On the role of confinement on solidification in pure materials and binary alloys

Department of Materials Science and Engineering, Iowa State University, Ames, Iowa, United States
Philosophical Magazine A 07/2006; 86(24). DOI: 10.1080/14786430500157060
Source: arXiv


We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.

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Available from: Jonathan Dantzig, Jun 13, 2013
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    • "[30] [26] were carried out with phase-field models that do not describe alloy solidification well, because the solute diffusivity was taken identical in both phases. Works that use quantitative models for alloy solidification are either limited to the vicinity of the cellular bifurcation [31] or to confined systems [32] [33] [34]. Here, we present preliminary results of three-dimensional phase-field simulations of dilute binary alloys in domains that are large enough to contain between 15 and 40 cells, such that the effect of confinement (if present) is weak. "
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    ABSTRACT: The structure and dynamics of cellular solidification fronts produced during the directional solidification of dilute binary alloys are studied by phase-field simulations. A quantitative phase-field model in conjunction with a multi-scale simulation algorithm allows us to simulate arrays with 10-40 cells in three dimensions on time scales that are long enough to allow for a significant reorganization of the array. We analyze the geometry of the complex two-phase structure (mushy zone) and extract the fraction of solid and the connectivity of the two phases as a function of depth. We find a transition from stable arrays at high values of the crystalline anisotropy to unsteady arrays at low anisotropy that continuously exhibit tip splitting and cell elimination events.
    Full-text · Article · Jan 2014 · Journal of Crystal Growth
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    ABSTRACT: Important phenomena in materials processing, such as dendritic growth during solidification, involve a wide range of length scales from the atomic level up to product dimensions. The phase-field approach, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with a part of this range of scales, from few tens of microns to millimeters, and provides an effective continuum modeling technique for moving boundary problems. A serious limitation of the usual representation of the phase-field model however, is that it fails to keep track of the underlying crystallographic anisotropy, and thus is unable to capture lattice defects and model polycrystalline microstructure without non-trivial modifications. The phase-field crystal (PFC) model on the other hand, is a phase field equation with periodic solutions that represent the atomic density. It natively incorporates elasticity, and can model formation of polycrystalline films, dislocation motion and plasticity, and nonequilibrium dynamics of phase transitions in real materials. Because it describes matter at the atomic length scale however, it is unsuitable for coping with the range of length scales in problems of serious interest. This thesis takes a first step towards developing a unified multiscale approach spanning all relevant lengths, from the nanoscale up, by combining elements from the phase-field and phase-field crystal modeling approaches, perturbative renormalization group theory, and adaptive mesh refinement. A chapter of this thesis also examines the effect of confinement on dendritic growth, during equiaxed solidification in a pure material and the directional solidification of a dilute binary alloy, using phase-field models. Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6687. Advisers: Jonathan A. Dantzig; Nigel D. Goldenfeld. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. Includes bibliographical references (leaves 128-136)
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    ABSTRACT: The phase field approach is used to model heterogeneous crystal nucleation in an undercooled pure liquid in contact with a foreign wall. We discuss various choices for the boundary condition at the wall and determine the properties of critical nuclei, including their free energy of formation and the contact angle as a function of undercooling. For particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly nonclassical behavior, where the contact angle decreases from its value taken at the melting point towards complete wetting at a critical undercooling, an analogue of the surface spinodal of liquid-wall interfaces.
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