Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates
Abstract
Abstract Phyllosilicate minerals, due to their sheets structure and morphology, are known to cause anisotropy in bulk rock properties and make the bulk rock more compliant. Accurately characterizing the micromechanical behavior of phyllosilicate minerals from laboratory observations, which eventually translates to the bulk rock behavior, is still challenging due to their fine‐grained nature. Recent advances in atomistic simulations open the possibility of theoretically investigating such mineral mechanical behavior. We compare the elastic properties of biotites recovered by spherical nanoindentation with those predicted from density functional theory (DFT) simulations to investigate to what extent theoretical predictions reproduce actual phyllosilicate properties. Spherical nanoindentation was conducted using schist rocks from Poorman Formation, South Dakota, USA, to recover continuous indentation stress‐strain curves. Loading in the layer‐normal orientation shows an average indentation modulus ( ) of about 35 GPa, while loading in the layer‐parallel orientation gives a higher average of about 95 GPa. To facilitate comparison, the elastic stiffness constants ( c ij ) determined from DFT were converted to indentation modulus ( ) using solutions proposed in this study. The majority of the nanoindentation modulus results are below the values inferred from the simulation results representing ideal defect‐free minerals. We suggest that crystal defects present atmore »
- Authors:
-
[1];
[1];
[2];
[3];
[3]
- Univ. of Wisconsin, Madison, WI (United States). Dept. of Chemical and Biological Engineering. Geological Engineering Program
- Univ. of Wisconsin, Madison, WI (United States). Dept. of Material Science and Engineering
- Univ. of Wisconsin, Madison, WI (United States). Dept. of Civil and Environmental Engineering
- Publication Date:
- Research Org.:
- Univ. of California, Los Angeles, CA (United States)
- Sponsoring Org.:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E); National Science Foundation (NSF)
- OSTI Identifier:
- 1848371
- Alternate Identifier(s):
- OSTI ID: 1817226
- Grant/Contract Number:
- AR0001147; 20160622016960; DMR-1720415; ARPA‐E: DE‐AR‐0001147
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Geophysical Research. Solid Earth
- Additional Journal Information:
- Journal Volume: 126; Journal Issue: 8; Journal ID: ISSN 2169-9313
- Publisher:
- American Geophysical Union
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; Geochemistry & Geophysics
Citation Formats
Lanin, Eril Suhada, Sone, Hiroki, Yu, Zheng, Liu, Qitong, and Wang, Bu. Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates. United States: N. p., 2021.
Web. doi:10.1029/2021jb021902.
Lanin, Eril Suhada, Sone, Hiroki, Yu, Zheng, Liu, Qitong, & Wang, Bu. Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates. United States. https://doi.org/10.1029/2021jb021902
Lanin, Eril Suhada, Sone, Hiroki, Yu, Zheng, Liu, Qitong, and Wang, Bu. Fri .
"Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates". United States. https://doi.org/10.1029/2021jb021902. https://www.osti.gov/servlets/purl/1848371.
@article{osti_1848371,
title = {Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates},
author = {Lanin, Eril Suhada and Sone, Hiroki and Yu, Zheng and Liu, Qitong and Wang, Bu},
abstractNote = {Abstract Phyllosilicate minerals, due to their sheets structure and morphology, are known to cause anisotropy in bulk rock properties and make the bulk rock more compliant. Accurately characterizing the micromechanical behavior of phyllosilicate minerals from laboratory observations, which eventually translates to the bulk rock behavior, is still challenging due to their fine‐grained nature. Recent advances in atomistic simulations open the possibility of theoretically investigating such mineral mechanical behavior. We compare the elastic properties of biotites recovered by spherical nanoindentation with those predicted from density functional theory (DFT) simulations to investigate to what extent theoretical predictions reproduce actual phyllosilicate properties. Spherical nanoindentation was conducted using schist rocks from Poorman Formation, South Dakota, USA, to recover continuous indentation stress‐strain curves. Loading in the layer‐normal orientation shows an average indentation modulus ( ) of about 35 GPa, while loading in the layer‐parallel orientation gives a higher average of about 95 GPa. To facilitate comparison, the elastic stiffness constants ( c ij ) determined from DFT were converted to indentation modulus ( ) using solutions proposed in this study. The majority of the nanoindentation modulus results are below the values inferred from the simulation results representing ideal defect‐free minerals. We suggest that crystal defects present at the nano‐scale, potentially ripplocations, are the dominant cause of the lower indentation modulus recovered from nanoindentation compared to those inferred from DFT simulations. Results highlight the importance of acknowledging the defects that exist down to the nano‐scale as it modifies the mechanical properties of phyllosilicates compared to its pure defect‐free form.},
doi = {10.1029/2021jb021902},
journal = {Journal of Geophysical Research. Solid Earth},
number = 8,
volume = 126,
place = {United States},
year = {Fri Jul 30 00:00:00 EDT 2021},
month = {Fri Jul 30 00:00:00 EDT 2021}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
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
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
Experiental deformation of single crystals of biotite
journal, January 1973
- Etheridge, M. A.; Hobbs, B. E.; Paterson, M. S.
