FACET RIDGE ENDPOINTS IN EQUILIBRIUM CRYSTALS

AND THEIR EQUIVALENCE TO 1D KPZ GROWTH.



  • Facet Ridge End Points in Crystal Shapes,
    Douglas Davidson and Marcel den Nijs, Phys. Rev. Lett. 84, 326 (2000).

  • Temperature Dependence of Facet Ridges in Crystal Surfaces,
    Douglas Davidson and Marcel den Nijs, Phys. Rev. E 59, 5029 (1999).

  • Crossover Scaling Functions in One Dimensional Dynamic Growth Models,
    John Neergaard and Marcel den Nijs, Phys.Rev.Lett. 74 730 (1995).




  • facet.gif


    Facet-ridge end points in equilibrium crystal shapes are points where a sharp first-order boundary between two facets splits into two lines with rough rounded crystal in between.

    The figure above shows a typical temperature evolution of such a crystal structure.

    We found an exact mapping of the transfer matrix at the facet ridge end point in the so-called BCSOS model onto one dimensional KPZ type growth . The spatial direction parallel to the facet ridge play the role of time in the dynamic process.

    This equivalence requires the transfer matrix to be stochastic at the facet-ridge end-point. This must be coincidental, and the question arises whether the scaling exponents of facet-ridge end-points are different from the KPZ values in general.

    Indeed, the inclusion of more interactions leads to crystal shapes with more structure . In particular, we find first-order lines sticking into the rough rounded part of the crystal and first-order boundaries between the facets and the rounded parts .



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