First-principles theory of vibrational effects on the phase stability of Cu-Au compounds and alloys

The importance of vibrational effects on the phase stability of Cu-Au alloys is investigated via a combination of first-principles linear response calculations and a statistical mechanics cluster expansion method. We find that (i) the logarithmic average of the phonon density of states in ordered compounds is lower than in the pure constituents, thus leading to positive vibrational entropies of formation and to negative free energies of formation, stabilizing the compounds and alloys with respect to the phase separated state. (ii) The vibrational free energy is lower in the configurationally random alloy than in ordered ground states, which leads to lower order-disorder transition temperatures. (iii) The random alloys have larger thermal expansion coefficients than ordered ground states, and therefore the vibrational entropy difference between the random and ordered states is a strongly increasing function of temperature. However, (iv) due to the associated increase in the static internal energy, the effect of thermal expansion on the free energy (and thus on the phase diagram) is only half that of the entropy alone.