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On the kinetics of nucleation and growth reactions in inhomogeneous systems

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Abstract

Nucleation and growth kinetics in systems with a small degree of inhomogeneity are usually modeled through the KJMA (Kolmogorov–Johnson–Mehl–Avrami) theory, that is by using the local values of the nucleation and growth rates which are proper to the region where the transition takes place. In this study, a general expression for the kinetics is derived which applies, in principle, to any degree of inhomogeneity and conforms to previous approaches. The model is employed to study, analytically, first order corrections to the KJMA formula in the case of simultaneous nucleation and interface-limited growth. It is shown that under these circumstances, the nucleus shape is a circle (two-dimensional) whose center is displaced with respect to the point where the nucleation event occurs. The displacement of the center and the radius of the nucleus are both functions of time. The behavior of the Avrami exponent and the impingement factor as a function of the fraction of transformed volume is investigated and discussed.

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Notes

  1. Strictly speaking the evolution of the local curvature of the nucleus, under interface-limited growth, is governed by the equation \( {\frac{\text{d}\Re }{{\rm d}t}} = {\frac{\partial \Re }{\partial t}} + {\frac{\partial \Re }{\partial x}}\upsilon_{x} \equiv \alpha c(x) \) where \( \upsilon_{x} = {\frac{\text{d}\Re }{{\rm {d}}t}}\hat{n}\hat{x} \) is the local growth rate along x and \( \hat{n} \) is the normal to the nucleus surface. Combining these equations one gets \( {\frac{\partial \Re }{\partial t}} = \alpha c(x)\left[ {1 + {\frac{\partial \Re }{\partial x}}\,{\frac{\partial y/\partial x}{{\sqrt {1 + (\partial y/\partial x)^{2} } }}}} \right]. \) Equation 10 holds provided \( \partial \Re /\partial x \ll 1. \) It can be proved that this condition is fulfilled in the case r0/λ ≪ 1 here considered.

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  1. Dipartimento di Scienze e Tecnologie Chimiche, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Rome, Italy

    Massimo Tomellini

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  1. Massimo Tomellini
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Tomellini, M. On the kinetics of nucleation and growth reactions in inhomogeneous systems. J Mater Sci 45, 733–743 (2010). https://doi.org/10.1007/s10853-009-3992-8

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