Model for growth of binary alloys with fast surface equilibration

Drossel, Barbara; Kardar, Mehran

doi:10.1103/physreve.55.5026

Cited by 27 publications

(25 citation statements)

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“…Additionally, in d ¼ 1 there exists an exact mapping between structures in and out of equilibrium, allowing one to describe patterns generated at a finite rate of growth in terms of an equilibrium system with "renormalized" coupling constants, but the same cannot be true here: structures seen in snapshots (Fig. 2) are visibly anisotropic [27], reflecting a memory of the assembly's growth direction. Therefore, if there exists an equivalent equilibrium system [23,29], it has an anisotropic energy function.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in two and three dimensions. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature. DOI: 10.1103/PhysRevLett.112.155504 PACS numbers: 81.16.Dn, 05.20.-y, 81.16.Fg Nature builds its materials using multiple component types. The properties of these materials depend on the properties of their components, and on how components are distributed spatially: the exciton transfer properties of a light-harvesting complex, for instance, depend on the way that its constituent proteins cluster [1]. Achieving similar mesoscale spatial control with many synthetic selfassembled materials [2] is made difficult by the fact that the self-assembly of multicomponent systems generally happens "far" from equilibrium, where we possess few predictive theoretical tools. Although self-assembly is a nonequilibrium process, much of our understanding of it is based upon a physical picture that assumes dynamics to play no role except to convey a system along the "easiest" pathways on its free-energy landscape [3]. This "nearequilibrium" or "quasiequilibrium" assumption tends to hold, for instance, for simple one-component systems under mild nonequilibrium conditions [4][5][6][7][8]. It fails when there exist time scales within a given self-assembly process that exceed the time of the experiment or computer simulation. For one-component systems, long time scales can emerge if bonds between particles are strong, and so break infrequently, which can happen when subjected to "harsh" nonequilibrium conditions (e.g., conditions of deep supercooling). Binding errors made as components associate can then fail to anneal as structures grow, and the result is a kinetically trapped structure rather than an object corresponding to a favored position on the free-energy landscape [9][10][11][12].The self-assembly of multicomponent solid structures, however, is also affected by kinetic traps that emerge even under mild nonequilibrium conditions. The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig. 1(a), which shows in cartoon form a fluid of two types of mutually attractive particles (call them "red" and "blue"), present in equal number, self-assembling into a solid structure. The equilibrium pattern of red and blue within this structure-shown in the figure as demixed red and blue domains-is determined only by the particles' mutual interactions. But achieving this equilibrium pattern via self-assembly requires that particle types interchange their positio...

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“…To model a growth dynamics, we used a simulation protocol that satisfies detailed balance but makes no assumptions about relative rates of growth and structural relaxation [27]. We chose at random a lattice site.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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“…Simple models for layer by layer growth assume either that the probability that an incoming atom sticks to a given surface site depends on the state of the neighboring sites in the layer below [2], or that the top layer is fully thermally equilibrated [3]. Assuming that the bulk mobility is zero, once a site is occupied, its state does not change any more.…”

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Phase Ordering and Roughening on Growing Films

Drossel

Kardar

2000

Phys. Rev. Lett.

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We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimensions, we find a variety of different scaling behaviors, depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations. PACS numbers: 68.35. Rh, 05.70.Jk, 05.70.Ln, 64.60.Cn Thin solid films are grown for a variety of technological applications, using molecular beam epitaxy (MBE) or vapor deposition. In order to create materials with specific electronic, optical, or mechanical properties, often more than one type of particle is deposited. When the particle mobility in the bulk is small, surface configurations become frozen in the bulk, leading to anisotropic structures that reflect the growth history, and are different from bulk equilibrium phases [1]. Characterizing structures generated during composite film growth is not only of technological importance, but represents also an interesting and challenging problem in statistical physics.In this paper, we examine the growth of binary films through vapor deposition, and study some of the rich phenomena resulting from the interplay of phase separation and surface roughening. Simple models for layer by layer growth assume either that the probability that an incoming atom sticks to a given surface site depends on the state of the neighboring sites in the layer below [2], or that the top layer is fully thermally equilibrated [3]. Assuming that the bulk mobility is zero, once a site is occupied, its state does not change any more. If the growth rules are invariant under the exchange of the two particle types, the phase separation is in the universality class of an equilibrium Ising model. Correlations perpendicular to the growth direction are characterized by the critical exponent ν of the Ising model, and those parallel to the growth direction by the exponent νz m , with z m being the dynamical critical exponent of the Ising model. However, the layer by layer growth mode underlying these simple models is unstable, and the growing surface becomes rough. In many cases the fluctuations in the height h(x, t), at position x and time t are self-affine, with correlationswhere χ is the roughness exponent, and z h is a dynamical scaling exponent. A computer model with local sticking probabilities that allows for a rough surface was introduced in [4]. In 1+1 dimensions, the authors find phase separation into domains (with sizes consistent with the Ising model), and a very rough surface profile with sharp minima at the domain boundaries. We may ask the following questions: (1) Are the roughness exponents different at the phase transition point? (2) Are the critical exponents modified on a rough surface? We shall demonstrate that the coupling of roughening and phase separation leads to a rich phase diagram, and to nontrivial critical exponents already in 1+1 dimensions.To characterize phase separation, we introduce a...

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“…The nonideal polydisperse or multicomponent systems are of great scientific and practical interest [7,8]. Recently, various growth models with two species or phases in competition [9][10][11][12][13][14], and also the multicomponent Potts growth model [15,16] have been investigated. The two-component growth model of Saito and Muller-Krumbhaar (SMK) [9] generalizes the Eden model [17] for the case of two different species (A and B) competition.…”

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Relationship between Resistivity and Structure of Photosensitive Organic Silsesquioxanes by Impedance Spectroscopy and Solid-State ²⁹Si Nuclear Magnetic Resonance

Kusaka¹,

Nakamura²,

Azuma³

et al. 2008

jjap

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We study numerically the two-component spreading model (SMK) for concave and convex radial growth two-dimensional geometries. The seed is chosen to be an occupied circle line, and the growth spreads inside the circle (concave geometry) or outside the circle (convex geometry). On the basis of a generalized diffusion-annihilation equation for domain evolution, we derive mean-field relations that describe quite well the results of numerical investigations. We conclude that the intrinsic universality of the SMK does not depend on the geometry, and that the dependence of criticality on curvature observed in numerical experiments is only an apparent effect. We discuss the dependence of the apparent critical exponent χ a upon the growth geometry and initial conditions.

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Model for growth of binary alloys with fast surface equilibration

Cited by 27 publications

References 15 publications

Self-Assembly at a Nonequilibrium Critical Point

Self-Assembly at a Nonequilibrium Critical Point

Phase Ordering and Roughening on Growing Films

Relationship between Resistivity and Structure of Photosensitive Organic Silsesquioxanes by Impedance Spectroscopy and Solid-State ²⁹Si Nuclear Magnetic Resonance

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Model for growth of binary alloys with fast surface equilibration

Cited by 27 publications

References 15 publications

Self-Assembly at a Nonequilibrium Critical Point

Self-Assembly at a Nonequilibrium Critical Point

Phase Ordering and Roughening on Growing Films

Relationship between Resistivity and Structure of Photosensitive Organic Silsesquioxanes by Impedance Spectroscopy and Solid-State 29Si Nuclear Magnetic Resonance

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Product

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Relationship between Resistivity and Structure of Photosensitive Organic Silsesquioxanes by Impedance Spectroscopy and Solid-State ²⁹Si Nuclear Magnetic Resonance