Atomistic relaxation of systems containing plasticity elements

• The convergence rates of seven different relaxation methods are analyzed.
• The use of the energy as sole parameter to end a relaxation is discussed.
• Convergence of the energy is compared with that of the global and local stresses.
• The relation between the avg. and the Std. Dev. of the energies is studied.
• A more accurate method to determine static equilibrium of a system is proposed.

Molecular statics simulations are usually carried out by applying discrete deformation increments to a sample. After each step, the system is relaxed until a new equilibrium is found. This relaxation procedure is the most computationally expensive part of the simulation and, depending on the complexity of the problem, it can take considerable time. In order to optimize the search for an equilibrium after each deformation increment, a comparison of the convergence rates and final structures obtained with seven different relaxation methods is presented and applied to molecular statics simulations of dislocations.Additionally, it turns out that in cases where the stress field rather than the overall energy is the quantity of real interest, equilibration is a particularly delicate operation, and can lead to errors in simulations if not handled carefully. To address this issue, the equilibration of a single crystal, a system containing a dislocation and one with a grain boundary are analyzed. The use of the overall energy as sole parameter to end a relaxation is discussed and compared with the local energy and the global and local stresses. From this, a new and more accurate method to determine whether a system has reached static equilibrium is proposed.