Modeling the lattice parameters of zircon-type MXO₄ (M=divalent, trivalent or tetravalent metal, X=V, P, As, Si) crystals

Abstract The relations between the crystal lattice parameters and the properties of the constituting ions in a group of 109 compounds with the general formula MXO₄ (M stands for a divalent, trivalent or tetravalent metal, and X=V, P, As, Si) having the zircon-type structure are considered in the present paper. It was shown that both a and c lattice parameters are linear functions of the sum of ionic radii and difference of electronegativities of the M ions and oxygen. The mean relative error between the experimental and modeled crystal lattice parameters is only about 0.23%. The linear equations of the model can be readily applied to estimate the lattice parameters of new compounds with the same crystal structure. Several two-dimensional diagrams plotted for certain combinations of the properties of constituting ions and experimental lattice constants suggest criteria of stability for the considered zircon-type structure.