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 $4f$ (or $5f$) electron interaction with the ligands. Yet, so as to estimate quantitatively the agreement between experimental and calculated values, two performance indexes are utilized: a scale factor $S_k\left(\frac{B_{\mathrm{expt}}^k}{B_{\mathrm{calc}}^k}\right)$ and a reliability factor measuring the angle between $B_{\mathrm{expt}}^k$ and $B_{\mathrm{calc}}^k$. The dipolar and quadrupolar contributions do not significantly change the scale factor which is about a factor of 2 too large when screening is taken into account. The reliability factor is rather worsened by the quadrupolar contribution which is higher than the dipolar. An estimation of the octupolar correction confirms the divergence of the multipolar series which might be ascribed to overestimated high-order polarizabilities.

• Received 22 April 1982

DOI:https://doi.org/10.1103/PhysRevB.26.5451