Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond
Abstract
Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g. diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently, the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than themore »
- Authors:
-
- Washington State Univ., Pullman, WA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Washington State Univ., Pullman, WA (United States). Inst. for Shock Physics
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
- OSTI Identifier:
- 1328745
- Alternate Identifier(s):
- OSTI ID: 1254206; OSTI ID: 1334535
- Report Number(s):
- SAND-2016-9948J
Journal ID: ISSN 2469-9950; PRBMDO; 648006
- Grant/Contract Number:
- AC04-94AL85000; NA0002007
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 17; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Hmiel, A., Winey, J. M., Gupta, Y. M., and Desjarlais, M. P. Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.174113.
Hmiel, A., Winey, J. M., Gupta, Y. M., & Desjarlais, M. P. Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond. United States. https://doi.org/10.1103/PhysRevB.93.174113
Hmiel, A., Winey, J. M., Gupta, Y. M., and Desjarlais, M. P. Mon .
"Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond". United States. https://doi.org/10.1103/PhysRevB.93.174113. https://www.osti.gov/servlets/purl/1328745.
@article{osti_1328745,
title = {Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond},
author = {Hmiel, A. and Winey, J. M. and Gupta, Y. M. and Desjarlais, M. P.},
abstractNote = {Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g. diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently, the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Lastly, our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.},
doi = {10.1103/PhysRevB.93.174113},
journal = {Physical Review B},
number = 17,
volume = 93,
place = {United States},
year = {Mon May 23 00:00:00 EDT 2016},
month = {Mon May 23 00:00:00 EDT 2016}
}
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Works referenced in this record:
Optical phonons and elasticity of diamond at megabar stresses
journal, October 1986
- Nielsen, O. H.
- Physical Review B, Vol. 34, Issue 8
First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry
journal, March 2007
- Zhao, Jijun; Winey, J. M.; Gupta, Y. M.
- Physical Review B, Vol. 75, Issue 9
Experimental Determination of Third-Order Elastic Constants of Diamond
journal, March 2011
- Lang, J. M.; Gupta, Y. M.
- Physical Review Letters, Vol. 106, Issue 12
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
New stable Re–B phases for ultra-hard materials
journal, October 2014
- Zhao, Xin; Nguyen, Manh Cuong; Wang, Cai-Zhuang
- Journal of Physics: Condensed Matter, Vol. 26, Issue 45
Properties and Performance of Polycrystalline Cubic Boron Nitride
journal, January 2015
- Swab, Jeffrey J.; Vargas-Gonzalez, Lionel; Wilson, Elizabeth
- International Journal of Applied Ceramic Technology, Vol. 12
Physics of solids under strong compression
journal, January 1996
- Holzapfel, W. B.
- Reports on Progress in Physics, Vol. 59, Issue 1
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
Chemical vapor deposition diamond for tips in nanoprobe experiments
journal, May 1996
- Niedermann, Ph.; Hänni, W.; Blanc, N.
- Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 14, Issue 3
Ground State of the Electron Gas by a Stochastic Method
journal, August 1980
- Ceperley, D. M.; Alder, B. J.
- Physical Review Letters, Vol. 45, Issue 7, p. 566-569
Research Update: Direct conversion of amorphous carbon into diamond at ambient pressures and temperatures in air
journal, October 2015
- Narayan, Jagdish; Bhaumik, Anagh
- APL Materials, Vol. 3, Issue 10
Conditions of diamond crystallization in kimberlite melt: experimental data
journal, January 2015
- Palyanov, Yu. N.; Sokol, A. G.; Khokhryakov, A. F.
- Russian Geology and Geophysics, Vol. 56, Issue 1-2
Elastic Moduli of Diamond as a Function of Pressure and Temperature
journal, July 1972
- McSkimin, H. J.; Andreatch, P.
- Journal of Applied Physics, Vol. 43, Issue 7
Elasticity of carbon allotropes. I. Optimization, and subsequent modification, of an anharmonic Keating model for cubic diamond
journal, January 2003
- Cousins, C. S. G.
- Physical Review B, Vol. 67, Issue 2
Second-order and third-order elastic properties of diamond: An ab initio study
journal, October 2005
- Clerc, Daryl G.; Ledbetter, Hassel
- Journal of Physics and Chemistry of Solids, Vol. 66, Issue 10
Novel Rhenium Nitrides
journal, August 2010
- Friedrich, Alexandra; Winkler, Björn; Bayarjargal, Lkhamsuren
- Physical Review Letters, Vol. 105, Issue 8
Determination of the third-order elastic constants of diamond by shock wave simulations
journal, June 2015
- Modak, P.; Verma, Ashok K.; Sharma, Surinder M.
- EPL (Europhysics Letters), Vol. 110, Issue 5
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996
- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186
The Role Played by Computation in Understanding Hard Materials
journal, June 2011
- Lowther, John Edward
- Materials, Vol. 4, Issue 6
Higher Order Elastic Constants of Solids
journal, August 1981
- Hiki, Y.
- Annual Review of Materials Science, Vol. 11, Issue 1
Effect of uniaxial stress on the zone-center optical phonon of diamond
journal, July 1978
- Grimsditch, M. H.; Anastassakis, E.; Cardona, M.
- Physical Review B, Vol. 18, Issue 2
Third-order elastic constants of diamond determined from experimental data
journal, June 2016
- Winey, J. M.; Hmiel, A.; Gupta, Y. M.
- Journal of Physics and Chemistry of Solids, Vol. 93
Thermodynamic Definition of Higher Order Elastic Coefficients
journal, March 1964
- Brugger, K.
- Physical Review, Vol. 133, Issue 6A
Piezo-Raman measurements and anharmonic parameters in silicon and diamond
journal, April 1990
- Anastassakis, E.; Cantarero, A.; Cardona, M.
- Physical Review B, Vol. 41, Issue 11
Works referencing / citing this record:
Tensorial stress−strain fields and large elastoplasticity as well as friction in diamond anvil cell up to 400 GPa
journal, October 2019
- Levitas, Valery I.; Kamrani, Mehdi; Feng, Biao
- npj Computational Materials, Vol. 5, Issue 1