Thermal shift

The thermal shift of Mossbauer lines arises from the second-order Doppler effect (Pound Rebka, 1959). If i is the mean-square velocity of the Mossbauer nucleus in the crystal, then the relative shift in energy of the Mossbauer line will be given by AE/Eq= — i /2c. In the Debye model approximation this leads to AE 

In the more general case r can be expressed in terms of the phonon frequency distribution function G(Q) which can be measured experimentally 

In the case of a Mossbauer impurity in a host crystal, G( l) of the host should be replaced by Gimp( i) of the impurity which is related to G(Q) by the ratio of masses of the host and impurity atoms, and the ratio of impurity-host to host-host interaction parameters (Mannheim Simopoulos, 1968). This is the same procedure as outlined for the calculation of the mean-square displacement x in Section 2.2. 

The thermal shift may be obscured by additional shifts associated with the isomer shift. The sensitivity of the thermal shift to the particular lattice dynamics parameters of the crystal is much less than that of the recoil-free fraction. In particular, at high temperatures the thermal shift AE T)/Eq is model independent and linear with temperature, and is given by — ik T/ 2Mc. Nevertheless many experimental studies have been reported from which the various lattice dynamics parameters can be determined and compared with those obtained from the recoil-free fraction. A combined measurement of AE(T)/E and f T) can also yield the zero point mean-square velocity, which is of significance to studies of superconductivity (Kitchens, Craig Taylor, 1970 Kimball, Taneja, Weber Fradin, 1974). 

The information obtained from Mossbauer spectroscopic studies of the temperature dependence of the recoil-free fraction is quite similar to that obtained by bulk measurements of the heat capacity. In the case of monatomic crystals, if G(Q) is the normalised phonon spectrum, then the heat capacity at constant volume C is given by 

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The terminal lobes of the HOMO will be of the same phase in a nonatetraenyl radical also, i.e. for (36, x = 3), and 1,9-shifts (in a lOe system overall) should thus be allowed, and suprafacial. Formation of the required 10-membered T.S. could present some geometrical difficulty, however, and it is somewhat doubtful whether any such concerted 1,9-shifts have actually been observed. Suprafacial thermal shifts have not been observed in other allowed , i.e. (4n + 2)e overall —(36, x = 3,5. ..), systems either. 

Fluorescence and fluorescence-based thermal shift assay 359... 

Heberle J (1971) The Debye integrals, the thermal shift and the Mossbauer fraction. In Mossbauer Effect Methodology Vol 7. Gruverman IJ (ed), Plenum, p 299-308 Herzberg G (1945) Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules. Von Nostrand Reinhold, New York Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136 B864-871... 

Housley RM, Hess F (1966) Analysis of Debye-Waller-factor and Mossbauer-thermal-shift measurements. 1. General theory. Phys Rev 146 517-526... 

The main unit is the catalytic primaiy process reactor for gross production, based on the ATR of biodiesel. After the primary step, secondary units for both the CO clean-up process and the simultaneous increase of the concentration are employed the content from the reformated gas can be increased through the water-gas shift (WGS) reaction by converting the CO with steam to CO and H. The high thermal shift (HTS) reactor is operating at 575-625 K followed by a low thermal shift (LTS) reactor operating at 475-535 K (Ruettinger et al., 2003). A preferential oxidation (PROX) step is required to completely remove the CO by oxidation to COj on a noble metal catalyst. The PROX reaction is assumed to take place in an isothermal bed reactor at 425 K after the last shift step (Rosso et al., 2004). 

Pantoliano MW, Petrella EC, Kwasnoski JD, Lobanov VS, Myslik J, GrafE, Carver T, Asel E, Springer BA, Lane P, Salemme FR High-Density miniaturized thermal shift assays as a general strategy for drug discovery. / Biomol Screen 2001, 6, 429-440. 

