We studied the melting behavior of two-dimensional colloidal crystals with a Yukawa pair potential by Brownian dynamics simulations. The melting follows the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario with two continuous phase transitions and a middle hexatic phase. The two phase-transition points were accurately identified from the divergence of the translational and orientational susceptibilities. Configurational temperatures were employed to monitor the equilibrium of the overdamped system and the strongest temperature fluctuation was observed in the hexatic phase. The inherent structure obtained by rapid quenching exhibits three different behaviors in the solid, hexatic, and liquid phases. The measured core energy of the free dislocations, E(c) = 7.81 ± 0.91 k(B)T, is larger than the critical value of 2.84 k(B)T, which consistently supports the KTHNY melting scenario.
We performed Brownian dynamics simulations on the melting of two-dimensional colloidal crystals in which particles interact via a Yukawa potential. A stable hexatic phase was found in the Yukawa systems, but we also found that the melting of Yukawa systems is a two-stage melting, which is inconsistent with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. A two-phase coexistence region between the stable hexatic phase and the isotropic liquid phase was found. The behavior of point defects in the coexistence region is very complicated. The emergence of some unstable free disclinations and grain boundaries was a characteristic representative of the isotropic liquid phase, and a large number of free dislocations indicated the existence of a hexatic phase. This indicates the existence of a phase of hexatic-isotropic liquid phase coexistence. The big picture in the melting of a two-dimensional Yukawa system is that first the system undergoes a transition induced by the formation of free dislocations, then it goes through a phase coexistence, and finally, it comes into an isotropic fluid phase. This melting process is consistent with experiments and simulations.PACS numbers: 64.70.D-, 82.70.Dd, 61.72.Lk I. INTRODUCTIONIn contrast to the case of melting in three-dimensional systems, it has by now been well established that in twodimensional (2D) crystals, long-range positional order does not exist due to long-wavelength fluctuations [1]. Despite this, in a 2D crystal, there exists a special kind of long-range bond orientational order. A microscopic scenario of 2D melting has been posited in the form of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [2,3,4,5]. The KTHNY theory predicts a new phase, the so-called hexatic phase, that exists between the solid and liquid phases in 2D melting [6].According to the KTHNY theory, the melting of a two-dimensional system is a two-stage transition. In the first stage we start with the two-dimensional system in a solid phase, which has both quasi-long-range positional order and long-range bond orientation order; the system then undergoes a continuous transition and becomes to a hexatic phase with short-range positional order and quasi-long-range orientational order. In the second stage, another continuous transition drives the hexatic phase to an isotropic liquid phase in which both positional and bond orientational order have short ranges.The KTHNY theory predicts the unbinding of topological defects to break the symmetry in the two-stage transitions. The physical driving force behind the two-stage transitions is the dissociation of bound defect pairs, specifically pairs of dislocation (solid→hexatic) and pairs of disclinations (hexatic→liquid). Two-dimensional systems are characterized by two different order parameters, namely, the orientational and translational order, corresponding to the two types of topological defects. Dissociation of the dislocation pairs causes the translational symmetry to be broken, and dissociation of free dislocations melts cau...
We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with shortranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: (1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s 2 , reaches −4.5 ± 0.5 k B . Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information. We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with short-ranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: Two features at the two-dimensional freezing transitions(1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s 2 , reaches −4.5 ± 0.5 k B . Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information.
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