Quaternions are a simple and powerful tool for handling rotations and double groups. This book gives a complete treatment of finite point groups as subgroups of the full rotation group and emphasizes… Expand

Preface. 0: How to use this book. 1: Introduction. 2: Basic group theory: definitions and formulae. 3: Parametrization of symmetry operations. 4: Symmetry operations: notation and properties. 5:… Expand

A review is given of some conventions and definitions required for the derivation of the irreducible representations of the space groups, and of a method to obtain lattice harmonics. These are given… Expand

0. Notation 1. The free-electron picture 2. Symmetry and group theory 3. Space groups 4. The reciprocal lattice and the Fourier series 5. Block functions and Brillouin zones 6. Space group… Expand

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared, for its importance, with the invention of triple coordinates by… Expand

This paper extends the work described in a previous paper by one of the authors (Altmann 1957). The spherical harmonics that belong to the irreducible representations of the cubic groups are now… Expand

A Lifson-Warshel force field (1968), which goes beyond the harmonic approximation and is well adapted for calculations in defect structures, has been developed for the silicon crystal. The parameters… Expand