Debye diagram relaxation

Fig. 14. Cole-Cole diagrams illustrating dipole relaxation behavior. a) Debye single relaxation time model, b) Williams-Watts expression with p = 0.5. c) Cole-Cote expression with...

Within the complex plane, two circles are obtained. The overlapping of these two circles depends on the vicinity of the relaxation time or relaxation frequency of the two polar groups. This assumption could be applied to more than two polar groups. Are there two isolated Debye s relaxations or a distribution of relaxation times for a single relaxation process If the latter, it is better to use the Cole and Cole or Davidson and Cole models. Results from permittivity measurements are often displayed in this type of diagram. The disadvantage of these methods is that the frequency is not explicitly shown. 

Equation (53) describes Debye relaxation. Magnesium and calcium-doped lithium fluorides have a characteristic Debye relaxation diagram from vhich the dopant concentration and the relaxation time can be deduced. Many others crystals containing mobile lattice defects have similar Debye s relaxation processes. Major understanding of the structure of color centers results from dielectric relaxation spectra. Nuclear magnetic resonance, optical and Raman spectroscopy can be used efficiently in conjunction vith dielectric spectroscopy. 

Figure 36. The wideband loss frequency dependence (a) and the far-infrared part of Cole-Cole diagram (b) calculated (solid lines) and measured [51] (dashed lines) for liquid H20 at 22.2°C. The right and left vertical lines refer to the ends of the Debye and of the second-relaxation regions, respectively.

Materials that exhibit a single relaxation time constant can be modeled by the Debye relation which appears as a characteristic response in the permittivity as a function of frequency. The complex permittivity diagram is called Cole-Cole diagram constructed by plotting e" vs. e with frequency as independent parameter. 

FiGtJRE 2-6 Schematic diagram of e and c". (a) Plotted according to the Debye equations, (b) Plotted according to Cole and Cole. Solid lines, a single relaxation time broken lines, distributions of relaxation times. 

When a is dose to unity this again reduces to Debye s model and for a smaller than unity an asymmetric diagram is obtained. The Cole-Cole diagram arise from symmetrical distribution of relaxation times whereas the Cole-Davidson diagram is obtained from a series of relaxation mechanisms of decreasing importance extending to the high-frequency side of the main dispersion. 

Fig. 11. Argand diagram e" vs. e of a 0.48 M NaCI04 solution in propylene carbonate-dimethoxy-ethane (20 weight % of PC) at 25 °C (upper curve with measured points) Data analysis yields three relaxation times and appropriate Debye circles...

Fig. 7.13 The Debye (a) and Cole-Cole (b) diagrams for calculations of characteristic dipole relaxation times...

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