Phase relations in the systems Cu-Fe-As-S and Cu-Fe-S-0 are described in terms of the fugacities of the various components. Construction of qualitatively correct and useful fugacity diagrams is permitted by the geometric requirements of natural mineral associations within an incomplete thermochemical framework, even though complete thermochemical data are not available. The effect on the diagrams of solid solution at high temperature can be described only qualitatively. The diagrams are subject to revision as new thermochemical data become available and as knowledge of natural mineral associations is increased. The diagrams enable correlation of experimental work in the various simpler subsystems, and highlight areas of most useful laboratory investigation and natural observation. The fugacity diagrams and the phase rule are used to set up thermodynamic-system models of hydrothermal ore formation. Primary mineralization is described by consideration of a completely-open-system model. Paragenetic and zonal relations in sulfide ores are described in this model by paths through the fugacity diagrams. Precipitation of minerals from a hydrothermal solution is closely analogous to crystallization from a silicate melt, and the fugacity diagrams are very similar to liquidus diagrams for ternary compositional systems. Precipitation from hydrothermal solutions may be congruent (eutectic type) or incongruent (peritectic type), resulting in either simultaneous precipitation of phases or replacement of early phases by later phases on reaction with hydrothermal fluids. Relations in a metamorphosed ore can be described by consideration of a partly-open-system model. Post-mineralization changes in sulfide ores can be described by consideration of closed-system models.

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