The mean-field theory of order in ternary alloys was applied to the case of vacancy-containing B2-type intermetallic alloys. It was recalled that, in such alloys, the vacancy content could be so high that the alloy could be treated as a ternary system which was characterized by 2 long-range order parameters, ξ and η, in the Bragg-Williams approximation. At fixed overall concentrations of the 3 components and low temperatures, the ternary system adopted one of 2 possible states having (ξ,η) pairs of unlike sign (state Ia) or like sign (state IIa). State-Ia was characterized by the presence of defects on both sub-lattices (vacancies on the α sub-lattice and antisite a-atoms on the β sub-lattice). State-IIa contained both defects on the β sub-lattice. These states could be transformed into each other by a reaction which involved the interchange of vacancies and antisite a-atoms, with a reaction energy of B = εab - εaa (where εij represented the pair interaction energy). Using numerical calculations of the free energy as a function of ξ, η and T, states Ia and IIa were found to be stable for B > 0 and B < 0, respectively, provided that the overall concentrations of atoms and vacancies were fixed. At thermodynamic equilibrium, the vacancy content had to be adjusted for each temperature. As T tended to zero, this led to 2 possible states; depending upon the overall composition and the pair interactions. The first of these ground states was the classical vacancy-free B2-phase, while the second state (a special case of state-IIa) contained structural vacancies, in addition to b-atoms on one sub-lattice, in order to compensate excess a-atoms on the other sub-lattice. The latter state was predicted to occur in off-stoichiometric alloys having components with quite different cohesive energies, such as CoGa and NiAl. This prediction was in qualitative agreement with experimental data on vacancies in some of these intermetallic compounds.

Ordered States in Ternary B2-Type Intermetallic Alloys Including Vacancies. F.W.Schapink: Philosophical Magazine A, 2001, 81[4], 883-901