Arrhenius behavior, effective diffusivity

In Eqn. (5.36),/ varies slowly with (as/RT) and the coordination number, and it is nearly one. es and ew are average values. From Eqns. (5.35) and (5.36), we conclude that, with respect to diffusion, the two kinds of disorder (in S and W) compensate each other. The disorder effects would cancel each other exactly if cts/o v = 1 (Eqn. (5.35)) or os/ow = ]/f (Eqn. (5.36)). Therefore, the normally observed Arrhenius behavior of diffusion coefficients is indeed to be expected unless cts/ctVv>1 or as/aw [Pg.104]

It should be noted that relation (2.51) is valid within the sudden approximation. However, the relaxation of heavy particle impurities typically involves motion that is slow compared with vibrations of the host lattice (i.e., the tunneling takes place in the adiabatic limit). The net effect of the adiabatic approximation is to renormalize the effective moment of inertia of the particle. This approach was used, for example, to describe vacancy diffusion in light metals. The evolution of the rate constant from Arrhenius behavior to the low-temperature plateau was described within the framework of one-dimensional tunneling of a... 

As can be observed in Fig. 8.10, in the case of conventional drying, the dependence of effective diffusivity fitted an Arrhenius-type equation adequately, the activation energy being a characteristic of the product. For ultrasonically assisted dried samples an Arrhenius behavior was observed at low temperatures however, when the temperature reached 70 °C the identified diffusivity was quite similar for both methods of drying, with and without ultrasound application. 

The spin-lattice relaxation time 7] as a function of temperature T in liquid water has been studied by many researchers [387-393], and in all the experiments the dependence T (T) showed a distinct non-Arrhenius character. Other dynamic parameters also have a non-Arrhenius temperature dependence, and such a behavior can be explained by both discrete and continuous models of the water structure [394]. In the framework of these models the dynamics of separate water molecules is described by hopping and drift mechanisms of the molecule movement and by rotations of water molecules [360]. However, the cooperative effects during the self-diffusion and the dynamics of hydrogen bonds formation have not been practically considered. 

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