Mathematical Techniques in Crystallography and Materials Science

By: Edward Prince

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Paperback | 23 March 2004 | Edition Number 3

At a Glance

Paperback
240 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 1.3

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Crystallographers have to apply many mathematical methods in their daily work. Mathematical Techniques in Crystallography and Materials Science brings together common and less familiar mathematical procedures used in studies of the structures and physical properties of solids. This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature. Based Prince's decades of practical experience, it can be recommended as an introduction for beginners in crystallography, as a refresher and handy guide for crystallographers working on specific problems, and as a reference for others seeking a dictionary of basic mathematical and crystallographic terms. The third edition further clarifies key points, as well as offers new sections on two topics: the projection matrix and the fast Fourier transform.

Industry Reviews

From the reviews of the third edition:

"Mathematical Techniques in Crystallography and Material Science brings together common and less familiar mathematical procedures used in studies of the structures and physical properties of solids. This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature. Based Prince's decades of practical experience, it can be recommended as an introduction for beginners in crystallography, as a refresher and handy guide for crystallographers working on specific problems ... ." (Chimie Nouvelle Societe, Vol. 23 (89), 2005)

"This book presents a series of mathematical methods and procedures ... . The material is well set out ... . In a refreshing approach, the references are introduced with a historical flavour. ... This type of book would be particularly useful for students and professionals who are new to crystallography. It would also be a handy guide to materials scientists ... . this book generally fulfils its aims as a practical guide and reference to students and professionals in the field of crystallography." (Dougal McCulloch, Chemistry in Australia, November, 2004)

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Matrices: Definitions and Fundamental Operations	p. 1
Fundamental Matrix Operations	p. 3
Linear Algebra	p. 5
Eigenvalues	p. 9
Linear Transformations	p. 13
Rotation of Axes	p. 14
The Metric Tensor	p. 17
Symmetry of Finite Objects	p. 20
Groups	p. 20
Representations	p. 21
Point Groups	p. 22
Basis Functions	p. 37
Symmetry of Infinitely Repeated Patterns	p. 40
Bravais Lattices	p. 40
Space Groups	p. 41
Vectors	p. 49
Scalar and Vector Products	p. 50
The Reciprocal Lattice	p. 52
The Orientation Matrix	p. 54
Zones and Forms	p. 56
Sublattices and Superlattices	p. 56
Tensors	p. 58
Covariance and Contravariance	p. 59
The Multivariate Normal Disribution	p. 60
Anisotropic Atomic Displacement Factors	p. 62
The Equivalent Isotropic Temperature Factor	p. 65
Effect of Symmetry	p. 65
Tensors of Higher Ranks	p. 67
Moments and Cumulants	p. 69
Rigid Body Motion	p. 72
Data Fitting	p. 77
Fitting Functions	p. 77
Finding the Minimum	p. 82
False Minima	p. 92
Estimation of Uncertainty	p. 95
Estimates	p. 96
The Precision of Estimates of Precision	p. 100
Models with More than One Parameter	p. 102
Estimates of Precision When the Model Is Not Least Squares	p. 103
Significance and Accuracy	p. 107
The F Distribution	p. 107
Student's t Distribution	p. 111
Correlation	p. 112
Relationship Between Precision and Accuracy	p. 115
Uncertainties of Derived Functions	p. 120
The Projection Matrix	p. 120
Constrained Crystal Structure Refinement	p. 124
The Observed Data	p. 124
The Model	p. 126
The General Form for a Constrained Model	p. 128
Shape Constraints	p. 129
Rigid Body Thermal Motion Constraints	p. 131
Chemical Constraints	p. 133
Representing non-Gaussian Distributions	p. 134
The Fast Fourier Transform	p. 140
The Discrete Fourier Transform	p. 140
The Good-Thomas Algorithm	p. 142
The Cooley-Tukey Algorithm	p. 144
Prime Numbers	p. 145
FFTs for Real Sequences	p. 149
Space Group Symmetry	p. 152
Stereographic Projection	p. 157
Eigenvalues and Eigenvectors of 3 x 3 Symmetric Matrices	p. 161
Sublattices and Superlattices	p. 163
The Probability Integral, the Gamma Function, and Related Topics	p. 165
The Harmonic Oscillator in Quantum Mechanics: Bloch's Theorem	p. 173
Symmetry Restrictions on Second, Third, and Fourth Rank Tensors	p. 181
Some Useful Computer Programs	p. 187
Bibliography	p. 217
Index	p. 219
Table of Contents provided by Rittenhouse. All Rights Reserved.

Mathematical Techniques in Crystallography and Materials Science

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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