Table Of ContentVictor A. Drits
Electron Diffraction
and High-Resolution
Electron Microscopy
of Mineral Structures
With 126 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Professor Dr. VIClOR A. Durs
Geological Institute of the
Academy of Sciences of the USSR,
7 Pyzhevsky per
109017 Moscow, USSR
Translated from Russian by:
BELLA B. SMOLIAR
Geological Institute of the
Academy of Sciences of the USSR
7 Pyzhevsky per
109017 Moscow, USSR
Title of the original Russian edition:
Strukturnoye issledovaniye mineralov metodami mikrodifraktsii i elektronnoi
mikroskopii vysokogo razresheniya
© by Nauka. Moscow 1981
ISBN-13:978-3-642-71731-4 e-ISBN-13:978-3-642-71729-1
DOl: 10.1007/978-3-642-71729-1
Library of Congress Cataloging-in-Publication Data. Drits, Viktor Anatol'evich. Electron dif
fraction and high resolution electron microscopy of mineral structures. lhmslation of:
Strukturnoe issledovanie mineralov metodami mikrodifraktsii i elektronnoi mikroskopii
vysokogo razresheniia. Bibliography: p. Includes index. I. Mineralogy, Determinative. 2. Elec
tron microscopy. 3. Optical mineralogy. I. Title. QE369.M5D7513 1987 549'.125 86-33874
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Preface
The decision of Springer-Verlag to publish this book in English
came as a pleasant surprise. The fact is that I started writing the
first version of the book back in 1978. I wished to attract attention
to potentialities inherent in selected-area electron diffraction
(SAED) which, for various reasons, were not being put to use. By
that time, I had at my disposal certain structural data on natural
and synthetic minerals obtained using SAED and high-resolution
electron microscopy (HREM), and this stimulated my writing this
book. There were several aspects concerning these data that I
wished to emphasize. First, it was mostly new and understudied
minerals that possess the peculiar structural features studied by
SAED and HREM. This could interest mineralogists, crystallo
chemists, and crystallographers. Second, the results obtained indi
cated that, under certain conditions, SAED could be an effective,
and sometimes the only possible, method for structure analysis of
minerals. This inference was of primary importance, since fine
dispersion and poor crystallinity of numerous natural and synthe
tic minerals makes their structure study by conventional diffrac
tion methods hardly possible. Third, it was demonstrated that in
many cases X-ray powder diffraction analysis of dispersed miner
als ought to be combined with SAED and local energy dispersion
analysis. This was important, since researchers in structural min
eralogy quite often ignored, and still ignore even the simplest in
formation which is readily available from geometrical analysis of
SAED patterns obtained from microcrystals. Thus it is commonly
neglected that SAED, as compared with X-ray powder diffrac
tion, is a simpler technique for determination of unit-cell parame
ters and revealing superperiodicity, commensurate and incom
mensurate modulated structures, intergrowth, and other types of
structural imperfection. At the same time, there are numerous ex
amples of invalid structural and crystal-chemical conclusions
based on X-ray powder diffraction alone.
SAED structure analysis of minerals, however, was shown to
be possible only if there were clear understanding of the processes
resulting from the interaction between electrons and the crystal.
Specifically, the relationship between reflection intensities and
structure factors should be established correctly.
VI Preface
Electron diffraction (ED) is closely associated with HREM.
The progress in HREM and, in particular, in HREM of minerals,
has been especially successful since 1971. The development and
undeniable advantages of HREM, however, do not at all mean
that the latter can be used to solve all kinds of structural problems
and that the role of SAED may be restricted to geometrical analy
sis of diffraction patterns. In other words, HREM and SAED
supplement each other, but HREM cannot replace SAED.
The above considerations have predetermined the composition
of the book, which consists of two main parts. The first part deals
with theoretical and methodological foundations of ED and
HREM, and with their relative merits for mineral structure stud
ies. The results obtained by a number of well-known scientists
such as Bethe, Blackman, Cowley, Heidenreich, Hirsch, Vainsh
tein, and others have been used. I have attempted to present this
material in such a way that readers who have no special training in
this field but are familiar with the fundamentals of crystallogra
phy and crystal chemistry of minerals could grasp the contents.
My aim was that the reader should grasp the general outline of the
physical foundations of the methods involved, their advantages
and limitations, problems in structure analysis and methods for
interpreting experimental data, and that he should be able to read
modern periodicals on this subject. The second part contains both
the original and the reported results of SAED and HREM struc
ture studies of minerals having mostly layer and chain structures.
Special attention is given to methodological procedures for the so
lution of specific structural problems.
