Wagner theory

Fej04 . A similar correspondence between theory and practice has been found for growth of Fej04 by the solid state reactions from FeO and Fe, , between 600 and 1 200°C. The growth rate of FeO is within 10% of the theoretical rate expected from Fe lattice diffusion, calculated according to the Wagner theory . 

C. Wagner Theory for the Coarsening of Solid Precipitates Caused hy Ostwald Ripening. Z. Elektrochem. 65, 581 (1961). 

C. Franze H.Gg. Wagner, Theorie der Fiammenausbreitung(Theory of flame propagation), p 562—4... 

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

C. Wagner. Theorie der Alterung von Niederschlagen durch Umlosen (Ostwald-reifung). Z. Elektrochem., 65(7-8) 581-591, 1961. 

A.J. Ardell. Experimental Confirmation of the Lifshitz-Wagner Theory of Particle Coarsening, pages 111-116. Institute of Metals, London, 1969. 

Fig. 10.4. Thickness dependence of the dimensionless oxygen flux j 02 calculated using Eq. (10.18). The quantity / 02 is defined by the ratio of the oxygen flux over the maximum achievable oxygen flux in the surface exchange limited regime. Only if L Lo the oxygen flux becomes proportional to 1/L withy= 1 in agreementwifli tile Wagner theory.For smaller thicknesses, yrangesbetweenl andO...

Finally, attempts are made on a theoretical basis to explain the unusually large dielectric increments and relaxation times of DNA. The discussion is limited to ionic-type polarizations in this report. The available theories, such as the Maxwell-Wagner theory 29) and the surface conductivity treatment, are reviewed and analyzed. These theories do not explain the dielectric relaxation of DNA satisfactorily. Finally, the counter ion polarization theory is described, and it is demonstrated that it explains most reasonably the dielectric relaxation of DNA. 

This is the well known Maxwell-Wagner theory of spherical suspensions (29). According to this theory, the dielectric increment of a spherical suspension is determined solely by the dielectric constant and the conductivities of the particle and the solvent. 

The dielectric constant of the wet resin is according to the Maxwell-Wagner theory ... 

The dielectric constant at 20°C increased from 3.39 to 3.84 due to the 1.7 %wt. moisture (2.0 %v.). The calculated increase of the dielectric constant from 3.39 to 3.60 is only about 50 % of the total effect. The Maxwell-Wagner theory thus seems to describe roughly the frequency/temperature location of the dielectric loss maximum due to absorbed moisture. However, it does not adequately describe the increase of the dielectric constant due to the moisture uptake from the air. A possible reason for this discrepancy might be that one of the assumptions does not hold, viz. that the conductivity of the resin matrix is negligibly small. 

When oxygen-ionic diffusion is purely the limiting step, the one dimensional oxygen permeation flux can be expressed by Eq. 6.1 according to the Wagner theory ... 

C, Wagner, Theorie der alterung von niederschlagen durch umlosen (ostwald-reifimg). 

Fig. 9 Arrhenius-plot of the parabolic rate constant measured for the growth of CoO on Co in air [91] compared with that calculated from Wagners theory and the tracer diffusion coefficient for Co in CoO [89, 90].

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