Negative thermal expansion in isotropic crystals

Abstract

The purpose of this article is to take away some of the mystery associated with understanding the phenomenon of negative thermal expansion (NTE) in isotropic crystals. For sure, NTE is counter to our textbook intuition about the normal positive thermal expansion of chemical bonds, but there are now sufficient results from experimental and theoretical investigations to enable us to rationalise the existence of NTE in most materials with cubic symmetry, and indeed to be able to predict its possible existence in any new material. In this article, we posit the existence of four principles that can enable us to rationalise the existence of NTE: the existence of a network structure, the ability of the structure to support low-frequency vibrations, the spreading of the important vibrations into a sufficiently-large volume of reciprocal space, and the limiting factor of dynamic disorder. We describe these with regard to a number of key examples. We point out that the same principles will operate for anisotropic crystals, but we offer the caution that NTE in anisotropic materials can also arise from factors missing in isotropic materials. We also point out that NTE arises in the face of competing mechanisms that ordinarily would give positive thermal expansion, so the practical existence of NTE arises as a balance between mechanisms pulling in opposite directions. We therefore argue that one should not point to a single simplemechanismforNTE.Instead,NTEisassociatedwiththefourprinciplestogetherwithchemical effects that can tilt how these principles are balanced against the drive of the chemical bonds towards positive thermal expansion. There is a long-standing and well-demonstrated importance of glass ceramics for many technical and domestic applications, which practically achieve many of the goals of the NTE materials community. In the light of this, it is our feeling that the key achievement of much of NTE research over the past 30 years has not so much been in terms of finding alternative NTE materials as in what we have been able to learn from these materials, which in turn has enabled us to elucidate the general principles that underpin our understanding of how NTE materials work.