Finite computational cell-size effects and the nature of the melting transition of Kr adlayers deposited on graphite.

Abstract

The recently developed histogram Monte Carlo (MC) method is employed in conjunction with a (N,\ensuremath{\rho},T) MC ensemble with periodic boundary conditions to study monolayer and submonolayer melting transitions of a krypton adlayer physisorbed on a graphite substrate. The simulation results are found to depend on the size of the model system. The number of atoms in the MC cell are 900, 400, 324, 289, and 100. The calculated coverage-temperature (\ensuremath{\rho},T) phase diagram exhibits three distinct regions: an upper section (0.7\ensuremath{\lesssim}\ensuremath{\rho}\ensuremath{\le}1) in which the melting temperature ${\mathit{T}}_{\mathit{m}}$ is very sensitive to \ensuremath{\rho}, a steep intermediate region (0.25\ensuremath{\lesssim}\ensuremath{\rho}\ensuremath{\lesssim}0.7) where ${\mathit{T}}_{\mathit{m}}$\ensuremath{\approxeq}85 K and is relatively insensitive to \ensuremath{\rho}, and a lower part (0\ensuremath{\lesssim}0.25) in which sensitivity to the density resumes. The N=400 solid-fluid boundary agrees well with the experimental phase diagram, and investigations at N=900 confirm that the N\ensuremath{\gtrsim}=400 results are closely approaching those of the thermodynamic limit; the N=400 simulation is taken to be a reasonable model of the krypton-graphite system in the \ensuremath{\rho}\ensuremath{\le}1 regime. Departures from such large-N behavior with decreasing N are understood by applying artificial stabilization arguments in the upper and intermediate regimes of the solid-liquid phase boundary, and using finite-patch size-effect arguments in the lower regime. Examination of a series of atomic configurations shows that the three separate parts of the phase boundary correspond to different types of melting: vacancy-mediated melting in the upper wing, the melting of a connected atomic network in the intermediate section, and individual patch melting on the lower portion where sensitivity of ${\mathit{T}}_{\mathit{m}}$ with \ensuremath{\rho} resumes.