The electron distribution in silicon - II. Theoretical interpretation

Abstract

The absolute structure factors of silicon measured in Part I are examined in detail using Dawson’s structure factor formalism with recent theoretical estimates of free atom Hartree-Fock wavefunctions (Clementi 1965). It is not possible to describe the structure of silicon with only Kubic Harmonic expansions having physically reasonable coefficients. If the valence-shell form factor is radially compressed by 6.8% then we can obtain an excellent fit using only the third- and fourth-order Kubic Harmonics with amplitudes F 3 ═ + 1.012 and G 4 ═ — 0.206. There is some evidence that the anomalous dispersion corrections for silicon which are available in the literature are in error by 0.02 electron units. From the high-order reflexions we have measured the X-ray Debye temperatures of silicon as ⊝ M ═ 536.3 ± 5.0 K at 92.2 K and ⊝ M ═ 532.5 ± 2.0 K at 293.2K . The increase in ⊝ M at low temperature is smaller than had been expected theoretically. Our measurements of the 555 structure factor permit us to confirm Nunes’s (1971) upper-bound estimate of the anharmonic force constant for silicon. Finally, we have compared our results with the self-consistent orthogonalized-plane-wave band structure calculations of Stukel & Euwema (1970) for silicon atoms in a crystal. We find that the Kohn-Sham-Gaspar model of exchange results in structure factors which are in much better agreement with those measured than are structure factors calculated using Slater’s exchange term. As in the interpretation based on Dawson’s formalism there is evidence here that the theoretical anomalous dispersion corrections may be inadequate.