Thermodynamic modeling of the Pd-Zn system with uncertainty quantification and its implication to tailor catalysts

TL;DR

This study develops a thermodynamic model of the Pd-Zn system using DFT and CALPHAD, incorporating uncertainty quantification, to understand phase behavior and site occupancy, informing catalyst design.

Contribution

It introduces a comprehensive thermodynamic model of Pd-Zn with uncertainty quantification and detailed site occupancy analysis based on first-principles calculations.

Findings

Pd prefers OT and OH sublattices in the {\

The model's site occupancy predictions align with experimental data.

Increased Pd occupancy in the OH sublattice correlates with the formation of Pd trimers on the surface.

Abstract

Pd-Zn intermetallic catalysts show encouraging combinations of activity and selectivity on well-defined active site ensembles. Thermodynamic description of the Pd-Zn system, delineating phase boundaries, and enumerating site occupancies within intermediate alloy phases, are essential to determining the ensembles of Pd-Zn atoms as a function of composition and temperature. Combining the present extensive first-principles calculations based on density functional theory (DFT) and available experimental data, the Pd-Zn system was remodeled using the CALculation of PHAse Diagrams (CALPHAD) approach. High throughput modeling tools with uncertainty quantification, i.e., ESPEI and PyCalphad, were incorporated in the phase analysis. The site occupancies across the {\gamma}-phase composition region were given special attention. A four-sublattice model was used for the {\gamma}-phase owing to its four Wyckoff positions, i.e., the outer tetrahedral (OT) site 8c, the inner tetrahedral (IT) site 8c, the octahedral (OH) 12e, and the cuboctahedral (CO) site 24g. The site fractions of Pd and Zn calculated from the present thermodynamic model show the occupancy preference of Pd in the OT and OH sublattices in agreement with experimental observations. The force constants obtained from DFT-based phonon calculations further supports the tendency of Pd occupying the OH sublattice compared with the IT and CO sublattice. The catalytic assembles changing from Pd monomers (Pd1) to trimers (Pd3) on the surface of the {\gamma}-phase is attributed to the increase of Pd occupancy in the OH sublattice.