Colloidal crystals are three-dimensional regular structures formed by colloidal particles with submicron size.The formation of colloidal crystals  has received much attention for their application as photonic crystals.With regard to the distance between particles, the colloidal crystals are classified under two types.When the distance between particles is as large as the diameter of particles, i.e  the particles are packed tightly,the crystals are called  close-packed colloidal crystals. They are now the focus of attention as templates for inverse opals with three-dimensional photonic bandgaps.

  From now on, many groups have tried to create a close-packed colloidal crystal by some techniques, e.g. using a template with a regulararray of pyramidal pits [1], and sedimentation by gravitation [2]. However, the colloidal crystals  formed in those studies [1,2] are thin or narrowly columnar. In order to use a templates for inverse opals, it has been necessary to increase  the size of the grain of colloidal crystals.

 Recently, Suzuki and co-workers[3,4] used a centrifugation method and succeed in creating a three-dimensional colloidal crystal with large grain size.In one of their experiments[4], they controlled the direction of the centrifugal force. When the direction of the force is tilted from the normal direction of the wall of a  container,
the grain size is larger than that with an external force  perpendicular to a wall.

 Keeping their experiment[4] in mind, we carry out a simulation of Brownian dynamics, and study how ordering of particles with short ranged repulsion interaction changes by the direction and the strength of a uniform external force. When the external force is added to particles with a uniform density, the particles move to the direction to the force. Two-dimensional ordering of particles occurs on walls. Then, three-dimensional ordering starts from the walls. The density of particles on the walls increases all at once when the direction of external force is  perpendicular to the walls, so that the positions of the particles attached on the walls do not move easily and ordering on the walls is law. On the other hands, the density of particles increases from an edge with a tilted force, so that ordering of particles, which proceeds from the edge, is high.

 The difference in ordering on walls affects on the grain size of colloidal crystal. In bulk, both grains with the face-centered cubic structure and those with the hexagonal close-packed structure are formed. Irrespective of the type of structure,  a lot of large grains are formed with a tilted external force.

References

[1] Y. Yin, Z. Li, and Y. Xia, Langmuir 19, 622 (2003).

[2] K. E. Davis, W. B. Russel, and W. J. Glantschnig, Science 245, 507 (1983).

[3] Y. Suzuki, T. Sawada, and K. Tamura, J. Cryst. Growth 318, 780 (2011).

[4] K. Hashimoto, A. Mori, K. Tamura, and Y. Suzuki, Jpn. J. Appl. Phys. 52, 030201 (2013).

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