Crystal Period Vectors under External Stress in Statistical Physics

Gang Liu

doi:10.20944/preprints201904.0076.v2

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preprints.org > physical sciences > condensed matter physics > doi: 10.20944/preprints201904.0076.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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

A basic and general equation to determine period vectors (cell edge vectors) is necessary in physics, especially when crystals are under external stress. It has been derived in Newtonian dynamics. Since statistical physics should also generate such equation, we will provide a derivation. By extending the normal derivation for crystals under external pressure, regarding crystal cells as being filled with continuous media, formulating the work done by the external stress on the crystal explicitly, and deriving the forces on the surfaces of the cells by the external stress, we arrived at the equation for the period vectors, which is in principle the same as the above mentioned counterpart achieved in Newtonian dynamics. Everything also restores when the external stress reduces to the special case of external pressure. It should be applicable when crystals are under different pressures in different directions, like in piezoelectric and piezomagnetic phenomena.

Keywords

period vectors; external stress; crystal struture prediction; statistical physics

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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