Lorentzian temperature-dependence

Fig. A2.2. Temperature dependences measured for the haliwidths Av n of the IR absorption bands for valence vibrations of OH(D) groups on Si02 surface (filled markers) and recalculated for the halfwidths w of three components of Lorentzian lines (empty markers) for OH (1) and (OD) groups of high concentration (2), and for (OD) groups of low concentration (3).2"2...

Table I lists the comparative parameters for the various indochinite spectra. Two methods were used in preparing these samples. The first two samples listed were prepared by grinding the indochinite specimen and binding the powder with water glass. The other samples were sliced with a diamond saw. The two spectral lines are given with their position, width, height, and area. The quadrupole splitting and isomer shift are listed in the columns labeled QS and IS. (The isomer shift is really a combination of isomer shift and temperature-dependent shift, and the values are relative to iron in palladium.) The raw data points were fitted with a two-peak Lorentzian using an IBM 7094 least-squares fit.

Shibayama et al. conducted a study of the concentration and temperature dependence of SANS functions from NIPA gels which undergo a volume phase transition [80]. They observed a divergence of E, and the scattered intensity of the Lorentzian component at q = 0, IL(0), which is defined by Eq. (4.8)... 

Figure 8. Temperature-dependent Lorentzian lifetime distributions for 10 /xM PRODAN in CF3H.

In several applications the mechanism of spectral HB is not the photochemical decomposition but a transition in the nuclear-spin wave function of the methyl group in the electronically excited state. The corresponding transition in the electronic ground state is very slow. This reaction leads only to a small but well-defined shift of the transition frequency. The photoproduct hence appears as Lorentzian antiholes in the spectrum <92JPC2080>. These can be used to study the temperature dependence of the spin conversion rate <92JCP(96)6335,93JCP(99)l>. 

These equations reduce to the ones derived by van t Hof and Schmidt and also Harris when the scattering amplitudes in the ground and excited states are identical. We further note that in case of negligible exchange (r i2 34 r,2) for both transitions also Lorentzian lineshapes are predicted with widths determined by T,y. The temperature-dependent shift will now be induced by the acoustic phonons of the crystal. 

Fig. 48. Comparison of the temperature dependence of width A (open symbols) and field fluctuation rate v (solid symbols) derived from fits to the Lorentzian Kubo-Toyabe spectra of UN (left) and USb (right). For UN the absolute values, and for USb the reduced values of parameters are plotted. At T -C width and rate for the two compounds are comparable. The lines are guides to the eye. Adapted ftom Mtinch et al. (1993) and...

Fig. 56. Left ZF- and LF-(iSR spectra of polycrystalline DyAg at 18K. The solid lines are fits to a nearly static Lorentzian Kubo-Tc abe fiinction. Right Temperature dependence of distribution width and fluctuation rate of the field at the muon site as obtained from fils to the Lorentzian Kubo-Toyabe patterns seen in ZF data of cr-DyAg up to 51K. From Kalvius et al. (1986, 1990)...

Here i/ (z) = d In T(z) /dz is the digamma function and W is the band width of the Lorentzian conduction electron density of states. Furthermore, T) is the effective temperature-dependent coupling strength of the longitudinal sound waves to quasiparticles. It may be written as... 

The dissipation of the Im[e(w,T)J -curves on the Lorentzians was carried out for the p-type Hgo.3Cdo.2Te sample (see Fig. 6). The parameters of these oscillators are presented in Tables 2 and 3. There are eight well-resolved oscillators for p-type Hgo.3Cdo.2Te at 30 K and eleven for this sample at 300 K, The temperature dependencies of the phonon mode frequencies for p-Hgo.3Cdo.2Te are presented in Fig. 8. We can see a considerably larger number of lines here in comparison with n-type sample but the temperature shift of the phonon mode frequencies is similar. Analogically was fined for what basic cells (tetrahedra) belongs each observed... 

At both wavebands, EPR PAni-TSA demonstrates Lorentzian spectrum with Dyson contribution due to the appearance of skin-layer on its surface (Figure 1.17). The temperature dependences of the linewidth of the vacuum-processed PAni-TSA sample determined at both 3 cm and 2 mm wavebands EPR are also presented in Figure 1.17. 

The quantity is a part of the line width, which is due to the fluctuational mechanism and is designated as T in eq. (168). Its value does not depend on the resonance frequency o>o at parallel orientation at other orientations that dependence has an approximate form Tj =c +c"v. The measurements in TmES at high frequencies (v>20MHz) confirm the expected dependence (fig. 19). At low frequencies the temperature-dependent broadening is small, and the lineshape is strongly deflected from the Lorentzian. 

The width r(T) at low temperatures is of the order of the Kondo temperature, 7. In VF systems this characteristic temperature is rather high (several hundred K), which leads to a weak temperature dependence of r T) in these systems. On the other hand, the temperature region T) for T and an inelastic peak of Im t(co)/co for (Kojima et al. 1984). Earlier calculations of Schlottmann (1982) based on the Mori technique, although not completely reliable, indicate a small maximum in r (T) (as obtained from the slope of Im f(a)) for co->0) in HF systems and a considerably stronger hump in VF systems. Possibly, this is an indication of stronger deviations from the Lorentzian at low temperatures in VF systems compared to HF systems. 

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