First-Principles Calculations on Relative Energetic Stability, Mechanical, and Thermal Properties of B2-AlRE (RE = Sc, Y, La-Lu) Phases

The relative energetic stability, mechanical properties, and thermodynamic behavior of B2-AlRE (RE = Sc, Y, La-Lu) second phases in Al alloys have been investigated through the integration of first-principles calculations with the quasi-harmonic approximation (QHA) model. The results demonstrate a linear increase in the calculated equilibrium lattice constant a0 with the ascending atomic number of RE, while the enthalpy of formation ΔHf exhibits more fluctuating variations. The lattice mismatch δ between B2-AlRE and Al matrix is closely correlated with the transferred electron et occurring between Al and RE atoms. Furthermore, the mechanical properties of the B2-AlRE phases are determined. It is observed that the calculated elastic constants Cij, bulk modulus BH, shear modulus GH, and Young’s modulus EH initially decrease with increasing atomic number from Sc to Ce and then increase up to Lu. The calculated Cauchy pressure C12-C44, Pugh’s ratio B/G, and Poisson’s ratio ν for all AlRE particles exhibit a pronounced directional covalent characteristic as well as uniform deformation and ductility. With the rise in temperature, the calculated vibrational entropy (Svib) and heat capacity (CV) of AlRE compounds exhibit a consistent increasing trend, while the Gibbs free energy (F) shows a linear decrease across all temperature ranges. The expansion coefficient (αT) sharply increases within the temperature range of 0~300 K, followed by a slight change, except for Al, AlHo, AlCe, and AlLu, which show a linear increase after 300 K. As the atomic number increases, both Svib and CV increase from Sc to La before stabilizing; however, F initially decreases from Sc to Y before increasing up to La with subsequent stability. All thermodynamic parameters demonstrate similar trends at lower and higher temperatures. This study provides valuable insights for evaluating high-performance aluminum alloys.