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  • 1
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    Directional solidification in an imperfect furnace (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The upward directional solidification of a binary alloy in which the rejected solute is more dense than the solvent is considered. The system is stably stratified both thermally and solutally. If heat is lost through the sidewalls, horizontal thermal gradients drive a steady double-diffusive convection. Solidification cells with small aspect ratios (width/length) A are considered, and asymptotic solutions to the steady double-diffusive system are obtained as A tends to 0 under the assumption heat losses are also small. When the thermal Grashof number is large, buoyancy boundary layers are at the sidewalls. The shape of the crystal-melt interface is determined by the coupled effects of local thermodynamic equilibrium, diffusion and convection.
    Keywords: SOLID-STATE PHYSICS
    Type: PCH/PhysicoChemical Hydrodynamics (ISSN 0191-9059); 9; 1-2,; 9-14
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  • 2
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    Pulsatile instability in rapid directional solidification: Strongly-nonlinear analysis (1992)
    In:  CASI
    Details
    Publication Date: 2013-08-29
    Description: In models of rapid directional solidification, non-equilibrium interfacial conditions are employed. As a result, there is an oscillatory mode of instability, as well as the steady cellular mode, found in the equilibrium model of Mullins and Sekerka. When the temperature field is decoupled from the problem, the preferred wave number for the oscillatory mode is zero, and the interface pulsates in time while remaining spatially uniform. Results from multiple scale analyses in the two limiting cases of the parameters are reported. In these limits, it is found that the instability is a bifurcation to relaxation oscillations; these nonlinear oscillations may be related to the observed microstructure that results from rapid solidification processes such as laser surface remelting.
    Keywords: SOLID-STATE PHYSICS
    Type: ESA, Proceedings of the 8th European Symposium on Materials and Fluid Sciences in Microgravity, Volume 2; p 559-562
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  • 3
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    Shallow cells in directional solidification (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The existing theory on two-dimensional transitions (appropriate to thin parallel-plate geometries) is presented in such a way that it is possible to identify easily conditions for the onset of shallow cells. Conditions are given under which succinonitrile-acetone mixtures should undergo supercritical bifurcation in experimentally accessible ranges. These results suggest a means for the quantitative test of the Mullins and Sekerka (1964) model and its weakly nonlinear extensions.
    Keywords: SOLID-STATE PHYSICS
    Type: Physical Review Letters (ISSN 0031-9007); 63; 573-575
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  • 4
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    Directional solidification with heat losses (1988)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered. Heat losses from the sidewalls produce curved isotherms, interface deformations, and melt convection. An asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions are obtained for the resulting melt convection, interface deflection, and the distribution of heat and solute. The model is compared to the numerical results of Chang and Brown (1983) which exclude the effects of solute buoyancy and thermodynamic equilibrium at the interface. The radial segregation at the interface (consistent with both interface shapes and temperature fields) is computed, and it is found that the radial segregation is independent of interfacial shapes; the radial segregation cannot be calculated from only a knowledge of the interface shape.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 91; 4, Se; 538-556
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  • 5
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    Similarity solutions for phase-change problems (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A modification of Ivantsov's (1947) similarity solutions is proposed which can describe phase-change processes which are limited by diffusion. The method has application to systems that have n-components and possess cross-diffusion and Soret and Dufour effects, along with convection driven by density discontinuities at the two-phase interface. Local thermal equilibrium is assumed at the interface. It is shown that analytic solutions are possible when the material properties are constant.
    Keywords: SOLID-STATE PHYSICS
    Type: Metallurgical Transactions A - Physical Metallurgy and Materials Science (ISSN 0360-2133); 20A; 225-235
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  • 6
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    Thermal effects in rapid directional solidification - Linear theory (1993)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: We study the morphological instability of the planar solid/liquid interface for a unidirectionally-solidified dilute binary mixture. We use a model developed by Boettinger et al. (1985, 1986), Aziz (1982), and Jackson et al. (1980), which allows for nonequilibrium effects on the interface through velocity-dependent segregation and attachment kinetics. Two types of instabilities are found in the linear stability analysis: (1) a cellular instability, and (2) an oscillatory instability driven by disequilibrium effects. Merchant and Davis (1990) characterized these instabilities subject to the frozen-temperature approximation (FTA). The present work relaxes the FTA by including the effects of latent heat and the full temperature distribution. Thermal effects slightly postpone the onset of the cellular instability but dramatically postpone the onset of the oscillatory instability; however, the absolute-stability conditions, at which at high speed the cellular and oscillatory instabilities are suppressed, remain unchanged from the FTA.
    Keywords: SOLID-STATE PHYSICS
    Type: Acta Metallurgica et Materialia (ISSN 0956-7151); 41; 7; p. 2025-2043.
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  • 7
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    Morphological instability in epitaxially strained dislocation-free solid films - Linear stability theory (1993)
    In:  Other Sources
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    Publication Date: 2019-08-28
    Description: The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Applied Physics (ISSN 0021-8979); 73; 10:00 PM; p. 4955-4970.
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  • 8
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    Crystal growing from the melt (1987)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The mechanical and electrical properties of crystals produced by a unidirectional process depend strongly on the temperature and flow fields since these control the concentration of solute at the melt-crystal interface. The solute gradient there drives morphological instabilities that lead to cellular or dendritic interfaces. In the presentation several features of flow-solidification interactions will be discussed. These will include the effects of convection driven by density changes and buoyancy and the imposition of forced flow.
    Keywords: SOLID-STATE PHYSICS
    Type: Interdisciplinary issues in materials processing and manufacturing; Dec 13, 1987 - Dec 18, 1987; Boston, MA; United States
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  • 9
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    Buoyancy effects of a growing, isolated dendrite (1991)
    In:  Other Sources
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    Publication Date: 2019-08-27
    Description: The buoyancy effect of a growing isolated dendrite on the solidification process in the undercooling liquid material was investigated by developing an analytic solution to the growth/convection problem in powers of a buoyancy parameter G. The solution depends on the Prandtl number P and the Stefan number S (undercooling) for the local velocity and thermal fields and also the buoyant alteration of the interface shape. Results suggest that buoyancy effect for metals (low P) may be qualitatively different from that for organics (high P).
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 114; 1-2,; 153-185
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