibrium temperature before the measurement is made. It is also desirable to maintain a stock of standard materials of homogeneous composition (e.g. the NBS, now NISTC, (USA) makes standard soda-lime, and lead silica glasses), the viscosity of which can be measured from time to time

150

E.D. Zanotto and A.R. Migliore Jr.

to ensure that no change has taken place in the apparatus used. This is good practice when making measurements of any physical property. It is also essential to take into account delayed elastic effects, specially in the neighborhood of Tg. In this case, one has to wait for the relaxation of elastic response before the glass enters into Newtonian behavior. For polymers, which are not Newtonian, one has to determine the viscosity as a function of shear rate. In some instances, the zero shear viscosity is reported, where one extrapolates the viscosity value to zero shear rate.

References 1. S. Brawer: Relaxation in Viscous Liquids and Glasses (The American Ceramic Society, Columbus, USA, 1985). 2. E. D. Zanotto: J. Non-Cryst. Solids 89, 361 (1987). 3. E. Caillot, C. R. Douclot, J. L. Souguet: Acad. Sci. Paris 312, 447 (1991). 4. C. A. Scamerhorn, C. A. Angell: Geochim. Cosmochim. Acta 55, 721 (1991). 5. S. V. Nemilov: J. Glass Phys. Chern. [Fizika i Khimiya Stekla] 3, 148 (1977). 6. C. H. Hsueh: J. Am. Ceram. Soc. 69, c48 (1986). 7. F. T. Trouton: Proc. R. Soc. Lond. A 519, 426 (1906). 8. R. Corrieri: in Melt Rheology (International School of Advanced Studies in Polymer Science, Ferrara, Italy, 1992). 9. H. R. Lillie: J. Am. Ceram. Soc. 14, 502 (1931). 10. ASTM Std. C336-71 (1977). 11. J. 0. Jones: J. Soc. Glass Tech. 28, 432-62T (1946). 12. H. E. Hagy: J. Am. Ceram. Soc. 46, 93 (1963). 13. ASTM Std. C598-72 (1976). 14. S. Timoshenko, J. N. Goodier: Theory of Elasticity (McGraw Hill, London, 1951). 15. F. Streicher: Bauin Genier 48, 949 (1965).

8. Diffusion Structural Analysis in the Characterization of Inorganic Materials v.

BALEK

Nuclear Research Institute, CZ-25068 Rez, Czech Republic

Abstract. The fundamentals of the emanation thermal analysis are described and sample preparation for different inert gas operations are considered and discussed. The mechanisms of releasing inert gases from solids are exposed in relation to the measurements of the diffusion of gases in solid samples. Thus, the applications to ceramics investigation, surface roughness and defects of powders are described. Applications for glasses, clay minerals and cements are discussed from our own experimental work. The corrosion on materials can be also investigated with this method.

8.1 Basic Principles of the Method Diffusion structural analysis (DSA) is a method by means of which information about the solid state and its changes is obtained on the basis of inert gas release from solids, measured under "in-situ" conditions of the sample treatment. The inert gas atoms are used as trace indicators of the solid state and its changes, but do not react with the solid in which they are incorporated. Their release is controlled by diffusion processes in the solid, being influenced by structural changes, changes of morphology and porosity, by interactions of the solid sample with the surrounding medium, and/or chemical reactions taking place in the solid. Both radioactive and nonradioactive (stable) inert gas atoms can be used in the DSA, although the use of radioactive inert gases is more advantageous due to their simple and sensitive detection.

8.2 Sample Preparation for DSA Measurements Most of the solids to be investigated by DSA do not naturally contain inert gas and it is necessary to label them with a trace amount of inert gas. Various techniques can be used for the introduction of the inert gas atoms into the samples to be investigated [1, 2].

8.2.1 Diffusion Technique This is based on the diffusion of the inert gas into solids at elevated temperatures and pressure of the gas. The substance to be labeled and the inert gas (usually

152

V. Balek

labeled with radioactive nuclides, e.g. 85 Kr) are placed in a high-pressure vessel which is then closed and heated for several hours at a temperature of approximately 0.3-0.5 T melt of the substance to be labeled, and finally quenched in liquid nitrogen. The amount of inert gas introduced into the sample depends on time, temperature and pressure, as given by the diffusion equation.

8.2.2 Sample Preparation in the Inert Gas Atmosphere If the sample preparation is carried out in an inert gas (e.g. argon, krypton) atmosphere as it is in the case of physical vapor deposition (PVD), the inert gas atoms are captured in the structure of the deposited substance. In this method, the thin films prepared are automatically labeled by the inert gas, the release of which can be used for diagnostics of the film during its subsequent heating [3].

8.2.3 Implantation of Accelerated Ions of Inert Gases This technique has also been used for labelling samples to be measured by DSA. The amount of inert gas introduced and its concentration profile depends on the energy of ion bombardment and the properties of the labeled matrix. A number of techniques can be used for inert gas ion bombardment [1]. A defined ion beam can be produced using a magnetic separator. A versatile low-cost technique can be used for sample labelling in a low-temperature plasma produced by a highfrequency discharge in which the ionization and acceleration of ions take place

[1]. 8.2.4 Inert Gases Produced from Nuclear Reactions The recoil energy of nuclear reactions producing inert gases can be used for the implantation of gases into solid samples. Some of the nuclear reactions which have been used for the production of inert gas atoms and their introduction into solid samples are listed in Table 1.

8.2.5 Introduction of Parent Radionuclides as a Source of Inert Gas Atoms In cases when carrying out longer and/or high-temperature measurements of surface and morphology changes, it is useful to introduce parent radionuclides of the inert gas, e.g. radon, as a source of the labelling gas. For example, trace amounts of thorium 228 Th can be introduced into the sample by coprecipitation during the sample preparation from a solution or by adsorption on the surface of the sample. 220 Rn is formed by spontaneous alpha decay according to the scheme

T1;2 = 1.9 y T1;2 = 3.8 d T1;2 = 55.8 s

8. Diffusion Structural Analysis of Inorganic Materials

153

Table 1. Nuclear reactions which can be used for production of inert gas atoms and their introduction into solid samples a-decay

,8-decay

226Ra ｾ＠

222Rn

22sTh ｾ＠

224Rn ｾ＠

-(3

220Rn

-(3

83Se---+ 83Br---+ 83Kr -(3

-(3

133Te---+ 133I---+ 133Xe

(n,a)

4°Ca(n, a) 37 Ar 88 Sr(n, a) 85 mKr 136Ba(n, a) 133Xe

(n,p)

39K(n,p) 39 Ar 85Rb(n,p) ssKr 133Cs(n,p) 133mxe -(3

(n, 1')

37Cl(n,f') 3sCl---+3sAr

and ,8-decay

79 Br (n, 1') 80 Br---+ 8°Kr

-(3

-(3

121 1 (n, !') 12s 1 ---+ 12sXe

Fission (n, f)

238 U(n, f)Xe, Kr, ...

and can be introduced into the solid owing to the recoil energy (85 ke V per atom). The above nuclear reactions which give rise to the radon nuclides, have also been used for the incorporation of the inert gas into the solid sample using 228 Th and 224 Ra adsorbed on the sample surface as the source of 220 Rn. Radon atoms penetrate into the sample several tens of nanometers, depending on the composition of the target materials: for example, the penetration depth of 220 Rn in MgO is 41.7 nm; in Si0 2 , it is 65.4 nm. The parent isotopes of 228 Th and 224 Ra serve as "recoil ion implantators" of radon.

8.3 Mechanisms and Theories for Release of the Inert Gases from Solids The solubility of inert gas atoms (such as xenon, krypton and radon) in inorganic solids is small. The inert gases are trapped at lattice defects such as vacancy clusters, grain boundaries and pores. The defects in the solids can serve both as traps and as diffusion paths for the inert gas. A survey of the influence of various factors on the migration of inert gases in solids is given in a monograph by Balek [1]. In instances when the inert gas atoms are incorporated into the solids without their parent isotopes, diffusion in the matrix is the main mechanism for the gas release from solids. In instances when the parent nuclides of the inert gas are

154

V. Balek

incorporated into the solid samples as a quasi-permanent source of the inert gas, the recoil mechanism of the inert gas release should be taken into account in addition to the diffusion. Recoil plays an especially important role in samples of large surface area and at temperatures where diffusion of the inert gas is negligible. The theoretical concepts describing the release mechanisms consider separately the cases in which the inert gases are incorporated without and with their parent nuclides [1]. For simplicity, in the first approach, it is assumed that no structural or phase changes take place in the solid during heating in the considered temperature range.

8.3.1 Cases when the Inert Gas has been Incorporated into a Solid without its Parent Nuclide(s) The inert gas can be released by diffusion processes which depend on the diffusion mechanisms. A number of equations have been proposed to describe the temperature dependence of the inert gas release [1, 5, 6]. Assuming that the release of the inert gas (introduced by, for example, ion bombardment) is a reaction of the first order, the rate of gas release can be expressed in differential form -dNldt

= vN exp( -LJ.HI RT),

(1)

where N is the number of atoms trapped per unit surface area, v is a constant (the frequency of oscillation of atoms in the lattice is assumed to equal 10- 13 s- 1 , iJ.H is the activation enthalpy of the inert gas diffusion and R is the molar gas constant equal to 8.3143 J K- 1 mol- 1 . A linear rise of temperature (T = T0 + (3t) where (3 is the heating rate and iJ.H is independent of N, is also assumed. By differentiating (1) and equating it to zero, the following expression for Tmax is obtained [1, 4] iJ.HI RTmax = (vI (3) exp(- iJ.H I RTmax) ; iJ.HITmax = ln(vTmax11(3)- 3.64.

(2)

The value of the activation enthalpy iJ.H can be determined directly from the iJ.H value found experimentally at the temperature of the maximum. The relationship between iJ.H and T max in the given temperature range is close to linear. Similar formulae have been derived [7] taking into account different gas distributions. The temperature dependences of the inert gas release rate generally exhibit peaks, the maxima of which (Tmax) are governed mainly by the value of iJ.H.

