Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T18:15:07.527Z Has data issue: false hasContentIssue false
  • English
  • Français

A Phase-Field – Finite Element Model for Instabilities in Multilayer Thin Films

Published online by Cambridge University Press:  10 March 2011

Mohsen Asle Zaeem ,
Sinisa Dj. Mesarovic ,
Haitham El Kadiri  and
Paul T. Wang
Mohsen Asle Zaeem
Affiliation:
Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS, U.S.A.
Sinisa Dj. Mesarovic
Affiliation:
School of Mechanical and Materials Engineering, Washington State University, WA, U.S.A.
Haitham El Kadiri
Affiliation:
Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS, U.S.A. Mechanical Engineering Department, Mississippi State University, Starkville, MS, U.S.A.
Paul T. Wang
Affiliation:
Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS, U.S.A.
Get access

Abstract

Cahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C0 interpolation functions for the displacement, and C1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model.

Using the PF – FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface.

Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and metastable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.

Keywords

thin filmphase transformationsimulation
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1297: Symposium P – Deformation Mechanisms, Microstructure Evolution and Mechanical Properties of Nanoscale Materials , 2011 , mrsf10-1297-p03-37
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Jankowski, A. F., Nanostructured Mater. 6, 170–190 (1995).Google Scholar
2. Movchan, B. A. and Lemkey, F. D., Mater. Sci. Eng. A 224, 136–145 (1997).Google Scholar
3. Atkinson, R. and Dodd, P. M., J Magn Magn Mater 173, 202–214 (1997).Google Scholar
4. Stobiecki, T., Czapkiewicz, M., Kopcewicz, M., Zuberek, R. and Castano, F. J., Thin Solid Films 317, 306–309 (1998).Google Scholar
5. Czapkiewicz, M., Stobiecki, T. and Kopcewicz, M., J. Magn. Magn. Mater. 160, 357–358 (1996).Google Scholar
6. Cahn, J. W. and Larche, F.C., Acta Metall. Mater. 30, 51–56 (1982).Google Scholar
7. Chen, L. Q., Annu. Rev. Mater. Res. 32, 113–140 (2002).Google Scholar
8. Cahn, J. W. and Kobayashi, R., Acta Metall. Mater. 43, 931–944 (1995).Google Scholar
9. Chen, L. Q., Wang, Y. and Khachaturyan, A. G., Phil. Mag. Lett. 64, 241–251 (1991).Google Scholar
10. Johnson, W. C., Acta Mater. 48, 1021–1032 (2000).Google Scholar
11. Li, D. Y., Chen, L.Q., Acta Mater. 4,6 (1998) 639–649.Google Scholar
12. Chen, L.Q., Shen, J., Comput. Phys. Commun. 108, 147–158 (1998).Google Scholar
13. Vaithyanathan, V., Wolverton, C., Chen, L.Q., Acta Mater. 52, 2973–2987 (2004).Google Scholar
14. Cahn, J. W. and Hilliard, J. E., J. Chem. Phys. 28, 258–267 (1958).Google Scholar
15. Asle Zaeem, M. and Mesarovic, S. Dj., J. Comput. Phys. 229, 9135–9149 (2010).Google Scholar
16. El Kadiri, H., Horstemeyer, M. F. and Bammann, D. J., J. Mech. Phys. Solids 56, 3392–3415 (2008).Google Scholar
17. Denton, A. R. and Ashcroft, N. W., Phys. Rev. A 43, 3161–3164 (1991).Google Scholar
18. Hughes, T. J. R., The finite element method, (Dover publications, New York, 2000).Google Scholar
19. Asle Zaeem, M. and Mesarovic, S. Dj., Solid State Phenom. 150, 29–41 (2009)Google Scholar
20. Asle Zaeem, M. and Mesarovic, S. Dj., ASME Conf. Proc. 12, 267–272 (2008), doi:10.1115/IMECE2008-66767.Google Scholar
21. Yeon, D.-H., Cha, P.-R., Kim, J.-H., Grant, M. and Yoon, J.-K., Modelling Simul. Mater. Sci. Eng. 13, 299 (2005).Google Scholar
22. Asle Zaeem M, M., El Kadiri, H., Mesarovic, S. Dj., Wang, P. T. and Horstemeyer, M. F., Phi. Mag. Lett., (2010) (submitted).Google Scholar
23. Asle Zaeem, M. and Mesarovic, S. Dj., Comput. Mater. Sci. 50, 1030–1036 (2011).Google Scholar