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Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method

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Eilks, C. and Elliott, Charles M.. (2008) Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Journal of Computational Physics, Vol.227 (No.23). pp. 9727-9741. ISSN 0021-9991

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Official URL: http://dx.doi.org/10.1016/j.jcp.2008.07.023

Abstract

In this article we formulate a numerical method for the simulation of dealloying of a binary alloy by the selective removal of one component via electrochemical dissolution such that there is phase separation of the other component at the solid/electrolyte interface. The evolution of the interface is modelled by a forced mean curvature flow strongly coupled to the solution of a Cahn-Hilliard equation modelling surface phase separation. The method is based on a triangulated hypersurface whose evolution is calculated as well as the solution of the Cahn-Hilliard equation by the evolving surface finite element method (ESFEM). The numerical experiments simulate complex morphology and concentration patterns providing evidence that the mathematical model may describe the formation of nanoporosity. (C) 2008 Published by Elsevier Inc.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
Q Science > QC Physics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Phase transformations (Statistical physics) -- Mathematical models, Phase rule and equilibrium -- Mathematical models, Finite element method

Journal or Publication Title:

Journal of Computational Physics

Publisher:

Academic Press Inc. Elsevier Science

ISSN:

0021-9991

Official Date:

1 December 2008

Dates:

Date	Event
1 December 2008	Published

Volume:

Vol.227

Number:

No.23

Number of Pages:

Page Range:

pp. 9727-9741

Identification Number:

10.1016/j.jcp.2008.07.023

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

Deutsche Forschungsgemeinschaft (DFG)

References:

[1] J.W. Barrett, J.F. Blowey, H. Garcke, Finite element approximation of the Cahn-Hilliard equation with degenerate mobility, SIAM J. Numer. Anal. 37
(1999) 286–318.
[2] M. Copetti, C.M. Elliott, Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy, Numer. Math. 63 (1992) 39–65.
[3] K.P. Deckelnick, G. Dziuk, C.M. Elliott, Computation of geometric PDEs and mean curvature flow, Acta Numer (2005) 139–232.
[4] J. Dogel, R. Tsekov, W. Freyland, Two dimensional connective nano-structures of electrodeposited Zn on Au (111) induced by spinodal decomposition,
J. Chem. Phys. 122 (2005) 094703.
[5] G. Dziuk, Finite elements for the Beltrami operator on arbitrary surfaces, in: S. Hildebrandt, R. Leis (Eds.), (Herausgeber): Partial Differential Equations
and Calculus of Variations. Lecture Notes in Mathematics, vol. 1357, Springer, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988, pp. 142–155.
[6] G. Dziuk, C.M. Elliott, Finite elements on evolving surfaces, IMA J. Numer. Anal. 27 (2007) 262–292.
[7] G. Dziuk, C.M. Elliott, Surface finite elements for parabolic equations, J. Comp. Math. 25 (2007) 385–407.
[8] G. Dziuk, C.M. Elliott, Eulerian finite element method for parabolic PDES on implicit surfaces, Interface. Free Bound. 10 (2008) 119–138.
[9] G. Dziuk, C.M. Elliott, Eulerian level set method for PDEs on evolving surfaces, Comput. Visual. Sci., in press, doi:10.1007/s00791-008-0122-0.
[10] G. Dziuk, An algorithm for evolutionary surfaces, Numer. Math. 58 (1991) 603–611.
[11] G. Dziuk, U. Clarenz, Numerical methods for conformally parametrized surfaces, Talk at CPDW04-Interphase 2003: numerical methods for free
boundary problems. <www.newton.cam.ac.uk/webseminars/pg+ws/2003/CPDW04/0415/dziuk>.
[12] C.M. Elliott, D. French, F. Milner, A second order splitting method for the Cahn-Hilliard equation, Numer. Math. 54 (1989) 575–590.
[13] Xianfeng Gu, Shing-Tung Yau, Global conformal surface parameterization, in: SGP’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH
Symposium on Geometry Processing, 2003, pp. 127–137.
[14] J. Erlebacher, An atomistic description of dealloying, J. Electrochem. Soc. 151 (10) (2004) C614–C626.
[15] J. Erlebacher, M.J. Aziz, A. Karma, N. Dimitrov, K. Sieradzki, Evolution of nanoporosity in dealloying, Nature 410 (2001) 450–453.
[16] J. Erlebacher, K. Sieradzki, Pattern formation during dealloying, Scripta Mater. 49 (2003) 991–996.
[17] P.L. Lions, B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal. 16 (1979) 964–979.
[18] O. Schönborn, R.C. Desai, Kinetics of phase ordering on curved surfaces, Physica A 239 (1997) 412–419.
[19] A. Schmidt, K.G. Siebert, Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA, Lecture Notes in Computational Science
and Engineering, vol. 42, Springer, 2004.
[20] Ping Tang, Feng Qiu, Hongdong Zhang, Yuliang Yang, Phase separation patterns for diblock copolymers on spherical surfaces: a finite volume method,
Phys. Rev. E 72 (2005) 016710.