Experimental and thermodynamic determination of the liquid–vapor topology of binary silicate–H₂O systems and the physical properties of supercritical silicate-bearing fluids at deep-crust and upper-mantle conditions

A 2007 analysis by Hack, Hermann and Mavrogenes of pressure–temperature–composition (PTX) topologies in the binary systems $SiO_2$–$H_2O$ and $NaAlSi_3O_8$ (albite)–$H_2O$ identified a set of linked open problems: the liquid–vapor (L–V) solvus and critical curve of $SiO_2$–$H_2O$ above the wet solidus were only semi-constrained; the compositions of vapor coexisting with hydrous albite liquids and the subsolidus solubility of albite in aqueous fluid were poorly known; and the density and compressibility of silicate-bearing supercritical fluids — which govern the curvature of critical curves and possible density inversions — were essentially unmeasured. The albite–H₂O component has been substantially resolved by experiment: Makhluf, Newton and Manning (2016, 2020) determined liquidus and solvus relations from 1.0 to 1.7 GPa, formulated the critical curve, and constrained the critical endpoint on the wet solidus at 1.63 ± 0.02 GPa and 659 ± 5 °C. In contrast, the $SiO_2$–$H_2O$ solvus, critical curve and upper critical endpoint remain model-constrained only (thermodynamic models bracket the upper critical endpoint near 1 GPa and 1340–1350 K, close to the 1962 experimental bracket, with no experimental data on the coexisting vapor), and the density and compressibility of silicate-bearing supercritical fluids are still inferred from models and simulations rather than measured. The surviving open problem is the direct experimental determination of the L–V solvus, critical curve and critical endpoint of $SiO_2$–$H_2O$ at deep-crust to upper-mantle conditions, together with measurement of the PVT properties of supercritical silicate-bearing fluids, sufficient to relate critical-curve geometry to density inversion and to calibrate calculated phase diagrams for natural rock–water systems.

Background

Water is the most abundant volatile in Earth's interior, and at high pressure and temperature it is stored both in aqueous fluids and dissolved in silicate melts. In a binary system $A$–$H_2O$ (where $A$ is a silicate component such as quartz, $SiO_2$, or albite, $NaAlSi_3O_8$), the 'wet' or fluid-saturated solidus is the melting curve of the solid in the presence of an aqueous fluid phase; above it coexist a hydrous silicate melt ('liquid', L) and an H₂O-rich fluid ('vapor', V). At sufficiently high pressure and temperature L and V become completely miscible, producing a single supercritical fluid; the two-phase L+V field is bounded in composition–temperature space by a solvus, whose crest projected into pressure–temperature space is the L=V critical curve. Where the critical curve meets the wet solidus, the L+V field terminates at a critical endpoint (in rock–water systems often called the second critical endpoint; on the silicate-rich side, the upper critical endpoint, UCEP). The full arrangement of these surfaces in pressure–temperature–composition space — the PTX topology — controls whether a rising slab fluid separates into melt and aqueous phases, stays a single supercritical fluid, or ponds at a density barrier, and therefore controls element transport and melting above subduction zones. The PTX topology is also sensitive to the sign of the Clapeyron slope (the slope $dP/dT$ of a phase boundary in pressure–temperature space) of the critical curve: a negative slope requires the coexisting vapor to be denser than the liquid (a density inversion), and a temperature minimum or maximum on the critical curve implies $\Delta V = 0$ (zero volume difference between the coexisting phases) and requires a density inversion amongst the phases at the critical curve — relations that are well defined theoretically but poorly calibrated with data.

