Electric Field Gradient Calculations in Transition-Metal Sesquioxides

We present computations of the electric field gradient at the cation sites in the Cr, Fe, Ti, and V sesquioxides isomorphous to corundum. We include dipolar as well as monopolar contributions. Except for $\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3$ we find that the dipolar and the monopolar field-gradient contributions are opposite in sign and roughly of the same order of magnitude. In so far as existing data permit, we have used these tabulations to determine the electric nuclear quadrupole moment ($Q$) of the odd isotopes. The $Q$ values found here seem to be somewhat larger than the results of others. In the cases of ${\mathrm{Cr}}^{53}$ and ${\mathrm{V}}^{51}$ existing data are such that only $\mathrm{}\left|Q\right|\mathrm{}$ can be determined. Our calculation for ${\mathrm{Al}}^{27}$ has been given previously. In $\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3$ the dipolar field-gradient term has the same sense as the monopolar, and is comparatively small. We find $Q\left({\mathrm{Fe}}^{57m}\right)$ to be 0.41 b. A recent $\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3$ field-gradient calculation which yielded a $Q\left({\mathrm{Fe}}^{57m}\right)$ value of 0.277 b is believed to be in error.