Correlating elasticity and cleavage

For brittle cleavage under Load Mode I, a model for single crystals is presented which derives the critical stress in terms of the cleavage energy and the uniaxial elastic modulus. The model parameters are determined by fitting to results of ab initio density functional calculations. The crucial concept for establishing an accurate correlation between cleavage and elastic properties is based on a generalization of the traditionally applied Orowan–Gilman model by introducing a localization length Lb as a new materials parameter. By that, a precise correlation between elastic and cleavage properties is established. We propose that, with an average value of Lb≈2.4Å, the critical stress can be directly estimated from the cleavage energy and the uniaxial stress within an error of ±10%.