Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates

Lanin, Eril Suhada; Sone, Hiroki; Yu, Zheng; Liu, Qitong; Wang, Bu

doi:10.1029/2021jb021902

Title: Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates

Journal Article · 30 July 2021 · Journal of Geophysical Research. Solid Earth

DOI: https://doi.org/10.1029/2021jb021902 · OSTI ID:1848371

^[1];

^[2];

^[3];

^[4];

^[4]

Univ. of Wisconsin, Madison, WI (United States). Dept. of Chemical and Biological Engineering. Geological Engineering Program; Univ. of Wisconsin, Madison, WI (United States)
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

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 (M) 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 (cij) determined from DFT were converted to indentation modulus (M) 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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE Advanced Research Projects Agency - Energy (ARPA-E); National Science Foundation (NSF)

Grant/Contract Number:: AR0001147

OSTI ID:: 1848371

Journal Information:: Journal of Geophysical Research. Solid Earth, Journal Name: Journal of Geophysical Research. Solid Earth Journal Issue: 8 Vol. 126; ISSN 2169-9313

Publisher:: American Geophysical UnionCopyright Statement

Country of Publication:: United States

Language:: English

References (64)

Effect of the damping function in dispersion corrected density functional theory Grimme, Stefan; Ehrlich, Stephan; Goerigk, Lars Journal of Computational Chemistry, Vol. 32, Issue 7 https://doi.org/10.1002/jcc.21759	journal	March 2011
Experiental deformation of single crystals of biotite Etheridge, M. A.; Hobbs, B. E.; Paterson, M. S. Contributions to Mineralogy and Petrology, Vol. 38, Issue 1 https://doi.org/10.1007/BF00371724	journal	January 1973
Chemical and deformational controls on recrystallization of mica Etheridge, M. A.; Hobbs, B. E. Contributions to Mineralogy and Petrology, Vol. 43, Issue 2 https://doi.org/10.1007/BF00572714	journal	January 1974
Hertzian contact of anisotropic bodies Willis, J. R. Journal of the Mechanics and Physics of Solids, Vol. 14, Issue 3 https://doi.org/10.1016/0022-5096(66)90036-6	journal	May 1966
Measuring the elastic properties of anisotropic materials by means of indentation experiments Vlassak, Joost J.; Nix, W. D. Journal of the Mechanics and Physics of Solids, Vol. 42, Issue 8 https://doi.org/10.1016/0022-5096(94)90033-7	journal	August 1994
Dislocation interactions in experimentally deformed biotite Christoffersen, Roy; Kronenberg, Andreas K. Journal of Structural Geology, Vol. 15, Issue 9-10 https://doi.org/10.1016/0191-8141(93)90157-6	journal	September 1993
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
The indentation characterisation of the mechanical properties of various carbon materials: Glassy carbon, coke and pyrolytic graphite Fielda, J. S.; Swain, M. V. Carbon, Vol. 34, Issue 11 https://doi.org/10.1016/S0008-6223(96)00071-1	journal	January 1996
The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape Vlassak, J. J.; Ciavarella, M.; Barber, J. R. Journal of the Mechanics and Physics of Solids, Vol. 51, Issue 9 https://doi.org/10.1016/S0022-5096(03)00066-8	journal	September 2003
On the measurement of stress–strain curves by spherical indentation Herbert, E. G.; Pharr, G. M.; Oliver, W. C. Thin Solid Films, Vol. 398-399 https://doi.org/10.1016/S0040-6090(01)01439-0	journal	November 2001
A review of nanoindentation continuous stiffness measurement technique and its applications Li, Xiaodong; Bhushan, Bharat Materials Characterization, Vol. 48, Issue 1 https://doi.org/10.1016/S1044-5803(02)00192-4	journal	February 2002
Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves Kalidindi, Surya R.; Pathak, Siddhartha Acta Materialia, Vol. 56, Issue 14 https://doi.org/10.1016/j.actamat.2008.03.036	journal	August 2008
Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models Donohue, Brendan R.; Ambrus, Adrian; Kalidindi, Surya R. Acta Materialia, Vol. 60, Issue 9 https://doi.org/10.1016/j.actamat.2012.03.034	journal	May 2012
Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation Zhang, G.; Wei, Z.; Ferrell, R. Applied Clay Science, Vol. 43, Issue 2 https://doi.org/10.1016/j.clay.2008.08.010	journal	February 2009
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] Bobko, Christopher P.; Ortega, J. Alberto; Ulm, Franz-Josef Applied Clay Science, Vol. 46, Issue 4 https://doi.org/10.1016/j.clay.2009.08.008	journal	December 2009
Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress Sone, Hiroki; Zoback, Mark D. International Journal of Rock Mechanics and Mining Sciences, Vol. 69 https://doi.org/10.1016/j.ijrmms.2014.04.002	journal	July 2014
Long-term creep tests and viscoelastic constitutive modeling of lower Paleozoic shales from the Baltic Basin, N Poland Trzeciak, Maciej; Sone, Hiroki; Dabrowski, Marcin International Journal of Rock Mechanics and Mining Sciences, Vol. 112 https://doi.org/10.1016/j.ijrmms.2018.10.013	journal	December 2018
Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters Delafargue, Antoine; Ulm, Franz-Josef International Journal of Solids and Structures, Vol. 41, Issue 26 https://doi.org/10.1016/j.ijsolstr.2004.06.019	journal	December 2004
On spherical nanoindentations, kinking nonlinear elasticity of mica single crystals and their geological implications Basu, S.; Zhou, A.; Barsoum, M. W. Journal of Structural Geology, Vol. 31, Issue 8 https://doi.org/10.1016/j.jsg.2009.05.008	journal	August 2009
Lessons learned from the Floyd shale play Dembicki, Harry; Madren, Jonathan D. Journal of Unconventional Oil and Gas Resources, Vol. 7 https://doi.org/10.1016/j.juogr.2014.03.001	journal	September 2014
Spherical nanoindentation stress–strain curves Pathak, Siddhartha; Kalidindi, Surya R. Materials Science and Engineering: R: Reports, Vol. 91 https://doi.org/10.1016/j.mser.2015.02.001	journal	May 2015
Viscous creep in room-dried unconsolidated Gulf of Mexico shale (I): Experimental results Chang, Chandong; Zoback, Mark D. Journal of Petroleum Science and Engineering, Vol. 69, Issue 3-4 https://doi.org/10.1016/j.petrol.2009.08.018	journal	December 2009
Viscous relaxation model for predicting least principal stress magnitudes in sedimentary rocks Sone, Hiroki; Zoback, Mark D. Journal of Petroleum Science and Engineering, Vol. 124 https://doi.org/10.1016/j.petrol.2014.09.022	journal	December 2014
Determination of an effective zero-point and extraction of indentation stress–strain curves without the continuous stiffness measurement signal Pathak, S.; Shaffer, J.; Kalidindi, S. Scripta Materialia, Vol. 60, Issue 6 https://doi.org/10.1016/j.scriptamat.2008.11.028	journal	March 2009
Creep of Crystals Poirier, Jean-Paul https://doi.org/10.1017/CBO9780511564451	book	October 2009
The Rock Physics Handbook Mavko, Gary; Mukerji, Tapan; Dvorkin, Jack Cambridge University Press https://doi.org/10.1017/CBO9780511626753	book	January 2009
Deformation of Earth Materials Karato, Shun-ichiro https://doi.org/10.1017/CBO9780511804892	book	January 2008
Contact Mechanics Johnson, K. L. https://doi.org/10.1017/CBO9781139171731	book	January 1985
Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field Cygan, Randall T.; Liang, Jian-Jie; Kalinichev, Andrey G. The Journal of Physical Chemistry B, Vol. 108, Issue 4 https://doi.org/10.1021/jp0363287	journal	January 2004
Molecular Dynamics Simulations of Structural and Mechanical Properties of Muscovite: Pressure and Temperature Effects Teich-McGoldrick, Stephanie L.; Greathouse, Jeffery A.; Cygan, Randall T. The Journal of Physical Chemistry C, Vol. 116, Issue 28 https://doi.org/10.1021/jp303143s	journal	July 2012
Ripplocations in van der Waals Layers Kushima, Akihiro; Qian, Xiaofeng; Zhao, Peng Nano Letters, Vol. 15, Issue 2 https://doi.org/10.1021/nl5045082	journal	January 2015
