Electronic charge distribution in silicon

The structure factors $F_h$ of eight high-order [0.64≤(sinθ)/λ≤1.56 A${\mathrm{̊}}^{\mathrm{-}1}$] reflections were measured for a number of wavelengths to an accuracy of a few thousandths of an electron per atom. Most of these have never been measured before to this level of accuracy. A monolithic double-crystal diffractometer of novel design was employed in measuring thin-crystal Laue-case rocking curves which exhibit fine structure strongly dependent on $F_h$. Computer fitting of the theoretical curve to the measured one yields $F_h$. An energy-dispersive mode of operation allowed simultaneous measurements of the rocking curves of a whole family of planes to be carried out. The $F_h$ values obtained, while in excellent agreement with previously measured and theoretical ones for (sinθ)/λ${\mathrm{̊}}^{\mathrm{-}1}$, are consistently and increasingly lower than the theoretical relativistic Hartree-Fock $F_h$ values for (sinθ)/λ>1 A${\mathrm{̊}}^{\mathrm{-}1}$. This systematic trend most probably reflects the inadequacy of the Debye parameter B calculated from medium- and low-order $F_h$’s for high-order reflections. Assuming different vibrational amplitudes for intermediate- and inner-shell electrons, our data yield $B_{\mathrm{low}=0.4632\mathrm{}\pm 0.0041}$ A${\mathrm{̊}}^2$ for reflections up to 880 [(sinθ)/λ=1.04 A${\mathrm{̊}}^{\mathrm{-}1}$], in excellent agreement with previous measurements, and $B_{\mathrm{high}=0.5085\mathrm{}\pm 0.0035}$ A${\mathrm{̊}}^2$ for reflections higher than 10 10 0 [(sinθ)/λ≥1.30 A${\mathrm{̊}}^{\mathrm{-}1}$]. We also find no anharmonic contribution to the temperature factor of $F_h$ within the limit of accuracy of the experiment, in good agreement with previous x-ray measurements and some neutron measurements, but in contradiction to some of the neutron forbidden-222-reflection results.