Solid-solution mineral equilibrium

This example shows a tendency with solid-solution minerals. There is a supersaturation or an equilibrium regarding the solid-solution minerals but an... 

This equation shows that activity of Ca + is related to pH, concentration of H2CO3 and temperature. Because pH is related to the concentration of Cl for the equilibrium curves 1 and 2 in Fig. 2.14, the relationship between the concentrations of Ca " " and Cl" can be derived for calcite-albite-sericite-K-feldspar-quartz equilibrium (curves 4 and 7 in Fig. 2.14) and calcite-albite-sericite-Na-montmorillonite-quartz equilibrium (curves 5 and 8 in Fig. 2.14) with constant w2h2C03- The range of zh2C03 in the solution in equilibrium with calcite is assumed to be 10 to 10 . The other equilibrium curves for the assemblage including Ca minerals are also drawn (Fig. 2.14). These assemblages are wairakite-albite-sericite-K-feldspar-quartz (curve 3), Ca-montmotillonite-albite-sericite-Na-montmorillonite-quartz (curve 6), Ca-montmorillonite-albite-sericite-K-feldspar-quartz (curve 9) and anhydrite (curve 10). The effect of solid solution on the equilibrium curves is not considered because of the lack of thermochemical data of solid solution. 

A calculation procedure could, in theory, predict at once the distribution of mass within a system and the equilibrium mineral assemblage. Brown and Skinner (1974) undertook such a calculation for petrologic systems. For an -component system, they calculated the shape of the free energy surface for each possible solid solution in a rock. They then raised an n -dimensional hyperplane upward, allowing it to rotate against the free energy surfaces. The hyperplane s resting position identified the stable minerals and their equilibrium compositions. Inevitably, the technique became known as the crane plane method. 

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

Mass fluxes of alkali elements transported across the solid-solution interfaces were calculated from measured decreases in solution and from known surface areas and mineral-to-solution weight-to-volume ratios. Relative rates of Cs uptake by feldspar and obsidian in the batch experiments are illustrated in Figure 1. After initial uptake due to surface sorption, little additional Cs is removed from solution in contact with the feldspars. In contrast, parabolic uptake of Cs by obsidian continues throughout the reaction period indicating a lack of sorption equilibrium and the possibility of Cs penetration into the glass surface. 

Let us now consider in detail some of the theoretical possibilities of solid solution. We will look at the microscopic and sub-microscopic effect of each type and how this determines the observed X-ray properties and treatment of phase equilibrium relations of the minerals. 

Calculations involving mineral saturation state (D in Equations (19) and (20)) are dependent on accurate characterization of the thermodynamic states of the reactants and products and are commonly calculated using speciation codes (see Chapter 5.02 for additional information). Although the equilibrium constants for most simple primary silicates have been determined, thermodynamic data do not exist for many complex silicates or for solid solutions. 

In other words, the mole fraction ratio of / in the coexisting phases at equilibrium for a given T and P should be constant. This is Nernst s law (cf. Lewis and Randall 1961). K is also called the distribution coefficient, often symbolized by >, and is used in the study of trace element partitioning between coexisting mineral solid solutions. 

Surface complexation models of the solid-solution interface share at least six common assumptions (1) surfaces can be described as planes of constant electrical potential with a specific surface site density (2) equations can be written to describe reactions between solution species and the surface sites (3) the reactants and products in these equations are at local equilibrium and their relative concentrations can be described using mass law equations (4) variable charge at the mineral surface is a direct result of chemical reactions at the surface (5) the effect of surface charge on measured equilibrium constants can be calculated and (6) the intrinsic (i.e., charge and potential independent) equilibrium constants can then be extracted from experimental measurements (Dzombak and Morel, 1990 Koretsky, 2000). 

From the preceding equations, we can see that when calcite approaches equilibrium with water at high pH, an excess of negative HCOs and C03 will exist, whereas at low pH an excess of positive Ca and CaHCOs and CaOH" will occur. These ionic species may be produced at the solid/solution interface or may form in solution and subsequently adsorb on the mineral in amounts proportional to their concentration in solution. In either case, the net result will be a positive charge on the surface at low pH and a negative charge at high pH. 

