2/20/14 ACMP-I 12 Problems • 1. Kittel 21.3 (hint: under shear stress a dislocation moves a distance L through the crystal) • 2. Show by logical arguments that the force per unit length required to bend a dislocation into an arc with curvature R is T/R, where T is the dislocation line tension, which is equal to dislocation self-energy per unit length. • 3. Estimate the yield strength of a copper-silica alloy with spherical silica precipitates of 100 nm radius. The volume fraction of silica phase is 1 %, the shear modulus of copper is 42 GPa and the Burgers vector 0.26 nm.

2/20/14 ACMP-I 12 Problems • 1. Kittel 21.3 (hint: under shear stress a dislocation moves a distance L through the crystal) • 2. Show by logical arguments that the force per unit length required to bend a dislocation into an arc with curvature R is T/R, where T is the dislocation line tension, which is equal to dislocation self-energy per unit length. • 3. Estimate the yield strength of a copper-silica alloy with spherical silica precipitates of 100 nm radius. The volume fraction of silica phase is 1 %, the shear modulus of copper is 42 GPa and the Burgers vector 0.26 nm. (Hint: assume that the critical shear stress is achieved after dislocation pinned by two precipitates bows out in a semicircle. Moreover, remember that the average distance between precipitates can be estimated from the volume fraction).