# American Institute of Mathematical Sciences

October  2007, 8(3): 623-648. doi: 10.3934/dcdsb.2007.8.623

## Growth regimes in phase ordering transformations

 1 Department of Chemical Engineering and McGill Institute of Advanced Materials, McGill University, 3610 University Street, Montreal, Quebec H3A 2B2, Canada, Canada

Received  July 2006 Revised  February 2007 Published  July 2007

Growth, shape and texturing dynamics of single 2D spherulites are analyzed using the Landau-de Gennes (LdG) liquid crystal model of isotropic-nematic phase ordering. Direct numerical simulation shows that non-circular nucleation due to anisotropy in the interfacial tension results in non-circular shapes in the early stages of growth. However, interfacial heterogeneities in growth and structure then lead to interfacial defect nucleation and shedding and a reshaping of the interface into a circular shape. The formulated dynamics show that a growing spherulite in the early stage of phase ordering also acquires topological higher charges than expected from the well-known Kibble mechanism. In agreement with experiments under strong quenching, the predicted growth dynamics of a spherulite of characteristic radius R is linear: $R$~$t$. To better understand these computational results, a dynamic shape equation is obtained from the LdG model and is shown to have the same form as the growth and shape equations of crystal growth. The shape equation is used to reveal the mechanisms involved in shape transformations, interfacial defect shedding, and growth dynamics computed by direct numerical simulation of the bulk LdG equations.
Citation: Benjamin Wincure, Alejandro D. Rey. Growth regimes in phase ordering transformations. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 623-648. doi: 10.3934/dcdsb.2007.8.623
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