Significance of the Lattice Contribution to Mössbauer Quadrupole Splitting: Re-Evaluation of theFe57mNuclear Quadrupole Moment

We have considered in detail the lattice contribution to the electric-field gradient at the ${\mathrm{Fe}}^{57}$ nucleus in several ferrous compounds. Using x-ray crystallographic data and a high-speed computer, direct lattice-sum calculations have been carried out for FeSi${\mathrm{F}}_6$·6${\mathrm{H}}_2$O, FeS${\mathrm{O}}_4$·7${\mathrm{H}}_2$O, Fe${\mathrm{Cl}}_2$·4${\mathrm{H}}_2$O, and Fe${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, yielding the magnitudes and signs of the lattice effect in these compounds. The results obtained ranged from negligible to substantial levels, in terms of the lattice contribution to the observed Mössbauer quadrupole splitting. Of particular importance is the inconsistency between our results and the analytic treatment given by Ingalls, which would predict a much larger lattice contribution with a sign opposite to that of the local electronic field gradient. On the other hand, we find that one cannot, in general, assume the effect of the lattice to be small, as has frequently been done. Using the computed lattice contribution to the electric-field gradient in FeSi${\mathrm{F}}_6$·6${\mathrm{H}}_2$O, and the experimentally measured low-temperature quadrupole splitting in this crystal, we have re-evaluated the nuclear quadrupole moment of the 14.4-keV state in ${\mathrm{Fe}}^{57}$ to be +0.20 b.