Bond Valence Analysis of Tetragonal Zirconias

Abstract

In tetragonal zirconia, the cation is coordinated by two interpenetrating tetrahedra of oxygen ions, implying two different cation–oxygen bond lengths. On substituting the different tetravalent ions Ge, Ti, Sn, and Ce into tetragonal ZrO2–2 mol% Y2O3, the mean value of the shorter cation–anion bond length varies linearly with the concentration of the substituent ion where the bond length increases or decreases depending on whether the substituted ion is larger or smaller than the zirconium ion it replaces. It is argued in this paper that the length of the longer bond is determined by the requirement that the bond valence sum remains constant. In each case the length of the longer bond calculated on this basis is in good agreement with the measured bond length (from neutron diffraction), and following small adjustments of the bond valence constants, excellent agreement is obtained. The requirement for the bond valence sum evidently accounts for the physics of the situation, and at the same time the available bond length data allow very precise determination of the bond valence constants of the different ions in the tetragonal zirconia environment. It is shown how these bond length considerations provide an explanation for the variation with composition of oxygen position and lattice parameters in all of the materials considered. Among the interesting features accounted for by this analysis are the increase in cell volume occurring when Zr is replaced by the smaller Sn ion, and slight departures from Vegard's law observed in the substitution of Zr by Ti.