Diffuse X-ray Scattering and Models of Disorder

Name: Diffuse X-ray Scattering and Models of Disorder
Brand: OUP Oxford
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T. R. Welberry(Author)

OUP Oxford (Publisher)

1st Edition

Published on 28. April 2022

400 pages

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978-0-19-260740-9 (ISBN)

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Content

Cover
Titlepage
Copyright
Preface
Preface to second edition
Contents
Part I Experiment
1 Measurement of diffuse scattering
1.1 Introduction
1.2 2D data collection
1.2.1 Using a linear position-sensitive detector
1.2.2 Using image-plates at a synchrotron
1.3 3D data collection
1.3.1 Using an automatic IP detector
1.3.2 Using a CCD detector
1.3.3 Single photon-counting hybrid pixel detectors
1.4 Diffuse neutron scattering
1.4.1 Spallation neutrons I -SXD instrument at ISIS
1.4.2 Spallation neutrons II-cross-correlation spectrometer Corelli at SNS
1.5 Electron diffraction
Part II Disorder Models
2 Disorder in one dimension
2.1 Diffraction intensity
2.2 One-dimensional disorder-layer structures
2.3 Correlations and short-range order
2.4 Restrictions on correlation coefficients
3 Particular disorder models
3.1 The simple Markov chain
3.2 Alternative treatment for Markov chains-stochastic matrices
3.3 The 1D Ising model
3.4 Models involving second-nearest-neighbour and more distant interactions
3.4.1 Linear form
3.4.2 Non-linear form
3.5 Second-neighbour Ising model
4 Displacements in one dimension
4.1 General
4.2 Perturbed regular lattice
4.3 Diffraction from a perturbed regular lattice
4.4 Real example of a 1D perturbed regular lattice
5 Disorder in higher dimensions
5.1 General considerations
5.2 A simple 2D model of disorder
5.2.1 Simple linear growth model, d= 0
5.2.2 Simple growth model with constraint, ?(1-ß) = -ad
5.3 Ising models and growth models in 2D
5.4 An alternative approach to growth-disorder models
5.5 A useful parameterisation of growth-disorder models
5.6 General discussion of binary models
5.7 Some symmetry considerations
5.8 Direct synthesis of disordered distributions
6 Displacements in two or three dimensions
6.1 Gaussian growth-disorder models in 2D
6.2 Gaussian growth-disorder models-examples
6.2.1 Simple lattice with small s
6.2.2 Lattices with large s-paracrystals
6.3 Generalised Gaussian models
6.4 Hexagonal paracrystals
6.4.1 Effect of the variance, s2L
6.4.2 Effect of varying ?T for given ?L
6.4.3 Transverse vs longitudinal correlations
6.5 Gaussian growth-disorder models in 3D and higher
6.6 Conversion of Gaussian to binary variables
7 Interactions between occupancies and displacements
7.1 General intensity expressions
7.2 A possible Ising-like model for occupations and displacements
7.3 Use of force models and Monte Carlo simulation
7.4 Illustration of the meaning of the different intensity components
7.5 Size-effect and multi-site correlations
Part III Examples Of Real Disordered Systems I
8 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene (Bemb2)
8.1 Introduction
8.2 Symmetry considerations
8.2.1 q = 0 modulations
8.2.2 q = 0 modulations
8.3 Calculated diffraction patterns
8.3.1 The (0 k l) section
8.3.2 The (h k barh) section
8.4 Displacement modulations
8.5 Comparison with correlation description
9 p-chloro-N-(p-methyl-benzylidene)aniline (MeCl)
9.1 Introduction
9.2 Cell data
9.3 X-ray diffuse scattering data
