5:15 PM - 7:15 PM
[SCG62-P12] Temperature and Pressure Variation of the Real Contact Area between α-Quartz Particles: Calculation by Molecular Dynamics Simulation
Keywords:alpha-quartz, elastic constants, real contact area, molecular dynamics simulation
Alpha-quartz, one of the common minerals in the crust, is abundant in faults. For a better understanding of fault behavior, it is essential to know the frictional properties of alpha-quartz. In general, friction between alpha-quartz particles depends on the real contact area and the force that breaks the adhesion at the point of real contact. Knowledge of the temperature and pressure dependence of these properties is essential for further development of the friction constitutive law. However, the temperature and the pressure variation of the real contact area are challenging to observe experimentally and remain unresolved. According to the Greenwood-Williamson (GW) model [1], the real contact area can be estimated from the elastic constants of minerals. Therefore, if the elastic constants of quartz can be obtained at arbitrary temperature and pressure, the temperature and pressure variation of the real contact area can be clarified. In this study, we examine an atomic interaction model that can accurately reproduce the elastic constants of quartz using molecular dynamics (MD) simulations and theoretically calculate the elastic constants of quartz in the temperature and pressure ranges from room temperature and ambient pressure to high temperature and high pressure corresponding to crustal conditions. The elastic constants obtained will be used to gain insight into the temperature and pressure variation of the real contact area. In this study, dry conditions, where the effect of water can be neglected, are first studied.
First, we determined the lattice constants with a constant number of atoms under pressure and temperature (NPT) conditions. Using the equilibrium lattice constants, we applied a small strain to calculate the stresses under a constant number of atoms, volume, and temperature (NVT) conditions. From the strain-stress relationships, we theoretically calculated the elastic constants. This study compared the results of the Vashishta model [2], the Tersoff model [3], and the BMH-EXP model [4, 5], which are conventionally used in MD calculations for SiO2 systems. As a result, we decided to adopt the BMH-EXP model to calculate elastic constants of quartz at high temperatures and pressures because the BMH-EXP model best reproduced the experimental values [6] of elastic constants from room temperature to 800K.
Based on the elastic constants at high temperature and high pressure calculated using the BMH-EXP model, the temperature and pressure dependence of the real contact area were determined by the GW model. The results showed that the real contact area increased by 12 % as the temperature changed from room temperature to 800 K under a sealing pressure of 250 MPa. Assuming that the temperature dependence of the force that breaks the adhesion at the contact point is negligible, this change is harmonic with the results of friction tests on quartz and granite gouge [7, 8], indicating that the temperature variation of the friction coefficient can be explained by the change in the real contact area.
References.
[1] Greenwood and Williamson, Proc. Roy. Soc. Lond. A. 295, 300-319 (1966).
[2] Vashishta, et al., Phys. Rev. B, 41, 12197 (1990).
[3] Munetoh et al., Comp. Mat. Sci., 39, 334-339 (2007).
[4] Ishikawa et al., J. Mineral. Petrol. Sci., 111, 297-302 (2016).
[5] Yokoyama and Sakuma, Geochim. Cosmochim. Acta, 224, 301-312 (2018).
[6] Ohno, J. Phys. Earth, 43, 157-169 (1995).
[7] Masuda et al., Prog Earth Planet Sci, 6(50), (2019).
[8] Lockner et al. PAGEOPH, 124, 445-469 (1986).
First, we determined the lattice constants with a constant number of atoms under pressure and temperature (NPT) conditions. Using the equilibrium lattice constants, we applied a small strain to calculate the stresses under a constant number of atoms, volume, and temperature (NVT) conditions. From the strain-stress relationships, we theoretically calculated the elastic constants. This study compared the results of the Vashishta model [2], the Tersoff model [3], and the BMH-EXP model [4, 5], which are conventionally used in MD calculations for SiO2 systems. As a result, we decided to adopt the BMH-EXP model to calculate elastic constants of quartz at high temperatures and pressures because the BMH-EXP model best reproduced the experimental values [6] of elastic constants from room temperature to 800K.
Based on the elastic constants at high temperature and high pressure calculated using the BMH-EXP model, the temperature and pressure dependence of the real contact area were determined by the GW model. The results showed that the real contact area increased by 12 % as the temperature changed from room temperature to 800 K under a sealing pressure of 250 MPa. Assuming that the temperature dependence of the force that breaks the adhesion at the contact point is negligible, this change is harmonic with the results of friction tests on quartz and granite gouge [7, 8], indicating that the temperature variation of the friction coefficient can be explained by the change in the real contact area.
References.
[1] Greenwood and Williamson, Proc. Roy. Soc. Lond. A. 295, 300-319 (1966).
[2] Vashishta, et al., Phys. Rev. B, 41, 12197 (1990).
[3] Munetoh et al., Comp. Mat. Sci., 39, 334-339 (2007).
[4] Ishikawa et al., J. Mineral. Petrol. Sci., 111, 297-302 (2016).
[5] Yokoyama and Sakuma, Geochim. Cosmochim. Acta, 224, 301-312 (2018).
[6] Ohno, J. Phys. Earth, 43, 157-169 (1995).
[7] Masuda et al., Prog Earth Planet Sci, 6(50), (2019).
[8] Lockner et al. PAGEOPH, 124, 445-469 (1986).