An Approximate Theory of Order in Alloys

Short-range order parameters ${\ensuremath{\alpha}}_{i}$ are defined to express the interaction of a given atom in an alloy with the atoms of the ith shell of atoms surrounding it. From simple thermodynamic reasoning, involving a certain degree of approximation, equations relating the ${\ensuremath{\alpha}}_{i}$ with energy terms and the temperature are derived. Equations for the long-range order parameter, $S$, are obtained by considering the limiting case of $i$ very large. The values of the long- and short-range order parameters obtained by solving these equations are in good agreement with experimental values recently found by x-ray diffraction methods. The theory is extended to the calculation of configurational energy and specific heat, and to the determination of order parameters for alloys of arbitrary composition in such binary systems as that of the copper-gold alloys. In these cases qualitative agreement with experimental observations is obtained.