Binary silicate melts

added react almost entirely so that activity, aj o remains at a low level. However as the orthosilicate composition is approached the possibilities for the oxide to react with the melt by depolymerization virtually disappear, and further additions of basic oxide cause a sharp rise in oxide activity. 

The thermodynamic activity of the oxide component may be determined for each composition by a n-umber of methods. For example, the melts may be equilibrated with a pure metal so as to allow the volatile oxide component to be absorbed by the molten metal until equilibrium is achieved (Richardson and Webb, 1956). Alternatively, activities may be extracted from phase diagrams, or measured directly by making e.m.f. measurements using Ca0/Zr02 solid electrolytes (e.g. Sato Ulmer, 1971)- 

The activity-composition curves shown in Fig. 7 may be interpreted if a suitable reaction model involving the basic oxide is available. Since silicate melts appear to contain large numbers of different molecular species, reaction models have been developed which are based on the concepts of organic polymer theory. Two such models will be described below  

Masson (1965) has considered the building up of polymeric silicate species in melts by a series of condensation reactions opposite to the process described above as titration, and in which ion is produced at each step. 

These polymerization reactions can be described by equilibria of the form  

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However, the validity of the polymer theory was extended to include cyclic and spherical particles, i.e also for more polymerized silicate melts, by Pretnar (1968), Baes (1970), and Esin (1973, 1974). Pretnar assumed that in binary silicate melts, short chains n < 5)... 

Table 32 1. Equilibrium Constants K and Number Average Degrees of Polymerization (X)nfor Binary Silicate Melts (After Data by C.R. Masson.)...

Similar calculations of size distribution of ions in silicate melts were made by Hess (213). Structural models of binary silicate melts have also been proposed by Gaskell (214), who discussed experimental evidence for and against the validity of the models. 

Titration curves for a number of binary silicate melts are shown in Fig. These were obtained by adding successive amounts of each basic oxide to Si02. Th first amounts of basic oxide,... 

Fig. 7. Oxide activities in binary silicate melts compared with theoretical curves calculated using equation (lo) after Masson, (1968).

The Temkin model holds in binary silicate melts, M0-Si02. 

Fig. 8. Integral free energies of mixing in binary silicate melts. Data for systems Pb0-Si02 and CaO-SiOo compared with curves calculated from equations ik) and (l5 using different values of K (after Toop and Samis, I962).

Polymer models of the type described above have been used with considerable success to interpret the mixing properties of certain binary silicate melts. Althoiagh the polymerization constants for melts of geological complexity are as yet unknown and the... 

Figure 7J Gibbs free energy curves and T-X phase stability relations between a phase with complete miscibility of components (silicate melt L) and a binary solid mixture with partial miscibility of components (crystals ]8). 

Uphill diffusion of some components is reported in silicate melts (e.g., Sato, 1975 Watson, 1982a Zhang et al., 1989 Lesher, 1994 Van Der Laan et al., 1994). Recall that uphill diffusion in binary systems is rare and occurs only when the two-component phase undergoes spinodal decomposition. In multicomponent systems, uphiU diffusion often occurs even when the phase is stable, and may be explained by cross-effects of diffusion by other components. 

With each level of increased sophistication, the complexity of treating a diffusion problem increases tremendously, especially for natural silicate melts that have a large number of components. The simplest method (effective binary approach) is the most often used, but it cannot treat the diffusion of many components (such as those that show uphill diffusion). All the other methods have not been applied much to natural silicate melts. 

Despite the various drawbacks, the effective binary approach is still widely used and will be widely applied to natural systems in the near future because of the difficulties of better approaches. For major components in a silicate melt, it is possible that multicomponent diffusivity matrices will be obtained as a function of temperature and melt composition in the not too distant future. For trace components, the effective binary approach (or the modified effective binary approach in the next section) will likely continue for a long time. The effective binary diffusion approach may be used under the following conditions (but is not limited to these conditions) with consistent and reliable results (Cooper, 1968) ... 

If the compositional difference along the diffusion direction is primarily in one component, and the difference in other components is due to the dilution effect, then diffusion of this component (not necessarily the other components) may be treated as effective binary, and the EBDC can be applied reliably to similar situations. Some examples are a diffusion couple made of dry rhyolite on one half and hydrous rhyolite on the other half, the hydration or dehydration of a silicate melt, and adsorption of a gas component by a glass. 

For the calculation of convective dissolution rate of a falling crystal in a silicate melt, the diffusion is multicomponent but is treated as effective binary diffusion of the major component. The diffusivity of the major component obtained from diffusive dissolution experiments of the same mineral in the same silicate melt is preferred. Diffusivities obtained from diffusion-couple experiments or other types of experiments may not be applicable because of both compositional effect... 

Table 4-4 Effective binary diffusivities in "dry silicate melts 404...

Application of the model to different systems. The thermodynamic model of silicate melts has been applied in the calculation of various types of binary, ternary, and pseudo-ternary phase diagrams. 

As a consequence of impossibility to arrange particles in the liquid phase in one solution only, the formation of two liquids, which are not miscible, may occur. Such a situation can be frequently observed in glass-forming silicate melts in the region of high concentrations of SiOa. Partial miscibility in the liquid phase is quite uncommon in binaries of molten salts. Partial miscibility is more frequent in reciprocal salt systems and probably as a rule, in the high metal concentrations of the metal-metal halide systems. 

Addition of PbO to silicate melts almost always reduces their viscosity. The viscosity of binary lead silicate melts, for example, decreases monotonically with increasing PbO concentration. These melts also become more fragile with increasing PbO content. Lead oxide also increases the dissolution rate into the melt for impurity particles such as refractory fragments, so that a small concentration of PbO improves the quality of many melts. 

The main problem in using the Hall process for silicon electrodeposition is that silicon melts at a much higher temperature than aluminum (1412°C compared to 660°C). Cryolite can not be used at this temperature due to volatization problems, so a binary or ternary melt containing SiOg had to be developed that would be stable above this temperature. Johnson (29) indicated that calcium and magnesium based silicate melts looked favorable, while other alkaline earth and alkali metal silicates were less desirable. 

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