THE SOMMERFELD MODEL AND THE HEAT OF SOLUTION OF AN ALLOY

Abstract

An approximately self-consistent method, using a Sommerfeld model, and incorporating an approximation to the second-order perturbation energy (Lennard-Jones 1930), is used to calculate the heat of solution of both monovalent–monovalent and monovalent–polyvalent alloy systems. The heat of solution, as given by the second-order approximation, varies directly with the square of the perturbing potential, and inversely with the mean total energy of the free electrons in the solvent. Varley's (1954.) result resembles this, except that his expression varies inversely with the mean kinetic energy of the free electrons in the pure solute. The first-order approximation to the energy of the alloy system is identical, except for a change of sign, with the expression suggested by Friedel (1952, 1954) for the heat of solution. The charge accumulation about a solute site is found to vary directly with the strength of the perturbation, and inversely with the mean energy of the free electrons in the solvent. Varley obtained a comparable expression; however, his function varies inversely with the mean kinetic energy of the free electrons in the pure solute. The calculated charge accumulations in the copper–silver system, and for gold dissolved in silver, agree qualitatively with those of Arafa (1949) and Huang (1948).