Preprint Article Version 3 This version is not peer-reviewed

Microscopic Equations of State, Thermodynamical Properties, and System Collapse: Application of the Dynamical Equation of Period Vectors in Crystal Structure Prediction under External Temperature and Stress/Pressure

Version 1 : Received: 28 December 2018 / Approved: 4 January 2019 / Online: 4 January 2019 (09:11:50 CET)
Version 2 : Received: 9 January 2019 / Approved: 11 January 2019 / Online: 11 January 2019 (16:25:05 CET)
Version 3 : Received: 20 January 2019 / Approved: 22 January 2019 / Online: 22 January 2019 (11:33:00 CET)
Version 4 : Received: 19 February 2019 / Approved: 20 February 2019 / Online: 20 February 2019 (11:11:30 CET)

How to cite: Liu, G. Microscopic Equations of State, Thermodynamical Properties, and System Collapse: Application of the Dynamical Equation of Period Vectors in Crystal Structure Prediction under External Temperature and Stress/Pressure. Preprints 2019, 2019010038 (doi: 10.20944/preprints201901.0038.v3). Liu, G. Microscopic Equations of State, Thermodynamical Properties, and System Collapse: Application of the Dynamical Equation of Period Vectors in Crystal Structure Prediction under External Temperature and Stress/Pressure. Preprints 2019, 2019010038 (doi: 10.20944/preprints201901.0038.v3).

Abstract

In crystal structure prediction, Newton's second law can always be applied to particles (atoms or ions) in a cell to determine their positions. However the values of the period vectors (crystal cell edge vectors) should be determined as well. Here we applied the dynamical equations of period vectors derived recently based on Newton's laws (doi:/10.1139/cjp-2014-0518) for that purpose, where the period vectors are driven by the imbalance between the internal and external pressures/stresses. For equilibrium states, they became equations of state, which essentially turn out the equilibrium conditions of crystals from mechanical point of view. Additionally for external pressure, they became Mie-Gruneisen equation supposing the Gruneisen constant is 1/3, which means phonon frequency is inversely proportional to the cell length. Since the internal stress has both a full kinetic energy term and a full interaction term, the influences of both external temperature and stress/pressure on crystal structures can be calculated, then thermodynamical properties and processes were presented. Contrary to usual ideas, the equations show that pure harmonic vibrating phonons can result in thermal expansion in crystals when the external temperature is changed. Finally, crystal system collapse due to temperature and/or stress/pressure change was discussed.

Subject Areas

dynamical equation of period vectors, crystal structure prediction, microscopic equations of state, thermodynamical properties, system collapse, external stress

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