Structural, vibrational, and thermodynamic properties of Al-Sc alloys and intermetallic compounds

We present results of a theoretical study of the temperature-dependent structural and thermodynamic properties of solid-phase Al-Sc alloys and compounds based upon first-principles calculations of electronic free energies and ionic vibrational spectra. This work extends a previous first-principles study of the fcc portion of the Al-Sc phase diagram which demonstrated a large effect of vibrational free energy upon calculated Sc solid-solubility limits [V. Ozoliņš and M. Asta, Phys. Rev. Lett. 86, 448 (2001)]. Here the contributions of nonconfigurational (electronic and vibrational) entropies to the free energies of solid-phase Al-Sc alloys and compounds are analyzed in further detail, and the accuracy of the approximations employed in these calculations is assessed. For each of the reported intermetallic compounds in this system, calculated formation enthalpies agree to within 10% (0.05 eV/atom) of published calorimetry measurements. Large negative entropies of formation, equal to $-{0.77k}_B/\mathrm{atom},$ $-{0.58k}_B/\mathrm{atom},$ and $-{0.24k}_B/\mathrm{atom}$ are calculated for cubic ${\mathrm{Al}}_3\mathrm{Sc},$ cubic AlSc, and orthorhombic AlSc compounds, respectively, resulting primarily from the stiffening of nearest-neighbor Al-Sc bonds in the intermetallic phases relative to elemental Al and Sc. The net effects of nonconfigurational free energy contributions to the fcc portion of the Al-Sc phase diagram are 100 and 450 K decreases in the calculated Al solvus phase boundary temperatures associated with electronic and vibrational entropy, respectively, at the maximum measured Sc solid-solubility limit.