In the new version of the book, the main contents have re
mained unchanged. At the same time, I have included new experi
mental data on mineral structure studies by SAED and HREM in
which I have taken part. This concerns, in particular, the struc
tures and structural peculiarities of manganese minerals. I have al
so taken account of the most important, to my point of view, the
oretical, methodological and experimental results published in the
literature in recent years. I was especially pleased to include those
works where SAED was used as a method for structure analysis. I
have additionally included a chapter on oblique-texture electron
diffraction (OTED). Books on this method, Structural electro
nography by Vainshtein (1956) and Electron diffraction analysis
of clay mineral structures by Zvyagin (1967), were published in
English earlier. However, the advantages of OTED for the struc
ture studies of finely dispersed minerals, and especially of phyllo
silicates, have been largely underestimated in the West. The chap
ter in question shows that an increase in precision for the estima
tion of reflection intensities provides a new level in structure re
finements of complex polycrystalline substances. Examples are
given of the advantages of OTED over X-ray powder diffraction
Preface VII
for the study of extremely poorly crystallized minerals such as
smectites.
In the first part of the book, the chapter devoted to the forma
tion of phase contrast in HREM has been extended: direct crystal
structure determination methods based on the combination of
HREM and SAED data are considered; the concept of a pseudo
weak phase-object, simulation of HREM images and the advan
tages of high-resolution high-voltage electron microscopy, etc. are
discussed.
The section "Structural modulations resulting from the lateral
misfit of octahedral and tetrahedral sheets in phyllosilicates" has
been included in the second part of the book. Structural features
of chain silicates revealed by HREM are here discussed in greater
detail.
The writing of this book became possible owing to my success
ful collaboration with a number of colleagues in the Geological
Institute (GIN) of the USSR Academy of Sciences, as well as in
other institutes. In this connection, I would like to thank A. L.
Dmitrik, GIN, Moscow, who worked together with me for many
years, spending hours and hours at the electron microscope to ob
tain the experimental material required.
Dr. N. I. Organova, IGEM, Moscow, and I have used SAED
for the first time to determine a number of mineral structures un
known before. Her contribution is gratefully acknowledged. Par
ticular thanks are due to Academician F. V. Chukhrov and Dr. A.
I. Gorshkov, IGEM, Moscow, with whom I have been successful
ly working for the past decade on the crystal chemistry of man
ganese minerals, using SAED as the main means for structure
analysis.
Prof. lu. I. Goncharov (Polytechnical Inst., Belgorod) and
Dr. I. P. Hadji (VNIISIMS, Moscow) were the first to synthesize
new-type triple-chain silicates of various compositions, and Dr.
N. D. Zakharov (IKAN, Moscow) obtained the HREM images of
these structures that are given in this book. I am deeply grateful to
them all. In particular I thank Dr. I. P. Hadji with whom I
worked intensively on the problems of interpretation of SAED
patterns from various chain silicates.
I particularly wish to express my deep gratitude to Prof. S.
Guggenheim, University of Illinois, Chicago, USA, for providing
unpublished data and a number of original photographs. These
exceptionally elegant results have formed a basis for the section
on modulated structures. I am also grateful to Dr. A. Plan~on,
Orleans University, France and Dr. S. I. Tsipursky, GIN, Mos
cow for their contribution to OTED studies.
For a number of years I have been a constantly admirer of the
excellent works of Prof. P. R. Buseck, Arizona State University,
USA and Prof. Dr. R. Veblen, The John Hopkins University,
VIII Preface
Maryland, USA, and I am pleased to thank them for providing a
list of their papers and numerous preprints. Although the size of
the book has not allowed including all their data even in brief,
many of their results have been referred to.
Prof. B. B. Zvyagin, IGEM, Moscow, kindly agreed to read
the page proofs of Chapters 9, 10, and 11. He found a number of
errors and made valuable comments, for which I express my sin
cere gratitude.
Thanks are due to L. G. Daynyak, A. L. Sokolova, G. V. Kar
pova, G. V. Sokolova and E. V. Pokrovskaya for kind assistance
in the preparation of the manuscript.
