In the course of 30 years as a practicing crystallographer I have frequently been faced with the necessity of finding out a little bit about some general branch of mathematics with which I was previously unfamiliar. Under these circumstances I have usually followed the common practice of seeking out some colleague who would be expected to have a thorough knowledge of the subject. I would then find myself faced either with an involved lecture in which the colleague would attempt to distill a lifetime of experience into a form that was comprehensible to a novice with a very different background, or with a book about the subject, written by a specialist, that contained far more information than I really wanted to know. I would have to separate the few kernels of useful material from a large volume of what would probably be wheat to someone else, but was chaff to me. In the course of that time I have acquired a collection of books to which I frequently refer. Most of these have a small number of thoroughly dog-eared pages, along with many that have scarcely been opened. During the same period I have been privileged to associate and collabo rate with a number of materials scientists who were not trained as crystal lographers, but whose interests required them to understand particular details of some structural problem.
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Dateigröße
ISBN-13
978-1-4684-0136-3 (9781468401363)
DOI
10.1007/978-1-4684-0136-3
Schweitzer Klassifikation
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.- 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 Distribution.- Anisotropic Temperature 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 Uncertainty When the Algorithm Is Not Least Squares.- 8 Significance and Accuracy.- The F Distribution.- Student's t Distribution.- Correlation.- The Relation between Precision and Accuracy.- Uncertainties of Derived Functions: Propagation of Errors.- 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.
