Isomer shifts calibration

The entity ot is the so-called isomer shift calibration constant, c is the speed of light, Co is the electric constant, and Eq is the nuclear transition energy. (The Coulomb constant k = l/(47rco), which was dropped in (4.1), is re-inserted here.) A comprehensive derivation of this expression is found in [8, 9]. 

The addition of two electrons has increased the 55-occupation considerably. Up = +0-62, so that with rj = 0-98 we have Uy — Uy= +0-41. A limiting value for electron removal is obtained by setting Uy = 0 so 17, = 0-41 and Uy = 0-82, whence hp = 4-76 and h, = 0-50. These figures correspond to a removal of 0-88e per fluorine atom from I. It can be seen that these crudely estimated figures for IF7, IF5, IFe, and IF " are reasonably self-consistent despite the fact that the chemical isomer shift calibration is being extrapolated to large values of hp. A possible structure for IFg" is based on that of IF7 but with a lone-pair of electrons replacing one of the equatorial fluorine atoms. 

The MB spectroscopy is apphcable in investigating the stmctures of metal nitrosyls, as MNO electronic stmcmre is extremely sensitive to its coordination environment. It is particularly effective when the spectroscopic measurements are combined with the results of DFT calculations. The application of the MB parameters in the isomer shift calibration allows one to precisely estimate the Fe and NO spin populations (see, e.g., [121]). Recently DFT has become an increasingly popular tool to calculate structures and Mossbauer properties [118, 138]. MB... 

One calls S the isomer shift. From an electron structure point of view, the parameter of interest is Ap(0) and one combines all other factors into the isomer shift calibration constant a, i.e. 

Relative to the isomer shift of Gd2Cu2Si2 ( + 0.6mm/s versus the EurFd source) or NpCu2Si2 (-h 14.7mm/s versus NpAlj), respectively. The ratio of isomer shift calibration constants is ... 

The charge density at the nucleus is mainly determined by s electrons and only partially by p-elec-trons. The main effect of the p electrons and d electrons and any other electron shells that do not contribute directly to the electron density ip(0) p, is to shield the s electrons. The determination of the scale factor (r -rl) in Equation [9] is called the isomer shift calibration. The interpretation of isomer shifts in Mossbauer spectra involves the correlation of a given A/ (0)=l /(0)l -l /(0)lg value (the electron density difference) with the known electronic structure of the Mossbauer atom or the change of the... 

Fig. 3.4 Calibration spectrum of metallic iron and magnetic hyperfine splitting of the nuclear levels. The values of the hyperfine splitting in a-iron are = 1.677 mm >2 = 6.167mms >3 = 10.657 mm s. The center of the calibration spectrum is defined as velocity zero left). The isomer shift of a specific sample with respect to metallic iron is indicated as 5 (right)...

Interestingly, the correct polarity of the Mossbauer drive can be checked by using the isomer shift of oc-iron with respect to the materials in Table 3.1. After folding of the raw data, the center of the calibration spectrum without further correction must be at —0.12 mm s relative to the Co/Rh source material. 

A calibration of the popular B3LYP and BP86 density functionals for the prediction of Fe isomer shifts from DFT calculations [16], using a large number of complexes with a wide range of iron oxidation states and a span of about 2 mm s for the isomer shifts, yielded a value for the calibration constant a = —0.3666 mm s a.u. (see Chap. 5). Note the negative sign, which indicates that a positive isomer shift of a certain compound relative to a reference material reveals a lower electron density at the nuclei in that compound as compared to nuclei in the reference material. 

For a comparison of experimental Mossbauer isomer shifts, the values have to be referenced to a common standard. According to (4.23), the results of a measurement depend on the type of source material, for example, Co diffused into rhodium, palladium, platinum, or other metals. For Fe Mossbauer spectroscopy, the spectrometer is usually calibrated by using the known absorption spectrum of metallic iron (a-phase). Therefore, Fe isomer shifts are commonly reported relative to the centroid of the magnetically split spectrum of a-iron (Sect. 3.1.3). Conversion factors for sodium nitroprusside dihydrate, Na2[Fe(CN)5N0]-2H20, or sodium ferrocyanide, Na4[Fe(CN)]6, which have also been used as reference materials, are found in Table 3.1. Reference materials for other isotopes are given in Table 1.3 of [18] in Chap. 1. 

If one pursues the calibration approach, one has to stick to a given combination of density functional and basis set, since the calibration will change for each such combination. Calibration curves have been reported for a number of widely used density functionals and basis sets. The results of a relatively comprehensive study are collected in Table 5.4. The standard deviation of the best fits is on the order of 0.08 mm s which appears to be the intrinsic reliability of DFT for predicting Mossbauer isomer shifts. 

