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Mathematical Techniques in Crystallography and Materials Science - Edward Prince

Mathematical Techniques in Crystallography and Materials Science

Paperback

Published: 23rd March 2004
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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.

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)

Matrices: Definitions and Fundamental Operationsp. 1
Fundamental Matrix Operationsp. 3
Linear Algebrap. 5
Eigenvaluesp. 9
Linear Transformationsp. 13
Rotation of Axesp. 14
The Metric Tensorp. 17
Symmetry of Finite Objectsp. 20
Groupsp. 20
Representationsp. 21
Point Groupsp. 22
Basis Functionsp. 37
Symmetry of Infinitely Repeated Patternsp. 40
Bravais Latticesp. 40
Space Groupsp. 41
Vectorsp. 49
Scalar and Vector Productsp. 50
The Reciprocal Latticep. 52
The Orientation Matrixp. 54
Zones and Formsp. 56
Sublattices and Superlatticesp. 56
Tensorsp. 58
Covariance and Contravariancep. 59
The Multivariate Normal Disributionp. 60
Anisotropic Atomic Displacement Factorsp. 62
The Equivalent Isotropic Temperature Factorp. 65
Effect of Symmetryp. 65
Tensors of Higher Ranksp. 67
Moments and Cumulantsp. 69
Rigid Body Motionp. 72
Data Fittingp. 77
Fitting Functionsp. 77
Finding the Minimump. 82
False Minimap. 92
Estimation of Uncertaintyp. 95
Estimatesp. 96
The Precision of Estimates of Precisionp. 100
Models with More than One Parameterp. 102
Estimates of Precision When the Model Is Not Least Squaresp. 103
Significance and Accuracyp. 107
The F Distributionp. 107
Student's t Distributionp. 111
Correlationp. 112
Relationship Between Precision and Accuracyp. 115
Uncertainties of Derived Functionsp. 120
The Projection Matrixp. 120
Constrained Crystal Structure Refinementp. 124
The Observed Datap. 124
The Modelp. 126
The General Form for a Constrained Modelp. 128
Shape Constraintsp. 129
Rigid Body Thermal Motion Constraintsp. 131
Chemical Constraintsp. 133
Representing non-Gaussian Distributionsp. 134
The Fast Fourier Transformp. 140
The Discrete Fourier Transformp. 140
The Good-Thomas Algorithmp. 142
The Cooley-Tukey Algorithmp. 144
Prime Numbersp. 145
FFTs for Real Sequencesp. 149
Space Group Symmetryp. 152
Stereographic Projectionp. 157
Eigenvalues and Eigenvectors of 3 x 3 Symmetric Matricesp. 161
Sublattices and Superlatticesp. 163
The Probability Integral, the Gamma Function, and Related Topicsp. 165
The Harmonic Oscillator in Quantum Mechanics: Bloch's Theoremp. 173
Symmetry Restrictions on Second, Third, and Fourth Rank Tensorsp. 181
Some Useful Computer Programsp. 187
Bibliographyp. 217
Indexp. 219
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9783540211112
ISBN-10: 354021111X
Audience: General
Format: Paperback
Language: English
Number Of Pages: 224
Published: 23rd March 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.57 x 15.7  x 1.42
Weight (kg): 0.37
Edition Number: 3
Edition Type: Revised