Lorentz Corrections in Rutile

Equations for calculating the Lorentz corrections in cassiterites (space group ${D_{4h}}^{14}$) are derived which take into account the actual crystal structure. The calculation of critical polarizabilities necessary to cause a polarization catastrophe is demonstrated for a few ferroelectric and antiferroelectric polarizations. The Lorentz corrections are evaluated in the case of rutile (Ti${\mathrm{O}}_2$); they are quite different from the normal value $\frac{4\pi }{3}$. The ionic polarizability of titanium in rutile at 300°K is found to be within 5% of the critical value for a ferroelectric transition. The calculated internal fields and polarizabilities in rutile are similar to the results of corresponding calculations for the case of cubic barium titanate.