The two natural model systems are $SiO_2$(quartz)–$H_2O$, the simplest silicate–water binary, and $NaAlSi_3O_8$(albite)–$H_2O$, the simplest analogue of granite. Kennedy, Wasserburg, Heard and Newton (1962) mapped the upper three-phase region of $SiO_2$–$H_2O$ and estimated its critical endpoint near 0.97 GPa and 1353 K, where the quartz-wet solidus terminates. Shen and Keppler (1997) directly observed complete miscibility between hydrous albite melt and aqueous fluid in a hydrothermal diamond-anvil cell (a miniature high-pressure cell with transparent diamond windows that lets the sample be watched optically at run conditions) and located part of the $NaAlSi_3O_8$–$H_2O$ critical curve. Kessel, Ulmer, Pettke, Schmidt and Thompson (2005) later documented a second critical endpoint in the water–basalt system (where basalt occurs as eclogite, its high-pressure metamorphic equivalent) at 4–6 GPa, showing that complete miscibility is a general feature of rock–water systems at mantle pressures. Against this background, Hack, Hermann and Mavrogenes (2007) assembled a semi-quantitative PTX model for both binaries from the then-available solubility data and topological reasoning, and stated explicitly what remained unresolved: the L+V solvus of $SiO_2$–$H_2O$ above the wet solidus was constrained by almost no direct data; albite solubility in aqueous fluid below the solidus (subsolidus solubility) was poorly established, complicated by reports of incongruent (non-stoichiometric) dissolution; the compositions of vapors coexisting with hydrous albite liquids were poorly known; and the density and compressibility of silicate-bearing supercritical fluids — the properties that connect critical-curve curvature to density inversion — were essentially unmeasured, so that several distinct PTX topologies remained compatible with the data and thermodynamic models of the day could not be calibrated for natural rock–water systems. Subsequent thermodynamic treatments (Newton and Manning 2008; Hunt and Manning 2012; Gao, Li and Zhang 2024) built quantitative models of the $SiO_2$–$H_2O$ fluid near the UCEP from quartz-solubility measurements, and piston-cylinder experiments by Makhluf, Newton and Manning (2016, 2020) redetermined the albite–H₂O phase relations.

Problem Statement

Determine, by direct experiment and in thermodynamically consistent form, the pressure–temperature–composition topology of the open binary silicate–water system $SiO_2$–$H_2O$ at deep-crust and upper-mantle conditions (the $NaAlSi_3O_8$–$H_2O$ topology being an already-resolved input that enters this objective only as the reference calibration, not as a target of new determination), comprising: (i) the $SiO_2$–$H_2O$ liquid–vapor solvus and the L=V critical curve above the wet solidus, and the location and composition of the critical endpoint at which the critical curve terminates on the wet solidus; (ii) the compositions of coexisting hydrous silicate liquid and aqueous vapor across the $SiO_2$–$H_2O$ two-fluid field, and the solubility of the solid silicate in the coexisting fluid below and along the solidus; and (iii) the density and compressibility of silicate-bearing supercritical fluids, so that the relation between critical-curve curvature — including the sign of its $dP/dT$ slope and any pressure–temperature extrema — and density inversion between liquid and vapor is quantified rather than merely inferred. These components serve one common objective: an experimentally calibrated PTX description of the $SiO_2$–$H_2O$ binary complete enough to discriminate among the alternative topologies that the 2007 analysis showed to be compatible with the data, and to serve as the calibration basis for calculated phase diagrams of natural rock–water systems. Taken for the $SiO_2$–$H_2O$ system, components (i)–(iii) are jointly the whole required determination — no required deliverable lies outside them — and together they constitute the surviving open core: direct experimental constraint on the $SiO_2$–$H_2O$ liquid–vapor solvus, critical curve and upper critical endpoint (currently known only through thermodynamic models that bracket the endpoint near 1 GPa and 1340–1350 K and through quartz-solubility data, with no experimental data on the coexisting vapor phase), and direct measurement of the PVT properties of supercritical silicate-bearing fluids. The $NaAlSi_3O_8$–$H_2O$ binary between about 0.3 and 2.4 GPa has been experimentally resolved since 2007 and now constitutes the reference calibration against which the $SiO_2$–$H_2O$ determination is to be tested.

References

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