Closing of Fluid Miscibility Gaps and Emergence of Supercritical Phenomena: a Conceptual Framework Based on Phase Relationship Analysis in Geologically Relevant Ternary Systems

Abstract Supercritical phenomena arising from the closure of miscibility gaps between vapor/gas and liquid/melt represent an intriguing aspect of deep Earth processes. While corresponding phase relationships have been discussed predominantly in binary systems, these relationships remain inadequately explored in higher–order systems. In this study, we analyse the phase relationships of fluid miscibility in three geologically relevant ternary systems (CaO–CO2–H2O, MgO–SiO2–H2O, SiO2–NaAlSiO4–H2O). This analysis clarifies the definitions of second critical endpoint (SCE) and ordinary critical point by highlighting their differences. We also introduce a new related concept—critical pressure—to underscore the importance of distinguishing between these terms. It is demonstrated that SCEs are invariant points, independent of system composition, whereas both ordinary critical points and critical pressures vary with system composition. A systematic examination of the metastability of certain SCEs and critical curves is also provided, along with a discussion of the geological implications. The extension of our considerations to the quaternary system SiO2–KAlSi3O8–NaAlSi2O6–H2O further reveals that SCEs and critical curves are hierarchically organized in higher–order systems, with critical curves linking SCEs across systems of different orders. Although the phase relationships presented here are largely schematic, the general topologies, together with the conceptual framework developed, provide a useful foundation for future experimental and natural observations.