Anmerkung: Intro -- Contents -- 1 Introduction to diffraction -- 1.1 Introduction -- 1.2 X-ray scattering from electrons -- 1.3 X-ray scattering from atoms -- 1.4 X-ray scattering from a unit cell -- 1.5 The effects of the crystal lattice -- 1.6 X-ray scattering from the crystal -- 1.7 The structure-factor equation -- 1.8 The electron-density equation -- 1.9 A mathematical relationship -- 1.10 Bragg's law -- 1.11 Resolution -- 1.12 The phase problem -- 2 Introduction to symmetry and diffraction -- 2.1 The relationship between a crystal structure and its diffraction pattern -- 2.2 Translation symmetry in crystalline solids -- 2.3 Symmetry of individual molecules, with relevance to crystalline solids -- 2.4 Symmetry in the solid state -- 2.5 Diffraction and symmetry -- 2.6 Further points -- Exercises -- 3 Crystal growth and evaluation -- 3.1 Introduction -- 3.2 Protect your crystals -- 3.3 Crystal growth -- 3.4 Survey of methods -- 3.4.1 Solution methods -- 3.4.2 Sublimation -- 3.4.3 Fluid-phase growth -- 3.4.4 Solid-state synthesis -- 3.4.5 General comments -- 3.5 Evaluation -- 3.5.1 Microscopy -- 3.5.2 X-ray photography -- 3.5.3 Diffractometry -- 3.6 Crystal mounting -- 3.6.1 Standard procedures -- 3.6.2 Air-sensitive crystals -- 3.6.3 Crystal alignment -- 4 Space-group determination -- 4.1 Introduction -- 4.2 Prior knowledge and information other than from diffraction -- 4.3 Metric symmetry and Laue symmetry -- 4.4 Unit cell contents -- 4.5 Systematic absences -- 4.6 The statistical distribution of intensities -- 4.7 Other points -- 4.8 A brief conducted tour of some entries in International Tables for Crystallography, Volume A -- Exercises -- 5 Background theory for data collection -- 5.1 Introduction -- 5.2 A step-wise theoretical journey through an experiment -- 5.3 The geometry of X-ray diffraction -- 5.3.1 Real-space considerations: Bragg's law. , 5.3.2 Reciprocal-space considerations: the Ewald sphere -- 5.4 Determining the unit cell: the indexing process -- 5.4.1 Indexing: a conceptual view -- 5.4.2 Indexing procedure -- 5.5 Relating diffractometer angles to unit cell parameters: determination of the orientation matrix -- 5.6 Data-collection procedures and strategies -- 5.6.1 Criteria for selecting which data to collect -- 5.6.2 How best to measure data: the need for reflection scans -- 5.7 Extracting data intensities: data integration and reduction -- 5.7.1 Background subtraction -- 5.7.2 Data integration -- 5.7.3 Crystal and geometric corrections to data -- Exercises -- 6 Practical aspects of data collection -- 6.1 Introduction -- 6.2 Collecting data with area-detector diffractometers -- 6.3 Experimental conditions -- 6.3.1 Radiation -- 6.3.2 Temperature -- 6.3.3 Pressure -- 6.3.4 Other conditions -- 6.4 Types of area detector -- 6.4.1 Multiwire proportional chamber (MWPC) -- 6.4.2 Phosphor coupled to a TV camera -- 6.4.3 Image plate (IP) -- 6.4.4 Charge-coupled device (CCD) -- 6.5 Some characteristics of CCD area-detector systems -- 6.5.1 Spatial distortion -- 6.5.2 Non-uniform intensity response -- 6.5.3 Bad pixels -- 6.5.4 Dark current -- 6.6 Crystal screening -- 6.6.1 Unit cell and orientation matrix determination -- 6.6.2 If indexing fails -- 6.6.3 Re-harvest the reflections -- 6.6.4 Still having problems? -- 6.6.5 After indexing -- 6.6.6 Check for known cells -- 6.6.7 Unit cell volume -- 6.7 Data collection -- 6.7.1 Intensity level -- 6.7.2 Mosaic spread -- 6.7.3 Crystal symmetry -- 6.7.4 Other considerations -- Exercises -- 7 Practical aspects of data processing -- 7.1 Data reduction and correction -- 7.2 Integration input and output -- 7.3 Corrections -- 7.4 Output -- 7.5 A typical experiment? -- 7.6 Examples of more problematic cases -- 7.7 Twinning and area-detector data. , 7.8 Some other