A theoretical study of thermodynamic properties and of the phase diagram for crystalline hcp-based Cd-Mg alloys is presented. Many first-principles studies of phase diagrams for metallic alloys have considered only configurational contributions to the free energy, which arise from the effects of substitutional disorder on the entropy and enthalpy. In this paper, the additional effects of the vibrational free energy, the electronic entropy, and the energy associated with structural relaxations on the thermodynamic properties and calculated phase equilibria for Cd-Mg alloys are studied. Ground-state properties and the densities of states of stable and metastable Cd-Mg compounds with hcp-based structures have been calculated with the linear muffin-tin orbital (LMTO) method. The results of these LMTO calculations are combined with the cluster variation method to calculate the configurational free energy and electronic entropy of ordered and disordered alloys from first principles. The vibrational free energy is treated using the Debye model; the configurational dependence of the Debye temperature is obtained semiempirically from experimentally measured entropies of formation in combination with the results of the LMTO calculations. The energy associated with structural relaxations is estimated from experimentally measured lattice parameters and elastic constants. We find that, although the configurational free energy is the largest component of the total alloy free energy, nonconfigurational effects contribute significantly to thermodynamic properties, and hence appreciably affect the calculated Cd-Mg phase diagram.

• Received 15 January 1993

DOI:https://doi.org/10.1103/PhysRevB.48.748