The thermodynamics of crystal lattices

In 1939 I published a paper in the American Journal of Chemical Physics (Born( 1 )) in which I tried to develop the thermodynamics of a crystal lattice in the domain of classical (Boltzmann) statistics. Definite formulae and numerical tables for the temperature dependence of the elastic constants up to the melting point were obtained; nevertheless the work was unsatisfactory not only because the approximations used were rough and their accuracy not known, but because a fundamental difficulty with respect to lattice stability turned up. This led to a series of investigations by my collaborators and myself, published in these Proceedings under the title ‘On the stability of crystal lattices’ (quoted here as S I to SIX), by which the difficulty mentioned has been removed. It is now possible to return to the original problem, to which the present series of papers is devoted. In this introduction I wish to recapitulate the whole situation and to explain the plan of the following papers which will be published by my collaborators.