Fourier methods in crystallography:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Wiley-Interscience
1970
|
| Schriftenreihe: | Wiley monographs in crystallography
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 259 S. Ill., graph. Darst. |
| ISBN: | 0471707058 |
Internformat
MARC
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| 100 | 1 | |a Ramachandran, Gopalasamudram N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fourier methods in crystallography |c G. N. Ramachandran ; R. Srinivasan |
| 264 | 1 | |a New York u.a. |b Wiley-Interscience |c 1970 | |
| 300 | |a XIII, 259 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley monographs in crystallography | |
| 650 | 4 | |a Fourier, Transformations de | |
| 650 | 4 | |a Radiocristallographie | |
| 650 | 4 | |a Fourier transformations | |
| 650 | 4 | |a X-ray crystallography | |
| 650 | 0 | 7 | |a Fourier-Transformation |0 (DE-588)4018014-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Srinivasan, Ramachandran |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804116370517917696 |
|---|---|
| adam_text | Contents
1. Fourier representation of electron density 1
Introduction 1
Theory of diffraction by an assemblage of particles and a continuous
medium 1
Set of N scattering points 2
Continuous medium 3
Scattering by atoms 4
Scattering by a free electron 4
Scattering by the electron distribution in an atom 6
Fourier transforms 7
Fourier transform of a delta function 9
Effect of translation 10
Fourier transform of a molecule 11
Diffraction by a crystal structure 12
Reciprocal lattice and Fourier series 14
Relation to experiment 16
The phase problem 16
Structure from Fourier synthesis 18
F synthesis or the inverse structure 19
Negative structure and the inverse negative structure 19
Sharpening functions 20
Appendix 23
A. General Fourier transforms 23
Fourier cosine and sine transforms 25
B. Convolution integral and its Fourier transform 26
C. Convolutions involving delta functions 27
D. Proof of the grating formula 28
E. Periodic functions, their Fourier transforms and inversion in terms
of Fourier series 29
F. Spherical distributions 31
References 32
2. Patterson and Patterson type syntheses 34
Convolution of two structures 34
ix
x Contents
Patterson structure 36
Noncentrosymmetric structure 36
Centrosymmetric structures 37
Squared structure 38
Modulus structure 39
Thesyntheses |Fs2| andF» 40
References 44
3. Patterson function and the theory of Images 45
The Patterson as a sum of images 45
Noncentrosymmetric structure 45
Centrosymmetric case 47
Image seeking functions 48
Sum function 49
Product function 49
Minimum function 49
Resolution of images 49
Noncentrosymmetric case 50
Weighted superposition functions 51
Centrosymmetric case 52
Representation of the image seeking function as a Fourier synthesis . 53
The sum function 53
The product function 54
The minimum function 54
Relation between image functions and electron densities 56
Cumulative functions 56
References 58
4. The phase synthesis and other standard syntheses 60
The phase synthesis 60
Importance of phase angles 62
Phase synthesis 62
Random synthesis 66
Interpretation of results 67
Reciprocal structure 68
Phase squared structure 69
Cosine and sine syntheses 70
References 70
5. Syntheses for partially known structures 72
Introduction 72
The weighted sum function—Fourier interpretation 73
Interpretation of the alpha synthesis 73
Peaks in the noncentrosymmetric case 74
Centrosymmetric case 76
Contents xi
Effect of wrong atoms in the alpha synthesis 77
References 78
6. Syntheses for partially known structures; other types of syntheses .... 80
General form of the syntheses 80
The beta synthesis 82
The gamma prime synthesis 84
The gamma general, alpha prime and beta prime syntheses 85
The modified syntheses 86
The effect of centrosymmetry on beta and gamma prime syntheses ... 87
References 88
7. Syntheses for partially known structures; second order approximation and
effect of wrong atoms 89
Calculation to the second order of approximation 89
Refinement of the standard syntheses 89
Peak strength in the beta, gamma prime, and other syntheses .... 92
Effect of wrong atoms 93
Derivation for the centrosymmetric alpha synthesis 94
Derivation for the noncentrosymmetric beta synthesis 95
Discussion for the limiting case when tti2 tends to unity 95
References 95
8. Tests for the various syntheses 96
Introduction 96
Weighting functions for gamma prime and beta syntheses 97
Weighting function for the beta synthesis 100
Tests of the beta and gamma prime syntheses 101
Hypothetical structures 101
Actual structure analyses 105
Tests of a and j8 syntheses 109
Weighting and cutoff in combination 112
Difference beta synthesis 113
Comparison of the /3 and y syntheses with wrong atoms 114
References 116
9. Isomorphous replacement: general aspects 120
Introduction 120
Phase determination with isomorphous crystals 121
Centrosymmetric P group 124
Centrosymmetric crystals 124
The method of double isomorphous replacement 126
Simulation of isomorphism by use of different wavelengths 128
References 129
xii Contents
10. Isomorphous replacement: special Fourier syntheses 131
The alpha and beta syntheses applied to isomorphous crystals 131
Tests of the isomorphous syntheses 135
