Rough–Smooth Transition of Step and Surface

Akutsu, Noriko; Yamamoto, Takao

doi:10.1016/b978-0-444-56369-9.00006-x

Cited by 22 publications

(26 citation statements)

References 111 publications

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“…4). 13,19,44 Examples of the calculated Andreev free energy for ϵ int /ϵ = −0.9 at several temperatures are shown in Fig. 5.…”

Section: Calculation Of Thermodynamic Quantitiesmentioning

confidence: 99%

“…The roughening transition temperature of the (001) surface, T R (001) , is determined so that the principal curvature, κ, equals the universal value, 2/(πk B T R (001) ), 6,13 where κ is calculated numerically from the equation κ = lim |⃗ η|→ 0 ∆p/∆|⃗ η|. As seen in Fig.…”

Section: Roughening Transition Temperaturementioning

confidence: 99%

“…From the thermodynamics of the ECS 13,19 (see Appendix C in the supplementary material 39 ), we have…”

Section: A Shape Transitionmentioning

confidence: 99%

“…Using the PWFRG method, the surface gradient, 13,19 Simultaneously, the external parameter is changed from ⃗ η to ⃗ p. The surface tension, γ surf (⃗ p), is obtained from equation 45 …”

Section: Calculation Of Thermodynamic Quantitiesmentioning

confidence: 99%

“…4 The GMPT form of the surface free energy was established in association with the study of the roughening transition and the faceting transition. [5][6][7][8][9][10][11][12][13] At temperatures less than the roughening transition temperature of a terrace, the surface free energy (density) is described as…”

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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“…4). 13,19,44 Examples of the calculated Andreev free energy for ϵ int /ϵ = −0.9 at several temperatures are shown in Fig. 5.…”

Section: Calculation Of Thermodynamic Quantitiesmentioning

confidence: 99%

Section: Roughening Transition Temperaturementioning

confidence: 99%

“…From the thermodynamics of the ECS 13,19 (see Appendix C in the supplementary material 39 ), we have…”

Section: A Shape Transitionmentioning

confidence: 99%

Section: Calculation Of Thermodynamic Quantitiesmentioning

confidence: 99%