1) High pressure and temperature laser heated diamond cell experiments
The present limitation on experimental determination of melt relations and melt phase diagrams corresponds to the pressure limit of the multi-anvil press using tungsten carbide anvils. This is a routine experimental protocol in large-volume presses, but a similar protocol has remained technically unmanageable in the laser-heated diamond anvil cell (LHDAC), the only tool reaching higher pressures and temperatures to cover all plausible conditions of magma ocean crystallisation on Earth, for two reasons. The first stems from the inability to accurately control experimental conditions in the LHDAC at extreme conditions, specifically the precise control of temperature required to slowly crystallise the melt and attain controlled degrees of crystallisation (e.g. fractions of residual melt). Secondly, the size of the phases produced in the LHDAC is nanometric, so that the analysis of the run products requires the use of high-resolution analytical techniques that enable at least a 100-fold gain in spatial resolution.
Now we have undertaken a novel approach to dridge that gap, and establish phase diagrams and melting relations in the LHDAC. Our protocol consists in carrying out a series of experiments where samples are molten at a fixed pressure and then slowly cooled down and fractionally crystallised to various degrees in a narrow temperature range, a feat deemed impossible just two years ago in the LHDAC. Using FIB and TEM, we track the crystallisation sequence of silicate melts, and are able to unambiguously determine the mineralogy and composition of liquidus phase, e.g. the first mineral phase to crystallise in a cooling magma ocean, as well at the composition of the residual liquid. As crystallisation proceeds, the liquid line of descent follows a cotectic melt composition while crystallising equilibrium phases, whose mineralogy and composition are also measured, thus delineating the melting phase diagram. With this phase diagram in hand, we can calculate (at any given pressure, or depth, inside the Earth's mantle) the composition, modal abundance, and evolution of solids and liquids as temperature drops and they start solidifying. We have also provided a new method based on non-negative matrix factorization-aided phase unmixing to quantify trace element concentrations down to 100 ppm level in our LHDAC samples, paving the way to full geochemical characterisation using our expeirmental advances.
2) Geodynamics and geodynamical modelling and simulations
Recent mathematical and numerical advances now allow to extend the multiphase flow formalism to geodynamic regimes appropriate for magma ocean solidification dynamics with vigorous convection (expressed by the thermal Rayleigh number > 109) and high melt fraction (from 0 to 100\%). We used that to create a new code, in which we model the solid-liquid multiphase physics using a numerical implementation of a multiphase flow mathematical formalism based on the averaging method under the assumption of infinite Prandtl number and Boussinesq approximation. Our code accounts for thermochemical convection in both the liquid and solid states, solid-melt phase equilibrium, mineralogical phase change and solid-melt phase separation. Convective motion in a solidifying magma ocean is driven by three types of density differences. These originate from thermal expansivity (due to temperature differences), compositional differences (due to changes in iron content) and phase changes (due to the varying melt fraction). An additional mechanism that generates motion in a partially molten convective medium is the solid-liquid phase separation driven by shear deformation, in addition to the density contrasts between the melt and the solid. Phase separation is limited by matrix deformation, i.e. compaction, and viscous friction between the melt and the solid via Darcy’s law. We implemented a depth-dependent density contrast between liquid and solids, and used a thermodynamically self-consistent compositional evolution of melts and solids based on our (WP1) experimental melting phase diagrams.