8.3.2 Cases when the Parent Nuclide(s) of the Inert Gas are used for Sample Labelling The inert gas is formed by radioactive decay of the parent nuclide incorporated into the solid or adsorbed on its surface. The gas atoms may escape from the

8. Diffusion Structural Analysis of Inorganic Materials

155

solid either by recoil energy ejection or by any one of several types of diffusion processes [1]. When the radium atom lies close to the surface of the grain of the solid, the recoil energy (85 keV per atom) that the radon atoms gains during decay of the parent may be sufficient to eject the gas atom from the grain. Alternatively, the radon atom may escape by diffusion before it undergoes the decay. Using the theories of both recoil and diffusion processes, several expressions have been proposed for the release rate of the inert gas [e.g.1, 8, 9]. Hahn [10] defined the term emanating power E as the ratio of the rate of gas release to the rate of gas formation in the solid. A simplified model for inert gas (radon) release from solids was described by Balek [1, 2]. The term Er of the emanating power attributable to recoil can be expressed as

(3) where K1 is a temperature-independent constant, which depends on the path of the recoiled gas atoms in the solid, and 5 1 is the external surface area of the sample. The path of recoiled atoms of radon has been estimated; for example, it is 40 nm in thoria. Equation (3) is valid for isolated grains of the solid that are larger than the path of the recoiled radon atoms. For finely dispersed solids, the constant K 1 depends on the dispersity and morphology of the sample. The term Ep of the emanating power due to the inert gas diffusion in the intergranular space and open pores can be expressed as

(4) where K2 is a constant that depends on temperature, and 5 2 is the internal surface area of the sample. The term E 8 of the emanating power due to the inert gas diffusion in the solid matrix of the sample can be expressed as

(5) where K3 is a temperature-independent constant, i1H is the activation enthalpy of inert gas diffusion in the solid matrix, R is the molar gas constant, T is the absolute temperature and 5 3 is the area representing the sum of the crosssections of all diffusion paths, such as dislocations, grain boundaries, etc. The total emanating power E can be obtained by summing these;

(6)

8.4 Measurement of Inert Gas Release The apparatus for diffusion structural analysis consists of several components designed to ensure the detection of inert gas, released from the sample. Figure 1 shows a schematic of the DSA apparatus.

156

V. Balek

6

5

Fig. 1. Scheme of the apparatus for diffusion structural analysis: 1 - gas supply; 2 gas flow stabilizer; 3- labeled sample; 4- sample holder; 5- thermostat (furnace); 6 - temperature controller; 7 - measuring chamber; 8 - inert gas detector; 9 - flow rate meter; 10 - countmeters; 11 - data processor and printer-plotter

During an DSA measurement, the carrier gas (air, nitrogen or other gas) carries the inert gas released by the sample situated in a reaction vessels into a detector for the inert gas. For example, to measure the a-activity of radon, a scintillation counter, ionization chamber or semiconductor detectors can be used. On the other hand, /1-activity measurements of 85 Kr, are made by Geiger-Muller tubes. Gamma-active radionuclides of xenon can be measured by a gammaspectrometer. The stable nuclides of inert gases are measured by a mass spectrometer. To ensure optimum conditions for a direct comparison of DSA data with results obtained by other methods, devices were constructed to provide simultaneous measurement of additional parameters [11]. The equipment for simultaneous measurements by DSA, differential thermal analysis (DTA), thermogravimetry/ differential thermogravimetry (TG /DTG) or dilatometry, available from Netzsch Ltd, Germany, ensures the optimal conditions for direct comparison of the results [12].

8. Diffusion Structural Analysis of Inorganic Materials

157

8.5 Potential Use of Diffusion Structural Analysis The theoretical considerations summarized above indicate that the diffusion structural analysis can be applied to the investigation of processes taking place in solids or on their surfaces. Any process in a solid or its phase boundary leading to a change in either the surface and/or changes in the inert gas diffusivity (permeability) becomes observable from the DSA measurements. DSA has been used in the study of such solid state processes as ageing of precipitates or geleous materials, recrystallization, annealing of structure defects and changes in the defect state of both crystalline and non-crystalline solids, sintering, phase changes, surface and morphology changes accompanying thermal decomposition of solids, and chemical reactions in solids and on their surfaces, including solid-gas, solid-liquid and solid-solid interactions. Processes of practical importance for preparation of advanced materials, testing chemical durability of materials as well as for environmental science and technology, have been studied by means of DSA. The kinetics of surface area changes, mechanisms of defect annealing, pore sintering and the kinetics of morphology changes, in general can be evaluated from DSA results in both isothermal and non-isothermal conditions. In contrast to X-ray diffractometry, DSA makes it possible to investigate poorly crystalline or amorphous solids. In contrast to adsorption measurements for surface area determination, DSA permits a continuous investigation of the surface, even at elevated temperatures during heat treatment of solid samples or their hydration, under wet conditions, without the necessity of interrupting the heat treatment or the hydration and cooling the sample to liquid nitrogen temperatures. For this reason, the DSA may reflect the nature of the surface at elevated temperatures more accurately than adsorption measurements. In contrast to DTA and thermogravimetry, diffusion structural analysis makes it possible to investigate processes that are not accompanied by thermal effects or mass changes. DSA permits, to examine consolidation, annealing of defects and sintering of powdered or geleous samples, which would be difficult to examine by means of dilatometry. Moreover, by applying different radioactive labeling techniques of either the surface alone or the volume of solids, the processes taking place in the surface and in the bulk of the sample have been discerned by DSA. This is especially advantageous when studying the behavior of thin films or coatings on substrates. By labeling the thin film to a depth not exceeding its thickness, DSA gives information concerning the thin film alone, without the influence of the larger substrate. This is the advantage of DSA over X-ray investigations, when the thin film represents a negligible part of the sample. On the other hand, when the interaction of the thin film with the substrate during heating is to be investigated, a deeper inert gas implantation can be used. The high sensitivity of DSA to the chemical interactions between a solid surface labeled with the radioactive inert gas and aggressive agents made it possible to reveal the very beginning of corrosion reactions. The durability of

158

V. Balek

materials towards aggressive liquids and gases, as well as the effectiveness of preserving coatings, can be tested by means of DSA. The possibility of thin-film labeling by inert gases during physical deposition (PVD) or chemical vapor deposition (CVD) on a substrate can be applied for diagnostics of the thin layers, during their processing, thermal treatment and durability testing. In addition, DSA measurements make it possible to obtain information about the diffusion parameters of the inert gas in the solid. The diffusion coefficient D and the activation enthalpy iJ.H of the inert gas diffusion can be evaluated. The diffusion parameters of inert gases in inorganic and hybrid organic-inorganic composites are important for characterisation of the transport properties of materials. The determination of inert gas permeability in hybrid materials is a possible way of testing the local structure and revealing irregularities in coatings made of these materials.

8.6 Examples of DSA Applications 8.6.1 Diagnostics of the Defect State Inert gas diffusion parameters evaluated from DSA measurements reflect the mobility of inert gases in the solids, which can be used to determine the state of the defects in the solids. Inert gas atoms incorporated into solids are situated on the natural and/or artificial defects produced, for example, by ion bombardment, neutron irradiation or mechanical treatment. The release of the inert gases on sample heating is controlled by thermally stimulated processes, i.e. diffusion, annealing of defects, etc. It was shown that the mobility of inert gas atoms in ionic crystals differs in various crystallographic directions, owing to the channeling effect. The mobility of the inert gases (the activation energy) can be used as a parameter characterizing the defect state of an ionic crystal lattice and may cause the formation of the metamict phase. The annealing of the metamict phase is indicated by a sharp DSA peak (see Fig. 2). The activation energy of inert gas release and of recrystallization of the metamict phase can be evaluated from the peak temperature. A number of alkali halides, alkali earth halides and oxides, have been tested in this way by DSA [1, 13-15].

8.6.2 Assessment of Inorganic Materials Prepared by Heat Treatment From the DSA curves measured during the cooling of heat-treated materials, the active state of the powders (the non-equilibrium defect state) can be assessed. The values of the activation energy iJ.H of radon diffusion in samples labeled by radon parent nuclides, 228 Th and 224 Ra were used as a parameter characterizing

8. Diffusion Structural Analysis of Inorganic Materials dRdt

0

159

(b)

200

400

600

800

Temperature ["C]

1000

Fig. 2. Temperature dependence of krypton 85 Kr release from a corundum single crystal treated by ion bombardment 10 14 ionscm- 2 • The peak corresponds to the inert gas release accompanying the recovery of the metamict amorphous layer produced by the ion beam treatment of the sample surface

differences in the defect (active) state of iron(III) oxide samples prepared by heat-treatment of various iron salts [16, 17]. The influence of the thermal and chemical history on the active state of powdered iron(III) oxide was assessed from values of the activation energy of radon diffusion, determined from the experimental results of DSA at temperatures below 0.5Tm, where Tm is the melting point in Kelvin [16]. In this temperature range the activation energy of radon diffusion reflects the concentration and type of non-equilibrium defects remaining in the structure of iron(III) oxide after the decomposition of initial iron salts used for the preparation of the oxide samples. Hedvall [18] called this phenomenon "the structure memory of solids". The DSA revealed annealing of structure defects, affecting the active state of solids. The decrease in the "activity" of a solid is indicated by an increase in the activation energy of radon diffusion [1, 16].

8.6.3 Characterization of Geleous Materials 8.6.3.1 Sol-gel Transition During Formation of Silica Gels The mixture ofTEOS:H 2 0:C 2 H 5 0H = 1:10:2.5 was hydrolysed at a temperature of 80°C under reflux and cooled. Trace amount of radionuclides 228 Th and 224 Ra in ethanol solution were added to the mixture before the hydrolysis. (The specific activity of the hydrolysate was 10 3 Bqml- 1 ) The labeled hydrolysate was used for the gelation studies by means of DSA [19]. In Fig. 3 we demonstrate the time dependence of radon release rate E (curve1), optical transparency (curve2) and pH (curve3) measured during formation of silica-gel at a temperature of 20°C. A slight decrease of the radon release rate observed from the very beginning of the measurement on curve 1 corresponds to the formation of the gel particles. The intense decrease of the radon release rate can be ascribed to the agglomeration of the gel particles, as

160

V. Balek

100

7.5

(%]

Transparency

2

0.2

3

pH

ｾ＠

·c:

=!

