Specific Heat in Two-Dimensional Melting

Deutschländer, Sven; Puertas, Antonio M.; Maret, Georg; Keim, Peter

doi:10.1103/physrevlett.113.127801

Cited by 48 publications

(42 citation statements)

References 76 publications

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“…The 2D systems are well established, and we investigated crystallization, defects (37)(38)(39)(40), and the glass transition (30,35,36) with this setup. They consist of colloidal monolayers where individual particles are sedimented by gravity to a flat a water/air interface in hanging-droplet geometry.…”

Section: Colloidal Systemsmentioning

confidence: 99%

Mermin–Wagner fluctuations in 2D amorphous solids

Illing

Fritschi

Kaiser

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016) J Phys Condens Matter 28:481001]. It was due to the lack of broken translational symmetry in two dimensions-doubting the existence of 2D crystalsand the first computer simulations foretelling 2D crystals (at least in tiny systems). The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact, but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin-Wagner fluctuations, which conserve the homogeneity of space on long scales.Mermin-Wagner fluctuations | 2D ensembles | glass transition | phase transition | confined geometry F or structural phase transitions, it is well known that the microscopic mechanisms breaking symmetry are not the same in two and in three dimensions. Whereas 3D systems typically show first-order transitions with phase equilibrium and latent heat, 2D crystals melt via two steps with an intermediate hexatic phase. Unlike in 3D, translational and orientational symmetry are not broken at the same temperature in 2D. The scenario is described within the Kosterlitz, Thouless, Halperin, Nelson, Young (KTHNY) theory (1-5), which was confirmed (e.g., in colloidal monolayers) (6, 7). However, for the glass transition, it is usually assumed that dimensionality does not play a role for the characteristics of the transition, and 2D and 3D systems are frequently used synonymously (8-12), whereas differences between the 2D and 3D glass transition are reported in ref. 13.In the present work, we compare data from colloidal crystals and glasses and show that Mermin-Wagner fluctuations, well known from 2D crystals, are also present in amorphous solids (14, 15). Mermin-Wagner fluctuations are usually discussed in the framework of long-range order (magnetic or structural). However, in the context of 2D crystals, they have also had an impact on dynamic quantities like mean squared displacements (MSDs). Long before 2D melting scenarios were discussed, there was an intense debate as to whether crystals and perfect longrange order (including magnetic order) can exist in 1D or 2D at all (16)(17)(18)(19). A beautiful heuristic argument was given by Peierls (17): Consider a 1D chain of particles with nearest neighbor interaction. The relative distance fluctuation between particle n and particle n + 1 at finite temperature may be ξ. Similar is the fluctuation between particle n + 1 and n + 2. The relative fluctuation between second nearest neig...

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Section: Colloidal Systemsmentioning

confidence: 99%

Mermin–Wagner fluctuations in 2D amorphous solids

Illing

Fritschi

Kaiser

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

144

165

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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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confidence: 99%

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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“…Additionally, there are various methods such as optical techniques 4,5 for controlling colloidal ordering and manipulating individual colloids. Examples of phenomena that have been studied with colloids include two-dimensional melting transitions 6,7 , solid-to-solid phase transitions 8 , glassy dynamics 3 , commensurate and incommensurate phases [9][10][11][12] , depinning behaviors [13][14][15][16] , self-assembly 17,18 , and dynamic sorting [19][20][21] . It is also possible to use colloids to study plastic deformation under shear in crystalline 22 or amorphous 23 colloidal assemblies.…”

Section: Introductionmentioning

confidence: 99%

Avalanches, plasticity, and ordering in colloidal crystals under compression

McDermott

Reichhardt

2016

Phys. Rev. E

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Using numerical simulations we examine colloids with a long-range Coulomb interaction confined in a two-dimensional trough potential undergoing dynamical compression. As the depth of the confining well is increased, the colloids move via elastic distortions interspersed with intermittent bursts or avalanches of plastic motion. In these avalanches, the colloids rearrange to minimize their colloid-colloid repulsive interaction energy by adopting an average lattice constant that is isotropic despite the anisotropic nature of the compression. The avalanches take the form of shear banding events that decrease or increase the structural order of the system. At larger compressions, the avalanches are associated with a reduction of the number of rows of colloids that fit within the confining potential, and between avalanches the colloids can exhibit partially crystalline or even smectic ordering. The colloid velocity distributions during the avalanches have a non-Gaussian form with power law tails and exponents that are consistent with those found for the velocity distributions of gliding dislocations. We observe similar behavior when we subsequently decompress the system, and find a partially hysteretic response reflecting the irreversibility of the plastic events.

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Specific Heat in Two-Dimensional Melting

Cited by 48 publications

References 76 publications

Mermin–Wagner fluctuations in 2D amorphous solids

Mermin–Wagner fluctuations in 2D amorphous solids

The melting of the classical two-dimensional Wigner crystal

Avalanches, plasticity, and ordering in colloidal crystals under compression

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