Fundamentals of thermal expansion and thermal contraction

Thermal expansion is an important property of substances. Its theoretical prediction has been challenging, particularly in cases the volume decreases with temperature, i.e., thermal contraction or negative thermal expansion at high temperatures. In this paper, a new theory recently developed by the authors has been reviewed and further examined in the framework of fundamental thermodynamics and statistical mechanics. Its applications to cerium with colossal thermal expansion and Fe₃Pt with thermal contraction in certain temperature ranges are discussed. It is anticipated that this theory is not limited to volume only and can be used to predict a wide range of properties at finite temperatures.