Mathematical Techniques in Crystallography and Materials Science

E. Prince (Autor)

Buch | Hardcover

192 Seiten

1982 | 1982 ed.
Springer-Verlag New York Inc.
978-0-387-90627-0 (ISBN)

Infos

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.

Inhalt

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.

Produkt-Details

• Zusatzinfo: 192 p.
• Verlagsort: New York, NY
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Chemie ► Anorganische Chemie
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Mineralogie / Paläontologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-387-90627-4 / 0387906274
• ISBN-13: 978-0-387-90627-0 / 9780387906270
• Zustand: Neuware