Isomer shift conversion

Isomer Shifts. Conversion of the data of Table 2 to Ans for Sn and Anc for Au must be considered individually for the two atoms because their valence structures differ. Sn is polyvalent but Au is a one-electron metal with filled d bands not far below ey. 

Fe isomer shift conversion for some frequently used standard matrices. To obtain isomer shift values relative to a-Fe, one has to add the corresponding value in column 2 to the isomer shift measured relative to the standard material In column 1... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

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. 

Van der Woude and Miedema [335] have proposed a model for the interpretation of the isomer shift of Ru, lr, Pt, and Au in transition metal alloys. The proposed isomer shift is that derived from a change in boundary conditions for the atomic (Wigner-Seitz) cell and is correlated with the cell boundary electron density and with the electronegativity of the alloying partner element. It was also suggested that the electron density mismatch at the cell boundaries shared by dissimilar atoms is primarily compensated by s —> electron conversion, in agreement with results of self-consistent band structure calculations. 

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". ... 

The conjugation process 1,4-diene — 1,3-diene goes by interconversion of 7r-Pd complexes I and III via the intermediate 7r-allyl-Pd hydride complex II and involves 1,3-hydrogen shifts. Conversion of cis,trans to the thermodynamically favored trans,trans-conjugated dienes occurs, but both of these isomers would be carboxylated the same way. CO insertion via a Pd carbonyl hydride (allyl or olefin) intermediate gives unsatu-... 

Results of the analysis made by Van der Kraan and Buschow are shown in fig. 92, where the experimental results are seen to behave as expected on the basis of eq. (85). The values of P and Q derived from this plot are equal to —0.75 and -t-F.65, respectively. This means that for a variety of different amorphous alloys one can describe the isomer shift satisfactorily in terms of two contributions —0.75 A4> -I-1.65 4 5/ , associated with charge transfer and intra-atomic s - d electron conversion, respectively. According to the analysis, in the metal-metal alloys the... 

For some time even the sign of SR/R was in doubt (79). However, measurements of the internal conversion of electrons in stannic oxide and 6-tin clearly showed that the 5s-electron density near the nucleus was less for the oxide than for the metal (14). Since the isomer shift of the oxide is also less than that of the metal, SR/R must be positive. A value of 3.3 X 10 was calculated and was thought reliable to about 30%. This is the highest value yet reported—... 

The isomer shifts are usually given relative to a-Fe. If the isomer shift is given relative to a particular source matrix, conversion is possible with the help of Table 25.3. 

Figure 9.12 shows the crystal structure of [Fe(pyrazine) Pt(CN)4 ] [13]. This complex shows a thermally induced spin-crossover transition (Tct = 284 K, T l = 308 K) with a thermal hysteresis of 24 K, which was observed by means of magnetic susceptibility measurement and Raman spectroscopy. The spin-crossover transition has been confirmed by Fe Mossbauer spectroscopy [13]. The Mossbauer spectrum at 300 K in the cooling mode consists of a single doublet with quadrupole splitting (QS) of 1. 159(5) mm s and isomer shift (IS) of 1.047(3) mm s whose values are typical of the HS state ( T2g, S = 2) of Fe(ll). At 80 K, a new doublet with quadrupole splitting of 0.306(4) mm s and isomer shift of 0.439(2) mm s whose values are typical of the LS state ( A g, 5 = 0) of Fe(ll). The photoinduced spin conversion between the LS and HS states around room temperature has been confirmed by means of Raman spectroscopy within the thermal hysteresis loop of spin-crossover transition, which is shown in Fig. 9.13 [13]. In this complex, the frequency of...

One can see that the isomer shifts of species B and C get closer to each other as the Pr content increases. Even the quadrupole splitting of B increases, although it does not reach that of C. Thus, the decreasing thermodynamical parameters of the conversion are consistent with the presumably changing spatial and electronic structure of the relevant species. 

Equation (24.1) was used to estimate isomer shifts of ferrate(VII) and ferrate(VIII) as — 1. 18 and — 1.40 mm s , relative to a-Fe, respectively [102]. More recently, density function theory calculations were performed on ferrates ranging from +4 to +8 oxidation states of iron [102]. Figure 24.9 depicts relationship of isomer shift with Fe O bond length and electron density on the iron nucleus An increase in Fe—O bond distance with decrease in oxidation states of iron from ferrate(VIII) to ferrate(IV) was determined. A positive linearity between isomer shift and bond distance of ferrate was found (Fig. 24.9). Conversely, values of isomer shifts showed a negative relationship with po (Fig- 24.9). An increase in the Po with increase of the oxidation state of iron was expected. The relationship of Eq. (24.1) was used to understand the mechanism of decomposition and formation reactions of solid ferrates under different conditions, which are described below. 

A number of examples will be provided in this section of the use of in situ Mossbauer spectroscopy as applied to the study of electrochemical phenomena, involving transmission, emission, and quasi in situ conversion electron modes. It is expected that these examples may serve as a guide for the design of experiments involving a much wider variety of interfacial systems. Except where otherwise indicated, the isomer shifts, 5, are referred to the a-Fe standard, and 5, the quadrupole splittings A, and widths F are given in mm s ... 

---