Alfred Wilson , Andrew Walker , Dario Alfè , Chris Davies 

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 supercooled to temperatures below the melting temperature. For systems at low to moderate undercooling, waiting times are too long for freezing to be observed via experiment or 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 crystallising Earth’s solid iron inner core, these thermodynamic parameters are not well known and waiting times from simulations must be extrapolated over ~60 orders of magnitude. In this work, we develop a new approach negating the need for freezing to be observed. We collect statistics on solid-like particles in molecular dynamic simulations of supercooled liquids. 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 behaviour of nucleation at otherwise inaccessible conditions such that the nucleation of any system at small undercooling can be characterised alongside the thermodynamic quantities which define the first formed solids.