Debye peak

The preceding analysis provides a powerful method for determining the diffusivities of species that produce an anelastic relaxation, such as the split-dumbbell interstitial point defects. A torsional pendulum can be used to find the frequency, u>p, corresponding to the Debye peak. The relaxation time is then calculated using the relation r = 1/ojp, and the diffusivity is obtained from the known relationships among the relaxation time, the jump frequency, and the diffusivity. For the split-dumbbell interstitials, the relaxation time is related to the jump frequency by Eq. 8.63, and the expression for the diffusivity (i.e., D = ra2/12), is derived in Exercise 8.6. Therefore, D = a2/18r. This method has been used to determine the diffusivities of a wide variety of interstitial species, particularly at low temperatures, where the jump frequency is low but still measurable through use of a torsion pendulum. A particularly important example is the determination of the diffusivity of C in b.c.c. Fe, which is taken up in Exercise 8.22. 

Solution. Using a torsion pendulum, find the anelastic relaxation time, r, by measuring the frequency of the Debye peak, cup, and applying the relation cupr = 1. Having r, the relationship between r and the C atom jump frequency F is found by using the procedure to find this relationship for the split-dumbbell interstitial point defects in Exercise 8.5. Assume the stress cycle shown in Fig. 8.16 and consider the anelastic relaxation that occurs just after the stress is removed. A C atom in a type 1 site can jump into two possible nearest-neighbor type 2 sites or two possible type 3 sites. Therefore,... 

Figure 11 a illustrates the frequency dependence of e for Eq. (3-6). Note that e is midway between eu and er when co = l/id. The corresponding plots for s" are more complex, because one must assess the relative contributions of a and the dipole loss. The simplest case is for cr = 0 (Fig. lib), where the characteristic dipolar loss peak of amplitude (sr — eu)/2 is observed at frequency co = l/td. For non-zero ct, however, the 1/co dependence of e" greatly distorts the e" curve from the ideal Debye peak. Log-log scales are helpful, as illustrated in Fig. 12. The ct = 0 case is replotted from Fig. lib also plotted are the frequency dependences of e" for CTTd/Eo having various values relative to er — eu. Asct increases, it becomes increasingly difficult to discern the dipole loss peak. Roughly speaking, for CTTd/Eo greater than about three times er, the observed e" is entirely dominated by ct. (Ideally, even when cr dominates the dipolar contribution to e", it should still be possible to observe the dipolar contribution to e however, when o is large, electrode polarization effects tend to dominate the e measurement as well. See Sec. 3.2.1).

Inspection of the reductively methylated, hexylated, and octylated de-cacylenes shows evidence only for the broad Debye peaks no hydrocarbon material in the product gave Bragg peaks (e.g., as found in the initial decacyclene). The reductively methylated decacyclene showed a peak at 5.9 A of full width at half maximum of 3.3°20 on top of a much broader peak. The reductively hexylated material showed peaks at 4.0 A (major) and 5.3 A (minor). 

CONCEPTS More about relaxation process within solids Typical loss peaks are broader and asymmetric in solids, and frequency is often too low compared with Debye peaks. A model using hypotheses based on nearest-neighbor interactions predicts a loss peak with broader width, asymmetric shape, and lower frequency [27]. This behavior is well suited to polymeric, glassy materials and ferroelectrics. Low temperature loss peaks typically observed for polymers need many-body interactions to be obtained. Although current understanding of these processes is not yet sufficient to enable quantitative forecasting the dielectric properties of solids may offer insight into the mechanisms of many-body interactions. 

When the conductivity is of pure electronic origin, M exhibits a Debye peak, typically showing Arrhenius temperature activation [136]. 

Figure 16. Real and imaginary parts of the complex permittivity of fructose at 90 °C. The region where the slope in e (on a logarithmic scale) is close to unity is due to d.c. conductivity, as confirmed by the invariance in e and the Debye peak in Af (the slight asymmetry on the high frequency side is due to the relaxation process that is starting at the edge of the frequency window). At the lowest frequencies, electrode polarization is influencing z lowering the e slope while leaving Af unaffected.

TW-TSDC deconvolutes a global peak of a particular motional process into ensemble of Debye peaks TSPC would be able to measure initial structure of ASD with no need of thermal cleaning Cleaning of thermal history disadvantageous to measure initial structure of sample by TSDC... 

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