Point-Charge Model Developed at HDL

Abstract

In the classical point-charge model, the crystal-field parameters, B_nm, for the crystal-field interaction of the form

$${H_3}=\sum\limits_{nm}{B_{nm}^*\sum\limits_i{{C_{nm}}(i)}}$$

((13.1))

were calculated as

$${B_{nm}}=<{r^n}>{A_{nm}}$$

((13.2))

where the <rⁿ> are the expectation values of rⁿ of the rare-earth ion, and the A_nm are the multipole components of the energy at the site occupied by the rare-earth ion. In the earlier models, the radial integrals used in the evaluation of rⁿ were taken from Hartree-Fock calculations (Freeman and Watson, 1962), and the A_nm were calculated using the point charges at the valence values for the constituent ions. These calculations generally gave the twofold field 10 times too large, the fourfold fields approximately in good agreement, and the sixfold fields 10 times too small.