Molecular dynamics simulations of the structural and dynamic properties of graphite-supported bimetallic transition metal clusters

Molecular dynamics simulations were carried out for $\mathrm{Pd}\ensuremath{-}\mathrm{Pt}$, $\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$, and $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}$ nanoclusters supported on a static graphite substrate using the quantum Sutton-Chen potential for the metal-metal interactions. The graphite substrate was represented as layers of fixed carbons sites and modeled with the Lennard-Jones potential model. Metal-graphite interaction potentials obtained by fitting experimental cohesive energies were utilized. Monte Carlo simulations employing the bond order simulation model were used to generate initial configurations. The melting temperatures for bimetallic nanoclusters of varying composition were estimated based on variations in thermodynamic properties such as potential energy and heat capacity. Melting transition temperatures were found to decrease with increasing Cu (for $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}$) and Pd (for $\mathrm{Pd}\ensuremath{-}\mathrm{Pt}$ and $\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$) concentrations and are at least $100\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ higher than those of the same-sized free clusters. Density distributions perpendicular to the surface and components of the velocity autocorrelation functions in the plane of the surface indicate that one of the metals in the bimetallic nanoclusters wets the graphite surface more, and that this weak graphite substrate is able to structure the melted fluid in the first few monolayers. The wetting characteristics are dictated by the delicate balance between metal-metal and metal-graphite interactions. Components of velocity-autocorrelation functions characterizing diffusion of constituent atoms in these bimetallics suggest greater out-of-plane movement, which increases with Cu (for $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}$) and Pd (for $\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$ and $\mathrm{Pd}\ensuremath{-}\mathrm{Pt}$) concentrations. Deformation parameters showed that the core (Pd in $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}$, Rh in $\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$ and Pt in $\mathrm{Pd}\ensuremath{-}\mathrm{Pt}$) atoms diffuse out and the surface-segregated (Cu in $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}$, Pd in $\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$ and $\mathrm{Pd}\ensuremath{-}\mathrm{Pt}$) atoms diffuse into the nanoclusters upon melting. Near linear dependence of melting temperature on composition was found for unsupported clusters in our recent work, which results from the balance between the extent of surface melting and the radius of remaining solid core. Nonlinear dependence was found in these supported clusters, as a result of reduced surface melting at higher Pd concentrations, due to the substrate effect. Shell-based diffusion coefficients for layers perpendicular to the graphite substrate suggest surface melting to start from the cluster surface experiencing least influence of the graphite field. Surface melting was seen in all three nanoclusters, with calculated bond orientational order parameters revealing the order of $\mathrm{Pd}\ensuremath{-}\mathrm{Cu}g\mathrm{Pd}\ensuremath{-}\mathrm{Pt}g\mathrm{Pd}\ensuremath{-}\mathrm{Rh}$, for onset of melting. Cluster snapshots on the graphite substrate and calculated cluster diffusion coefficients indicate these nanoclusters to diffuse as single entities with very high diffusivities, consistent with experimental observations.