Electronic charge distribution in silicon

The structure factors Fh of eight high-order [0.64(sin)/1.56 A-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 Fh. Computer fitting of the theoretical curve to the measured one yields Fh. An energy-dispersive mode of operation allowed simultaneous measurements of the rocking curves of a whole family of planes to be carried out. The Fh values obtained, while in excellent agreement with previously measured and theoretical ones for (sin)/<1 A-1, are consistently and increasingly lower than the theoretical relativistic Hartree-Fock Fh values for (sin)/>1 A-1. This systematic trend most probably reflects the inadequacy of the Debye parameter B calculated from medium- and low-order Fhs for high-order reflections. Assuming different vibrational amplitudes for intermediate- and inner-shell electrons, our data yield Blow=0.46320.0041 A2 for reflections up to 880 [(sin)/=1.04 A-1], in excellent agreement with previous measurements, and Bhigh=0.50850.0035 A2 for reflections higher than 10 10 0 [(sin)/1.30 A-1]. We also find no anharmonic contribution to the temperature factor of Fh 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.