9.4 The average structure and model for the disorder
9.5 Molecular interactions and MC simulation
9.6 Results
10 Urea inclusion compounds
10.1 Introduction
10.2 X-ray diffuse scattering data
10.3 Monte Carlo simulation
10.3.1 Ordering of alkanes
10.3.2 Modelling interactions with the urea framework
10.4 Relaxation simulation
10.5 Results
11 Mullite
11.1 Introduction
11.2 X-ray diffuse scattering data
11.3 A simple model
11.4 Results
11.5 Conclusions
12 Wüstite
12.1 Introduction
12.2 X-ray diffuse scattering data
12.3 Summary of X-ray diffraction features
12.4 Paracrystal model to account for diffraction features
12.5 Relaxation of structure around defects
12.6 Effect of cluster volume fraction
12.7 Effect of cluster size
13 Cubic stabilised zirconias
13.1 Introduction
13.2 Model for relaxation
13.3 Vacancy ordering via MC simulation of pair correlations
13.4 Multi-site correlations
13.5 Modulation-wave direct synthesis of vacancy distributions
14 Automatic refinement of a Monte Carlo model
14.1 Introduction
14.2 X-ray diffuse scattering data
14.3 Monte Carlo model
14.3.1 Ordering of (+/-) orientations
14.3.2 Centre-of-mass displacements
14.3.3 Orientational relaxation
14.3.4 Refinement procedure
14.4 Calculation of diffraction patterns
14.5 Least-squares
14.6 Estimation of the differentials, ??I / ?pi
14.7 Progress of refinement
14.8 Discussion of solution
14.9 Conclusion
15 Further applications of the automatic Monte Carlo method
15.1 Introduction
15.2 Benzil, C14H10O2
15.2.1 X-ray diffuse scattering data
15.2.2 Structure specification
15.2.3 Intermolecular interactions
15.2.4 MC simulation
15.2.5 Automatic fitting of MC model
15.3 p-methyl-N-(p-chloro-benzylidene)aniline (ClMe)
15.3.1 X-ray diffuse scattering data
15.3.2 Structure specification
15.3.3 Intermolecular interactions
15.3.4 Occupancy distributions
15.3.5 MC simulation
15.3.6 Results for ClMe
15.4 Conclusion
16 Disorder involving multi-site interactions
16.1 Introduction
16.2 Oxygen/fluorine ordering in K3MoO3F3
16.2.1 Observed diffuse scattering patterns
16.2.2 Chemical constraint for K3MoO3F3
16.2.3 MC simulation using a simple constraint
16.3 Short-range order in (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7
16.3.1 Observed diffuse scattering patterns
16.3.2 Chemical considerations
16.3.3 MC simulaton of occupancy disorder
16.3.4 MC simulaton of size-effect distortions
16.4 Conclusion
17 Strain effects in disordered crystals
17.1 Introduction
17.2 A simple potential used in sol-gel systems
17.2.1 Simulation on a square lattice
17.2.2 Significance of the modified Lennard-Jones potential result
17.3 Cubic stabilised zirconia
17.3.1 Model for local structure
17.3.2 Origin of strain
17.3.3 Results of MC simulation
17.4 The organic inclusion compound didecylbenzene/urea
17.4.1 Results of MC simulation
17.5 The 'diffuse hole' in Bemb2
17.5.1 Background
17.5.2 MC simulation of the ' diffuse hole' effect
17.6 Conclusion
18 Miscellaneous examples
18.1 Introduction
18.2 The defect structure of the zeolite mordenite
18.2.1 Background
18.2.2 Computer simulations
18.3 The defect structure of sodium bismuth titanate
18.3.1 Background
18.3.2 MC simulation-SRO
18.3.3 MC simulation-GP zones
18.4 Size-effect-like distortions in quasicrystalline structures
18.4.1 Background
18.4.2 MC simulation
18.4.3 Diffraction patterns
Part IV Examples Of Real Disordered Systems II
19 Pentachloronitrobenzene, C6Cl5NO2
19.1 Introduction
