Microhardness anisotropy and the density of atoms in the unit identity volume of crystals

A new criterion of the reticular and polar anisotropy of microhardness is proposed: the density of atoms in the unit identity volume, i.e., the ratio of the number of atoms of one species in the atomic planes (plane) contained within the limits of the unit identity volume to the sum of the areas of these planes (plane) containing atoms of that species. It is shown that these densities of lanthanide, actinide, and boron atoms correlate satisfactorily with the reticular and polar microhardness anisotropy of their tetraborides and hexaborides. This criterion can be used to predict the nature of the variation of the reticular and polar microhardness anisotropy for other classes of compounds as well.