The results of the chemical equilibrium calculations for the refractory lithophiles are also confirmed by the mineralogy and chemistry of the Ca, Al-rich inclusions in Allende and other meteorites. The major minerals in CAIs are the same ones predicted by the calculations, namely melilite (a solid solution of gehlenite CaALSiOr and akermanite Ca2MgSi2C>7), spinel, corundum, grossite, hibonite, and perovskite. Chemical analyses of CAIs show that the refractory lithophiles are enriched by an average of 20 times solar elemental... 

The non-equilibrium condition of most groundwater systems with respect to many primary minerals, or similarly the metastability which exists with respect to many semi-crystalline or amorphous phases are common problems, especially for silicates. Some clear identification is needed for system reaction time, or the rate at which equilibrium is approached, and similarly identification is needed for metastable plateaus of pseudo-equilibrium, especially for compounds such as amorphous silica, cristobalite, quartz, clay minerals, etc. The likely magnitude of saturation indices which could apply to a given mineral could be specified for a variety of conditions. In this volume, Glynn, and elsewhere others, have recently shown that some error occurs in the calculated saturation values for trace elements when pure end member minerals are assumed to be present, when actually the phases are solid solutions. The consensus among modelers appears to be that error is present and significant the challenge is to develop procedures that quantify the error, so models become tools that provide realistic and interpretable results. 

Field or laboratory observations of miscibility gaps, spinodal gaps, critical mixing points or distribution coefficients can be used to estimate solid-solution excess-free-energies, when experimental measurements of thermodynamic equilibrium or stoichiometric saturation states are not available. As an example, a database of excess-free-energy parameters is presented for the calcite, aragonite, barite, anhydrite, melanterite and epsomite mineral groups, based on their reported compositions in natural environments. 

As pointed out by Seal et al. (2000), many studies of ancient hydrothermal systems have utilized equilibrium sulfate-sulfide sulfur isotope fractionation models, but these should be applied with great caution. As shown in Figure 9, seafloor hydrothermal vent fluid 5" Sh2S values do not conform to simple equilibrium fractionation models. Shanks et al. (1981) first showed experimentally that sulfate in seawater-basalt systems is quantitatively reduced at temperatures above 250°C when ferrous minerals like the fayalitic olivine are present. When magnetite is the only ferrous iron-bearing mineral in the system, sulfate-reduction proceeds to sulfate-sulfide equilibrium, but natural basalts contain ferrous iron-bearing olivine, pyroxene, titanomagnetite, and iron-monosulfide solid-solution (mss) (approximately pyrrhotite). It is the anhydrite precipitation step... 

Dissolved arsenic concentrations can be limited either by the solubility of minerals containing arsenic as a constituent element (or in solid solution) or by sorption of arsenic onto various mineral phases. For both the precipitation-dissolution of arsenic-containing minerals and sorption-desorption of arsenic onto solid phases, equilibrium calculations can indicate the level of control over dissolved arsenic concentrations that can be exerted by these processes. However, neither of these types of reactions is necessarily at equilibrium in natural waters. The kinetics of these reactions can be very sensitive to a variety of environmental parameters and to the level of microbial activity. In particular, a pronounced effect of the prevailing redox conditions is expected because potentially important sorbents (e.g., Fe(III) oxyhydroxides) are unstable under reducing conditions and because of the differing solubilities of As(V) and As(III) solids. 

Most modem quantitative trace element geochemistry assumes that trace elements are present in a mineral in solid solution through substitution and that their concentrations can be described in terms of equilibrium thermodynamics. Trace elements may mix in either an ideal or a non-ideal way in their host mineral. Their very low concentrations, however, lead to relatively simple relationships between composition and activity. When mixing is ideal the relationship between activity and composition is given by RaoulFs Law, i.e. 

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