Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed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)

How to cite: Liu, G. Crystal Period Vectors under External Stress in Statistical Physics. Preprints 2019, 2019040076 (doi: 10.20944/preprints201904.0076.v7). Liu, G. Crystal Period Vectors under External Stress in Statistical Physics. Preprints 2019, 2019040076 (doi: 10.20944/preprints201904.0076.v7).

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.

Subject Areas

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

Comments (1)

Comment 1
Received: 2 April 2020
Commenter: Gang Liu
Commenter's Conflict of Interests: Author
Comment: Significantly more details including Figure 1 were added in reasoning Equation (5) and other minor writting were improved.
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