On the existence of a structural instability in sub-critical crystalline fluctuations in a supercooled liquid

Influence on crystal nucleation of an order-disorder transition among the subcritical clusters

Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of precritical clusters with varying degrees of structural disorder on their way to forming a growing stable crystal. To investigate the role precritical clusters play in nucleation, we develop a simple thermodynamic model for crystal nucleation in terms of cluster size and the degree of cluster order that allows us to alter the work of forming the precritical clusters without affecting the properties of the critical cluster. The steady state and transient nucleation behavior of the system are then studied numerically, for different microscopic ordering kinetics. We find that the model exhibits a generic order-disorder transition in the precritical clusters. Independent of the types of ordering kinetics, increasing the accessibility of disordered precritical clusters decreases both the steady state nucleation rate and the nucleation lag time. Furthermore, the interplay between the free-energy surface and the microscopic ordering kinetics leads to three distinct nucleation pathways.

Density functional theory for carbon dioxide crystal

We present a density functional approach to describe the solid-liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO2. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO2 at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.

Structure of finite sphere packings via exact enumeration: implications for colloidal crystal nucleation

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres N, and their diversity of structure and symmetry increases with increasing N and decreases with increasing hyperstaticity H≡N_{c}-N_{ISO}, where N_{c} is the number of pair contacts and N_{ISO}=3N-6. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction f of nuclei with order compatible with the bulk (rhcp) crystal decreases sharply with increasing N due to a high propensity for stacking faults, five- and near-fivefold symmetric structures, and other motifs that preclude rhcp order. While f increases with increasing H, a significant fraction of hyperstatic nuclei for N as small as 11 retain non-rhcp structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of N≲10 particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.