Theories and techniques of crystal structure determination
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| Sprache: | English |
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Oxford [u.a.]
Oxford Univ. Press
2007
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | IUCr texts on crystallography
9 |
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| adam_text | THEORIES AND TECHNIQUES OF CRYSTAL STRUCTURE DETERMINATION URI SHMUELI
SCHOOL OF CHEMISTRY, TEL AVIV UNIVERSITY INTERNATIONAL UNION OF
CRYSTALLOGRAPHY OXFORD UNIVERSITY PRESS CONTENTS SYMMETRY IN CRYSTALS:
FUNDAMENTALS 1 1.1 INTRODUCTION 1 1.2 THE LATTICE PLANE 5 1.3 THE
RECIPROCAL LATTICE 10 1.4 PERMISSIBLE ROTATIONAL SYMMETRIES OF A
THREE-DIMENSIONAL LAT- TICE 13 1.5 EVERY LATTICE IS CENTROSYMMETRIC 16
1.6 ORIENTATION OF SYMMETRY AXES WITH RESPECT TO THE LATTICE 17 1.7
PERMISSIBLE COMBINATIONS OF AXES OF ROTATION 18 1.8 CRYSTAL SYSTEMS 22
1.9 EXERCISES FOR CHAPTER 1 26 POINT GROUPS AND LATTICE TYPES 29 2.1
INTRODUCTION 29 2.2 FUNDAMENTAIS OF GROUP THEORY 29 2.2.1 SOME IMPORTANT
DEFINITIONS 33 2.2.2 MATRIX REPRESENTATION OF SYMMETRY OPERATIONS 33
2.2.3 ISOMORPHISM, COSET DECOMPOSITION, AND THE LAGRANGE THEOREM 34 2.3
CRYSTALLOGRAPHIC POINT GROUPS 37 2.3.1 THE AXIAL POINT GROUPS 38 2.3.2
COMPLETION OF THE PRESENTATION OF THE POINT GROUPS 39 2.4 BRAVAIS
LATTICES 45 2.5 EXERCISES FOR CHAPTER 2 47 SPACE-GROUP SYMMETRY 49 3.1
INTRODUCTION 49 3.2 SPACE-GROUP SYMMETRY OPERATORS 49 3.3 NONSYMMORPHIC
SPACE-GROUP OPERATORS 52 3.4 SOME GENERAL CONSIDERATIONS 59 3.5
CLASSIFICATION AND TABULATION OF CRYSTALLOGRAPHIC SPACE GROUPS 65 3.6
LOCATION OF SYMMETRY ELEMENTS 65 3.7 GRAPHICAL REPRESENTATION OF SPACE
GROUPS 68 3.8 SOME COMPUTATIONAL ASPECTS 76 3.8.1 DESCRIPTION OF TABLE
3.4 - EXPLICIT SPACE-GROUP SYMBOLS 82 3.9 EXERCISES FOR CHAPTER 3 83
X-RAY DIFFRACTION TECHNIQUES 85 4.1 INTRODUCTION 85 CONTENTS 4.2
DIFFRACTION CONDITIONS 86 4.2.1 THE LAUE AND BRAGG EQUATIONS 86 4.2.2
EWALD S SPHERE OF REFLECTION 90 4.3 PRODUCTION OF X-RAYS 91 4.3.1
THEX-RAYTUBE 91 4.3.2 SYNCHROTRON RADIATION 96 4.4 DETECTORS OF X-RAYS
100 4.4.1 X-RAY FILM 100 4.4.2 IMAGING PLATE 101 4.4.3 CHARGE-COUPLED
DEVICE (CCD) DETECTOR 102 4.5 THE ROTATING-CRYSTAL METHOD 102 4.6
MOVING-CRYSTAL-MOVING-FILM METHODS 105 4.6.1 THE WEISSENBERG METHOD 106
4.6.2 THE DE JONG-BOUMAN METHOD 106 4.6.3 THE BUERGER PRECESSION METHOD
106 4.7 THE FOUR-CIRCLE DIFFRACTOMETER 107 4.7.1 GEOMETRICAL
CONSIDERATIONS 107 4.7.2 THE ORIENTATION MATRIX 110 4.7.3 COORDINATES
AND ANGLES 111 4.7.4 COMMENTS ON THE EXPERIMENT 112 4.8 THE LAUE METHOD
113 4.8.1 PRINCIPLE OF THE METHOD 113 4.8.2 CALCULATION OF THE LAUE
PATTERN 114 4.9 EXERCISES FOR CHAPTER 4 117 THE STRUCTURE FACTOR AND THE
ELECTRON DENSITY 119 5.1 INTRODUCTION 119 5.2 SCATTERING BY A FREE
CHARGED PARTICLE 119 5.3 SCATTERING BY A MATERIAL UNIT 123 5.4
