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Simulating Phase Transformations with the Cahn-Hilliard Equation – Potential and Limitations –

Published online by Cambridge University Press:  10 February 2011

Lothar Löchte  and
Günter Gottstein
Lothar Löchte
Affiliation:
Institut für Metallkunde und Metallphysik, RWTH Aachen, Germany Kopernikusstr. 14, 52074 Aachen, loechte@imm.rwth-aachen.deCollaborative Research Center 370„Integral Modeling of Materials“ of the DFG
Günter Gottstein
Affiliation:
Institut für Metallkunde und Metallphysik, RWTH Aachen, Germany Kopernikusstr. 14, 52074 Aachen, Collaborative Research Center 370„Integral Modeling of Materials“ of the DFG
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Abstract

An extension of the classical Cahn-Hilliard equation, including elastic interactions is presented. This generalized diffusion equation allows real time simulation of phase-transformations, such as GP-zone formation in a near-commercial ΔICu alloy. No a priori assumptions about kinetics, diffusion fields, as well as precipitate shape are necessary. Shape of precipitates and kinetic of simulated GP-zone formation are in qualitatively good agreement with experiments of Sato and Takahashi, and the concurrenltly derived interfacial energies are reasonable.

Two algorithms for a numerical solution of the Cahn-Hilliard equation are presented. While the simple finite difference scheme does not converge, a slightly more complicated Fourier spectral method behaves reasonable as tested for a synthetic chemical potential.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 529: Symposia BB – Computational & Mathematical Models of Microstructural Evolution , 1998 , 71
Copyright
Copyright © Materials Research Society 1998

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References

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