Recent Developments in Modeling Heteroepitaxy/Heterogeneous Nucleation by Dynamical Density Functional Theory
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LIQUIDS cooled below their melting point are metastable with respect to crystallization, and exist in such a state until nucleation occurs; i.e., seeds of the crystalline phase form via thermal fluctuations.[1] If these crystal-like fluctuations are larger than a critical size determined by the interplay of the driving force of freezing and the solid–liquid interface free energy, they grow further with a high probability, whereas the smaller ones tend to melt. The crystallites of the critical size are termed nuclei and their free energy of formation is the thermodynamic barrier of nucleation that the system needs to pass to reach the bulk crystalline state. Nucleation may be either homogeneous or heterogeneous. The homogeneous process is expected in an idealized pure undercooled liquid (which is well approximated by colloidal systems), where the internal fluctuations of the liquid enable the system in passing of the thermodynamic barrier toward crystallization, whereas heterogeneous nucleation takes place in ‘‘impure’’ liquids, where FRIGYES PODMANICZKY, Ph.D. Student, and GYO¨RGY TEGZE, Senior Scientist, are with the Wigner Research Centre for Physics, P.O.Box 49, Budapest 1525, Hungary. GYULA I. TO´TH, Post-Doctoral Research Fellow, is with the Wigner Research Centre for Physics, and also with the Department of Physics and Technology, University of Bergen, Alle´gaten 55, 5007 Bergen, Norway. LA´SZLO´ GRA´NA´SY, Professor, Scientific Advisor, is with the Wigner Research Centre for Physics, and also with the BCAST, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. Contact e-mail: [email protected] Manuscript submitted September 18, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS A
foreign surfaces (container walls or the perimeter of foreign particles) assist nucleation by reducing the free energy barrier associated with crystal nucleation. This happens, when the ordering of the liquid layers adjacent to the foreign wall helps the formation of the crystalline phase. This is, however, not necessarily so: a foreign wall may have a structure that is incompatible with that of the crystal, which may even hinder nucleation. Besides the essential role played in materials science, heterogeneous nucleation attracts a growing attention recently due to the emerging technological interest, for example, in micro- and nanopatterning techniques,[2] and controlling the related nanoscale processes, such as crystallization on patterned surfaces, the formation of quantum dots,[3–6] the controlling of the properties of partly crystalline glass ceramics,[1] phase selection in alloys,[7] and nucleation of metals on graphene.[8] Particulate additives are often used as nucleating agents to control the grain size of the solidified matter.[1] A similar mechanism appears to control the undercoolability of living organisms.[1] Despite its practical importance, and recent investigations in the field,[9–18] which include atomistic simulations,[9–14] phase-field,[15,16] and density functional studies,[17,18] further work is needed to
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