Electrostatic crystal-field contributions in rare-earth compounds with consistent multipolar effects. I. Contribution tok-even parameters

Abstract

Electrostatic crystal-field parameters (CFP: $B_q^k$) including the contributions of point charges, consistent dipoles, and quadrupoles induced in a crystalline lattice, are calculated for 15 rare-earth or rare-earth-doped compounds and one actinide compound, i.e., for LiY${\mathrm{F}}_4$: ${\mathrm{Nd}}^{3+}$, YOBr and YOCl: ${\mathrm{Eu}}^{3+}$, BaFCl and SrFCl: ${\mathrm{Sm}}^{2+}$, BaTi${\mathrm{O}}_3$: ${\mathrm{Eu}}^{3+}$, NdAl${\mathrm{O}}_3$, LaAl${\mathrm{O}}_3$: ${\mathrm{Eu}}^{3+}$, U${\mathrm{F}}_6$Cs, ${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$, ${\mathrm{Nd}}_2$ ${\mathrm{O}}_2$S, La${\mathrm{F}}_3$ and La${\mathrm{Cl}}_3$: ${\mathrm{Nd}}^{3+}$, ${\mathrm{Y}}_2$ ${\mathrm{O}}_3$ and K${\mathrm{Y}}_3$ ${\mathrm{F}}_{10}$: ${\mathrm{Eu}}^{3+}$, and ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$: ${\mathrm{Nd}}^{3+}$. The method for solving the unknown moments is described and the correction formulas to the $B_q^k$ are given. The necessary input data are the crystallographic structure, point charges (valence values), the dipolar and quadrupolar polarizabilities (recently computed ab initio values), and the $4f$ (or $5f$) radial integrals $〈r^k〉$. The model disregards overlap and covalency, which are likely to provide important contributions via the

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