Crystallography and statics of Coulomb crystals

Three-dimensional and two-dimensional Coulomb crystals have been formed in plasmas by growing carbon fine particles, of which size has been controlled using the Mie-scattering ellipsometry. Lattice constants of the crystals were determined from CCD images of top view and side view taken at the same time and at the same position. Smaller particles of 1.4 mu m in diameter formed the structure of a three-dimensional Coulomb crystal, which was face-centered orthorohmbic. It is suggested that the ratio of the lattice constants of the crystal is decided so that Coulomb energy takes a minimum value under the condition of constant particle density in horizontal layers. Larger particles of 5 mu m in diameter formed a two-dimensional crystal structure, simple hexagonal one. The result of the dependence of lattice constants with particle density for the crystal indicates that the force acting on particles in the vertical direction is repulsive for smaller value of the vertical lattice constant while attractive for larger one. The vertical directional forces are mainly external ones for smaller particles, however a directional attractive force between particles plays an important role for the formation of Coulomb crystal for larger particles.