Tile Hamiltonians for Decagonal Phases

TL;DR

This paper develops a tile Hamiltonian model for decagonal quasicrystals, revealing how effective tile interactions and chemical ordering influence structural stability and quasiperiodicity.

Contribution

It introduces a tile Hamiltonian approach for decagonal phases, incorporating chemical ordering and energetics, to explain stability and structural transformations.

Findings

Dominant term favors H and B tiles over S tiles.

Chemical ordering affects tile edge arrowing but does not enforce quasiperiodicity.

Favored structures resemble crystalline approximants.

Abstract

A tile Hamiltonian (TH) replaces the actual atomic interactions in a quasicrystal with effective interactions between and within tiles. We study Al-Co-Ni and Al-Co-Cu decagonal quasicrystals described as decorated Hexagon-Boat-Star (HBS) tiles using {\em ab-initio} methods. A dominant term in the TH counts the number of H, B and S tiles, favoring tilings of H and B only. In our model for Al-Co-Cu, chemical ordering of Cu and Co along tile edges defines tile edge arrowing. Unlike the edge arrowing of Penrose matching rules, however, the energetics for Al-Co-Cu do not force quasiperiodicity. Energetically favored structures resemble crystalline approximants to which the actual quasicrystalline compounds transform at low temperature.