Tracer self-diffusion

Calculate the correlation factor for tracer self-diffusion by the vacancy mechanism in the two-dimensional close-packed lattice illustrated in Fig. 8.22. The tracer atom at site 7 has just exchanged with the vacancy, which is now at site 6. Following Shewmon [4], let p. be the probability that the tracer will make its next jump to its kth nearest-neighbor (i.e., a 7 — k jump). 6k is the angle between the initial 6 —> 7 jump and the 7 —> k jump. The average of the cosines of the angles between successive tracer jumps is then... 

Suppose that an ionic solid contains charged cation vacancies such as NaCl containing Na+ vacancies. Find a relationship, comparable to Eq. 3.50, between the cation tracer self-diffusion coefficient, Dcatlon, and the electrical conductivity, p, due to voltage-induced motion of the cations. 

Figure 9.11 shows a typical diffusion penetration curve for tracer self-diffusion into a dislocated single crystal from an instantaneous plane source at the surface [17]. In the region near the surface, diffusion through the crystal directly from the surface source is dominant. However, at depths beyond the range at... 

Figure 9.11 Typical penetration curve for tracer self-diffusion from a free surface at...

A model for the tracer self-diffusivity of the interstitials is now developed for a system in which the total concentration of inert interstitials and chemically similar radioactive-tracer interstitials is constant throughout the specimen but there is a gradient in both concentrations. Since the inert and tracer interstitials are randomly intermixed in each local region,... 

In a typical tracer self-diffusion experiment, the tracer concentration probability, p, depends upon position, whereas the total interstitial concentration probability, p, does not. 

For tracer self-diffusion, a similar initial equation for the flux is... 

FIGURE 5.2 Schematic representation of the differences between (a) tracer self-diffusion and (b) selfdiffusion. 

If the tracer is composed of the same species as that of the solid host, then the diffusion coefficient is named the tracer self-diffusion coefficient, where DA is the tracer self-diffusion coefficient. It is necessary to clarify that self-diffusion is a particle transport process that takes place in the absence of a chemical potential gradient [13]. This process is described, as explained later, by following the molecular trajectories of a large number of molecules, and determining their mean square displacement (MSD). 

The difference in the microphysical situations between the tracer self-diffusion coefficient and the self-diffusion coefficient is schematically represented in Figure 5.2 [12],... 

In Figure 5.2a, the tracer self-diffusion process, and in Figure 5.2b, the self-diffusion process, are represented. 

The relationship between the transport diffusivity (D), as measured under non-equilibrium conditions in an uptake experiment and the tracer self diffusivity (Ds), measured under equilibrium conditions in an NMR experiment, has been discussed by Ash and Barrer(30) and Karger(31,32)t who show that... 

Tracer self-diffusion coefficients for sodium ion and cesium ion have been measured for 1200 equivalent weight Nafion membranes 04-7). Results obtained at 25°C are listed in Table I, along with... 

For translational long-range jump diffusion of a lattice gas the stochastic theory (random walk, Markov process and master equation) [30] eventually yields the result that Gg(r,t) can be identified with the solution (for a point-like source) of the macroscopic diffusion equation, which is identical to Pick s second law of diffusion but with the tracer (self diffusion) coefficient D instead of the chemical or Fick s diffusion coefficient. 

Lindman, B., Payal, M.-C., Kamenka, N., Rymden, R., and Stilbs, R, Micelle formation of anionic and cationic surfactants from Fourier transform proton and lithium-7 nuclear magnetic resonance and tracer self-diffusion studies, J. Phys. Chem., 88, 5048, 1984. 

Fig. 83. Arrhenius plot of the oxygen tracer self-diffusion coefficient Z>. Comparison of the data of Conder et al. (1994b) with those of Rothman et al. (1989, 1991). After Conder et al. (1994b).

Hor] Horvath, J., Pfahler, K., Uftert, W., Frank, W., Mehrer, H., Fe Tracer Self-Diffusion in Amor-... 

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