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

TL;DR

This paper derives extended dynamical equations for crystal period vectors under constant external stress, incorporating many-body interactions, showing how external stress influences crystal structure through internal stress imbalance.

Contribution

It extends previous pair potential models to include many-body interactions in the dynamical equations of crystal period vectors under external stress.

Findings

Dynamical equations driven by internal and external stress imbalance.

Extension from pair potentials to many-body interactions.

Structural changes in crystals due to external stress.

Abstract

Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical 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, since 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 extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.