Electric-Field Gradient Tensor in Ferrous Compounds

The electric-field gradient tensor at the iron nucleus in ferrous (${\mathrm{Fe}}^{2+}$) compounds is investigated. One sees that under the combined action of axial and rhombic crystalline fields and the spin-orbit interaction, the ferrous-ion $(^{5}D,3{d}^{6}){d}_{\ensuremath{\epsilon}}$ states produce a large, temperature-dependent, contribution to the electric-field gradient tensor. It is found that this direct contribution is diminished by that from the lattice itself (the second-order axial and rhombic components of the crystalline field), as well as Sternheimer polarization effects and covalency. The results of this investigation are then applied to M\"ossbauer results in FeSi${\mathrm{F}}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O to obtain an estimate of the electric quadrupole moment of ${\mathrm{Fe}}^{57m}(0.29\ifmmode\pm\else\textpm\fi{}0.02\mathrm{b})$, which is in agreement with that from ferric (${\mathrm{Fe}}^{3+}$) studies. Finally, estimates also based upon M\"ossbauer measurements, are made of the ${d}_{\ensuremath{\epsilon}}$ energy splittings in the ferrous compounds, FeSi${\mathrm{F}}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O, FeS${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}7${\mathrm{H}}_{2}$O, Fe${\mathrm{C}}_{2}$${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O, Fe${(\mathrm{N}{\mathrm{H}}_{4}\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O, FeS${\mathrm{O}}_{4}$, Fe${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}4${\mathrm{H}}_{2}$O, and Fe${\mathrm{F}}_{2}$.