Electronic origin of the incommensurate modulation in the structure of phosphorus IV

TL;DR

This paper investigates the electronic origins of incommensurate modulation in phosphorus IV's structure under high pressure, using a nearly-free-electron model to explain stability through Brillouin zone-Fermi surface interactions.

Contribution

It introduces a model analyzing electronic configurations to explain the incommensurate modulation in phosphorus IV's structure, linking it to band structure energy lowering.

Findings

Incommensurate modulation causes satellite reflections and additional Brillouin zone planes.

Stability is due to electronic band structure energy reduction from zone-Fermi surface interactions.

A commensurate approximant with an 11-fold supercell closely matches experimental modulation vector.

Abstract

An incommensurate modulated structure was found recently in a light group V element phosphorous in the phase P-IV stable in the pressure range 107-137 GPa. We consider configurations of the Brillouin zone and Fermi sphere within a nearly-free-electron model in order to analyze the importance of these configurations for the crystal structure energy. For the phase P-IV with the base-centered orthorhombic structure, oC2, we consider a commensurate approximant with an 11-fold supercell along the c-axis and a modulation wave vector equal 3/11 which is close to the experimentally observed value of 0.267. Atomic shifts due to the modulation result in appearance of satellite reflections and hence in a formation of additional Brillouin zone planes. The stability of this structure is attributed to the lowering of the electronic band structure energy due to Brillouin zone - Fermi surface interactions.