Underneath the Bragg Peaks 2e : Structural Analysis of Complex Materials - Simon Billinge

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Underneath the Bragg Peaks 2e

Structural Analysis of Complex Materials

By: Simon Billinge, Takeshi Egami

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Hardcover | 22 November 2012 | Edition Number 2

At a Glance

Hardcover
422 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 15.24 x 3.81

Hardcover

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Underneath the Bragg Peaks: Structural Analysis of Complex Materials focuses on the structural determination of crystalline solids with extensive disorder. Well-established methods exist for characterizing the structure of fully crystalline solids or fully disordered materials such as liquids and glasses, but there is a dearth of techniques for the cases in-between, crystalline solids with internal atomic and nanometer scale disorder. Egami and Billinge discuss how to fill the gap using modern tools of structural characterization. This problem is encountered in the structural characterization of a surprisingly wide range of complex materials of interest to modern technology and is becoming increasingly important.

Takeshi Egami received the 2003 Eugene Bertram Warren Diffraction Physics Award for the work described in the book.

The authors received 2010 J. D. Hanawalt Award from the International Union of Crystallography largely based on the success of this book.

Introduces a unique method to study the atomic structure of nanomaterials
Lays out the basic theory and methods of this important emerging technique
The first edition is considered the seminal text on the subject

Industry Reviews

"Egami and Billinge are experts in the application of PDF analysis and their writing is both clear and insightful. The organisation of the book is also excellent, with illuminating examples provided throughout. ...If you have an interest in atomic structure of materials, and local structural details in particular, PDF methods can be profoundly useful. I would heartily recommend this book as a starting point if you are considering using PDF analysis in your own work. For more experienced practitioners, this text is a useful reference."--MATERIALS TODAY

