Crystal structure of hard spheres under gravity by Monte Carlo simulation

Abstract

Monte Carlo simulations were performed for hard spheres (HSs) under gravity. The gravity was increased stepwise. HSs were placed between the bottom and the top hard walls. For g*R0.9, we observed that a 'sediment' was comprised of two crystalline and one fluid regions. 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 T the temperature multiplied by Boltzmann's constant. The bottom crystal was less defective or well-ordered and the crystal lay between the bottom one and the fluid phase was defective or less-ordered. In this paper, we investigate the structure of the crystals. Despite no apparent defects, the crystal has highly been distorted. That is, the fcc lattice has been contracted in the vertical direction more than in the horizontal direction. The crystal-fluid coexistence condition for the bulk HS system does, in principle, not hold for the present systems at the crystal-fluid interface. In addition, though the fine scale density profile exhibits a discontinuity apparently across the crystal-crystal interface, the interlayer separation increases linearly with the height. q

Monte Carlo simulation of growth of hard-sphere crystals on a square pattern

“…Moreover, we have already found a configuration which was succeeded in newly grown crystal in the fluid phase in simulations of the same condition [17]. In addition, we confirmed that a coherent growth occurred in the simulations [18]. Complementarily to the simulations, we have given elastic energy calculations to understand the driving force of upward move of the Shockley partial dislocation [19,20].…”

“…The separation between neighboring groove edges was 0:338s. Accordingly, the periodicity of the lattice was 1:045s and the diagonal distance 1:478s; i.e., we set the bottom lattice so as to coincide with the bottom (0 0 1) layer of the fcc crystal of the previous flat wall simulation [18].…”

“…The purpose of the present simulation is to resolve the shortcoming of previous simulations [14,15,17,18]. In those simulation fcc (0 0 1) stacking was forced due to the stress from a small periodic boundary simulation box.…”

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

“…The other point characteristic of these simulations is that the coherent growth [12] occurred as already mentioned. We find that the lattice constant c increases linearly with the altitude z whereas the lattice constants a ¼ b are constant.…”

Computer Simulations of Crystal Growth Using a Hard-Sphere Model

“…Although numerical estimation has been carried out using an elastic constant for the HS crystal, this effect is not limited to colloidal crystals. However, the condition of coherent growth (which was reported in Reference [77]) was used. The glide mechanism of a partial dislocation for the reduction of stacking disorder was revealed in Reference [74].…”