Liquid‐vapor phase relations in the Si‐O system: A calorically constrained van der Waals‐type model

Abstract

This work explores the use of several van der Waals (vW)‐type equations of state (EoS) for predicting vaporous phase relations and speciation in the Si‐O system, with emphasis on the azeotropic boiling curve of SiO2‐rich liquid. Comparison with the observed Rb and Hg boiling curves demonstrates that prediction accuracy is improved if the a‐parameter of the EoS, which characterizes vW forces, is constrained by ambient pressure heat capacities. All EoS considered accurately reproduce metal boiling curve trajectories, but absent knowledge of the true critical compressibility factor, critical temperatures remain uncertain by ~500 K. The EoS plausibly represent the termination of the azeotropic boiling curve of silica‐rich liquid by a critical point across which the dominant Si oxidation state changes abruptly from the tetravalent state characteristic of the liquid to the divalent state characteristic of the vapor. The azeotropic composition diverges from silica toward metal‐rich compositions with increasing temperature. Consequently, silica boiling is divariant and atmospheric loss after a giant impact would enrich residual silicate liquids in reduced silicon. Two major sources of uncertainty in the boiling curve prediction are the heat capacity of silica liquid, which may decay during depolymerization from the near‐Dulong‐Petit limit heat capacity of the ionic liquid to value characteristic of the molecular liquid, and the unknown liquid affinity of silicon monoxide. Extremal scenarios for these uncertainties yield critical temperatures and compositions of 5200–6200 K and Si1.1O2–Si1.4O2. The lowest critical temperatures are marginally consistent with shock experiments and are therefore considered more probable.

Critical vaporization of MgSiO 3

“…Incongruent vaporization requires that the vapor pressure line is actually a two-phase coexistence region of finite width. However, a thermochemical modeling study of the silica system ( 15 ) indicates that the width of the two-phase region is on the order of 10% of the critical pressure and therefore not resolvable in our simulations within our present uncertainties.…”

“…The conditions of silicate vaporization extend from the solid–liquid–vapor triple point up to the critical point, which is unknown. In SiO 2 previous estimates of the critical point range from 5,000 K to 13,000 K and from 0.07 g to 1.1 g , illustrating the magnitude of uncertainty that remains ( 15 ). Predictions based on the extrapolation of experimental data ( 16 – 18 ) are accurate near the triple point, but their range of validity at higher temperatures is unknown.…”

“…The results of our study may be used to improve the liquid-phase model, for example, by providing information on these molecular components. A recent study of the silica system ( 15 ) argued that it is important to include SiO and O 2 as liquid-phase species, particularly near the critical point.…”

Stochastic accretion of the Earth

“…Where C P is that for molten peridotite near its liquidus (1800 J/kg.K 62 ), M planet is the final mass of the planet, and ν imp is the impact velocity given in the N-body simulation. Temperature increases if the energy delivered is in excess of the latent heat of fusion (Δ H fus = 4 × 10 5 J/kg at 1400 K 63 ), then vaporisation (Δ H vap = 5 × 10 6 J/kg at 2000 K 61 ) and finally an upper limit at 6000 K, whereupon behaviour becomes supercritical 64 , 65 . The mass of material that experiences peak temperatures (the isobaric core) scales with impactor radius 44 , 61 .…”

A new equation of state applied to planetary impacts

“…In the most recent ANEOS version (Stewart et al 2019) the high pressure phase change is abandoned in favor of a more accurate melt transition and liquid properties. Connolly (2016) and Melosh (2007). We fit the EOS to two different kinds of experimental data.…”