Yielding of crystals toward the quasistatic limit: A slip-plane condensation transition

A novel scenario for the yielding of three-dimensional crystals in the quasistatic limit is presented. To this end, a face-centered cubic Lennard-Jones crystal under deformation and periodic boundary conditions is studied using Monte Carlo simulation in combination with successive umbrella sampling. As a reaction coordinate, a non-affinity parameter X is introduced. In terms of this parameter, the yielding of the crystal can be described as a phase transition, where at the system-size-dependent yield strain ɛ(y), a deformed crystal, the "N phase," transforms into a nearly stress-free state, the "M phase." The N-M phase transition is dominated by the long-ranged elasticity of the crystal. As a consequence, there are no mixed states of both phases. Moreover, the free energy barrier between them is not associated with interfacial contributions, but rather scales with the total volume V of the crystal, implying non-convexity of the X-dependent free energy F(X). On the path from the N to the M phase with increasing X, the free energy F(X) develops two kinks that are associated with jumps of a field conjugate to the non-affinity parameter X. At the first kink, corresponding to the maximum of F(X), there is the nucleation of a partial slip plane, associated with the formation of a stacking fault that is circumvented by a loop of Shockley partial dislocations. At the second kink, at a lower free energy, the dislocations are annihilated leaving behind the stacking fault around now fully developed slip planes. The resulting M phase is inhomogeneous with periodically repeating stacking faults around the fully developed slip planes (here, the distance between the slip planes is determined by the periodic boundary conditions and the initial orientation of the crystal in the simulation box).