THEORY OF THE ELECTRONIC SUSCEPTIBILITIES OF STOICHIOMETRIC RUTILE (TiO$sub 2$)

A theoretical analysis of the symmetry properties of crystalline rutile is made, leading to the conclusion that the isotropic solution of the local field equations for this material is correct. It is shown that this conclusion is supported by the experimentally determined isotropic nature of the magnetic susceptibility of rutile. The isotropic solution of the local field equations yields a value for the electronic polarizability of the titanium ion in rutile of ${\ensuremath{\alpha}}_{T}=2.2$ ${\mathrm{\AA{}}}^{3}$, an order of magnitude greater than the free-ion values usually assigned to the ${\mathrm{Ti}}^{4+}$ ion. This result is supported by a correlation of the ionic sizes as obtained from an electron-density map of rutile determined by x-ray analysis with the polarizabilities in a manner described previously. In addition, this conclusion is in reasonably good quantitative agreement with a theoretical prediction made previously of the effect of the crystalline potential on the cation polarizability. The results of this study give a specific example of a conclusion arrived at in an earlier work to the effect that a cation polarizability in a crystal may be many times its free-ion value. Moreover, it demonstrates the unreliability of the usually accepted additivity rule for the ionic radii.