The Structure Factors for Silicon and Core Electron-Scattering in Charge Density Studies

Abstract

Extant extensive and accurate silicon structure factors have been fitted by multipolar models involving harmonic and anharmonic thermal parameters, anisotropic valence electron functions of variable radii, and a Is orbital with independent thermal parameters. The best model involves normal thermal and valence orbital population parameters together with variable 1s orbital population and cubic and quartic anharmonic thermal parameters. We conclude that, given their importance in this rather rigid material (B≈5000 pm²)it is probably necessary to introduce anharmonic parameters into the refinement process routinely for charge density studies in more complex systems. From the data at a single temperature we are unable to conclude whether the small change in 1s orbital population and the anharmonicity are real or are artefacts of an underlying breakdown of the assumption of rigid atoms. However, the thermal parameters derived agree with the results of other diffraction experiments involving variable temperature, including neutron studies.