Holdings: Foundations of crystallography with computer applications

Foundations of crystallography with computer applications:

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Bibliographic Details
Main Author:	Julian, Maureen M. (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] CRC Press 2008
Subjects:	Datenverarbeitung Crystallography > Data processing Crystallography, Mathematical Kristallographie
Online Access:	Inhaltsverzeichnis
Physical Description:	XXVI, 340 S. Ill., graph. Darst.
ISBN:	1420060759 9781420060751

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adam_text	FOUNDATIONS OF CRYSTALLOGRAPHY WITH COMPUTER APPLICATIONS MAUREEN M. JULIAN DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING VIRGINIA TECH, USA (G) CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC PRESS IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE, XVII ACKNOWLEDGMENTS, XXI THE AUTHOR, XXIII INTRODUCTION, XXV CHAPTER 1 * LATTICES CHAPTER OBJECTIVES 2 1.1 INTRODUCTION 3 1.2 TWO-DIMENSIONAL LATTICES 3 1.3 TWO-DIMENSIONAL BASIS VECTORS AND UNIT CELLS 6 1.3.1 HANDEDNESS OF BASIS VECTORS 6 1.3.2 DESCRIBING THE LATTICE MATHEMATICALLY 7 1.3.3 THE UNIT CELL 8 1.4 TWO-DIMENSIONAL TRANSFORMATIONS BETWEEN SETS OF BASIS VECTORS 9 1.5 THREE-DIMENSIONAL BASIS VECTORS, UNIT CELLS, AND LATTICE TRANSFORMATIONS 11 1.5.1 BASIS VECTORS 11 1.5.2 UNIT CELL 11 1.5.3 TRANSFORMATIONS BETWEEN SETS OF BASIS VECTORS 12 1.6 CONVERSION TO CARTESIAN COORDINATES 14 1.6.1 TWO-DIMENSIONAL CONVERSION TO CARTESIAN COORDINATES 14 1.6.2 THREE-DIMENSIONAL CONVERSION TO CARTESIAN COORDINATES 15 VN VIII * CONTENTS 1.7 ACRYSTAL: HEXAMETHYLBENZENE 17 1.7.1 DEFINITION OF ANGSTROM 18 1.7.2 TWO-DIMENSIONAL UNIT CELL FOR HMB 18 1.7.3 THREE-DIMENSIONAL UNIT CELL OF HMB 19 1.8 A CRYSTAL: ANHYDROUS ALUM 20 1.9 EFFECTS OF TEMPERATURE AND PRESSURE ON LATTICE PARAMETERS 21 1.9.1 TEMPERATURE VARIATIONS AND THERMAL EXPANSION 21 1.9.2 PRESSURE VARIATIONS AND COMPRESSIBILITY 22 DEFINITIONS 26 EXERCISES 26 STARTER CODE FOR DRAWING HMB TWO-DIMENSIONAL CELL 29 CHAPTER 2 * UNIT CELL CALCULATIONS 31_ CHAPTER OBJECTIVES 33 2.1 INTRODUCTION 33 2.2 FRACTIONAL COORDINATES 33 2.3 PLOTTING ATOMS IN THE UNIT CELL 35 2.3.1 PLOTTING A SINGLE ATOM 35 2.3.2 PLOTTING ATOMIC COORDINATES DIRECTLY FROM THE CRYSTALLOGRAPHIC LITERATURE 36 2.3.3 MOVING ATOMS INTO THE UNIT CELL 37 2.3.4 TRANSLATING THE MOLECULE INTO THE UNIT CELL 39 2.4 CALCULATION OF INTERATOMIC BOND DISTANCES 39 2.4.1 CALCULATION OF THE MAGNITUDE OF A VECTOR 40 2.4.2 THE METRIE MATRIX, G 40 2.4.3 USING THE METRIE MATRIX 41 2.4.4 TWO-DIMENSIONAL CALCULATION OF INTERATOMIC BOND DISTANCES 41 2.4.5 THREE-DIMENSIONAL CALCULATION OF INTERATOMIC BOND DISTANCES 42 2.5 CALCULATION OF INTERATOMIC BOND ANGLES 43 2.5.1 TWO-DIMENSIONAL ATOMIC BOND ANGLES 44 2.5.2 THREE-DIMENSIONAL ATOMIC BOND ANGLES 44 2.6 AREA AND VOLUME OF THE UNIT CELL 45 2.7 SUMMARY OF METRIC MATRIX CALCULATIONS 46 2.8 QUARTZ EXAMPLE 46 CONTENTS * IX 2.9 TRANSFORMATION MATRICES 49 2.9.1 TRANSFORMATION MATRIX, P 49 2.9.2 TRANSFORMATION OFFRACTIONAL COORDINATES 49 2.9.3 TRANSFORMATION OF THE G MATRIX 50 2.9.4 AREA AND VOLUME TRANSFORMATIONS 51 2.10HEXAMETHYLBENZENEEXAMPLE 52 2.10.1 CALCULATION OF THE TRANSFORMATION