Thermal Expansion of Germanium Isotopes at Low Temperature

The focus of this paper is the vanishing of the thermal expansion in certain diamond-like semiconductors. In silicon becomes zero at T = 122. K. In germanium the situation is less clear. Previous investigations show that in natural germanium a zero in is reported at 15.5 K and that a second zero for T > 30 K is not observed. This paper reports on data taken on four monoisotopic Ge crystals. All plots of lattice parameter vs temperature shows a minimum between 40 and 50 K. The minimum is very deep for 70Ge, which also shows anomalous behaviour for the thermal expansion alpha. The data are discussed with ab initio theoretical results obtained by Debernardi and Cardona. Some data do not support the Virtual Crystal Approximation.