A review on the theory of stable dendritic growth

Abstract

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)’.

Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

“…In conclusion, we note several important aspects of the development of the theory under consideration in the future. First, since in practice the bulk phase transitions often occur together with directional solidification and the formation of a two-phase zone, it is important to combine the theories of bulk and directional growth of a new phase in a metastable liquid, taking into account previously developed approaches [59][60][61][62][63][64][65][66][67][68][69]. Second, the present theory of evolution of an ensemble of ellipsoidal particles during the intermediate stage should be extended to the final stage when such processes as Ostwald ripening, coagulation and disintegration of particles are capable to occur.…”

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid

“…It is well known that the processes of phase transformations from a metastable liquid state to a solid state are widely spread across various research areas ranging from materials physics, geophysics and chemical industry to biophysics and life sciences [1][2][3][4][5][6][7][8][9][10]. These processes are accompanied by nucleation and growth of crystals at the initial and intermediate stages of phase transformation in supercooled melts and supersaturated solutions, as well as their coagulation, Ostwald ripening and disintegration at the concluding stage.…”

Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz–Slyozov theory

“…Let us especially emphasize in conclusion that the present theory can be developed to take into account the effects of mass influx and withdrawal of crystals [35][36][37][38][39], the shape of growing particles [40,41], the simultaneous occurrence of bulk and directional phase transformations [42][43][44][45][46], concurrent crystallization and polymerization [47,48] and external stochastic fluctuations [49].…”