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Title: Revisit of the relationship between the elastic properties and sound velocities at high pressures

Abstract

The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find that the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.

Authors:
;  [1];  [2]; ;  [1]; ;  [1];  [2];  [3];  [2]
  1. National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, PO Box 919-102, Mianyang, Sichuan 621900 (China)
  2. (China)
  3. Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065 (China)
Publication Date:
OSTI Identifier:
22305973
Resource Type:
Journal Article
Journal Name:
Journal of Applied Physics
Additional Journal Information:
Journal Volume: 116; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CUBIC LATTICES; ELASTICITY; LAGRANGIAN FUNCTION; RHENIUM; SOUND WAVES; STRAINS; STRESSES; TANTALUM; WAVE EQUATIONS

Citation Formats

Wang, Chenju, Yan, Xiaozhen, Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065, Xiang, Shikai, E-mail: skxiang@caep.ac.cn, Chen, Haiyan, Gu, Jianbing, Yu, Yin, College of Physical Science and Technology, Sichuan University, Chengdu 610064, Kuang, Xiaoyu, and International Centre for Materials Physics, Academia Sinica, Shenyang 110016. Revisit of the relationship between the elastic properties and sound velocities at high pressures. United States: N. p., 2014. Web. doi:10.1063/1.4895495.
Wang, Chenju, Yan, Xiaozhen, Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065, Xiang, Shikai, E-mail: skxiang@caep.ac.cn, Chen, Haiyan, Gu, Jianbing, Yu, Yin, College of Physical Science and Technology, Sichuan University, Chengdu 610064, Kuang, Xiaoyu, & International Centre for Materials Physics, Academia Sinica, Shenyang 110016. Revisit of the relationship between the elastic properties and sound velocities at high pressures. United States. doi:10.1063/1.4895495.
Wang, Chenju, Yan, Xiaozhen, Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065, Xiang, Shikai, E-mail: skxiang@caep.ac.cn, Chen, Haiyan, Gu, Jianbing, Yu, Yin, College of Physical Science and Technology, Sichuan University, Chengdu 610064, Kuang, Xiaoyu, and International Centre for Materials Physics, Academia Sinica, Shenyang 110016. Sun . "Revisit of the relationship between the elastic properties and sound velocities at high pressures". United States. doi:10.1063/1.4895495.
@article{osti_22305973,
title = {Revisit of the relationship between the elastic properties and sound velocities at high pressures},
author = {Wang, Chenju and Yan, Xiaozhen and Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065 and Xiang, Shikai, E-mail: skxiang@caep.ac.cn and Chen, Haiyan and Gu, Jianbing and Yu, Yin and College of Physical Science and Technology, Sichuan University, Chengdu 610064 and Kuang, Xiaoyu and International Centre for Materials Physics, Academia Sinica, Shenyang 110016},
abstractNote = {The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find that the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.},
doi = {10.1063/1.4895495},
journal = {Journal of Applied Physics},
issn = {0021-8979},
number = 10,
volume = 116,
place = {United States},
year = {2014},
month = {9}
}