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Computing Methods in Crystallography

Computing Methods in Crystallography

Authors
Publisher Elsevier Science Publishers
Year 01/10/2013
Edition First
Pages 264
Version other
Language English
ISBN 9781483156873
Categories Science: general issues
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Book description

Computing Methods in Crystallography is a collection of lectures given at a two-week Summer School held in Oxford, UK in August 1962. About forty-five crystallographers focused on advances in the use of computing methods in crystallography. The discussions are organized around four themes: algebra, statistics, phase determination, and programming. This book is comprised of 20 chapters and begins with an introduction to the algebra required for the fundamental operations of transformation of coordinates, interpolation, and approximation of trigonometric and exponential functions, as well as solution of linear equations and derivation of latent roots and vectors. Methods for calculation of structure factors, least-squares adjustment, Fourier series evaluation, and a number of other operations are described. The statistical properties of reciprocal space are also considered, along with probability methods for centrosymmetric crystals. The final chapter looks at some crystallographic programs in FORTRAN. This monograph will be a valuable resource for crystallographers as well as physics students and researchers interested in the application of computing methods to crystallography.

Computing Methods in Crystallography

Table of contents


  • Computing Methods in Crystallography

  • Copyright Page

  • Table of Contents

  • PREFACE

  • PART I: ALGEBRA

  • CHAPTER 1. MATRIX OPERATIONS

  • MATRIX NOTATION

  • MATRIX ADDITION

  • SPECIAL MATRICES

  • SCALAR MULTIPLICATION

  • MATRIX MULTIPLICATION

  • SCALAR PRODUCT

  • TRANSPOSITION

  • FORMS

  • NORMS

  • PARTITIONED MATRICES

  • CHAPTER 2. MATRIX INVERSION AND SOLUTION OF EQUATIONS

  • THE INVERSE TRANSFORMATION

  • SOLUTION OF SIMULTANEOUS EQUATIONS

  • GAUSS ELIMINATION

  • POSITIVE DEFINITE MATRICES

  • THE CHOLESKI PROCESS

  • MATRIX INVERSION

  • CHAPTER 3. APPLICATION OF MATRIX OPERATIONS

  • NATURAL AND ORTHOGONAL AXES

  • SYMMETRY OPERATIONS

  • DISTANCE AND ANGLE CALCULATIONS

  • DIFFRACTOMETER CALCULATIONS

  • LOCATION OF HYDROGEN ATOMS

  • CHAPTER 4. ALGEBRA OF LEAST SQUARES

  • LINEAR OBSERVATIONAL EQUATIONS

  • NON-LINEAR OBSERVATIONAL EQUATIONS

  • WEIGHT OF FUNCTIONS OF UNKNOWNS

  • ELECTRON DENSITY INTERPOLATION

  • CHAPTER 5. STRUCTURE FACTOR ROUTINES

  • GENERAL CONSIDERATIONS

  • CALCULATION OF TRIGONOMETRIC FUNCTIONS

  • FORM-FACTOR INTERPOLATION

  • A GENERAL PURPOSE STRUCTURE FACTOR ROUTINE

  • SPECIAL PURPOSE ROUTINES

  • CHAPTER 6. LEAST-SQUARES ROUTINES

  • OBSERVATIONAL EQUATIONS FOR REFINEMENT

  • NORMAL EQUATIONS

  • CHOICE OF PARAMETERS

  • SOLUTION OF EQUATIONS

  • REPEATED USE OF THE NORMAL MATRIX

  • A GENERAL PURPOSE LEAST-SQUARES REFINEMENT ROUTINE

  • CHAPTER 7. LATENT ROOTS AND VECTORS

  • PROPERTIES OF LATENT ROOTS AND VECTORS

  • THE MODAL MATRIX

  • SYMMETRIC M

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