Equilibrium Distribution of Dissolved Carbon in PdC_x: Density Functional Theory and Canonical Monte Carlo Simulations

Subsurface carbon in Pd-based catalysts plays a key role in the selectivity of hydrogenation reactions. The existing model for subsurface carbon distribution (uniform Pd₆C) in Pd inadequately interprets the structure of all as-prepared PdC_x catalysts. Additionally, compared with neighboring element boron and nitrogen forming PdA_0.5 (A = B or N) alloys, the carbon concentration in Pd is fairly low (usually PdC_0.13). Utilizing density functional theory calculations combined with Canonical Monte Carlo (CMC) simulations, our present work investigates the carbon diffusion into Pd(111) and Pd(100) and equilibrium distribution of carbon with various concentrations in Pd(111). A zigzag trajectory of C atom diffusion into Pd(111) and a spiral trajectory of C atom diffusion into Pd(100) from the most stable adsorption site of the surface are verified. Then, CMC simulations suggest a nonuniform distribution of dissolved C atoms in the Pd(111) slab and provide the equilibrium distribution configurations of dissolved C atoms at different ratios of C/Pd (0.04, 0.13, and 0.18) and the maximum of C atom coverage (0.33 ML) in odd number sublayers (Sub^y, y = 1, 3, 5...). Finally, low carbon concentration and distribution patterns of dissolved C atoms in Pd(111) are ascribed to strong in-plane first nearest neighboring (1NN) C–C repulsion and isotropic character of repulsion in Pd(111). Our results have provided a clear microscopic description for carbon in Pd-based catalysts and been instructive for understanding the role of C in hydrogenation reactions.