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Mathematical Techniques in Crystallography and Materials Science [electronic resource] / by Edward Prince

Author
Prince, Edward
Published
New York, NY : Springer US, 1982.
Physical Description
192p : online resource
Additional Creators
SpringerLink (Online service)
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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 -- 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.
Subject(s)
ISBN
9781468401363
Digital File Characteristics
text file PDF
Note
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
Part Of
Springer eBooks
View MARC record | catkey: 11944705