MATRIX P 53 2.10.2 CALCULATION OF THE TRANSFORMED FRACTIONAL COORDINATES 53 2.10.3 CALCULATION OFG 2 54 2.10.4 CALCULATION OF THE LATTICE PARAMETERS IN THE NEW BASIS 55 2.10.5 COMPARISONOFTHE VOLUME OFTHE CELL IN BOTH BASES 55 2.10.6 MAGNITUDE OF A VECTOR R 55 2.10.7 INTERATOMIC BOND ANGLE 56 2.11 CRYSTALLOGRAPHIC DIRECTIONS 57 2.12 CRYSTALLOGRAPHIC PLANES AND MILLER INDICES 58 2.13 DENSITY 60 2.14 REVISITING THERMAL EXPANSION AND ISOTHERMAL COMPRESSIBILITY 61 2.14.1 VOLUMETRIE THERMAL EXPANSION 61 2.14.2 VOLUMETRIE COMPRESSIBILITY 62 DEFINITIONS 63 EXERC1SES 63 STARTER PROGRAM 65 CHAPTER 3 * POINT GROUPS 69 CHAPTER OBJECTIVES 71 3.1 INTRODUCTION 71 3.2 GROUP THEORY 72 3.2.1 ELEMENTS IN A SET 72 3.2.2 OPERATIONS 72 3.2.3 GROUP 74 3.3 SYMMETRY OPERATIONS 75 3.3.1 CONVENTIONS OF THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 76 3.3.2 MIRROR SYMMETRY OPERATION 76 3.3.3 IDENTITY SYMMETRY OPERATION 79 X * CONTENTS 3.3.4 N-FOLD ROTATION SYMMETRY OPERATIONS 79 3.3.4.1 TWOFOLD ROTATION SYMMETRY OPERATION 79 3.3.4.2 THREEFOLD ROTATION SYMMETRY OPERATION 80 3.3.4.3 N-FOLD ROTATION SYMMETRY OPERATIONS 81 3.4 CRYSTALLOGRAPHIC ROTATIONS 82 3.5 SUMMARY OF THE TWO-DIMENSIONAL CRYSTALLOGRAPHIC OPERATIONS 85 3.6 TWO-DIMENSIONAL CRYSTALLOGRAPHIC POINT GROUPS 85 3.6.1 POINT GROUP 1 87 3.6.2 POINT GROUP 2 88 3.6.3 POINT GROUP M 89 3.6.4 POINT GROUP 3 90 3.6.5 POINT GROUP 4 91 3.6.6 POINT GROUP 6 93 3.6.7 POINT GROUP 2MM 93 3.6.8 POINT GROUP 3M 95 3.6.9 POINT GROUP 4MM 98 3.6.10 POINT GROUP 6MM 99 3.6.11 IDENTIFICATION OF A CRYSTALLOGRAPHIC POINT GROUP 99 3.7 TWO-DIMENSIONAL CRYSTAL SYSTEMS 100 3.7.1 OBLIQUE SYSTEM 101 3.7.2 RECTANGULAR SYSTEM 102 3.7.3 SQUARE SYSTEM 102 3.7.4 HEXAGONAL SYSTEM 102 3.8 TWO-DIMENSIONAL POINT GROUP TREE 103 3.9 THREE-DIMENSIONAL POINT GROUPS 106 3.9.1 N-FOLD ROTATIONS 106 3.9.1.1 N-FOLD ROTATION SYMMETRY OPERATIONS 107 3.9.1.2 N-FOLD ROTATION CYCLIC POINT CROUPS 107 3.9.2 N-FOLD ROTOINVERSIONS 108 3.9.2.1 INVERSION SYMMETRY OPERATION 108 3.9.2.2 MIRROR OPERATION 109 3.9.2.3 ROTOINVERSION OPERATIONS 3, 4, AND 6 111 3.9.2.4 N-FOLD ROTOINVERSION CYCLIC POINT CROUPS 111 3.10 THREE-DIMENSIONAL CRYSTAL SYSTEMS 113 CONTENTS * XI 3.11 EXAMPLES OF THREE-DIMENSIONAL POINT GROUPS WITH MULTIPLE GENERATORS 115 3.11.1 POINT GROUP 2/M 115 3.11.2 POINT GROUP 32 117 3.12 THREE-DIMENSIONAL POINT GROUP TREES 118 3.13 POINT GROUP SYMMETRY AND SOME PHYSICAL PROPERTIES OF CRYSTALS 119 3.13.1 PIEZOELECTRICITY 119 3.13.2 ETCH FIGURES 121 DEFINITIONS . 122 EXERCISES 123 STARTER PROGRAM 126 CHAPTER 4 * SPACE GROUPS 129 CHAPTER OBJECTIVES 132 PART I: TWO DIMENSIONS 132 4.1 INTRODUCTION 132 4.2 TWO-DIMENSIONAL BRAVAIS LATTICES 133 4.2.1 OBLIQUE 133 4.2.2 RECTANGULAR PRIMITIVE 134 4.2.3 RECTANGULAR CENTERED 134 4.2.4 SQUARE 135 4.2.5 HEXAGONAL 135 4.3 CRYSTAL SYSTEMS AND THE G MATRICES 136 4.4 TWO-DIMENSIONAL SPACE GROUPS 136 4.4.1 OVERVIEW 137 4.4.2 SPACE GROUP NO. L,PL 138 4.4.3 SPACE GROUP NO. 2, P2 140 4.4.4 SPACE GROUP NO. 3, PM 143 4.4.5 SPACE GROUP NO. 4, PG 145 4.4.6 SPACE GROUP NO. 5, CM 147 4.4.7 SPACE GROUP NO. 6, PLMM; SPACE GROUP NO.7, PLMG 149 4.4.8 SPACE GROUP NO. 8,P2GG; SPACE GROUP NO. 9, C2MM; SPACE GROUP NO. 10, P4; SPACE GROUP NO. 11, P4MM; SPACE GROUP