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Finding Critical Nuclei in Phase Transformations by Shrinking Dimer Dynamics and its Variants

Published online by Cambridge University Press:  03 June 2015

Lei Zhang ,
Jingyan Zhang  and
Qiang Du
Lei Zhang*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
Jingyan Zhang*
Affiliation:
Department of Mathematics, Pennsylvania State University, PA 16802, USA
Qiang Du*
Affiliation:
Department of Mathematics, Pennsylvania State University, PA 16802, USA Beijing Computational Science Research Center, Beijing, 100084, China
*
Email:zhangl@math.pku.edu.cn
Email:j_zhang@math.psu.edu
Corresponding author.Email:qdu@math.psu.edu
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Abstract

We investigate the critical nuclei morphology in phase transformation by combining two effective ingredients, with the first being the phase field modeling of the relevant energetics which has been a popular approach for phase transitions and the second being shrinking dimer dynamics and its variants for computing saddle points and transition states. In particular, the newly formulated generalized shrinking dimer dynamics is proposed by adopting the Cahn-Hilliard dynamics for the generalized gradient system. As illustrations, a couple of typical cases are considered, including a generic system modeling heterogeneous nucleation and a specific material system modeling the precipitate nucleation in FeCr alloys. While the standard shrinking dimer dynamics can be applied to study the non-conserved case of generic heterogeneous nucleation directly, the generalized shrinking dimer dynamics is efficient to compute precipitate nucleation in FeCr alloys due to the conservation of concentration. Numerical simulations are provided to demonstrate both the complex morphology associated with nucleation events and the effectiveness of generalized shrinking dimer dynamics based on phase field models.

Keywords

37M0549K3537N3034K2865P99Critical nucleusphase field modelssaddle pointshrinking dimer dynamicsheterogeneous nucleationprecipitate nucleationphase transformation
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 3 , September 2014 , pp. 781 - 798
Copyright
Copyright © Global Science Press Limited 2014

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