Statistical theory of crystallization in a system of hard spheres

Ryzhov, V. N.; Tareeva, E. E.

doi:10.1007/bf01019321

Cited by 37 publications

(3 citation statements)

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“…However, in 2D the singular uctuations of the order parameter (dislocations and disclinations) may cause the qualitative differences between 2D and 3D behavior of matter. [26][27][28][29] Despite the long history of investigations, the melting transition of most materials in 2D is not well understood, because theories explaining the transition on a microscopic scale are not available. Furthermore, the mechanism of melting depends on the details of the interactions between the particles forming the crystal lattice.…”

Section: Introductionmentioning

confidence: 99%

How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system?

et al. 2014

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We present a computer simulation study of the phase diagram and anomalous behavior of two-dimensional (2D) and three-dimensional (3D) classical particles repelling each other through an isotropic core-softened potential. As in the analogous three-dimensional case, in 2D a reentrant-melting transition occurs upon compression under not too high pressure, along with a spectrum of thermodynamic and dynamic anomalies in the fluid phase. However, in two dimensions the order of the region of anomalous diffusion and the region of structural anomaly is inverted in comparison with the 3D case, where there exists a water-like sequence of anomalies, and has a silica-like sequence. In the low density part of the 2D phase diagram, melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario for this melting transition. On the other hand, at high density part of the phase diagram one first-order transition takes place.

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Section: Introductionmentioning

confidence: 99%

How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system?

et al. 2014

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“…Kirkwood & Monroe first suggested the identification of the bifurcation point of solutions to the first equation of the BBGKY hierarchy with the freezing transition (Kirkwood & Monroe 1941); the version of the theory we use is based on the improved implementations developed by Ryzhov & Tareeva (1981) and Cerjan et al (1985). All of these implementations use several approximations that compromise the accuracy of the predicted properties of the transition, e.g.…”

Section: Introductionmentioning

confidence: 99%

A density functional theory of one- and two-layer freezing in a confined colloid system

Rice

2007

Proc. R. Soc. A.

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We report an analysis of the change in character of the fluid-to-solid transition in a quasi-two-dimensional hard-sphere colloid system as the confining wall separation changes from one to two hard-sphere diameters. Our analysis is based on a study of the bifurcation of solutions of the integral equation for the singlet density, using both direct and pair correlation function representations. Two approximations used in previous bifurcation analyses of freezing are improved in the work reported in this paper. The results of the analysis correctly predict the qualitative change in freezing as a function of the confining wall separation and density, specifically the change from a fluid-to-onelayer hexagonal solid transition to a fluid-to-two-layer square solid transition at a wall separation of 1.6 hard-sphere diameters. The numerical predictions of the theory are in semi-quantitative agreement with simulation data for the density dependence of the liquid-solid transition line for wall separations up to 1.6 hard-sphere diameters.

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“…Consistent with this notion, a number of workers have, in practice, accomplished the program of building a periodic crystal state starting from the uniform liquid state, starting from the pioneering work of Kirkwood and Monroe [102]. Subsequent, detailed calculations along similar lines [103,104] explicitly confirmed the discontinuous nature of the transition. At the same time, they showed that physical quantities, such as the liquid and crystal densities at the transition, converge slowly, if at all, with number of the reciprocal vectors in the expansion (27) [104].…”

Section: Placing the Glass Transition On The Map Thermodynamics-wise:...mentioning

confidence: 98%

Theory of the Structural Glass Transition: A Pedagogical Review

Lubchenko

2015

Preprint

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The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including: the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.

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Statistical theory of crystallization in a system of hard spheres

Cited by 37 publications

References 11 publications

How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system?

How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system?

A density functional theory of one- and two-layer freezing in a confined colloid system

Theory of the Structural Glass Transition: A Pedagogical Review

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