The effect of nonspherical charge distributions on X-ray and neutron scattering factors has been calculated for d- and f-electrons in cubic, tetrahedral, and hexagonal crystalline fields. The theory indicates that large deviations from the usual spherically symmetric approximation are to be expected, especially from electrons in a hexagonal environment, and that these deviations lead to a new technique for determining the spatial symmetry of the outer electrons in crystalline fields. Using this technique the measured X-ray and neutron scattering factors have been analyzed to determine the outer electron distribution in iron and nickel and compared with the calculated effects of asphericity. The polarized neutron data of Nathans, Shull, et al. indicates that in b.c.c. iron the doubly and triply degenerate orbitals are equally populated, while in nickel the holes are 75 per cent in the triply degenerate orbitals and 25 per cent in doubly degenerate orbitals. Combining these results with the X-ray data, further analysis shows that in b.c.c. iron the spin density arises from 2.2 3d atom-like electrons in one spin direction, whereas in nickel the spin density arises from 5.0 3d atom-like electrons with spin up and 4.4 3d atom-like electrons with spin down. In nickel it is shown that the spin-up electrons have a radial charge density slightly more compressed than that of the spin-down electrons.
|Number of pages||15|
|Journal||Journal of Physics and Chemistry of Solids|
|Publication status||Published - Jul 1959|
ASJC Scopus subject areas
- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials