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

Abstract

We have considered in detail the lattice contribution to the electric-field gradient at the Fe 57 nucleus in several ferrous compounds. Using x-ray crystallographic data and a high-speed computer, direct latticesum calculations have been carried out for FeSiF 6 '6H 2 0, FeS04«7H 2 0, FeCl 2 »4H 2 0, and FeCl 2 «2H 2 0, 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 Mossbauer 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 FeSiF6«6H 2 0, 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 Fe 57 to be +0.20 b.

High-spin Iron Complexes

“…The quadrupole splitting is large (3'612 mm S-1 at 29 K [32]) because of the lack of appreciable state mixing. Direct lattice-sum calculations give only a very small value for the lattice term contribution to the electric field gradient tensor [30], a result not predicted in earlier work [5]. Direct lattice-sum calculations give only a very small value for the lattice term contribution to the electric field gradient tensor [30], a result not predicted in earlier work [5].…”

“…6.7. Independent data obtained on polycrystalline powders [29] confirm the perpendicular relation and directions of the electric field gradient tensor and H. Direct lattice-sum calculations have been used to estimate the lattice contribution to the electric field gradient [30]. The quadrupole temperature dependence is consistent with an electronic ground state which is predominantly I xy) with an I xz) state at ,....,520 cmt • The combined quadrupole-magnetic interactions show that the spin axis is in the ac plane along the direction of the short Fe-CI bond (x axis), and that the asymmetry parameter ' YJ = 0·2.…”

Mixed Orbital Ground States of Fe2+ in Prussian Blues

“…In case of octahedral high-spin Fe 2+ , the magnetic susceptibility of an ion is contributed by the orbital motion of the t 2g valence electron that is added to the spin S=2 throgh the spin-orbit coupling. The valence contri- bution of the electric field gradient (EFG) is predominant and exceeds the lattice EFG term by an order of magnitude 29,30 . The t 2g group is the source of valence term of EFG that is the main contribution of the observed quadrupole splitting.…”

“…Finally, it is tempting to take into account the temperature-independent lattice term. Most frequently the lattice term is opposite in sign to the valence term and smaller by an order of magnitude 29 . If the lattice term is subtracted from valence term, the overal ∆E Q (T ) slope would decrease, thus producing the underestimate of the crystal-field splitting.…”

Moessbauer spectrometry

“…In addition, peak asymmetry that is produced by mixed quadrupole and magnetic dipole interaction can be due to relaxation effects (68,123,124,177,211,274,344,346,353,361,485). These effects are the result of the interaction of the fluctuating magnetic field produced by atomic electrons with the nuclear Mossbauer levels (59, 350). The field fluctuation rate is controlled by spin-spin and/or spin-lattice interactions, and the peak asymmetry is a function of the relaxation rate.…”