The Electric Field Gradient and the Quadrupole Interaction

Abstract

The Mössbauer effect has become a popular method in analytical chemistry. In contrast to other techniques such as x-ray spectroscopy, NMR, EPR, and MCD where highly sophisticated evaluation procedures are applied to obtain reliable information on the chemical compound, the Mössbauer effect is generally used on a low level concerning the evaluation of quadrupole split spectra. This procedure on a low level is favored by the structure of the spectra especially the simple doublet of the 3/2 → 1/2 nuclear transitions in paramagnetic and diamagnetic compounds. The separation of the two absorption lines, the quadrupole splitting ΔE _Q and the center of the two lines, the isomer shift, are easily derived from the spectra. To obtain these two parameters, which comprise already a lot of chemical information, there is no need of a complete theory. Further information from the quadrupole split spectra is given by the sign and the asymmetry of the electric field gradient tensor at the nucleus and its orientation with respect to the crystal axes. The evaluation of these parameters from the Mössbauer spectra requires already a relatively complicated theory which is only available in original publications.^1–3 The situation is made even more difficult by the matter of fact that in most cases the tensor components cannot be uniquely measured; rather, only interrelations between them are obtained from the measured quantities of the spectra.⁴ A further complication is introduced by an anisotropic vibrational amplitude of the Mössbauer atom which gives rise to an anisotropic Debye—Waller factor. These points prevented a general application of all possibilities of the Mössbauer effect, although very nice work had been done on sodium nitroprusside⁵ and on the heme group of deoxymyoglobin⁶ and on CO-liganded myoglobin⁷ where the difficulties concerning the preparation of sufficiently large single crystals enriched in ⁵⁷Fe had to be overcome. On the other hand the calculation of the electric field gradient in molecular crystals by molecular orbital (MO) approaches has been improved very much,⁸ so that a comparison with detailed experimental data has become desirable. It seems therefore to be justified to present in detail the mathematical tool for the evaluation of the quadrupole split Mössbauer spectra.