- Contributions to Mineralogy and Petrology, Vol. 38, Issue 1
Comment on “Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation” by G. Zhang, Z. Wei and R.E. Ferrell [Applied Clay Science 43 (2009) 271-281]
journal, December 2009
- Bobko, Christopher P.; Ortega, J. Alberto; Ulm, Franz-Josef
- Applied Clay Science, Vol. 46, Issue 4
TEM observations of defects in biotite and their relationship to polytypism
journal, January 1986
- Bell, Ian A.; Wilson, Christopher J. L.
- Bulletin de Minéralogie, Vol. 109, Issue 1
Hertzian contact of anisotropic bodies
journal, May 1966
- Willis, J. R.
- Journal of the Mechanics and Physics of Solids, Vol. 14, Issue 3
Dislocation interactions in experimentally deformed biotite
journal, September 1993
- Christoffersen, Roy; Kronenberg, Andreas K.
- Journal of Structural Geology, Vol. 15, Issue 9-10
GULP: A computer program for the symmetry-adapted simulation of solids
journal, January 1997
- Gale, Julian D.
- Journal of the Chemical Society, Faraday Transactions, Vol. 93, Issue 4
Spherical nanoindentation stress–strain curves
journal, May 2015
- Pathak, Siddhartha; Kalidindi, Surya R.
- Materials Science and Engineering: R: Reports, Vol. 91
Viscous creep in room-dried unconsolidated Gulf of Mexico shale (I): Experimental results
journal, December 2009
- Chang, Chandong; Zoback, Mark D.
- Journal of Petroleum Science and Engineering, Vol. 69, Issue 3-4
Long-term creep tests and viscoelastic constitutive modeling of lower Paleozoic shales from the Baltic Basin, N Poland
journal, December 2018
- Trzeciak, Maciej; Sone, Hiroki; Dabrowski, Marcin
- International Journal of Rock Mechanics and Mining Sciences, Vol. 112
Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation
journal, February 2009
- Zhang, G.; Wei, Z.; Ferrell, R.
- Applied Clay Science, Vol. 43, Issue 2
HRTEM analysis of dislocation cores and stacking faults in naturally deformed biotite crystals
journal, December 1999
- Noe, David Christopher; Veblen, David R.
- American Mineralogist, Vol. 84, Issue 11-12
Determination of an effective zero-point and extraction of indentation stress–strain curves without the continuous stiffness measurement signal
journal, March 2009
- Pathak, S.; Shaffer, J.; Kalidindi, S.
- Scripta Materialia, Vol. 60, Issue 6
A simple predictive model for spherical indentation
journal, February 1993
- Field, J. S.; Swain, M. V.
- Journal of Materials Research, Vol. 8, Issue 2
Ripplocations in van der Waals Layers
journal, January 2015
- Kushima, Akihiro; Qian, Xiaofeng; Zhao, Peng
- Nano Letters, Vol. 15, Issue 2
The indentation characterisation of the mechanical properties of various carbon materials: Glassy carbon, coke and pyrolytic graphite
journal, January 1996
- Fielda, J. S.; Swain, M. V.
- Carbon, Vol. 34, Issue 11
Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters
journal, December 2004
- Delafargue, Antoine; Ulm, Franz-Josef
- International Journal of Solids and Structures, Vol. 41, Issue 26
Top-seal leakage through faults and fractures: the role of mudrock properties
journal, January 1999
- Ingram, Gary M.; Urai, Janos L.
