The bcc-based Heusler alloys exhibit a series of order-disorder phase transitions as a function of temperature. The high-temperature phase is a disordered bcc solid solution, and the low-temperature phase is the Heusler structure. An intermediate ordered phase is also typically observed in real systems. A prototype cluster variation method (CVM) analysis is presented that shows that the relative stabilities of the Heusler and intermediate phases can vary continuously, depending on a fine balance between ordering tendencies in the constituent binary systems. Given these basic conclusions, a first-principles analysis of order-disorder transitions in ${\mathrm{Cd}}_2$AgAu was performed. A cluster expansion Hamiltonian was constructed based on a series of linearized muffin-tin orbital calculations in the atomic sphere approximation. CVM calculations were then performed in the ternary bcc tetrahedron approximation. In addition to the transition temperatures, long-range order parameters, and sublattice occupations for ${\mathrm{Cd}}_2$AgAu, an isoplethal section of the ternary phase diagram was also calculated. In general, agreement with experiment is excellent, given the first-principles nature of the calculation. This study clearly demonstrates the ability of first-principles statistical-mechanical calculations to treat complex ordering phenomena in ternary systems. © 1996 The American Physical Society.

• Received 6 May 1996

DOI:https://doi.org/10.1103/PhysRevB.54.9746