Diffuse X-ray scattering and models of disorder / T. R. Welberry.

Format:

Book

Author/Creator:

Welberry, T. R. (Thomas Richard), author.

Contributor:

International Union of Crystallography, associated with work.

Series:

IUCr monographs on crystallography ; 31.

Oxford scholarship online.

IUCr monographs on crystallography ; 31

Oxford scholarship online

Language:

English

Subjects (All):

X-rays--Scattering.

X-rays.

X-ray crystallography.

Physical Description:

1 online resource (425 pages)

Edition:

Second edition.

Place of Publication:

New York, New York : Oxford University Press, [2022]

Summary:

Diffuse X-ray scattering is a rich source of local structural information over and above that obtained by conventional crystallography. The text shows how computer simulation of a model crystal provides a general method by which scattering of all kinds and from all types of materials can be analysed.

Contents:

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, δ= 0

5.2.2 Simple growth model with constraint, γ(1-β) = -αδ

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 σ

6.2.2 Lattices with large σ-paracrystals

6.3 Generalised Gaussian models

6.4 Hexagonal paracrystals

6.4.1 Effect of the variance, σ2L

6.4.2 Effect of varying ρT for given ρL

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, ∂ΔI / ∂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.

Notes:

This edition also issued in print: 2022.

Previous edition published: 2004.

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Welberry, T. R. Diffuse X-Ray Scattering and Models of Disorder

ISBN:

0-19-189530-X

0-19-260740-5

OCLC:

1312160183