Eutectics under pressures: definition of a universal limit of liquid stability

Introduction: The fundamental thermodynamic concept of the eutectic (from Greek εὐ-τῆξῐς, “easy-melt”), defines an invariant point in temperature-concentration (T-X) space at which the liquid will transition entirely into a mixture of solid phases. In planetary science eutectics play a crucial role in defining minimum temperature of stability of liquids (i.e. water, silicate melt). Characterization of eutectics are central in understanding the behavior of aqueous systems in various icy ocean worlds processes such as cryo-volcanism, crustal melt transport, or long term oceanic and high-pressure ice mantle evolution [1].

The canonical definition of the eutectic is often considered at a fixed pressure (typically 1 atmosphere for aqueous systems); however, increased states of compression substantially affect the melting curves of solids, resulting in a change of eutectic T-X coordinates. When pressure is varied, the eutectic becomes a univariant line in the P-T-X space, the trajectory of which depends upon the geometry of the liquidus curves of the contributing solid phases.

In this work we focus on the effect of pressure on eutectics coordinates using a novel isochoric (i.e. constant volume) experimental technique, and determine the absolute limit of liquid stability of several aqueous systems: Na₂CO₃, KCl, MgSO₄, Na₂SO₄, Urea, NaCl, MgCl₂, and NaHCO₃

Methods: We use isochoric freezing chambers made of Al7075 with an internal volume of approximately 5.5 mL, designed to withstand up to 300 MPa [2]. The loaded solutions are cooled slowly (1-0.5K/hour) as low as 180K. The growth of ice Ih of greater volume than the aqueous fluid within the isochoric chamber results in a significant pressure increase, up to 260 MPa. Once the sample fully frozen, the temperature is then slowly increased up to full melting and the resulting pressure change is monitored. At constant volume and with variable temperature the Gibbs’ Phase rule [3] implies that the state of system will naturally follow the triple equilibrium univariant line (the eutectic). Using this principle we are able to determine with unmatched accuracy and high throughput the eutectic lines pressures and temperatures coordinates of many crucial aqueous systems for icy worlds.

Results and Conclusions: Our experimental result show that most systems eutectics follow a similar behavior driven by the negative Clapeyron slope of ice Ih melting surface. We also report that all systems reach a minimum liquid stability temperature around 213 MPa, roughly 22K below the known 1 bar eutectic. This pressure corresponds to the quadruple point with ice III or ice II (and the aqueous brine, ice Ih and the salt containing phase). This quadruple point in a binary system represents the lowest possible temperature of stability of a liquid in the system and is located at the end of the eutectic line. Surprisingly this invariant thermodynamic point of crucial importance has not yet been described or defined in the literature. We propose a definition and a name for this new fundamental concept: the cenotectic, from Greek “κοινός-τῆξῐς”, “universal-melt”). We also explore in this work the implication of the cenotectic on the long term evolution of large icy moons and exoplanets [4].

.

 

References:

[1] Journaux, B., et al., (2020). Space Science Reviews 216:7.

[2] Chang, B., et al. (2022) Cell Reports Physical Science 3, 100856

[3] Gibbs, J. W., (1874) On the equilibrium of heterogeneous substances, New Haven: Published by the Academy.

[4] Zarriz, A., et al. (2024), arXiv:2403.01028