Qj

7.0

'-

IJ.J

0.1

ＰＫＭｾｲＶＮＵ＠

0

2

Time (h)

3

Fig. 3. Time dependences of radon release rate E (curve 1), optical transparency (curve 2) and pH (curve 3) measured during formation of silica gel at a temperature of 20°C

it follows from the pH increase. After 90 min, the abrupt decrease of E indicated the structure change in the system, caused by condensation of the gel. The bottom of the curve decrease corresponds to the gelation point. The results obtained by the DSA are in good agreement with the results of the measurements of rheological properties. The microscopic information about the nanostructure changes obtained by the DSA is reflected in the macroscopic changes in the viscosity changes measured during gelation. It is to note, that no change in the transparency was observed in the course of the gelation of pure silica-gel [19].

8.6.3.2 Characterization of Gels During their Thermal Treatment DSA was used in the characterization of the processes taking place during gelation, as well as during subsequent treatment of the gels, i.e. ageing, drying, dehydration and densification on heating. Ageing is indicated by a decrease of E, as a result of continuing polycondensation or reprecipitation of the gel network. During gel drying an increase of radon release E was observed, indicating removal of a liquid from the interconnected pore network. The removal of surface OH groups from the pore network is reflected by an increase of radon release rate E, indicating increase of the surface area and nanoporosity. The removal of other volatiles, e.g. residues of gelation agents from

8. Diffusion Structural Analysis of Inorganic Materials

161

Temperature, (°C)

Fig. 4. Temperature dependence of argon release rate from 250 nm thick TaSb thin film deposited by sputtering in argon atmosphere (argon atoms were captured during the sputtering process in the thin film defects)

intermediate products of ceramics, is usually accompanied by an increase of E, the subsequent decrease in E may indicate the decrease of surface area and nanoporosity taking place on heating. Geleous materials such as silica-gel, xerogels of urania, titania, zirconia, alumina/SiC and others prepared by the "sol-gel" technique were advantageously investigated by DSA directly during drying, crystallization or sintering [20, 21]. Differences in the behavior of the urania xerogels caused by various concentrations of gelation additives, various means of drying, by ageing, etc., have been determined by DSA [20, 22]. Figure 4 shows the temperature dependence of argon release rate from 250 nm thick TaSi 2 thin film deposited by sputtering in argon atmosphere [3] (argon atoms were captured during the sputtering process in the thin film defects). The DSA gives information about changes of surface area and nanoporosity of materials under "in-situ" conditions of their treatment. This method can be recommended for testing quality of intermediate and final products of ceramics and glasses prepared by various techniques, e.g. sol-gel, chemical vapor deposition (CVD), physical vapor deposition (PVD), etc. The DSA was also used for the determination of optimal temperature for thermal treatment of ZnS layers deposited by CVD on glass plates [23]. The morphology changes of TaSh thin layers (transition from a very disordered state to a crystalline one) were revealed by the measurement of argon release which was included in the structure defects of the thin film prepared by sputtering [3] (see Fig. 4). Both bulk samples, ul-

162

V. Balek

trafine powders, fibers, thin film coatings and membranes can be characterized by the DSA. 8.6.3.3 Annealing of Surface Roughness and Defects of Ceramic Powders It was demonstrated in a number of cases [24, 25] that changes of surface and morphology of ceramic powders can be characterized by DSA under "in-situ" conditions of their treatment. For example the behavior of magnesia, alumina, and thoria powders were characterized by this method. The DSA results of thoria powder are demonstrated in Fig. 5, indicating the kinetics of the annealing of surface roughness. The kinetic parameters of this process taking place in the temperature interval 705-825°C were determined [26]. The results obtained obey the kinetic law log Self

= n log t + constant ,

(7)

where n = 0.64 and Self is the surface area reflected by the radon diffusion in the respective temperature range. 8.6.3.4 Structure Transitions in Glasses Differences between surface and volume stages of the crystallization and melting of glasses were revealed by means of DSA. The results obtained for the systems Pb0-Si0 2 and Ge-Se-Te are presented in [27, 28]. This method found application also in the field of the vitrification of hazardous waste, namely in the determination of optimal conditions for immobiblization of the waste containing Sr and Cs from nuclear power plants, and in testing the durability of this glass towards hydrolytic corrosion [29, 30]. 8.6.3.5 Thermal Behavior of Clay Minerals The results of DSA characterizing thermal behavior of clay minerals, such as boehmite, kaolinite, goethite, lepidicrocite, montmorillonite, saponite, beidelite, vermiculite, and others [31-34] are in good agreement with the results of traditional methods (such as DTA, TG). A high sensitivity of DSA to changes in the surface layers of altered (weathered) minerals was found. The effect of grinding on the thermal behavior of clay minerals was characterized by DSA. 8.6.3.6 Hydration of Cementitious Binders Morphology changes taking place during hydration reactions of Portland cement clinker mineral- tricalcium silicate 3 CaO · Si0 2 and various cements were monitored by DSA [35, 36]. Figure 6 shows the DSA results obtained during the hydration of Portland cement (PC-400) in water (w / c = 0.3) under isothermal conditions at 35, 45 and 65°C, resp. The reactivity of the cement towards water was determined from the DSA results from the early stage of the interaction with water. Changes of surface and morphology taking place in the hydration products of cement have also been monitored by this method [36] under "in-situ" conditions of the setting of the cement paste.

8. Diffusion Structural Analysis of Inorganic Materials £[cps]

163

(a)

70 60

50

40 30 20 10 0

5

10 15

20 25 30 35 40 45 50 55 60 Time [min] (b)

1.5

0.5

1.0

5

10

1.5

2.0 logt

20 30 405060 Time [min]

Fig. 5. Time dependences of radon release rate from thoria powder labeled by 228 Th, measured during sample heating in air in the temperature range from 705 to 825°0. In this temperature range the annealing of the surface roughness took place

It should be pointed out that DSA can be advantageously used for monitoring changes in the microstructure of a cement paste, when the size of the micropores is comparable to the size of radon atoms, d = 0.4 nm. Good agreement between DSA results and adsorption measurements was found. This method was suggested [36] for the characterization of the reactivity of cement under various technological conditions. 8.6.3. 7 Testing Corrosion of Materials DSA was used for the study of ｳｯｬｩ､ｾｧ｡＠ and ｳｯｬｩ､ｾｱｵ＠ reactions involved in corrosion. Radioactively labeled surfaces are sensitive to all chemical influences

164

V. Balek

1'

+ I

15

3

I

I

f ｾ＠

l 0

0..

ｾ＠

...

Q:

5

I

+.... --5

I

--+

5

2

3 4

t(minl

Fig. 6. Time dependences of radon relea;;e rate from Portland cement paste sample (w/c -0.3) labeled with 228 Th. The sample setting wa;; characterized under in-situ conditions of the setting carried out at temperatures 65°C (curve 1), 45°C (curve2) and 35°C (curve3). The results of the penetration resistance RF testing of the paste treated at the respective temperatures are demonstrated as dotted lines. The time interval corresponding to the setting period of the sample at 20°C determined by the Vicat method is shown as the dashed area

that cause changes in the surface of a crystalline lattice. Current methods used to evaluate anti-corrosive or protective agents are generally unreliable, and in many instances take several months to complete. Inert gas release measurements made it possible to carry out such investigations relatively quickly and simply. Corrosion of glasses, building materials and metals imperceptible to be human eye can be revealed within a few minutes or hours. This method is suitable primarily for relative measurements or for comparisons of various substances using a comparative scale [37]. 8.6.3.8 Testing Reactivity of Ceramic Powders A number of reactions between solid powders, e.g. Zn0-Fe 2 0 3 [38], BaC03Ti02, BaSOrTi0 2 [39], have been studied by means of DSA. A systematic study [38] of the ZnO- Fe 2 03 system demonstrated that DSA can be used advantageously for the determination of the initial stage of the reaction, and kinetics of the formation of the ferrite structure. DTA, dilatometry and x-ray diffraction were not sensitive enough to indicate the initial reaction stage. The high sensitivity of DSA towards reaction between powders permitted the determination of the reactivities of the components used in reaction mixtures. The reactivities of

8. Diffusion Structural Analysis of Inorganic Materials

165

iron(III) oxide samples with various chemical and thermal histories, determined by DSA [40], agreed well with the results of other experimental techniques. This method revealed differences in the reactivities of commercial iron(III) oxide samples, declared as identical when using traditional surface area measurements [41]. The difference in the reactivities was checked by DSA during heat treatments of reaction mixtures corresponding to the technological conditions of ferrite manufacture. The DSA has been recommended as a suitable tool for testing reactivity of ceramic powders giving supplementary information on the reactivity under "in situ" conditions of solid-state reactions [41-43].

