On stability of self-assembled nanoscale patterns

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 7, 2007, Pages 1357-1384

  Hu, Shaowen ^a   Nathan, Girish ^a   Hussain, Fazle ^b   Kouri, Donald J ^a   Sharma, Pradeep ^a,b   Gunaratne, Gemunu H ^a,c  

^a University of Houston   (United States)

^b UNIVERSITY OF HOUSTON   (United States)

^c INSTITUTE OF FUNDAMENTAL STUDIES   (Sri Lanka)

Author keywords

Nanostructures; Self assembly; Stability analysis

Indexed keywords

BAND STRUCTURE; MONOLAYERS; PHASE TRANSITIONS; SELF ASSEMBLY; SUBSTRATES;

SPATIO-TEMPORAL DYNAMICS; STABILITY ANALYSIS;

NANOSTRUCTURES;

EID: 34248231357     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.01.003     Document Type: Article

References (35)

1. Bracewell R. The Hankel transform. The Fourier Transform and its Applications. third ed. (1999), McGraw-Hill, New York 244
2. Brand H.R. Envelop equations near the onset of a hexagonal pattern. Prog. Theor. Phys. Suppl. 99 (1989) 442
3. Busse F.H. On the stability of two-dimensional convection and its relation to an extremum principle. J. Fluid Mech. 30 (1967) 625
4. Cahn J.W., and Hilliard J.E. Free energy of a nonuniform system, I. Interfacial free energy. J. Chem. Phys. 28 (1958) 258
5. Cross M.C., and Hohenberg P.C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65 3 (1993) 851
6. Glas F. Thermodynamics of a stressed alloy with a free surface: coupling between the morphological and compositional instabilities. Phys. Rev. B 55 (1997) 11277
7. Golovin A.A., Nepomnyashchy A.A., and Pismen L.M. Interaction between short-scale Marangoni convection and long-scale deformational instability. Phys. Fluids 6 (1994) 34
8. Golovin A.A., Nepomnyashchy A.A., and Pismen L.M. Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid-gas system with deformable interface. J. Fluid. Mech. 341 (1997) 317
9. Gunaratne G.H., Ouyang Q., and Swinney H.L. Pattern formation in the presence of symmetries. Phys. Rev. E 50 (1994) 2802
10. Gunaratne G.H., Ratnaweera A., and Tennekone K. Emergence of order in textured patterns. Phys. Rev. E 59 (1999) 5058
11. Guyer J.E., and Voorhees P.W. Morphological stability and compositional uniformity of alloy thin films. J. Cryst. Growth 187 (1998) 150
12. Haken H. Advanced Synergetics (1987), Springer, Berlin
13. Hoyle R.B. Universal instabilities of rolls, squares and hexagons. In: Tyvand P.A. (Ed). Time-Dependent Non-linear Convection (1998), Computational Mechanics Publications, Southampton
14. Hu, S., 2006. Characterization of the dynamics of pattern formation and analysis of self-assembly of nanostructure. Ph.D. Thesis, University of Houston.
15. Huang R. Kinetic wrinkling of an elastic film on a viscoelastic substrate. J. Mech. Phys. Solids 53 (2005) 63-89
16. Kuznetsov E.A., Nepomnyashchy A.A., and Pismen L.M. New amplitude equation for Boussinesq convection and nonequilateral hexagonal patterns. Phys. Lett. A 205 (1995) 261
17. Lu W., and Suo Z. Coarsening, refining, and pattern emergence in binary epilayers. Z. Metal. 90 (1999) 956
18. Lu W., and Suo Z. Dynamics of nanoscale pattern formation of an epitaxial monolayer. J. Mech. Phys. Solids 49 (2001) 1937
19. Lu W., and Suo Z. Symmetry breaking in self-assembled monolayers on solid surfaces: anisotropic surface stress. Phys. Rev. B 65 (2002) 085401
20. Manneville P. Dissipative Structures and Weak Turbulence (1990), Academic, San Diego, CA
21. Matthews P.C., and Cox S.M. Pattern formation with a conservation law. Nonlinearity 13 (2000) 1293
22. Newell A.C., and Whitehead J.A. Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38 (1969) 279
23. Ng K., and Vanderbilt D. Stability of periodic domain structures in a two-dimensional dipolar model. Phys. Rev. B 52 (1995) 2177
24. Palm E. On the tendency toward hexagonal cells in steady convection. J. Fluid Mech. 8 (1960) 183
25. Plass R., Last J.A., Bartelt N.C., and Kellogg G.L. Nanostructures: self-assembled domain patterns. Nature 412 (2001) 875
26. Pohl K., Bartelt M.C., De La Figuera J., Bartelt N.C., Hrbek J., and Hwang R.Q. Identifying the forces responsible for self-organization of nanostructures at crystal surfaces. Nature 297 (1999) 238
27. Pomeau Y., and Manneville P. Wavelength selection in cellular flow. Phys. Lett. A 75 (1980) 296
28. Segel L. Distant side-walls cause slow amplitude modulations of cellular convection. J. Fluid Mech. 38 (1969) 203
29. Suo Z., and Lu W. Forces that drive nanoscale self-assembly on solid surface. J. Nano. Res. 2 (2000) 233
30. Suo Z., and Lu W. Self-organizing nanophases on a solid surface. In: Chuang T.J. (Ed). Multi-scale Deformation and Fracture in Material and Structures (2001), Kluwer Academic Publisher, Dordrecht
31. Thibos, L.N., 2003. Fourier Analysis for Beginners, third ed. Digitally published by the Visual Sciences Group, webpage: 〈http://www.research.opt.indiana.edu/Library/FourierBook/title.html〉.
32. Umezawa K., Nakanishi S., Yoshimura M., Ojima K., Ueda K., and Gibson W.M. Ag/Cu(1 1 1) surface structure and metal epitaxy by impact-collision ion-scattering spectroscopy and scanning tunneling microscopy. Phys. Rev. B 63 (2001) 35402
33. Wahlström E., Ekvall I., Olin H., Lindgren S., and Walldén L. Observation of ordered structures for S/Cu(111) at low temperature and coverage. Phys. Rev. B 60 (1999) 10699
34. Walgraef D. Spatio-Temporal Pattern Formation (1997), Springer, New York
35. Whitesides G.M., and Grzybowski B. Self-assembly at all scales. Science 295 (2002) 2148