Striped, honeycomb, and twisted moire patterns in surface adsorption systems with highly degenerate commensurate ground states

Atomistically thin adsorbate layers on surfaces with a lattice mismatch display complex spatial patterns and ordering due to strain-driven self-organization. In this work, a general formalism to model such ultrathin adsorption layers that properly takes into account the competition between strain and adhesion energy of the layers is presented. The model is based on the amplitude expansion of the two-dimensional phase field crystal (PFC) model, which retains atomistic length scales but allows relaxation of the layers at diffusive time scales. The specific systems considered here include cases where both the film and the adsorption potential can have either honeycomb (H) or triangular (T) symmetry. These systems include the so-called (1 × 1), (√3 × √3) R30∘, (2 × 2), (√7 × √7) R19.1∘, and other higher order states that can contain a multitude of degenerate commensurate ground states. The relevant phase diagrams for many combinations of the H and T systems are mapped out as a function of adhesion strength and misfit strain. The coarsening patterns in some of these systems is also examined. The predictions are in good agreement with existing experimental data for selected strained ultrathin adsorption layers

Commensurate-incommensurate transition and domain wall dynamics of adsorbed overlayers on a honeycomb substrate

© EPLA, 2016.We introduce an effective one-mode phase-field crystal model for studying the commensurate-incommensurate transition and domain wall dynamics of the ( √ 3×√3)R30 phase found in systems such as Xe/Pt(111), or Xe and Kr on graphite. The model allows us to study large systems where the domain walls can be separated over large macroscopic distances and at the same time incorporate the microscopic details of the domain wall structures. The resulting phase diagram shows that an intermediate stripe incommensurate phase always separates the commensurate phase from the honeycomb incommensurate phases. The energy of the domain wall crossing is investigated. We also find that near a step edge, the domain walls tend to align perpendicularly to the step edge, in agreement with recent experimental observations

Honeycomb and triangular domain wall networks in heteroepitaxial systems

© 2016 Author(s).A comprehensive study is presented for the influence of misfit strain, adhesion strength, and lattice symmetry on the complex Moiré patterns that form in ultrathin films of honeycomb symmetry adsorbed on compact triangular or honeycomb substrates. The method used is based on a complex Ginzburg-Landau model of the film that incorporates elastic strain energy and dislocations. The results indicate that different symmetries of the heteroepitaxial systems lead to distinct types of domain wall networks and phase transitions among various surface Moiré patterns and superstructures. More specifically, the results show a dramatic difference between the phase diagrams that emerge when a honeycomb film is adsorbed on substrates of honeycomb versus triangular symmetry. It is also shown that in the small deformation limit, the complex Ginzburg-Landau model reduces to a two-dimensional sine-Gordon free energy form. This free energy can be solved exactly for one dimensional patterns and reveals the role of domains walls and their crossings in determining the nature of the phase diagrams