Critical and co-operative phenomena. IV. A theory of disorder in solids and liquids and the process of melting

Abstract It is probably true to say that at present there is no satisfactory theory of the process of melting. By this is meant that none of the existing theories can account satisfactorily for the sharp transition in properties which occurs at a precise temperature when a pure single component substance melts. An adequate theory must find a reason for the existence of a sharp temperature and must explain the change of volume and the latent heat of fusion in terms of interatomic forces. For this purpose it is necessary to devise a model of the solid and liquid states of such a kind that a change from one phase to the other can be regarded as taking place by a continuous process and represented mathematically by a continuous change of one or more suitable variables. An attempt to construct such a model has been made by the authors in a recent paper (Lennard-Jones and Devonshire 1939). It was based on the hypothesis that the essential difference between a solid and a liquid is that one is ordered and the other disordered and that a change from one state to the other can be followed by a continuous transition of a variable suitably chosen to represent the state of order. For this purpose the concept of disorder used by Bethe (1935) in his theory of binary alloys was used but adapted to a substance consisting only of one component. This was done by considering the distribution of atoms not only on their normal lattice sites (called α-sites) but also on certain other abnormal sites (called β-sites). These latter sites were taken to be certain positions in the interstices of the normal lattice positions. Owing to the repulsive fields of atoms at close quarters these sites must necessarily be positions of higher energy than the normal sites and will rarely be occupied at low temperatures.