Contribution of the Conduction Electrons in a Metal to the Thermal Expansion

Abstract

The approximate proportionality between the thermal-expansion coefficient and the atomic heat of a metal in the moderate temperature region is well-known. However, it seems that this relation should be changed at those extremely low temperatures, where the contribution of the conduction electrons to the atomic heat is relatively large. It is the purpose of this paper to construct a formula for thermal expansion to cover this temperature region. The result is that in this region the thermal-expansion coefficient is no longer proportional to the atomic heat, and that it consists of two parts, corresponding to the Debye and the electronic terms of the latter respectively. The electronic term of the thermal-expansion coefficient is generally not proportional to that of the atomic heat. The former, however, as well as the latter, is proportional to the absolute temperature at low temperatures. From the new formula a possible explanation of the small expansibility of “Invar”has been suggested