A simple method for the potential in ionic crystals

During the past sixty years many methods for finding the potential inside ionic crystals were proposed. Recently, the author developed a simple and accurate method based on summing Coulomb terms. Most of these methods succeeded in some cases but failed in other cases with no obvious reason. Some methods have procedures which could not be accounted for. Here, a basis theory is found which explains the failures, the successes, and the strange procedures of these methods. The theory is based on the fact that the finite block which represents the ’’infinite’’ crystal and which is used for computing the potential must be free from electric moments, the most important of which are the dipole, quadrupole, and octapole moments. It is shown that for a crystal of regular structure (with no defects) such a block does not exist and the potential is not defined. However, a satisfactory definition is found based on this theory. Starting with these facts, more simplifications were introduced into the computations and more insight was introduced into the problem of the general oblique structure.