Physics of Crystal Growth

Pimpinelli, Alberto; Villain, Jacques

doi:10.1017/cbo9780511622526

Cited by 795 publications

(975 citation statements)

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“…Note that the interface between the A and the B region is not perfectly straight and the island edges are rounded, in accordance with theoretical calculations which yield T R = 0 as roughening temperature of two-dimensional crystals [26]. Similar results are obtained for various values of E AB and temperature T .…”

Section: Symmetric Treatment Of Adsorbate Speciessupporting

confidence: 89%

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Volkmann¹,

Much²,

Biehl³

et al. 2005

Surface Science

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We study the formation of nanostructures with alternating stripes composed of bulk-immiscible adsorbates during submonolayer heteroepitaxy. We evaluate the influence of two mechanisms considered in the literature: (i) strain relaxation by alternating arrangement of the adsorbate species, and (ii) kinetic segregation due to chemically induced diffusion barriers. A model ternary system of two adsorbates with opposite misfit relative to the substrate, and symmetric binding is investigated by off-lattice as well as lattice kinetic Monte Carlo simulations. We find that neither of the mechanisms (i) or (ii) alone can account for known experimental observations. Rather, a combination of both is needed. We present an off-lattice model which allows for a qualitative reproduction of stripe patterns as well as island ramification in agreement with recent experimental observations for CoAg/Ru(0001) [R. Q. Hwang, Phys. Rev. Lett. 76, 4757 (1996)]. The quantitative dependencies of stripe width and degree of island ramification on the misfit and interaction strength between the two adsorbate types are presented. Attempts to capture essential features in a simplified lattice gas model show that a detailed incorporation of non-local effects is required.

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Section: Symmetric Treatment Of Adsorbate Speciessupporting

confidence: 89%

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Volkmann¹,

Much²,

Biehl³

et al. 2005

Surface Science

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“…Other effects that occur on a real surface are ignored, such as surface diffusion [3], electromigration [72]- [74], the Schwoebel effect [75,76], impurity effects [77]- [79], strain effects [80]- [84], and the effect of surfactants [85]- [86].…”

Section: )) the Energy E(h(i J)) Is Calculated Using The P-rsos Hammentioning

confidence: 99%

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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“…Generally speaking (see, e.g., [2] for a detailed introduction to the subject), the free energy of a surface ( F=lNÀpV+rA) can be written as follows:…”

Section: Tensionless Surfacesmentioning

confidence: 99%

“…(1) for m=0, in the presence of an external potential. A second instance of tensionless surfaces arises in the growth of thin films by molecular beam epitaxy (MBE) [2,6]. MBE is a process of high technological interest, in which atoms or molecules are deposited on the surface of the growing sample in conditions such that evaporation is largely suppressed.…”

Section: Examples Of Tensionless Surfacesmentioning

confidence: 99%

“…Tensionless surfaces are of great importance in different fields and applications, ranging from biology, where lipid membranes are tensionless for practical purposes [1], to nanotechnology, where molecular beam epitaxy and related techniques used to grow devices are carried out in conditions for which surface tension is negligible [2]. Therefore, from the viewpoint of these and other applications, understanding the different regimes in which tensionless surfaces can grow is a very relevant issue.…”

Section: Introductionmentioning

confidence: 99%

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Phase transition in tensionless surfaces

Ruiz‐Lorenzo

Cuerno

Moro

et al. 2005

Biophysical Chemistry

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We study the critical behavior of the Laplacian roughening model, which describes the growth of tensionless surfaces. This type of growth phenomena is very important, for instance, in biological membranes and in molecular beam epitaxy. We summarize previous analytical and numerical results and point out their contradictions and differences, thus making clear the context of our work. Our contribution, achieved through large scale numerical simulations, is the confirmation that the model exhibits a single continuous phase transition: the transition takes place between a continuum massless (i.e., with infinite correlation length) bilaplacian behavior and a massive propagator (finite correlation length).

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Physics of Crystal Growth

Cited by 795 publications

References 0 publications

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Non-universal equilibrium crystal shape results from sticky steps

Phase transition in tensionless surfaces

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