[S-CG49] Innovation through the Integration of Solid Earth Science and Materials Science

[SCG49-04] Elastic Constants of Alpha-Quartz at High Temperatures: Derivation from Molecular Dynamics Simulation

*Riku Sugimoto¹, Hiroshi Sakuma^1,2, Kenji Kawai¹ (1.The University of Tokyo, 2.National Institute for Materials Science)

Keywords:Alpha-Quartz, Molecular Dynamics Simulation, Elastic Constant, Real Contact Area

Alpha-quartz, one of the common minerals in the crust, is abundant in faults. For a better understanding of fault behavior, it is important to know the frictional properties of alpha-quartz. Following the adhesion theory, friction between alpha-quartz particles depends on the real contact area and the force to break the adhesion on the real contact point. Knowledge of these two properties is essential for developing the rate and state friction (RSF) law. However, the temperature variation of the true contact area is not resolved. It is also difficult to observe true contact area experimentally. Generally the real contact area can be estimated from the elastic constants of the minerals. In this study, we consider methods and models for estimating the elastic constants of alpha-quartz from molecular dynamics simulations, and theoretically compute the elastic constants of alpha-quartz from room to high temperatures, which correspond to crustal conditions. We will also use these elastic constants to gain insight into the temperature variation of the real contact area.
This study used the molecular dynamics (MD) simulation. First, we determined the lattice constants with 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 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 [1], the Tersoff [2], and the BMH-EXP models [3, 4], which are conventionally used in MD calculations for SiO₂ systems.
Alpha-quartz is a trigonal system with six independent elastic constants: C₁₁, C₁₂, C₁₃, C₁₄, C₃₃, and C₄₄ [5]. Using the Vashishta model, calculated elastic constants other than C₁₄ at room temperature (300 K) differ greatly from the experimental value [6]. C₁₁ and C₁₃, using the Tersoff model, well reproduced the experimental values but could not reproduce other elastic constants. BMH-EXP model well reproduced all experimental values. Based on these results, we decided to use BMH-EXP model for calculating the elastic constants of quartz at high temperatures.
In the presentation, we will discuss changes in the real contact area of the quartz with temperatures using the elastic constants calculated with the BMH-EXP model.

References.
[1] Vashishta, et al., Phys. Rev. B, 41, 12197 (1990).
[2] Mumetoh et al., Comp. Mat. Sci., 39, 334-339 (2007).
[3] Ishikawa et al., J. Mineral. Petrol. Sci., 111, 297-302 (2016).
[4] Yokoyama and Sakuma, Geochim. Cosmochim. Acta, 224, 301-312 (2018).
[5] J. F. Nye. Physical Properties of Crystals, Clarendon Press, Oxford, (1957).
[6] Ohno, J. Phys. Earth, 43, 157-169 (1995).