Quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations

This is the first report of a quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations. The multiplication was studied as a function of dislocation density and effective shear stress in periodic boundary conditions close to melting point of Ge, utilizing a specifically developed diamond cubic dislocation mobility module in agreement with experiments in literature. We report an average dislocation velocity law of a dislocation ensemble linearly proportional to the resolved shear stress – analogous to the single dislocation velocity law – with a reduced average dislocation mobility. Exponential dislocation multiplication was observed with a multiplication parameter δ linear proportional to the effective shear stress for various stress states and simulation volumes. The coefficient of the dislocation multiplication law was determined to be 4.0 ⋅10−3 [mN−1].