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|The sign of the surface potential for complex non-reactive ionic solids cannot be predicted solely from consideration of the hydration energy of gaseous ions which constitute the ionic lattice. Accurate analysis of these systems must involve the hydration energy of surface ions, which requires knowledge of the crystal structure, the identification of cleavage planes, and the calculation of binding energies of surface ions. Surface binding energies for ionic solids can be deter- mined if the Surface Madelung Constant is known. A computational technique was developed for the calculation of Madelung Constants for infinite lattices which gives excellent agreement with the values calculated by other more complicated methods reported in the literature. Extension of this technique permits the calculation of Surface Madelung Constants and binding energies of surface ions, ?Us, for semi-infinite solids. The hydration free energy of gaseous Ions, ?Fh, together with the calculated binding energy of surface ions, ?Us, allows calculation of the hydration energy of surface ions, ?Gh, as for the case of the ionic solid, MX:|