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Preface	p. xi
Preface to the first edition	p. xvii
Structure of Complex Materials	p. 1
Crystallography and Beyond	p. 1
Complexity at the Atomic and Molecular Level	p. 1
Local View of the Structure	p. 3
Shadow of Bragg's Law: Why Knowing the Crystal Structure Is Not Sufficient	p. 6
The Methods of Local Crystallography	p. 7
Real and Reciprocal Space	p. 10
The Power of Total Scattering and PDF Methods	p. 11
The Difference Between the Local and Average Structures: Alloys	p. 11
Short- Versus Long-Range Correlations: Molecular Solids	p. 12
Relevance to the Properties I: Bulk Nanostructured Thermoelectrics	p. 14
Relevance to the Properties II: CMR Manganites	p. 15
Dynamical Disorder and Symmetry Lowering in Silica	p. 17
Chemical Short-Range Order: ß-Na₃BiO₄	p. 20
Resources for Learning Total Scattering and PDF Methods	p. 23
References	p. 24
Crystallographic Analysis of Complex Materials	p. 27
Theoretical Background	p. 27
Scattering Intensity	p. 27
Sample Scattering Amplitude	p. 30
DW Approximation	p. 34
Diffuse Scattering	p. 35
Crystallographic Analysis	p. 39
Rietveld Refinement Method	p. 39
Single Crystal Fourier (Patterson) Analysis	p. 41
Crystallographic Methods and Disorder: Limitations of Crystallographic Methods	p. 42
DW Factor	p. 43
Values of Refined Parameters I: Imperfect Models	p. 45
Values of Refined Parameters II: Correlated Parameters	p. 46
Values of Rietveld Refined DW Factors: Caveat Emptor	p. 47
References	p. 52
The Method of Total Scattering and Atomic Pair Distribution Function Analysis	p. 55
Total Scattering and the PDF	p. 56
Introduction	p. 56
The PDF as the Fourier Transform of the Scattered Intensity	p. 57
The PDF and All Its Friends and Relations	p. 69
Brief History	p. 73
Multicomponent Systems	p. 77
Compositionally Resolved Partial PDF	p. 80
Differential PDF	p. 80
Anomalous X-Ray Scattering	p. 81
Isotopic Substitution	p. 83
Joint Total and Differential PDF Studies	p. 86
Magnetic Correlation Functions	p. 86
Magnetic Scattering of Neutrons	p. 86
Magnetic PDF	p. 87
The PDF in Higher Dimensions	p. 89
PDF Defined in Three Dimensions	p. 89
Anisotropic PDF	p. 90
One-Dimensional PDF and Layer-Layer Correlations	p. 91
Two-Dimensional PDF and Intralayer Correlation	p. 92
Three-Dimensional PDF and the Powder PDF	p. 95
Error Analysis for the PDF	p. 95
Error Diagnostics	p. 95
Termination and Normalization Errors	p. 96
Statistical Errors	p. 97
Effect of Q-Resolution	p. 98
Effect of Other Systematic Errors	p. 99
Remedies of Errors	p. 100
Information Content in the PDF and the Nyquist-Shannon Sampling Theorem	p. 100
References	p. 109
Total Scattering Experiments	p. 113
General Considerations	p. 113
Monochromatic Versus Polychromatic (Energy-Dispersive) Diffraction Methods	p. 113
Single Crystal and Powder Diffraction Methods	p. 114
Accuracy of the Measurement	p. 114
The Neutron Scattering Experiment	p. 116
Sources	p. 116
Diffractometer	p. 117
Neutron Detection	p. 127
Beam Monitor	p. 128
Measurement Geometry	p. 130
The X-ray Scattering Experiment	p. 131
Sources	p. 131
Diffractometer	p. 133
X-ray Detection	p. 139
Beam Monitor	p. 142
Measurement Geometry and Sample Issues	p. 142
Energy-Dispersive X-ray Diffraction Measurements	p. 144
The Electron PDF Experiment	p. 144
References	p. 156
Data Collection Analysis	p. 159
Introduction	p. 160
Data Analysis Overview	p. 163
Quantitatively Reliable PDFs Using Ad Hoc Data Corrections	p. 165
Obtaining S(Q) in Practice	p. 169
Elastic, Inelastic, Coherent, and Incoherent Scattering	p. 169
Real-Time PDFs	p. 170
Detector Dark Counts and Dead-time Corrections	p. 171
Propagating Random Errors	p. 173
Flux Normalization	p. 175
Absorption and Multiple-Scattering Corrections	p. 176
X-Ray-Specific Corrections	p. 180
Time-of-Flight Neutron-Specific Corrections	p. 193
Electron-Specific Data Corrections	p. 201
Combining Datasets	p. 204
Terminating Data	p. 206
Fourier Transforming the Data	p. 208
Instrument Resolution Function	p. 209
Real-World Data Analysis	p. 210
Data Analysis Programs	p. 210
Correction of Large Hydrogen Backgrounds in tof Neutron Measurements	p. 211
Statistical Uncertainties on PDFs	p. 213
References	p. 255
Extracting Structural Information from the PDF	p. 259
Introduction	p. 259
Direct Information	p. 260
The PDF from a Structure	p. 260
Direct Information from the PDF	p. 261
Examples	p. 262
Modeling the PDF	p. 269