SCATTERING BY A PERIODIC ARRAY OF MATERIAL UNITS 125 5.5 THE ATOMIC
SCATTERING FACTOR 128 5.6 SPACE-GROUP SYMMETRY AND THE STRUCTURE FACTOR
130 5.7 THE FOURIER SYNTHESIS OF THE ELECTRON DENSITY 131 5.7.1
COMPUTATIONAL CONSIDERATIONS 133 5.8 THE PHASE PROBLEM 134 5.9 EFFECTS
OF SPACE-GROUP SYMMETRY 135 5.9.1 EFFECT OF THE LATTICE TYPE 138 5.9.2
EFFECT OF SCREW AXES AND GLIDE PLANES 139 5.10 EXERCISES FOR CHAPTER 5
142 THE PATTERSON FUNCTION 143 6.1 INTRODUCTION 143 6.2 THE PATTERSON
FUNCTION 143 6.2.1 PERIODICITY OF THE PATTERSON FUNCTION 145 6.2.2 THE
HEAVY ATOM METHOD 146 CONTENTS XI 6.2.3 OVERLAP OF INTERATOMIC VECTORS
147 6.3 CLASSIFICATION OF PATTERSON VECTORS 148 6.4 SYMMETRY OF THE
PATTERSON FUNCTION 149 6.5 HARKER PEAKS 151 6.6 OVERVIEW OF ADVANCED
APPLICATIONS 152 6.6.1 SUPERPOSITION METHODS 152 6.6.2 ROTATION
FUNCTIONS 153 6.6.3 TRANSLATION FUNCTIONS 155 6.6.4 MOLECULAR
REPLACEMENT 157 6.7 EXERCISES FOR CHAPTER 6 159 7. STRUCTURE-FACTOR
STATISTICS 161 7.1 INTRODUCTION 161 7.2 WILSON S METHOD OF SCALING THE
INTENSITIES 162 7.3 BASIC WILSON STATISTICS 164 7.3.1 CUMULATIVE
DISTRIBUTIONS 167 7.3.2 MOMENTS OF E 168 7.4 NON-IDEAL
STRUCTURE-FACTOR STATISTICS 170 7.5 EXERCISES FOR CHAPTER 7 173 8.
DIRECT METHODS 177 8.1 INTRODUCTION 177 8.2 PHASE INVARIANTS AND
SEMINVARIANTS 179 8.2.1 PHASE INVARIANTS 179 8.2.2 STRUCTURE
SEMINVARIANTS 181 8.3 SPECIFICATION OF THE ORIGIN 183 8.4 INEQUALITIES
186 8.5 THE SAYRE EQUATION AND THE TANGENT FORMULA 190 8.6 CONDITIONAL
PROBABILITY DENSITY OF A THREE-PHASE INVARIANT 192 8.7 OTHER
PROBABILISTIC CONSIDERATIONS 198 8.8 SOME PRACTICAL COMMENTS ON THE
SOLUTION OFTHE PHASE PROBLEM 201 9. ATOMIC DISPLACEMENT PARAMETERS 207
9.1 INTRODUCTION 207 9.2 ATOMIC DISPLACEMENT PARAMETERS IN THE GAUSSIAN
APPROXIMA- TION 210 9.2.1 NON-CARTESIAN REPRESENTATIONS 211 9.2.2
CARTESIAN REPRESENTATIONS 213 9.3 A RIGID-BODY MODEL 215 9.3.1
INTRODUCTION 215 9.3.2 ROTATIONAL DISPLACEMENT 215 9.3.3 RIGID-BODY
MODEL PARAMETERS 217 10. REFINEMENT OF STRUCTURAL PARAMETERS 219 10.1
INTRODUCTION 219 10.2 THE LINEAR LEAST-SQUARES METHOD 219 XLL CONTENTS
10.2.1 AN EXAMPLE OF A LINEAR LEAST-SQUARES PROBLEM 223 10.3 THE
NON-LINEAR LEAST-SQUARES METHOD 224 10.4 CONVENTIONAL REFINEMENT 226
10.4.1 RIGID-GROUP CONSTRAINTS 228 10.4.2 INTRODUCTION OF RESTRAINTS 231
APPENDIX A. SOME GEOMETRICAL CONSIDERATIONS 235 A.L TRANSFORMATION TO A
CARTESIAN SYSTEM 235 A.2 CHANGE OF BASIS AND TRACE INVARIANCE 236 A.3
THE FINITE ROTATION OPERATOR 237 B. FUNDAMENTALS OF TENSOR NOTATION 241
B.L INTRODUCTION 241 B.2 TRANSFORMATIONS 242 B.3 THE SCALAR PRODUCT AND
METRIC TENSORS 242 B.4 EXAMPLES 243 C. BASIC NOTIONS FROM THEORY OF
PROBABILITY 247 C.L INTRODUCTION 247 C.2 RANDOM VARIABLES 247 C.3 THE
PROBABILITY DENSITY FUNCTION AND RELATED QUANTITIES 248 C.4 JOINT AND
CONDITIONAL PDFS 249 C.5 CHARACTERISTIC FUNCTION AND CUMULANTS 250 D.
