The enthalpy of solution for solid binary alloys of two 4d-transition metals

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A demonstration is given how to derive the enthalpy of solid solution of alloys of two 4d transition metals for the three main crystallographic structures, fcc, hcp and bcc. Because of two additional terms the enthalpy of solution for solid phases differs from that in the corresponding liquid alloys. The first of these, accounting for elastic mismatch, can be estimated from Eshelby/Friedel-type elastic continuum theory. In our case we correct the atomic size mismatch for volume changes that accompany the formation of alloys. The second term accounts for the variation of structure dependent energies (i.e. the preference for either the fcc, bcc or hcp type of crystal structure) with the average number of electrons per atom. We derive an empirical curve for these structure dependent enthalpy terms, which is essentially based on theoretical results and gives a fair account of binary phase diagram characteristics.