Cleavage describes the tendency of a crystal to break easily along specific crystallographic planes. Acquiring the information about cleavage in a given crystal microstructure is essential for the investigation of key mechanical properties such as fracture toughness, plasticity and strength. Although cleavage planes are commonly known for some simple materials (e.g. (110) and (111) of silicon), such information about any arbitrary crystal is not available. There are no simple computational methods to predict cleavage planes in single crystals, apart from interactive visual inspection of three-dimensional structures using graphical programs (like CrystalMaker or VESTA). Developing such a method may contribute significantly to the understanding of physical and mechanical properties of crystals. It also provides a solid prediction of their cleavage planes, and may open the door to find new ones. This work aims to develop an algorithm and a computer program for automatic inspection of crystal structures and prediction of its likely cleavage planes. The algorithm enumerates all possible lattice planes, listing their Miller indices, counting the number of intersected atoms for every plane and its position along the related crystallographic direction. We modelled atoms by thermal ellipsoids - probability density functions (PDFs) derived from their atomic displacement parameters (ADPs). Our algorithm was tested on three inorganic crystal structures Si, ɑ-SiO2 and LiNbO3. We believe that our algorithm can be used for fast, efficient and intuitive prediction of cleavage planes to be further approved by rigorous and more time-consuming density functional theory calculations.