- Geological Society, London, Special Publications, Vol. 158, Issue 1
Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation
journal, September 2002
- Yamakov, Vesselin; Wolf, Dieter; Phillpot, Simon R.
- Nature Materials, Vol. 1, Issue 1
Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models
journal, May 2012
- Donohue, Brendan R.; Ambrus, Adrian; Kalidindi, Surya R.
- Acta Materialia, Vol. 60, Issue 9
Mechanical properties of shale-gas reservoir rocks — Part 1: Static and dynamic elastic properties and anisotropy
journal, September 2013
- Sone, Hiroki; Zoback, Mark D.
- GEOPHYSICS, Vol. 78, Issue 5
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
journal, April 2010
- Grimme, Stefan; Antony, Jens; Ehrlich, Stephan
- The Journal of Chemical Physics, Vol. 132, Issue 15
Effect of the damping function in dispersion corrected density functional theory
journal, March 2011
- Grimme, Stefan; Ehrlich, Stephan; Goerigk, Lars
- Journal of Computational Chemistry, Vol. 32, Issue 7
Basal slip and mechanical anisotropy of biotite
journal, January 1990
- Kronenberg, Andreas K.; Kirby, Stephen H.; Pinkston, John
- Journal of Geophysical Research, Vol. 95, Issue B12
Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field
journal, January 2004
- Cygan, Randall T.; Liang, Jian-Jie; Kalinichev, Andrey G.
- The Journal of Physical Chemistry B, Vol. 108, Issue 4
The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape
journal, September 2003
- Vlassak, J. J.; Ciavarella, M.; Barber, J. R.
- Journal of the Mechanics and Physics of Solids, Vol. 51, Issue 9
Hardness, toughness, and modulus of some common metamorphic minerals
journal, February 2007
- Whitney, D. L.; Broz, M.; Cook, R. F.
- American Mineralogist, Vol. 92, Issue 2-3
Evaluation of the elasticity normal to the basal plane of non-expandable 2:1 phyllosilicate minerals by nanoindentation
journal, May 2010
- Zhang, G.; Wei, Z.; Ferrell, R. E.
- American Mineralogist, Vol. 95, Issue 5-6
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996
- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50
First-principles calculation of the elastic moduli of sheet silicates and their application to shale anisotropy
journal, December 2010
- Militzer, B.; Wenk, H. - R.; Stackhouse, S.
- American Mineralogist, Vol. 96, Issue 1
Measuring the elastic properties of anisotropic materials by means of indentation experiments
journal, August 1994
- Vlassak, Joost J.; Nix, W. D.
- Journal of the Mechanics and Physics of Solids, Vol. 42, Issue 8
Crystal chemistry of Al-rich biotites coexisting with muscovites in peraluminous granites
journal, March 2000
- Brigatti, Maria Franca; Frigieri, Paola; Ghezzo, Claudio
- American Mineralogist, Vol. 85, Issue 3-4
Microhardness, toughness, and modulus of Mohs scale minerals
journal, January 2006
- Broz, Margaret E.; Cook, Robert F.; Whitney, Donna L.
- American Mineralogist, Vol. 91, Issue 1
Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution
journal, February 2001
- Swadener, J. G.; Pharr, G. M.
- Philosophical Magazine A, Vol. 81, Issue 2
Viscous relaxation model for predicting least principal stress magnitudes in sedimentary rocks
journal, December 2014
- Sone, Hiroki; Zoback, Mark D.
- Journal of Petroleum Science and Engineering, Vol. 124
The impact of different clay minerals on the anisotropy of clay matrix in shale
journal, June 2019
- Sayers, Colin M.; den Boer, Lennert D.
- Geophysical Prospecting, Vol. 67, Issue 9
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
journal, June 1992
- Oliver, W. C.; Pharr, G. M.
- Journal of Materials Research, Vol. 7, Issue 06, p. 1564-1583
Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology
journal, January 2004
- Oliver, W. C.; Pharr, G. M.
