Vol 25, No 5 (2017)

Reactions and partial melting of peraluminous rocks in the presence of H₂O-CO₂–salt fluids under parameters of granulite-facies metamorphism were modeled in experiments on interaction between orthopyroxene–cordierite–biotite–plagioclase–quartz metapelite with H₂O, H₂O-CO₂, H₂O-CO₂-NaCl, and H₂O-CO₂-KCl fluids at 600 MPa and 850°C. Rock melting in the presence of H₂O and equimolar H₂O-CO₂ fluids generates peraluminous (A/CNK¹ > 1.1) melts whose composition corresponds to magnesian calcic or calc–alkaline S-type granitoids. The melts are associated with peritectic phases: magnesian spinel and orthopyroxene containing up to 9 wt % Al₂O₃. In the presence of H₂O-CO₂-NaCl fluid, cordierite and orthopyroxene are replaced by the association of K-Na biotite, Na-bearing gedrite, spinel, and albite. The Na₂O concentrations in the biotite and gedrite are functions of the NaCl concentrations in the starting fluid. Fluids of the composition H₂O-CO₂-KCl induce cordierite replacement by biotite with corundum and spinel and by these phases in association with potassium feldspar at X_KCl = 0.02 in the fluid. When replaced by these phases, cordierite is excluded from the melting reactions, and the overall melting of the metapelite is controlled by peritectic reactions of biotite and orthopyroxene with plagioclase and quartz. These reactions produce such minerals atypical of metapelites as Ca-Na amphibole and clinopyroxene. The compositions of melts derived in the presence of salt-bearing fluids are shifted toward the region with A/CNK < 1.1, as is typical of so-called peraluminous granites of type I. An increase in the concentrations of salts in the fluids leads to depletion of the melts in Al₂O₃ and CaO and enrichment in alkalis. These relations suggest that the protoliths of I-type peraluminous granites might have been metapelites that were melted when interacting with H₂O-CO₂-salt fluids. The compositions of the melts can evolve from those with A/CNK > 1.1 (typical of S-type granites) toward those with A/CNK = 1.0–1.1 in response to an increase in the concentrations of alkali salts in the fluids within a few mole percent. Our experiments demonstrate that the origin of new mineral assemblages in metapelite in equilibrium with H₂O-CO₂-salt fluids is controlled by the activities of alkaline components, while the H₂O and CO₂ activities play subordinate roles. This conclusion is consistent with the results obtained by simulating metapelite mineral assemblages by Gibbs free energy minimization (using the PERPE_X software), as shown in log(\({a_{{H_2}O}}\))–log(\({a_{N{a_2}O}}\)) and log(\({a_{{H_2}O}}\))–log(\({a_{{K_2}O}}\)) diagrams.

Possible topologies of miscibility gaps in arsenian (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores are examined. These topologies are based on a thermodynamic model for fahlores whose calibration has been verified for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores, and conform with experimental constraints on the incompatibility between As and Ag in (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores, and with experimental and natural constraints on the incompatibility between As and Zn and the nonideality of the As for Sb substitution in Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores. It is inferred that miscibility gaps in (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores have critical temperatures several °C below those established for their Sb counterparts (170 to 185°C). Depending on the structural role of Ag in arsenian fahlores, critical temperatures for (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores may vary from comparable to those inferred for (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores, if the As for Sb substitution stabilizes Ag in tetrahedral metal sites, to temperatures approaching 370°C, if the As for Sb substitution results in an increase in the site preference of Ag for trigonal-planar metal sites. The latter topology is more likely based on comparison of calculated miscibility gaps with compositions of fahlores from nature exhibiting the greatest departure from the Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ and (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ planes of the (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlore cube.

Gibbs energy minimization is the means by which the stable state of a system can be computed as a function of pressure, temperature and chemical composition from thermodynamic data. In this context, state implies knowledge of the identity, amount, and composition of the various phases of matter in heterogeneous systems. For seismic phenomena, which occur on time-scales that are short compared to the timescales of intra-phase equilibration, the Gibbs energy functions of the individual phases are equations of state that can be used to recover seismic wave speeds. Thermodynamic properties relevant to modelling of slower geodynamic processes are recovered by numeric differentiation of the Gibbs energy function of the system obtained by minimization. Gibbs energy minimization algorithms are categorized by whether they solve the non-linear optimization problem directly or solve a linearized formulation. The former express the objective function, the total Gibbs energy of the system, indirectly in terms of the partial molar Gibbs energies of phase species rather than directly in terms of the Gibbs energies of the possible phases. The indirect formulation of the objective function has the consequence that although these algorithms are capable of attaining high precision they have no generic means of treating phase separation and expertise is required to avoid local minima. In contrast, the solution of the fully linearized problem is completely robust, but offers limited resolution. Algorithms that iteratively refine linearized solutions offer a compromise between robustness and precision that is well suited to the demands of geophysical modeling.