Existence of minimum molar volumes (maximum packing densities) in morphotropic series of mixed oxides and fluorides

Abstract

Plots of the cubic root of the formula volume, (V/Z)1/3, vs. cation radius have been built for several morphotropic series of mixed oxides and fluorides. These plots are linear for isostructural compounds but exhibit discontinuities at morphotropic transitions. The classical homology rule ‘larger cation – higher its coordination number (CN) – denser the structure’ is only valid (with few exceptions) for substitutions of relatively small cations. Substitutions of large cations usually lead to opposite volume changes, regardless of increase or decrease in CNs. As a result, the densest structure types often appear with ions of somewhat intermediate size in a series. The discovery of the post-perovskite silicate phase, which greatly influenced mineralogy and geophysics, could be predicted four decades earlier, if proper attention had been paid to the small negative deviation of the layered CaIrO3 from the plot for CaMO3 perovskites. An analysis of the volume relations reveals some errors and leads to several predictions.