Weak crystallization theory of metallic alloys

TL;DR

This paper extends Weak Crystallization theory to metallic alloys by including itinerant electrons, explaining the stabilization of complex phases like quasicrystals through free energy dependence on wave vector angles.

Contribution

It introduces a novel extension of Weak Crystallization theory that accounts for itinerant electrons, predicting stabilization of FCC, Rhombohedral, and icosahedral quasicrystalline phases.

Findings

Stabilization of FCC, Rhombohedral, and icosahedral quasicrystals.

Condition for iQC stability aligns with Hume-Rothery rules.

Fermi surface diameter relates to primary Bragg peak wavevector.

Abstract

We extend the Weak Crystallization theory to the case of metallic alloys. The additional ingredient -- itinerant electrons -- generates nontrivial dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of FCC, Rhombohedral, and icosahedral quasicrystalline (iQC) phases, which are absent in the generic theory with only local interactions. The condition for stability of iQC that we find, is consistent with the Hume-Rothery rules known empirically for majority of stable iQC; namely, the length of the primary Bragg peak wavevector is approximately equal to the diameter of the Fermi surface.