Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - IMPACT (The giant impact and the Earth and Moon formation)

Teaser

The early age of the solar system has seen numerous giant impacts, on a scale energetic enough to un-make and make proto-planets, planetesimals and moons. The Earth did not escape this pattern; if early giant impacts could have formed ponds or even seas of magma, their...

Summary

The early age of the solar system has seen numerous giant impacts, on a scale energetic enough to un-make and make proto-planets, planetesimals and moons. The Earth did not escape this pattern; if early giant impacts could have formed ponds or even seas of magma, their signature cannot be directly retrieved today, but only inferred. But the last giant impact was large enough to result in a total breakup of the initial bodies and to transform the proto-Earth and the impactor, Theia, into a disk or a synestia. This object was formed of hot liquid droplets and gas. Large parts of it were probably in supercritical state. After its formation this starts to cool and condense.

The central accumulation of dense matter forms the Earth. The timescale for its accumulation is on the order of a few tens of hours. The central body is surrounded for a long time of an atmosphere. Models predict either the formation of a distinct central body and outer atmosphere or of a continuous transitional state with no sharp distinction, like a surface. The first case happens if the liquid-gas

The two scenarios have tremendous implications, for explaining the observed geochemical similarities between the Earth and the Moon. In the first case the disk must have been extremely homogenous from the beginning, for example because the impactor and the proto-Earth would have been very similar in composition. In the second case this similarity constrain is relaxed, as a persistent continuous object would be better mixed.

Choosing the right scenario depends on many things, like the energy of the impact, the masses, the angular momentum of the system. But also it largely depends on the thermodynamic relations of the different mineral components. As a function of the energy of the impact the supercritical state can be reached. And more importantly, depending on the position of the critical point the supercritical state can be maintained for a shorter or longer time. (Figure 1).

However, some of the most important thermodynamic parameters that are necessary in the modelling of such an impact are missing today: the position of the critical points, the boundaries of the critical state for multicomponent systems, the liquid-vapour equilibria, and the equation of state for both liquids and the supercritical fluids.

The estimations of the critical points currently in use have been based on extrapolations of the thermodynamic parameters from ambient conditions up to the high temperatures and low densities specific to silicate critical points. Only very recently more through approaches based on ab initio simulations have started to address simple relevant mineral systems, like silica and forsterite.

In our project we are computing these missing parts of the phase diagrams for the representative systems of the protolunar disk. So far, during these first 30 months we have addressed a wide set of chemical compositions, both pure idealized phases, i.e. iron, feldspars, brucite, and silica, as well as a realistic average composition of the Earth’s mantle, the Bulk Silicate Earth. We have also considered a series of volatiles, like CO, CO2, He, H2O, and Zn, whose behaviour during the Impact and its aftermath we are tracking.

We obtain the liquid spinodal points from which we infer the position of the critical points. We compute the equation of states of the liquids and of the supercritical fluids, we determine the fluid structure, the chemical speciation, and we calculate the transport properties.

Work performed

The good realization of the project required a considerable methodological development. In the beginning in parallel with producing the raw data by simulations, we spent a large amount of time building the tools necessary for the interpretation of these raw data. Today we have available a powerful library for analysing molecular-dynamics runs. We are currently in the processing of beautification of the code and performing the last tests. The entire package will be released as open source to the entire community during 2019, and a paper will be submitted to an appropriate journal with the code description.
In the following we describe the methodology and then list the status of the simulations and interpretation of the results for the various mineralogical systems we are working on.
Methodology
For single component systems, the schematic phase relations are represented in Figure 1. (For multicomponent system this represents a cross-section through the compositional space). Solids are typically stable at high density and low temperature, liquids at high density and high temperature and gases at low density. All the grey areas in the Figure are two-phase regions. At high-enough temperature there is no transition between gases and liquids. This is the realm of the supercritical state, above the critical point.
In order to find the critical point, the closure point of the gas-liquid two-phase region (dome), we calculate the pressure and the internal energy as a function of density at different isotherms. Upon decompression, the pressure on the melt decreases and the behaviour of the melts follows the Maxwell construction of the liquid - vapor equilibrium. At high density from high pressures down to the saturation vapor pressure, the melts are stable. Below this, they become metastable with respect to the mixture of vapor and liquid. During this interval the pressure continues to decrease and the melt is more and more stretched, such as void spaces may appear inside the liquid at the atomic level. The minimum of the pressure marks the liquid spinodal. At densities smaller than that of the spinodal, the melts become unstable with respect to a mixture of gas and liquid, and bubbles filled with gas start to differentiate even at the scale of our simulation box. If the volume of the simulation box continue to increase the total pressure on the cell starts to increase, as more and more atoms fill in the gas bubbles.
We compute the variation of the pressure (as well as energy) as a function of density using first-principles (FP) molecular-dynamics simulations (MD). In MD the atoms move according to the Newtonian mechanism under the action of the interatomic forces. We compute these forces using the Projection-Augmented Wavefunction (PAW) implementation of the density-functional theory as in the VASP package. We employ the PBE GGA functional for the exchange-correlation part. Our simulations are performed in NVT ensembles, i.e. the Number of particles and the Volume of the cell are kept fixed. The Temperature is controlled by the use of external thermostats to oscillate around a desired average value.

In-house software
We developed a post-processing utility, described at point 1.2, which will be made available to the entire computational community, be it in geosciences, in physics, or in chemistry. We are currently in the final stage of source development and will be able to release a first complete version and submit a publication before the summer of 2019.
The UMD package consists of:
A parser between various ab initio molecular dynamics codes (VASP, QBox, abinit, more to come at a later stage) and the UMD format file
A tool to compute the pair distribution function
A tool to compute the speciation and clusterization based on an interconnectivity matrix (the atoms are bonded if they lie inside their corresponding first coordination sphere)
A tool to distinguish “gas”-like and “liquid”-like components
A tool to compute the gas v

Final results

* We have refined the Maxwell construction to obtain critical points for a variety of mineralogical systems
* We have implemented the method of the Gibbs ensemble to determine the vapor -liquid equilibrium. According to this procedure we define two simulation boxes, one at high density, i.e. the liquid, and one at low density, i.e. the vapor. We allow transfer of atoms between the two boxes with the Boltzmann probability based on the energy of the systems. At equilibrium the probability of the transfer is the same in the two directions. Given appropriate computational resources, this procedure can be used also to find the chemical equilibrium and the element partitioning between two geochemical reservoirs. This is a methodological development that we adopted during the project.
* We expect to obtain the critical points of a large majority of mineralogical systems, in agreement with what was initially planned for the project. But we will also apply the Gibbs ensemble method to a series of systems, including multi component silicate melts, like pyrolite, to compute element partitioning between vapor and liquids, or between two liquids
* We will fully characterize the structural and the transport properties of a large series of melts and supercritical fluids that are relevant for the early Earth

Website & more info

More info: http://moonimpact.eu/.