Construction and investigation of a hard-sphere crystal-melt interface by a molecular dynamics simulation

Mori, Ayumi; Manabe, Ryoji; Nishioka, Kazumi

doi:10.1103/physreve.51.r3831

Cited by 39 publications

(28 citation statements)

References 10 publications

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“…1͑a͒, where one can observe that the fluid has already crystallized in the proximity of the solid after the preliminary equilibration stage. This behavior had already been observed in previous simulations, 9 but should not affect the calculations. One can choose to start with different relative amounts of liquid and solid, as long as the system accommodates bulk regions of each phase.…”

Section: Resultssupporting

confidence: 57%

“…[9][10][11] The most extensive of these works is due to Davidchack and Laird, 11 who examined the structure and dynamics of the fcc ͑111͒ and ͑100͒ crystalliquid interfaces for systems of about 10 000 hard spheres using constant-energy MD simulation. As the overall volume of the system is kept constant in the course of their simulations, possible stress in the bulk solid was eliminated by trial adjustment of the dimensions of the simulation cell.…”

Section: The Journal Of Chemical Physics 128 154507 ͑2008͒mentioning

confidence: 99%

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Determination of the melting point of hard spheres from direct coexistence simulation methods

Noya

Vega

Miguel

2008

The Journal of Chemical Physics

107

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We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the ͑planar͒ fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p = 11.54͑4͒k B T / 3 , which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p = 11.54͑4͒k B T / 3 . We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.

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Section: Resultssupporting

confidence: 57%

Section: The Journal Of Chemical Physics 128 154507 ͑2008͒mentioning

confidence: 99%

Determination of the melting point of hard spheres from direct coexistence simulation methods

Noya

Vega

Miguel

2008

The Journal of Chemical Physics

107

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“…Although the initial results for LJ and inverse twelve power were not very successful (probably due to the small size of the systems and to the short length of the runs), the method is becoming more popular in the last few years. In fact it has been applied to simple fluids [172,173,174,175,153,176], metals [177,178,179,180], silicon [181], ionic systems [182,183], hard dumbells [184], nitromethane [135] and water [108,109,185,186,187,188,189,190,191]. Two simulation boxes, having an equilibrated solid and liquid respectively, are joined along the z axis (the direction perpendicular to the plane of the interface).…”

Section: Direct Fluid-solid Coexistencementioning

confidence: 99%

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Vega¹,

Sanz

Abascal

et al. 2008

J. Phys.: Condens. Matter

275

452

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Abstract. In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations, agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behaviour of charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites).

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“…Note that the maximum density values in the crystal are 4.0 Ϫ3 and 4.6 Ϫ3 for ͑100͒ and ͑111͒ orientations, respectively, which agrees with the results of the KB Monte Carlo simulation. 11 In the MMN simulation 12 the corresponding values are 3.2 Ϫ3 and 3.7 Ϫ3 . This discrepancy is due to the fact that in out simulation the bins are required to move together with the average positions of the crystal layers, which eliminates artificial broadening of the crystal density peaks caused by the drift of the average crystal position with respect to the simulation cell.…”

Section: A Density Profilesmentioning

confidence: 99%

Simulation of the hard-sphere crystal–melt interface

Davidchack

Laird

1998

The Journal of Chemical Physics

206

170

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In this work, we examine in detail the structure and dynamics of the face-centered cubic ͑100͒ and ͑111͒ crystal-melt interfaces for systems consisting of approximately 10 4 hard spheres using molecular dynamics simulation. A detailed analysis of the data is performed to calculate density, pressure, and stress profiles ͑on both fine and coarse scales͒, as well as profiles for the diffusion and orientational ordering. The strong dependence of the coarse-grained profiles on the averaging procedure is discussed. Calculations of 2-D density contours in the planes perpendicular to the interface show that the transition from crystal to fluid occurs over a relatively narrow region ͑over only 2-3 crystal planes͒ and that these interfacial planes consist of coexisting crystal-and fluidlike domains that are quite mobile on the time scale of the simulation. We also observe the creation and propagation of vacancies into the bulk crystal.

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Construction and investigation of a hard-sphere crystal-melt interface by a molecular dynamics simulation

Cited by 39 publications

References 10 publications

Determination of the melting point of hard spheres from direct coexistence simulation methods

Determination of the melting point of hard spheres from direct coexistence simulation methods

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Simulation of the hard-sphere crystal–melt interface

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