Calculation of the vibrational contribution to the Gibbs energy of formation for Al3Sc

The ground-state energies were calculated for the stoichiometric compound Al3Sc in the L12 structure, and its constituents (fcc-Al and hcp-Sc) using the Vienna ab initio simulation package (VASP). The enthalpy of formation for Al3Sc at 0 K was obtained. On the basis of the calculated equation of state (EOS) at 0 K, the vibrational contribution to the Gibbs energy of formation at finite temperatures was estimated using the Mean-Field Potential (MFP) method, and compared with the phonon spectrum calculation and the existing CALPHAD assessments. The calculated entropy of formation can serve as a reasonable start value in a CALPHAD assessment although it is not as accurate as the enthalpy of formation calculated at 0 K. Both high-temperature x-ray scattering measurements and first-principles calculation show that Al3Sc is almost perfectly ordered up to its melting point and thus the configurational contribution can be neglected.