Structure stability in the simple element sodium under pressure

TL;DR

This paper investigates the stabilization mechanisms of various complex phases of sodium under high pressure, highlighting the role of electronic structure and the Hume-Rothery mechanism in phase stability.

Contribution

It provides a detailed analysis of how electronic energy reduction via Brillouin-Jones zone formation stabilizes sodium's high-pressure phases, suggesting divalency at certain densities.

Findings

High-pressure phases of Na satisfy Hume-Rothery criteria.

Stabilization involves formation of planes in Brillouin-Jones zones.

Na may become divalent in the oP8 phase at high density.

Abstract

The simple alkali metal Na, that crystallizes in a body-centred cubic structure at ambient pressure, exhibits a wealth of complex phases at extreme conditions as found by experimental studies. The analysis of the mechanism of stabilization of some of these phases, namely, the low-temperature Sm-type phase and the high-pressure cI16 and oP8 phases, shows that they satisfy the criteria for the Hume-Rothery mechanism. These phases appear to be stabilized due to a formation of numerous planes in a Brillouin-Jones zone in the vicinity of the Fermi sphere of Na, which leads to the reduction of the overall electronic energy. For the oP8 phase, this mechanism seems to be working if one assumes that Na becomes divalent metal at this density. The oP8 phase of Na is analysed in comparison with the MnP-type oP8 phases known in binary compounds, as well as in relation to the hP4 structure of the NiAs-type.