Crystal Period Vectors under External Stress in Statistical Physics

Gang Liu

doi:10.20944/preprints201904.0076.v4

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preprints.org > physical sciences > condensed matter physics > doi: 10.20944/preprints201904.0076.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Crystal Period Vectors under External Stress in Statistical Physics

Gang Liu

Version 1 : Received: 3 April 2019 / Approved: 8 April 2019 / Online: 8 April 2019 (08:48:22 CEST)
Version 2 : Received: 23 April 2019 / Approved: 23 April 2019 / Online: 23 April 2019 (12:18:56 CEST)
Version 3 : Received: 16 November 2019 / Approved: 18 November 2019 / Online: 18 November 2019 (04:39:26 CET)
Version 4 : Received: 20 February 2020 / Approved: 21 February 2020 / Online: 21 February 2020 (07:35:09 CET)
Version 5 : Received: 25 February 2020 / Approved: 26 February 2020 / Online: 26 February 2020 (02:32:35 CET)
Version 6 : Received: 28 February 2020 / Approved: 2 March 2020 / Online: 2 March 2020 (03:39:40 CET)
Version 7 : Received: 1 April 2020 / Approved: 2 April 2020 / Online: 2 April 2020 (05:28:32 CEST)
Version 8 : Received: 20 April 2020 / Approved: 21 April 2020 / Online: 21 April 2020 (09:41:59 CEST)
Version 9 : Received: 1 July 2020 / Approved: 2 July 2020 / Online: 2 July 2020 (07:21:53 CEST)
Version 10 : Received: 10 August 2020 / Approved: 19 August 2020 / Online: 19 August 2020 (17:25:24 CEST)

A peer-reviewed article of this Preprint also exists.

Liu, G. A new equation for period vectors of crystals under external stress and temperature in statistical physics: mechanical equilibrium condition and equation of state. Eur. Phys. J. Plus 136, 48 (2021). https://doi.org/10.1140/epjp/s13360-020-01010-6 Liu, G. A new equation for period vectors of crystals under external stress and temperature in statistical physics: mechanical equilibrium condition and equation of state. Eur. Phys. J. Plus 136, 48 (2021). https://doi.org/10.1140/epjp/s13360-020-01010-6

Abstract

In crystal periodic structure prediction, a basic and general equation is needed to determine their period vectors (cell edge vectors), especially under arbitrary external stress. It was derived in Newtonian dynamics years ago, which can be combined with quantum physics by further modeling. Here a new and concise approach based on the principles of statistical physics was employed to derive it into a new form, then applicable to both classical physics and quantum physics by its own. The new form also turned out to be the specific explicit equilibrium condition and the equation of state for crystals under external stress and temperature. Contrary to a general belief, the new form also concluded that harmonic oscillators can cause crystal thermal expansion.

Keywords

crystal structure; equation of period vectors; external stress; quantum statistics; equilibrium condition; equation of state for crystals

Subject

Physical Sciences, Condensed Matter Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 21 February 2020
Commenter: Gang Liu
Commenter's Conflict of Interests: Author

Comment: Equation (6) turned out to be the specific explicit equilibrium condition and the equation of state for crystals under external stress and temperature, and also concluded that harmonic oscillators can cause crystal thermal expansion.

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