  Exact expressions for ensemble averaged Madelung energies of finite volumes
are derived. The extrapolation to the thermodynamic limit converges
unconditionally and can be used as a parameter-free real-space summation method
of Madelung constants. In the large volume limit, the surface term of the
ensemble averaged Madelung energy has a universal form, independent of the
crystal structure. The scaling of the Madelung energy with system size provides
a simple explanation for the structural phase transition observed in cesium
halide clusters.
