Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling

Abstract

Relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd 5 Si-μ, Pd 9 Si 2 -α, Pd 3 Si-β, Pd 2 Si-γ, and PdSi-δ are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-δ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd 5 Si-μ, Pd 9 Si 2 -α, Pd 3 Si-β, and Pd 2 Si-γ are treated as stable phases down to 0 K (-273 °C), while the PdSi-δ is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. Moreover, the liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd 5 Si-μ, Pd 9 Si 2 -α, Pd 3 Si-β, Pd 2 Si-γ, and PdSi-δ. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.