Diffuse neutron scattering from crystalline materials / Victoria M. Nield and David A. Keen.

Format:

Book

Author/Creator:

Nield, Victoria M.

Contributor:

Keen, David A.

Series:

Oxford series on neutron scattering in condensed matter

Language:

English

Subjects (All):

Crystals.

Neutrons--Scattering.

Neutrons.

Physical Description:

xvi, 317 pages : illustrations ; 24 cm.

Place of Publication:

Oxford : Clarendon ; New York : Oxford University Press, 2001.

Contents:

1.1 What is diffuse scattering? 1

1.2 Types of disorder leading to diffuse scattering 2

1.2.1 Static disorder 2

1.2.2 Dynamic disorder 3

1.2.3 Orientational disorder 3

1.2.4 Magnetic disorder 4

1.3 The history of diffuse scattering studies 4

1.4 Diffuse scattering studies today 5

1.4.1 Studies using electron diffraction 6

1.4.2 Studies using X-rays 7

1.4.3 Studies using neutrons 8

2 Neutron scattering formalism 13

2.2 The double differential cross-section 13

2.3 Elastic scattering 18

2.4 Static approximation 22

2.5 Scattering functions and pair correlation functions 23

2.5.1 Faber-Ziman formalism 25

3 Diffuse scattering theory 29

3.1.1 Orientational disorder 29

3.1.2 Binary systems 30

3.2 Calculating diffuse scattering 31

3.3 Diffuse scattering from molecular crystals 35

3.4 Calculation of the scattering from molecular crystals 40

3.4.1 Rigid molecule with no orientational disorder 40

3.4.2 Freely rotating molecules 41

3.4.3 Symmetry adapted functions 41

3.4.4 Diffraction from powdered samples 43

3.4.5 Weak-graph method 45

3.5 Historical approach to the study of binary systems 46

3.5.1 Laue monotonic diffuse scattering 46

3.5.2 Short range order parameters 47

3.5.3 Warren size effect 49

3.5.4 Huang scattering 50

3.6 Correlation approach 51

3.6.1 Changing the notation 51

3.6.2 Expressions for the different components of the diffuse scattering 53

3.6.3 Methods of treating higher order terms 55

3.7 Borie-Sparks separation method 57

3.8 Georgopoulos and Cohen separation method 60

3.9 Quality of the separations from the correlation approach 61

3.10 Cumulant expansion method 62

3.11 Microdomain approach 63

3.12 Modulation wave approach 65

3.13 Thermal diffuse scattering 66

3.13.1 Equations for one phonon thermal diffuse scattering 67

3.13.2 TDS close to Bragg peaks 69

3.13.3 Uses of thermal diffuse scattering analysis 71

4 Experimental techniques 75

4.2 Compromises in instrument design 77

4.2.1 Measuring the diffuse scattering from C[subscript 60] 78

4.3 Powder diffuse scattering instruments 79

4.4 Single crystal diffuse scattering instruments 80

4.4.1 The four-circle diffractometer 81

4.4.2 Time-sorted Laue diffraction 82

4.4.3 The triple-axis spectrometer 84

4.4.4 Pulsed source triple-axis spectrometer 87

4.4.5 Time-of-flight spectrometers 87

4.4.6 Other optimised instruments 89

4.5 Polarization analysis 89

4.6 Sample environment 90

5 Data correction 93

5.2 The experiment 93

5.3 Preliminary data manipulation 94

5.4 Attenuation corrections 96

5.5 Multiple scattering and vanadium normalisation 97

5.6 Inelasticity corrections 98

5.7 Merging data from detector banks at different angles 99

5.8 The effect of instrumental resolution 100

5.9 Limiting values of normalised data 100

5.10 Obtaining the pair correlation function, G(r) 101

5.11 Propagation of errors 102

5.11.1 Counting statistics 102

5.11.2 Instrumental resolution 103

5.11.3 Termination errors 104

5.11.4 Experimental corrections 105

5.12 Single crystal corrections 105

6 Computer simulation and modelling 107

6.2 Molecular dynamics simulation 108

6.3 Monte Carlo simulation 110

6.3.2 Importance sampling and the Metropolis method 111

6.3.3 Algorithm 112

6.4 Reverse Monte Carlo modelling 116

6.4.3 Disordered magnetic systems 122

