Soft mode anisotropy in negative thermal expansion material ReO$_3$

TL;DR

This study investigates the negative thermal expansion in ReO$_3$ using neutron pair distribution function analysis, revealing that local structural rigidity limits NTE and that rigid unit modes exhibit high anisotropy.

Contribution

It introduces a symmetry-based analysis of local structure in ReO$_3$, highlighting the role of structural flexibility and anisotropic rigid unit modes in NTE behavior.

Findings

ReO$_3$'s local structure is dominated by in-phase octahedral tilting.

Limited flexibility in ReO$_3$ restricts NTE to smaller reciprocal space regions.

No second NTE region observed at high temperatures.

Abstract

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the mechanism of negative thermal expansion (NTE) in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than the octahedra in the related compound ScF$_3$. These results support the idea that structural flexibility is an important factor in NTE materials, allowing the phonon modes that drive a volume contraction of the lattice to occupy a greater volume in reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. In addition, we investigate the thermal expansion properties of the material at high temperature and do not find the reported second NTE region. Finally, we show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that the motions associated with rigid unit modes are highly anisotropic in these systems.