Dynamical Theory of Crystal Lattices

THIS book was begun during the War, about fourteen years ago. My first book on crystals had appeared during the First World War, under the title Dynamik der Kristallgitter (Teubner, 1915). A few years later I was invited by Sommerfeld to write an article on the subject for the Mathemtical Encyclopaedia. This appeared in volume V, p. 527, under the title ‘Atomtheorie des festen Zustandes’ and was published as a separate book (Teubner, 1923). This was two years before the discovery of quantum mechanics. A report on the situation up to the year 1933 has been published as an article in the Handbuch der Physik by Maria Goppert-Mayer and myself. There are several other articles in this Handbuch by K. F. Herzfeld, R. de W. Kronig, A. Smekal, H. G. Grimm, and H. Wolff, dealing with problems of lattice dynamics. Meanwhile several books on crystal theory have been published which take proper account of quantum mechanics. The most comprehensive is that by F. Seitz, A Modern Theory of Solids (McGraw-Hill, N.Y. and London, 1940) ; other books, for example that by N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Clarendon Press, Oxford, 1940), deal only with restricted sets of problems. Some special subjects, like the theory of specific heat, infra-red absorption, and Raman effect, have become standard chapters in general textbooks. A great number of single investigations have been published since my article in the Encyclopaedia. The situation seemed to demand an attempt at a new, comprehensive presentation. But the subject has become much too large to be dealt with from all aspects. The contributions of my own school during the last few years have been mainly concerned with non-conducting materials, It seemed to be desirable to give a description of the methods and results in this field. My plan was to start from the.most general principles of quantum theory and to derive in a deductive way the structures and properties of crystals, as far as one could proceed.