Abstract
Deformation of phyllosilicate can control the dynamics of the Earth’s crust. The phenomenological relationship between stress and deformation is known for some typical phyllosilicates; however, the underlying physics originating from the crystal structures is poorly understood. In this study, the deformation mechanism of pyrophyllite along basal planes was revealed through density functional theory calculations and atomic-scale theory of friction. The stable and metastable interlayer structures formed by interlayer slide were consistent with the experimental results reported previously by high-resolution transmission electron microscopy. The difference in potential energies between stable and metastable interlayer structures can be interpreted as the diference in the stacking of dioctahedral sheets between the adjacent layers. The estimated friction coefficient of the pyrophyllite between adjacent layers was consistent with the results of atomic force microscopy, suggesting that atomic-scale friction can be adequately estimated by this method. The calculated shear stress in our simulations has a linear relationship with the normal stress and has no significant crystallographic dependence on sliding direction along the basal planes. The crystallographic isotropy of interlayer friction is explained by the absence of interlayer cations in pyrophyllite, while muscovite showed crystallographic anisotropy as observed in previous studies. The macroscopic friction of a single crystal of pyrophyllite was estimated from atomic-scale friction by using the area of contact. The macroscopic friction coefficient of ideal interlayer sliding was estimated to be 0.134, which was smaller than a reported value (0.276) in shear experiments conducted for wet polycrystalline gouge layers. This diference can be primarily explained by the degree of orientation of pyrophyllite particles in the gouge layers. The friction coeficient estimated by a simple model of randomly oriented pyrophyllite gouge layer was 0.203 ± 0.001, which was similar to the reported value of 0.276 and clearly smaller than the values (0.6–0.85) of common minerals estimated by the empirical Byerlee’s law. These results indicate that weak interlayer friction of phyllosilicates has a large effect on the low frictional strength of gouge layers in natural faults. Our methodology and results are useful for understanding the physics behind the phenomenological friction laws of phyllosilicate gouge.
Acknowledgments and Funding
We acknowledge H. Okuda for a discussion onmodeling the gouge friction. The DFT calculationswere conducted using the Numerical Materials Simulator at NIMS. This work was supported by JSPS KAKENHI grant number 17H05320.
References cited
Abe, S., Dieterich, J.H., Mora, P., and Place, D. (2002) Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model. Pure and Applied Geophysics, 159, 1967–1983.10.1007/978-3-0348-8203-3_5Search in Google Scholar
Amiguet, E., Reynard, B., Caracas, R., Van de Moortèle, B., Hilairet, N., and Wang, Y. (2012) Creep of phyllosilicates at the onset of plate tectonics. Earth and Planetary Science Letters, 345-348, 142–150.10.1016/j.epsl.2012.06.033Search in Google Scholar
Amontons, M. (1699) De la resistance cause’e dans les machines. Histoire de l’Académie Royale des Sciences, 206–223.Search in Google Scholar
Barone, V., Casarin, M., Forrer, D., Pavone, M., Sambi, M., and Vittadini, A. (2009) Role and effective treatment of dispersive forces in materials: Polyethylene and graphite crystals as test cases. Journal of Computational Chemistry, 30, 934–939.10.1002/jcc.21112Search in Google Scholar
Behnsen, J., and Faulkner, D.R. (2012) The effect of mineralogy and effective normal stress on frictional strength of sheet silicates. Journal of Structural Geology, 42, 49–61.10.1016/j.jsg.2012.06.015Search in Google Scholar
Bengtsson, L. (1999) Dipole correction for surface supercell calculations. Physical Review B, 59, 12,301–12,304.10.1103/PhysRevB.59.12301Search in Google Scholar
Bos, B., and Spiers, C.J. (2001) Experimental investigation into the microstructural and mechanical evolution of phyllosilicate-bearing fault rock under conditions favouring pressure solution. Journal of Structural Geology, 23, 1187–1202.10.1016/S0191-8141(00)00184-XSearch in Google Scholar
Bucholz, E.W., Zhao, X., Sinnott, S.B., and Perry, S.S. (2012) Friction and wear of pyrophyllite on the atomic scale. Tribology Letters, 46, 159–165.10.1007/s11249-012-9927-6Search in Google Scholar
Byerlee, J. (1978) Friction of rocks. Pure and Applied Geophysics, 116, 615–626.10.1007/978-3-0348-7182-2_4Search in Google Scholar
