The molar volume of silicon

Abstract

Molar masses M and densities /spl rho/ of silicon in 1 kg Si almost perfect single crystals have been measured over the last several years to very small uncertainties in order to improve our knowledge of the Avogadro constant. Combining both is an excellent way to determine the molar volume of silicon. Small variations in isotopic composition and hence in molar mass must have the same effect on M as on /spl rho/: more of a light isotope (e.g. /sup 28/Si) will automatically reduce both M and and S values, but leave M//spl rho/ invariant. Since the three Avogadro projects (PTB-IRMM, IMGC-IRMM and NRLM-IRMM) used different crystals, it is worthwhile to review experimental values for M and /spl rho/ and determine our present best knowledge of M//spl rho/ the molar volume of Si in a single crystal. The (linked) improvements in the geometry and surface quality of the spherical artifacts and the measurement of mass and volume (hence density) as well as of molar mass, allow the testing of the hypothesis of the invariance of M//spl rho/ to reduced levels of uncertainty. The comparison of the relative standard uncertainties of M and /spl rho/ with those on M//spl rho/ reveal possible-albeit extremely small-systematic differences in isotopic composition in the various Si crystals used. This paper reports on that and indicates our present best knowledge of the molar volume of Si in single crystals.