Crystal Period Vectors under External Stress in Statistical Physics

Gang Liu

doi:10.20944/preprints201904.0076.v10

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preprints.org > physical sciences > condensed matter physics > doi: 10.20944/preprints201904.0076.v10

Preprint Article Version 10 Preserved in Portico This version is not peer-reviewed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

For crystals under external stress and temperature, a general equation to determine their period vectors (cell edge vectors) was derived based on the principles of statistical physics. This equation applies to both classical systems and quantum systems. It is consistent and can be combined with the previously derived one in the Newtonian dynamics. The existing theory for crystals under external pressure is covered as a special case. The new equation is also the mechanical equilibrium condition and the equation of state for crystals under external stress and temperature. It should be helpful in studying piezoelectric and piezomagnetic materials, since the period vectors change with external stress. For linear elastic crystals, it is the microscopic and temperature-dependent form of the generalized Hooke's law, therefore, it can be used to calculate the corresponding elastic constants, for given temperatures.

Keywords

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

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: 19 August 2020
Commenter: Gang Liu
Commenter's Conflict of Interests: Author

Comment: The section "Equation derivation for external stress" was moved from the back of the section of the existing theory but for external pressure, to the front of it. As a result, Eqs.(5) and (6) in the previous versions are now Eqs.(1) and (2) in the current version. In the previous versions, the external stress case may possibly be thought of as an extension of the external pressure case. In the current version, the external stress case was formulated/derived completely independently, and was used to reduce to the special case of the external pressure. Additionally, figures and texts are also improved.

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