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While in principle, finite temperature density functional theory (ftDFT)should be a powerful tool for the study of crystallization, in practice thishas not so far been the case. Progress has been hampered by technical problemswhich have plagued the study of the crystalline systems using the mostsophisticated Fundamental Measure Theory models. In this paper, the reasons forthe difficulties are examined and it is proposed that the tensor functionalscurrently favored are in fact numerically unstable. By reverting to an older,more heuristic model it is shown that all of the technical difficulties areeliminated. Application to a Lennard-Jones fluid results in a demonstration ofpower of ftDFT to describe crystallization in a highly inhomogeneous system.First, we show that droplets attached to a slightly hydrophobic wallcrystallize spontaneously upon being quenched. The resulting crystallites areclearly faceted structures and are predominantly HCP structures. In contrast,droplets in a fully periodic calculational cell remain stable to lowertemperatures and eventually show the same spontaneous localization of thedensity into 'atoms' but in an amorphous structure having many of thestructural charactersitics of a glass. A small change of the protocol leads, atthe same temperature, to the formation of crystals, this time with the FCCstructure typical of bulk Lennard-Jones solids. The FCC crystals have lowerfree energy than the amorphous structures which in turn are more stable thanthe liquid droplets. It is demonstrated that as the temperature is raised, thefree energy differences between the structures decreases until the solidclusters become less stable than the liquid droplets and spontaneously melt.The presence of energy barriers separating the various structures is thereforeclearly demonstrated.

Classical density functional theory, unconstrained crystallization, and polymorphic behavior