Chen, J., and Spiers, C.J. (2016) Rate and state frictional and healing behavior of carbonate fault gouge explained using microphysical model. Journal of Geophysical Research: Solid Earth, 121, 8642–8665.10.1002/2016JB013470Search in Google Scholar
Chen, J., Niemeijer, A.R., and Spiers, C.J. (2017) Microphysically derived expressions for rate-and-state friction parameters, ab and Dc Journal of Geophysical Research: Solid Earth, 122, 9627–9657.10.1002/2017JB014226Search in Google Scholar
Cieplak, M., Smith, E.D., and Robbinst, M.O. (1994) Molecular origins of friction: the force on adsorbed layers. Science, 265, 1209–1212.10.1126/science.265.5176.1209Search in Google Scholar
Dieterich, J.H. (1979) Modeling of rock friction: 1. Experimental results and constituve equations. Journal of Geophysical Research, 84, 2161–2168.10.1029/JB084iB05p02161Search in Google Scholar
Dieterich, J.H., and Kilgore, B.D. (1996) Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic. Tectonophysics, 256, 219–239.10.1016/0040-1951(95)00165-4Search in Google Scholar
Garrity, K.F., Bennett, J.W., Rabe, K.M., and Vanderbilt, D. (2014) Pseudopotentials for high-throughput DFT calculations. Computational Materials Science, 81, 446–452.10.1016/j.commatsci.2013.08.053Search in Google Scholar
Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., and others. (2009) QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21, 395502.10.1088/0953-8984/21/39/395502Search in Google Scholar PubMed
Giannozzi, P., Andreussi, O., Brumme, T., Bunau, O., Buongiorno Nardelli, M., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Cococcioni, M., and others (2017) Advanced capabilities for materials modelling with QUANTUM ESPRESSO. Journal of Physics: Condensed Matter, 29, 465901.10.1088/1361-648X/aa8f79Search in Google Scholar PubMed
Grimme, S. (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry, 27, 1787–1799.10.1002/jcc.20495Search in Google Scholar PubMed
Hohenberg, P., and Kohn, W. (1964) Inhomogeneous electron gas. Physical Review, 136, B864–B871.10.1103/PhysRev.136.B864Search in Google Scholar
Horn, H.M., and Deere, D.U. (1962) Frictional characteristics of minerals. Géotechnique, 12, 319–335.10.1680/geot.1962.12.4.319Search in Google Scholar
Ikari, M. J., Saffer, D.M., and Marone, C. (2007) Effect of hydration state on the frictional properties of montmorillonite-based fault gouge. Journal of Geophysical Research, 112, B06423.10.1029/2006JB004748Search in Google Scholar
Jefferies, S.P., Holdsworth, R.E., Wibberley, C.A.J., Shimamoto, T., Spiers, C.J., Niemeijer, A.R., and Lloyd, G.E. (2006) The nature and importance of phyllonite development in crustal-scale fault cores: an example from the Median Tectonic Line, Japan. Journal of Structural Geology, 28, 220–235.10.1016/j.jsg.2005.10.008Search in Google Scholar
Katayama, I., Kubo, T., Sakuma, H., and Kawai, K. (2015) Can clay minerals account for the behavior of non-asperity on the subducting plate interface? Progress in Earth and Planetary Science, 2, 30.10.1186/s40645-015-0063-4Search in Google Scholar
Kawai, K., Sakuma, H., Katayama, I., and Tamura, K. (2015) Frictional characteristics of single and polycrystalline muscovite and influence of fluid chemistry. Journal of Geophysical Research B: Solid Earth, 120, 6209–6218.10.1002/2015JB012286Search in Google Scholar
Kogure, T., and Kameda, J. (2008) High-resolution TEM and XRD simulation of stacking disorder in 2:1 phyllosilicates. Zeitschrift für Kristallographie: Crystalline Materials, 223, 69–75.10.1524/zkri.2008.0004Search in Google Scholar
Kogure, T., Jige, M., Kameda, J., Yamagishi, A., Miyawaki, R., and Kitagawa, R. (2006) Stacking structures in pyrophyllite revealed by high-resolution transmission electron microscopy (HRTEM). American Mineralogist, 91, 1293–1299.10.2138/am.2006.1997Search in Google Scholar
Kohn, W., and Sham, L.J. (1965) Self-consistent equations including exchange and correlation effects. Physical Review, 140, 1133–1138.10.1103/PhysRev.140.A1133Search in Google Scholar
Lee, J.H., and Guggenheim, S. (1981) Single crystal X‑ray refinement of pyrophyllite-1Tc. American Mineralogist, 66, 350–357.Search in Google Scholar
Mariani, E., Brodie, K.H., and Rutter, E.H. (2006) Experimental deformation of muscovite shear zones at high temperatures under hydrothermal conditions and the strength of phyllosilicate-bearing faults in nature. Journal of Structural Geology, 28, 1569–1587.10.1016/j.jsg.2006.06.009Search in Google Scholar
Monkhorst, H.J., and Pack, J.D. (1976) Special points for Brillouin-zone integrations. Physical Review B, 13, 5188–5192.10.1103/PhysRevB.13.5188Search in Google Scholar
