Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals

TL;DR

This paper uses a bulk tiling model to explain the Fibonacci-spaced atomic terraces observed on the surface of icosahedral AlPdMn quasicrystals, achieving quantitative agreement with experimental STM data.

Contribution

It applies a 6D hypercubic lattice tiling model to analyze surface structures of quasicrystals, linking theoretical predictions with experimental observations.

Findings

Fibonacci spacing of atomic planes matches STM observations

Derived atomic densities and correlation functions agree with experiments

Provided a geometric explanation for surface terrace patterns

Abstract

Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral Bergman clusters within an icosahedral tiling T^*(2F) and is projected from the 6D face-centered hypercubic lattice. We derive the occurrence and Fibonacci spacing of atomic planes perpendicular to any 5fold axis, compute the variation of planar atomic densities, and determine the (auto-) correlation functions. Upon interpreting the planes as terraces at the surface we find quantitative agreement with the STM experiments.