Matching rules from Al-Co potentials in an almost realistic model

TL;DR

This paper models a decagonal Al-Co quasicrystal using realistic pair potentials, demonstrating that the ground state aligns with Penrose's matching rules, with the second-neighbor potential well playing a key role.

Contribution

It provides a rationalization of the quasicrystal's ground state structure based on realistic pair potentials, linking potential features to matching rules.

Findings

Ground state is a Hexagon-Boat-Star tiling satisfying Penrose's matching rules.

Second-neighbor potential well in Al-Co interactions is crucial.

Model closely relates to actual quasicrystal structures.

Abstract

We consider a model decagonal quasicrystal of composition Al$_{80.1}$Co$_{19.9}$ -- closely related to actual structures, and using realistic pair potentials -- on a quasilattice of candidate sites. Its ground state, according to simulations, is a Hexagon-Boat-Star tiling satisfying Penrose's matching rules. In this note, we rationalize these results in terms of the potentials; the Al-Co second-neighbor potential well is crucial.