Small Box Modeling	p. 271
Big Box Modeling	p. 276
Complex Modeling	p. 280
Ab Initio Nanostructure Solution from PDF Data	p. 289
References	p. 293
Dynamics of the Local Structure	p. 297
Measurement of Inelastic Scattering	p. 297
Neutron Triple-Axis-Spectrometer	p. 298
IXS Measurement	p. 299
Chopper Spectrometer	p. 301
Dynamic Structure Factor	p. 303
Single-Phonon Scattering	p. 303
Multi-Phonon Process	p. 306
Correlated Dynamics and the PDF	p. 308
Dynamic Pair-Density Function	p. 310
Effect of Inelastic Scattering on the PDF	p. 314
Placzek Correction	p. 314
Effective Energy Window for the Neutron PDF Method	p. 319
Phonon Dispersion and the PDF	p. 319
Hybrid Techniques	p. 320
References	p. 323
Local Structure of Well-Ordered Crystals and Systems with Competing Interactions	p. 325
Structure of Weil-Ordered Crystals	p. 326
PDF of Ideal and Distorted Perovskites	p. 326
Complex Periodic Structure: AFE lead Zirconate	p. 333
Negative Thermal Expansion Materials	p. 338
Quasicrystals	p. 342
Competing Interactions in Complex Oxides	p. 343
PZT, Pb(Zr_1-xTi_x)O₃	p. 345
Relaxor FE PMN, Pb(Mg_1/3Nb_2/3)O₃	p. 347
Charge Ordering, Nanophase Separation, and Colossal Magnetoresistance in the Manganites	p. 349
Local Correlations and Phase Transitions	p. 351
Phase Transitions in Complex Materials	p. 354
Phase Transitions in Systems with Competing Interactions I: Relaxor Ferroelectricity	p. 357
Mechanism of Relaxor Ferroelectricity	p. 359
Phase Transition in Systems with Competing Interaction: Lithium-Nickelate	p. 363
Hidden Phase Transition and Local Structure in LiNiO₂	p. 364
Domain Formation in LiNiO₂	p. 364
References	p. 366
Defects in Crystals and Crystallographically Challenged Materials	p. 371
Introduction	p. 372
Defective Crystals	p. 374
Nanocluster-Enhanced Thermoelectricity in Lead Tellurides	p. 374
A Novel Nanostructure in Gamma Alumina	p. 375
Oxygen ion conductors	p. 377
Intermediate Range Order in Cerium Oxides	p. 378
Defects in Catalytic Support Cerium Oxide, CeO₂	p. 380
Carbon Nanostructures	p. 386
Earth Science: The Strange Case of Ferrihydrite	p. 393
Earth Science: Biotic Manganese Oxides	p. 394
Structural Response to Metal-Insulator and Magnetic Transitions: Culr₂S₄	p. 396
Chemical Short-Range Order	p. 397
In Situ and In Operando Studies	p. 399
In Situ RAPDF Studies of Chemical Reactions Under Flow	p. 399
PDF of an Operating Fuel Cell In Operando	p. 401
References	p. 403
Nanoparticles and Clusters	p. 407
Introduction	p. 408
Information in the PDFs of Nanoparticles	p. 408
Nanoparticle Size and Shape	p. 411
Nanoparticle Structure and Defects	p. 412
Ab Initio Solution of Unknown Nanostructures	p. 416
Homogeneous Size-Dependent Strain in Nanoparticles	p. 416
Nanoparticle Thermodynamic Quantities from the PDF	p. 417
Surface to Volume Ratio and Inhomogeneous Strains in Nanoparticles	p. 418
Size-Dependent Bond Stiffness in Nanoparticles	p. 419
Modeling Heterogeneous Nanoparticles	p. 420
Surface Capping Ligand Dependence of Nanoparticle Structure	p. 422
Clusters Suspended in a Solvent	p. 423
Precursors to Gold Nanoparticle Formation	p. 424
Time-Resolved Studies of Hydrothermal Chemical Reactions	p. 426
Structures of Surfactant Micelles Suspended in Water	p. 428
Structure of Pt(II) ion Complexes in Water	p. 430
Clusters and Molecules Intercalated in Nanoporous Solids	p. 431
Hydrogen in a Cyanide Host	p. 431
Metal Organic Frameworks and ZIFs	p. 432
Mercury in Silica	p. 434
Sodium in Silica	p. 434
References	p. 437
Local Packing in Molecular Materials	p. 441
Introduction	p. 441
Fingerprinting	p. 442
Sensitivity Dependence On Q_Max	p. 448
Modeling Molecular Systems	p. 452
References	p. 452
Structure of Amorphous Materials	p. 455
PDF Analysis of Amorphous Materials	p. 455
Structure of Multicomponent Glasses	p. 456
Compositionally Resolved Structure	p. 456
Structural Changes due to Structural Relaxation	p. 457
Structural Relaxation in Glasses	p. 457
Structural Relaxation Observed by the PDF Method	p. 458
Structural Changes due to Mechanical Deformation	p. 459
Elastic Deformation	p. 459
Anelastic Deformation	p. 461
Plastic Deformation	p. 462
References	p. 464
Concluding Remarks	p. 467
Index	p. 471
Table of Contents provided by Ingram. All Rights Reserved.

Underneath the Bragg Peaks 2e

Structural Analysis of Complex Materials

At a Glance

Hardcover

Industry Reviews

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