- Journal of Materials Research, Vol. 19, Issue 1
Seismic velocity anisotropy of phyllosilicate-rich rocks: characteristics inferred from experimental and crack-model studies of biotite-rich schist: Velocity anisotropy of phyllosilicate-rich rocks
journal, April 2010
- Nishizawa, O.; Kanagawa, K.
- Geophysical Journal International
Molecular Dynamics Simulations of Structural and Mechanical Properties of Muscovite: Pressure and Temperature Effects
journal, July 2012
- Teich-McGoldrick, Stephanie L.; Greathouse, Jeffery A.; Cygan, Randall T.
- The Journal of Physical Chemistry C, Vol. 116, Issue 28
Ripplocations: A universal deformation mechanism in layered solids
journal, January 2019
- Barsoum, M. W.; Zhao, X.; Shanazarov, S.
- Physical Review Materials, Vol. 3, Issue 1
Chemical and deformational controls on recrystallization of mica
journal, January 1974
- Etheridge, M. A.; Hobbs, B. E.
- Contributions to Mineralogy and Petrology, Vol. 43, Issue 2
Rheological characterization of a sedimentary formation from a stress profile inversion
journal, January 2007
- Gunzburger, Y.; Cornet, F. H.
- Geophysical Journal International, Vol. 168, Issue 1
A viscoplastic model of creep in shale
journal, May 2020
- Haghighat, Ehsan; Rassouli, Fatemeh S.; Zoback, Mark D.
- GEOPHYSICS, Vol. 85, Issue 3
Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress
journal, July 2014
- Sone, Hiroki; Zoback, Mark D.
- International Journal of Rock Mechanics and Mining Sciences, Vol. 69
A review of nanoindentation continuous stiffness measurement technique and its applications
journal, February 2002
- Li, Xiaodong; Bhushan, Bharat
- Materials Characterization, Vol. 48, Issue 1
Indentation modulus of elastically anisotropic half spaces
journal, May 1993
- Vlassak, Joost J.; Nix, W. D.
- Philosophical Magazine A, Vol. 67, Issue 5
Simulation of Screw Dislocation Motion in Iron by Molecular Dynamics Simulations
journal, November 2005
- Domain, Christophe; Monnet, Ghiath
- Physical Review Letters, Vol. 95, Issue 21
Elastic and Viscoelastic Calculations of Stresses in Sedimentary Basins
journal, December 1989
- Warpinski, Norman R.
- SPE Formation Evaluation, Vol. 4, Issue 04
Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves
journal, August 2008
- Kalidindi, Surya R.; Pathak, Siddhartha
- Acta Materialia, Vol. 56, Issue 14
Determination of the effective zero point of contact for spherical nanoindentation
journal, January 2008
- Moseson, Alexander J.; Basu, Sandip; Barsoum, Michel W.
- Journal of Materials Research, Vol. 23, Issue 1
The Rock Physics Handbook
book, January 2009
- Mavko, Gary; Mukerji, Tapan; Dvorkin, Jack
- Cambridge University Press
Lessons learned from the Floyd shale play
journal, September 2014
- Dembicki, Harry; Madren, Jonathan D.
- Journal of Unconventional Oil and Gas Resources, Vol. 7
Ripplocations provide a new mechanism for the deformation of phyllosilicates in the lithosphere
journal, February 2019
- Aslin, Joe; Mariani, Elisabetta; Dawson, Karl
- Nature Communications, Vol. 10, Issue 1
Mechanical properties of shale-gas reservoir rocks — Part 2: Ductile creep, brittle strength, and their relation to the elastic modulus
journal, September 2013
- Sone, Hiroki; Zoback, Mark D.
- GEOPHYSICS, Vol. 78, Issue 5
Elasticity of muscovite and its relationship to crystal structure
journal, January 1986
- Vaughan, Michael T.; Guggenheim, Stephen
- Journal of Geophysical Research, Vol. 91, Issue B5
On spherical nanoindentations, kinking nonlinear elasticity of mica single crystals and their geological implications
journal, August 2009
- Basu, S.; Zhou, A.; Barsoum, M. W.
- Journal of Structural Geology, Vol. 31, Issue 8
On the determination of spherical nanoindentation stress–strain curves
journal, October 2006
- Basu, Sandip; Moseson, Alexander; Barsoum, Michel W.
- Journal of Materials Research, Vol. 21, Issue 10