Complex structures in the Au-Cd alloy system: Hume-Rothery mechanism as origin

TL;DR

This paper investigates the complex crystal structures in the Au-Cd alloy system using the nearly free-electron model and Fermi sphere-Brillouin zone interactions to explain phase stability and structural distortions.

Contribution

It applies the Fermi sphere-Brillouin zone interaction model to elucidate the origins of structural complexities in Au-Cd alloys, highlighting the role of valence electrons and superlattices.

Findings

Complex structures relate to simple cells via reciprocal space analysis.

Additional planes are crucial for the stability of superslattices.

Certain structures are derived from rhombohedral distortions of basic cells.

Abstract

The binary (simple metal) phase diagram Au-Cd contains a number of intermetallic compounds with various distortions, superlattices and vacancies. To understand the reasons of these structural complexities and their phase stability, we analyze these crystal structures within the nearly free-electron model in the frame of Fermi sphere - Brillouin zone interactions. Examination of the Brillouin-Jones configuration in relation to the nearly-free electron Fermi sphere provides insights for significance of the valence electron energy contribution to the phase stability. Representation of these complex structures in the reciprocal space clarifies their relationship to simple basic cells. This approach shows the importance of the additional planes for the stability of superslattices. The AuCd-hP18, AuCd3-hP24 and AuCd4-hP273 structures are shown to be related to the AuCd-cP2 via rhombohedral distortion with superlattices and vacancies.