Using bond-length-dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys

Abstract

A model is tested to rapidly evaluate the vibrational properties of alloys with site disorder. It is shown that length-dependent transferable force constants exist and can be used to accurately predict the vibrational entropy of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and Cu-Pd. For each relevant force constant, a length-dependent function is determined and fitted to force constants obtained from first-principles pseudopotential calculations. We show that these transferable force constants can accurately predict vibrational entropies of $\mathrm{L}{1}_2$-ordered and disordered phases in ${\mathrm{Cu}}_3\mathrm{Au},$ ${\mathrm{Au}}_3\mathrm{Pd},$ ${\mathrm{Pd}}_3\mathrm{Au},$ ${\mathrm{Cu}}_3\mathrm{Pd},$ and ${\mathrm{Pd}}_3\mathrm{Au}.$ In addition, we calculate the vibrational entropy difference between $\mathrm{L}{1}_2$-ordered and disordered phases of ${\mathrm{Au}}_3\mathrm{Cu}$ and ${\mathrm{Cu}}_3\mathrm{Pt}.$