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Modelling Solid Nucleation and Growth In Supercooled Liquid

Published online by Cambridge University Press:  15 February 2011

J.P. Leonard and
James S. Im
J.P. Leonard
Affiliation:
Program in Materials Science and Engineering, School of Engineering and Applied Science, Columbia University, New York NY 10027
James S. Im
Affiliation:
Program in Materials Science and Engineering, School of Engineering and Applied Science, Columbia University, New York NY 10027
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Abstract

In this paper, we present a numerical model that incorporates algorithms to simulate nucleation and growth in supercooled liquid in a manner that properly accounts for the stochastic nature of nucleation. The basis of our model relies on a discretization of space and time to address thermal evolution, rapid growth of the undercooled interface, and nucleation in supercooled liquid. The present formulation of nucleation permits the spatially and temporally random nature of the phenomenon to be manifested in the transformation and resultant microstructure. This is accomplished by (1) calculating the probability of nucleation in each and every liquid node during each time step using the Poisson expression, and (2) triggering nucleation if and only when the random number assigned to a node for the time step is less than the calculated nucleation probability. No empirical or deterministic conditions for nucleation are imposed; nucleation occurs spontaneously and solely based on nucleation kinetics. We demonstrate the effectiveness of the overall model by analyzing conditions similar to those encountered in pulsed laser-induced crystallization of thin Si films, and discuss the generality of the proposed stochastic formulation of nucleation.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 580: Symposium E – Nucleation & Growth Processes in Materials , 1999, 233
Copyright
Copyright © Materials Research Society 2000

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