Preroughening, fractional-layer occupancies, and phase separation at a disordered flat metal surface

Abstract

We study the phase separation that a particle-conserving ͑''canonical''͒ full-layered metal surface must undergo at temperatures between preroughening and roughening. The separation is into two disordered flat ͑DOF͒ domains of opposite order parameter with a step between them, each domain exhibiting a half-filled top layer. It is shown that both Gibbs-ensemble simulation and canonical Monte Carlo plus finite-size scaling, carried out on a specific lattice Hamiltonian model, demonstrate this phase-separation phenomenon microscopically. A number of existing particle-conserving molecular-dynamics simulations for fcc͑110͒ metal surfaces are then analyzed, and it is found that some display clear, previously unnoticed evidence of this DOF phase separation. Its main signal is a plateau of layer occupancies with temperature, around values close to 3 4 for the first surface layer, and around 1 4 for the adatom layer. It is proposed that this unusual type of phase separation could be observable on sufficiently step-free metal surfaces.

Disordered flat phase separation of the Lennard-Jones fcc(111) surface

“…Moreover, comparison of SF and LF indicates a stronger size-dependence of δh 2 at the breakdown temperature. Both features, in accordance with previous discussions based on the FCSOS model [20], strongly suggest that preroughening is taking place at the breakdown temperature, T PR ≃ 0.83 T m . A strong size-dependence of δh 2 reappears again at higher temperature, compatible with an estimated roughening temperature, T R ≃ 0.94 T m .…”

“…Finally, why did such an important singularity go unnoticed in so many previous, good-quality MD simulations?We surmised recently [20] that the answer might be that in MD, the singularity is masked by particle conservation, turning a sharp critical onset into a subtler, Ising-like phase separation. A Monte Carlo study of a lattice RSOS (restricted solid-on-solid) model did indeed show that under canonical, particle-conserving conditions, an initially full surface monolayer spontaneously phase separates above T PR into two DOF regions, each of which has essentially population 1/2 in the top layer [20]. However, lattice models may be oversimplified, and a more realistic study of this question is strongly needed.Here, we describe new extensive canonical MD simulations of the LJ fcc(111) surface, specifically aimed at understanding whether the DOF phase separation is real or not.…”

“…Next we calculated the layer occupancies, shown in fig. 2, as a crucial indicator of phase separation [20]. Due to phase separation, we would expect that (neglecting vacancies in the second and deeper layers) the concentration of vacancies in the first layer, n v , and of adatoms one layer above, n a , should be n v = N v /M = (1 − σ)/2, n a = N a /M = σ/2, with σ the "Ising magnetization" of this problem.…”