Centre shift

Since its solution is rather complex, let us restrict ourselves to consideration of a collapsed spectrum at T 1, when it is already symmetrical with a centre shifted to frequency coq=0. As we are interested only in its broadening, we may neglect the rotational structure of the Q-branch in Eq. (6.27) assuming... 

Figure 2. Approximate range of room temperature centre shifts (relative to a-Fe) observed for iron compounds. Black bars refer to data compiled from Greenwood and Gibb (1971), Maddock (1985) and Hawthorne (1988). Grey bars represent ranges for high-spin Fe and Fe in minerals reported by Seifert (1990), where additional data from Bums and Solberg (1990) have been added for pentacooidinated Fe. ...

Both the isomer shift, 5q, and the second-order Doppler shift, 6sod, are pressure dependent through the volume dependence of the electronic charge density at the nucleus. The pressure dependence of the centre shift at constant temperature can be approximated by... 

The quadmpole splitting is sensitive to pressure through both the valence and lattice terms as well as the covalency effect, and may increase or decrease with pressure, depending on the relative magnitude of these contributions. Similar to the temperature variation, the pressure variation of the quadmpole splitting is more likely than the centre shift to show either a discontinuity or a change in slope when a phase transformation occurs. 

Mossbauer and Wiedemann 1960) where is the recoil energy (= 3.13425 x 10 J for the 14.4 keV transition of Fe), ke is the Boltzmann constant, and 0m is the characteristic Mossbauer temperature, where m can be determined from temperature dependant measurements of the centre shift as described by Equation (2). The recoil-free fraction of the absorber can also be determined through temperature dependant measurements of the relative area according to Equation (13). In either case, a phase transformation can be recognised as either a discontinuity or a change in slope of the recoil-free fraction plotted as a function of temperature. 

Application of the Debye model The centre shift data collected at room pressure and variable temperature were fit to the Debye model (Eq. 2, this Chapter). The integral can be evaluated using a series approximation, where only a few terms of the series are needed needed to achieve an accuracy that exceeds the experimental one (Heberle 1971). 

The equation describing the variation of centre shift with temperature (Eq. 1, this Chapter) contains two adjustable parameters, m and 5q. Using a non-linear least squares method, the values of these parameters which best fit the data were determined (Table A2). The centre shift data together with the Debye model calculations are plotted in Figure A3. 

Table A2. Best-fit Debye model parameters for Ca2peo osMgo 97Si20y Fe- ermanite derived from Mossbauer centre shift data...

Figure A3. Variation of centre shift with temperature based on spectral fits incorporating two quadrapole doublets. The solid line represents the Debye model fit (Eqns. 1 and 2, this Chapter) to the centre shifts (data taken from McConnell et al. 2000).

More recently, anticooperative effects between the two H-bonds established by H2O molecules have also been displayed (25), by simply showing that an HDO molecule that establishes an H-bond with a pyridine or tetrahydrofuran molecule with its H-atom and none with its D-atom has a I /O-H- ) band centred at 3375cm . When the D-atom also establishes a D-bond with another pyridine molecule, the i, (0-H- ) band centre shifts to 3420cm . This... 

In an attempt to measure the charge distributions in complexes, the group moments of a number of P-Ir-Cl and OC-lr-Cl systems have been obtained. Mdssbauer spectra of 15 iridium(iii) complexes have been reported. Centre shifts are in a... 

Fig. 2.12 Illustration of the division of the two multiplets from spins 1 and 2 into subspectra according to the spin state of spin 3. The transitions associated with spin 3 in the a state (indicated by the full lines on the energy level diagram) give rise to a pair of doublets, but with their centres shifted from the Larmor frequencies by half the coupling to spin 3. The same is true of those transitions associated with spin 3 being in the fS state (dashed lines), except that the shift is in the opposite direction.

The Eo Coulombic interaction alters the energy separation between the ground state and the excited state of the nucleus, thereby causing a slight shift in the position of the observed resonance line. The shift will be different in various chemical compounds, and for this reason is generally known as the chemical isomer shift. It is also frequently referred to as the isomer shift or chemical shift, but in view of the earlier use of these terms in optical spectroscopy and nuclear magnetic resonance spectroscopy respectively, the longer expression is preferred. A less frequently used synonym is centre shift. 

The isomer shift of the absorption lines in the Mossbauer spectrum, also sometimes known as the chemical shift, the chemical isomer shift or the centre shift, is a result of the electric monopole (Coulomb) interaction between the nuclear charge distribution over the finite nuclear volume and the electronic charge density over this volume. This shift arises because of the difference in the nuclear volume of the ground and excited states, and the difference between the electron densities at the Mossbauer nuclei in different materials. In a system where this electric monopole interaction is the only hyperfine interaction affecting the nuclear energy levels, the nuclear ground and excited states are unsplit, but their separation is different in the source and absorber by an amount given by the isomer shift <5. 

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