MW Pantoliano, AW Rhind, FR Salemme. Microplate thermal shift assay for ligand development and multivariable protein chemistry optimization. U.S. Patent 6,020,141, 3-Dimensional Pharmaceuticals, 2000. 

In orthopyroxenes, the very intense Fe2+/M2 site bands near 11,000 cm-1 and 5,000 cm-1 in spectra measured at atmospheric pressure (cf. fig. 5.15), as well as the Fe2+/Ml site band located at 8,333 cm-1, show pressure-induced blue-shifts (Shankland et al., 1974 Mao and Bell, 1971). At elevated temperatures, the Fe2+/M2 site 1 micron (11,000 cm-1) band shows negligible thermal shifts (Sung et al., 1977 Singer and Roush, 1985). However, the 2 micron (5,000 cm-1) band shows a significant red-shift in orthopyroxenes and a blue-shift in clinopyroxenes (Singer and Roush, 1985). These effects, which have important applications in remote-sensed spectral measurements of hot planetary surfaces, are described in chapter 10 ( 10.7). 

For these first experiments, a temperature relatively close to Tg, T=123°C, was chosen with the intention of minimizing the relaxation of stress and chain orientation during the quenching the weight-average relaxation time of sample SI at 123°C is calculated from that at 140°C and the thermal shift factor between 123°C and 140°C Xw(123°C) 380s. On the other hand the cooling time of the stretched specimens can be estimated to a few seconds [19], which is very small compared to the polymer relaxation time at the temperature of the experiments. 

A concerted [1,3] thermal shift of hydrogen to convert 7-31 to 7-32 is not a reasonable mechanism because such shifts are ruled out by the selection rules for pericyclic reactions (see Chapter 6). 

Heberle J (1971) The Debye integrals, the thermal shift and the Mossbauer fraction. In IJ Gruverman (ed) Mossbauer Effect Methodology, Vol 7. Plenum Press, New York, p 299-308... 

Stabilization of the protein target by buffer additives or complex formation is a powerful way to enhance crystal-lizabihty. Biophysical techniques such as thermal-shift assays and NMR can be used for the identification of suitable hgands or additives. 

The thermal shift 6j of the Mdssbauer spectrum is the sum of a contribution due to the second-order Doppler effect (6sod) and a possible contribution due to an intrinsic dependence of the isomer shift (8j) on temperature. The second-order Doppler shift is proportional to the mean square velocity of the Mdssbauer nucleus. For the purpose of a comparison with thermodynamic data, the SOD shift may be described in terms of the Debye approximation,6... 

The inadequacy of the Debye approximation in describing the details of the frequency distribution function in a real solid is well known. This results in noticeable disparities between Debye temperatures derived from the results of different experimental techniques used to elucidate this parameter on the same solid, or over different temperature ranges. Substantial discrepancies may be expected in solids containing two (or more) different atoms in the unit cell. This has been demonstrated by the Debye-Waller factors recorded for the two different Mdssbauer nuclei in the case of Snl4,7 or when the Debye-Waller factor has been compared with the thermal shift results for the same Mdssbauer nucleus in the iron cyanides.8 The possible contribution due to an intrinsic thermal change of the isomer shift may be obscured by an improper assignment of an effective Debye temperature. 

Extensive data of this type are necessary in order to verify the stability of a spectrometer and identify the potential sources of drift. The stability displayed in the figure is not sufficient for the thermal studies described above because the assignment of the isomer shift depends on the determination of the Debye temperature from the small changes in the slope of the thermal shift curve. The data presented in Figures 3,4, and 5 have been monitored with a constant velocity spectrometer with a verified long-term stability of 0.001 mm/s, which was integrated into a fully automated data-acquisition system. 

Lo M-C, Aulabaugh A, Jin G, Cowling R, Bard J, Malamas M, Ellestad G (2004) Evaluation of fluorescence-based thermal shift assays for hit identification in drug discovery. Anal Biochem 332 153-159... 

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