References 1. V. Balek, J. Tolgyessy: Emanation thermal analysis and other radiometric emanation methods, (Wilson and Wilson Eds., Comprehensive Analytical Chemistry, Part XIIC, Elsevier, Amsterdam, 1984). 2. V. Balek: Thermochim. Acta 22, 1 (1978). 3. R.A. Levy, P.K. Gallagher: J. Electrochem. Soc. 132, 606 (1985). 4. P.A. Redhead: Vacuum, 21, 203 (1962). 5. G. Carter, J.S. Colligan: Ion Bombardment of Solids, (Heinemann, London, 1968). 6. M.D. Norgett, H.B. Lidiard: Philos. Mag. 18, 1193 (1968). 7. R. Kelly, Hj. Matzke: J. Nucl. Mater. 17, 197 (1965); 20, 175 (1966). 8. J. Kfiz, V. Balek: Thermochim. Acta 78, 377 (1984); 110, 245 (1987). 9. S. Fliigge, K.E. Zimens: Z. Phys. Chern., Abt. B. 42, 179 (1939). 10. 0. Hahn: J. Chern. Soc. Suppl., S 259 (1949). 11. V. Balek: Cz. Patent No. 151172. 12. W.D. Emmerich, V. Balek: High Temp. High Press. 5, 67 (1973). 13. C. Jech, R. Kelly: Proc. Br. Ceram. Soc. 9, 359 (1976). 14. F.W. Felix, K. Meier: Phys. Status Solidi 32, 139 (1969). 15. A.S. Ong, T.S. Elleman: J. Nucl. Mater. 42, 191 (1972). 16. V. Balek: J. Mater. Sci. 5, 166 (1979). 17. V. Balek: Farbe und Lack 85, 252 (1979). 18. J.A. Hedvall: Solid State Chemistry, (Elsevier, 1969). 19. V. Balek, Z. Malek, H.J. Pentinghaus: J. Sol-gel Sci. Techno!. 2, 301 (1997). 20. V. Balek, M. Vobofil, V. Baran: Nucl. Techno!. 50, 53 (1980). 21. V. Balek, E. Klosova, M. Murat, N. Almeida Camargo: Bull Am. Ceram. Soc. 75, 73 (1996). 22. V. Balek, H. Landspersky, M. Vobofil: Radiochem. Radioanal. Lett. 28, 289 (1977). 23. V. Balek, J. Fusek, 0. Kfiz, M. Leskelii, L. Niinisto, E. Nykiinen, J. Rautanen, P. Soininen: J. Mater. Res. 9, 119 (1994). 24. C. Quet, P. Bussiere: C.R. Acad. Sci., Ser. C 280, 859 (1976). 25. V. Balek: Sprechsaal 116, 978 (1983). 26. V. Balek: J. Mater. Sci. 17, 1269 (1982). 27. V. Balek, J. Gotz: Proc. 11th Int. Glass Congress, Prague, Vol. 3, pp. 35. (J. Gotz Ed., Prague, 1977). 28. S. Bordas, M. Clavaguera-Mora, V. Balek: Thermochim. Acta 93, 283 (1985).

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29. V. Balek, Z. Malek, A. Clearfield: Surface reactivity of high level matrices characterized by radiometric emanation method (Proc. 7th Int. Conference on high level radioactive waste management, Las Vegas, Nevada, 1996) p. 474. 30. V. Balek, Z. Malek, A. Clearfield: Alteration of nuclear waste glasses characterized by radon emanation method, (Summary of an International Workshop "Glass as a waste form and vitrification technology", held at NAS, Washington D.C., May 1996) (NRS Paper E.58) p. 102. 31. W.D. Emmerich, V. Balek: High Temp.-High Pressures 5, 67 (1973). 32. V. Balek, J. Subrt: J. Pure Appl. Chern. 67, 1839 (1995). 33. Z. Malek, V. Balek, D. Garfinkel-Schwekey, S. Yariv: J. Thermal Anal. 48, 83 (1997). 34. V. Balek, M. Murat: Thermochim. Acta 282/283, 385 (1996). 35. V. Balek: Thermochim. Acta 72, 147 (1984). 36. V. Balek, J. Dohnalek: J. Mater. Sci. 17, 2281 (1982). 37. V. Balek, Z. Malek, B. Casensky, D. Niznansky, J. Subrt, E. Vecernfkova, H. Romich, M. Pilz: J. Sol-gel Sci Technol 8, 591 (1997). 38. V. Balek: J. Am. Ceram. Soc. 53, 540 (1970). 39. T. Ishii: Thermochim. Acta 88, 277 (1985); 93, 469 (1985); 109, 252 (1979). \40. V. Balek: J. Appl. Chern. (London) 20, 73 (1970). 41. V. Balek: J. Therm. Anal. 12, 111 (1977). 42. V. Balek: Thermochim. Acta 110, 221 (1987). 43. V. Balek: J. Thermal Anal. 35, 405 (1989).

Part IV

X-Ray Resonance and Nuclear Methods

9. Texture Determination by Using X ray Diffraction F.

WAGNER

LM2P /ISGMP, University of Metz, lie du Saulcy, F-57045 Metz, France

Abstract. The crystallographic texture is defined as the relative "organization" of the grains in an anisotropic solid which influences frequently its physics and mechanical properties. This is the case of majority of polycrystalline materials: rocks, ceramics, metals, polymers, etc. Here the several parameters for defining the texture concept is explained and the experimental tools, as well as the mathematical procedures are shown and discussed for materials characterization. The using of xray beams in measuring the diffracted intensity given by a specimen under various geometrical conditions is exposed as the nowadays more useful method for texture determination in materials. The Orientation Density Function (ODF) is defined and the calculations for the general knowledge about texture analysis in polycrystalline materials. The difference between local and global textures allows to determine the ODF more precisely and to describe the grains orientation relationships.

9.1 Introduction Most of the materials which are used today in a solid state are polycrystalline materials made up from grains (or crystallites) separated by grain boundaries. This is the case for metals and alloys but also for rocks, ceramics, some polymers etc. By considering such materials it appears very often that physical or mechanical properties are anisotropic. Among the several causes which can induce such an anisotropy the "organization" of the grains, which we will later more precisely define as the crystallographic texture, is very often the most important. Of course, the "organization" of the grains can lead to anisotropic properties in a polycrystal only if there is an anisotropy in the grain itself, which is quite usual due to the arrangement of the atoms. An intuitive idea of this phenomenon can be obtained from the following example: let us consider two samples of a given magnetic material with an easy magnetization direction. Let us also assume that the easy magnetization directions are parallel in all the grains of the first sample whereas they are randomly distributed in the second sample. By applying an external magnetic field H the energy which is necessary to lead the material to magnetic saturation will be different for the two previously described samples. Moreover, this energy will also vary with the direction of application of H in the first sample. As already mentioned, many properties depend on the distribution of crystalline directions in the grains of a polycrystalline material. According to the

170

F. Wagner

property considered and the utilization considered, the anisotropy can be an advantage or a drawback. It is therefore important to understand it in order to obtain the best performance of a given material. A prerequisite to the calculation of anisotropic physical or mechanical properties consists of the characterization of the "organization" of the grains, i.e. in the determination of the crystallographic texture. The aim of the present chapter is to explain the several quantities which are considered in this field, the experimental tools which can be used and the mathematical procedures to be applied to reach this characterization. There are in fact two main ways to obtain information on the crystallographic texture of a given specimen. In the first, one measures directly the individual orientations of a set of grains (assumed to be representative of the polycrystal) by using for each one a diffraction pattern or a Kikuchi pattern in transmission electron microscopy (TEM) or a pseudo-Kikuchi pattern in scanning electron microscopy (SEM). Since, up to now, a full automatization has not been reached this way requires a lot of "human time" in order to obtain statistically relevant results. The second way consists of using neutron or x ray beams and in measuring the diffracted intensity delivered by a given specimen under various geometrical conditions. Today, the x ray goniometry is by far the most used technique for such studies and special attention will therefore be paid to it in the following.

9.2 Experimental Information: The Pole Figures 9.2.1 Principle of a Pole Figure Measure When a crystal is submitted to a monochromatic x ray beam with wavelength A, a given crystallographic family plane {hkl}, with an interplanar spacing dhkl, gives rise to a cooperative diffusion, i.e. to diffraction, if the normal to these {hkl} planes makes an angle (11"/2) - e with the beam: this is the well known Bragg's law,

A=

2dhkl

sine.

(1)

In a polycrystalline material the diffracted intensity is proportionnal to the volume fraction of the specimen wich is oriented so that the Bragg's law is fulfilled. Let us specify now the information required and how to obtain it with a diffraction technique. For a given specimen an arbitrary orthogonal co-ordinate system (A, B, C) 1 is chosen. A unit vector y can be defined in this specimen co-ordinate system by its two polar angles r.p and x. If one imagines that the specimen is surrounded with a sphere of radius 1 the unit vector y intercepts it at a point P called a pole; the sphere is therefore called a pole sphere (Fig. 1). The point P' is the stereographic projection of P (P' is the intersection with the equator of the segment SP consisting of the point P and the south poleS). 1

Bold letters are used to denote vectors.

9. Texture Determination by Using X ray Diffraction

171

c

s

Fig. 1. A pole P and its stereographic projection P'

The information required is as follows: for each y vector, what is the volume fraction of the specimen which is oriented so that the normal to a given (hkl)i crystallographic family of planes is parallel to y? If one can answer this question it is obvious that one obtains some information about the 'organization' or orientation of the grains of this specimen. It is clear also that the knowledge of the 'organization' of the grains increases if one repeats the experiment for a great number of geometrical positions, i.e. a great number of y vectors. This can be achieved by moving either the incident beam and the detector or the specimen. For convenience it is easier to build a tool where the incident beam is fixed and where the orientation of the specimen versus the geometry of diffraction can be varied: such a tool is a texture goniometer. Figure 2 shows schematically the arrangement for such an experiment: a fixed xray tube delivers monochromatic radiation which is collimated on the specimen; by choosing the position 28 of the detector one selects, according to Bragg's law, a given (hkl)i crystallographic plane family. The specimen is attached to the specimen holder in a Eulerian craddle and can therefore be rotated through the angles X and tp around 2 orthogonal axes. These rotations are called tilt and azimuthal rotations respectively. For each ( tp, x) position of the specimen one can measure and store the diffracted intensity J(hkl)i(t.p, x) = hi(tp, x). A set of diffracted intensities for 0 < ¢ < 21r and 0 < x < 1r /2 is called the (hkl)i pole figure. As it is impossible to perform measurements for the infinity of the ( tp, x) positions so one chooses, in practice, a set of positions, usually regularly spaced, and one registers the diffracted intensities for these specimen positions. For example, if one chooses the steps .dt.p =5° and .:1x =5° a (hkl)i pole figure will consist in a set of 72 x 18 = 1296 measurements. Figure 3 shows a Siemens texture goniometer. The technique of pole figure measurement in the reflection mode was proposed by Schulz as early as 1949

172

F. Wagner

-

qJ• 1az lmuth)

X- ray source

9

detector

Debye ring

polycrystalllne sample Fig. 2. Schematic view of the experimental arrangement for a pole figure measure in reflection mode

[1]. For thin specimens it is also possible to perform pole figure measurements in transmission mode [2]. Because of the difficulty of preparing thin specimens with a constant thickness this last mode is not often used today for x ray diffraction. In addition to the two rotations in the Eulerian craddle it is usually possible to oscillate the specimen (parallel to itself) so that a large number of grains are involved in each measurement, which ensures statistical significance. This is no longer the case if the grains are very large (2:, 100 J..Im) where special specimen holders or neutron diffraction are required. Two sets of slits (vertical and horizonthal) are set in front of the detector. The vertical slits are used to select the diffracted intensity in a g iven domain [28; - L18 /2, 28;- L18 /2] where ,18 allows one to integrate the whole peak centered at 28; which corresponds to the chosen (hkl); reflection. The horizontal slits are used to select on the Debye ring, a part corresponding to the fixed L1x step in tilt angle; the relation between the distance h between these horizonthal slits and the step L1x is,

h = 2RL1xsin8,

(2)

with R the distance between the slits and the specimen. 9.2.2 Corrections of the Data

Once the measurements have been performed several corrections have to be applied due to the operating conditions.

