Symmetry-broken crystal structure of elemental boron at low temperature

TL;DR

This paper uses advanced computational methods to reveal a low-temperature, symmetry-broken crystal structure of elemental boron, resolving longstanding questions about its stability and atomic arrangement.

Contribution

It introduces a novel, energy-minimizing configuration of boron that breaks the known symmetry, explaining stability at low temperatures and the role of entropy at higher temperatures.

Findings

Identifies a unique, stable, symmetry-broken structure at low temperature.

Shows that larger unit cells can have even lower energies.

Suggests entropy from partial occupancy stabilizes the structure at moderate temperatures.

Abstract

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the beta-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calculations found its energy to be greater than the energy of the alpha-rhombohedral (red) form, implying beta cannot be stable at low temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in conflict with the thermodynamic requirement that entropy vanish at low temperature. Using electronic density functional theory methods and an extensive search of the configuration space we find a unique, energy minimizing pattern of occupied and vacant sites that can be stable at low temperatures but that breaks the beta-rhombohedral symmetry. Even lower energies occur within larger unit cells. Alternative configurations lie nearby in energy, allowing the entropy of partial occupancy to stabilize the beta-rhombohedral structure through a phase transition at moderate temperature.