X-ray and neutron scattering from electrons in a crystalline field and the determination of outer electron configurations in iron and nickel

R. J. Weiss, Arthur J Freeman

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94 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)147-161
Number of pages15
JournalJournal of Physics and Chemistry of Solids
Volume10
Issue number2-3
Publication statusPublished - Jul 1959

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Neutron scattering
Nickel
X ray scattering
neutron scattering
Iron
nickel
Crystalline materials
iron
Electrons
configurations
scattering
electrons
x rays
orbitals
Atoms
asphericity
deviation
atoms
electron distribution
Charge distribution

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

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abstract = "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.",
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AU - Weiss, R. J.

AU - Freeman, Arthur J

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N2 - 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.

AB - 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.

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