Probing the nucleation of iron in Earth's core using molecular dynamics simulations of supercooled liquids

Abstract

Classical nucleation theory describes the formation of the first solids from supercooled liquids and predicts an average waiting time for a system to freeze as it is cooled below the melting temperature. For systems at low to moderate undercooling, waiting times are too long for freezing to be observed via simulation. Here a system can be described by estimated thermodynamic properties, or by extrapolation from practical conditions where thermodynamic properties can be fit directly to simulations. In the case of crystallizing Earth's solid iron inner core, these thermodynamic parameters are not well known and waiting times from simulations must be extrapolated over approximately 60 orders of magnitude. In this work, we develop a new approach negating the need for freezing to be observed. We collect statistics on solidlike particles in molecular dynamic simulations of supercooled liquids at 320 GPa. This allows estimation of waiting times at temperatures closer to the melting point than is accessible to other techniques and without prior thermodynamic insight or assumption. Our method describes the behavior of nucleation at otherwise inaccessible conditions such that the nucleation of any system at small undercooling can be characterized alongside the thermodynamic quantities which define the first formed solids.

Can homogeneous nucleation resolve the inner core nucleation paradox?

“…To frame these calculations at relevant pressure and temperatures, equations of state and melting curves must also be calculated for these models. We use the methodology of Wilson et al (2021) expanded to binary systems to identify nuclei, calculate nucleation rates and predict waiting times for systems to freeze.…”

“…Both approaches, find that these simple systems reproduce the original prediction of Huguet et al (2018) with a 675 -807 K supercooling requirement for spontaneous homogeneous nucleation of the inner core. A metadynamic approach shows that metastable iron phases may lower the nucleation barrier in a two-step nucleation process (Sun et al, 2022) but much of this reduction is owed to a lower melting temperature and this metastable phase has not been reported in molecular dynamic studies of the same systems (Davies et al, 2019;Wilson et al, 2021). A recent laser driven shock experiment study on the melting curve of iron has suggested that the paradox does not exist and that the nucleation barrier is far lower than previously thought for planetary interiors (Kraus et al, 2022).…”

“…Davies et al (2019) directly observed homogeneous nucleation in molecular dynamic simulations of Fe and FeO systems at extreme supercooling and extrapolated results to Earth-like conditions, confirming the existence of the paradox. Others have probed the relevant conditions with molecular dynamic simulations of pure Fe to characterise the size distribution of sub-critical (those which re-melt) nucleation events (Wilson et al, 2021). Both approaches, find that these simple systems reproduce the original prediction of Huguet et al (2018) with a 675 -807 K supercooling requirement for spontaneous homogeneous nucleation of the inner core.…”

“…Adding to the controversial timing of inner core formation, a more recent problem has come to light. Theory and atomic scale simulations predict that there is a substantial barrier to the formation of new solid in liquid iron under core conditions (Huguet et al, 2018;Davies et al, 2019;Wilson et al, 2021) that means substantial supercooling is expected to be needed before inner core formation.…”

“…We only consider homogeneous nucleation because there are no obvious solid surface on which iron can first nucleate at the centre of the core. We will first describe the methods used to simulate supercooled liquids and characterise nucleation within them following our previous work (Wilson et al, 2021). We will then present predictions of critical nucleus sizes for Fe x O 1-x , Fe x C 1-x , Fe x Si 1-x and Fe x S 1-x at x = 1 and 3 mol.…”