NO. 12, PAGM 153 4.4.9 SPACE GROUP NO. 13, P3 153 4.4.10 SPACE GROUP NO. I4,P3ML; SPACE GROUP NO. 15,P31M 156 4.4.11 SPACE GROUP NO. 16, 6; SPACE GROUP NO. 7,P6MM 158 XII * CONTENTS 4.5 OVERVIEW OF THE ASYMMETRIC UNIT 158 4.6 RECIPE FOR ANALYZING A PERIODIC PATTERN 160 4.7 PRIMITIVE CELLS FOR CM AND C2MM 16 0 4.7.1 PRIMITIVE CELL FOR CM 161 4.7.2 PRIMITIVE CELL FOR CIMM 162 4.8 TWO-DIMENSIONAL SPACE GROUP TREE 164 4.9 SUMMARY OF TWO-DIMENSIONAL SPACE GROUPS 168 PART II: THREE DIMENSIONS 169 4.10 THREE-DIMENSIONAL BRAVAIS LATTICES 169 4.10.1 TRICLINIC 171 4.10.2 MONOCLINIC 171 4.10.3 ORTHORHOMBIC 171 4.10.4 TETRAGONAL 171 4.10.5 HEXAGONAL 172 4.10.6 RHOMBOHEDRAL 172 4.10.7 CUBIC 173 4.10.8 SUMMARY OF BRAVAIS LATTICES 173 4.11 THREE-DIMENSIONAL SPACE GROUPS 173 4.11.1 CLASSIFICATION OF THE SPACE GROUPS 173 4.11.2 MINIMAL SYMMETRIES FOR CRYSTAL SYSTEMS 175 4.11.3 GMATRICES 177 4.11.4 SYMMETRY OPERATIONS WITH TRANSLATIONS AS COMPONENTS 178 4.11.4.1 GLIDES 178 4.11.4.2 SCREWS 179 4.11.5 SYMMORPHIC AND NONSYMMORPHIC SPACE GROUPS 179 4.12 HMB AND SPACE GROUP NO. 2, PT 182 4.12.1 INTERPRETATION OF SPACE GROUP SYMMETRIES FROM THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 183 4.12.2 SPACE GROUP TREE NEAR PI 186 4.12.3 HMB CRYSTAL DATA 186 4.12.4 UNIT CELL AND THE ASYMMETRIE UNIT FOR HMB 186 4.12.5 POPULATED CELL FOR HMB 187 4.12.6 SPECIAL PROTECTIONS FOR HMB 187 4.12.7 INTERPRETATION OF HMB CRYSTAL STRUCTURE 188 4.12.8 DISCUSSION 188 CONTENTS * XIII 4.13 AA AND THE SPACE GROUP NO. 150, P321 191 4.13.1 INTERPRETATION OF THE SPACE GROUP SYMMETRIES FROM THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 191 4.13.2 SPACE GROUP TREE NEAR P321 192 4.13.3 AA CRYSTAL DATA 192 4.13.4 UNIT CELL AND THE ASYMMETRIE UNIT FOR AA 193 4.13.5 CALCULATIONOFTHENUMBER OF FORMULA UNITS 193 4.13.6 WYCKOFFPOSITIONS 194 4.13.7 SPECIAL PROTECTIONS FOR AA 196 4.13.8 POLYHEDRONS IN THE AA CRYSTAL STRUCTURE 198 4.13.9 ISOTYPIC CRYSTAL STRUCTURES 199 DEFINITIONS 200 EXERCISES 202 STARTER PROGRAM 206 CHAPTER 5 * THE RECIPROCAL LATTICE 211_ CHAPTER OBJECTIVES . 212 5.1 INTRODUCTION 213 5.2 THE RECIPROCAL LATTICE 213 5.3 RELATIONSHIPS BETWEEN DIRECT AND RECIPROCAL LATTICES 216 5.3.1 RELATIONSHIPS FOR BASIS VECTORS AND LATTICE PARAMETERS 216 5.3.2 RELATIONSHIP BETWEEN METRIE MATRICES G AND G* 217 5.3.3 RELATIONSHIP BETWEEN VOLUMES V AND V* 219 5.3.4 RELATIONSHIP BETWEEN DIRECT AND RECIPROCAL LATTICE VECTORS REVISITED 220 5.3.5 SUMMARY OF TRANSFORMATIONS BETWEEN DIRECT AND RECIPROCAL LATTICES 220 5.4 RECIPROCAL LATTICE CALCULATIONS FOR THREE CRYSTALS 221 5.4.1 HEXAMETHYLBENZENE 221 5.4.1.1 CALCULATION OFG* ANDV* 22 1 5.4.1.2 OVERLAYING THE RECIPROCAL UNIT CELL ON THE DIRECT UNIT CELL 223 5.4.2 ANHYDROUS ALUM 226 5.4.3 CRYSTALS WITH OC, SS, AND Y ALL 90 227 5.5 RELATIONSHIPS BETWEEN TRANSFORMATION MATRICES 228 5.6 DIFFRACTION PATTERN AND THE RECIPROCAL LATTICE 231 5.6.1 MOTIVATION FOR RECIPROCAL LATTICE 231 5.6.2 IDENTIFICATION OF THE D-SPACINGS IN CRYSTALS 232 5.6.3 MILLER INDICES, LAUE INDICES, AND BRAGG S LAW 233 XIV * CONTENTS 5.6.4 RECIPROCAL LATTICE VECTORS AND SETS OF CRYSTALLOGRAPHIC PLANES 234 5.6.4.1 DIRECTION OF A RECIPROCAL LATTICE VECTOR 235 5.6.4.2 MAGNITUDE OF A RECIPROCAL LATTICE VECTOR 