special cases (in brief) -- Exercises -- 8 Fourier syntheses -- 8.1 Introduction -- 8.2 Forward and reverse Fourier transforms -- 8.3 Some mathematical and computing considerations -- 8.4 Uses of different kinds of Fourier syntheses -- 8.4.1 Patterson syntheses -- 8.4.2 E-maps -- 8.4.3 Full electron-density maps, using (8.2) or (8.3) as they stand -- 8.4.4 Difference syntheses -- 8.4.5 2F[sub(o)] - F[sub(c)] syntheses -- 8.4.6 Other uses of difference syntheses -- 8.5 Weights in Fourier syntheses -- 8.6 Illustration in one dimension -- 8.6.1 F[sub(c)] synthesis -- 8.6.2 F[sub(o)] synthesis, as used in developing a partial structure solution -- 8.6.3 F[sub(o)] - F[sub(c)] synthesis -- 8.6.4 Full F[sub(o)] synthesis -- Exercises -- 9 Patterson syntheses for structure determination -- 9.1 Introduction -- 9.2 What the Patterson synthesis means -- 9.3 Finding heavy atoms from a Patterson map -- 9.3.1 One heavy atom in the asymmetric unit of P1 -- 9.3.2 One heavy atom in the asymmetric unit of P2[sub(1)]/c -- 9.3.3 One heavy atom in the asymmetric unit of P2[sub(1)]2[sub(1)]2[sub(1)] -- 9.3.4 One heavy atom in the asymmetric unit of Pbca -- 9.3.5 One heavy atom in the asymmetric unit of P2[sub(1)] -- 9.3.6 Two heavy atoms in the asymmetric unit of P1 and other space groups -- 9.4 Patterson syntheses giving more than one possible solution, and other problems -- 9.5 Patterson search methods -- 9.5.1 Rotation search -- 9.5.2 Translation search -- Exercises -- 10 Direct methods of crystal-structure determination -- 10.1 Amplitudes and phases -- 10.2 The physical basis of direct methods -- 10.3 Constraints on the electron density -- 10.3.1 Discrete atoms -- 10.3.2 Non-negative electron density -- 10.3.3 Random atomic distribution -- 10.3.4 Maximum value of & -- #961 -- [sup(3)](x)dV -- 10.3.5 Equal atoms -- 10.3.6 Maximum entropy. , 10.3.7 Equal molecules and & -- #961 -- (x) = const. -- 10.3.8 Structure invariants -- 10.3.9 Structure determination -- 10.3.10 Calculation of E values -- 10.3.11 Setting up phase relationships -- 10.3.12 Finding reflections for phase determination -- 10.3.13 Assignment of starting phases -- 10.3.14 Phase determination and refinement -- 10.3.15 Figures of merit -- 10.3.16 Interpretation of maps -- 10.3.17 Completion of the structure -- Exercises -- 11 An introduction to maximum entropy -- 11.1 Entropy -- 11.2 Maximum entropy -- 11.2.1 Calculations with incomplete data -- 11.2.2 Forming images -- 11.2.3 Entropy and probability -- 11.3 Electron-density maps -- 12 Least-squares fitting of parameters -- 12.1 Weighted mean -- 12.2 Linear regression -- 12.2.1 Variances and covariances -- 12.2.2 Restraints -- 12.2.3 Constraints -- 12.3 Non-linear least squares -- 12.4 Ill-conditioning -- 12.5 Computing time -- Exercises -- 13 Refinement of crystal structures -- 13.1 Equations -- 13.1.1 Bragg's law -- 13.1.2 Structure factors from the continuous electron density -- 13.1.3 Electron density from the structure amplitude and phase -- 13.1.4 Structure factor from a parameterized model -- 13.2 Reasons for performing refinement -- 13.2.1 To improve phasing so that computed electron density maps more closely represent the actual electron density -- 13.2.2 To try to verify that the structure is 'correct' -- 13.2.3 To obtain the 'best' values for the parameters in the model -- 13.3 Data quality and limitations -- 13.3.1 Resolution -- 13.3.2 Completeness -- 13.3.3 Leverage -- 13.3.4 Weak reflections and systematic absences -- 13.3.5 Standard uncertainties -- 13.3.6 Systematic trends -- 13.4 Refinement fundamentals -- 13.4.1 & -- #969 -- , the weight -- 13.4.2 & -- #947 -- [sub(1)], the observations -- 13.4.3 & -- #947 -- [sub(2)], the calculations. , 13.4.4 Issues -- 13.5 Refinement strategies -- 13.6 Under- and