Moore, D.E., and Lockner, D.A. (2004) Crystallographic controls on the frictional behavior of dry and water-saturated sheet structure minerals. Journal of Geophysical Research, 109, 1–16.10.1029/2003JB002582Search in Google Scholar
Moore, D.E., and Lockner, D.A. (2007) Friction of the Smectite Clay Montmorillonite, A review and interpretation of data. In T.H. Dixon and J.C. Moore, Eds., The Seismogenic Zone of Subduction Thrust Faults, p. 317–345. Columbia University Press.10.7312/dixo13866-011Search in Google Scholar
Morrow, C.A., Moore, D.E., and Lockner, D.A. (2000) The effect of mineral bond strength and adsorbed water on fault gouge frictional strength. Geophysical Research Letters, 27, 815–818.10.1029/1999GL008401Search in Google Scholar
Morrow, C.A., Moore, D.E., and Lockner, D.A. (2017) Frictional strength of wet and dry montmorillonite. Journal of Geophysical Research: Solid Earth, 122, doi:10.1002/2016JB013658.10.1002/2016JB013658Search in Google Scholar
Okuda, H., Kawai, K., and Sakuma, H. (2019) First-principles investigation of frictional characteristics of brucite: an application to its macroscopic frictional characteristics. Journal of Geophysical Research: Solid Earth, 124, 10,423–10,443.10.1029/2019JB017740Search in Google Scholar
Perdew, J.P., Burke, K., and Ernzerhof, M. (1996) Generalized gradient approximation made simple. Physical Review Letters, 77, 3865–3868.10.1103/PhysRevLett.77.3865Search in Google Scholar PubMed
Ruina, A. (1983) Slip instability and state variable friction laws. Journal of Geophysical Research: Solid Earth, 88, 10359–10370.10.1029/JB088iB12p10359Search in Google Scholar
Sakuma, H. (2013) Adhesion energy between mica surfaces: implications for the frictional coefficient under dry and wet conditions. Journal of Geophysical Research: Solid Earth, 118, 6066–6075.10.1002/2013JB010550Search in Google Scholar
Sakuma, H., and Suehara, S. (2015) Interlayer bonding energy of layered minerals: implication for the relationship with friction coefficient. Journal of Geophysical Research B: Solid Earth, 120, 2212–2219.10.1002/2015JB011900Search in Google Scholar
Sakuma, H., Otsuki, K., and Kurihara, K. (2006) Viscosity and lubricity of aqueous NaCl solution confined between mica surfaces studied by shear resonance measurement. Physical Review Letters, 96, 046104.10.1103/PhysRevLett.96.046104Search in Google Scholar PubMed
Sakuma, H., Kondo, T., Nakao, H., Shiraki, K., and Kawamura, K. (2011) Structure of hydrated sodium ions and water molecules adsorbed on the mica/water interface. The Journal of Physical Chemistry C, 115, 15,959–15,964.10.1021/jp111936sSearch in Google Scholar
Sakuma, H., Tachi, Y., Yotsuji, K., Suehara, S., Arima, T., Fujii, N., Kawamura, K., and Honda, A. (2017) Stability of montmorillonite edge faces studied using first-principles calculations. Clays and Clay Minerals, 65, 252–272.10.1346/CCMN.2017.064062Search in Google Scholar
Sakuma, H., Kawai, K., Katayama, I., and Suehara, S. (2018) What is the origin of macroscopic friction? Science Advances, 4, eaav2268.10.1126/sciadv.aav2268Search in Google Scholar
Schwarz, U.D., and Hölscher, H. (2016) Exploring and explaining friction with the Prandtl-Tomlinson model. ACS Nano, 10, 38–41.10.1021/acsnano.5b08251Search in Google Scholar
Shea, W.T., and Kronenberg, A.K. (1993) Strength and anisotropy of foliated rocks with varied mica contents. Journal of Structural Geology, 15, 1097–1121.10.1016/0191-8141(93)90158-7Search in Google Scholar
Tetsuka, H., Katayama, I., Sakuma, H., and Tamura, K. (2018) Effects of humidity and interlayer cations on the frictional strength of montmorillonite. Earth, Planets and Space, 70, 56.10.1186/s40623-018-0829-1Search in Google Scholar
Weck, P.F., Kim, E., and Jové-Colón, C.F. (2015) Relationship between crystal structure and thermo-mechanical properties of kaolinite clay: beyond standard density functional theory. Dalton Transactions, 44, 12550–12560.10.1039/C5DT00590FSearch in Google Scholar
Wintsch, R.P., Christoffersen, R., and Kronenberg, A.K. (1995) Fluid-rock reaction weakening of fault zones. Journal of Geophysical Research, 100, 13,021–13,032.10.1029/94JB02622Search in Google Scholar
Zhang, J., Hu, L., Pant, R., Yu, Y., Wei, Z., and Zhang, G. (2013) Effects of interlayer interactions on the nanoindentation behavior and hardness of 2:1 phyllosilicates. Applied Clay Science, 80-81, 267–280.10.1016/j.clay.2013.04.013Search in Google Scholar
Zhong, W., and Tománek, D. (1990) First-principles theory of atomic-scale friction. Physical Review Letters, 64, 3054–3057.10.1103/PhysRevLett.64.3054Search in Google Scholar PubMed
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