The Effect of Surface Tension Anisotropy on the Rayleigh Instability in Materials Systems

Mathematical and Computational Sciences Division

National Institute of Standards and Technology

Possible Reasons for Enhanced Stability

Quantum effects (Kassubek et al. [2001]).

Elastic effects with substrate (Chen et al. [2000])

Stabilization by contact angle (McCullum et al. [1996])

Radial thermal gradients (McFadden et al. [1993])

Surface energy anisotropy (this work)

"Anisotropic Gibbs-Thomson Equation"

Anisotropic Gibbs-Thomson Equation

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Surface Energy

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Numerics

SLEIGN2: Associated Sturm–Liouville Solver

Spectral Decomposition with RS (a real symmetric eigenvalue routine)

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Conclusions

Anisotropic surface energy plays a significant role in the stability of a rod.

Both the magnitude and sign of the anisotropy determine whether the contribution promotes or suppresses the Rayleigh instability.

Different cubic orientations react quite differently to the surface tension anisotropy.

References

P.B. Bailey, W.N. Everitt, and A. Zettl, Algorithm 810: The SLEIGN2 Sturm-Liouville code, ACM T Math Software 27: (2) Jun 2001 143--192.

Y. Chen, D.A.A. Ohlberg, G. Medeiros-Ribeiro, Y.A. Chang, and R.S. Williams, Self-assembled growth of epitaxial erbium disilicide nanowires of silicon(001), App. Phys. Lett., Vol. 76, No. 26 (2000), 4004--4006.

M.G. Forest and Q. Wang, Anisotropic microstructure-induced reduction of the Rayleigh instability for liquid crystalline polymers, Phys. Lett. A, 245 (1998) 518--526.

J.W. Cahn, Stability of rods with anisotropic surface free energy, Scripta Metall. 13 (1979) 1069-1071.

F. Kassubek, C.A. Stafford, H. Grabert, and R.E. Goldstein, Quantum suppression of the Rayleigh instability in nanowires, Nonlinearity 14 (2001) 167--177.

P. Kurowski, S. de Cheveigne, G. Faivre, and C. Guthmann, Cusp instability in cellular growth, J. Phys. (Paris) 50 (1989) 3007-3019.

Y. Kondo and K. Takayanagi, Gold nanobridge stabilized by surface structure, Phys. Rev. Lett. 79 (1997) 3455-3458.

B. Majumdar and K. Chattopadhyay, The Rayleigh Instability and the Origin of Rows of Droplets in the Monotectic Microstructure of Zinc-Bismuth Alloys, Met. Mat. Trans. A, Vol 27A, July (1996) 2053--2057.

M.S. McCallum, P.W. Voorhees, M.J. Miksis, S.H. Davis, and H. Wong, Capillary instabilities in solid thin films: Lines, J. Appl. Phys. 79 (1996) 7604-7611.

G.B. McFadden, S.R. Coriell, and R.F. Sekerka, Effect of surface tension anisotropy on cellular morphologies, J. Crystal Growth 91 (1988) 180--198.

G.B. McFadden, S.R. Coriell, and B.T. Murray, The Rayleigh instability for a cylindrical crystal-melt interface, in Variational and Free Boundary Problems, (ed. A. Friedman and J. Spruck), Vol. 53 (1993) pp. 159-169.


	Mathematical and Computational Sciences Division
	National Institute of Standards and Technology


	Quantum effects (Kassubek et al. [2001]).

	Elastic effects with substrate (Chen et al. [2000])

	Stabilization by contact angle (McCullum et al. [1996])

	Radial thermal gradients (McFadden et al. [1993])

	Surface energy anisotropy (this work)


	SLEIGN2: Associated Sturm–Liouville Solver

	Spectral Decomposition with RS (a real symmetric eigenvalue routine)


	Anisotropic surface energy plays a significant role in the stability of a rod.
	Both the magnitude and sign of the anisotropy determine whether the contribution promotes or suppresses the Rayleigh instability.
	Different cubic orientations react quite differently to the surface tension anisotropy.


	P.B. Bailey, W.N. Everitt, and A. Zettl, Algorithm 810: The SLEIGN2 Sturm-Liouville code, ACM T Math Software 27: (2) Jun 2001 143--192.

	Y. Chen, D.A.A. Ohlberg, G. Medeiros-Ribeiro, Y.A. Chang, and R.S. Williams, Self-assembled growth of epitaxial erbium disilicide nanowires of silicon(001), App. Phys. Lett., Vol. 76, No. 26 (2000), 4004--4006.

	M.G. Forest and Q. Wang, Anisotropic microstructure-induced reduction of the Rayleigh instability for liquid crystalline polymers, Phys. Lett. A, 245 (1998) 518--526.

	J.W. Cahn, Stability of rods with anisotropic surface free energy, Scripta Metall. 13 (1979) 1069-1071.

	F. Kassubek, C.A. Stafford, H. Grabert, and R.E. Goldstein, Quantum suppression of the Rayleigh instability in nanowires, Nonlinearity 14 (2001) 167--177.

	P. Kurowski, S. de Cheveigne, G. Faivre, and C. Guthmann, Cusp instability in cellular growth, J. Phys. (Paris) 50 (1989) 3007-3019.



	Y. Kondo and K. Takayanagi, Gold nanobridge stabilized by surface structure, Phys. Rev. Lett. 79 (1997) 3455-3458.

	B. Majumdar and K. Chattopadhyay, The Rayleigh Instability and the Origin of Rows of Droplets in the Monotectic Microstructure of Zinc-Bismuth Alloys, Met. Mat. Trans. A, Vol 27A, July (1996) 2053--2057.

	M.S. McCallum, P.W. Voorhees, M.J. Miksis, S.H. Davis, and H. Wong, Capillary instabilities in solid thin films: Lines, J. Appl. Phys. 79 (1996) 7604-7611.

	G.B. McFadden, S.R. Coriell, and R.F. Sekerka, Effect of surface tension anisotropy on cellular morphologies, J. Crystal Growth 91 (1988) 180--198.

	G.B. McFadden, S.R. Coriell, and B.T. Murray, The Rayleigh instability for a cylindrical crystal-melt interface, in Variational and Free Boundary Problems, (ed. A. Friedman and J. Spruck), Vol. 53 (1993) pp. 159-169.