Crystal nucleation in binary hard-sphere mixtures: the effect of order parameter on the cluster composition

We study crystal nucleation in a binary mixture of hard spheres and investigate the composition and size of the (non)critical clusters using Monte Carlo simulations. In order to study nucleation of a crystal phase in computer simulations, a one-dimensional order parameter is usually defined to identify the solid phase from the supersaturated fluid phase. We show that the choice of order parameter can strongly influence the composition of noncritical clusters due to the projection of the Gibbs free-energy landscape in the two-dimensional composition plane onto a one-dimensional order parameter. On the other hand, the critical cluster is independent of the choice of the order parameter, due to the geometrical properties of the saddle point in the free-energy landscape, which is invariant under coordinate transformation. We investigate the effect of the order parameter on the cluster composition for nucleation of a substitutional solid solution in a simple toy model of identical hard spheres but tagged with different colours and for nucleation of an interstitial solid solution in a binary hard-sphere mixture with a diameter ratio q¼0.3. In both cases, we find that the composition of noncritical clusters depends on the order parameter choice, but are well explained by the predictions from classical nucleation theory. More importantly, we find that the properties of the critical cluster do not depend on the order parameter choice.