Core electrons are highly relativistic and DFT methods may show systematic errors in calculating the charge density at the nucleus because of the inherent approximations. Fortunately, this does not hamper practical calculations of isomer shifts of unknown compounds, because only differences of li//(o)P are involved. In practice, the reliability of the results depends more on the number of compounds used for calibration and how wide the spread of their isomer shift values was. The isomer shift scale for several Mossbauer isotopes has been calibrated by this approach, among which are Au [1], Sn [4], and Fe [5-9]. For details on practical calculation of Mossbauer isomer shifts, see Chap. 5. 

Wdowik, U.D., Ruebenbauer, K. Calibration of the isomer shift for the 77.34 keV transition in 197-Au using the full-potential linearized augmented plane-wave method. J. Chem. Phys. 129 (10), 104504 (2008)... 

Other Iodine Compounds. By studying the isomer shift and the quad-rupole hfs for a series of compounds, Perlow and Perlow (29) have calibrated the isomer shift scale which is independent of Equation 7. The number of p holes, hp, for the compounds of I2, KICI4 H2O, KIC12 H2O, and ICl has been inferred from the measured value of the quadrupole coupling constant, eqQ, and from the symmetry of the iodine lattice site. Since they found that the isomer shifts and hp are linearly related for these compounds, it appears that 5 electrons do not participate directly in the bonding, and the sp hybridization is negligible. Because of this linearity, they have been able to determine dh/dhp, which leads to a calibration of the isomer shift scale. 

This internal pressure effect may actually be quite general in Mbssbauer effect studies of small particles, as discussed by Schroeer et al. for the recoil-free fraction (156) and the isomer shift (157). In addition, Schroeer (152) has summarized a number of origins for Mossbauer parameters being particle size dependent. Thus, from the above discussion, it seems apparent that a priori particle size determination using the recoil-free fraction, quadrupole splitting, or isomer shift is not possible for an arbitrary catalytic system. However, the "experimental calibration of these parameters, which not only facilitates particle size measurement, may also provide valuable information about the chemical state (e.g., electronic, defect, stress) of the small particles. This point will be illustrated later. 

FIGURE 2.1 Energy levels, isomer shift, and quadrupole splitting for 57Fe. The Mossbauer spectrum shown was recorded at T— 4.2 K with a sodium nitroprusside absorber, a diamagnetic (.S 0) compound often used for velocity calibrations. The isomer shift, indicated by the vertical dashed line, has the value 5 — —0.18 mm/s relative to Fe metal. 1 mm/s Doppler shift... 

Figure 1. Isomer shift versus quadrupole splitting data for Fe2+ ions in a variety of coordination environments in silicate and oxide minerals. Calibration of each 295K Mossbauer spectrum from which the parameters are derived is based on reference zero velocity at the midpoint of the a-Fe spectrum. The legend to mineral symbols is contained in Table I.

By combining data for a range of almost completely ionic iodides, it has been possible to calibrate the isomer shift scales in terms of the electron configurations. The closed-shell configuration of the iodide ion is again taken as the reference point, and the following relationships have been derived1,5 ... 

The very low isomer shift of Na2[Fe(CN)5NO] 2H2O, a compound that has been often used as calibration standard, can be understood on the basis of the strong covalent effects present in the Fe-NO bond. The ground state of the iron in the nitropnisside molecules is (Ax, (Axy) The electrons in the orbitals with (d, dj, ) character are delocalized by back donation to the 2p orbitals of the NO ligand. In addition, as in the cyanides shown in Table 2,... 

Figure 20 Calibration of the B3LYP method for the prediction of Fe isomer shifts. The calculated electron density at the iron nucleus is plotted versus the experimentally determined isomer shift for a series of 15 iron-containing compounds. (Reprinted from Neese. 2002, with permission from Elsevier)...

Nieuwpoort, W. C., D. Post, and P. Th. van Duijnen (1978). Calibration constant for Fe Mdssbauer isomer shifts derived from ab initio self-consistent-field calculations on octahedral FeFj, and Fe(CN)s clusters. Phys. Rev. B17, 91-98. 

The potential of the SW approach to systematize inneratomic properties and processes can be easily illustrated by reconsidering chemically induced nuclear lifetime variations which, among others, are of relevance to the calibration problem of Moessbauer isomer shifts. Highly excited atom states carrying single or multiple vacancies in inner shells form another promising subject of SW simulations. In the latter case the results of a DV-Xa study of the K-shell x-ray satellite intensities of metal fluorides can be used for a comparative assessment of both methods. 

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