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

Abstract

The 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 ${\rm Pd}_{5}{\rm Si}{\text{-}}{\mu }$, ${\rm Pd}_{9}{\rm Si}_2{\text{-}}{\alpha }$, ${\rm Pd}_3{\rm Si}{\text{-}}{\beta }$, ${\rm Pd}_2{\rm Si}{\text{-}}{\gamma }$, and ${\rm PdSi}{\text{-}}{\delta }$ 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 ${\rm PdSi}{\text{-}}{\delta }$ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds ${\rm Pd}_{5}{\rm Si}{\text{-}}{\mu }$, ${\rm Pd}_{9}{\rm Si}_{2}{\text{-}}{\alpha }$, ${\rm Pd}_{3}{\rm Si}{\text{-}}{\beta }$, and ${\rm Pd}_2{\rm Si}{\text{-}}{\gamma }$ are treated as stable phases down to 0 K (−273 °C), while the ${\rm PdSi}{\text{-}}{\delta }$ 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. 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 ${\rm Pd}_{5}{\rm Si}{\text{-}}{\mu }$, ${\rm Pd}_{9}{\rm Si}_2{\text{-}}{\alpha }$, ${\rm Pd}_3{\rm Si}{\text{-}}{\beta }$, ${\rm Pd}_2{\rm Si}{\text{-}}{\gamma }$, and ${\rm PdSi}{\text{-}}{\delta }$. 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.