Contributions to the theory of the specific heat of crystals I—Lattice theory and continuum theory

Abstract

The variation of the specific heat of crystals with temperature received a satisfactory general explanation as soon as quantum statistics were applied to the motion of the particles of which a crystal is composed. The first formula on such a basis, proposed by Einstein, gave fairly satisfactory results, but showed large discrepancies at the lowest temperatures; an empirical formula due to Nernst and Lindemann gave better agreement but lacked a satisfactory physical basis. Two consistent theories were advanced practically simultaneously by Debye and Born and v. Kármán. Debye's theory is based on the ingenious idea of replacing a crystal by a continuum as far as the distribution of the vibrations is concerned, cutting off the spectrum at a suitable point. Because of its inherent simplicity and because it can be applied to non-crystals as well as to crystals, the continuum theory has taken precedence and now is practically the only one which received attention.