# Entropic elasticity and negative thermal expansion in a simple cubic crystal

## TL;DR

This paper demonstrates that negative thermal expansion in a simple cubic crystal, ScF3, is driven by entropic elasticity similar to polymers, challenging previous beliefs that its origin was different.

## Contribution

It provides a quantitative theory linking NTE in solids to entropic elasticity, supported by neutron scattering experiments on ScF3.

## Key findings

- Correlation in fluorine atom positions fades with temperature
- Uncorrelated thermal motion constrained by rigid bonds
- Quantitative agreement between theory and experiment

## Abstract

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.