Lattice induced crystallization of nanodroplets: the role of finite-size effects and substrate properties in controlling polymorphism

Harvesting nucleating structures in nanoparticle crystallization: The example of gold, silver, and iron

The thermodynamics and kinetics of nanoparticle crystallization, as opposed to bulk phases, may be influenced by surface and size effects. We investigate the importance of such factors in the crystallization process of gold, silver, and iron nanodroplets using numerical simulations in the form of molecular dynamics combined with path sampling. This modeling strategy is targeted at obtaining representative ensembles of structures located at the transition state of the crystallization process. A structural analysis of the transition state ensembles reveals that both the average size and location of the critical nucleation cluster are influenced by surface and nanoscale size effects. Furthermore, we also show that transition state structures in smaller nanodroplets exhibit a more ordered liquid phase, and differentiating between a well-ordered critical cluster and its surrounding disordered liquid phase becomes less evident. All in all, these findings demonstrate that crystallization mechanisms in nanoparticles go beyond the assumptions of classical nucleation theory.

Explicitly stable fundamental-measure-theory models for classical density functional theory

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness [Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)2470-004510.1103/PhysRevE.98.012604]. It is shown that within the present paradigm, explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities. It is argued that this is an acceptable trade-off since the main value of DFT lies in the study of dense systems. Explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular White Bear models while sharing some of their weaknesses when applied to non-close-packed solids.

Out-of-Equilibrium Polymorph Selection in Nanoparticle Freezing

The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physicochemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via the cooling rate during nanoparticle freezing in the case of Ni₃Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow us to rationalize the complex nucleation process, discovering a switch between two kinetic pathways, yielding the equilibrium structure at room temperature and an alternative metastable one at higher temperature. Our findings address the key challenge in the synthesis of nanoalloys for technological applications, i.e., rationally exploiting the competition between kinetics and thermodynamics by designing a treatment history that forces the system into desirable metastable states.

How crystals form: A theory of nucleation pathways

Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical nucleation pathways based on no input other than the interaction potential of the particles making up the system. The theory is formulated directly in terms of the density field, thus forgoing the need to define collective variables. It is illustrated by application to diffusion-limited nucleation of macromolecules in solution for both liquid-liquid separation and crystallization. Both involve nonclassical pathways with crystallization, in particular, proceeding by a two-step mechanism consisting of the formation of a dense-solution droplet followed by ordering originating at the core of the droplet. Furthermore, during the ordering, the free-energy surface shows shallow minima associated with the freezing of liquid into solid shells, which may shed light on the widely observed metastability of nanoscale clusters.

Classical density functional theory, unconstrained crystallization, and polymorphic behavior

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into "atoms" but in an amorphous structure having many of the structural characteristics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the fcc structure typical of bulk Lennard-Jones solids. The fcc crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decrease until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.