Abstract
Equilibrium shapes of crystals in contact with more than one substrate, e.g., droplets at a corner or the edge of two planes, are described. This generalizes a construction due to Wulff and Winterbottom and, unlike them, allows non-convex equilibrium shapes. Since this construction may require a central inversion of the Wulff plot, it is dubbed “the summertop construction.”
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G. Wulff,Z. Krist. Mineral. 34:449 (1901); see also C. Herring, inStructure and Properties of Solid Surfaces, R. Gomer and C. S. Smith, eds. (University of Chicago, Chicago, 1953).
R. K. P. Zia and J. E. Avron,Phys. Rev. B 25:2042 (1982).
W. L. Winterbottom,Acta Metal. 15:303 (1967).
J. W. Cahn,J. Chem. Phys. 66:3667 (1977); C. Ebner and W. F. Saam,Phys. Rev. Lett. 38:1486 (1977).
D. E. Sullivan and M. M. Telo de Gama, inFluid Interfacial Phenomena, C. A. Croxton, ed. (Wiley, New York, 1985).
J. K. Lee and H. I. Aaronson,Surf. Sci. 47:692 (1975).
J. W. Cahn, private communication.
J. E. Taylor, J. E. Avron, and R. K. P. Zia, to be published.
J. E. Taylor,Asterisque, to appear.
H. van Beijeren and I. Nolden, inTopics in Current Physics, Vol. 43, W. Schommers and P. von Blanckenhagen, eds. (Springer, Berlin, 1987), p. 259.
J. E. Avron, J. E. Taylor, and R. K. P. Zia,J. Stat. Phys. 33:493 (1983).
A. K. Datye, A. D. Logan, and N. J. Long,J. Catalysis, to appear.
P. Concus and R. Finn,Acta Math. 132:177 (1974).
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Zia, R.K.P., Avron, J.E. & Taylor, J.E. The summertop construction: Crystals in a corner. J Stat Phys 50, 727–736 (1988). https://doi.org/10.1007/BF01026498
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DOI: https://doi.org/10.1007/BF01026498