Ordered states in ternary B2-type intermetallic alloys including vacancies

Abstract

Abstract The mean-field theory of order in ternary alloys is applied to the special case of vacancy-containing B2-type intermetallic alloys. In such alloys the vacancy content may be so large that the alloy should be treated as a ternary system, characterized by two long-range order parameters ξ and η in the Bragg–Williams approximation. At fixed overall concentrations of the three components and low temperatures the ternary system adopts essentially one of two possible states, having (ξ, η) pairs of unlike sign (state Ia) and like sign (state IIa) respectively. State Ia is characterized by defects on both sublattices (vacancies on the α sublattice and antisite a atoms on the β sublattice) whereas state IIa contains both defects on the β sublattice. These states can be transformed into each other by a reaction involving the interchange of vacancies and antisite a atoms with reaction energy B = εab – εaa (ε ij representing the pair interaction energy). From numerical computations of the free energy as a function of ξ,η and T, states Ia and IIa are found to be stable for B > 0 and B < 0 respectively, provided that the overall concentrations of atoms and vacancies are fixed. However, at thermodynamic equilibrium the vacancy content has to be adjusted at each temperature. For T → 0 this leads to two possible states, depending on the overall composition and the pair interactions. The first of these ground states is the classical vacancy-free B2 phase, whereas the second state (a special case of state IIa) contains structural vacancies in addition to b atoms on one sublattice to compensate for the excess a atoms on the other sublattice. The latter state is predicted to occur in off-stoichiometric alloys having components with quite different cohesive energies such as CoGa and NiAl, in qualitative agreement with experimental data on vacancies in some of these intermetallic compounds.