9. Texture Determination by Using X ray Diffraction

173

Fig. 3. A Siemens texture goniometer a: xray tube; b: collimator; c- c ': (}and 2(} circles; d: specimen; e: Eulerian craddle; f slits; g: detector

Background Correction. During the diffraction experiment the detector receives a useful intensity and, at the same time, an extraneous intensity. The latter one is due to a number of reasons, such as fluorescence which cannot be completely avoided, imperfect monochromaticity of the source, etc. In order to subtract this extraneous intensity one measures, after the measurement of the pole figure itself, the intensities for all positions ( 1c(

...I

w a::

Fig. 19. The Mi:issbauer effect of 119 Sn in gel (1), glass and crystal (2) and crystal (3) samples; at heat treatment 120°C with 8 = 0.22mms- 1 , .1 = 0.57mms- 1 and at 500° and 1000°C with 8 = 0.0 mm s- 1 , respectively

11. Mi:issbauer Spectroscopy Applied to Inorganic Materials

215

0

2 4 0

2 4

0 1"""1

ｾ＠

0

v c: c

-

2

c .. c 0

'-

v,)

-C . -+ 0 and Q -+ oo is impossible. The confined integration limits have a marked influence on the RDF obtained, especially at short distances, where sharp oscillations are observed (termination effect) [7]. From the properties of the Fourier transformation it follows that the condition Qmax =1- oo limits the experimental resolution in real space. The function,

P(R)

=

ｾ＠

J

M(Q)cos(RQ)dQ,

(12)

defines the resolution and has a full width at half maximum height (FWHM) of the structure factor of 5.437/Qmax· The resolution effect is a ｣ｯｮｶｬｵｴｩｾ＠ with a resolution function. Namely the neutron diffraction method (b; = const) enables measurement of S(Q) up to 500-1000nm- 1 and a resolution L1R = 0.010.005 nm to be attained. For a material with n types of atoms, there are n( n+ 1) /2 independent PRDFs 47rR 2 p;1(R). If the partial structure factors S;1(Q) are known, the PRDFs can be obtained from,

12. Neutron Diffraction in Amorphous Structures

4nR 2 [Pi1 (R)- Po]=

ｾ＠

J

Q [Sij (Q)- 1] sin (QR) M (Q) dQ.

225

(13)

Unambiguous determination of the PRDF in amorphous structures is possible in systems consisting of practically no more than two types of atoms. The structure factor S( Q) equation contains in this case three unknown quantities Sn, S12 and S22,

(14) Neutron scattering together with x-ray and electron diffraction, i.e. experiments in which bi are dependent on the different radiations, provides the possibility to determine the system of three equations for the three unknown partial structure factors. In combination with isotope substitution techniques, ND is another method for PRDF determination. In [8] PRDFs of amorphous Ni 2B are obtained. Three samples in the form of a ribbon are prepared from 11 B and natural Ni, bcoh = 1.031 X w- 14 m, 60 Ni, bcoh = 0.283 X w- 14 m mixture of natural Ni and 62 Ni giving an average neutron scattering amplitude for Ni bcoh = 0.002 x 10- 14 m. From the PRDF, the authors conclude that a direct B-B contact in NhB glass exists. Strong chemical short-range order is confirmed which is reflected in the first-order neighbor distances. The authors in [8] suppose that a general amorphous structure is more probable than some special structures, corresponding to the crystalline counterparts. The isotope substitution method combined with x-ray diffraction is used to obtain complete sets of Si1 (Q) for metallic glasses Ni33 Y 67 and Cu33Y 67 [9]. It is established that PNi-Ni (R) differs greatly from Pcu-cu(R), whereas all other PRDFs show similarity. Note that Pij(R) are onedimensional functions and the determination of all of them is insufficient to deduce three-dimensional amorphous structure.

12.4 Nuclear Reactor as Neutron Source A conventional neutron diffractometer uses reactor neutrons. The fission reaction with thermal neutrons of 235 U (II1 = 586 barns) and 239 Pu (IIf = 748 barns) takes place in the reactor core. Each fission act produces 2-3 neutrons of energy spectrum,

N (E)

= e-E sh.J2E,

(15)

with E ｾ＠ 2 MeV. After thermalization in the moderator, the neutrons have Maxwellian distribution of the most probable velocity, Vp

=

f2kT , v--;;;;;

(16)

and

(17)

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S. Neov and V. Kozhukharov

where T is the moderator temperature, k is the Boltzmann constant. At 300 K the most probable neutron energy is Ep = 0.025 eV, which corresponds to Ap = 0.18 nm. This .A value is of the same order of magnitude as the interatomic distances in solids and permits effective diffraction studies of condensed matter. From the Ap formula we can conclude that the neutron spectrum may be changed by varying T values. In fact, this dependence is utilized in many reactors as a thermally isolated container with light atoms (H 2 , D 2 , He, Be, C) placed in the moderator or reflector volume. In the "cold" sources for small angle neutron scattering (SANS) studies of amorphous solids the neutrons are thermalized in liquid hydrogen or deuterium at T ｾ＠ 20 K. For investigations of amorphous solids, however, neutrons with shorter wavelength are necessary, .A :::; 0.1 nm, Qmax ｾ＠ lOOnm- 1 . From the spectral density expression, p (.X)

_x4 = 2cfJo Ｎａｾ＠

exp

( _x2) )./

,

(18)

it follows that the number of neutrons with .A < Ap decreases rapidly, and in practice only .A ｾ＠ 0.3.Ap are available for diffraction experiments. To enrich the spectrum with higher energy neutrons a thermally isolated graphite block is mounted near to the reactor core and is heated by reactor radiation up to 2400 K. At this temperature the quantity of 0.05 nm neutrons increases 15 times compared to the equilibrium spectrum. The extraction of neutrons from the reactor moderator is accomplished by special channels which can be straight or curved mirror guides. On the external end of a neutron guide, in the reactor biological shielding, a Soller type collimator is placed to limit the horizontal divergence of the neutron beam. For monochromatization Bragg reflections from Be, Si, Cu, Zn, Ge, Pb, monocrystals or pyrolitic graphite are used (all methods developed in x-ray optics are applicable). In front of the specimen and the detector Soller collimators fix the monochromator Bm and the diffraction 2() angles. For studies of the short-range order in non-crystalline solids it is possible, by decreasing the diffractometer resolution, to produce a considerable increase of the neutron intensity. The best steady state reactor for neutron diffraction investigations is the 57 MW high flux reactor at the Institute Laue-Langevin, Grenoble giving 1.2 x 10 15 ncm- 2 s- 1 thermal neutron flux in the reflector. A two-axis diffractometer is mounted at H8 beam tube from the hot neutron source D4, which is specially adapted for structural investigation of amorphous solids.

12.5 Neutron Detectors The neutron detector systems are based on the principle of product registration from nuclear reactions, taking place in the counter volume. Proportional detectors filled by a counting gas containing 10 B or 3 He nuclei are widely used. The following nuclear reactions with neutrons take place:

12. Neutron Diffraction in Amorphous Structures

+ n-+ 7 Li + a(Q = 2.3MeV), 3 He + n -+ 3 H + p(Q = 0.76MeV), 10 B

227

aa. = 3835 barns aa.

= 5333barns.

The high tension on the counter anode causes an additional gas ionization and the output signal is sufficient to be registered by standard techniques. An important advantage of these detectors is the low sensitivity to "( background, which always attends the reactor neutrons. The use of one or a few counters has several disadvantages: very long experiments - about two days, big samples, and measurement of the whole diffraction diagram before changing anything in the experiment. New versions of proportional counters (developed in the 70s) are position-sensitive detectors (PSD), using a digital technique, which can be multiwire or monowire with a resistive anode [10]. The scintillator PSD with a solid Li-glass converter has better resoluton. The efficiency of such a system is about 20%, which is 2-4 times smaller in comparison to a gas-filled PSD.

12.6 Time of Flight (TOF) Neutron Diffraction A new branch of neutron diffraction, successfully developed in the last 3 decades, is the TOF method. Its application for structural investigations began in 1963 [11]. Starting from the Bragg equation A = 2d sine, at fixed angle the variable parameter is,

A=

!!.._ =

ht . (19) mv mL If the "white" neutron beam passes through the specimen, measuring the neutron time of flight t = (2mL/h)dsin e of distance L between the source and detector, the interplanar spacing d can be determined. The wide interval of wavelengths from pulsed neutron sources, especially in the epithermal region, is very favorable for amorphous structure studies. In the case of amorphous solids the scattering vector is given by Q = 4nmL(sin8jht) and attains up to 500nm- 1 at A = 0.025nm. The first experiments with the TOF method were accomplished on stationary reactors, obtaining a pulsed neutron beam by mechanical choppers. The real potential of the method was realized after the building of pulsed neutron sources, such as pulsed reactors, electron linear accelerators and proton synchrotrons - "spallation" sources. In electron linear accelerators (LINAC) and proton synchrotrons, targets from 239 U or other heavy atoms are used. Slowingdown radiation in LINAC induces photo fission of target nuclei and fast neutrons (E ｾ＠ 2 MeV) are produced. As in reactors, the neutrons are thermalized in light atoms moderator, whose surface is considered as a neutron source in TOF experiments [12]. The most powerful 2nd generation pulsed spallation source is ISIS, at the Rutherford Appleton Laboratory. At 800 MeV proton energy and ｾ＠ 80 ｾＭｴａ＠ average beam current onto the target there are 3 x 10 16 fast neutrons per second.