THE DISCRETE FOURIER TRANSFORM 253 D.L SOME PROPERTIES OF THE DISCRETE
FOURIER TRANSFORM 253 D.2 THE FAST FOURIER TRANSFORM 257 REFERENCES 261
INDEX 267
|
| adam_txt |
THEORIES AND TECHNIQUES OF CRYSTAL STRUCTURE DETERMINATION URI SHMUELI
SCHOOL OF CHEMISTRY, TEL AVIV UNIVERSITY INTERNATIONAL UNION OF
CRYSTALLOGRAPHY OXFORD UNIVERSITY PRESS CONTENTS SYMMETRY IN CRYSTALS:
FUNDAMENTALS 1 1.1 INTRODUCTION 1 1.2 THE LATTICE PLANE 5 1.3 THE
RECIPROCAL LATTICE 10 1.4 PERMISSIBLE ROTATIONAL SYMMETRIES OF A
THREE-DIMENSIONAL LAT- TICE 13 1.5 EVERY LATTICE IS CENTROSYMMETRIC 16
1.6 ORIENTATION OF SYMMETRY AXES WITH RESPECT TO THE LATTICE 17 1.7
PERMISSIBLE COMBINATIONS OF AXES OF ROTATION 18 1.8 CRYSTAL SYSTEMS 22
1.9 EXERCISES FOR CHAPTER 1 26 POINT GROUPS AND LATTICE TYPES 29 2.1
INTRODUCTION 29 2.2 FUNDAMENTAIS OF GROUP THEORY 29 2.2.1 SOME IMPORTANT
DEFINITIONS 33 2.2.2 MATRIX REPRESENTATION OF SYMMETRY OPERATIONS 33
2.2.3 ISOMORPHISM, COSET DECOMPOSITION, AND THE LAGRANGE THEOREM 34 2.3
CRYSTALLOGRAPHIC POINT GROUPS 37 2.3.1 THE AXIAL POINT GROUPS 38 2.3.2
COMPLETION OF THE PRESENTATION OF THE POINT GROUPS 39 2.4 BRAVAIS
LATTICES 45 2.5 EXERCISES FOR CHAPTER 2 47 SPACE-GROUP SYMMETRY 49 3.1
INTRODUCTION 49 3.2 SPACE-GROUP SYMMETRY OPERATORS 49 3.3 NONSYMMORPHIC
SPACE-GROUP OPERATORS 52 3.4 SOME GENERAL CONSIDERATIONS 59 3.5
CLASSIFICATION AND TABULATION OF CRYSTALLOGRAPHIC SPACE GROUPS 65 3.6
LOCATION OF SYMMETRY ELEMENTS 65 3.7 GRAPHICAL REPRESENTATION OF SPACE
GROUPS 68 3.8 SOME COMPUTATIONAL ASPECTS 76 3.8.1 DESCRIPTION OF TABLE
3.4 - EXPLICIT SPACE-GROUP SYMBOLS 82 3.9 EXERCISES FOR CHAPTER 3 83
X-RAY DIFFRACTION TECHNIQUES 85 4.1 INTRODUCTION 85 CONTENTS 4.2
DIFFRACTION CONDITIONS 86 4.2.1 THE LAUE AND BRAGG EQUATIONS 86 4.2.2
EWALD'S SPHERE OF REFLECTION 90 4.3 PRODUCTION OF X-RAYS 91 4.3.1
THEX-RAYTUBE 91 4.3.2 SYNCHROTRON RADIATION 96 4.4 DETECTORS OF X-RAYS
100 4.4.1 X-RAY FILM 100 4.4.2 IMAGING PLATE 101 4.4.3 CHARGE-COUPLED
