1. 1. Recently, much work has been done in attempting to explain the observed size and shape of crystals in terms of their interionic forces. To do this, a highly idealised form of the crystal has been postulated in which the ions of the crystal (in accordance with Kossel’s theory) are regarded as pointcharges, of magnitude equal to the resultant ionic charge and situate at the points of the crystal lattice determined by X-ray analysis. For ions which are surrounded symmetrically by other ions, these points doubtless correspond to the nuclei of the respective atoms, but for unsymmetrically situated ions there is some uncertainty as to the exact position to which to assign the pointcharge. Moreover, in order that the crystal may be in equilibrium, other repulsive forces, in addition to the electrostatic forces of attraction and repulsion between the ionic point-charges, are assumed to be operative between the various ions. These are termed “intrinsic repulsive” forces, and have been represented by an inverse power law varying with the distance according to the
n
th power, and expressible in the form μ
n
r
-
n
. Consequently, in order to determine the equilibrium configuration of the crystal, as given by the minimum value of the potential energy of the crystal, it is necessary to determine (i) the electrostatic potential energy of an infinite array of point-charges, arranged according to the crystal pattern, and (ii) the potential energy due to the intrinsic repulsive forces between the ions.