Temperature and Density on the Forsterite Liquid-Vapor Phase Boundary

Abstract

The physical processes during planet formation span a large range of pressures and temperatures. Giant impacts, such as the one that formed the Moon, achieve peak pressures of 100s of GPa. The peak shock states generate sufficient entropy such that subsequent decompression to low pressures intersects the liquid-vapor phase boundary. The entire shock-and-release thermodynamic path must be calculated accurately in order to predict the post-impact structures of planetary bodies. Forsterite (Mg₂SiO₄) is a commonly used mineral to represent the mantles of differentiated bodies in hydrocode models of planetary collisions. Here, we performed shock experiments on the Sandia Z Machine to obtain the density and temperature of the liquid branch of the liquid-vapor phase boundary of forsterite. This work is combined with previous work constraining pressure, density, temperature, and entropy of the forsterite principal Hugoniot. We find that the vapor curves in previous forsterite equation of state models used in giant impacts vary substantially from our experimental results, and we compare our results to a recently updated equation of state. We have also found that due to under-predicted entropy production on the principal Hugoniot and elevated temperatures of the liquid vapor phase boundary of these past models, past impact studies may have underestimated vapor production. Furthermore, our results provide experimental support to the idea that giant impacts can transform much of the mantles of rocky planets into supercritical fluids.

Keywords: Hugoniot; equation of state; melting; shock wave; supercritical; vaporization.

Figure 1

Schematic single‐component phase diagram of the shock, release, and re‐shock experiments to determine the temperature and density on the liquid‐vapor phase boundary. In blue is the principal Hugoniot, the dark blue arrow is the isentropic release path, and in red is the re‐shock Hugoniot from state B. The dotted black line is the unknown vapor curve with the critical point at the black dot. The solid black lines are the melt curve.

Figure 2

Generalized schematic of the flyer plate experiments on the Sandia Z Machine. In each experiment, both the anode and cathode are 1.2 mm thick aluminum flyer plates that impact target panels with several science samples and diagnostic windows. The ability to field up to 14 samples per shot enables multiple types of measurements in a single experiment: Shock and partial release, shock‐and‐release, and reverse impact experiments.

Figure 3

Example of raw VISAR data, showing intensity of light with time where the principal source of light is the VISAR laser at 532 nm. A schematic of the main events observed in the data is presented in Figure 4. For this detector, higher intensities of light produce a more negative voltage signal. See text for discussion of the main events. VISAR, Velocity Interferometer System for Any Reflector.

Figure 4

Cartoon of the main events in the reverse impact experiment observed in the raw data shown in Figure 3.

Figure 5

(a) Release isentrope in green from a 430 GPa shock, similar to the highest reverse impact experiment, in ρ‐T space, starting from the principal Hugoniot (blue) and intersecting the liquid‐vapor phase boundary (black) at point B (Figure 1). (b) Characteristics in Lagrangian coordinates, showing the plateau in the density profile that occurs at the intersection of the phase boundary. Higher density characteristics are opaque and opacity decreases with decreasing density.

Figure 6

Thermal emission data from SVS4 from shot Z3172 N5 which had a shock pressure of 450.7 ± 4.9 GPa. (a) The SVS streak camera records thermal emission over time, resolved in wavelength. Events of the experiment are easily distinguished; pre‐impact before time 0, quartz shock from 0–18 ns, forsterite shock from 20 to 35 ns, and post‐shock emission from 40 to 70 ns. (b) Vertical line out over wavelengths 475–485 nm in time from (a). Post shock emission has on order of 100s of counts. (c) Ideal greybody for quartz (red line), horizontal lineout of forsterite data from 24 to 30 ns and (blue), and a fitted greybody (black line). (d) Horizontal lineout of post‐shock emission from 50 to 60 ns, and its fitted blackbody (black line). For (c and d) uncertainty for data and fits are given by the associated envelopes. SVS, Streaked Visible Spectrometer.

Figure 7

(a) Schematic of a typical steady shock experiment, where the red dashed line is the Rayleigh line, the red curve is the unknown sample Hugoniot, and the black curve is the known flyer Hugoniot. The intersection between the reflected flyer Hugoniot and the sample Rayleigh line is the shock state achieved by the experiment, which lies on the sample Hugoniot by definition. (b) Schematic of the reverse impact experiment, where shock states of the windows are determined by their known Hugoniots. Impedance matching the shock states in the windows with the unknown liquid flyer gives two P and u _p states to use to constrain the initial density of the liquid flyer.

Figure 8

Shock states, window Hugoniots, liquid Rayleigh lines, and a fitted linear Hugoniot for shot Z3422 which generated a shock pressure of 428.53 ± 2.05 GPa in forsterite. Fitted values for C ₀ and s are given in Table 5 along with the calculated density of the liquid forsterite flyer.

Figure 9

(a) Experimentally determined density and specific entropy of states on the liquid‐vapor curve (red points) and their associated shock states (black points). (b) Measured apparent temperatures and specific entropies of states on the liquid‐vapor curve and their associated shock states. The blue curve, with 1‐σ error envelope, is the experimentally determined forsterite principal Hugoniot (Davies et al., 2020; Root et al., 2018). The yellow (ANEOS‐C, Canup et al., 2013) and orange (ANEOS‐G, Ćuk & Stewart, 2012; Nakajima & Stevenson, 2014) lines are different forsterite ANEOS models previously used in giant impact simulations. The ANEOS model for forsterite was recently revised by Stewart et al. (2020) (new ANEOS); the new ANEOS model phase boundaries are shown by black lines and the model Hugoniot in brown lines. The gray line denotes the triple point temperature. The shock states (black points) decompress along an isentrope to intersect the vapor curve (red points).

Figure 10

(a) Density profiles in Eulerian coordinates at different times after release from a downrange free surface in an experiment with shock pressure of 430 GPa. The liquid density plateau is denoted by ρ _0L. (b) Liquid‐vapor phase boundary in T−S space, where the dashed lines are the predicted observed apparent temperatures due to absorption of droplets ahead of the liquid layer. Larger liquid condensates in the liquid‐vapor mixture causes the optical depth to become shorter, obscuring the temperature emission from the liquid wall.

Figure 11

Thermal profiles through the Earth after a canonical Moon‐forming impact event, comparing two forsterite EOS models for the mantle: ANEOS‐G (a) and New ANEOS (b). Dots show the pressure‐entropy in the midplane (±1,000 km) within the Roche radius compared to the phase boundaries (orange line: vapor curve from ANEOS‐G; black lines are the melt curve and vapor curve from New ANEOS. The highest pressures are at the core‐mantle boundary and the lowest pressures are in the disk. The pressure profiles through the mantle and disk fall above the forsterite critical point. ANEOS, Analytic Equations of State; EOS, equations of state.