Incommensurate host-guest structures in compressed elements: Hume-Rothery effects as origin

TL;DR

This paper explores incommensurate host-guest structures in compressed elements, linking their stability to Hume-Rothery effects and Fermi surface interactions, revealing how electron count changes influence structure formation.

Contribution

It establishes a structural relationship between host-guest phases in compressed elements and Hume-Rothery phases, highlighting electron count effects on stability.

Findings

Incommensurate structures are related to Hume-Rothery phases.

Valence electron count increases under compression, affecting stability.

Structural similarity between host-guest phases and binary alloy phases.

Abstract

Discovery of the incommensurate structure in the element Ba under pressure 15 years ago was followed by findings of a series of similar structures in other compressed elements. Incommensurately modulated structures of the host-guest type consist of a tetragonal host structure and a guest structure. The guest structure forms chains of atoms embedded in the channels of host atoms so that the axial ratio of these subcells along the c axis is not rational. Two types of the host-guest structures have been found so far: with the host cells containing 8 atoms and 16 atoms; in these both types the guest cells contain 2 atoms. These crystal structures contain a non-integer number of atom in their unit cell: tI11* in Bi, Sb, As, Ba, Sr, Sc and tI19* in Na, K, Rb. We consider here a close structural relationship of these host-guest structures with the binary alloy phase Au3Cd5-tI32. This phase is related to the family of the Hume-Rothery phases that is stabilized by the Fermi sphere - Brillouin zone interaction. From similar considerations for alkali and alkaline-earth elements a necessary condition for structural stability emerges in which the valence electrons band overlaps with the upper core electrons and the valence electron count increases under compression.