Nucleation and Growth Model of Martensitic Phase Transition

H. Abe, K. Ohshima and T. Suzuki

Institute of Applied Physics, University of Tsukuba, Tsukuba 305, Japan

Mater. Trans. JIM, Vol.36, pp. 1200-1205 (1995). 

A two-dimensional idealized nucleation and growth (2D-ING) model is considered, in order to understand the experimental results relating to martensitic phase transition. It is an extension of the Kakeshita model for nucleation process (Kakeshita et al. : Mater. Trans., JIM, 34 (1993), 423 ), based on the nucleation probability derived from a nucleation barrier. We extend the Kakeshita model to an ideal growth process by introducing the concept of a dynamic embryo and a frozen nucleus. A dynamic embryo is a "non-classical" nucleus in the non-equilibrium state. After the size of an embryo is over a critical size, the embryo is transformed into a frozen nucleus. Domains in the low-temperature phase are assumed to develop gathering frozen nuclei. The results of a computer simulation based on the above model show the presence of an incubation time, which is one of the essential properties of the first-order phase transition, and display the cooperative formation of domains and the fractal distribution of their size. The experimental results on the kinetics of the martensitic phase transition in In-Tl alloys have been interpreted in terms of the above simulation results.

	FIG.1 Two types of phase transition from the parent phase represented by a square to the low-temperature phase represented by a rectangle through a slightly deformed intermediate rectangle are considered in our two-dimensional model. One is to the variant I of the low-temperature phase and the other is to the variant II. Notice that a frozen nucleus never transforms back to the parent phase, although the size of a dynamic embryo, which is represented by a slightly deformed rectangle is variable.
	FIG.2 The value of S(i, j) at the (i, j) site is fluctuating between -1 and 1 in our ideal nucleation and growth model. This represents the state of dynamic embryos. A frozen nucleus of variant I appears when S(i, j) is greater than 1 and a frozen nucleus of variant II appears when S(i, j) is less than -1.
	FIG.3 The dependence of the calculated growth curves on (a) a (b/g = 6.7) and (b) b/g (a = 4) are compared with experimental data at 256.7 K for In-23 at.%Tl alloy. Open circles, open triangles and open squares represent experimental data corresponding to the variant I+variant II, the variant I and the variant II, respectively.
	FIG.4 The dependence of the final domain distribution on the parameter (a) a and (b) b/g at 256.7 K in a two-dimensional idealized nucleation and growth model.
	FIG.5 Calculated growth curves at each temperature using the parameter values in Table 1.
	FIG.6 Growth domain distribution at 256.7 K. Red and Green regions correspond to the area covered by the variant I and the variant II, respectively.
	FIG.7 Fractal dimension D for the domain distribution shown in Fig.6 is found to be 1.80 +- 0.01 by the scaling method in this two-dimensional model.

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