Isomer shift coefficient

With the observed temperature shift data for (dSldT)p and calculated (within the framework of the Debye model) numbers for the temperature shift of SOD and with the known thermal expansion coefficient as well as results from Ta Mossbauer experiments under pressure, the authors [191] were able to evaluate the true temperature dependence of the isomer shift, (dSisIdT) as —33 10 " and —26 10 " mm s degree for Ta and W host metal, respectively. 

The expressions (4.22)-(4.23) found in chap. 4 for the isomer shift 5 in nonrelativ-istic form may be applied to lighter elements up to iron without causing too much of an error. In heavier elements, however, the wave function j/ is subject to considerable modification by relativistic effects, particularly near the nucleus (remember that the spin-orbit coupling coefficient increases with Z ). Therefore, the electron density at the nucleus l /(o)P will be modified as well and the aforementioned equations for the isomer shift require relativistic correction. This has been considered [1] in a somewhat restricted approach by using Dirac wave functions and first-order perturbation theory in this approximation the relativistic correction simply consists of a dimensionless factor S (Z), which is introduced in the above equations for S,... 

High spin Fe2+ has the configuration 3 de (tig eg). Although we could examine the relationship between Rv and dS as for Mn2+, Co2+, and Ni2+, we prefer in this case to look at Ry as a function of the occupation of the combination of 3d and 4s orbital by ligand electrons which is measured by the Mossbauer isomer shift. In general, the coefficient f0, fn, and fs are not known for Fe2+. In addition, possible spin-orbit coupling makes it difficult to determine the spin reduction by magnetic structures. However, the isomer shift allows us to determine approximately the occupancy of the 4 s orbitals and there are many experimental results available. 

Oxidation State Formal Valence EPR g Values (Temperature) Mossbauer Isomer Shift, 8 (mm/s) Cx (nm), (Extinction Coefficient, xl0 3, per Fe)... 

All these conflicts can now be resolved because of what appears to be a deflnitive experiment by Bocquet et al. (4), who directly measured the internal conversion coefficients of the transition from the first nuclear level to the ground state. They directly compared the L, M, N, and O conversion electron intensities in two different states—namely, in stannic oxide and white tin. They found that the 5s electron density is 30% smaller in stannic oxide than in white tin, and since the isomer shift of stannic oxide is negative with respect to white tin, AR is clearly positive. From these data, the Brookhaven group has calculated the value for AR/R for tin-119 as +3.3 X 10". ... 

Mossbauer spectroscopy is the study of recoilless resonant fluorescence " Sn Mossbauer spectroscopy has been found to be a most usefifl method for studying the bonding and stereochemistry of tin compounds in the solid state. The two most important parameters are the isomer shift (5, mm s ) and the quadrupole sphtting (A q, nuns ), although the recoil-free fractions and temperature coefficients can also supply useful structural indications. 

This hydrogen bonding also impacts Mossbauer spectroscopic properties as shown in Table 3. It should be noted that the use of the B3LYP method has enabled accurate predictions of the Mossbauer quadrupole splittings and isomer shifts in a wide variety of iron proteins and model systems covering all iron spin states and coordination states [8-14,23], with a theory-versus-experiment correlation coefficient R2=0.98 over an experimental range of 8.80 mm/s in 47 systems... 

Mossbauer spectroscopy has proved to be of great value in inorganic tin chemistry (Table 6). Particularly useful have been isomer shift (5) and quadrupole splitting (A) data. The recoil-free fraction and its temperature coefficient are other parameters that have found use in structural elucidations variable temperature Mossbauer studies can be used, for example, in gaining information regarding the degree of aggregation in solid tin compounds. 

To evaluate the coefficients it is necessary to know the isomer shift of at least two systems for which the electron configurations are also known, which is a matter of some difficulty (Parish, 1982h). 

