Abstract
Experimental evidence has accumulated in the recent decade that nanoscale patterns can self-assemble on solid surfaces. A two-component monolayer grown on a solid surface may separate into distinct phases. Sometimes the phases select sizes about 10 nm, and order into an array of stripes or disks. This paper reviews a model that accounts for these behaviors. Attention is focused on thermodynamic forces that drive the self-assembly. A double-welled, composition-dependent free energy drives phase separation. The phase boundary energy drives phase coarsening. The concentration-dependent surface stress drives phase refining. It is the competition between the coarsening and the refining that leads to size selection and spatial ordering. These thermodynamic forces are embodied in a nonlinear diffusion equation. Numerical simulations reveal rich dynamics of the pattern formation process. It is relatively fast for the phases to separate and select a uniform size, but exceedingly slow to order over a long distance, unless the symmetry is suitably broken.
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References
Ball P., 1999. The Self-Made Tapestry. Oxford University Press, UK.
Böhringer M.K.,W.-D. Morgenstern, R. Schneider, F. Berndt, A. Mauri, De Vita & R. Car, 1999. Two dimensional self-assembly of supramolecular clusters and chains. Phys. Rev. Lett. 83, 324–327.
Brune H., M. Giovannin, K. Bromann & K. Kern, 1998. Self-organized growth of nanostructure arrays on strain-relief patterns. Nature 394, 451–453.
Cahn J.W., 1961. On spinodal decomposition. Acta Metall. 9, 795–801.
Cahn J.W. & J.E. Hilliard, 1958. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267.
Cammarata R.C., 1994. Surface and interface stress effects in thin films. Prog. Surf. Sci. 46, 1–38.
Chen L.-Q. & A.G. Khachaturyan, 1993. Dynamics of simultaneous ordering and phase separation and effect of long-range coulomb interactions. Phys. Rev. Lett. 70, 1477–1480.
Chen L.-Q. & J. Shen, 1998. Applications of semi-implicit Fourier-spectral method to phase field equations. Computer Physics Communications 108, 14–158.
Chen L.Q. & Y. Wang, 1996. The continuum field approach to modeling microstructural evolution. JOM 48 (December Issue), 13–18.
Chou S.Y. & L. Zhuang, 1999. Lithographically-induced self-assembly of periodic polymer micropillar arrays. J. Vac. Sci. Tech. B 17, 3197–3202.
Clark P.G. & C.M. Friend, 1999. Interface effects on the growth of cobalt nanostructures on molybdenum-based structures. J. Chem. Phys. 111, 6991–6996.
Giess E.A., 1980. Magnetic-bubble materials. Science 208, 938–943.
Ibach H., 1997. The role of surface stress in reconstruction, epitaxtial growth and stabilization of mesoscopic structures. Surf. Sci. Rep. 29, 193–263.
Johnson K.L., 1985. Contact Mechanics. Cambridge University Press, UK.
Kern K., H. Niebus, A. Schatz, P. Zeppenfeld, J. George & G. Comsa, 1991. Long range spatial self-organization in the adsorbate-induced restructuring of surfaces: Cu{110}-(2 x 1)O. Phys. Rev. Lett. 67, 855–858.
Lu W. & Z. Suo, 1999. Coarsening, refining, and pattern emergence in binary epilayers. Zeitschrift fur Metallkunde, 90, 956–960.
Lu W. & Z. Suo, 2001. Dynamics of nanoscale pattern formation of an epitaxtial monolayer. Prepared for a special issue of Journal of the Mechanics and Physics of Solids dedicated to Professors of J.W. Hutchinson and J.R. Rice on the occasion of their 60th birthdays.
Martin J.W., R.D. Doherty & B. Cantor, 1997. Stability of Microstructure in Metallic Systems. 2nd edn. Cambridge University Press, UK.
Murray C.B., C.R. Kagan & M.G. Bawendi, 2000. Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 30, 545–610.
Narasimhan S. & D. Vanderbilt, 1992. Elastic stress domain and herringbone reconstruction on Au (111). Phys. Rev. Lett. 69, 1564–1567.
Ng K.-O. & D. Vanderbilt, 1995. Stability of periodic domain structures in a two dimensional dipolar model. Phys. Rev. B 52, 2177–2183.
Park M., C. Harrison, P.M. Chaikin, R.A. Register & D.H. Adamson, 1997. Block copolymer lithography: periodic arrays of ~1011 holes in 1 square centimeter. Science 276, 1401–1404.
Parker T.M., L.K. Wilson & N.G. Condon, 1997. Epitaxy controlled by self-assembled nanometer-scale structures. Phys. Rev. B 56, 6458–6461.
Pohl K., M.C. Bartelt, J. de la Figuera, N.C. Bartelt, J. Hrbek & R.Q. Hwang, 1999. Identifying the forces responsible for self-organization of nanostructures at crystal surfaces. Nature 397, 238–241.
Röder H., R. Schuster, H. Brune & K. Kern, 1993. Monolayer-confined mixing at the Ag-Pt(111) interface. Phys. Rev. Lett. 71, 2086–2089.
Seul M. & D. Andelman. Domain shapes and patterns: the phenomenology of modulated phases. Science 267, 476–483.
Su C.H. & P.W. Voorhees, 1996. The dynamics of precipitate evolution in elastically stressed solids. Acta Mater 44, 1987–2016.
Suo Z., 2000. Evolving materials structures of small feature sizes. Int. J. Solids Structures. 37, 367–378.
Suo Z. & W. Lu, 2000a Composition modulation and nanophase separation in a binary epilayer. J. Mech. Phys. Solids. 48, 211–232.
Suo Z. & W. Lu, 2000b. Self-organizing nanophases on a solid surface. In: ChuangT.J., ed. Multi-Scale Deformation and Fracture in Materials and Structures. A book dedicated to Professor James R. Rice on the occasion of his 60th birthday. (to be published by Kluwer Academic Publishers)
Timoshenko S.P. & J.N. Goodier, 1970. Theory of Elasticity. McGraw-Hill Book Company, New York.
Vanderbilt D., 1997. Ordering at surfaces from elastic and electrostatic interactions. Surface Rev. Lett. 4, 811–816.
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Suo, Z., Lu, W. Forces that Drive Nanoscale Self-assembly on Solid Surfaces. Journal of Nanoparticle Research 2, 333–344 (2000). https://doi.org/10.1023/A:1010041505860
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DOI: https://doi.org/10.1023/A:1010041505860