Elasticity of muscovite and its relationship to crystal structure Vaughan, Michael T.; Guggenheim, Stephen Journal of Geophysical Research, Vol. 91, Issue B5 https://doi.org/10.1029/JB091iB05p04657	journal	January 1986
Basal slip and mechanical anisotropy of biotite Kronenberg, Andreas K.; Kirby, Stephen H.; Pinkston, John Journal of Geophysical Research, Vol. 95, Issue B12 https://doi.org/10.1029/JB095iB12p19257	journal	January 1990
Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation Yamakov, Vesselin; Wolf, Dieter; Phillpot, Simon R. Nature Materials, Vol. 1, Issue 1 https://doi.org/10.1038/nmat700	journal	September 2002
Ripplocations provide a new mechanism for the deformation of phyllosilicates in the lithosphere Aslin, Joe; Mariani, Elisabetta; Dawson, Karl Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-08587-2	journal	February 2019
GULP: A computer program for the symmetry-adapted simulation of solids Gale, Julian D. Journal of the Chemical Society, Faraday Transactions, Vol. 93, Issue 4 https://doi.org/10.1039/A606455H	journal	January 1997
GULP: A computer program for the symmetry-adapted simulation of solids Gale, Julian D. Journal of the Chemical Society, Faraday Transactions, Vol. 93, Issue 4 https://doi.org/10.1039/a606455h	journal	January 1997
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu Grimme, Stefan; Antony, Jens; Ehrlich, Stephan The Journal of Chemical Physics, Vol. 132, Issue 15 https://doi.org/10.1063/1.3382344	journal	April 2010
Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution Swadener, J. G.; Pharr, G. M. Philosophical Magazine A, Vol. 81, Issue 2 https://doi.org/10.1080/01418610108214314	journal	February 2001
Indentation modulus of elastically anisotropic half spaces Vlassak, Joost J.; Nix, W. D. Philosophical Magazine A, Vol. 67, Issue 5 https://doi.org/10.1080/01418619308224756	journal	May 1993
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Simulation of Screw Dislocation Motion in Iron by Molecular Dynamics Simulations Domain, Christophe; Monnet, Ghiath Physical Review Letters, Vol. 95, Issue 21 https://doi.org/10.1103/PhysRevLett.95.215506	journal	November 2005
Ripplocations: A universal deformation mechanism in layered solids Barsoum, M. W.; Zhao, X.; Shanazarov, S. Physical Review Materials, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevMaterials.3.013602	journal	January 2019
The impact of different clay minerals on the anisotropy of clay matrix in shale Sayers, Colin M.; den Boer, Lennert D. Geophysical Prospecting, Vol. 67, Issue 9 https://doi.org/10.1111/1365-2478.12829	journal	June 2019
Rheological characterization of a sedimentary formation from a stress profile inversion Gunzburger, Y.; Cornet, F. H. Geophysical Journal International, Vol. 168, Issue 1 https://doi.org/10.1111/j.1365-246X.2006.03140.x	journal	January 2007
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 Nishizawa, O.; Kanagawa, K. Geophysical Journal International https://doi.org/10.1111/j.1365-246X.2010.04614.x	journal	April 2010
Top-seal leakage through faults and fractures: the role of mudrock properties Ingram, Gary M.; Urai, Janos L. Geological Society, London, Special Publications, Vol. 158, Issue 1 https://doi.org/10.1144/GSL.SP.1999.158.01.10	journal	January 1999
Mechanical properties of shale-gas reservoir rocks — Part 1: Static and dynamic elastic properties and anisotropy Sone, Hiroki; Zoback, Mark D. GEOPHYSICS, Vol. 78, Issue 5 https://doi.org/10.1190/geo2013-0050.1	journal	September 2013
Mechanical properties of shale-gas reservoir rocks — Part 2: Ductile creep, brittle strength, and their relation to the elastic modulus Sone, Hiroki; Zoback, Mark D. GEOPHYSICS, Vol. 78, Issue 5 https://doi.org/10.1190/geo2013-0051.1	journal	September 2013
A viscoplastic model of creep in shale Haghighat, Ehsan; Rassouli, Fatemeh S.; Zoback, Mark D. GEOPHYSICS, Vol. 85, Issue 3 https://doi.org/10.1190/geo2018-0700.1	journal	May 2020
