An Epitaxial Model for Heterogeneous Nucleation on Potent Substrates
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SOLIDIFICATION of metallic materials usually comprises two distinct stages: nucleation and growth. However, the overwhelming majority of research has been focused on the understanding of crystal growth with the nucleation stage being under-investigated mainly because of experimental difficulties.[1] The classical heterogeneous nucleation theory[2,3] considers the balance between the interfacial energy change and the volume free energy change during the creation of a spherical cap on the substrate, and uses contact angle as a measure of the substrate potency. The energy barrier for nucleation is surmounted stochastically by energy fluctuation in the melt, and a steady-state nucleation rate can be derived as a function of temperature by statistical analysis.[3] Hence, heterogeneous nucleation is treated as a stochastic process, which is dependent on both temperature and time. However, it is now realized that the classical heterogeneous nucleation theory is not applicable for potent nucleating substrates, where the contact angle is so small (effectively zero) that the creation of a spherical cap becomes unphysical.[4] Heterogeneous nucleation involving potent substrates is better treated as an athermal and deterministic process, in which the number of nucleation events is determined only by the driving force, being independent of time.[5,6] This has led to the development of the free growth model for grain ZHONGYUN FAN, Professor and Director of BCAST, is with the Brunel Solidification Centre for Advanced Technology (BCAST), Brunel University, Uxbridge, Middlesex, UB8 3PH, U.K. Contact e-mail: [email protected] Manuscript submitted April 19, 2012. Article published online November 8, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
initiation on a potent substrate.[5] The free growth model suggests that a new crystalline phase could start growing freely, without any delay, at an undercooling inversely proportional to the diameter of the substrate, indicating that grain initiation is neither time dependent nor stochastic. This means that growth starts first on the largest particle in the melt as soon as the required undercooling is reached, followed by progressively smaller ones as the undercooling is increased. Grain size is limited by recalescence, after which no further grain initiation occurs. In addition, there have been other approaches to heterogeneous nucleation on potent substrates. The hypernucleation hypothesis[7,8] suggests that a solute-rich layer structurally similar to a-Al forms on the surface of TiB2 particles even over the alloy liquidus, and that this layer serves as precursor for the formation of a-Al. The adsorption model[4,9] supposes that beyond a critical undercooling, a new crystalline phase forms on the substrate surface by adsorption of solute elements, and it is likely to act as a precursor for heterogeneous nucleation. At the atomic level, the process of heterogeneous nucleation on a potent substrate can be considered to be atom-by-atom building of the initial solid phase on a template. The
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