FRENKEL-KONTOROVA MODEL WITH A NONCONVEX TRANSVERSE DEGREE-OF-FREEDOM - A MODEL FOR RECONSTRUCTIVE SURFACE GROWTH

We study the ground state (GS) of a generalized Frenkel-Kontorova model with a nonconvex transverse degree of freedeom. The model describes a lattice of atoms with a given concentration interacting by exponential repulsive or Morse-type forces. The lattice is subjected to a two-dimensional substrate potential which is periodic in one direction and nonconvex (Morse) in the transverse direction. The model exhibits transitions from the trivial (linear) GS to a GS with escaped atoms when the amplitude of repulsion or the concentration of atoms increases. The results are used to describe reconstructive crystal growth which occurs when the growth of the second atomic layer leads to a reconstruction of the underlying first layer, and the ''complicated exchange-mediated diffusion mechanism'' recently observed in molecular-dynamics simulations [J.E. Black and Zeng-Ju Tian, Phys. Rev. Lett. 71, 2445 (1993)]. © 1995 The American Physical Society.