عنوان

Mathematical Techniques in Crystallography and Materials Science

3642975763

9783642975769

b576760

Mathematical Techniques in Crystallography and Materials Science

[Book]

by Edward Prince.

Second edition

Berlin, Heidelberg

Springer Berlin Heidelberg

1994

(xi, 223 pages 30 illustrations)

1 Matrices: Definitions and Fundamental Operations --; Fundamental Matrix Operations --; Linear Algebra --; Eigenvalues --; Linear Transformations --; Rotation of Axes --; The Metrie 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 Harmonie Oscillator in Quantum Mechanics: Bloch's Theorem --; Appendix F Symmetry Restrictions on Seeond, Third, and Fourth Rank Tensors --; Appendix G Some Useful Computer Programs.

Crystallographers have to apply many mathematical methods in their daily work. If ever they have a problem, this book will help to solve it. The newcomer starting work will learn how to apply these tools, the practicing crystallographer will find all the data and background material he wants to look up. In the decade since the first edition was published, new things have happened that required revision beyond correction of errors. Two chapters have been added: a section on the projection matrix and another on fast Fourier Transform. The author collected the information during his professional career. The success of the first edition indicates that many other practicing crystallographers just need exactly that information.

Chemistry -- Mathematics.

Chemistry, Inorganic.

Chemistry.

by Edward Prince.

Edward Prince

[Book]

Y