228

S. Neov and V. Kozhukharov

On LAD-liquids and amorphous materials diffractometer many investigations of disordered materials were accomplished through the use of the TOF method [13]. The pulse reactors have neutron spectra, analogous to electron LINACs but one order of magnitude wider thermal neutrons pulse. The best machine in this class is the reactor IBR-2 [14]. Its peak power is Pmax = 8300 MW and average power P ｾ＠ 4 MW. The FWHM of thermal neutron pulse is ｾ＠ 150 ps, a value which satisfies the requirements of noncrystalline solids diffraction studies. The TOF diffraction pattern is superimposed on the neutron impulse, which has a complex form. For correct interpretation of the structural information, TOF experiments should include the following scattering measurements of: 1) specimen+ container; 2) vanadium or hydrogen standard; 3) container; 4) background without container [15]. The Q resolution of a TOF spectrometer is, LlQ

Q =

(

(-t ) Llt

(cot 8 Ll8)2 +

2

2 LlL ) + CL + Lo))

1/2

.

(20)

The cot8/8 term defines the stronger 8-influence on LlQjQ -in the interval of 28 E [10, 150°] LlQjQ decreases more than 10-fold. The spectrum form requires measurements at different scattering angles in the interval 5-160°. The basic requirement for TOF spectrometers is the simultaneous registration of neutrons with equal >. by separate detectors. It is shown in [12] that by suitable choice of the detector bank disposition this can be attained without strict collimation. Thus the high intensity of the neutron beam is maintained and the resolution is not reduced. The condition (L + L 0 ) sin(} = const. is fulfilled when tgnd = 0.5(L/Lo)cotB, tgnm = -0.5(LjL0 )cot8, where lld and ll!m are the angles between the detector plane and moderator plane in relation to the L and £ 0 directions, respectively. The same FWHM of interference maxima may be obtained by Soller collimators but with much lower intensity of the neutron beam. One of the most serious problems in TOF diffractometry of multicomponent amorphous objects is the separation of elastic and inelastic components in a neutron diffraction spectrum. In practice, an approximate procedure is used [12]. The method proposed by Placzek of correcting the static approximation, i.e. the assumption that the energy transfer is negligible (k ｾ＠ k0 ), accounts also for the recoil effects and appears to be sufficiently accurate. By optimization of TOF diffractometer parameters it is possible to minimize the inelastic scattering. For this purpose it is necessary to remove from the incident neutron spectrum the high energy neutrons which are not used in the analysis and to satisfy the relation L 0 j(L+Lo) « 1 at the high intensity so retained. A comprehensive description of LINAC TOF methods and some applications on liquid and amorphous materials structure studies are presented in [15]. Using the Harwell UK LINAC as the pulsed neutron source, diffraction patterns from vitreou Ge0 2 up to 350 nm- 1 are obtained. The better resolution in comparison to the steady state reactor methods is apparent in the second total RDFs peak which is clearly resolved

12. Neutron Diffraction in Amorphous Structures

ｾ＠

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I

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0

0

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I

-o-Te-0-Te-0

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229

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0 0 0 0\0 0 I II I I I I -0-Te-0-P-0-Te-0-P=O -o -Te-0-Te ·· 01

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I

I

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IX

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-O······Te-0-Te-0-Te-0-Te-0

0 =P-0-Te -0-

1

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0

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-0- Te ·· .. 0 -Te-0-Te -01

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Fig. 3. A schematic two-dimensional representation of Te02-P 20

5

glass network

on Ge-Ge and 0-0 distributions. Often, combined measurements by TOF and conventional ND methods are performed in order to avoid the disadvantages of the two techniques. Structural factors of glassy samples with composition (Sr;Ba(P03)2)x · (CaF2 · AlF3hoo-x, x = 5, 10, 20, 50, 100 are measured with this method [16]. The well separated interatomic distances allow one to determine partial co-ordination numbers for Al-F and P-0 pairs and to identify the basic structural units (AlF 6 and P0 4 ), which are similar to these in the corresponding crystalline materials.

12.7 Small Angle Neutron Scattering (SANS) Small angle neutron diffraction method permits the observation of large scale structures with clusters (particles) size from 1 nm to 100 nm. From the properties of the Fourier transform, [4], it follows that the diffraction intensity from objects of this size is concentrated in a small angle region, 0.2 < < 10- 6 radians, in the so-called "zero" peak. In conventional diffractometers the "zero" peak is inseparable from the instrumental broadening of the incident neutron beam. To make the measurement possible, SANS method applies "cold" neutron sources and filtration of the incident neutron flux by mirror guides or Be filters. In SANS, the angular interval (Q < 1nm- 1 ),(sinQR/QR) in (2) is practically constant and p(R) can be considered as continuous function of R. The results obtained by SANS permit the observation of inhomogeneities in the bulk specimen volume (due to the small neutron absorption cross-section). By SANS of very cold neutrons [17] in the Te0 2-P 20 5 vitreous system (Fig. 3) the concentration and clusters size are determined. At 20 mol% P 2 0 5 their concentration is 65 x 10- 14 cm- 3 and their diameter is about 10 nm. In a sample with 25 mol% P 20 5 the cluster concentration increases to 1.2 x 10 16 em - 3 , while the diameter is about 5 nm.

e

230

S. Neov and V. Kozhukharov

These results confirm the earlier conclusion [18] that at 26 ± 5 mol% P 2 0 5 there is a stable immiscibility in Te0 2 -P 2 0 5 glasses. combination of SANS and TOF methods is very powerful. The use of pulsed neutron sources and position sensitive detectors permits the construction of a TOF apparatus at L::.>.j >. 2 0.1 with performances, compatible to or better than the best x-ray small angle scattering instruments.

References 1. G. E. Bacon: Neutron diffraction (Third edition, Oxford University Press, part I, 1975). 2. M. Domenici, F. Pozza: J. Mater. Sci. 5, 746 (1970). 3. S. Neov, V. Kozhukharov, I. Gerasimova, K. Krezhov, B. Sidzhimov B: J. Phys. C (Sol. State Phys.) 12, 2475 (1979). 4. V. Sigaev, I. Yamzin, Y. Kedrovitz, Z. Konstant: Soviet J. Glass Phys. Chern., Consultant Bur. Trans!. 6, 513 (1980). 5. J. Dubois, J. Pannetrier: In Spontaneous vitrification in Tirio Cr4o alloys: Diffraction data, ILL Experimental Reports 1989. 6. E. Lorch E: J. Phys. C (Solid State Phys.) 2,229 (1969) 7. R. Kaplow, S. L. Strong, B. L. Averbach: Phys. Rev. 139, A1336 (1965). 8. E. Svab, L. Koszegi, S. Meszaros, S. Isakov, I. Sadikov: in Partial distributions in amorphous Ni 2 B, Workshop on neutron physics, Budapest-Hungary, 1986, pp. 145-148. 9. M. Maret, P. Chieux, P. Rister, M. Atzmon, W. L. Johnson W. L.: In Short range order in Ni33 Y67 and Cu33 Y67 amorphous ribbons, Proceedings of the fifth Conference on "Rapid Quenching and Solidification of Metals (RQ5) Wiirzburg, 1984. 10. P. Convert, E. Roudaut: New detectors for powders diagrams. Reactor Centrum Netherland Report -234 "New methods and techniques in neutron diffraction" (1975) p. 238. 11. B. Buras: Time-of-flight diffractometry. Reactor Centrum Netherland Report -234 "New methods and techniques in neutron diffraction" (1975) pp. 307-346. 12. C. G. Windsor, Pulsed Neutron Scattering (Taylor & Francis; London 1981). 13. R. Delaplane, U. Dahlborg, W. S. Howells: Neutron Diffraction Study of Amorphous Boron. Annual Report ISIS-1988, p. A52. 14. Y. Alexandrov, E. Sharapov, L. Czer: Moskwa-Energoizdat 132 (1981). 15. R. Sinclair, D. Johnson, J. Dore, J. Clarke, A. C. Wright: Nucl. Instr. Methods 117, 445 (1974). 16. W. Matz, U. Barenva1, M. Dubei1: Phys. Status Solidi 90, 107 (1985). 17. S. Neov, I. Gerasimova, P. Mikula: In Neutron Diffraction Investigation of the Short-Range Atomic Order in Tellurite Glasses, Proceedings of an International Conference on Advanced Methods in X-Ray and Neutron Structure Analysis of Materials, Czechoslovakia (1987). 18. S. Neov, I. Gerasimova, V. Kozhukharov, M. Marinov: J. Mater. Sci. 15, 153 (1980). 19. V. F. Sears: Neutron News 3, 26 (1992).

