Cleavage fracture of a crystal: Density functional theory calculations based on a model which includes structural relaxations

Based on density functional theory calculations, we study cleavage under loading mode I, in which the atomic layers are allowed to relax after a crack with a given opening was initiated. By introducing the new materials parameter l(r), the critical opening for relaxed cleavage, we derive a simple analytic formulation describing the decohesion energy and the corresponding stress for relaxed cleavage. In this model, for crack openings smaller than x