Incongruent diffusion

A diffusion flow against its conjugate gradient driven by the dissipation of another diffusional process would be called incongruent diffusion. For example, the flow of the tth component across a membrane may be expressed by ... 

As was mentioned in the introduction to this chapter "diffusion-controlled dissolution" may occur because a thin layer either in the liquid film surrounding the mineral or on the surface of the solid phase (that is depleted in certain cations) limits transport as a consequence of this, the dissolution reaction becomes incongruent (i.e., the constituents released are characterized by stoichiometric relations different from those of the mineral. The objective of this section is to illustrate briefly, that even if the dissolution reaction of a mineral is initially incongruent, it is often a surface reaction which will eventually control the overall dissolution rate of this mineral. This has been shown by Chou and Wollast (1984). On the basis of these arguments we may conclude that in natural environments, the steady-state surface-controlled dissolution step is the main process controlling the weathering of most oxides and silicates. 

Fig. 5.16 illustrates the schematic building of a cation depleted layer of thickness y from a hypothetical mineral with constituents A and B (stoichiometry 1 1). Initially incongruent dissolution of AB results in the rapid migration (diffusion) of constituent B from the core of the mineral grain through a layer that is depleted in B (Eq. 5.21)... 

Wallace and Butt (chapter 3) present an extensive review of experimental results in both areas as well as methods for modeling the incongruent vaporization process. Lengauer et al. (chapter 4), present diffusivity data for Group 5 carbides and nitrides and the latest phase diagrams in these systems. 

Incongruent mass transfer in the case of parabolic kinetics based on diffusion control can be readily explained by differences in the diffusion coefficients of chemical species. However, the proposed mechanisms invoked to explain linear kinetics involve the dissolution of the bulk silicate phase, which, over extended periods, should result in the chemical components being transferred to solution from the silicate in their stoichiometric ratios (25). However, many field studies have shown that silicates weather incongruently in nature (27). This is supported by our studies of ground waters associated with vitric rhyolite tuffs. 

There are several other processes that modify the Cl-Br systematics in formation waters. These include the incongruent dissolution of halite, the incongment dissolution of chloride salts other than halite, differential rates of molecular diffusion, and the introduction of bromide from organic compounds (Land and Prezbindowski, 1981). Br/ Cl ratios in excess of those normally associated with subaerial evaporation may result from the incongment dissolution of Na-K-Mg-Cl mineral assemblages during progressive burial (Hanor, 1987 Land et al., 1995). 

Recent studies have shown the formation of altered surface layers thicker than one or two unit cell layers on feldspar surfaces, in apparent support of the leached layer theory. Thick (> 100 nm), silica-rich surface layers were detected by XPS on feldspar samples weathered in solutions having pH < 3 (Casey et at, 1988b) or >9 (Heilman et al., 1990). At these extreme pH values, the rate of release of Al and charge-balancing cations to solution is much faster than the rate of hydrolysis of silica. Under these conditions, oversaturation with respect to amorphous silica could occur, and a highly hydrated, residual leached or precipitated layer of silica could form. However, this layer is probably too porous and discontinuous to be a diffusion-limiting mechanism, but would still account for incongruence under these conditions (Hellmann et al., 1990). Whether the altered layer formed by a leached layer process or by simple precipitation from oversaturated solutions was not determined. 

The electrolyte flux is naturally affected by osmosis. Namely, a strong positive osmosis carries the electrolyte from the dilute solution to the concentrated one, which is incongruous salt flux. Conversely, electrolyte diffusion is retarded when the mobility of the co-ion is faster (negative osmosis). The flux of the solvent provides the energy required to transfer the electrolyte against its chemical potential gradient. 

Dissolution rate constants for major elements are summarized as a function of temperature in Fig. 2. Apparent activation energies have the same relationship as dissolution rate. Alkali metal and alkali earth metal ion have -20 to 40 kJ/mol apparent activation energy, due to a diffusion effect from the mineral surface. The existing reaction condition does not correspond to the critical reaction rate, but this condition is more applicable for natural water-rock interactions, because the nature of incongruent dissolution on the mineral surface controls fluid chemistry and metastable reaction processes. 

Figure 10.15 shows a model of thermally induced phase transformation in a spherical HAp powder particle, considering a paraboUc temperature gradient according to Fourier s law. During the short residence time of the particle in the plasma jet, the innermost core wiU remain at a temperature well below 1550°C owing to the low thermal diffusivity, showing HAp and OAp as stable phases (see Steps 1 and 2 in Scheme 10.1). The second shell has been heated to a temperature above the incongruent melting point of hydroxyapatite (1570 °C), and consists of...

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