Faceting diagram for sticky steps

Faceting diagrams for the step-faceting zone, the step droplet zone, and the Gruber-Mullins-Pokrovsky-Talapov (GMPT) zone for a crystal surface are obtained by using the density matrix renormalization group method to calculate the surface tension. The model based on these calculations is the restricted solid-on-solid (RSOS) model with a point-contact-type step-step attraction (p-RSOS model) on a square lattice. The point-contact-type step-step attraction represents the energy gain obtained by forming a bonding state with orbital overlap at the meeting point of the neighboring steps. In the step-faceting zone, disconnectedness in the surface tension leads to the formation of a faceted macrostep on a vicinal surface at equilibrium. The disconnectedness in the surface tension also causes the first-order shape transition for the equilibrium shape of a crystal droplet. The lower zone boundary line (ZBL), which separates the step-faceting zone and the step droplet zone, is obtained by the condition γ1=limn→∞γn/n, where γn is the step tension of the n-th merged step. The upper ZBL, which separates the GMPT zone and the step droplet zone, is obtained by the condition Aq,eff = 0 and Bq,eff = 0, where Aq,eff and Bq,eff represent the coefficients for the |q→|2 term and the |q→|3 term, respectively, in the |q→|-expanded form of the surface free energy feff(q→). Here, q→ is the surface gradient relative to the (111) surface. The reason why the vicinal surface inclined in the 〈101〉 direction does not exhibit step-faceting is explained in terms of the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero.