Models for Monolayers Adsorbed on a Square Substrate

TL;DR

This paper presents a zero-temperature model for monolayers adsorbed on square substrates, using Lennard-Jones potentials and a Farey tree-based rule to systematically identify the most stable phases and construct the phase diagram.

Contribution

It introduces a novel systematic method based on Farey trees to generate and analyze the energetically favored phases of monolayers on square substrates.

Findings

Identified stable monolayer phases using the Farey tree rule.

Constructed the phase diagram for monolayers on square substrates.

Demonstrated the model's relevance to experimental Hg and Pb monolayers.

Abstract

Motivated by recent experimental studies of Hg and Pb monolayers on Cu(001) we introduce a zero temperature model of a monolayer adsorbed on a square substrate. Lennard-Jones potentials are used to describe the interaction between pairs of adlayer-adlayer and adlayer-substrate atoms. We study a special case in which the monolayer atoms form a perfect square structure and the lattice constant, position and orientation with respect to the substrate can vary to minimize the energy. We introduce a rule based on the Farey tree construction to generate systematically the most energetically favored phases and use it to calculate the phase diagram in this model.