Dependence of crystallization of Brownian particles by sedimentation on the force direction

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.