When certain single-phase alloys are cooled from high temperatures they undergo transformations consisting of a change from a random distribution of atoms amongst the atomic sites to an ordered one. The thermodynamics of such transformations have been considered by Bragg and Williams and also by Bethe and Peierls; the former assume that the energy involved in any atomic interchange is directly proportional to the statistical degree of order (superlattice order) throughout the whole alloy crystal, whilst the latter consider that it depends only on the relative number of like and unlike atoms immediately surrounding the atoms concerned in the interchange (order of nearest neighbours). Both assumptions enable relations to be derived for the change in degree of order (as separately defined) with temperature under equilibrium conditions. These relations are then used to calculate the change in energy content produced as a result of the atomic rearrangement. According to the theory of Bragg and Williams, the superlattice order disappears entirely on heating the alloy through the critical temperature and the energy content is affected only by the ordering process below the critical temperature. The theory of Bethe predicts that, although superlattice order disappears at the critical temperature, a high degree of local order persists, which vanishes only at very high temperatures; an abnormally high specific heat is to be expected, therefore, even above the critical temperature. In the case of
β
brass (CuZn) both theories give practically the same result for the total change in internal energy below the critical temperature, which is in reasonable agreement with experimental measurement. Neither theory gives the correct rate of release of energy in the neighbourhood of the critical temperature, and it would appear that the final disappearance of superlattice order is more sudden than theory indicates. The specific heat is abnormally high above the critical temperature owing presumably to the presence of local order.
The atomic rearrangement process in the copper-gold alloy Cu
3
Au