Role of high-order Fourier terms for stability of monolayer-surface structures: Numerical simulations

Abstract

The role of high-order atom-surface Fourier terms is analyzed for the monolayer with coverage = 3 7 on ͑111͒ surface in cells with variable number of adsorbate atoms, allowed to relax to obtain the global minimum in each of the unit cells. A Fourier expansion with one or two shells of reciprocal cell vectors is used and three different models for the lateral interactions in the monolayer are tested, from purely repulsive to a real HFD-B2 potential. It is found that the simple commensurate ͑ ͱ 7 ϫ ͱ 7͒R19.1°three-atom structure is the most stable only when the contribution of the second Fourier term is included. In contrast to the conventional view, higher corrugation of the single-term Fourier model favors incommensurability. Evidence is collected that the highorder Fourier terms are mandatory for the stabilization of commensurate structures of an infinite monolayer.

A one-dimensional high-order commensurate phase of tilted molecules

“…In fact, a termination with such energetically preferred molecules stabilizes any HOC phase with finite extent. 2,3 DHTAP molecules of type 2 and 2′ lie between two Cu–O rows (configuration B) but appear slightly shifted to the left or right of the centre position, respectively (see Fig. 1).…”

“…Besides the fundamental commensurate (C) and fully incommensurate (IC) structures more complex structural coincidences such as domain wall phases, rotational epitaxy and moiré structures can occur, depending on the relative size of the competing interactions and the natural lattice misfit. 2,3 The relative stability of these different phases also depends on external parameters like the surface coverage and temperature, which can give rise to complex phase diagrams with a variety of solid phases with different superstructures. 4,5 The simplest case is that of a (quasi) one-dimensional (1D) arrangement of atoms or molecules with natural spacing b on a corrugated surface with periodicity a , corresponding to a nominal lattice mismatch δ = ( b — a )/ a .…”