Computing Methods in Crystallography

Computing Methods in Crystallography is a collection of lectures delivered at a Summer School, held in Oxford in August 1962. The book presents the underlying mathematics and computing methods in crystallography. The text covers topics on the algebra required for the fundamental operations of transformation of coordinates, interpolation, approximation of trigonometric and exponential functions, solution of linear equations and derivation of latent roots and vectors; methods for calculation of structure factors, least-squares adjustment, and Fourier series evaluation; the theory and practice of intensity scaling and symmetry determination; and methods of direct phase determination. Crystallographers, physicists, and students in allied fields will find the book very useful.

Preface

Part I. Algebra

1. Matrix Operations

2. Matrix Inversion and Solution of Equations

3. Application of Matrix Operations

4. Algebra of Least Squares

5. Structure Factor Routines

6. Least-Squares Routines

7. Latent Roots and Vectors

8. Applications of Latent Roots and Vectors

9. Convergence of Iterative Processes

10. Fourier Series Routines

11. Data Reduction Routines

Part II. Statistics

12. General Theory of Statistics

13. Errors in Fourier Series

14. Errors in Least-Squares Methods

15. Statistical Properties of Reciprocal Space

16. The Scaling of Intensities

Part III. Phase Determination

17. Probability Methods for Centrosymmetric Crystals

18. Applications of the Sayre Sign Relationship

19. Isomorphous Replacement Methods

Part Iv. Programming

20. Some Crystallographic Programs in Fortran

Appendix

Examples

Answers to Examples

References

Index