Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics

Abstract

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the time evolution of the order parameter in systems undergoing first-order phase transformations has been extended by Sekimoto to the level of two-point correlation functions. Here, this extended KJMA theory is applied to a kinetic Ising lattice-gas model, in which the elementary kinetic processes act on microscopic length and time scales. The theoretical framework is used to analyze data from extensive Monte Carlo simulations. The theory is inherently a mesoscopic continuum picture, and in principle it requires a large separation between the microscopic scales and the mesoscopic scales characteristic of the evolving two-phase structure. Nevertheless, we find excellent quantitative agreement with the simulations in a large parameter regime, extending remarkably far towards strong fields (large supersaturations) and correspondingly small nucleation barriers. The original KJMA theory permits direct measurement of the order parameter in the metastable phase, and using the extension to correlation functions one can also perform separate measurements of the nucleation rate and the average velocity of the convoluted interface between the metastable and stable phase regions. The values obtained for all three quantities are verified by other theoretical and computational methods. As these quantities are often difficult to measure directly during a process of phase transformation, data analysis using the extended KJMA theory may provide a useful experimental alternative. PACS numbers(s): 64.60. Qb,

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

“…(8), (12) and (13) are valid in the phase-field model using cell dynamics method. A similar study to test the validity of KJMA picture in Ising-type spin model was conducted by Shneideman et al [17] and Ramos et al [18].…”

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

“…Naively, faster relaxation for larger systems may appear unexpected, but is easily explained using the wellknown nucleation theory of Kolmogorov-Johnson-MehlAvrami [22,23]. We assume that critical droplets of the stable phase are created with a small uniform rate ǫ per unit time per unit area, and once formed, the droplet radius grows at a constant rate v. Then, the probability that any randomly chosen site is still not invaded by the stable phase is given by exp[−ǫ t 0 dt ′ V (t ′ )], where V (t ′ ) is the area of the region such that a nucleation event within this area will reach the origin before time t ′ .…”

Spatial dynamics of invasion: the geometry of introduced species

“…Originally formulated to model processes such as crystallization, nucleation theory readily addresses ecological clustering generated by local propagation in viscous populations (Gandhi et al, 1999). We emphasize that under multi-cluster growth of the exotic species, the dynamics of competition for space, specifically the timedependent decay of the resident's density, follows a powerful analytic approximation referred to as Avrami's law (Duiker and Beale, 1990;Ishibashi and Takagi, 1971;Ramos et al, 1999;Rikvold et al, 1994).…”