Zipping process on the step bunching in the vicinal surface of the restricted solid-on-solid model with the step attraction of the point contact type

Akutsu, Noriko

doi:10.1016/j.jcrysgro.2010.10.088

Cited by 16 publications

(28 citation statements)

References 27 publications

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“…As we reported previously for ϵ int /ϵ = −0.5, [14][15][16][17][18] there are two characteristic temperatures, T f ,1 and T f ,2 , for the ECS. For T > T f ,1 , the surface free energy has the GMPT form, as shown in Figs.…”

Section: A Shape Transitionsupporting

confidence: 76%

“…1), and, in an ECS, a first-order shape transition occurs at the facet edge in the shape. [14][15][16][17][18] The inhibition of the crystal growth, due to the step-faceting near equilibrium, 17 has been observed experimentally, 24 and this inhibition degrades the quality of the crystal.…”

Section: Introductionmentioning

confidence: 92%

“…In our previous work, [14][15][16][17][18] we presented a restricted solid-on-solid (RSOS) model on a squared lattice ( Fig. 2) with a point-contact-type step-step attraction (the p-RSOS model).…”

Section: Introductionmentioning

confidence: 99%

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Faceting diagram for sticky steps

Akutsu

2016

AIP Advances

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Faceting diagrams for the step-faceting zone, the step droplet zone, and the GruberMullins-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 γ 1 = lim n→ ∞ γ n /n, where γ n 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 A q,eff = 0 and B q,eff = 0, where A q,eff and B q,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 f eff (⃗ 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 stepfaceting is explained in terms of the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Section: A Shape Transitionsupporting

confidence: 76%

Section: Introductionmentioning

confidence: 92%

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Faceting diagram for sticky steps

Akutsu

2016

AIP Advances

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“…8. As seen from the figure, the (001) facet ends at (X c , Y c ) and the curved region between the (001) and (111) facets represents a first-order shape transition at the edge of the (111) facet (X q , X q ) [54,55].…”

Section: First-order Shape Transition On the Ecs Profilementioning

confidence: 98%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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Abstract. The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z = z(x, y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal GruberMullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) n(p) using the Monte Carlo method, where p = (∂z/∂x, ∂z/∂y), and · represents the thermal average. Using the result of the |p| dependence of n(p) , we derive a |p|-expanded expression for the non-universal surface free energy f eff (p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f eff (p).

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“…Recently, various microscopic models that show an ECS similar to Type II in Figure 6.24 have been presented; these include the p-RSOS model [86,96,124,125], the RSOS-I model [126][127][128], and a modified RSOS-I model [129]. The p-RSOS model ( Figure 6.25), explained in the following subsection, is the RSOS model with a pointcontact type of step-step attraction.…”

Section: Stability Of a Macrostepmentioning

confidence: 99%