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Spinodal Decomposition of the Interface in a Nonlinear Growth Model with Noise

Published online by Cambridge University Press:  21 February 2011

Leonardo GoluBovic  and
R. P. U. Karunasiri
Leonardo GoluBovic
Affiliation:
Chemical Engineering 210–41, Caltech, Pasadena, CA 91125
R. P. U. Karunasiri
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974
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Abstract

We consider a non-linear version of Edwards-Wilkinson interface model for the growth in the presence of a collimated partjcie flux. We include both surface tension and surface diffusion relaxation. In a range of positive small values of the surface tension, the interface develops a state which fulfills standard criteria for spinodal decomposition. This suggests the existence of a phase transition from the ordinary state with the interface perpendicular to the incoming flux to a novel, noue.induced state with the interface apontaneously tilted with respect to the direction of the flux.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 237: Symposium Ca – Interface Dynamics and Growth , 1991 , 199
Copyright
Copyright © Materials Research Society 1992

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References

[1] Herring, C., J. Appl. Phys. 21, 301 (1950);Google Scholar
Mullms, W. W., J. Appl. Phys. 28, 333(1957).Google Scholar
[2] Movchan, B. A. and Demchishin, A. V., Phys. Met. Matalogr. 28, 83 (1969);Google Scholar
Thornton, J. A., Ann. Rev. Mater. Sci. 7, 239 (1977).Google Scholar
[3] Golubović, L. and Bruinsma, R., Phys. Rev. Lett, 66, 321 (1991);Google Scholar
Karunasiri, R. P. U. and Golubović, L., work in progress (1990).Google Scholar
[4] Wolf, D. and Villain, J., Europhys. Lett. 13, 389 (1990).Google Scholar
[5] Villain, J., preprint (1990).Google Scholar
[6] Des Sarma, S. and Tamborenea, P., Phys. Rev. Lett, 66, 325 (1991).CrossRefGoogle Scholar
[7] Edwards, S. F. and Wilkinson, D. R., Proc. Roy. Soc. London A381, 17 (1982).Google Scholar
[8] Kardar, M., Parisi, G. and Zhang, Y.-C., Phys. Rev. Lett. 56, 889 (1986).Google Scholar
[9] Mazor, A., Srolovitz, D. J., Hagan, P. S. and Bukiet, B. G., Phys. Rev. Lett. 60, 424 (1988).Google Scholar
[10] The full non-linear surface tension term in (1) is somewhat different from the ro-t at ion ally invariant term arising from evaporation/recondensation processes, see Mullins, Ref. 1. However, both terms yield essentially the same physics. See L.Golubović and R. P. U.Karunasiri, submitted to J. Phye. (Paris). We note that a short version of this work appeared in Phys. Rev. Lett. 66, 321 (1991).Google Scholar
[11] Cahn, J. W. and Hilliard, J. E., J. Chem. Phys. 28, 258, (1958),Google Scholar
Cahn, J. W. and Hilliard, J. E., J. Chem. Phys. 31, 688(1959);Google Scholar
Cahn, J., Acta Metall, 9, 795 (1961).Google Scholar
See also Langer, J. S., Baron, M., and Miller, H. D., Phys. Rev. All, 1417 (1975);Google Scholar
Billtet, C. and Binder, K., Z. Phys. B 32, 195 (1979).Google Scholar
Hillert, M., Acta Metall. 9, 522 (1961), numerically investigated spinodal decomposition in a one-dimensional nonlinear system.Google Scholar
[12] See Ma, S. K., Modern Theory of Critical Phenomena, (Benjamin, 1976) Section 13.Google Scholar
[13] Note that the change .Google Scholar
[14] In contrast to (5), Eqn. (7) is the standard imaginary time quantum mechanical action of a particle moving in the local potential in Eqn. (7). This enables to estimate the correlation length ξeq by a standard transfer matrix calculation. See our work Ref. 10.Google Scholar