Narrowing down the cause of the hard-sphere nucleation discrepancy: The free energy of precritical nuclei is consistent with predictions

Predicting the rate of crystal nucleation is among the most substantial long-standing challenges in condensed matter. In the system most studied (hard-sphere colloids), the discrepancy between experiments and computer simulations is more than 10 orders of magnitude. The situation with other materials (such as water) is no better. Here, we address this challenge with two developments. First, our work is a marked improvement in the precision of mapping the state point of experiments to simulation. For this, we used a combination of novel machine-learning methods for particle tracking and higher-order correlation functions. Second, we consider the free energy of precritical nuclei using confocal microscopy. These are in agreement with computer simulation. This is the first time that such free energies have been successfully compared between experiment and simulation in any material as far as we are aware.