The isomer shift

Usually we can expect nuclei in the source material to be in a different chemical environment from those in the absorber material. This leads to different transition energies for the two sorts of nuclei. This is because there is an electrostatic interaction between the charge distribution in the nucleus (which has different volumes in the ground and excited states) and the electron density at the nuclear position, which depends on the chemical environment of the nucleus. 

Only s electrons have a finite probability of overlapping with the nuclear density in non-relativistic cases (lighter atoms). This means that the s-electron density is dominant for this interaction, and any variation in it will lead to a shift of the whole spectrum to either lower or higher energies. 

The change in transition energy S, the isomer shift, is given by the equation 

As there is no obvious reference situation apart from an isolated (Sn) atom, a standard has to be defined for the isomer shifts of each Mossbauer nueleus. In the case of tin, SnOa is commonly chosen, and its isomer shift is therefore defined to be zero (but be aware that in old papers other standards might have been used, so it is always necessary to define the standard explicitly in reports). Other Sn(IV) compounds have isomer shifts either side of this standard. For example, the more electronegative substituent fluorine leads to a negative change in S[S(SnF4) = 0.47mm s ], whereas the more electropositive substituent ehlorine leads to a 

It is a bit harder to use Fe isomer shifts to determine the formal oxidation and spin state of iron in its compounds. There are more oxidation states possible, ranging from -II to +VI with aU possible steps between them. 

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The isomer shift, d, arises from the Coulomb interaction between the positively charged nucleus and the negatively charged s-electrons, and is thus a measure for the s-electron density at the nucleus, yielding useful information on the oxidation state of the iron in the absorber. An example of a single line spectrum is fee iron, as in stainless steel or in many alloys with noble metals. 

Most valuable chemical information can be extracted from Mbssbauer parameters such as the isomer shift (5), the quadrupole splitting (AEq), the magnetic splitting (AEm), and the asymmetry parameter (n). 

The spin state of the compounds XFe(R2dtc)2 is 3/2 (64). Mossbauer spectra of ClFe(Et2 tc)2 in solution are almost identical with the spectrum of the six-coordinated Fe(Et2magnetic susceptibility and in the isomer shift and quadrupole splitting parameters suggests a geometrical correspondency in solution, which can be attained by the binding of a solvent molecule to the sixth coordination site of the ClFe(Et2[Pg.98]

In Table 4 typical values are given for the isomer shift (IS) and the quadrupole splitting (QS) of dithiocarbamato complexes with iron in various formal oxidation states. 

The recoil-free fraction depends on the oxidation state, the spin state, and the elastic bonds of the Mossbauer atom. Therefore, a temperature-dependent transition of the valence state, a spin transition, or a phase change of a particular compound or material may be easily detected as a change in the slope, a kink, or a step in the temperature dependence of In f T). However, in fits of experimental Mossbauer intensities, the values of 0 and Meff are often strongly covariant, as one may expect from a comparison of the traces shown in Fig. 2.5b. In this situation, valuable constraints can be obtained from corresponding fits of the temperature dependence of the second-order-Doppler shift of the Mossbauer spectra, which can be described by using a similar approach. The formalism is given in Sect. 4.2.3 on the temperature dependence of the isomer shift. 

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. 

The term causes a uniform shift of the nuclear energy states which, however, is different for the ground and excited state because the nuclear volume and, therefore, also the entity R ) are different for ground and excited states. This gives rise to the isomer shift 6 of the Mbssbauer spectrum. The notation 6E = E is introduced to emphasize the very small change in energy ( 10 eV), which is only a fraction (about 10 ) of the transition energy. The isomer shift will be discussed in detail in Sect. 4.2. 

The isomer shift of a resonance line (or the centroid of a line multiplet) in an experimental Mossbauer spectrum in terms of the Doppler velocity (mm s ) necessary to achieve resonance absorption is given by... 

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. 

Relativistic quantum mechanics yields the same type of expressions for the isomer shift as the classical approach described earlier. Relativistic effects have to be considered for the calculation of the electron density. The corresponding contributions to i/ (0)p may amount to about 30% for iron, but much more for heavier atoms. In Appendix D, a few examples of correction factors for nonrelativistically calculated charge densities are collected. Even the nonrelativistically calculated p(0) values accurately follow the chemical variations and provide a reliable tool for the prediction of Mossbauer properties [16]. 

Fig. 4.2 Temperature dependence of the isomer shift due to the second-order Doppler shift, sod- The curves are calculated for different Mossbauer temperatures 0m by using the Debye model whereby the isomer shift was set to (5 = 0.4 mm s and the effective mass to Meff =100 Da, except for the dashed curve with Meff = 57 Da...

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

The isomer shift is considered the key parameter for the assignment of oxidation states from Mossbauer data. The early studies, following the first observation of an isomer shift for Fe203 [7], revealed a general correlation with the (formal) oxidation state of iron. However, isomer shifts have also been found to depend on the spin state of the Mossbauer atom, the number of ligands, the cr-donor and the... 

A typical example of a correlation diagram for Fe is given in Fig. 4.3. It summarizes the isomer shifts for a great variety of iron complexes with oxidation states (1) to (VI) in the order of the respective high-spin, intermediate-spin, and low-spin configurations. The plot of the corresponding values marked by grey, hatched and open bars demonstrates three major trends ... 

High-spin iron compounds the lower the oxidation state the more positive is the isomer shift. Note that the allocation of high-spin iron(ll) is unique for -values >1 mm s. ... 

Low-spin compounds exhibit lower isomer shifts than high-spin compounds, whereas the isomer shifts of intermediate-spin compounds often resemble those of the corresponding low-spin compounds. 

In addition to the variation in electronic configuration, the geometric details of the coordination sphere and the properties of iron-ligand bonds (different a- or 71-donor strength) also influence the isomer shift as observed for a series of compounds ... 

Similar dependencies and trends are observed for other Mossbauer isotopes, for which more information is found in Chap. 7. It should be pointed out again that the nuclear parameter l RIR is negative for Fe in contrast to many other nuclei. The sign of the isomer shift correlations is inverted for nuclei with A/ // > 0. 

Another example of the correlation between the isomer shift and covalent bonding properties is n-backbonding. The observed isomer shift of ferrous cyanides [Fe(ll)(CN)5X"] " [24] becomes more negative with increasing... 

Backdonation also explains why the isomer shifts of K4[Fe(CN)6] 3H20 and K3[Fe(CN)6] are nearly equal [36] the degree of 7t-backbonding changes upon oxidation or reduction of the metal site and compensates for the change in the number of valence 3d electrons. 

Fig. 4.6 Quadrupole splitting of the excited state of Fe with I = 3/2 and the resulting Mossbauer spectrum. Quadrupole interaction splits the spin quartet into two degenerate sublevels 7, OT/) with energy separation A q = 2 q. The ground state with I = 1/2 remains unsplit. The nuclear states are additionally shifted by electric monopole interaction giving rise to the isomer shift 8...

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

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