VICTOR A. DRITS
Contents
Introduction ....................................... 1
1 Geometrical Features of the Crystal and the Reciprocal
Lattices............................................ 4
1.1 Crystal Structure and Crystal Lattice ................... 4
1.2 The Bragg Equation. Reciprocal Lattice. Relationships
Between the Indices of Lines and Planes in the Direct and
Reciprocal Lattices .................................. 6
1.3 The Ewald Sphere and the Geometrical Interpretation for
Diffraction Patterns ................................. 11
2 The Kinematical Theory of Scattering of Electrons by
Crystals. Intensity of Diffraction Reflections ............ 14
2.1 Wave-Like Properties of Electrons ... . . . . . . . . . . . . . . . . . . 14
2.2 The Kinematical Theory of Scattering of Waves by Crystals 14
2.3 Behavior of Electrons in Medium, the SchrOdinger
Equation, Its Solution in the Kinematical Approximation. . 24
2.4 Atomic Scattering Amplitudes, or f-Curves . . . . . . . . . . . . . . 29
2.5 Structure Amplitude and Structure Factor. . . . . . . . . . . . . . . 32
2.6 Reflection Intensities in Point Electron Diffraction Patterns
in Terms of the Kinematical Approximation ............. 34
3 Geometrical Analysis of Point Electron-Diffraction
Patterns........................................... 43
3.1 Raypath in a Transmission Electron Microscope for
Imaging and Selected Area Diffraction ................. 43
3.2 Methods for Interpretation of Point Diffraction Patterns:
Indexing and Determination of Unit Cells ............... 45
3.3 Simulation of Diffraction Patterns for Objects with Known
Unit Cell and Space Symmetry ........................ 47
3.4 Interpretation and Simulation of Diffraction Patterns for
Triclinic Lattices with a Fixed Coordinate Plane . . . . . . . . . . 48
x
Contents
3.5 Determination of the Bravais Cell and the Space Group.
Secondary Diffraction Effects . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Diffraction Methods in Structure Analysis .............. 55
4.1 Fourier Series and Integrals: Their Role in the Theory of
Diffraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Fourier Series: Representation for the Electrostatic
Potential and Use in Structure Analysis ................. 59
4.3 The Trial-And-Error Method ......................... 64
4.4 Interatomic Vector Space. Patterson Function: Properties
and Application to Structure Analysis .................. 65
4.5 Direct Phasing Methods .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 Refinement of Atomic Coordinates by the Least-Squares
Method............................................ 69
5 Dynamical Theory of Electron Diffraction
(Two-Beam Approximation) .......................... 70
5.1 Quantum-Mechanical Solution. .. . ... . . .. . . .... ... .... 70
5.2 Integrated Diffraction Intensity in Terms of the Two-Beam
Dynamical Theory .................................. 81
5.3 Criteria for the Range of Validity of the Kinematical
Approximation ..................................... 83
6 Dynamical n-Beam Scattering of Electrons .............. 85
6.1 The "Physical Optics" Approach ...................... 85
6.2 Numerical Methods for Calculation of Diffraction
Patterns ........................................... 96
7 Electron Diffraction and High-Resolution Electron
Microscopy ........................................ 102
7.1 Diffraction Effects and Formation of High-Resolution
Electron-Microscopic Images ......................... 102
7.2 Fraunhofer Diffraction: An Intermediate Stage in the
Transfer of Information Between the Object and the
Image............................................. 103
7.3 Factors Defining the Contrast in Electron-Microscopic
Images............................................ 107
7.4 Contrast in Electron-Microscopic Images of Thin Crystals. 118
7.5 Direct Crystal Structure Determination Methods Under the
WPOA ............................................ 135
7.6 High-Resolution Electron Microscopy (HREM) of Crystals 137
Contents XI
7.7 HREM and Real Structure of Crystals .................. 142
7.8 Simulation ofHREM Images ......................... 144
7.9 High-Resolution High-Voltage Electron Microscopy
(HRHVEM) ........................................ 147
8 Oblique-Texture Electron Diffraction .................. 149
8.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.2 OTED Patterns: Peculiarities of Geometrical Arrangement
of Reflections and Integrated Intensities ................ 150
8.3 Two-Dimensional Intensity Distribution in OTED
Patterns ........................................... 154
8.4 Factors Affecting Diffracted Intensities. . . . . . . . . . . . . . . . . 157
8.5 A Technique for OTED Intensity Measurements ......... 159
8.6 Crystal Structure Refinements of Mica Polytypes on the
Basis of Electronometric Intensity Measurement ......... 161
8.7 Determination of Hydrogen Positions in Mica Structures by
OTED ............................................. 166
8.8 Study of Octahedral Cation Distribution in 2: 1 Layers of
Dioctahedral Smectites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
9 SAED and HREM Study of Mixed-Layer Minerals ....... 177
9.1 Hybrid-Structure Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.2 Structure Analysis of Hybrid Minerals . . . . . . . . . . . . . . . . . . 178
9.3 Crystal Structure of Tochilinite . . . . . . . . . . . . . . . . . . . . . . . . 179
9.4 Structure Analysis of Minerals Related to Tochilinite ..... 188
9.5 The Crystal Structure of Valleriite ..................... 193
9.6 A Three-Component Hybrid Mineral Containing Brucite-
Like, Sulfide and Silicate Layers ..... . . . . . . . . . . . . . . . . . . 197
9.7 Forms of Structural Heterogeneity ... . . . . . . . . . . . . . . . . . . 197
9.8 Structure Study of Asbolanes ......................... 203
9.9 Analysis of Basal Reflection Intensities in SAED Studies of
Mixed-Layer Minerals ............................... 208
9.10 Structure Studies of Mixed-Layer Minerals by HREM . . . . . 213
10 SAED and HREM Study of Order/Disorder and Stmctural
Heterogeneity in Layer Minerals ....... . . . . . . . . . . . . . . . . 217
10.1 A New Mica NaMg3(Si3.sMgo.s)OlO(OHh Having a Talc-
Like Stacking Sequence .............................. 218
10.2 Diffraction Effects from Layer Structures Having Partially
Ordered Cation Distribution .......................... 220
10.3 Structural Modulations Resulting from the Lateral Misfit of
Octahedral and Tetrahedral Sheets in Phyllosilicates ...... 233
