Frustrated crystallization of a monolayer of magnetized beads under geometrical confinement

We present a systematic experimental study of the confinement effect on the crystallization of a monolayer of magnetized beads. The particles are millimeter-scale grains interacting through the short range magnetic dipole-dipole potential induced by an external magnetic field. The grains are confined by repulsing walls and are homogeneously distributed inside the cell. A two-dimensional (2d) Brownian motion is induced by horizontal mechanical vibrations. Therefore, the balance between magnetic interaction and agitation allows investigating 2d phases through direct visualization. The effect of both confinement size and shape on the grains' organization in the low-energy state has been investigated. Concerning the confinement shape, triangular, square, pentagonal, hexagonal, heptagonal, and circular geometries have been considered. The grain organization was analyzed after a slow cooling process. Through the measurement of the averaged bond order parameter for the different confinement geometries, it has been shown that cell geometry strongly affects the ordering of the system. Moreover, many kinds of defects, whose observation rate is linked to the geometry, have been observed: disclinations, dislocations, defects chain, and also more exotic defects such as a rosette. Finally, the influence of confinement size has been investigated and we point out that no finite-size effect occurs for a hexagonal cell, but the finite-size effect changes from one geometry to another.