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  • 1
    Publication Date: 2011-08-19
    Description: A singular perturbation analysis valid for small grain-boundary slopes is used with the one-sided model for solidification to show that grain boundaries introduce imperfections into the symmetry of the developing cellular interfaces which rupture the junction between the family of planar shapes and the bifurcating cellular families. Undulating interfaces are shown to develop first near grain boundaries, and to evolve with decreasing temperature gradient either by a smooth transition from the almost planar family or by a sudden jump to moderate-amplitude cellular forms, depending on the growth rate.
    Keywords: SOLID-STATE PHYSICS
    Type: Physical Review B, 3rd Series (ISSN 0163-1829); 30; 3993-399
    Format: text
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  • 2
    Publication Date: 2019-08-28
    Description: The wide range of length and time scales involved in industrial scale solidification processes is demonstrated here by considering the Czochralski process for the growth of large diameter silicon crystals that become the substrate material for modern microelectronic devices. The scales range in time from microseconds to thousands of seconds and in space from microns to meters. The physics and chemistry needed to model processes on these different length scales are reviewed.
    Keywords: SOLID-STATE PHYSICS
    Type: In: Heat and mass transfer in materials processing (A93-10826 01-31); p. 137-153.
    Format: text
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