Thermodynamics of lattice disorder of the CsCl-type intermetallic phases at non-stoichiometric compositions and the thermodynamic properties of β′-AuCd and β′-AgMg phases

Orr's treatment, which extends the thermodynamic model of Wagner and Schottky for CsCl-phases to large departure from stoichiometry, is presented. In this model, a composition-dependent disorder parameter z is obtained by minimizing the Gibbs free energy of the alloys. Since z is a complicated and implicit function of χ and α with χ being the difference between the concentration of the alloy and that of the stoichiometric alloy and α a basic parameter of the theoretical model, several approximations are introduced to describe the concentration dependence of z . For small values of α, the one-and-half approximation adequately describes the composition dependence of z even at relatively large departure from stoichiometry. Using this approximation, equations describing the activities and partial entropies of the component elements are derived. It is found that the activity data of Olander for β′-AuCd are in excellent agreement with theoretical values using α = 0.0026 and ln a Cd , o = −3.46. Moreover, partial entropies are found to be in good accord with the theoretical values calculated on the basis of α = 0.0026. For β'-AgMg, activity and partial entropy data of Trzebiatowski and Terpilowski also agree well with theoretical values utilizing α = 0.014 and ln a Mg , o = −5.14. It is also found that the α-function is not necessarily a suitable function for evaluating and assessing data of ordered intermetallic phases. Rather data of this kind should be evaluated and assessed in light of the theoretical model presented in this paper. The disorder parameter z is related to the long-range order parameter S which is then used to discuss the transition of the lattice from a substantially ordered state to a substantially disordered one at some critical concentration, χ c .