We carry out Brownian dynamics simulations and study the crystallization of particles in an inverse pyramidal-shaped container induced by an external force. Owing to the side walls of the container, the face-centered cubic (fcc) structure is mainly formed. In the bulk, both disordered solidlike particles and hexagonal close-packed (hcp) structured particles are hardly formed. These two types of particle appear near the central axis of the container. Their numbers increase with increasing strength of the external force.

The formation of a large close-packed colloidal crystal with the fcc structure was observed during the sedimentation of colloidal particles in an inverted pyramidal pit [S. Matsuo et al., Appl. Phys. Lett. 82, 4285 (2003)]. Carrying out Brownian dynamics simulations, we confirmed that large grains with the fcc structure are formed when the apex angle of the inverted pyramidal container is suitable and the force direction is parallel to the the center axis [Y. Kanatsu and M. Sato, J. Phys. Soc. Jpn. 84, 044601 (2015)].To form a high-quality colloidal crystal without defects, it is important to investigate in detail how the quality of a colloidal crystal is affected by the force direction and container shape. In this paper, we focus on the effect of the force direction on crystal quality and investigate how the ratio of the number of the hcp structured particles, N hcp , to that of fcc structured particles, N fcc , is affected by the force direction.In our simulation, the ratio of N fcc to N hcp is hardly changed when the force direction deviates from the central axis: N fcc is much larger than N hcp irrespective of the force direction. Thus, our results show that the crystal structure is insensitive to the force direction in forming a colloidal crystal by sedimentation in an inverted pyramidal container.

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Keeping the formation of colloidal crystals by sedimentation in mind, we carry out Brownian dynamics simulations and study the crystallization of colloidal particles in an inverted pyramidal container. When an external force is added, the sedimentation of particles occurs and the particle density increases in the low region of the inverted pyramidal container. The crystallization of particles occurs and the face-centered cubic structure is formed in the container. When the force is large, the particles with the hexagonal close-packed structure and disordered particles are also formed and act as defects in bulk. After the sedimentation finishes, we decrease the force transiently. The defects in bulk are removed from the bulk.A close-packed colloidal crystal with the face-centered cubic (fcc) structure is considered as a coordinate of an inverted opal with a three-dimensional full photonic band gap, 1) and the sedimentation of colloidal particles 2) is a useful method to form close-packed colloidal crystals. During sedimentation, particles form a triangular lattice when they deposit on the flat bottom. The lattice acts as the {111} face of the fcc structure and the growth of grains with the fcc structure occurs. However, there are two stacking ways on the triangular lattice. Thus, grains with the hexagonal closepacked (hcp) structure can also grow on the lattice 2, 3) although the fcc structure is more stable than the hcp structure. 4, 5)To prevent the formation of grains with the hcp structure, Matsuo et al. used an inverted pyramidal pit 6) as a container. When the inclination of the pyramidal surfaces of the pit is suitable and the direction of an external force inducing the sedimentation is parallel to the central axis, the triangular lattice is formed on the pyramidal surfaces and the growing interface, which is perpendicular to the external force, becomes the {100} face of the fcc structure. Since the stacking way is unique on the {100} face, the crystal with the fcc structure grows without forming the grains with the hcp structure. Keeping the experiment of Matsuo et al. 6) in mind, we have carried out