The Hume-Rothery rules and phase stabilities in noble metal alloys

Results from martensitic transformations are used to evaluate stabilities of the equilibrium phases in the Hume-Rothery electron compounds based on Cu, Ag and Au, and to give arguments why the electron concentration plays such an important role in the selection of the crystal structures. It is shown that the vibrational entropy difference observed for the martensitic transformation from ordered bcc to the close packed martensite and its e/a dependence can also account for the entropy difference Delta S-alpha/beta between the equilibrium alpha and beta at high temperatures, and can be made largely responsible for the composition dependence of the (alpha + beta) two phase field. The enthalpy of mixing can be decomposed into a small term which depends on the average periodic lattice, which is different in alpha and beta but which is nearly the same in all alloys studied, and a contribution which is due to the difference in the properties of the atoms and which can be expressed by pair interchange energies. This contribution depends strongly on the specific alloy system, but is independent of structure, which is compatible with a pair interchange energy depending only on pair distance but not on structure, as suggested by simple pseudopotential theory. The same pair interchange energies account also for long range order and the critical ordering temperature. The evaluation for several alloy systems shows a surprisingly good agreement within this picture, and permits to understand better why the electron concentration plays such an important role also for other structures, although the energy contribution of the conduction electrons is only a small part of the total enthalpy of formation of any of the equilibrium structures.