Monte Carlo simulation of crystal-fluid coexistence states in the hard-sphere system under gravity with stepwise control

Abstract

Monte Carlo (MC) simulations were performed for hard spheres (with diameter sigma and mass m) placed between well-separated upper and lower hard walls. A periodic boundary condition was imposed in the horizontal direction. The system was exposed to the gravitational field with the acceleration due to gravity g. After preparing a melt as the initial state, g was increased stepwise up to mgsigma/k(B)T(identical with g(*))=1.5 or 2.0 with an increment Deltag(*) = 0.1; k(B)T is the temperature multiplied by Boltzmann's constant. We maintained g(*) at each value for 2.0 x 10(5) MC cycles. The transition of the system into a metastable state such as a polycrystalline state due to trapping phenomena was successfully avoided. A monotonic increase and subsequent saturation were observed for the development of the crystalline region formed at the bottom of the system. The development of this region accompanied a shrinkage of the defective (or less ordered) crystalline region that was formed between the bottom region and the fluid phase. As the development of the bottom region almost saturated, the defective region grew upward again.

Crystal structure of hard spheres under gravity by Monte Carlo simulation

“…The major results, which will be published in Ref. [29], are the findings of the defective or less ordered crystalline region above the bottom well-ordered crystal and conversion of that region into the well-ordered crystalline state as g* increases. In the present paper, as a part of the next step, we make some analyses on the structure we obtained by the simulations.…”

“…In a previous work [28], we reported that under the same geometry as these the system seemed to be trapped into a polycrystalline metastable state. In the present paper, we repot some detail of our MC simulation on the similar system with step-wise controlled gravitational number g* [29]. Here, g* is defined by g*Zmgs/k B T with m being the mass of a particle, s the HS diameter, g the acceleration due to gravity, and k B Boltzmann's constant, T the temperature.…”

Crystallization of Brownian Particles from Walls Induced by a Uniform External Force

“…In order to enlarge the grain size, it is necessary to increase the area of the base of columnar grains and to decrease the number of nuclei formed in the initial stage. In simulations, 10,11) it is shown that large grains of hard sphere particles without defects are formed by changing the external force during sedimentation, but controlling the force during sedimentation is probably difficult in the experiment. 9) In order to solve the problems in a previous study, 9) recently, Suzuki and co-workers 12,13) used a centrifugation method and succeeded in forming large three-dimensional colloidal crystals.…”

Adsorption, Desorption, Surface Diffusion, Lattice Defect Formation, and Kink Incorporation Processes of Particles on Growth Interfaces of Colloidal Crystals with Attractive Interactions

“…After some pioneering experiments, extensive fundamental studies on colloidal crystals have been conducted so far [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. On the other hand, the application of colloidal crystals as photonic bandgap (PBG) crystals has also received much attention.…”

“…However, almost all systems reported so far have mainly utilized repulsive interactions between particles for colloidal crystallization basically [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]20,21,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][42][43][44], whereas the growth of crystals of atoms or molecules usually proceeds via attractive interactions. In such systems, in situ observation of growth interfaces of colloidal crystals by optical microscopy is usually difficult because of high particle concentrations.…”