Negative thermal expansion: a review

J Mater Sci (2009) 44:5441–5451
DOI 10.1007/s10853-009-3692-4

REVIEW

Negative thermal expansion: a review
W. Miller Æ C. W. Smith Æ D. S. Mackenzie Æ
K. E. Evans

Received: 4 March 2009 / Accepted: 15 June 2009 / Published online: 2 July 2009
Ó Springer Science+Business Media, LLC 2009

Abstract Most materials demonstrate an expansion upon heating, however a few are known to contract, i.e. exhibit a negative coefficient of thermal expansivity (NTE). This naturally occurring phenomenon has been shown to occur in a range of solids including complex metal oxides, polymers and zeolites, and opens the door to composites with a coefficient of thermal expansion (CTE) of zero. The state of the art in NTE solids is reviewed, and understanding of the driving mechanisms of the effect is considered along with experimental and theoretical evidence.
The various categories of solids with NTE are explored, and experimental methods for their experimental characterisation and applications for such solids are proposed. An abstraction for an underlying mechanism for NTE at the supramolecular level and its applicability at the molecular level is discussed.

Introduction
In general, solids expand upon heating, i.e. they exhibit positive coefficients of thermal expansivity (CTE), denoted as a herein. However, a minority of solids show the inverse effect, i.e. of contracting upon heating, and thus exhibit negative thermal expansion (NTE). There has been an increasing amount of interest in these solids and their potential applications. The underlying mechanisms for
NTE have been found to be complex.

W. Miller Á C. W. Smith (&) Á D. S. Mackenzie Á K. E. Evans
School of Engineering, Computing and Mathematics,
University of Exeter, Exeter EX4 4QF, UK e-mail: [e-mail]

The reason that most solids have positive CTEs is well understood which is due primarily to an increase in the interatomic bond length, which manifests at the macroscopic