Preprint Article Version 2 This version is not peer-reviewed

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

Version 1 : Received: 6 September 2017 / Approved: 8 September 2017 / Online: 8 September 2017 (13:29:30 CEST)
Version 2 : Received: 8 August 2018 / Approved: 9 August 2018 / Online: 9 August 2018 (08:36:53 CEST)

How to cite: Liu, G. Extended Dynamical Equations of the Period Vectors of Crystals under Constant External Stress to Many-body Interactions. Preprints 2017, 2017090030 (doi: 10.20944/preprints201709.0030.v2). Liu, G. Extended Dynamical Equations of the Period Vectors of Crystals under Constant External Stress to Many-body Interactions. Preprints 2017, 2017090030 (doi: 10.20944/preprints201709.0030.v2).

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.

Subject Areas

dynamical equation; crystal; period vectors; periodic structure; period dynamics; pressure; stress; many-body interaction; molecular dynamics; periodic boundary conditions

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