A maximum density rule for surfaces of quasicrystals

TL;DR

This paper challenges Bravais's rule for crystal surfaces by showing that surface stability in quasicrystals depends on layered atomic densities rather than single-plane densities, aligning theoretical models with experimental observations.

Contribution

It introduces a layered density rule for quasicrystal surfaces that improves the prediction of surface stability over traditional single-plane density rules.

Findings

Surface stability correlates with layered atomic densities.

Layered density analysis predicts terrace spacings and pittedness.

Traditional densest-plane rule does not hold for quasicrystals.

Abstract

A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this correspondence breaks down and that surfaces parallel to the densest planes in the bulk are not the most stable, i.e. they are not so-called bulk terminations. The correspondence can be restored by recognizing that there is a contribution to the surface not just from one geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layer-like bulk terminations but the exact spacings between surface terraces and their degree of pittedness may be determined by a simple analysis of the density of layers predicted by the bulk geometric model.