235 5.7 THREE APPLICATIONS OF THE RECIPROCAL LATTICE 236 5.7.1 USING THE RECIPROCAL LATTICE TO CALCULATE RF-SPACINGS 236 5.7.2 CALCULATING ANGLES BETWEEN CRYSTAL FACES 238 5.7.3 RELATING DIFFERENT SETS OF LATTICE PARAMETERS FOR A CRYSTAL 241 5.7.3.1 POWDER DIFFRACTION FILES 241 5.Z3.2 CRYSTAL MORPHOLOGY 243 5.Z3.3 COMPARING INDEXING OF THE RECIPROCAL LATTICE 244 5.7.3.4 TRANSFORMINGFROM THE RECIPROCAL LATTICE TO THE DIRECT LATTICE 245 5.7.3.5 COMPARISON OF PDF FILES 246 DEFINITIONS 248 EXERCISES 248 STARTER PROGRAM 250 CHAPTER 6 * PROPERTIES OF X-RAYS 253 CHAPTER OBJECTIVES 254 6.1 INTRODUCTION 255 6.2 THE DISCOVERY OF X-RAYS 255 6.3 PROPERTIES OF WAVES 256 6.3.1 PRINCIPLE OF SUPERPOSITION 257 6.3.1.1 CONSTRUCTIVE INTERFERENCE 257 6.3.1.2 DESTRUCTIVE INTERFERENCE 258 6.3.1.3 PARTIAL INTERFERENCE 258 6.3.2 YOUNG S DOUBLE-SLIT EXPERIMENT 258 6.3.3 PROPERTIES OF ELECTROMAGNETIC WAVES 261 6.4 X-RAY SPECTRUM 263 6.4.1 BREMSSTRAHLUNG RADIATION 263 6.4.2 CHARACTERISTIC RADIATION 264 6.4.3 ABSORPTION 266 6.4.4 ELECTRONS AND X-RAYS 268 6.5 THE X-RAY TUBE 269 6.5.1 FILTERS 269 6.6 X-RAY DIFFRACTION 271 6.6.1 FIRST X-RAY DIFFRACTION PHOTOGRAPH 271 CONTENTS * XV 6.6.2 BRAGG S LAW 274 6.6.3 X-RAY POWDER DIFFRACTION CAMERA 275 DEFINITIONS 276 EXERC1SES 277 CHAPTER 7 * ELECTRON DENSITY MAPS 279 CHAPTER OBJECT1VES 280 7.1 INTRODUCTION 281 7.2 SCATTERING BY AN ELECTRON 281 7.3 SCATTERING BY AN ATOM 282 7.3.1 ATOMIC SCATTERING FACTOR 282 7.4 SCATTERING BY A CRYSTAL 284 7.4.1 PHASE ANGLE 285 7.4.2 AMPLITUDE 286 7.4.3 STRUCTURE FACTOR 288 7.5 SOME MATHEMATICAL IDENTITIES 289 7.6 STRUCTURE FACTORS FOR SOME CRYSTALS 289 7.6.1 SIMPLE CUBIC, POLONIUM 289 7.6.2 BODY-CENTERED CUBIC, CHROMIUM 293 7.6.3 FACE-CENTERED CUBIC, COPPER 295 7.6.4 CRYSTAL WITH TWO ELEMENTS, NACL 297 7.6.5 CRYSTAL WITH TWO ELEMENTS, SPHALERITE 299 7.6.6 STRUCTURE FACTORS FOR GLIDE PLANES 300 7.6.7 STRUCTURE FACTORS FOR SCREW AXES 302 7.7 STRUCTURE FACTORS FOR CENTROSYMMETRIC CRYSTALS 302 7.7.1 PARTITIONING THE SPACE GROUPS 303 7.7.1.1 CENTROSYMMETRIC SPACE GROUPS 303 7.7.1.2 NONCENTROSYMMETRIC SPACE GROUPS 303 7.7.2 INVERSION POINTS AND STRUCTURE FACTORS 304 7.7.3 HEXAMETHYLBENZENE (HMB): EXAMPLE OF A CENTROSYMMETRIC CRYSTAL 304 7.7.4 GENERALIZED CALCULATION OF STRUCTURE FACTORS 305 7.8 ELECTRON DENSITY MAPS 306 7.8.1 FRIEDEL S LAW 306 7.8.2 FOURIER SERIES 308 7.8.2.1 ONE-DIMENSIONAL FOURIER SERIES 308 7.8.2.2 THREE-DIMENSIONAL FOURIER SERIES 311 XVI * CONTENTS DEFINITIONS 312 EXERCISES 312 STARTER PROGRAM 314 REFERENCES, 317 BIBLIOGRAPHY, 319 APPENDIX: DEFINITIONS, 323 INDEX, 333
adam_txt	FOUNDATIONS OF CRYSTALLOGRAPHY WITH COMPUTER APPLICATIONS MAUREEN M. JULIAN DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING VIRGINIA TECH, USA (G) CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC PRESS IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE, XVII ACKNOWLEDGMENTS, XXI THE AUTHOR, XXIII INTRODUCTION, XXV CHAPTER 1 * LATTICES CHAPTER OBJECTIVES 2 1.1 INTRODUCTION 3 1.2 TWO-DIMENSIONAL LATTICES 3 1.3 TWO-DIMENSIONAL BASIS VECTORS AND UNIT CELLS 6 1.3.1 HANDEDNESS OF BASIS VECTORS 6 1.3.2 DESCRIBING THE LATTICE MATHEMATICALLY 7 1.3.3 THE UNIT CELL 8 1.4 TWO-DIMENSIONAL TRANSFORMATIONS BETWEEN SETS OF BASIS