Electron-density studies. III. A re-evaluation of the electron distribution in crystalline silicon

Abstract

Highly accurate absolute measurements of the X-ray structure factors of silicon [Aldred & Hart, Proc. R. Soc. London, Ser. A, (1973), 332, 223-238] have been used to analyse a number of models for the electron distribution. Initially, the valence-electron distribution (with the neon core assumed to be unmodified from that of the isolated silicon atoms) was built up with a radial basis of the form r ~ exp (-Q') and non-sphericity was allowed for by inclusion of octupole and hexadecapole terms. Improved representation was achieved with related models in which deformations from the total isolated-atom electron density were refined instead. The exact shape of the deformation electron density in the region of the bond was sensitively dependent on the monopole deformation term. The anomalous-dispersion contributions (Af') to the scattering factors were refined and found to be in agreement with recent interferometric measurements, but not with recent calculations. The octupole density term is slightly sharper at 293-2 than at 92.2 K, and the structure factor for the 222 reflection is predicted to be larger at the higher temperature. These effects may be due to a failure of the convolution approximation or to uncertainties in the anharmonic corrections to the structure-factor data.

Theoretical and Experimental Techniques for the Determination of X-ray Anomalous Dispersion Corrections

“…This difference tends to zero as A tends to A K , in accord with the observations made by synchrotron radiation users to the effect that, in general, on approaching the edge the predictions of Cromer andLiberman (1970, 1981) are in good agreement with experiment. Hart (1975) 0·0863(2) 0·0568(2) Price et al (1978) 0·085 (7) 0·047 (7) Gerward et al (1979) 0·099 (7) 0·070 (7) Creagh (1984) 0·091 (5) 0·060 (5) Deutsch & Hart (1984) 0·0847 (1) 0·0537 (1) We note in Table 2 that the nonrelativistic approach used by Wagenfeld (1975Wagenfeld ( , 1985 also is not in agreement with the observed values. This has been attributed by Deutsch and Hart (1984) to a failure to account properly for the effect of higher electron shells in the calculations.…”

“…Data for lithium fluoride and silicon are included in Table 2 together with the results of the deformation density study by Price et al (1978), who used the PendellOsung measurements for silicon reported by Aldred and Hart (1973). We note that the inclusion of these results in the table is valid only if it can be assumed that there is no functional dependence of 1'( w, ..:i) on ..:i.…”

“…Price et al (1978) have used a refinement technique to evaluate from this data values of the anomalous dispersion corrections. The data, however, are for I(w, ghkl)' and.…”

The electron distribution in silicon. A comparison between experiment and theory

“…see Scheringer (1980), Fehlmann (1979), * Present address: Department of Crystallography, University of Pittsburgh, Pittsburgh, PA 15260, USA. Price, Maslen & Mair (1978; referred to below as PMM), Yang & Coppens (1974; referred to as YC), Aldred & Hart (1973; referred to as AH) and references therein]. In this work we take advantage of recent highly accurate experimental reports on silicon, which, in combination with the earlier measurements of AH, provide data sets of extraordinarily high quality.…”

Recent Advances in the Calculation and Measurement of the X-ray Dispersion Corrections

“…Exceptions occur for Si and Al for the wavelength of Cu Ka l . The discrepancy Creagh (1984) 0·085 (5) 0·020 (10) 0·014(10) Deutsch & Hart (1985) 0·0217 (1) 0·0133 (1 Cusatis & Hart (1975) 0·0863 (2) 0·0568(2) Price et aL (1978) 0·085 (7) 0·047(7) Gerward et aL (1979) 0·244 (7) 0·099 (7) 0·070 (7) Creagh (1984) 0·236 (5) 0·091 (5) 0·060(5) Deutsch & Hart (1985) 0·0847 (1) 0·0537 ( Creagh (1984) 0·065 (20) 0·044(20) Takama et aL (1982) 0·20 ( between the theories is about 5%. Neither theory appears in reasonable agreement with experiment for Ge, although the RMP theory is in better accord than the RDP theory.…”