An Approximate Relation Between Elastic Moduli and Thermal Expansivities

Abstract

A large number of polycrystalline and amorphous materials ranging from pure metals to glassy polymers have been found to obey the relations α²E=150 [dyn cm⁻²°K⁻²]s at normal temperatures. The linear coefficient of expansion is denoted by α, Young's modulus by E, and s is a dimensionless spread factor (0.5<sE covered by the data. Notable exceptions to the relation are certain alloys, some inorganic glasses, cellular materials (e.g., wood), granular materials (e.g., cement), and rubbery materials. The variations with temperature of α, E, and heat capacity C_p are compared for representative materials and implications of the α²E relation are discussed. An empirical approach in which generalized Grüneisen numbers are utilized and a preliminary statistical mechanical attempt to relate α to C_v and the elastic properties of polymers are discussed. Both lead to the conclusion that for polymers, perhaps even more so than for metals, it would be of interest to make separate measurements to very low temperatures of α, C_p, and various elastic moduli.