VECTORS 9 1.5 THREE-DIMENSIONAL BASIS VECTORS, UNIT CELLS, AND LATTICE TRANSFORMATIONS 11 1.5.1 BASIS VECTORS 11 1.5.2 UNIT CELL 11 1.5.3 TRANSFORMATIONS BETWEEN SETS OF BASIS VECTORS 12 1.6 CONVERSION TO CARTESIAN COORDINATES 14 1.6.1 TWO-DIMENSIONAL CONVERSION TO CARTESIAN COORDINATES 14 1.6.2 THREE-DIMENSIONAL CONVERSION TO CARTESIAN COORDINATES 15 VN VIII * CONTENTS 1.7 ACRYSTAL: HEXAMETHYLBENZENE 17 1.7.1 DEFINITION OF ANGSTROM 18 1.7.2 TWO-DIMENSIONAL UNIT CELL FOR HMB 18 1.7.3 THREE-DIMENSIONAL UNIT CELL OF HMB 19 1.8 A CRYSTAL: ANHYDROUS ALUM 20 1.9 EFFECTS OF TEMPERATURE AND PRESSURE ON LATTICE PARAMETERS 21 1.9.1 TEMPERATURE VARIATIONS AND THERMAL EXPANSION 21 1.9.2 PRESSURE VARIATIONS AND COMPRESSIBILITY 22 DEFINITIONS 26 EXERCISES 26 STARTER CODE FOR DRAWING HMB TWO-DIMENSIONAL CELL 29 CHAPTER 2 * UNIT CELL CALCULATIONS 31_ CHAPTER OBJECTIVES 33 2.1 INTRODUCTION 33 2.2 FRACTIONAL COORDINATES 33 2.3 PLOTTING ATOMS IN THE UNIT CELL 35 2.3.1 PLOTTING A SINGLE ATOM 35 2.3.2 PLOTTING ATOMIC COORDINATES DIRECTLY FROM THE CRYSTALLOGRAPHIC LITERATURE 36 2.3.3 MOVING ATOMS INTO THE UNIT CELL 37 2.3.4 TRANSLATING THE MOLECULE INTO THE UNIT CELL 39 2.4 CALCULATION OF INTERATOMIC BOND DISTANCES 39 2.4.1 CALCULATION OF THE MAGNITUDE OF A VECTOR 40 2.4.2 THE METRIE MATRIX, G 40 2.4.3 USING THE METRIE MATRIX 41 2.4.4 TWO-DIMENSIONAL CALCULATION OF INTERATOMIC BOND DISTANCES 41 2.4.5 THREE-DIMENSIONAL CALCULATION OF INTERATOMIC BOND DISTANCES 42 2.5 CALCULATION OF INTERATOMIC BOND ANGLES 43 2.5.1 TWO-DIMENSIONAL ATOMIC BOND ANGLES 44 2.5.2 THREE-DIMENSIONAL ATOMIC BOND ANGLES 44 2.6 AREA AND VOLUME OF THE UNIT CELL 45 2.7 SUMMARY OF METRIC MATRIX CALCULATIONS 46 2.8 QUARTZ EXAMPLE 46 CONTENTS * IX 2.9 TRANSFORMATION MATRICES 49 2.9.1 TRANSFORMATION MATRIX, P 49 2.9.2 TRANSFORMATION OFFRACTIONAL COORDINATES 49 2.9.3 TRANSFORMATION OF THE G MATRIX 50 2.9.4 AREA AND VOLUME TRANSFORMATIONS 51 2.10HEXAMETHYLBENZENEEXAMPLE 52 2.10.1 CALCULATION OF THE TRANSFORMATION MATRIX P 53 2.10.2 CALCULATION OF THE TRANSFORMED FRACTIONAL COORDINATES 53 2.10.3 CALCULATION OFG 2 54 2.10.4 CALCULATION OF THE LATTICE PARAMETERS IN THE NEW BASIS 55 2.10.5 COMPARISONOFTHE VOLUME OFTHE CELL IN BOTH BASES 55 2.10.6 MAGNITUDE OF A VECTOR R 55 2.10.7 INTERATOMIC BOND ANGLE 56 2.11 CRYSTALLOGRAPHIC DIRECTIONS 57 2.12 CRYSTALLOGRAPHIC PLANES AND MILLER INDICES 58 2.13 DENSITY 60 2.14 REVISITING THERMAL EXPANSION AND ISOTHERMAL COMPRESSIBILITY 61 2.14.1 VOLUMETRIE THERMAL EXPANSION 61 2.14.2 VOLUMETRIE COMPRESSIBILITY 62 DEFINITIONS 63 EXERC1SES 63 STARTER PROGRAM 65 CHAPTER 3 * POINT GROUPS 69 CHAPTER OBJECTIVES 71 3.1 INTRODUCTION 71 3.2 GROUP THEORY 72 3.2.1 ELEMENTS IN A SET 72 3.2.2 OPERATIONS 72 3.2.3 GROUP 74 3.3 SYMMETRY OPERATIONS 75 3.3.1 CONVENTIONS OF THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 76 3.3.2 MIRROR SYMMETRY OPERATION 76 3.3.3 IDENTITY SYMMETRY OPERATION 79 X * CONTENTS 3.3.4 N-FOLD ROTATION SYMMETRY OPERATIONS 79 3.3.4.1 TWOFOLD ROTATION SYMMETRY OPERATION 79 3.3.4.2 THREEFOLD ROTATION SYMMETRY OPERATION 80 3.3.4.3 N-FOLD ROTATION SYMMETRY OPERATIONS 81 3.4 CRYSTALLOGRAPHIC ROTATIONS 82 3.5 SUMMARY OF THE TWO-DIMENSIONAL CRYSTALLOGRAPHIC OPERATIONS 85 3.6 TWO-DIMENSIONAL