Nucleation and growth transformation kinetics

Erukhimovitch, Vitaly; Baram, J.

doi:10.1103/physrevb.51.6221

Cited by 44 publications

(28 citation statements)

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“…It thus follows: (17) Using the latter two equations together with Eqs. 7-11 yields transformations functions for given c o , σ s , N o and k. A range of combinations of these parameters was investigated, and in all cases the transformation could be fitted well with Eq.…”

Section: Appendix IImentioning

confidence: 99%

“…Notwithstanding the apparent wide range of applicability, many cases of deviations from JMAK kinetics have been reported [7,[15][16][17][18][19][20][21][22][23][24][25][26][27]. Understanding the causes of deviations from standard JMAK kinetics and the development of improved models is an important interdisciplinary research area.…”

Section: Introductionmentioning

confidence: 99%

“…Taking into account that changing from a regular array to a random distribution of growing product phase will generally speed up the latter stages of the transformation, this indicates that also for parabolic growth reactions which conform to the JMAK assumptions, JMAK kinetics is, at least in good † Note that this proof shows that the treatment proposed in Refs. [16,17] in which the so-called phantom nuclei are eliminated, is incorrect. Hence, this treatment cannot form the basis for an explanation of deviations from the JMAK theory (see also [4,5,6]).…”

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confidence: 99%

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Starink

2001

Journal of Materials Science

165

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If certain preconditions are met, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation is exactly accurate for nucleation and growth reactions with linear growth and is, at least, a good approximation for nucleation and growth reactions with parabolic growth. These preconditions include randomly distributed product phases, isotropic growth and constant equilibrium state. Mechanisms causing deviations from these preconditions include: capillarity effect, vacancy annihilation, blocking due to anisotropic growth. It is shown that deviations lead to a modification of the overall transformation, which can be approximated well by a single equation:

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Section: Appendix IImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Starink

2001

Journal of Materials Science

165

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“…For cases where such correlations are minimal (as for the case considered herein), it has been quite successful in describing experimental data [3,5], and theoretical generalizations can be readily made [2,6,15,16]. The KAMJ description can be used in calculations of kinetic parameters and activation energies, and it provides information about the nature of the phase transition, i.e.…”

Section: Figmentioning

confidence: 99%

“…My,05.40.+j,82.40.Py,68.10.Gw The kinetic process by which first-order phase transitions take place is an important subject of longstanding experimental and theoretical interest [1]. Nucleation is the most common of first-order transitions, and remains of a great deal of interest [2][3][4][5][6]. There are two fundamentally different cases, homogeneous and heterogeneous nucleation.…”

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Karttunen

Provatas

Ala-Nissilä

et al. 1998

Journal of Statistical Physics

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We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good argeement with theoretical predictions.PACS numbers: 64.60. My,05.40.+j,82.40.Py,68.10.Gw The kinetic process by which first-order phase transitions take place is an important subject of longstanding experimental and theoretical interest [1]. Nucleation is the most common of first-order transitions, and remains of a great deal of interest [2][3][4][5][6]. There are two fundamentally different cases, homogeneous and heterogeneous nucleation. Homogeneous nucleation is an intrinsic process where embryos of a stable phase emerge from a matrix of a metastable parent phase due to spontaneous thermodynamic fluctuations. Droplets larger than a critical size will grow while smaller ones decay back to the metastable phase [7,8]. More commonplace in nature is the process of heterogeneous nucleation. There, impurities or inhomogeneities catalyze a transition by making growth energetically favorable.Here we show that the concepts of nucleation and growth can be usefully applied to understand some aspects of slow combustion. We use a phase-field model of two coupled reaction-diffusion equations to study the nucleation and growth of combustion centers in twodimensional systems. Such continuum reaction-diffusion equations have been used extensively in physics, chemistry, biology and engineering to describe a wide range of phenomena from pattern formation to combustion. However, the connection of reaction-diffusion equations to nucleation and interface growth has received little attention.In a recent study of slow combustion in disordered media, Provatas et al. [9,10] showed that flame fronts exhibit a percolation transition, consistent with mean field theory, and that the kinetic roughening of the reaction front in slow combustion is consistent with the KardarParisi-Zhang (KPZ) [11] universality class. In this paper we make a further connection between slow combustion started by spontaneous fluctuations, and the classical theory of the nucleation and growth of droplets from a metastable phase.We generalize the model of Provatas et al. by including an uncorrelated noise source η(x, t), as a function of position x and time t. The model then consists of equations of motion for the temperature field T (x, t) and the local concentration if reactants C(x, t). The temperature satisfiesThe first term on the right-hand-side accounts for thermal diffusion, with diffusion constant D, the second term gives Newtonian cooling due to coupling with a heat bath of background temperature T 0 , with rate constant Γ, and the third term R(T, C) is the exothermic reaction rate as a function of temperature and concentration o...

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Growth of Polymer Crystals

Tashiro

2013

Handbook of Polymer Crystallization

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Nucleation and growth transformation kinetics

Cited by 44 publications

References 25 publications

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Growth of Polymer Crystals

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