Determination of heavy atom positions 137
The difference Patterson technique 138
Location of heavy atom vectors on the difference Patterson by the
principle of maximum superposition 139
The modulus difference squared (MDY synthesis 141
Multiple isomorphism: relative positions of heavy atoms 144
Correlation functions 145
The MD squared synthesis as a correlation synthesis 148
Examples of the determination of the replaceable atom positions . . . 149
Principle of maximum superposition 150
MD squared synthesis 151
Practical aspects of treatment of isomorphous data 155
The effect of errors in the data on phase angle calculation 156
Statistical tests for isomorphism 161
References 163
11. Anomalous dispersion effect; general aspects 166
The anomalous dispersion effect for x rays 166
Determination of the phase angle 169
Resolution of phase ambiguity 172
Resolution of phase with anomalous dispersion data alone 174
Quasianomalous dispersion synthesis 175
Application of the quasianomalous dispersion synthesis 177
Magnitude of Bijvoet ratios 180
Crystal structures solved by anomalous dispersion method 182
Power of the anomalous dispersion method 184
The weighted anomalous dispersion synthesis 188
The double phased synthesis 190
Centrosymmetric anomalous dispersion group 191
Condition for the occurrence of Bijvoet differences 191
Determination of A/ 193
Chlorine and barium 193
Iodine 193
Silicon and oxygen 194
Aluminum and gallium 195
Refinement of structures in the presence of anomalous dispersion effects 195
References 197
12. Anomalous dispersion effect; Fourier syntheses 201
Syntheses of the alpha and beta classes with anomalous dispersion data 201
Alpha anomalous dispersion synthesis 201
Contents xiii
Beta anomalous dispersion synthesis 203
Centrosymmetric P group 205
Test of the beta anomalous dispersion synthesis 205
The Patterson function in the presence of anomalous dispersion .... 206
Determination of the positions of anomalous scatterers 210
Fourier representation of anomalous dispersion components .... 213
References 218
13. Combination of isomorphous replacement and anomalous dispersion data;
complete solution of phase 220
Choice of phase angle 220
Combination of the beta types of syntheses 221
Location of heavy atom positions using combination of data 223
Correlation of heavy atom positions in protein derivatives 225
Applications to neutron crystallography 228
Experimental verification 230
References 235
Author Index 239
Subject Index 242
|
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| author | Ramachandran, Gopalasamudram N. Srinivasan, Ramachandran |
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| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
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| id | DE-604.BV001930909 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:26Z |
| institution | BVB |
| isbn | 0471707058 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001258577 |
| oclc_num | 99754 |
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| owner_facet | DE-20 DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-83 DE-188 |
| physical | XIII, 259 S. Ill., graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Wiley-Interscience |
| record_format | marc |
| series2 | Wiley monographs in crystallography |
| spelling | Ramachandran, Gopalasamudram N. Verfasser aut Fourier methods in crystallography G. N. Ramachandran ; R. Srinivasan New York u.a. Wiley-Interscience 1970 XIII, 259 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley monographs in crystallography Fourier, Transformations de Radiocristallographie Fourier transformations X-ray crystallography Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Kristallographie (DE-588)4033217-2 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s Kristallographie (DE-588)4033217-2 s DE-604 Srinivasan, Ramachandran Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramachandran, Gopalasamudram N. Srinivasan, Ramachandran Fourier methods in crystallography Fourier, Transformations de Radiocristallographie Fourier transformations X-ray crystallography Fourier-Transformation (DE-588)4018014-1 gnd Kristallographie (DE-588)4033217-2 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4033217-2 |
| title | Fourier methods in crystallography |
| title_auth | Fourier methods in crystallography |
| title_exact_search | Fourier methods in crystallography |
| title_full | Fourier methods in crystallography G. N. Ramachandran ; R. Srinivasan |
| title_fullStr | Fourier methods in crystallography G. N. Ramachandran ; R. Srinivasan |
| title_full_unstemmed | Fourier methods in crystallography G. N. Ramachandran ; R. Srinivasan |
| title_short | Fourier methods in crystallography |
| title_sort | fourier methods in crystallography |
| topic | Fourier, Transformations de Radiocristallographie Fourier transformations X-ray crystallography Fourier-Transformation (DE-588)4018014-1 gnd Kristallographie (DE-588)4033217-2 gnd |
| topic_facet | Fourier, Transformations de Radiocristallographie Fourier transformations X-ray crystallography Fourier-Transformation Kristallographie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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