Subject Index

32 AAS (atomic absorption spectrometry) 3,8 absorber 204 accuracy, analytical 198 acidity, zeolite catalyst 134 Ackerman method 46 activation energy 95 - effective 106 adsorption 114 ageing 161 agglomeration 159 Al/SiC composite 59 Ab03 69 alloy - microalloys 3 - steel alloys 3 Al-Sc-Gd garnets (GSAG) 5 alumina 71, 73, 161, 162 aluminum sheet - deformed 183, 185 - rolled 177 amorphous materials/solids 138, 220 - neutron scattering 223-225 analytical programs, precalibrated 195 analyzer crystals 190 anisotropy 170 annealing 157, 158 - of surface roughness and defects 162 apex, single/round/successive 89, 90 argon 152 arrhenian viscosity /network liquids 138 - properties, table 139 atomic emission spectrometry, inductively coupled plasma (see ICP-AES) atomic position, localization 222 atomic resolution imaging 77 Au 22 - electrodeposited 30 - vapor deposited 30 a (exponent)

austenitic steel

58

(J (exponent) 31 (]-activity measurement, 85 Kr 156 B 4 CP-Al cermets 54 background correction 173 BaO-Pr203-Ti02 composition system

54 barrier height 20 base-lines 87 BaTi03 5 beam electron diffraction, convergent (see CBED) beam filter, primary 190 beam spreading 52 beam-bending method 147, 148 beidellite 162 BeO structure 60 boehmite 162 Bragg disc 48 Bragg's law 170 bright-field shadow image 43 Burger - model 143 - vector 54 calibration curve, Fe in steel 194 calorimetry, differential scanning (see

DSC) catalysis - of rare earths 4 - use of zeolite 115 catalytic potency 91 cathode ray tubes 5 cation-exchange 114 CBED (convergent beam electron diffraction) - applications 54-59 - basis and application 41-61

232

Subject Index

- characterization of ceramic powders 46-52 - future of the method 59, 60 - high spatial resolution CBED (HSCBED) 60 - large angle CBED (LACBED) 48,51 - patterns symmetries, table 49 - practical aspects 52, 53 cells 87 cementious binders, hydration 162, 163 ceramics/ceramic materials - advanced materials 11, 12 - ceramic matrix composites (CMC) 70 - electronic 5 - electro-optical 5 - monophase 68,69 - polyphase 69 chabazite 117 chemical history 159 chemical shift 203-205 chondrites 8, 9 chromatography, ion-exchange 7 - chromatographic concentration and separation 9, 10 clay minerals, thermal behavior 162 coatings 157 collimator 190 compression, cylinder 147 computation 76 contrast transfer function (CTF) 65 copper, colloidal 74 coprecipitation 152 correction - background 173 - defocalization 173, 174 - diffraction volume 174, 175 corrosion - anti-corrosive agent 164 - reaction 157 - testing 163, 164 crockery, decorated 5 crystal/ crystallographic - ionicity, measurement 59 - point group 48 -- relation between diffraction groups, table 50 - space group 44 -- determination by CBED 48 - symmetry 44, 178 -- determination by CBED 47-52 - texture 169, 179 crystallization 91

- recrystallization 157 CTF (contrast transfer function) 65 a Cu-Al alloy 96 ff. - activation energies, table 99 cubic symmetry 181 CVD (chemical vapor deposition) 161 cycling, thermal 91 cymrite 120 dark-field - in amorphous areas and HREM 76 - patterns 49 - shadow image 43 deconvolution 87 defect - annealing 162 - lattice defect 153 - point/planar 44 - structure defect -- annealing 157 -- diagnostic of the state 157 defocalization correction 173, 174 dehydroxylation 116 density of states, local (LDOS) 22 detector overflow 196 diamond films 26 diffraction group 48 - relation between crystal point groups, table 50 diffraction volume, correction 174, 175 diffraction - convergent beam electron diffraction (see CBED) - electron microdiffraction 41, 42, 60, 69 - methods, review 220-223 - neutron diffraction (ND) 220-230 - selected area diffraction patterns (SADP) 41, 42 - x-ray diffraction 169-185 diffusion - coefficient 26, 158 - in the matrix 153 - process 155 - technique 151, 152 - time 100 diffusion structural analysis (see DSA) dilatrometry 156 discrete method 180 dislocation density 106 disordered systems - imaging by STM 29-37 - topography 17

Subject Index divacancies 107 DO state 98 domains, twinned 58 doublets 211 drying 161 DSA (diffusion structural analysis) - apparatus, scheme 156 - applications, examples 158-165 - basic principles 151 - inert gas, release from solids 151 -- measurement 155, 156 -- mechanisms and theories 153-155 - potential use 157, 158 - sample preparations 151-153 DSC (differential scanning calorimetry) - experimental results 96-110 - theoretical basis 85-96 - thermograms, quenched alloys 97, 98 DTA (differential thermal analysis) 86, 156 durability, materials 157 EFT EM (energy filtering transmission electron microscopy) 59 elastic/inelastic components, separation 228 electrical properties, zeolite 129 electron/ electronic - density 205 - interactions with atoms 220 - scattering 221 - state 17 - structure 208 elements 201 ELNES (energy loss near-edge structure) 71 energy transition 200 enthalpy, changes 88 eq uili bri urn/ noneq uili brium processes 91-94 equivalent temperature 102 Euler angles/space 178 eutectic fusion 90 Ewald sphere 45 exponent - (3 32 - (3 31 exponential factor, pre- 95 extension, fiber 147 a-Fe 210 a-Fe203 spectrum FeF3j-compound 209, 210

233

Fe06, deformation 212 FETEM (field emission gun) 51, 77 fiber texture 176 field emission gun (FETEM) 51, 77 fluorescence spectrometry, x ray (see XRF) foil thickness, determination by CBED 46,47 FOLZ (first order Laue zones) 44 Fourier filtering 70 Fourier-transform 224 fractal - local dimension 32 - self-affine 30 fringes - high resolution electron fringes imaging (HREFI) 66 - Kossel-Mollestedt fringes 46, 52 fusion, eutectic/peritectic 90 garnets - Al-Sc-Gd garnets (GSAG) 5 - Gd-Fe garnets 6 - yttrium-aluminium garnets (see YAG) - Y-Fe garnets 6 Gd-Pt 11 Ge detectors, Li-doped 7 geleous materials 157 - characterization 159-165 Geo-Quant program 197 ghost image 52 Gjonnes Moodie lines 48 glass/-ceramics - and rare earths 4, 5 - optical glass 4 - studied by HREM 74 - transition 91-94, 162 - viscosity parameters, table 141 glassy pocket 61 glide planes 48 global textures 184 goethite 162 gold over silicon 74 goniometer, texture 171 ff. Goss orientation 183 grain - boundaries 153 -- oxide and non-oxide ceramics 69-72 - organization 171 - orientation 176-179 graphite 22 - crystal 54 - sphenoidal 3

234

Subject Index

gyromagnetic factor

207

harmonic method 179 - principles 180, 181 heat treatment, preparation of inorganic materials 158, 159 heating rate 90 heterogeneous nucleation 91 heulandite 117 hexagonal symmetry 181 hollow-cone beam method 59 holographic method 76-81 - holographic transmission microscopy 79 HOLZ (higher order Laue zones) 43 HREFI (high resolution electron fringes imaging) 66 HRELI (high resolution electron lattice imaging) 66 HREM (high resolution electron microscopy) - applications, key examples 68-76 - fundamentals 64, 65 - future prospects 76 - holographic HREM (HHREM) 80 - operating procedures and instrumental requirements 65-68 HSCBED (high spatial resolution CBED) 60 hybrid materials 158 hyperfine splitting, magnetic 206, 207 IBR-2 reactor 228 ICP-AES (inductively coupled plasma atomic emission spectrometry) 8-10 ICP-MS (inductively coupled plasmamass spectrometry) 3, 8-10 indentation techniques 148 indentor, cylindrical 149 inert gas/-atmosphere (see also DSA) - diffusion, activation enthalpy 154, 158 - produced from nuclear reactions 152 - release from solids 151,153-155 - sample preparation 152 inflection point, frontal/terminal, TA curve 88 inorganic materials 68 - characterization by diffusion structural analysis 151-165 interaction - solid-gas 157 - solid-liquid 157

- solid-solid 15 7 interfaces, oxide and non-oxide ceramics 69-72 invariant points 90 ion bombardment 152, 154 iron chemistry 208 iso-density lines 182 isomer shift 203-205 isothermal/nonisothermal 85 isotope ;mbstitution technique 225 isotopes, Mossbauer 199 - and transition 201, 202 Johnson- Mehl-A vrami-ErofeevKolmogorov model 96 kaolinite 162 Kelly method 46 Kelvin solid 142 Kikuchi -lines 43,53 - pseudo-Kikuchi pattern 170 kinetic 88 first-order kinetic law 101 model function 95 overall kinetics 100-103 - parameters/laws 99, 100 - studies 94-96 kinetical analysis, nonisothermal 99 Kissinger's peak-shift method 99 Kossel-lines 43 Kossel-Mollestedt fringes/diagram 46, 52 krypton 152,153 labeling - radioactive labeling technique 157 - samples 152 lanthano-zirconate-tantalate (PLZT) 5 LASER 5 lathanides 10 lattice defects 153 high resolution electron lattice imaging (HRELI) 66 - parameters 46 reciprocal 45 Laue zones - first order (FOLZ) 44 - higher order (HOLZ) 43 - zero order (ZOLZ) 43 LDOS (local density of states) 22 lead titanate

Subject Index - modified with gadolinium and manganese (Gd-Pt) 11 - lead titanate-zirconate (PLZT) lepidocrocite 162 light elements 193 lines - base-lines 87 - Gjonnes Moodie lines 48 - iso-density 182 - Kikuchi-lines 43, 53 - Ki.issel-lines 43 local textures 184

11

magnesia 162 magnetization direction 169 magnets, permanent 6 mass absorption coefficients, table 194 matrix effect 188, 193 MDP (microdiffraction patterns) 41, 60,69 Metal-Quant program 198 metamict phase 1.58 metastable phases, crystallization and transformation 94 MgO non-centrosymmetric crystals 59 microalloys 3 microdiffraction, electron 41 - microdiffraction patterns (MDP) 41, 60,69 microdomain regions 69 microscopy - high resolution electron microscopy (see HREM) - holographic transmission microscopy 79 - scanning tunneling microscopy (see STM) - transmission electron microscopy (see TEM) microstructure, intrinsic 80 MMC (metal matrix composites) 70 Mn-Zn ferrrite 44 modulated structure 78 montmorillonite 162 mordenite 117 Mi.issbauer isotopes 199 - and transition 201, 202 Mi.issbauer spectroscopy - basic characteristics, Mi.issbauer spectra 203-207 - bonding 208-218 - fundamental equations 200 - instrumentation 202, 203

