Electric-Field Gradient Tensor in Ferrous Compounds

Abstract

The electric-field gradient tensor at the iron nucleus in ferrous (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 ( b D,3d & )d e 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 Mossbauer results in FeSiF 6 -6H 2 0 to obtain an estimate of the electric quadrupole moment of Fe 57w (0.29±0.02b), which is in agreement with that from ferric (Fe 3+ ) studies. Finally, estimates also based upon Mossbauer measurements, are made of the d t energy splittings in the ferrous compounds, FeSiF 6 -6H 2 0, FeS0 4 -7H 2 0, FeC 2 04-2H 2 0, Fe(NH 4 S0 4 )2-6H 2 0, FeS0 4 , FeCl 2 -4H 2 0, and FeF 2 . . H. M. Foley, R. M. charge distribution of the aspherical 3d-"valence'' electron belonging to the ferrous ion ( 5 Z),3d 6 ). The subscript "lat" refers to the charge distribution of the neighboring ions in the crystalline lattice. The Sternheimer factors, 7-8 (1 -R) and (I-Y^), are added to correct for the polarization of the ferric-like ( 6 S,3d 5 ) core by the EFG of the valence and lattice charge distributions.The most important contribution to q, in Eq. (3) is # va i, which has an absolute value of 9 (4/7)(lA 3 )3d for the free ion, neglecting the spin-orbit interaction. However, this term, itself, is reduced from the free-ion value by the crystalline field at finite temperatures (Sec. II), the spin-orbit interaction (Sec. Ill), and covalency effects (Sec. V). In addition, the factors, (1 -R), and (1-y^giat (Sec. IV), further reduce the effect of this term. These arguments also hold for the quantity, ??vai<7vai> in Eq. (4), which is present when the valence charge distribution is not symmetric about the z axis. Thus, when all the contributions to the EFG are simultaneously treated, one obtains a significantly larger value for the quadrupole moment, Q, than if one were to use the free-ion approximation (Sec. VI). At the same time it is also possible to make reasonable estimates of the crystal-field splittings in several compounds (Sec. VII) based upon the Mossbauer data of Fig. 1. II. PRIMARY EFFECT OF THE CRYSTALLINE FIELDThe primary effect of the crystalline field is to lift the fivefold spatial degeneracy of the b D state of the freeferrous ion, splitting it into a series of orbital states, Of energies, e n , which may each produce different EFG tensors at the position of the nucleus. (Each of these orbital states will still have fivefold spin degeneracy.) Assuming the thermal transition times between Sternheimer, and D. Tvcko, Phys. Rev. 93, 734 (1954); R. M. Sternheimer and H. M. Foley, ibid. 102, 731 (1956); R. M. Sternheimer, ibid. 84, 244 (1951); 95, 736 (1954); 105, 158 (1957). 8 A.

Crystal-Field Effects on High-Spin Ferrous Ion

“…-Because of covalency effects (see ref. in [6]), the orbital observables will have smaller values than in the free-ion. Using the notations of ref.…”

“…The spin-orbit coupling and temperature effects reduce the calculated E. F. G. [6] (in absolute value). Therefore AE, is the actual maximum value for the quadrupole interaction of intra-atomic origin, and is often used to fit the data instead of Q < r~~ > 3 d .…”

“…The present expressions are useful in most cases, since the surroundings often show only small departures from cubic symmetry. Other expressions for X, may be written ; the advantage of those shown is to give axial symmetry to the non-cubic terms (as was done by Ingalls [6]). The cubic orbital splitting, 10 D,, is then given by :…”

“…When only Mossbauer data are available, additional information is needed and may come from the thermal dependence of the hyperfine interactions [6]. The assumption of a temperature independent crystal field is then required.…”

MAGNETIC ANISOTROPY IN THE Fe-BORACITES

“…' In our calculations which are based on ligand field theory including spin orbit coupling and the molecular field model, the electric polarization was taken into account by introducing permanent electric dipole moments at the ligand sites. We used one general covalency parameter az = 0.7 [12] and assumed the exchange interaction to be isotropic.…”