Steady-state kinetics of diffusionless first order phase transformations

Chan, S. H.

doi:10.1063/1.434833

Cited by 138 publications

(80 citation statements)

References 8 publications

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“…In the previous paper [21], using this phase-field model and the cell dynamics method, we could successfully simulate the interface-limited growth of a single nucleus [25] with a constant growth velocity v which is close to the theoretical prediction [21,25] …”

Section: Phase-field Model and Cell Dynamics Methodsmentioning

confidence: 99%

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Iwamatsu

2008

The Journal of Chemical Physics

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Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m = 3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids 160, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.

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Section: Phase-field Model and Cell Dynamics Methodsmentioning

confidence: 99%

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Iwamatsu

2008

The Journal of Chemical Physics

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“…Currently, the phase-field approach is mostly used as a numerical tool for tracing immiscible 30 interfaces [2,3,4,5]. In the current work, however, this approach is used as a comprehensive physical model capable of describing the thermo-and hydrodynamic evolution of multiphase binary mixtures with undergoing phase transformations.…”

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confidence: 99%

“…For the Fick's diffusion the diffusive flux is taken to be proportional to the gradient of concentration, There are two basic models to define the kinetics of the phase transition [28,29,30]. In the Landau-Ginzburg model, the rate of the concentration changes is assumed to be proportional to conservation law, which is the case for the diffusion process in a binary mixture, when concentration (used as a order parameter) obeys the law of conservation of the species mass [29].…”

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confidence: 99%

On the phase-field modelling of a miscible liquid/liquid boundary

Xie

Vorobev

2016

Journal of Colloid and Interface Science

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Mixing of miscible liquids is essential for numerous processes in industry and nature. Mixing, i.e. interpenetration of molecules through the liquid/liquid boundary, occurs via interfacial diffusion.Mixing can also involve externally or internally driven hydrodynamic flows, and can lead to de- approach that is used as a physics-based model for the thermo-and hydrodynamic evolution of binary mixtures. Within this approach, the diffusion flux is defined through the gradient of chemical potential, and, in particular, includes the effect of barodiffisuon. The dynamic interfacial stresses at the miscible interface are also taken into account. The simulations showed that such an approach can accurately reproduce the shape of the solute/solvent boundary, and some aspects of the diffusion dynamics. Nevertheless, all experimentally-observed features of the diffusion motion of the solute/solvent boundary, were not reproduced.

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“…Dynamics plays a central role in proper ferroelastic transitions 2,5,6,7,8,9,10,11,12,13,14,15,16,17 . As noted, these materials undergo diffusionless, displacive transitions, with strain (components) as the order parameter, and develop complex microstructures in their dynamical evolution, finally forming spatially varying, multiscale 'textures' or strain patterns.…”

Section: Introductionmentioning

confidence: 99%

“…Textured improper ferroelastics include materials of technological importance such as superconducting cuprates 18 and colossal magnetoresistance (CMR) manganites 19 . Many dynamical models have been invoked to follow aspects of (proper) ferroelastic pattern formation 5,6,7,8,9,10,11,12,13,14,15,16,17 such as nucleated twin-front propagation; width-length scaling of twin dimensions 20,21 ; tweed 22,23,24 ; stress effects; elastic domain misfits; and acoustic noise generation 25 .…”

Section: Introductionmentioning

confidence: 99%

Ferroelastic dynamics and strain compatibility

et al. 2003

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We derive underdamped evolution equations for the order-parameter (OP ) strains of a ferroelastic material undergoing a structural transition, using Lagrangian variations with Rayleigh dissipation, and a free energy as a polynomial expansion in the N = n + Nop symmetry-adapted strains. The Nop strain equations are structurally similar in form to the Lagrange-Rayleigh 1D strain dynamics of Bales and Gooding (BG), with 'strain accelerations' proportional to a Laplacian acting on a sum of the free energy strain derivative and frictional strain force. The tensorial St. Venant's elastic compatibility constraints that forbid defects, are used to determine the n non-order-parameter strains in terms of the OP strains, generating anisotropic and long-range OP contributions to the free energy, friction and noise. The same OP equations are obtained by either varying the displacement vector components, or by varying the N strains subject to the Nc compatibility constraints. A Fokker-Planck equation, based on the BG dynamics with noise terms, is set up. The BG dynamics corresponds to a set of nonidentical nonlinear (strain) oscillators labeled by wavevector k, with competing short-and long-range couplings. The oscillators have different 'strain-mass' densities ρ(k) ∼ 1/k 2 and dampings ∼ 1/ρ(k) ∼ k 2 , so the lighter large-k oscillators equilibrate first, corresponding to earlier formation of smaller-scale oriented textures. This produces a sequential-scale scenario for post-quench nucleation, elastic patterning, and hierarchical growth. Neglecting inertial effects yields a late-time dynamics for identifying extremal free energy states, that is of the time-dependent Ginzburg-Landau form, with nonlocal, anisotropic Onsager coefficients, that become constants for special parameter values. We consider in detail the two-dimensional (2D) unit-cell transitions from a triangular to a centered rectangular lattice (Nop = 2, n = 1, Nc = 1); and from a square to a rectangular lattice (Nop = 1, n = 2, Nc = 1) for which the OP compatibility kernel is retarded in time, or frequencydependent in Fourier space (in fact, acoustically resonant in ω/k). We present structural dynamics for all other 2D symmetry-allowed ferroelastic transitions: the procedure is also applicable to the 3D case. Simulations of the BG evolution equations confirm the inherent richness of the static and dynamic texturings, including strain oscillations, domain-wall propagation at near sound speeds, grain-boundary motion, and nonlocal 'elastic photocopying' of imposed local stress patterns.

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Steady-state kinetics of diffusionless first order phase transformations

Cited by 138 publications

References 8 publications

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

On the phase-field modelling of a miscible liquid/liquid boundary

Ferroelastic dynamics and strain compatibility

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