CRYSTALLOGRAPHIC POINT GROUPS 85 3.6.1 POINT GROUP 1 87 3.6.2 POINT GROUP 2 88 3.6.3 POINT GROUP M 89 3.6.4 POINT GROUP 3 90 3.6.5 POINT GROUP 4 91 3.6.6 POINT GROUP 6 93 3.6.7 POINT GROUP 2MM 93 3.6.8 POINT GROUP 3M 95 3.6.9 POINT GROUP 4MM 98 3.6.10 POINT GROUP 6MM 99 3.6.11 IDENTIFICATION OF A CRYSTALLOGRAPHIC POINT GROUP 99 3.7 TWO-DIMENSIONAL CRYSTAL SYSTEMS 100 3.7.1 OBLIQUE SYSTEM 101 3.7.2 RECTANGULAR SYSTEM 102 3.7.3 SQUARE SYSTEM 102 3.7.4 HEXAGONAL SYSTEM 102 3.8 TWO-DIMENSIONAL POINT GROUP TREE 103 3.9 THREE-DIMENSIONAL POINT GROUPS 106 3.9.1 N-FOLD ROTATIONS 106 3.9.1.1 N-FOLD ROTATION SYMMETRY OPERATIONS 107 3.9.1.2 N-FOLD ROTATION CYCLIC POINT CROUPS 107 3.9.2 N-FOLD ROTOINVERSIONS 108 3.9.2.1 INVERSION SYMMETRY OPERATION 108 3.9.2.2 MIRROR OPERATION 109 3.9.2.3 ROTOINVERSION OPERATIONS 3, 4, AND 6 111 3.9.2.4 N-FOLD ROTOINVERSION CYCLIC POINT CROUPS 111 3.10 THREE-DIMENSIONAL CRYSTAL SYSTEMS 113 CONTENTS * XI 3.11 EXAMPLES OF THREE-DIMENSIONAL POINT GROUPS WITH MULTIPLE GENERATORS 115 3.11.1 POINT GROUP 2/M 115 3.11.2 POINT GROUP 32 117 3.12 THREE-DIMENSIONAL POINT GROUP TREES 118 3.13 POINT GROUP SYMMETRY AND SOME PHYSICAL PROPERTIES OF CRYSTALS 119 3.13.1 PIEZOELECTRICITY 119 3.13.2 ETCH FIGURES 121 DEFINITIONS . 122 EXERCISES 123 STARTER PROGRAM 126 CHAPTER 4 * SPACE GROUPS 129 CHAPTER OBJECTIVES 132 PART I: TWO DIMENSIONS 132 4.1 INTRODUCTION 132 4.2 TWO-DIMENSIONAL BRAVAIS LATTICES 133 4.2.1 OBLIQUE 133 4.2.2 RECTANGULAR PRIMITIVE 134 4.2.3 RECTANGULAR CENTERED 134 4.2.4 SQUARE 135 4.2.5 HEXAGONAL 135 4.3 CRYSTAL SYSTEMS AND THE G MATRICES 136 4.4 TWO-DIMENSIONAL SPACE GROUPS 136 4.4.1 OVERVIEW 137 4.4.2 SPACE GROUP NO. L,PL 138 4.4.3 SPACE GROUP NO. 2, P2 140 4.4.4 SPACE GROUP NO. 3, PM 143 4.4.5 SPACE GROUP NO. 4, PG 145 4.4.6 SPACE GROUP NO. 5, CM 147 4.4.7 SPACE GROUP NO. 6, PLMM; SPACE GROUP NO.7, PLMG 149 4.4.8 SPACE GROUP NO. 8,P2GG; SPACE GROUP NO. 9, C2MM; SPACE GROUP NO. 10, P4; SPACE GROUP NO. 11, P4MM; SPACE GROUP NO. 12, PAGM 153 4.4.9 SPACE GROUP NO. 13, P3 153 4.4.10 SPACE GROUP NO. I4,P3ML; SPACE GROUP NO. 15,P31M 156 4.4.11 SPACE GROUP NO. 16, 6; SPACE GROUP NO. \7,P6MM 158 XII * CONTENTS 4.5 OVERVIEW OF THE ASYMMETRIC UNIT 158 4.6 RECIPE FOR ANALYZING A PERIODIC PATTERN 160 4.7 PRIMITIVE CELLS FOR CM AND C2MM 16 0 4.7.1 PRIMITIVE CELL FOR CM 161 4.7.2 PRIMITIVE CELL FOR CIMM 162 4.8 TWO-DIMENSIONAL SPACE GROUP TREE 164 4.9 SUMMARY OF TWO-DIMENSIONAL SPACE GROUPS 168 PART II: THREE DIMENSIONS 169 4.10 THREE-DIMENSIONAL BRAVAIS LATTICES 169 4.10.1 TRICLINIC 171 4.10.2 MONOCLINIC 171 4.10.3 ORTHORHOMBIC 171 4.10.4 TETRAGONAL 171 4.10.5 HEXAGONAL 172 4.10.6 RHOMBOHEDRAL 172 4.10.7 CUBIC 173 4.10.8 SUMMARY OF BRAVAIS LATTICES 173 4.11 THREE-DIMENSIONAL SPACE GROUPS 173 4.11.1 CLASSIFICATION OF THE SPACE GROUPS 173 4.11.2 MINIMAL SYMMETRIES FOR CRYSTAL SYSTEMS 175 4.11.3 GMATRICES 177 4.11.4 SYMMETRY OPERATIONS WITH TRANSLATIONS AS COMPONENTS 178 4.11.4.1 GLIDES 178 4.11.4.2 SCREWS 179 4.11.5 SYMMORPHIC AND NONSYMMORPHIC SPACE GROUPS 179 4.12 HMB AND SPACE GROUP NO. 2, PT 182 4.12.1 INTERPRETATION OF SPACE GROUP SYMMETRIES FROM THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 183 4.12.2 SPACE GROUP TREE NEAR PI 186 4.12.3 HMB