235

- isotopes and transition 201, 202 - interpretation 207, 208 mullite materials 48, 72-74 - application of CBED 54-59 multilayert thin film 188 multitasking 193 muscovite micas 60 natrolite 120 ND (neutron diffraction) 220-230 - time of flight (TOF) ＲＷｾＹ＠ Ndz03 4 Nd-Fe-B 6 neutron - detectors 226 - interaction with atoms 220 -source 225,226 - very cold neutrons 229 Newton's viscous deformation 142 Newtonian liquid/flow 142, 143 niobate materials 69 NNA (nuclear neutron activation) 3, 7 atomic absorption spectrometry (see AAS) nucleation, heterogeneous 91 nuclides - parent nuclide, radioactive decay 154, 155 - stable nuclides, measurement 156 ODF (orientation density function) 169 - determination 176-185 -- ambiguity 181, 182 - representation and examples 182, 183 ordering effect 59 - short-range 96 ff. - two-stage 98, 102 orientation density function (ODF) 169 orientation space 178 parallel-plate technique 149 parent nuclide, radioactive decay 154, 155 patterns - dark-field patterns 49 - microdiffraction patterns (MDP) 41, 60 - pseudo-Kikuchi pattern 170 - selected area diffraction patterns (SADP) 41, 42 symmetries, table 49 Tanaka-patterns 48, 51

236

Subject Index

- zone axis pattern (ZAP) 53 peak area, TA curve 88 peak-shift method, Kissinger 99 PEELS (parallel electron energy loss spectroscopy) 70 peritetic fusion 90 phase - factor 65 - transformations 60, 72-74 phase contrast method, Zernike 80 phase diagram boundary, determination 89-91 phillipsite 119 phosphovanadate 5 1-photon 204 piezoelectric elements 20 plasma-mass spectrometry, inductively coupled (see ICP-MS) PLZT (lanthano-zirconate-tantalate) 5, 11 Polanyi-Wagner equation 121 pole density 175 - function 180 pole figure - measure, principles 170 - normalisation 175 - representation 175, 176 polycrystalline materials 169, 184 porcelain 5 pores 153 powders - characterization 46-52 - reactivity, testing 164, 165 Prz03 4 process control, XRF 192 product registration 226 protective agent 164 PSZ (partly stabilised zirconia) 55 Pt 22 pulse reactor 228 pumice 131 PVD (physical vapor deposition) 161 quadrupole splitting 206, 213 quality control 192 quenched samples 85 quenching conditions, effect 104 radial distribution function (RDF) 74 radioactive labeling technique 157 radium atom 155 radon 152, 153 RDF (radial distribution function) 74

RE (rare earths) 3-12 reacting sintering 72 reaction kinetic (see kinetic) reaction-order model, basic 96 reactor - IBR-2 reactor 228 - pulse reactor 228 reciprocal space 65 recoil/-energy 154 recrystallization 157 reduced time 99 refractory 69 - materials 6 relaxation time 100 resolution - CBED 52 - STM -- atomic 22 -- vertical/lateral 19 rheological models/behavior, liquids 141-144 roughness 29 - surface, annealing 162 SADP (selected area diffraction patterns) 41,42 saponite 162 121 Sb 218 scaling, dynamic 30 scan 196 scanning tunneling microscopy (see STM) scattering - electron-scattering 221 - neutron scattering 223-225, 223-225 - small angle neutron scattering (SANS) 229,230 - x-ray-scattering 221 Scherzer focus/defocus 67, 80 selected area diffraction patterns (SADP) 41,42 self-diffusion 105 semiconductors 193 Sestak-Berggren model 96 shadow image, bright-field/dark-field 43 short range order (see SRO) Si3N4 69 SiC 69 sieving, molecular 114 silica gel 161 - sol-gel transition during formation 159,160 Silicium 51

Subject Index silicon 54 - silicon carbide ceramics 72, 73 silver over carbon 74 sintering 157 Si02-Zr02-B203 frit 5 Sm-Co 6 119 Sn 213, 216 sol-gel 159, 161 solid - solution effect 55, 59 - gas interaction 157 - liquid interaction 157 - solid-solid interaction 157 - solid-state reaction 165 solidification 91 solute-vacancy/-complexes 104, 105, 110 spatial resolution 52 - high spatial resolution CBED (HSCBED) 60 spectrometry/ spectroscopy atomic absorption spectrometry (AAS) 3,8 - atomic emission spectrometry, inductively coupled plasma (ICP-AES) 8 - Moss bauer spectroscopy (see there) - parallel electron energy loss spectroscopy (PEELS) 70 - plasma-mass spectrometry, inductively coupled (ICP-MS) 3, 8-10 - x-ray fluorescence spectrometry (see XRF) spellation sources 227 spinel type structure 69 spinodal decomposition phenomena 77 splitting, quadrupole 206, 213 spreading, beam 52 SRO (short range order) 220 - parameter 102 -- concentration dependence 107-110 - state 97 stacking fault 78 standardless, XRF analytical programs 195-197 steel - steel alloys 3 - austenitic steel 58 - Fe 3%Si steel (grain oriented steel) 176,183,184 - stainless steel 54 STM (scanning tunneling microscopy) - applications 22-37

237

- basic operating/-modes constant heigh mode 19 -- principles 17-20 -- topographic mode 19 - disordered systems, imaging 29-37 - resolution -- atomic 22 -- vertical/lateral 19 - STM design, schematic 18 - surface reactions 26-29 - theoretical outline 21, 22 stress field 57 strontium ferrate 211 structure/nanostructure change 160 structure defect 157 supersaturation 106, 107 surface area determination 157 surface - disorders 32 - labeled surface 163 - rough surface, STM Applications 3137 - steady state 32 - width 31 symmetry - crystal symmetry 44, 178 -- determination by CBED 47-52 - cubic/hexagonal 181

TA (thermal analysis) 85 - curves, characterization 86, 87 - differential scanning calorymetry (see calorymetry) - differential thermal analysis (DTA) 86,156 - information content 88, 89 - phase diagram boundary, determination 89-91 - thermogravimetry/ differential thermogravimetry (TG/DTG) 156 - in zeolite research and application 112-135 Tanaka method/patterns 48, 51 125 Te 216 technological properties, HREM 80 TEM (transmission electron microscopy) 41 - energy filtering TEM (EFTEM) 59 - high resolution electron microscopy (see HREM) - specimen preparation and operation 52,53

238

Subject Index

temperature - characteristic 92 - equivalent 102 Te02-P205 glass network 229 Te03-Li20 glass 223 texture analysis, equation 179, 180 texture goniometer 171 ff. TG /DTG (thermogravimetry/ differetial thermogravimetry) 156 thermal - cycling 91 - history 159 - treatment, characterization of gels 160 thermodielectrical curve, zeolite 130 thermogram, DSC for quenched alloys 97,98 thermometric 88 thickness, determination by CBED 46, 47 thin-film 157 - labeling 158 thoria 162 Ti2Nb10029 68 TiN (fine-grained polycrystalline thin film) 176, 183 titania 161 TOF (time of flight) 227-229 trace indicators 151 transformation dynamics 88 transition, glass 91-94, 162 tunneling current 18, 21, 22 TZP (polycrystal tetragonal zirconia doped) 55 undercooling urama 161

91

V203 crystals 69 vacancy - behavior 104-107 - equilibrium vacancies 100, 110 - excess vacancy /-mechanism 100, 103, 104, 107, 110 - migration 105 - mobility 109, llO - solute-vacancy/-complexes 104, 105, 110 - supersaturation 106, 107 vapor deposition, chemical (CVD)/physical (PVD) 161 vaporization, electrothermal 8 vermiculite 162

viscosity /viscous flow 93 - arrhenian viscosity/ -network liquids 138, 139 - determination 144 - measurement techniques 144-149 - physics 138-141 - range, table 145 - rheological models 141-144 Vogel- Fulcher-Tamman equation 139 Warren-Cowley parameter 102 water - desorption kinetics 121 - types 116 wavelengths, XRF 187 Williams-Landau-Ferry-equation

140

xenon 153 - gamma-active radionuclides, measurement 156 x-ray - diffraction, texture determination 169-185 - interaction with atoms 220 - scattering 221 - tubes 190 XRF (x-ray fluorescence spectrometry) 3, 10, 1l - analytical capability 187, 188 - analytical programs, precalibrated 194-198 - application 192, 193 - data evaluation 193 - instrumentation 190 - light element analysis 193 - preparation 188-190 - sample handling 191 Y203 6 Y- Fe garnets 6 YAG (yttrium-aluminium garnets) 5 - cubic particles 46 YAl03 perovskite oxide (YAP) 46 YAP (YAl03 perovskite oxide) 46 yttrium oxysulphide, Eu-activated 5 Y-TZO / Ce (tetragonal zirconia stabilized with ceria and yttria) 11 ZAP (zone axis pattern) 53 zeolite 4 - adsorbate/framework interactions 133, 134

Subject Index - chemistry 113 - catalyst -- acidity distribution, estimation 134 -- modification 134, 135 -- thermal characterization 132, 133 - content in multicomponent mixtures 129-132 - decomposition and gas evolution 123-126 - electrical properties 129 - features, chemical and structural, table 115 - highly-siliceous 132 - lattice 112 - minerals 112 - order-disorder transformation 126, 127 - phase transition 126, 127 - properties and applications 113-115 - structure collapse, recrystallization, melting 127-129

239

- synthetic zeolite 112 - thermal behavior 116 - water loss 116 Zernike phase contrast method 80 zirconia 161 - application of CBED 54-59 - composites 55 - inter-/intragranular 73, 74 - interphase 74 - martensitic transformation of tetragonal to monoclinic 61 - monoclinic 58, 72 - partly stabilised zirconia (PSZ) 55 - polycrystal tetragonal zirconia doped (TZP) 5.5 - tetragonal stabilized with ceria and yttria (Y-TZO/Ce) 11 ZOLZ (zero order Laue zones) 43 zone axis pattern (ZAP) 53 ZrSi04 73

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