Phase stability fields

Figure 7,8 Gibbs free energy curves and T-X phase relations for an intermediate compound (C), totally immiscible with pure components. Column 1 Gibbs free energy relations leading to formation of two eutectic minima separated by a thermal barrier. Column 2 energy relations of a peritectic reaction (incongruent melting). To facilitate interpretation of phase stability fields, pure crystals of components 1 and 2 coexisting with crystals C are labeled y and y", respectively, in T-X diagrams same notation identifies mechanical mixtures 2-C and C-1 in G-X plots.

Extensive efforts have been made to determine the phase stability fields and structures of alloys and compounds consisting of iron and one of the potential light elements at elevated pressures and... 

Fig. 4. Solidus portion of the pressure-dependent diagram for the PrS, jj-PrSioo system. Phase stability fields are marked as 1-6.

Gangue minerals and salinity give constraints on the pH range. The thermochemical stability field of adularia, sericite and kaolinite depends on temperature, ionic strength, pH and potassium ion concentration of the aqueous phase. The potassium ion concentration is estimated from the empirical relation of Na+/K+ obtained from analyses of geothermal waters (White, 1965 Ellis, 1969 Fournier and Truesdell, 1973), experimental data on rock-water interactions (e.g., Mottl and Holland, 1978) and assuming that salinity of inclusion fluids is equal to ffZNa+ -h m + in which m is molal concentration. From these data potassium ion concentration was assumed to be 0.1 and 0.2 mol/kg H2O for 200°C and 250°C. 

For a binary system at constant pressure the phase rule gives F=3-Ph and we need only two independent variables to express the stability fields of the phases. It is most often convenient and common to choose the temperature and composition, given for... 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressure. The Gibbs phase rule for a ternary system at isobaric conditions is Ph + F = C + 1=4, and there are four phases present in an invariant equilibrium, three in univariant equilibria and two in divariant phase fields. Finally, three dimensions are needed to describe the stability field for the single phases e.g. temperature and two compositional terms. It is most convenient to measure composition in terms of mole fractions also for ternary systems. The sum of the mole fractions is unity thus, in a ternary system A-B-C ... 

The stability fields for the condensed phases correspond to F = 2, which means that both temperature and the partial pressure of 02 can be varied independently. 

The segregation or demixing is a purely kinetic effect and the magnitude depends on the cation mobility and sample thickness, and is not directly related to the thermodynamics of the system. In some specific cases, a material like a spinel may even decompose when placed in a potential gradient, although both potentials are chosen to fall inside the stability field of the spinel phase. This was first observed for Co2Si04 [39]. Formal treatments can be found in references [37] and [38],... 

Electronic transitions like insulator-metal transitions, magnetic order-disorder transitions, spin transitions and Schottky-type transitions (due to crystal field splitting in the ground state in/element-containing compounds) profoundly influence the phase stability of compounds. A short description of the main characteristics of these transitions will be given below, together with references to more thorough treatments. 

The intermediate phases formed in the various binary systems have been represented, in a first approximation, as point compounds. The points, which in the different binaries correspond to phases having the same composition and structure, have then been connected, defining multi-component ternary stability fields (in this case, line fields). On each horizontal line of this multi-diagram triangle the same overall composition is found (the same Mg content and the same total... 

By combining the various observations obtained from the G-T diagrams in different P conditions, we can build up a P-P diagram plotting the stability fields of the various polymorphs, as shown in figure 2.5. The solid dots in figures 2.4 and 2.5 mark the phase transition limits and the triple point, and conform to the experimental results of Richardson et al. (1969) (A, R, B, C ) and Holdaway (1971) (A, H, B, C). The dashed zone defines the uncertainty field in the... 

A recent study by Holdaway and Mukhopadhyay (1993) essentially confirms the stability diagram of Holdaway (1971). However, it is of interest to show how even slight errors in the assigned Gibbs free energy of a phase drastically affect the stability fields of polymorphs. 

These coefficients are valid for a pressure of 1 bar, within the stability field of the phase. 

Chatterjee and Johannes (1974), is compared in figure 5.47A with the experimental results of Ivanov et al. (1973) for = co2 Figure 5.47A also superimposes the melting curves of granite in the presence of a fluid phase of identical composition. Note that the composition of the fluid dramatically affects stability relations if the amount of H2O in the fluid is reduced by half = 0.5), the stability field of muscovite is re-... 

We have already stated that the a-[3 transition of quartz may be described as a A transition overlapping a first-order transition. The heat capacity function for the two polymorphs is thus different in the two stability fields, and discontinuities are observed in the H and S values of the phase at transition temperature T rans cf section 2.8). For instance, to calculate the thermodynamic properties of ]8-quartz at T = 1000 K and P = bar, we... 

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