Debye diagram

FIGURE 2.2. Debye diagram for the 4-methoxy-4 -butylazoxybenzene (nematic phase, 40 °C [4]). Figures denote frequencies in MHz. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The relatively low Lamb-Mossbauer factors encountered in Ni Mdssbauer spectroscopy (a diagram showing the Lamb-Mdssbauer factor as a function of Debye temperature is given in [3]) require the cooling of both source and absorber, preferentially to temperatures S80 K. The cryogenic systems have been described, e.g., in [2, 4]. 

P. Debye, The Influence of Intramolecular Atomic Motion on Electron Diffraction Diagrams, J. Chem. Phys., 9 (1941) 55-60. 

Figure 11. Potential energy diagram for two spherical carbon black particles of radius 0.2 ym with Debye lengths and zeta potentials determined for 0.2% and 0.8% solutions of OLOA-1200 in odorless kerosene.

The same discussion may be extended to the other non-ring diagrams and it can then be shown that the Debye-HMckel theory is exact in the case of high dilution. We shall, however, not prove this result and refer the reader to the above mentioned literature for more details. 

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.

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...

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. 

The deformation of the lattice as a result of the mechanical working is seen from the broadening of the lines in the X-ray diffraction picture, which are narrow under normal circumstances (Debye-Scherrer or powder diagram). 

Figure 35. Kroger-Vink diagram of boundary layers for our model substance MX when 5(v m) > 0. The broken lines refer to the ionic defect concentrations at (two) different distances from the interface. The behavior of the electrons in boundary regions is not shown.The approach to the bulk values (printed boldface) for extreme abscissa values is attributable to the disappearing Debye length. The mirror symmetry on compa-rison of v m with Mi follows from Eq. (6S).94 (Reprinted from J. Maier, Ionic Conduction in Space Charge Regions. Prog. Solid St. Chem. 23, 171-263. Copyright 1995 with permission from Elsevier.)...

The motive diagram for the potential energy of electrons in an ignited mode thermionic converter has a more complicated shape, as shown at the top of Figure 4. The presence of positive ions in the plasma creates a minimum in the electron motive inside the interelectrode gap. There are narrow collisionless sheaths (the order of a Debye length in thickness) at both the emitter and collector edges of the plasma. 

The two following diagrams (figs. I and 2) illustrate typical ways in which may vary as a function of Cg as described by Debye in the Handbuch der Radiologic. I he values of the association for substances with a of... 

---