Two-dimensional melting

Strandburg, Katherine J.

doi:10.1103/revmodphys.60.161

Cited by 1,006 publications

(658 citation statements)

References 143 publications

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“…The 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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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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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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

The hexatic phase of the two-dimensional hard disk system

Jaster¹

2004

Physics Letters A

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“…Recently the layered close-packed crystalline structure and their structural transition were observed in experiments with dust rf discharge [3] and with ion layered crystals in ion traps [4]. Motivated by the theoretical works of Nelson, Halperin [5], and Young [6] who developed a theory for a two stage continuous melting of a two dimensional (2D) crystal and which was based on ideas of Berenzinskii [7], Kosterlitz and Thouless [8], several experimental [9][10][11][12] and theoretical studies [13][14][15][16][17][18][19][20][21][22][23][24][25] were devoted to the melting transition of mainly single layer crystals. In this case the hexagonal lattice is the most energetically favored structure for potentials of the form 1/r n [26,27].…”

Section: Introductionmentioning

confidence: 99%

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Schweigert

Peeters

1999

Phys. Rev. B

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The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the MonteCarlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard-Jones and 1/r 12 repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.

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“…Since 1973 it has been known that two-dimensional materials will exhibit qualitatively different behaviour when melting [99,100]. The theory predicts that orientational and translational order will be broken at two different temperatures, and the intermediate phase -referred to as the hexatic phase [101] -retains orientational, but no translational or long-range periodic order.…”

Section: The Connection Between Size and Dimensionalitymentioning

confidence: 99%

Cluster melting: new, limiting, and liminal phenomena

Gaston

2018

Advances in Physics: X

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The thermodynamic behaviour of clusters and nanoscale structures is both a challenge to the statistical basis of the theory, and of paramount importance to experiment. In this review, the competing influences that determine the melting temperature and behaviour of small atomic clusters is discussed, with reference to both experiment and theory. The liminal spaces between solid and liquid, the non-scaling and scaling regimes, and the metallic and non-metallic states are discussed, and presented as a primary cause of the emergence of new phenomena. Particular emphasis is given to recent theoretical work that combines each of these liminal regions and enables, through first principles calculations of dynamic atomic interactions in Born Oppenheimer molecular dynamics, the explanation of greater than bulk melting temperatures in certain atomic cluster systems. Some perspective is also given on the important questions in nanoscale thermodynamics that remain to be addressed. ARTICLE HISTORY

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Two-dimensional melting

Cited by 1,006 publications

References 143 publications

The hexatic phase of the two-dimensional hard disk system

The hexatic phase of the two-dimensional hard disk system

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Cluster melting: new, limiting, and liminal phenomena

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