Commun. Comput. Phys., 7 (2010), pp. 674-682.


Simultaneous Prediction of Morphologies of a Critical Nucleus and an Equilibrium Precipitate in Solids

Lei Zhang 1, Long-Qing Chen 2, Qiang Du 3*

1 Department of Mathematics, Penn State University, PA 16802, USA.
2 Department of Materials Science and Engineering, Penn State University, PA 16802, USA.
3 Department of Mathematics and Department of Materials Science and Engineering, Penn State University, PA 16802, USA.

Received 11 June 2009; Accepted (in revised version) 4 September 2009
Available online 12 October 2009
doi:10.4208/cicp.2009.09.099

Abstract

We investigate the critical nucleus and equilibrium morphologies during precipitation of a second-phase particle in a solid. We show that a combination of diffuse-interface description and a constrained string method is able to predict both the critical nucleus and equilibrium precipitate morphologies simultaneously without a priori assumptions. Using the cubic to cubic transformation as an example, it is demonstrated that the maximum composition within a critical nucleus can be either higher or lower than that of equilibrium precipitate while the morphology of an equilibrium precipitate may exhibit lower symmetry than the critical nucleus resulted from elastic interactions.

AMS subject classifications: 74G15, 74B20

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Key words: Phase field, diffuse interface, nucleation, critical nucleus, constrained string method, elasticity.

*Corresponding author.
Email: zhang_l@math.psu.edu (L. Zhang), lqc3@psu.edu (L. Q. Chen), qdu@math.psu.edu (Q. Du)
 

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