Diffusion classical aging effects

V. Aging Effects in Classical or Quantal Anomalous Diffusion... 

V. AGING EFFECTS IN CLASSICAL OR QUANTAL ANOMALOUS DIFFUSION... 

Information relating to the diffusion of metal-bearing compounds in catalytic materials at reaction conditions has been obtained indirectly through classic diffusion and reaction theory. Shah and Paraskos (1975) calculated effective diffusitivities of 7 x 10-8 and 3 x 10-8 cm2/sec for V and Ni compounds in reduced Kuwait crude at 760°F. These low values may be indicative of a small-pore HDS catalyst. In contrast, Sato et al. (1971) report that the effective diffusivity of vanadium compounds was one-tenth that of the nickel compounds on the basis of metal deposition profiles in aged catalysts. This large difference may be influenced by relative adsorption strengths not explicitly considered in their analysis. 

In Section VI, we consider a classical particle diffusing in an out-of-equilibrium environment. In this case, all the dynamical variables attached to the particle, even its velocity, are aging variables. We analyze how the drift and diffusion properties of the particle can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility of a particle immersed in an aging medium such as a colloidal glass give access to an out-of-equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced. 

The determination of the effective surface age is the key for comparison of results obtained by different experimental techniques. If for example the drop volume technique is used in its "classical" version, which is based on continuously growing drops, dynamic surface tensions are obtained as a function of drop formation time. It was shown in the previous chapter, that the process of adsorption at the surface of a growing drop is overlapped by a radial flow inside the drop, which changes the diffusion profile. In addition, the drop area increases and... 

Equation (6.29) illuminates the effects of viscoelastic retardation and aging, as well as stress, on the diffusion process. In the absence of those effects, the boundary condition, which reads i9Ao/i9ot = translates into the familiar statement m x,t) = mo t), X on boundary and mo prescribed. Therefore, the term corresponds to a classical process of diffusion through a mechanically inert solid. On the other hand, (6.29) states that when the equilibrium boundary value is approached gradually with time (even for exposure to constant ambient vapor pressure), it is affected by age and depends quadratically on the applied stress. 

IMC that formed at the interface of a solder ball and Ni/Au overplated Cu terminal pad with reflow time is given in Fig. 19. The effect of aging temperature and time on IMC growth (thickness) for the three solder systems is illustrated in Fig. 20. The Pb-Sn-Ag system was included as a benchmark. The growth rates of the various IMCs formed with the standard Pb-Sn-Ag EGA solder, and also the Pb-free alloys all followed the classical diffusion controlled relationship, as noted in Section 2.9. 

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