Elastic moduli, dislocation core energy, and melting of hard disks in two dimensions

Sengupta, Surajit; Nielaba, Peter; Binder, Kurt

doi:10.1103/physreve.61.6294

Cited by 100 publications

(110 citation statements)

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“…The investigation of melting in two dimensions still remains a very active research area, both experimentally (in colloids, [12][13][14][15][16][17] vortex flux lattices 18,19 and free-standing liquidcrystalline films 20 ) and numerically. [6][7][8][9][10][11][21][22][23][24][25][26][27] One reason the debate about the nature of the 2D melting transition is still continuing is that it is extremely difficult to distinguish between a weak, first-order melting transition and a continuous transition. The problem is that it is very hard to determine if the point where a solid becomes unstable toward dislocation unbinding is pre-empted by simple first-order melting.…”

Section: Introductionmentioning

confidence: 99%

Free Energy and Structure of Dislocation Cores in Two-Dimensional Crystals

Bladon

Frenkel

2004

J. Phys. Chem. B

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The nature of the melting transition in two dimensions is critically dependent on the core energy of dislocations. In this paper, we report calculations of the core free energy and the core size of dislocations in two-dimensional solids of systems interacting via square well, hard disk, and r -12 potentials. In all cases, we find that the dislocation core free energy is such that, at the densities studied, the density of free dislocation density is extremely low. We find that the core energies and core sizes are considerably smaller for the r -12 system than for the other systems studied. This illustrates the fact that, for hard-core systems, elastic continuum theory breaks down, even for relatively small strains.

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Section: Introductionmentioning

confidence: 99%

Free Energy and Structure of Dislocation Cores in Two-Dimensional Crystals

Bladon

Frenkel

2004

J. Phys. Chem. B

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“…Hoogenboom and coworkers looked for an intermediate hexatic phase during crystallization at the flat bottom wall in a gravitational field, although its existence could not be verified due to polycrystallinity [25]. Earlier observations of the hexatic phase, in experiments [21,26 -28] and in simulations [29,30], have been made in thin confined systems and not at a single wall in a 3D system. Moreover, Fig.…”

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Reentrant Surface Melting of Colloidal Hard Spheres

Dullens

Kegel

2004

Phys. Rev. Lett.

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Concentrated suspensions of model colloidal hard spheres at a wall were studied in real space by means of time-resolved fluorescence confocal scanning microscopy. Both structure and dynamics of these systems differ dramatically from their bulk analogs (i.e., far away from a wall). In particular, systems that are a glass in the bulk show significant hexagonal order at a wall. Upon increasing the volume fraction of the colloids, a reentrant melting transition involving a hexatic structure is observed. The last observation points to two-dimensional behavior of matter at walls. DOI: 10.1103/PhysRevLett.92.195702 PACS numbers: 64.60.Cn, 64.70.-p, 82.70.Dd Hard spheres under thermal excitation may be considered as the ''fruit flies'' of statistical mechanics, where the hard sphere potential is extensively used as a reference potential [1]. Therefore, rigorous insight into the behavior of hard spheres is imperative for understanding the wide class of systems where excluded volume interactions are important. In nature, all systems are bounded, either by walls or surfaces. These will tend to dominate the behavior as systems become smaller [2 -4]. Motivated by the increasing interest in nanometer-sized systems in science and technology, we address the question as to what surfaces do to the behavior of hard spheres. We expect our results to be relevant for the behavior of many other systems at walls or boundaries in general.Although the role of polydispersity is still being debated, most of the bulk behavior of hard spheres has been well established [5]. In contrast, much less is known about the influence of a single wall on the local structure and dynamics of hard spheres. In this Letter, we use colloidal model particles to address this issue. Colloidal suspensions are extensively used as experimental model hard spheres [5][6][7]. The colloidal model particles used here consist of a core of silica, 450 nm in diameter, labeled with the fluorescent dye fluorescein isothiocyanate [8]. The cores are covered with a thick shell of nonfluorescent polymethylmethacrylate (PMMA). The system is sterically stabilized by a layer of 12-poly-hydroxystearic acid that is covalently linked to the PMMA [9]. The spheres were dispersed in a mixture of tetralin, cis-decalin, and carbon tetrachloride, which (nearly) matches the refractive index and the mass density of the colloids. In this mixture the particles behave as hard spheres [6]. The particle diameter d is 1:4 m and the size polydispersity is 6%. Crystallization was absent in bulk [6].The volume fraction of the samples was defined relative to the volume fraction at random close packing of 6% polydisperse hard spheres. This fraction was set at 0.66 [10]. Confocal scanning laser microscopy was used to image the particles present in the first layer, parallel to the flat glass bottom of the container [11]. No signs of attraction between the particles and the glass wall were found. As the colloidal particles have a core-shell character, time-dependent particle coordinates could be obtai...

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“…From the linear behaviour of a local order parameter they derived bounds for a possible coexistence region. Sengupta, Nielaba and Binder [16] simulated a dislocation free triangular solid of hard disks using a constrained Monte Carlo algorithm and showed that a KTHNY transition preempts a first-order transition. Combining renormalisation groups ideas with MC input they derived also an estimate of ρ m = 0.914(2) for a possible hexatic-to-crystal transition [17].…”

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The hexatic phase of the two-dimensional hard disk system

Jaster¹

2004

Physics Letters A

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We report Monte Carlo results for the two-dimensional hard disk system in the transition region. Simulations were performed in the N V T ensemble with up to 1024 2 disks. The scaling behaviour of the positional and bond-orientational order parameter as well as the positional correlation length prove the existence of a hexatic phase as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.The analysis of the pressure shows that this phase is outside a possible first-order transition.Key words: Hard disk model, Two-dimensional melting, KTHNY theory PACS: 64.70.Dv, 64.60.CnThe nature of the two-dimensional melting transition has been an unsolved problem for many years [1,2]. The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [3,4,5,6] predicts two continuous transitions. The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation unbinding transition to the hexatic phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination unbinding transition which transforms this hexatic phase into an isotropic phase (short-range positional and orientational order). An alternative scenario has been proposed by Chui [7,8]. He presented a theory via spontaneous generation of grain boundaries, i.e. collective excitations of dislocations. He found that grain boundaries may be generated before the dislocations unbind if the core energy of dislocations is sufficiently small, and predicted a first-order transition. This is characterized by a coexistence region of the solid and isotropic phase, while no hexatic phase exists. Another proposal was given by Glaser and Clark [2]. They considered a detailed theory where the transition is handled as a condensation of localized, thermally generated geometrical defects and found also a first-order transition. Calculations based on the density-functional approach were done by Ryzhov and

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Elastic moduli, dislocation core energy, and melting of hard disks in two dimensions

Cited by 100 publications

References 45 publications

Free Energy and Structure of Dislocation Cores in Two-Dimensional Crystals

Free Energy and Structure of Dislocation Cores in Two-Dimensional Crystals

Reentrant Surface Melting of Colloidal Hard Spheres

The hexatic phase of the two-dimensional hard disk system

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