DEVICE (CCD) DETECTOR 102 4.5 THE ROTATING-CRYSTAL METHOD 102 4.6
MOVING-CRYSTAL-MOVING-FILM METHODS 105 4.6.1 THE WEISSENBERG METHOD 106
4.6.2 THE DE JONG-BOUMAN METHOD 106 4.6.3 THE BUERGER PRECESSION METHOD
106 4.7 THE FOUR-CIRCLE DIFFRACTOMETER 107 4.7.1 GEOMETRICAL
CONSIDERATIONS 107 4.7.2 THE ORIENTATION MATRIX 110 4.7.3 COORDINATES
AND ANGLES 111 4.7.4 COMMENTS ON THE EXPERIMENT 112 4.8 THE LAUE METHOD
113 4.8.1 PRINCIPLE OF THE METHOD 113 4.8.2 CALCULATION OF THE LAUE
PATTERN 114 4.9 EXERCISES FOR CHAPTER 4 117 THE STRUCTURE FACTOR AND THE
ELECTRON DENSITY 119 5.1 INTRODUCTION 119 5.2 SCATTERING BY A FREE
CHARGED PARTICLE 119 5.3 SCATTERING BY A MATERIAL UNIT 123 5.4
SCATTERING BY A PERIODIC ARRAY OF MATERIAL UNITS 125 5.5 THE ATOMIC
SCATTERING FACTOR 128 5.6 SPACE-GROUP SYMMETRY AND THE STRUCTURE FACTOR
130 5.7 THE FOURIER SYNTHESIS OF THE ELECTRON DENSITY 131 5.7.1
COMPUTATIONAL CONSIDERATIONS 133 5.8 THE PHASE PROBLEM 134 5.9 EFFECTS
OF SPACE-GROUP SYMMETRY 135 5.9.1 EFFECT OF THE LATTICE TYPE 138 5.9.2
EFFECT OF SCREW AXES AND GLIDE PLANES 139 5.10 EXERCISES FOR CHAPTER 5
142 THE PATTERSON FUNCTION 143 6.1 INTRODUCTION 143 6.2 THE PATTERSON
FUNCTION 143 6.2.1 PERIODICITY OF THE PATTERSON FUNCTION 145 6.2.2 THE
HEAVY ATOM METHOD 146 CONTENTS XI 6.2.3 OVERLAP OF INTERATOMIC VECTORS
147 6.3 CLASSIFICATION OF PATTERSON VECTORS 148 6.4 SYMMETRY OF THE
PATTERSON FUNCTION 149 6.5 HARKER PEAKS 151 6.6 OVERVIEW OF ADVANCED
APPLICATIONS 152 6.6.1 SUPERPOSITION METHODS 152 6.6.2 ROTATION
FUNCTIONS 153 6.6.3 TRANSLATION FUNCTIONS 155 6.6.4 MOLECULAR
REPLACEMENT 157 6.7 EXERCISES FOR CHAPTER 6 159 7. STRUCTURE-FACTOR
STATISTICS 161 7.1 INTRODUCTION 161 7.2 WILSON'S METHOD OF SCALING THE
INTENSITIES 162 7.3 BASIC WILSON STATISTICS 164 7.3.1 CUMULATIVE
DISTRIBUTIONS 167 7.3.2 MOMENTS OF \E\ 168 7.4 NON-IDEAL
STRUCTURE-FACTOR STATISTICS 170 7.5 EXERCISES FOR CHAPTER 7 173 8.
