A geometric model of deviations from Vegard's rule

Abstract

There is much evidence that X-ray measurements of sufficient accuracy reveal deviations from the linear dependence of unit-cell parameters on composition, i.e., departures from Vegard's rule. The dependence of such deviations on composition for a random solid solution with one substitutional position (Ax1 Bx2C is usually of a parabolic form: δa=x1x2σ where σ is positive. Many attempts to explain these observations are based on elastic models. It is known that less than 50% of the predictions of these models are correct. An alternative model under consideration is a simple geometric one. It is concerned with secondary atomic displacements around substitutional defects, i.e., shifts of the second nearest neighbors. The result is structurally dependent and the analysis deals with binary solid solutions of B1 (CN=6), B3 (CN=4), and B2 (CN=8) structure types. For instance, in sodium chloride structure-type solid solutions, the following simple equation is valid, δh=(3/2)x1x2(R)2/R, where R is the difference in interatomic distances of pure components and R is the average interatomic distance. Calculations for NaCl−KCl, NaCl−NaBr, KCl−KBr, and other systems are in good agreement with experimental data.