6.4.4 Disordered crystals 124

6.4.5 Powders 126

6.4.6 Single crystals 129

6.4.7 RMCPOW 134

6.5 The PDF analysis method 135

6.5.2 The basic method 135

6.5.3 PDFFIT 137

6.6 DISCUS 142

6.7 Optical transforms and the videographic method 143

7 Application of diffuse scattering theory to binary systems 148

7.2 Generating models 148

7.3 Simulating displacements 150

7.4 Mean-field approach 151

7.5 Cluster variation method 152

7.6 [gamma]-expansion method 153

7.7 Inverse Monte Carlo 153

7.8 Fermi surface information 154

7.9 Kanzaki forces 156

8 Alloys and other binary materials 159

8.2 Guinier-Preston zones 159

8.2.1 Aluminium copper alloys 160

8.2.2 Aluminium zinc alloys 162

8.2.3 Aluminium silver alloys 163

8.2.4 Aluminium lithium alloys 164

8.2.5 Copper beryllium alloys 164

8.3 Structural information from magnetic alloys 164

8.3.1 Antiferromagnetic alloys 164

8.3.2 Ferromagnetic and paramagnetic alloys 165

8.4 Other binary metallic alloys 168

8.4.1 Copper gold and silver gold alloys 168

8.4.2 Copper zinc and aluminium zinc alloys 169

8.4.3 Copper aluminium alloys 170

8.4.4 Vanadium and chromium containing alloys 171

8.5 Ternary alloys 171

8.6 Quasicrystals 175

8.6.1 The random cluster model 176

8.6.2 The AlPdMn icosahedral phase 177

8.6.3 Decagonal phase of AlNiCo 178

8.7 Hydrogen in rare earth metals 180

8.8 Hydrogen in vanadium, tantalum and niobium 182

8.9 Hydrogen in palladium 184

8.10 Fe[subscript 3]O[subscript 4] and Fe[subscript 1-x]O 184

8.11 Non-stoichiometric carbides 185

8.12 Other studies 186

9 Superionic conductors 191

9.1.2 Properties 191

9.1.3 Classification 192

9.2 Silver and copper based superionic materials 193

9.2.2 The bcc phase of AgI 196

9.2.3 The fcc rock salt phases of AgX (X = Cl, Br, I) 203

9.2.4 The fcc phases of CuI 205

9.2.5 Silver and copper chalcogenides 208

9.2.6 Doped systems 217

9.3 Fluorite 218

9.3.1 Fluorite structured halide-ion conductors 220

9.3.2 Cubic stabilised zirconias 225

9.4 Superionic conductors with various structures 232

9.4.1 Superionic conductivity in rotor phases 232

9.4.2 [beta]-Alumina, a 2D superionic conductor 233

9.4.3 Hollandite, a 1D superionic conductor 235

10 Diffuse scattering from molecular materials 241

10.2 Ice 241

10.2.1 Formalism 243

10.2.2 Bethe approximation 245

10.2.3 Random walk approximation 245

10.2.4 Graph theory 246

10.2.5 Computational methods 247

10.3 The Buckminster-Fullerene C[subscript 60] 251

10.3.1 Relevant theoretical work 252

10.3.2 Molecular geometry 252

10.3.3 Inter-molecular correlations: powder diffraction studies 255

10.3.4 Inter-molecular correlations: single crystal measurements 256

10.3.5 Summary of results 259

10.4 Small molecule materials 259

10.4.1 N[subscript 2] and mixtures of solid N[subscript 2] and Ar 259

10.4.2 Oxygen 259

10.4.3 Ammonia and related compounds 260

10.4.4 Carbon tetrabromide and sulphur hexafluoride 263

10.5 Organic materials 264

10.5.1 Alkane derivatives 264

10.5.2 Organics with dimers or steric hindrance 267

10.5.3 Anthracene and benzene derivatives 269

10.5.4 Other X-ray work 270

10.6 Large scale molecular materials 270

10.6.1 Inclusion compounds 270

10.6.2 Proteins 272

10.6.3 Polymers 274

10.7 Orientational disorder in non-molecular materials 275

10.7.1 Diffuse scattering from (ND[subscript 4])[subscript 1-x]K[subscript x]I 276

10.7.2 NaOH and KOH 276

10.7.3 Cyanide compounds 279

11 Framework structures 289

11.2 Low energy phonons and Rigid Unit Modes 291

11.3 The tetrahedral phases of silica 292

11.3.1 Quartz 293

11.3.2 Cristobalite 298

11.3.3 Tridymite 305

11.3.4 Comparing the structures with silica glass 306.

Notes:

Includes bibliographical references and index.

ISBN:

0198517904

OCLC:

45485010