### Abstract

The effects of crystalline fields on 3d charge densities and magnetic form factors for transition metal ions are discussed on the basis of recent theoretical investigations augmented by an analysis of optical absorption data. It is shown that the crystalline field has two effects on the free ion 3d wave functions and hence on their form factors as well: (1) a differentiation or "splitting" of the two types of cubic 3d functions by an expansion of the t2g(eg) orbitals and a contraction of the eg(t2g) orbitals resulting in two different radial charge densities, and (2) a net expansion of the charge distribution from the free ion value. The magnetic form factors due to this "splitting" effect when calculated according to the methods of Weiss and Freeman show measurable deviations from the free atom results. A form factor for Mn+2 based on optical absorption data shows a large expansion of the 3d charge density, in agreement with the magnetic form factor measurements of Hastings, Elliott, and Corliss. This agreement, based on the use of theoretical Fk(3d,3d) integrals, indicates that the well-known discrepancy between theoretical and experimental values of these integrals arises from the fact that the quantities obtained experimentally are not true Fk(3d,3d) integrals. The crystalline potential due to an array of negative ion charge densities has been employed to discuss these various effects and their meaning with respect to a proper (essentially molecular) treatment.

Original language | English |
---|---|

Pages (from-to) | 1168-1172 |

Number of pages | 5 |

Journal | Physical Review |

Volume | 118 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1960 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*118*(5), 1168-1172. https://doi.org/10.1103/PhysRev.118.1168

**Effect of crystalline fields on charge densities and magnetic form factors.** / Freeman, Arthur J; Watson, R. E.

Research output: Contribution to journal › Article

*Physical Review*, vol. 118, no. 5, pp. 1168-1172. https://doi.org/10.1103/PhysRev.118.1168

}

TY - JOUR

T1 - Effect of crystalline fields on charge densities and magnetic form factors

AU - Freeman, Arthur J

AU - Watson, R. E.

PY - 1960

Y1 - 1960

N2 - The effects of crystalline fields on 3d charge densities and magnetic form factors for transition metal ions are discussed on the basis of recent theoretical investigations augmented by an analysis of optical absorption data. It is shown that the crystalline field has two effects on the free ion 3d wave functions and hence on their form factors as well: (1) a differentiation or "splitting" of the two types of cubic 3d functions by an expansion of the t2g(eg) orbitals and a contraction of the eg(t2g) orbitals resulting in two different radial charge densities, and (2) a net expansion of the charge distribution from the free ion value. The magnetic form factors due to this "splitting" effect when calculated according to the methods of Weiss and Freeman show measurable deviations from the free atom results. A form factor for Mn+2 based on optical absorption data shows a large expansion of the 3d charge density, in agreement with the magnetic form factor measurements of Hastings, Elliott, and Corliss. This agreement, based on the use of theoretical Fk(3d,3d) integrals, indicates that the well-known discrepancy between theoretical and experimental values of these integrals arises from the fact that the quantities obtained experimentally are not true Fk(3d,3d) integrals. The crystalline potential due to an array of negative ion charge densities has been employed to discuss these various effects and their meaning with respect to a proper (essentially molecular) treatment.

AB - The effects of crystalline fields on 3d charge densities and magnetic form factors for transition metal ions are discussed on the basis of recent theoretical investigations augmented by an analysis of optical absorption data. It is shown that the crystalline field has two effects on the free ion 3d wave functions and hence on their form factors as well: (1) a differentiation or "splitting" of the two types of cubic 3d functions by an expansion of the t2g(eg) orbitals and a contraction of the eg(t2g) orbitals resulting in two different radial charge densities, and (2) a net expansion of the charge distribution from the free ion value. The magnetic form factors due to this "splitting" effect when calculated according to the methods of Weiss and Freeman show measurable deviations from the free atom results. A form factor for Mn+2 based on optical absorption data shows a large expansion of the 3d charge density, in agreement with the magnetic form factor measurements of Hastings, Elliott, and Corliss. This agreement, based on the use of theoretical Fk(3d,3d) integrals, indicates that the well-known discrepancy between theoretical and experimental values of these integrals arises from the fact that the quantities obtained experimentally are not true Fk(3d,3d) integrals. The crystalline potential due to an array of negative ion charge densities has been employed to discuss these various effects and their meaning with respect to a proper (essentially molecular) treatment.

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U2 - 10.1103/PhysRev.118.1168

DO - 10.1103/PhysRev.118.1168

M3 - Article

VL - 118

SP - 1168

EP - 1172

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 5

ER -