Geometrical prediction of cleavage planes in crystal structures

Cleavage is the ability of single crystals to split easily along specifically oriented planes. This phenomenon is of great interest for materials' scientists. Acquiring the data regarding cleavage is essential for the understanding of brittle fracture, plasticity and strength, as well as for the prevention of catastrophic device failures. Unfortunately, theoretical calculations of cleavage energy are demanding and often unsuitable for high-throughput searches of cleavage planes in arbitrary crystal structures. A simplified geometrical approach (GALOCS = gaps locations in crystal structures) is suggested for predicting the most promising cleavage planes. GALOCS enumerates all the possible reticular lattice planes and calculates the plane-average electron density as a function of the position of the planes in the unit cell. The assessment of the cleavage ability of the planes is based on the width and depth of planar gaps in crystal structures, which appear when observing the planes lengthwise. The method is demonstrated on two-dimensional graphene and three-dimensional silicon, quartz and LiNbO₃ structures. A summary of planar gaps in a few more inorganic crystal structures is also presented.