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

• The Au–Cd system contains great variety of compounds as compared with the lighter Cu-Zn system.
• Au–Cd compounds are stabilized with the Hume-Rothery rules at certain counts of electron per atom.
• Stimulating factor for Au and Cd to create ordered superlattices is a high atomic number difference.
• Complex Au-Cd phases tend to form nearly spherical Brillouin-Jones zones close to the Fermi sphere.

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 superlattices. 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.

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