The Influence of Order on the Nucleation Barrier
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where k is the Boltzmann constant, T is absolute temperature, and A* is a prefactor that contains information about the dynamical processes of nucleation. However, nucleation is more complex than is described by this classical onedimensional cluster-size evolution. For example, the interface-limited kinetics cannot quantitatively describe nucleation when long-range diffusion processes become comparable with interfacial ones; a quantitative description requires that these two stochastic fluxes be coupled.5,6 It is becoming increasingly clear that order-parameter fluctuations (i.e., fluctuations in the order parameters describing the structural, chemical, magnetic, etc., order) can also couple with the fluctuations associated with nucleation. For homogeneous nucleation, small regions of the new phase appear stochastically in time and space. Mostly, however, nucleation is heterogeneous, occurring randomly in time but at specific catalytic sites. Again, ordering is crucial; for the heterogeneous nucleation of solidification, it is the ordering of the liquid adjacent to the nucleation substrate.
The Influence of
Order on the Nucleation Barrier
K.F. Kelton, A.L. Greer, D.M. Herlach, and D. Holland-Moritz Abstract While it is conventionally thought that liquids turn to solids at their “freezing” point, it is often the case that materials must be supercooled (cooled below the freezing temperature) before nucleation actually happens. There is growing evidence that coupled processes, including chemical–structural ordering and orientational–translational ordering, are among the factors that affect exactly when and how nucleation occurs in liquids and crystals. Recent density functional calculations have demonstrated that such coupled routes, which are not incorporated within the one-dimensional framework of the classical theory, can dramatically influence the overall nucleation process. Here, some recently observed cases in metal alloys are discussed, establishing a relationship between developing order in undercooled liquids and the nucleation barrier, the influence of magnetic ordering on nucleation in Co-based melts, and the role of interfacial structure and chemistry on the catalytic efficiency of inoculants for heterogeneous nucleation.
Containerless Processing
Keywords: containerless processing, liquids, magnetic order, nucleation, quasicrystals.
Introduction In many cases, first-order phase transitions are sluggish. For example, Fahrenheit in 1724 noted that water often can be cooled to a temperature far below its freezing temperature before ice begins to form.1 Turnbull showed that this ability to undercool is common, even in metallic liquids.2,3 The barrier to the initial formation of the crystal from the liquid is a critical factor in the process of nucleation.4 Nucleation is not limited to the crystallization of liquids; it is the starting point for most first-order phase transitions of interest in the physical sciences. It can also play a fundamental role in transitions in biological and medical systems. The
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