Extended Dynamical Equations of the Period Vectors of Crystals under Constant External Stress to Many-body Interactions

Since crystals are made of periodic structures in space, determining their three independent period vectors in theory (starting from any values) is a basic physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, because the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is analyzed again with many-body potentials in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.