# Fileset

[2-SupplementalMaterial-Sakuma.pdf](https://mdr.nims.go.jp/filesets/a8c30bc7-25d4-4cc7-b9c3-29605b466499/download)

## Creator

[Hiroshi Sakuma](https://orcid.org/0000-0002-6522-0704), Diane E. Moore, David A. Lockner, Toshihiro Kogure

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Velocity-Independent Dry Friction on Mica: Realization of Ideal Amontons-Coulomb Friction](https://mdr.nims.go.jp/datasets/3d56cefa-dc6a-425b-b983-d98f86a3ca18)

## Fulltext

Supplemental Material for “Velocity-Independent Dry Friction on Mica: Realization of Ideal Amontons-Coulomb Friction”  Hiroshi Sakuma1,*, Diane E. Moore2, David A. Lockner2,†, and Toshihiro Kogure3  1National Institute for Materials Science, Tsukuba, Japan 2U.S. Geological Survey, Moffett Field, California 94035, USA 3University of Tokyo, Hongo, Japan  *Contact Author: sakuma.hiroshi@nims.go.jp †Contact Author: dlockner@usgs.gov  This file includes supplemental materials for the detail in experimental conditions, relationship between shear stress and normal stress, friction coefficients of mica at 65 and 100ºC, the results of slide-hold-slide tests at 22 and 200ºC, available temperature dependence of the “a” parameter for various materials, and the detail in molecular dynamics simulations.    FIG S1. (a) Single-crystal mica sheets. (b) Cross section of the sample assembly with mica sheets between 30º sawcut novaculite driving blocks.  During the experiments, the sample column was continuously evacuated through a 1.6 mm-diameter axial hole that extends to the upper porous novaculite driving block.      Fig. S2 Relationship between shear stress and normal stress of single-crystal mica measured using a triaxial shear apparatus in this study and a double-direct shear apparatus in a previous study [21] under room-temperature and dry conditions. The equation shown in the figure represents a linear fit to the data obtained in this study.    TABLE S1. Conditions of triaxial shear experiments and obtained “a” parameter.  Sample  no. Temperature  (ºC) Normal stress  (MPa) Experimental type a  HS11 22 100 Velocity-stepping 0.0058 (0.0011) HS14 65 100 Velocity-stepping 0.0028 (0.0005) HS13 100 100 Velocity-stepping 0.0005 (0.0002) HS12 200 100 Velocity-stepping <0.0001 (0.0002) HS15 22 100 Slide-hold-slide - HS16 200 100 Slide-hold-slide -      FIG S3. Friction coefficients of mica obtained from velocity-step tests at 65ºC (a) and 100ºC (b). The numbers near the lines indicate the sliding velocity parallel to the shear planes (µm/s). Dotted lines indicate the baseline of the steady-state friction used to calculate the difference in the friction coefficients before and after the velocity change.      FIG S4. Friction coefficients of mica obtained from slide-hold-slide tests at 22ºC and 200ºC.         FIG S5. Available temperature dependence of the “a” parameter for simulated gouges composed of a single mineral under dry (a) and wet (b) conditions, and a mixture of minerals under dry (c) and wet (d and e) conditions. The data was cited from the literature (anhydrite [35], plagioclase [36,37], Na-feldspar [31], antigorite [38], augite [39], biotite [40,41], hornblende [42], granite [16,43], illite and quartz [44], Alhama de Murcia fault [45], Alpine fault [46,47], blueschist [48], felsic gneiss [49], mafic gneiss [49], Hikurangi trench [50], Longitudinal Valley fault [51], phyllosilicate-rich mylonite [52], Shimanto and Sanbagawa belt [53], Tohoku subduction zone [54]).       Non equilibrium molecular dynamics (NEMD) simulations—Classical molecular dynamics simulations were conducted by using in-house program, MXDTRICL. Muscovite is a 2:1 type sheet-silicate mineral, consisting of an [AlO6] dioctahedral sheet sandwiched between two [(Si,Al)O4] tetrahedral sheets. One-fourth of the Si4+ ions are replaced by Al3+ ions in the tetrahedral sheets and the negative charge of the sheets is compensated by the interlayer K+ ions. Force field of muscovite used in this study is an interatomic potential model, and it has been developed to reproduce the muscovite structure and physical properties [32-34]. The calculated lattice parameters of 2M1 muscovite by this model are a = 5.159 Å, b = 8.966 Å, c = 20.065 Å, and b = 95.3º at 27ºC and 0.1 MPa. The electrostatic Coulomb interaction was calculated by using the Ewald method [55]. The differential equation of motion was solved by the velocity-Verlet algorithm with a time increment of 0.4 femtosecond (fs). Equilibrium lattice constants were obtained by NPT ensemble simulations at pressures of 6 GPa and temperatures of 27, 100, and 200ºC. The equilibrium lattice constants were used for initial structures for subsequent shear simulations. Dislocation-free and ripplocation-bearing supercells at 27ºC before the shear were a = 25.48 Å, b = 26.48 Å, c = 19.19 Å, b = 95.1º, and a = 167.1 Å, b = 26.35 Å, c = 39.58 Å, b = 94.9º, respectively. Two ripplocations were included in the ripplocation-bearing supercell; they were built with the length of 34 units of a in the primitive cell on two straight layers with the length of 165 Å in a direction (32 units of a in the primitive cell). By applying hydrostatic pressure, the initial structure for shear simulations was obtained. Shear direction and plane were fixed to <100> and (001), respectively. Shear strain was applied by tilting the c-axis of the supercell with the shear rates of 109, 1010, and 1011 s−1. Friction coefficients as a function of strain were calculated by simply dividing the shear stress by normal stress.