Atomic rearrangement process in the copper-gold alloy Cu 3 Au. II

Abstract

In a recent investigation (Sykes and Jones 1936) of the properties of the alloy Cu 3 Au we described the effect of the ordering process on the energy content of the alloy. The observed behaviour was found to be more complicated than was anticipated from the theoretical work (Bragg and Williams 1934; Peierls 1936), and the existence of a variety of metastable states of an unexpected type was established. The face-centred lattice of Cu3Au may be considered in terms of the four interpenetrating simple cubic lattices to which it is equivalent. When completely ordered one lattice contains nothing but gold atoms and the other three, copper atoms. As the alloy cools through the critical temperature gold atoms may segregate on any of the four lattices, consequently any individual crystal in the alloy will contain a large number of small volumes or nuclei, each of which has its own consistent scheme of order, but different nuclei will be out of phase with one another. The various metastable states observed experimentally are associated with the presence of these nuclei, since their rate of growth, which determines the rate of disappearance of disordered material from the boundaries, is small compared with the time of relaxation of the material inside the nuclei. The size of the nuclei can be obtained from the width of the superlattice lines present in the X-ray powder diagram; this information, together with a number of specific-heat temperature curves, was used to determine the effect of the nuclei on the energy content of the alloy. It was shown that the experimental results were consistent with the assumption that the nuclei in the individual crystals were separated by narrow boundaries (from about one to two atomic distances in width), the atoms inside the nuclei having the equilibrium degree of order at the temperature of the experiment. The electrical resistance of an alloy in equilibrium depends on the degree of order; the presence of nuclei corresponding to a metastable state introduces an extra resistance which is a function of the size of nuclei. The present paper describes experimental work carried out to determine the relation between the size of the nuclei and electrical resistance. The results show that at any given temperature the extra electrical resistance is inversely proportional to the size of the nuclei, that is to the number of boundaries, provided the linear dimensions of the nuclei are more than 20 atomic distances. The quantitative relations between nuclei size on the one hand, and resistance, lattice spacing, and intensity of superlattice lines on the other, are consistent with the view that the boundaries are quite narrow. By cold working the material it has been found possible to produce specimens in which the sizes of both nuclei and crystals are of the same order. The rate of growth of nuclei in the cold-worked material is appreciably slower than in the annealed material although the resistance for a given size of the nuclei is almost the same. Using the well-known expressions given by the wave theory for the resistance of a metal (Mott and Jones 1936, p. 268) the probability of reflexion of the conduction electrons at the boundary of the nuclei has been deduced from the experimental results and is about onetenth (assuming one conduction electron per atom).