Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Crystal Period Vectors under External Stress in Statistical Physics

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

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

Keywords

crystal structure; equation of period vectors; external stress; quantum statistics; equilibrium condition; equation of state for crystals; elasticity; plasticity; piezoelectricity; piezomagnetism; generalized Hooke's law

Subject

Physical Sciences, Condensed Matter Physics

Comments (1)

Comment 1
Received: 2 March 2020
Commenter: Gang Liu
Commenter's Conflict of Interests: Author
Comment: As the equation of state, Eq.(6) also turned out to be the microscopic but temperature-dependent form of Hooke's law, then can be used to calculate the corresponding elastic constants of the law for given temperatures. It should also play an essential role in piezoelectric and piezomagnetic studies.
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