Institute of Metals Division - Atomic Volume in Laves Phases: A Hemisubstitutional Solid- Solution Elastic Model

Laves phases, AB2, are considered as Izerrzisub-stitutional solutions m1hich are defined by a one-for-truo replacement scheme. Atomic-size tnisfit is considered in terms of deviations of the ratio 2V°b/V°A from unity, where v° = atomic volume. A simple elastic model has been used to calculated deviations from "Vegard&apos;s law of atomic vol-umes". Comparison has been made between calculated and observed atomic-volume deviations fov 222 Laves phases. Agreement is generally very good although there ave some few exceptions which appear to be excusable in terms of electronic changes that ore beyond the scope of the present model. We can consider the formation of a binary sub-stitutional solution A-B from an A solvent as one-for-one replacements of A atoms by B atoms. As the atomic-size ratio deviates from unity, the solution becomes thermodynamically less stable and hence more restricted because of atomic-misfit strain energy. In accordance with our previously presented conclusion1 that the atomic volume, v, is in general the most appropriate measure of atomic size, the ideal size ratio for a binary sub-stitutional solution is vg/vA = 1. The Laves phases have been described by Berry and Raynor2 in terms of various stacking sequences of hexagonal layers of B atoms for the three structures MgZn2(C14), MgCu2(C15), and MgNi2(C36). To form the Laves phase of ideal composition AB, we start with complete hexagonal layers of B atoms in the appropriate stacking sequence and we remove, according to an appropriate scheme for each structure, two out of every four B atoms and replace the two removed atoms by one A atom. We thus might expect to find that the ideal size ratio for the Laves phases is 2v/B/ VA= 1. From this point of view, then, we call Laves phases hemi-substitutional solutions since we employ one-for-two replacements. By analogy with substitutional solutions we can expect for Laves phases that as the ratio 2VB/Va deviates from unity the phase occurrence will be more restricted. Laves3 has plotted the distribution of Laves phases as a function of the radius ratio, ?A/rB, and found that, while the distribution extended from 1.05 < rA/B < 1.50, the