  We present a study of the structural properties of the crystalline phases for
a planar bilayer of particles interacting via repulsive Yukawa potentials in
the weak screening region. The study is done with Monte Carlo computations and
the long ranged contributions to energy are taken into account with the Ewald
method for quasi-two dimensional systems. Two first order phase transitions
(fluid-solid and solid-solid) and one second order transition (solid-solid) are
found when the surface density is varied at constant temperature. A particular
attention is pay to the characteristics of the crystalline phases by the
analysis of bond orientational order parameters and center-to-center
correlations functions.