CRYSTAL DATA 186 4.12.4 UNIT CELL AND THE ASYMMETRIE UNIT FOR HMB 186 4.12.5 POPULATED CELL FOR HMB 187 4.12.6 SPECIAL PROTECTIONS FOR HMB 187 4.12.7 INTERPRETATION OF HMB CRYSTAL STRUCTURE 188 4.12.8 DISCUSSION 188 CONTENTS * XIII 4.13 AA AND THE SPACE GROUP NO. 150, P321 191 4.13.1 INTERPRETATION OF THE SPACE GROUP SYMMETRIES FROM THE INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY 191 4.13.2 SPACE GROUP TREE NEAR P321 192 4.13.3 AA CRYSTAL DATA 192 4.13.4 UNIT CELL AND THE ASYMMETRIE UNIT FOR AA 193 4.13.5 CALCULATIONOFTHENUMBER OF FORMULA UNITS 193 4.13.6 WYCKOFFPOSITIONS 194 4.13.7 SPECIAL PROTECTIONS FOR AA 196 4.13.8 POLYHEDRONS IN THE AA CRYSTAL STRUCTURE 198 4.13.9 ISOTYPIC CRYSTAL STRUCTURES 199 DEFINITIONS 200 EXERCISES 202 STARTER PROGRAM 206 CHAPTER 5 * THE RECIPROCAL LATTICE 211_ CHAPTER OBJECTIVES . 212 5.1 INTRODUCTION 213 5.2 THE RECIPROCAL LATTICE 213 5.3 RELATIONSHIPS BETWEEN DIRECT AND RECIPROCAL LATTICES 216 5.3.1 RELATIONSHIPS FOR BASIS VECTORS AND LATTICE PARAMETERS 216 5.3.2 RELATIONSHIP BETWEEN METRIE MATRICES G AND G* 217 5.3.3 RELATIONSHIP BETWEEN VOLUMES V AND V* 219 5.3.4 RELATIONSHIP BETWEEN DIRECT AND RECIPROCAL LATTICE VECTORS REVISITED 220 5.3.5 SUMMARY OF TRANSFORMATIONS BETWEEN DIRECT AND RECIPROCAL LATTICES 220 5.4 RECIPROCAL LATTICE CALCULATIONS FOR THREE CRYSTALS 221 5.4.1 HEXAMETHYLBENZENE 221 5.4.1.1 CALCULATION OFG* ANDV* 22 1 5.4.1.2 OVERLAYING THE RECIPROCAL UNIT CELL ON THE DIRECT UNIT CELL 223 5.4.2 ANHYDROUS ALUM 226 5.4.3 CRYSTALS WITH OC, SS, AND Y ALL 90 227 5.5 RELATIONSHIPS BETWEEN TRANSFORMATION MATRICES 228 5.6 DIFFRACTION PATTERN AND THE RECIPROCAL LATTICE 231 5.6.1 MOTIVATION FOR RECIPROCAL LATTICE 231 5.6.2 IDENTIFICATION OF THE D-SPACINGS IN CRYSTALS 232 5.6.3 MILLER INDICES, LAUE INDICES, AND BRAGG'S LAW 233 XIV * CONTENTS 5.6.4 RECIPROCAL LATTICE VECTORS AND SETS OF CRYSTALLOGRAPHIC PLANES 234 5.6.4.1 DIRECTION OF A RECIPROCAL LATTICE VECTOR 235 5.6.4.2 MAGNITUDE OF A RECIPROCAL LATTICE VECTOR 235 5.7 THREE APPLICATIONS OF THE RECIPROCAL LATTICE 236 5.7.1 USING THE RECIPROCAL LATTICE TO CALCULATE RF-SPACINGS 236 5.7.2 CALCULATING ANGLES BETWEEN CRYSTAL FACES 238 5.7.3 RELATING DIFFERENT SETS OF LATTICE PARAMETERS FOR A CRYSTAL 241 5.7.3.1 POWDER DIFFRACTION FILES 241 5.Z3.2 CRYSTAL MORPHOLOGY 243 5.Z3.3 COMPARING INDEXING OF THE RECIPROCAL LATTICE 244 5.7.3.4 TRANSFORMINGFROM THE RECIPROCAL LATTICE TO THE DIRECT LATTICE 245 5.7.3.5 COMPARISON OF PDF FILES 246 DEFINITIONS 248 EXERCISES 248 STARTER PROGRAM 250 CHAPTER 6 * PROPERTIES OF X-RAYS 253 CHAPTER OBJECTIVES 254 6.1 INTRODUCTION 255 6.2 THE DISCOVERY OF X-RAYS 255 6.3 PROPERTIES OF WAVES 256 6.3.1 PRINCIPLE OF SUPERPOSITION 257 6.3.1.1 CONSTRUCTIVE INTERFERENCE 257 6.3.1.2 DESTRUCTIVE INTERFERENCE 258 6.3.1.3 PARTIAL INTERFERENCE 258 6.3.2 YOUNG'S DOUBLE-SLIT EXPERIMENT 258 6.3.3 PROPERTIES OF ELECTROMAGNETIC WAVES 261 6.4 X-RAY SPECTRUM 263 6.4.1 BREMSSTRAHLUNG RADIATION 263 6.4.2 CHARACTERISTIC RADIATION 264 6.4.3 ABSORPTION 266 6.4.4 ELECTRONS AND X-RAYS 268 6.5 THE X-RAY TUBE 269 6.5.1 FILTERS 269 6.6 X-RAY DIFFRACTION 271 6.6.1 FIRST X-RAY DIFFRACTION PHOTOGRAPH 271 CONTENTS * XV 6.6.2 BRAGG'S LAW 274 6.6.3 X-RAY POWDER DIFFRACTION CAMERA 275 