Lattice Parameters, Coefficients of Thermal Expansion, and Atomic Weights of Purest Silicon and Germanium

Abstract

Lattice parameter determinations of 99.97 percent pure silicon (containing 0.03 percent carbon) were carried out using the asymmetric method, a 64-mm precision camera in a thermostat at constant temperatures (10, 20, 30, 40, and 50°C). The powder mounts, about 0.12-mm in diameter, were translated and rotated during the exposure. Only the (444)-CuKα1 line was used for the determinations. The lattice parameter a=5.41991±0.00003kX (5.43086A) at 20°C, corrected for refraction, was obtained; the linear lattice expansion coefficient (between 10 and 50°C) was 4.15×10−6, the density at 20°C was 2.32831±0.00031 g/cm3 (determined by the suspension method), and the atomic weight was 28.083±0.013 (in agreement with the new chemical weight 28.09) showing that the silicon crystals used, under certain limitations, were sound although the possibility of interstitial atoms is not excluded. The lattice parameter of purest germanium (99.99 and 99.999 percent) was measured by the same method using the (422)-CrKα1 and α2 lines: a20=5.64607±0.00004kX (5.65748A) for both materials. The expansion coefficients were α=6.65×10−6 and 5.92 ×10−6, respectively. The density was 5.3234±0.0025 g/cm3 at 25°C and the calculated atomic weight 72.593±0.037 in agreement with the present chemical weight 72.60. Thus, germanium crystals are sound; however, interstitial atoms are possible. The precision of lattice parameter determination was about 1:200,000, but in the case of 99.999 percent germanium the precision was considerably better. This shows again that lattice constant determinations can be performed with highest precision and without use of any extrapolation method. The method of lattice parameter determination applied is an absolute one.