Vacancy concentration and arrangement of atoms and vacancies in metals and alloys

Abstract

With a method of statistical thermodynamics fundamental equations are derived which describe the arrangement of atoms and vacancies in the alloys in the state of thermal equilibrium, where an ordering or a clustering can take place. The solutions of these equations give, among other things, a more precise description on the concentration of vacancies than the classical ones. The vacancy concentration in pure metals may almost precisely be expressed by the usual approximate expression, but in dilute alloys it is not always expressed by Lomer's expression. The fraction of vacant sites in the alloys, furthermore, is very unlikely to be expressed by an Arrhenius type of equation, but it decreases or increases, according as a result of ordering or clustering. In binary alloys with short range orders or clusters the probability that one of the nearest neighbor sites of a vacancy is occupied by an atom of any particular kind does not always vary monotonically with temperature but in some alloys it increases after decreasing or decreases after increasing. A possibility for an interpretation of the anomalous behaviors of αCu-Al alloys is pointed out.