Mathematical Techniques in Chrystallography and Materials Science

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February 27, 2022 | History

Mathematical Techniques in Chrystallography and Materials Science

3rd Edition.
  • 0 Ratings
  • 0 Want to read
  • 0 Currently reading
  • 0 Have read

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.

Publish Date
Language
English
Pages
224

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Previews available in: English

Edition Availability
Cover of: Mathematical Techniques in Chrystallography and Materials Science
Mathematical Techniques in Chrystallography and Materials Science
2004
electronic resource / in English - 3rd Edition.

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Book Details


Table of Contents

1 Matrices: Definitions and Fundamental Operations
Fundamental Matrix Operations
Linear Algebra
Eigenvalues
Linear Transformations
Rotation of Axes
The Metric Tensor
2 Symmetry of Finite Objects
Groups
Representations
Point Groups
Basis Functions
3 Symmetry of Infinitely Repeated Patterns
Bravais Lattices
Space Groups
4 Vectors
Scalar and Vector Products
The Reciprocal Lattice
The Orientation Matrix
Zones and Forms
Sublattices and Superlattices
5 Tensors
Covariance and Contravariance
The Multivariate Normal Disribution
Anisotropic Atomic Displacement Factors
The Equivalent Isotropic Temperature Factor
Effect of Symmetry
Tensors of Higher Ranks
Moments and Cumulants
Rigid Body Motion
6 Data Fitting
Fitting Functions
Finding the Minimum
False Minima
7 Estimation of Uncertainty
Estimates
The Precision of Estimates of Precision
Models with More than One Parameter
^
Estimates of Precision When the Model Is Not Least Squares
8 Significance and Accuracy
The F Distribution
Student’s t Distribution
Correlation
Relationship Between Precision and Accuracy
Uncertainties of Derived Functions
The Projection Matrix
9 Constrained Crystal Structure Refinement
The Observed Data
The Model
The General Form for a Constrained Model
Shape Constraints
Rigid Body Thermal Motion Constraints
Chemical Constraints
Representing non-Gaussian Distributions
10 The Fast Fourier Transform
The Discrete Fourier Transform
The Good-Thomas Algorithm
The Cooley-Tukey Algorithm
Prime Numbers
FFTs for Real Sequences
Space Group Symmetry
Appendix A Stereographic Projection
Appendix B Eigenvalues and Eigenvectors of 3 × 3 Symmetric Matrices
Appendix C Sublattices and Superlattices
Appendix D The Probability Integral, the Gamma Function, and Related Topics
^
^^
Appendix E The Harmonic Oscillator in Quantum Mechanics: Bloch’s Theorem
Appendix F Symmetry Restrictions on Second, Third, and Fourth Rank Tensors
Appendix G Some Useful Computer Programs
ndex.
^^

Classifications

Dewey Decimal Class
541
Library of Congress
QD450-882

The Physical Object

Format
[electronic resource] /
Pagination
XI, 224p
Number of pages
224

ID Numbers

Open Library
OL27073322M
Internet Archive
mathematicaltech00prin
ISBN 13
9783642187117

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
February 27, 2022 Edited by ImportBot import existing book
July 5, 2019 Edited by MARC Bot import existing book
July 5, 2019 Created by MARC Bot Imported from Internet Archive item record