How close to two dimensions does a Lennard-Jones system need to be to produce a hexatic phase?

Gribova, N. V.; Arnold, Axel; Schilling, Tanja; Holm, Christian

doi:10.1063/1.3623783

Cited by 44 publications

(46 citation statements)

References 47 publications

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“…While systems governed by very short-range or hard-core interactions are reported to exhibit coexisting phases [11][12][13], thus contradicting the notion of a continuous transition, reports on soft repulsive particles in two dimensions favor the KTHNY scenario [14][15][16]. For particles interacting via long-range dipolar interactions scaling with the inverse cube of the particle separation, the KTHNY scenario has been unambiguously confirmed [17][18][19]. Video-microscopy experiments on superparamagnetic colloidal particles pending at an air-water interface, where an external magnetic field induces dipolar moments perpendicular to the surface, have verified the predictions of the KTHNY scenario in detail [20,21], including the elastic properties related to the mechanism of defect unbinding [22].…”

Section: Introductionmentioning

confidence: 88%

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

et al. 2013

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Using both video microscopy of superparamagnetic colloidal particles confined in two dimensions and corresponding computer simulations of repulsive parallel dipoles, we study the formation of fluctuating orientational clusters and topological defects in the context of the KTHNY-like melting scenario under quenched disorder. We analyze cluster densities, average cluster sizes, and the population of noncluster particles, as well as the development of defects, as a function of the system temperature and disorder strength. In addition, the probability distribution of clustering and orientational order is presented. We find that the well-known disorder-induced widening of the hexatic phase can be traced back to the distinct development characteristics of clusters and defects along the melting transitions from the solid phase to the hexatic phase to the isotropic fluid.

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Section: Introductionmentioning

confidence: 88%

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

et al. 2013

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“…This is undesirable behavior since our aim is to study nucleation in a 3d system rather than any 2d aspects of crystallization. 30 To inhibit a complete crystalline layer forming, it was necessary to reduce the strength of the attractions between the moving and surface particles. We achieved this by setting MS = 0.3 MM , i.e., by setting the well depth between a surface and a moving particle to 30% of the well depth between two moving particles.…”

Section: A Simulation Setup and Interaction Potentialsmentioning

confidence: 99%

Computer simulation of epitaxial nucleation of a crystal on a crystalline surface

Mithen

Sear

2014

The Journal of Chemical Physics

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We present results of computer simulations of crystal nucleation on a crystalline surface, in the Lennard-Jones model. Motivated by the pioneering work of Turnbull and Vonnegut [Ind. Eng. Chem. 44, 1292 (1952)], we investigate the effects of a mismatch between the surface lattice constant and that of the bulk nucleating crystal. We find that the nucleation rate is maximum close to, but not exactly at, zero mismatch. The offset is due to the finite size of the nucleus. In agreement with a number of experiments, we find that even for large mismatches of 10% or more, the formation of the crystal can be epitaxial, meaning that the crystals that nucleate have a fixed orientation with respect to the surface lattice. However, nucleation is not always epitaxial, and loss of epitaxy does affect how the rate varies with mismatch. The surface lattice strongly influences the nucleation rate. We show that the epitaxy observed in our simulations can be predicted using calculations of the potential energy between the surface and the first layer of the nucleating crystal, in the spirit of simple approaches such as that of Hillier and Ward [Phys. Rev. B 54, 14037 (1996)

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“…For all experimental systems mentioned above, the study of the phase transition between the ordered Wigner crystal and the disordered fluid-like phases has peculiar importance. Not only for a better understanding of the structural properties of these systems, but also for the theoretical study of the two dimensional meltings [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In this letter, we report an extensive Monte Carlo study of the melting of the classical two dimensional Wigner crystal.…”

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The melting of the classical two-dimensional Wigner crystal

Mazars¹

2015

EPL

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D--Solid-liquid transitions PACS 64.60.qe -General theory and computer simulations of nucleation PACS 64.60.an -Finite-size systems Abstract -We report an extensive Monte-Carlo study of the melting of the classical two dimensional Wigner crystal for a system of point particles interacting via the 1/r-Coulomb potential. A hexatic phase is found in systems large enough. With the multiple histograms method and the finite size scaling theory, we show that the fluid/hexatic phase transition is weakly first order. No set of critical exponents, consistent with a Kosterlitz-Thouless transition and the finite size scaling analysis for this transition, have been found.Like charged particles immersed in a homogeneous neutralizing background form crystals at low temperature [1][2][3] ; these crystals are called Wigner crystals after the seminal work of E.P. Wigner in 1934 on electrons in metals [1]. Since the original work of Wigner, Coulomb crystals have been observed in a large variety of systems: in plasma physics [4,5], in colloids science [6,7], in semiconductors [8][9][10] and in biology [7]. Two dimensional Wigner crystals are observed in complex plasmas [4,5], in electrons trapped on the surface of liquid Helium [11][12][13][14], in lasercooled 9 Be + ions confined in Penning traps [15], in inversion layer of semiconductors at low temperature [16]. Colloids and dusty plasmas are classical systems ; the classical regime for electrons and ions is defined, in absence of magnetic field, when the Fermi energy is small compared to interaction energy and temperature ; for surface electrons, it corresponds to low surface density [3,17,18]. The ground-state of the classical two dimensional Wigner crystal is known to be a triangular lattice [2,3,[19][20][21] and it is worthwhile to outline that the long ranged nature of the interaction in Coulomb systems does not fulfill the hypothesis of the Mermin theorem on the abscence of long ranged cristalline order in two dimensions [22]. For all experimental systems mentioned above, the study of the phase transition between the ordered Wigner crystal and the disordered fluid-like phases has peculiar importance. Not only for a better understanding of the structural properties of these systems, but also for the theoretical study of the two dimensional meltings [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In this letter, we report an extensive Monte Carlo study of the melting of the classical two dimensional Wigner crystal. The system is made of N charged point particles confined in a two dimensional plane ; periodic boundary conditions in two dimensions are used. The interaction energy between a pair of particles is the Coulomb energy V (r) = Q 2 /r with Q the charge of particles and r the distance in the plane between both particles. The charges of particles are neutralized by an uniform background of charge density σ 0 ; electroneutrality of the system reads as N Q + σ 0 S = 0 with S the surface of the simulation cell. The number density is noted ρ = N/S a...

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How close to two dimensions does a Lennard-Jones system need to be to produce a hexatic phase?

Cited by 44 publications

References 47 publications

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

Computer simulation of epitaxial nucleation of a crystal on a crystalline surface

The melting of the classical two-dimensional Wigner crystal

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