  A mechanism for orientation of bilayer classical Wigner crystals in a
piezoelectric medium is considered. For the GaAs system the piezoelectric
correction to the electrostatic interaction between electrons is calculated. It
is shown that taking into account the correction due to the piezoelectric
effect leads to a dependence of the total energy of the electron crystal on its
orientation with respect to the crystallographic axes of the surrounding
matrix. A generalization of Ewald's method is obtained for calculating the
anisotropic interaction between electrons in a Wigner crystal. The method is
used to calculate the energy of bilayer Wigner crystals in electron layers
parallel to the crystallographic planes (001), (0-11), and (111) as a function
of their orientation and the distance between layers, and the energetically
most favorable orientation for all types of electron lattices in a bilayer
system is found. It is shown that phase transitions between structures with
different lattice symmetry in a Wigner crystal can be accompanied by a change
of its orientation.
