Effective ionic charge and bulk modulus scaling in rocksalt-structured rare-earth compounds

The bulk moduli of rocksalt-type divalent and trivalent rare-earth ($R$) monochalcogenides exhibit a linear relationship when plotted on a log-log scale against the unit-cell volume, but fall on two distinct straight lines according to the effective valence product of the compound. By comparing the bulk modulus ratio of the $R$ monochalcogenide to the alkali halide at the same volume, we have estimated the effective ionic charges. These charges are found to be 1.7\ifmmode\pm\else\textpm\fi{}0.03 and 1.85\ifmmode\pm\else\textpm\fi{}0.05 for the ${R}^{2+}$ and ${R}^{3+}$ compounds, respectively, as against 2 and 2.45 expected from their valence products. The behavior of NaCl-type Ce monopnictides is somewhat anomalous.