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments Oliver, W. C.; Pharr, G. M. Journal of Materials Research, Vol. 7, Issue 06, p. 1564-1583 https://doi.org/10.1557/JMR.1992.1564	journal	June 1992
A simple predictive model for spherical indentation Field, J. S.; Swain, M. V. Journal of Materials Research, Vol. 8, Issue 2 https://doi.org/10.1557/JMR.1993.0297	journal	February 1993
Determination of the effective zero point of contact for spherical nanoindentation Moseson, Alexander J.; Basu, Sandip; Barsoum, Michel W. Journal of Materials Research, Vol. 23, Issue 1 https://doi.org/10.1557/JMR.2008.0012	journal	January 2008
Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology Oliver, W. C.; Pharr, G. M. Journal of Materials Research, Vol. 19, Issue 1 https://doi.org/10.1557/jmr.2004.19.1.3	journal	January 2004
On the determination of spherical nanoindentation stress–strain curves Basu, Sandip; Moseson, Alexander; Barsoum, Michel W. Journal of Materials Research, Vol. 21, Issue 10 https://doi.org/10.1557/jmr.2006.0324	journal	October 2006
Elastic and Viscoelastic Calculations of Stresses in Sedimentary Basins Warpinski, Norman R. SPE Formation Evaluation, Vol. 4, Issue 04 https://doi.org/10.2118/15243-PA	journal	December 1989
HRTEM analysis of dislocation cores and stacking faults in naturally deformed biotite crystals Noe, David Christopher; Veblen, David R. American Mineralogist, Vol. 84, Issue 11-12 https://doi.org/10.2138/am-1999-11-1220	journal	December 1999
Crystal chemistry of Al-rich biotites coexisting with muscovites in peraluminous granites Brigatti, Maria Franca; Frigieri, Paola; Ghezzo, Claudio American Mineralogist, Vol. 85, Issue 3-4 https://doi.org/10.2138/am-2000-0405	journal	March 2000
Microhardness, toughness, and modulus of Mohs scale minerals Broz, Margaret E.; Cook, Robert F.; Whitney, Donna L. American Mineralogist, Vol. 91, Issue 1 https://doi.org/10.2138/am.2006.1844	journal	January 2006
Hardness, toughness, and modulus of some common metamorphic minerals Whitney, D. L.; Broz, M.; Cook, R. F. American Mineralogist, Vol. 92, Issue 2-3 https://doi.org/10.2138/am.2007.2212	journal	February 2007
Evaluation of the elasticity normal to the basal plane of non-expandable 2:1 phyllosilicate minerals by nanoindentation Zhang, G.; Wei, Z.; Ferrell, R. E. American Mineralogist, Vol. 95, Issue 5-6 https://doi.org/10.2138/am.2010.3398	journal	May 2010
First-principles calculation of the elastic moduli of sheet silicates and their application to shale anisotropy Militzer, B.; Wenk, H. - R.; Stackhouse, S. American Mineralogist, Vol. 96, Issue 1 https://doi.org/10.2138/am.2011.3558	journal	December 2010
TEM observations of defects in biotite and their relationship to polytypism Bell, Ian A.; Wilson, Christopher J. L. Bulletin de Minéralogie, Vol. 109, Issue 1 https://doi.org/10.3406/bulmi.1986.7925	journal	January 1986

Similar Records

Nanoindentation study of bulk zirconium hydrides at elevated temperatures

Journal Article · 2017 · Journal of Alloys and Compounds · OSTI ID:1400216

Cinbiz, Mahmut Nedim; Balooch, Mehdi; Hu, Xunxiang; +2 more

Depth Dependence of the Mechanical Properties of Human Enamel by Nanoindentation

Journal Article · 2006 · Journal of Biomedical Materials Research Part A, vol. 81A, no. 1, April 1, 2007, pp. 66-74 · OSTI ID:919219

Zhou, J; Hsiung, L L

On capturing the grain-scale elastic and plastic anisotropy of alpha-Ti with spherical nanoindentation and electron back-scattered diffraction

Journal Article · 2016 · Acta Materialia · OSTI ID:1291295

Weaver, Jordan S.; Priddy, Matthew W.; McDowell, David L.; +1 more

Related Subjects

58 GEOSCIENCES
Geochemistry & Geophysics

Title: Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates

Citation Formats

References (64)

Similar Records

Related Subjects