DEFINITIONS 276 EXERC1SES 277 CHAPTER 7 * ELECTRON DENSITY MAPS 279 CHAPTER OBJECT1VES 280 7.1 INTRODUCTION 281 7.2 SCATTERING BY AN ELECTRON 281 7.3 SCATTERING BY AN ATOM 282 7.3.1 ATOMIC SCATTERING FACTOR 282 7.4 SCATTERING BY A CRYSTAL 284 7.4.1 PHASE ANGLE 285 7.4.2 AMPLITUDE 286 7.4.3 STRUCTURE FACTOR 288 7.5 SOME MATHEMATICAL IDENTITIES 289 7.6 STRUCTURE FACTORS FOR SOME CRYSTALS 289 7.6.1 SIMPLE CUBIC, POLONIUM 289 7.6.2 BODY-CENTERED CUBIC, CHROMIUM 293 7.6.3 FACE-CENTERED CUBIC, COPPER 295 7.6.4 CRYSTAL WITH TWO ELEMENTS, NACL 297 7.6.5 CRYSTAL WITH TWO ELEMENTS, SPHALERITE 299 7.6.6 STRUCTURE FACTORS FOR GLIDE PLANES 300 7.6.7 STRUCTURE FACTORS FOR SCREW AXES 302 7.7 STRUCTURE FACTORS FOR CENTROSYMMETRIC CRYSTALS 302 7.7.1 PARTITIONING THE SPACE GROUPS 303 7.7.1.1 CENTROSYMMETRIC SPACE GROUPS 303 7.7.1.2 NONCENTROSYMMETRIC SPACE GROUPS 303 7.7.2 INVERSION POINTS AND STRUCTURE FACTORS 304 7.7.3 HEXAMETHYLBENZENE (HMB): EXAMPLE OF A CENTROSYMMETRIC CRYSTAL 304 7.7.4 GENERALIZED CALCULATION OF STRUCTURE FACTORS 305 7.8 ELECTRON DENSITY MAPS 306 7.8.1 FRIEDEL'S LAW 306 7.8.2 FOURIER SERIES 308 7.8.2.1 ONE-DIMENSIONAL FOURIER SERIES 308 7.8.2.2 THREE-DIMENSIONAL FOURIER SERIES 311 XVI * CONTENTS DEFINITIONS 312 EXERCISES 312 STARTER PROGRAM 314 REFERENCES, 317 BIBLIOGRAPHY, 319 APPENDIX: DEFINITIONS, 323 INDEX, 333
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spelling	Julian, Maureen M. Verfasser aut Foundations of crystallography with computer applications Maureen M. Julian Boca Raton [u.a.] CRC Press 2008 XXVI, 340 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Crystallography Data processing Crystallography, Mathematical Kristallographie (DE-588)4033217-2 gnd rswk-swf Kristallographie (DE-588)4033217-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016261822&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Julian, Maureen M. Foundations of crystallography with computer applications Datenverarbeitung Crystallography Data processing Crystallography, Mathematical Kristallographie (DE-588)4033217-2 gnd
subject_GND	(DE-588)4033217-2
title	Foundations of crystallography with computer applications
title_auth	Foundations of crystallography with computer applications
title_exact_search	Foundations of crystallography with computer applications
title_exact_search_txtP	Foundations of crystallography with computer applications
title_full	Foundations of crystallography with computer applications Maureen M. Julian
title_fullStr	Foundations of crystallography with computer applications Maureen M. Julian
title_full_unstemmed	Foundations of crystallography with computer applications Maureen M. Julian
title_short	Foundations of crystallography with computer applications
title_sort	foundations of crystallography with computer applications
topic	Datenverarbeitung Crystallography Data processing Crystallography, Mathematical Kristallographie (DE-588)4033217-2 gnd
topic_facet	Datenverarbeitung Crystallography Data processing Crystallography, Mathematical Kristallographie
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work_keys_str_mv	AT julianmaureenm foundationsofcrystallographywithcomputerapplications

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