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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.de Collaborative 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.

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References

[1] Cahn, J. W.; Acta Metall.; 10 (1962) 179–183.Google Scholar
[2] Cahn, J.W., Hilliard, J. E., J. Chem. Phys.; 28 (1958) 258–267.Google Scholar
[3] Khachaturyan, A.G.; Theory of structural transformation; John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1983 Google Scholar
[4] Wang, Y., Chen, L.-Q., Khachaturyan, A.G.; “Computer Simulation in Materials Science”, eds. Kirchner, H.O. et al. , Kluwer Academic Publishers (1996) 325–371.Google Scholar
[5] Löchte, L., Gitt, A., Gottstein, G., to be publishedGoogle Scholar
[6] “Smithells Metals reference book”, ed. By Brandes, A.E., Butterworths, London, Boston, 1983 Google Scholar
[7] Hurtado, I., Meurer, B., Löchte, L., Düinnwald, J., Spencer, P.J., Neuschütz, D., Proc. 10th Congress of the Int. Fed. For Heat Treatment and Surface Eng., Grighton, England, Sept. 1996, to be published in 1998Google Scholar
[8] Chen, L.Q., Shen, J.; Applications of Semi-Implicit Fourier-Spectral Method to Phase-Field Equations, Comp. Phys. Comm., Feb. 1998 Google Scholar
[9] Frigo, M., Johnson, S.G.: FFTW: An Adaptive Software Architecture for the FFT; to be published at Int. Conf. On Acoustics, Speech and Signal Processing, May 1998, Seattle, Washington and http://theory.lcs.mit.edu/-fftw/Google Scholar
[10] Sato, T., Takahashi, T.; Scripta Metall.; 22 (1988), 941–946 Google Scholar