Thermal Expansions from 2 to 40°K of Ge, Si, and Four III-V Compounds

Abstract

Linear thermal-expansion data are given for Ge, Si, GaAs, GaSb, InAs, and InSb at temperatures from 1.89°K to approximately 40°K. The data were obtained using a variable transformer as a sensor and are absolute in sample length changes. At the lowest temperatures, the length-change data for 10-cm samples exhibit a scatter of ±0.02 Å (or ±2×${10}^{-11\mathrm{}}$ in $\frac{\Delta L}{L_0}$). The precision at all temperatures (within this limitation) is 2%. All of these substances show a positive thermal-expansion coefficient which is proportional to $T^3$ at low temperatures, while at higher temperatures the expansion coefficient becomes negative. The linear thermal-expansion data are used to calculate the temperature dependence of the Grüneisen constants for each of these. With the exception of Si, a correlation exists between the Debye temperature and both the magnitude of ${\gamma }_0$ and the shape of the $\gamma$-versus-$T$ curve. There is discrepancy between our observed values of ${\gamma }_0$ for Ge and Si (0.66 and 0.42, respectively) and those calculated from the 77°K third-order elastic-constant data. The reason for the discrepancy (which is a factor of 2 for Si) is not known.