19.2 Diffuse scattering data
19.3 Modelling the disorder
19.3.1 Occupancy disorder
19.3.2 Size-effect relaxation and displacement disorder
19.3.3 Atomic distributions
19.4 Summary
20 Polymorphs of benzocaine, C9H11O2N
20.1 Introduction
20.2 Average crystal structures
20.3 Observed diffuse scattering data
20.4 Monte Carlo simulations
20.5 Results
20.5.1 Displacement correlations
20.5.2 Symmetry of ribbon-pairs
20.5.3 Summary of results for thermal model
20.6 Phase transition in polymorph II
20.7 Disordered Form II structure model
20.7.1 Outline
20.7.2 Insertion of SRO
20.7.3 Example SRO distributions
20.7.4 Diffraction pattern of final room-temperature model
20.8 Summary
21 A new refinement strategy
21.1 Introduction
21.2 A new strategy
21.3 Buckingham potential and spring constants
21.3.1 Empirical spring constant formula
21.4 Example-paracetamol forms I and II
21.4.1 Average structures
21.4.2 Monte Carlo models
21.4.3 X-ray data
21.4.4 MC simulations and calculated diffraction patterns
22 Polymorphism in aspirin
22.1 Introduction
22.2 Aspirin, C9H8O4
22.2.1 The two polymorphs of aspirin
22.2.2 X-ray diffuse scattering
22.2.3 Monte Carlo modelling
22.2.4 The hk0 section diffuse scattering
22.2.5 The effects of strain
22.2.6 Aspirin summary
23 Lead perovskite relaxors, PZN and PMN
23.1 Introduction
23.2 Simple model of PZN using effective interactions
23.2.1 Average structure
23.2.2 Observed scattering
23.2.3 Discussion of diffuse scattering features
23.2.4 Model of planar nanodomains
23.3 Monte Carlo simulation
23.3.1 Pb ordering
23.3.2 Computer simulations
23.3.3 Insertion of Zn/Nb and O2- ions
23.3.4 Size-effect distortions
23.3.5 SRO of B-site ions
23.3.6 Calculated diffraction patterns
23.3.7 The effect of electric fields
23.4 Different models for the polar nanodomains in PZN
23.4.1 Simple 2D model with ?1 0 0? displacements
23.4.2 A 3D model with ?1 0 0? displacements
23.4.3 A 3D model with ?1 1 1? displacements
23.5 Atomistic shell model based on ab initio calculations
23.5.1 Molecular dynamics model for PMN
23.5.2 MD simulations
23.5.3 Results
23.5.4 Nanodomain structure
23.5.5 Conditional probability plots
23.6 Dynamic disorder in cubic BaTiO3
23.6.1 X-ray diffuse scattering data
23.6.2 Molecular dynamics simulation
23.6.3 Diffraction features
23.6.4 Real-space correlations of Ti displacements
23.6.5 The dynamical structure factor, S(q,?)
23.6.6 Summary
24 Pair distribution functions (PDF, 3D-PDF and 3D-?PDF)
24.1 The pair distribution function (PDF)
24.1.1 PDF sensitivity to different aspects of disorder
24.1.2 Different paracrystal distributions
24.1.3 Size-effect relaxation around defects
24.1.4 Concluding remarks
24.2 The 3D pair distribution functions
24.2.1 General intensity expression
24.2.2 The 3D pair distribution function
24.2.3 Important properties and features of ?PDFs
24.2.4 Example 1: displacement disorder
24.2.5 Example 2: occupational disorder
24.2.6 Example 3: mixed disorder
24.2.7 Summary
24.3 Real example: sodium-intercalated V2O5
24.3.1 Average structure of Na0.45V2O5
24.3.2 Diffuse X-ray scattering measurements
24.3.3 Ordering of Na within the two-leg ladders
24.3.4 ?PDF peak intensities in the z=0 plane
24.3.5 Temperature dependence of correlation length
24.4 Conclusion
References
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Diffuse X-ray Scattering and Models of Disorder

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