Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 379, Issue 2205, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2020.0325
Keywords
dendrites; selection criterion; microscopic solvability; heat and mass transfer; phase transformations; convection; rapid crystallization
Categories
Funding
- Russian Science Foundation [20-61-46013]
- German Science Foundation (DFG-Deutsche Forschungsgemeinschaft) [GA 1142/11-1]
- Russian Science Foundation [20-61-46013] Funding Source: Russian Science Foundation
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This review article summarizes the main outcomes of stable dendritic growth theories in melts, focusing on heat and mass transfer mechanisms and the determination of main process parameters. It also introduces stability analysis and selection criteria, discussing crystal structural states and transitions.
This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters-the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.
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