DIRECT METHODS 177 8.1 INTRODUCTION 177 8.2 PHASE INVARIANTS AND
SEMINVARIANTS 179 8.2.1 PHASE INVARIANTS 179 8.2.2 STRUCTURE
SEMINVARIANTS 181 8.3 SPECIFICATION OF THE ORIGIN 183 8.4 INEQUALITIES
186 8.5 THE SAYRE EQUATION AND THE TANGENT FORMULA 190 8.6 CONDITIONAL
PROBABILITY DENSITY OF A THREE-PHASE INVARIANT 192 8.7 OTHER
PROBABILISTIC CONSIDERATIONS 198 8.8 SOME PRACTICAL COMMENTS ON THE
SOLUTION OFTHE PHASE PROBLEM 201 9. ATOMIC DISPLACEMENT PARAMETERS 207
9.1 INTRODUCTION 207 9.2 ATOMIC DISPLACEMENT PARAMETERS IN THE GAUSSIAN
APPROXIMA- TION 210 9.2.1 NON-CARTESIAN REPRESENTATIONS 211 9.2.2
CARTESIAN REPRESENTATIONS 213 9.3 A RIGID-BODY MODEL 215 9.3.1
INTRODUCTION 215 9.3.2 ROTATIONAL DISPLACEMENT 215 9.3.3 RIGID-BODY
MODEL PARAMETERS 217 10. REFINEMENT OF STRUCTURAL PARAMETERS 219 10.1
INTRODUCTION 219 10.2 THE LINEAR LEAST-SQUARES METHOD 219 XLL CONTENTS
10.2.1 AN EXAMPLE OF A LINEAR LEAST-SQUARES PROBLEM 223 10.3 THE
NON-LINEAR LEAST-SQUARES METHOD 224 10.4 CONVENTIONAL REFINEMENT 226
10.4.1 RIGID-GROUP CONSTRAINTS 228 10.4.2 INTRODUCTION OF RESTRAINTS 231
APPENDIX A. SOME GEOMETRICAL CONSIDERATIONS 235 A.L TRANSFORMATION TO A
CARTESIAN SYSTEM 235 A.2 CHANGE OF BASIS AND TRACE INVARIANCE 236 A.3
THE FINITE ROTATION OPERATOR 237 B. FUNDAMENTALS OF TENSOR NOTATION 241
B.L INTRODUCTION 241 B.2 TRANSFORMATIONS 242 B.3 THE SCALAR PRODUCT AND
METRIC TENSORS 242 B.4 EXAMPLES 243 C. BASIC NOTIONS FROM THEORY OF
PROBABILITY 247 C.L INTRODUCTION 247 C.2 RANDOM VARIABLES 247 C.3 THE
PROBABILITY DENSITY FUNCTION AND RELATED QUANTITIES 248 C.4 JOINT AND
CONDITIONAL PDFS 249 C.5 CHARACTERISTIC FUNCTION AND CUMULANTS 250 D.
THE DISCRETE FOURIER TRANSFORM 253 D.L SOME PROPERTIES OF THE DISCRETE
FOURIER TRANSFORM 253 D.2 THE FAST FOURIER TRANSFORM 257 REFERENCES 261
INDEX 267 |
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| id | DE-604.BV022872353 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:47:44Z |
| indexdate | 2024-11-25T17:37:10Z |
| institution | BVB |
| isbn | 9780199213504 9780199219667 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016077428 |
| oclc_num | 255637167 |
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| owner | DE-703 DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-11 DE-91G DE-BY-TUM |
| physical | XII, 269 Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | IUCr texts on crystallography |
| series2 | IUCr texts on crystallography |
| spellingShingle | Shmueli, Uri Theories and techniques of crystal structure determination IUCr texts on crystallography Crystallography, Mathematical Kristallstrukturanalyse (DE-588)4137204-9 gnd |
| subject_GND | (DE-588)4137204-9 |
| title | Theories and techniques of crystal structure determination |
| title_auth | Theories and techniques of crystal structure determination |
| title_exact_search | Theories and techniques of crystal structure determination |
| title_exact_search_txtP | Theories and techniques of crystal structure determination |
| title_full | Theories and techniques of crystal structure determination Uri Shmueli |
| title_fullStr | Theories and techniques of crystal structure determination Uri Shmueli |
| title_full_unstemmed | Theories and techniques of crystal structure determination Uri Shmueli |
| title_short | Theories and techniques of crystal structure determination |
| title_sort | theories and techniques of crystal structure determination |
| topic | Crystallography, Mathematical Kristallstrukturanalyse (DE-588)4137204-9 gnd |
| topic_facet | Crystallography, Mathematical Kristallstrukturanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016077428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005455767 |
| work_keys_str_mv | AT shmueliuri theoriesandtechniquesofcrystalstructuredetermination |