Kinetics of rapid crystal growth: phase field theory versus atomistic simulations

Galenko, Peter; Salhoumi, A.; Ankudinov, Vladimir

doi:10.1088/1757-899x/529/1/012035

Cited by 6 publications

(14 citation statements)

References 25 publications

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“…This equation has a form of the hodograph equation that relates the interface acceleration and velocity to the interface curvature and the driving force for the phase transformation. The interface velocity predicted by this equation has been shown to be in good agreement with the results of MD simulations performed for pure metals and alloys [25,[32][33][34][35].…”

Section: Introductionsupporting

confidence: 75%

“…The results of MD simulations discussed for Cr and Si in §2b are related in this section to the solution of PFM, particularly, for the steady-state case, equations (3.3)- (3.7). This solution type has previously been applied to describe the MD data on the crystallization of Fe [7], Cu 50 Zr 50 and Ni 50 Al 50 [10] (see refs [25,32,33]). The material parameters used in PFM for Cr and Si are shown 3) (red circles [57]).…”

Section: (C) Comparison With MD Simulation Datamentioning

confidence: 99%

“…The results of MD simulations discussed for Cr and Si in §2b are related in this section to the solution of PFM, particularly, for the steady-state case, equations (3.3)–(3.7). This solution type has previously been applied to describe the MD data on the crystallization of Fe [7], Cu 50 Zr 50 and Ni 50 Al 50 [10] (see refs [25,32,33]). The material parameters used in PFM for Cr and Si are shown in tables 1 and 2, respectively, where the relaxation time of gradient flow, τ ϕ , the diffusion pre-factor, Dϕ0, and the energy barrier, E A , are considered as free parameters at a fixed pseudo-glass transition temperature T AB .…”

Section: Phase-field Model Predictionsmentioning

confidence: 99%

See 2 more Smart Citations

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

Karim

Salhoumi

et al. 2021

Phil. Trans. R. Soc. A.

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The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

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Section: Introductionsupporting

confidence: 75%

Section: (C) Comparison With MD Simulation Datamentioning

confidence: 99%

Section: Phase-field Model Predictionsmentioning

confidence: 99%

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Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

Karim

Salhoumi

et al. 2021

Phil. Trans. R. Soc. A.

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“…Taking into account (48), the expression for the velocitydependent interface width follows from the second term in square brackets in right-hand side of (54) as…”

Section: The Hodograph Equation and Traveling Waves With The Double-w...mentioning

confidence: 99%

Fast traveling waves in the phase-field theory: effective mobility approach versus kinetic energy approach

Salhoumi

Galenko

2020

J. Phys.: Condens. Matter

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A phase-field model for small and large driving forces on solidification and melting of a pure substance or alloys is formulated. Derivations of the phase-field model are based on the effective mobility approach and on the kinetic energy approach to analyze fast phase transformation from metastable liquid to solid phase. A hodograph equation (an accelerationvelocity dependent equation of the Gibbs-Thomson type) which predicts the non-linear behavior in the velocity of the crystal-liquid interface is found at the large driving force on transformation and analyzed for different thermodynamic potentials. Traveling wave solutions of this equation are found for double-well and double-obstacle potentials. The velocity-dependent traveling waves as a function of driving force on transformation exhibit non-linearity of the solutions. Namely, in the relationship 'velocity-driving force' exists a maximum at a fixed undercooling which is very well known in the solidification of glassforming metals and alloys. The predicted solidification velocity is quantitatively compared with the molecular dynamics simulation data obtained by Tang and Harrowell (2013 Nat. Mater. 12 507-11) for the solidification of congruently melting Cu-Zr binary alloy. The comparison confirms a crucial role of local non-equilibrium such as relaxation of gradient flow in the quantitative description of fast phase transformations.

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“…Note that the accuracy of these methods is usually insignificant, especially, for the systems at deep supercooling. On the other hand, classical molecular dynamics simulations are an excellent tool to extract complete information about a crystallizing system as well as for the study of nucleation and growth processes [19,25,21,24,23,20,22]. In this regard, the results of molecular dynamics simulations can be used to evaluate the kinetic rate factors.…”

Section: Introductionmentioning

confidence: 99%

Direct evaluation of attachment and detachment rate factors of atoms in crystallizing supercooled liquids

Yarullin

Galimzyanov

Мокшин

2020

The Journal of Chemical Physics

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Kinetic rate factors of crystallization have a direct effect on formation and growth of an ordered solid phase in supercooled liquids and glasses. Using crystallizing Lennard-Jones liquid as an example, in the present work we perform a direct quantitative estimation of values of the key crystallization kinetic rate factors -the rate g + of particle attachments to a crystalline nucleus and the rate g − of particle detachments from a nucleus. We propose a numerical approach, according to which a statistical treatment of the results of molecular dynamics simulations was performed without using any model functions and/or fitting parameters. This approach allows one to accurately estimate the critical nucleus size n c . We find that for the growing nuclei, whose sizes are larger than the critical size n c , the dependence of these kinetic rate factors on the nucleus size n follows a power law. In the case of the subnucleation regime, when the nuclei are smaller than n c , the n-dependence of the quantity g + is strongly determined by the inherent microscopic properties of a system and this dependence cannot be described in the framework of any universal law (for example, a power law). It has been established that the dependence of the growth rate of a crystalline nucleus on its size goes into the stationary regime at the sizes n > 3n c particles.

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Kinetics of rapid crystal growth: phase field theory versus atomistic simulations

Cited by 6 publications

References 25 publications

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

Fast traveling waves in the phase-field theory: effective mobility approach versus kinetic energy approach

Direct evaluation of attachment and detachment rate factors of atoms in crystallizing supercooled liquids

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