High-pressure experiments up to 8.3 GPa at 4.2 K were carried out by Kratzer et al. (1986). The observed rise in Curie temperature dTc/dP = 3.5 0.3 K GPa is well within the range predicted by a calculation using a modified RKKY exchange (Jaakkola and Hanninen 1980). The pressure coefficient of is extremely small dB, [/dP= — 0.4 0.1 TGPa Similarly, the ionic electric field gradient decreases by 5% between ambient pressure and 8.3 GPa. Isomer shifts exhibit the linear pressure dependence expected from a compression of mainly s-like conduction electrons. 

Xmax, nm absorption maxima, (per iron) absroption coefficient, AE, mm/s quadrupole splitting, 5, mm isomer shift, F, nm/s line width, D, cm l zero-field splitting, X rhombic parameter, p qurtic parameter... 

Fig. 3. The isomer shift 6, the area under the Mossbauer spectrum line S, the linewidth T (a), and thermal expansion coefficient a (b,c) vs Te concentration in the Sn-Te system 6 is recalculated relative to the BaH nQs source (Baltrunas et al., 1986). a 1 - 5,2 - S, 3 - T b dynamic regime c 1 - stationary regime 2 - dynamic regime (Nashchekina et al., 2008).

A dramatic change in the UV spectra was observed in going from the cis to the trans series of doubly-bridged ethylenes, and this can most clearly be shown between the pair of (Z) and ( )[8.8] isomers ( )[8.8], A.max 201.5 nm (log e 4.02) ( )[8.8], A.max222.5 nm (log 3.73). This bathochromic shift, as large as 21 nm, accompanied by a marked decrease in the extinction coefficient obviously reflects the unusual nature of double bond in this ( )[8.8] isomer 61c, which is caused by out-of-plane bending and rehybridization of the strained 7t bond 56). 

The pressure dependence of other properties can be used to calculate AV°. Because the volume differences between the spin states are relatively large, pressures of up to only 1000-3000 atm are sufficient to cause a significant shift in the spin equilibrium. Observation of the change in the electronic absorption spectrum, for example, enables calculation of A V°, with the help of certain assumptions and ancillary experiments (19). The extinction coefficients for absorption by the two isomers must be obtained. In the simplest model they are assumed to be independent of pressure. In one approach (19) they were found by examination of the temperature dependence of the electronic absorption spectrum. This required knowledge of the temperature dependence of the spin-equilibrium constant, which was obtained from the temperature dependence of the susceptibility observed in the Evans NMR experiment. Clearly a more direct measurement is preferable. 

The extinction coefficient for the OH adducts of w-bromotoluene (5200 dm mol cm ) is higher than that observed for its rm-isomer (3700 dm mol" cm ). The red shift in ortho- and w to-substituted isomeric OH adducts was attributed to the stabilization of their excited states because the unpaired spin, especially in the OH adducts of isomers, is delocalized on both -Cl and -CHj substituents and they are therefore, relatively more stable than the isomers. ... 

The reactivity of (20) is more typicai of anthraquinones in genera) whiie the formation of Dewar structures (21) and (22) is the first observation of this type of reaction for the anthraquinone system. The authors note that (18) and (19) show large perturbations in their U.V. absorption spectra compared with anthraquinone (20). These perturbations include bathochromic shifts and extinction coefficient enhancements of the longest wavelength, presumably n->7r , bands which may reflect steric interactions between one of the anthraquinone carbonyls and the adjacent ferr-butyl group. Anomalous reactivity has also been found for 9-ferf-butyl-lO-cyanoanthracene (23) which upon irradiation at -20 C gave the dibenzobicyclo(2.2. llheptane (24). This is in constrast to the photochemistry of 9-ferf-butylanthracene (25) which forms the Dewar isomer (26). The latter reaction and its reversal have been examined for their... 

The fluorescence of SAA is roughly a mirror image of the absorption of the cis-qulnold isomer (Table 7). Minor blue shifts have been observed if the hydrocarbon solvent is replaced by an alcoholic solvent, but the evidence is not sufficient to permit postulating an n—it fluorescent state (53). Evidence of the tt-tt character of the emitting state is the high absorption coefficient of the quinoid form of the order of e = 10. Furthermore, fluorescence from n-TT levels of ketonlc compounds is unusual. The fluorescence decay time has been measured to be xp = 20 10 ns... 

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