The Cohesion of Alloys: I. Intermetallic Systems formed by Copper, Silver and Gold, and Deviations from Vegard's Law

Abstract

In order to extend the theory of the cohesion of metals to alloy structures a new treatment is considered. The excess energy of the solid solution, as compared with that of a mixture of the pure components, is estimated by considering that the introduction of a solute atom causes a major disturbance extending only to its nearest neighbours, and a less serious disturbance in the surrounding matrix. For a face-centred cubic structure, therefore, attention is directed to the group of thirteen atoms formed by the solute atom and its twelve symmetrically situated solvent atoms. The size of the atomic polyhedra forming this group is different from the sizes of the polyhedra in the solvent matrix, and the equilibrium size of the polyhedra within the group is calculated from the known lattice energies of the components, the atomic radii of the components, and the strain energy introduced into the matrix, which is a measure of the long-range minor disturbance. For this purpose it is assumed that the variation with volume of the energies of the components in the alloy is the same as in the pure metals. Thus, the excess energy w associated with the group of thirteen atoms is w = {121(r) + 2(r)} - {121(r1) + 2(r2)}, where r1 and r2 are the radii of the solvent and solute atoms, and 1 and 2 are the cohesive energies of the solvent and solute metals. w may be plotted against r, and the attendant strain energy in the matrix may be similarly plotted. The sum of these energies is minimized to give the equilibrium size of the atomic polyhedra within a group of thirteen atoms. Using these conceptions, the deviations from Vegard's law to be expected in the solid solutions formed by copper, silver and gold taken in pairs are evaluated. The sign of the deviation is correctly predicted in all cases; quantitative agreement between the magnitudes of the expected and observed deviations is obtained for the copper-silver alloys, which provide the most favourable case for treatment. Application of the theory to problems of solid solution formation is briefly discussed. In its present form the theory applies only to dilute solid solutions