Abstract:The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its … Show more
“…This results in a finer-grained structure of the solid phase of the material and a shorter crystallization time for the sample. Figure 6The tip radius ( a ) and growth velocity ( b ) of a dendritic crystal according to the theory (expressions (3.11) and (4.18), lines) and enthalpy method simulations (symbols) for two-dimensional nickel dendrites growing in pure melt (n=4) at various flow velocities U (numbers in the inset) [58]. (Online version in colour.…”
Section: A Behaviour Of the Main Functionsmentioning
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)’.
“…This results in a finer-grained structure of the solid phase of the material and a shorter crystallization time for the sample. Figure 6The tip radius ( a ) and growth velocity ( b ) of a dendritic crystal according to the theory (expressions (3.11) and (4.18), lines) and enthalpy method simulations (symbols) for two-dimensional nickel dendrites growing in pure melt (n=4) at various flow velocities U (numbers in the inset) [58]. (Online version in colour.…”
Section: A Behaviour Of the Main Functionsmentioning
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)’.
“…In conclusion, it is important to note the development paths of this theory in the future. It is important, for example, to determine the shape of dendritic crystals in the presence of impurities and convective flows in an undercooled liquid, as well as to study the case of local non-equilibrium (rapid) crystallization [26,[32][33][34][35][36][37][38][39][40]. As a final note, a review of recent advances in these research areas is presented in an accompanying article of this theme issue [41].…”
This article is devoted to the study of the tip shape of dendritic crystals grown from a supercooled liquid. The recently developed theory (Alexandrov & Galenko 2020
Phil. Trans. R. Soc. A
378
, 20190243. (
doi:10.1098/rsta.2019.0243
)), which defines the shape function of dendrites, was tested against computational simulations and experimental data. For a detailed comparison, we performed calculations using two computational methods (phase-field and enthalpy-based methods), and also made a comparison with experimental data from various research groups. As a result, it is shown that the recently found shape function describes the tip region of dendritic crystals (at the crystal vertex and some distance from it) well.
This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.
“…The fundamental understanding of dendrite growth relies on the pioneering works of Ivantsov [10] which latches the Péclet number to the thermodynamical driving force, and the microscopic solvablity theory [11,12,12] which provides a selection criterion for the charactertistic wavelength of the tip [13][14][15][16][17][18][19][20][21][22]. As for secondary branching, the conventional theory [23][24][25][26] postulates that side-branches stem from selective (thermal) noise amplification close to the tip.…”
The present work is devoted to the phenomenon of induced side branching stemming from the disruption of free dendrite growth. Therein, we postulate that the secondary branching instability can be triggered by the departure of the morphology of the dendrite from its steady state shape. Thence, the instability results from the thermodynamic trade-off between non monotonic variations of interface temperature, surface energy, kinetic anisotropy and interface velocity within the Gibbs Thomson equation. For purposes of illustration, the toy model of capillary anisotropy modulation is prospected both analytically and numerically by means of phase field simulations. It is evidenced that side branching can befall both smooth and faceted dendrites, at a normal angle from the front tip which is specific to the nature of the capillary anisotropy shift applied.
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