over-parameterization -- 13.6.1 Under-parameterization -- 13.6.2 Over-parameterization -- 13.7 Pseudo-symmetry, wrong space groups and Z' > -- 1 structures -- 13.8 Conclusion -- Exercises -- 14 Analysis of extended inorganic structures -- 14.1 Introduction -- 14.2 Disorder -- 14.2.1 Site-occupancy disorder -- 14.2.2 Positional disorder -- 14.2.3 Limits of Bragg diffraction -- 14.3 Phase transitions -- 14.4 Structure validation -- 14.5 Case history 1 - BiMg[sub(2)]VO[sub(6)] -- 14.6 Case history 2 - Mo[sub(2)]P[sub(4)]O[sub(15)] -- Exercises -- 15 The derivation of results -- 15.1 Introduction -- 15.2 Geometry calculations -- 15.2.1 Fractional and Cartesian co-ordinates -- 15.2.2 Bond distance and angle calculations -- 15.2.3 Dot products -- 15.2.4 Transforming co-ordinates -- 15.2.5 Standard uncertainties -- 15.2.6 Assessing significant differences -- 15.3 Least-squares planes and dihedral angles -- 15.3.1 Conformation of rings and other molecular features -- 15.4 Hydrogen atoms and hydrogen bonding -- 15.5 Displacement parameters -- 15.5.1 & -- #946 -- s, Bs and Us -- 15.5.2 'The equivalent isotropic displacement parameter' -- 15.5.3 Symmetry and anisotropic displacement parameters -- 15.5.4 Models of thermal motion and geometrical corrections: rigid-body motion -- 15.5.5 Atomic displacement parameters and temperature -- Exercises -- 16 Random and systematic errors -- 16.1 Random and systematic errors -- 16.2 Random errors and distributions -- 16.2.1 Measurement errors -- 16.2.2 Describing data -- 16.2.3 Theoretical distributions -- 16.2.4 Expectation values -- 16.2.5 The standard error on the mean -- 16.3 Taking averages -- 16.3.1 Testing for normality using a histogram -- 16.3.2 The & -- #967 -- [sup(2)] test for normality -- 16.3.3 Averaging data when & -- #967. , [sup(2)sub(red)]»1.

Anmerkung: Couverture -- Avant-propos -- Sommaire -- 1. Aspects fondamentaux de cristallographie aux rayons X -- 1.1. Introduction -- 1.2. Comparaison de la cristallographie avec les autres techniques de détermination structurale -- 1.3. L'analogie de l'œil et du microscope -- 1.4. Principes fondamentaux de l'état cristallin -- 1.5. Diffraction des rayons X par les molécules et par les cristaux -- 1.6. Géométrie et symétrie de la diffraction des rayons X -- 1.7. Les intensités des rayons diffractés -- 1.8. Les sources de rayons X -- 1.9. Résumé -- 1.10. Exercices -- 2. La cristallographie aux rayons X en pratique -- 2.1. Introduction -- 2.2. La préparation et la sélection des échantillons -- 2.3. Mesure des figures de diffraction -- 2.4. Obtenir la géométrie et la symétrie de la maille -- 2.5. La mesure des intensités -- 2.6. Réduction de données -- 2.7. Résolution de structure -- 2.8. Compléter la structure basique -- 2.9. Affiner la structure -- 2.10. Désordre, macle et la détermination de la « structure absolue » -- 2.11. Présenter et interpréter les résultats -- 2.12. Archiver et présenter les structures cristallines -- 2.13. Résumé -- 2.14. Exercices -- 3. Études de cas de cristallographie aux rayons X -- 3.1. Introduction -- 3.2. Étude de cas 1 : un complexe de thiolate de mercure -- 3.3. Étude de cas 2 : un complexe chiral de rhodium solvaté -- 3.4. Étude de cas 3 : des microcristaux d'un composé organique chiral -- 3.5. Étude de cas 4 : chaîne de coordination de métal -- 3.6. Étude de cas 5 : un palladium en complexe avec une phosphine volumineuse pour des études de catalyse -- 3.7. Résumé -- 3.8. Exercices -- 4. Sujets associés -- 4.1. Introduction -- 4.2. Diffraction de neutrons par un cristal unique -- 4.3. Diffraction par des échantillons en poudre -- 4.4. Cristallographie des macromolécules biologiques. , 4.5. Prédiction de structure cristalline -- 4.6. Résumé -- 4.7. Exercices -- Glossaire -- Bibliographie -- Index.