Comparison of the real structure with the Fedorov installation of zircon crystals

Abstract

The method of calculating network densities, previously used in crystal chemical analysis, gives results that do not coincide with the results for the real structure, due to the fact that we are dealing not with one, but with several parallelepipedal systems of points inserted into each other. This circumstance was already noted by E. S. Fedorov himself in his article “On the question of determining the density of atoms in the faces of crystals.” However, Fedorov’s method for calculating grid densities can be used not only for individual parallelepipedal lattices, but also in the presence of a structure that forms lattices similar to the above-described “pseudo-octahedral” one, to calculate geometric atomic grid densities.