$Powder Diffraction : The Rietveld Method and the Two Stage Method to Determine and Refine Crystal Structures from Powder Diffraction Data - Georg Will$

Powder Diffraction

The Rietveld Method and the Two Stage Method to Determine and Refine Crystal Structures from Powder Diffraction Data

By: Georg Will

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Hardcover | 17 November 2005

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236 Pages

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Crystal structure analysis from powder diffraction data has attracted considerable and ever growing interest in the last decades. X-ray powder diffraction is best known for phase analysis (Hanawalt files) dating back to the 30s. In the late 60s the inherent potential of powder diffraction for crystallographic problems was realized and scientists developed methods for using powder diffraction data at first only for the refinement of crystal structures. With the development of ever growing computer power profile fitting and pattern decomposition allowed to extract individual intensities from overlapping diffraction peaks opening the way to many other applications, especially to ab initio structure determination.

Powder diffraction today is used in X-ray and neutron diffraction, where it is a powerful method in neutron diffraction for the determination of magnetic structures. In the last decade the interest has dramatically improved. There is hardly any field of crystallography where the Rietveld, or full pattern method has not been tried with quantitative phase analysis the most important recent application.

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Non-Fiction Science Physics Optical Physics Engineering & Technology Mechanical Engineering & Materials Materials Science Chemistry Mineralogy & Gems Inorganic Chemistry Physical Chemistry Industrial Chemistry & Manufacturing Technologies

Industrial Chemistry Powder Technology Crystallography

General Considerations	p. 1
Introduction	p. 1
Introduction	p. 1
Meaning of the Word "Powder"	p. 3
Sample and Specimen	p. 3
Why Powder Diffraction?	p. 4
Difficulties and Limitations of Powder Diffraction	p. 5
Fundamentals of Diffraction	p. 5
Analysis of Powder Diffraction Patterns	p. 7
Powder Diffraction	p. 9
History of Powder Diffraction	p. 9
Programs for the Analysis of Powder Diffraction Data	p. 11
Crystal Structures from Powder Diffraction Data	p. 13
Pattern Decomposition for Accurate Intensities	p. 15
Profile Shape Functions	p. 22
Early Ab Initio Crystal Structure Determinations from Powder Diffraction Data by Pattern Decomposition	p. 26
Ab Initio Structure Determination by Direct Methods in Powder Diffraction	p. 31
Crystal Structures Determined by Direct Methods	p. 34
Preferred Orientation in Powder Diffraction	p. 36
Line Broadening: Crystallite Size, Strain and Stress	p. 37
The Rietveld Method	p. 41
The Rietveld Method	p. 41
The Early Days of the Rietveld Method	p. 41
The Method	p. 44
Rietveld Refinement with X-Ray Powder Diffraction Data	p. 48
Critical Assessment of the Rietveld Method	p. 51
Guidelines for Rietveld Refinement	p. 56
Special Applications of the Rietveld Method	p. 64
Quantitative Phase Analysis by the Rietveld Method	p. 64
Texture Analysis Using the Rietveld Method	p. 70
The Two Stage Method	p. 73
Introduction and Background	p. 73
Concept of the Two Stage Method	p. 73
The Two Stage Method in Comparison to Rietveld Refinement	p. 76
Profile Analysis and Profile Fitting	p. 77
Characteristics of Powder Diffraction Line Profiles	p. 77
Outline of Profile Fitting	p. 78
Profile Functions	p. 79
The Instrument Function	p. 82
Instrument Function with Seven Lorentzians	p. 84
Determination of Integrated Intensities through Profile Fitting	p. 87
Angle Dependence of the Profile Shapes	p. 88
Resolution of Profile Fitting	p. 90
High Resolution Powder Diffraction - Lattice Parameters	p. 91
Examples of Profile Fitting in the Two Stage Method	p. 95
Examples for PROFAN	p. 95
Examples for HFIT	p. 98
POWLS	p. 99
Structure Refinement with POWLS	p. 99
The Program POWLS	p. 99
Preparation of a Model Structure	p. 103
Observations	p. 105
Refinement	p. 106
Preferred Orientation	p. 106
Specimen and Preferred Orientation	p. 107
Specimen Preparation	p. 107
Random Distribution	p. 108
Calculational Corrections	p. 109
Crystallite Size Effects	p. 110
R-Values	p. 112
General Remarks	p. 112
R-Values in Powder Diffraction	p. 113
Background	p. 114
Dealing with Background	p. 115
Background in Rietveld Programs	p. 115
The Profile R-Value	p. 119
The Weighted Profile R-Value	p. 120
The Bragg R-Value	p. 121
Conclusion	p. 125
Structure Refinement by the Two Stage Method	p. 125
Refinement with POWLS	p. 125
Examples Using the Two Stage Method and the Program POWLS	p. 128
Comparison of the Rietveld Method and the Two Stage Method	p. 128
Merits and Limitations of the Rietveld Method and the Two Stage Method	p. 134
Conclusion	p. 136
Analysis of Quartz	p. 136
Sample Preparation	p. 137
Experiments	p. 137
Sample Rotation during Experiments	p. 138
Crystal Structure Refinement with POWLS of [alpha]-Quartz Collected with Cu K[alpha] Radiation	p. 139
Refinement of [alpha]-Quartz Data Collected with Synchrotron X-Rays	p. 141
Texture Analysis with the Two Stage Method Using Neutron Diffraction	p. 147
Introduction	p. 147
The Position Sensitive Detector Julios	p. 149
Data Collection	p. 149
Data Evaluation	p. 151
Examples of Texture Analysis	p. 152
Selected Examples for the Application of the Two Stage Method	p. 160
Electron Density Distribution of an Olivine Sample by Fourier Methods	p. 160
Electron Density Distribution in CeO[subscript 2]	p. 164
Crystal Structure Analysis of Yb[subscript 2]O[subscript 3]	p. 167
Application in High Pressure Research	p. 172
Cation Distribution in a Thin Film Garnet Sample	p. 176
Structure Determination from Energy Dispersive Data	p. 181
Structure Determination from Energy Dispersive Data	p. 181
Synchrotron Radiation	p. 182
Neutron Diffraction by Time-of-Flight Measurements	p. 183
Simultaneous Angle and Position Resolving Neutron Diffraction by Time-of-Flight Measurements	p. 184
Electronic Zooming	p. 188
Analysis of TOF Data	p. 190
Laue Diffraction with Neutrons by Time-of-Flight Measurements	p. 193
Conclusion	p. 194
References	p. 195
An Example of POWLS for Quartz	p. 203
Index	p. 219
Table of Contents provided by Ingram. All Rights Reserved.

Powder Diffraction

The Rietveld Method and the Two Stage Method to Determine and Refine Crystal Structures from Powder Diffraction Data

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Hardcover

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