Thermodynamic Properties of Elements and Compounds in Al-Sc Binary System from Ab Initio Calculations Based on Density Functional Theory

The thermodynamic properties of FCC Al, HCP Sc, B2 AlSc, C15 Al₂Sc, B8₂ AlSc₂, and L1₂ Al₃Sc were studied using ab initio calculations based on density functional theory. The 0 K (−273 °C) total energies were calculated using the ab initio plane-wave pseudopotential method within the generalized gradient approximation. The ab initio calculations of the phonon dispersion curves and the density of state of FCC Al, HCP Sc, B2 AlSc, C15 Al₂Sc, B8₂ AlSc₂, and L1₂ Al₃Sc have been performed using the density functional theory and the direct method. Deduced from Helmholtz free energy, the thermal expansion, enthalpy, heat capacity, and entropy as a function of temperature were calculated and compared considerably with the experimental data and other computational results. Our calculations show that the enthalpies of formation are temperature-dependent, and the slope is about −3.4 J/mol/K for B2 AlSc, −2.3 J/mol/K for C15 Al₂Sc, −0.8 J/mol/K for B8₂ AlSc₂, and −2.7 J/mol/K for L1₂ Al₃Sc, respectively.