Geochemical controls on the kinetics of quartz fracture at subcritical tensile stresses

Abstract

A new kinetic model links physical and chemical controls on the subcritical fracture kinetics of quartz from the assumption that molecular level reactions governing fracture and dissolution proceed by similar pathways. The model formulation combines fracture theory with a mechanistically based description of chemical, thermal, and tensile stress effects on reactivity in aqueous environments. Water, as a vapor or liquid, promotes rupture of Si‐O bonds by end‐member processes: (1) reaction of a protonated surface with molecular water and (2) reaction of hydroxyl ions at an ionized surface. In humid environments, reaction frequency is determined by water accessibility to the crack tip. In wetted environments, the relative contributions of these mechanisms are determined by bulk solution composition which affects surface ionization and sol vent‐surf ace interactions. The macroscopic fracture rate law is given in meters per second by the fractional sum of these end‐member reaction mechanisms per a first‐order equation. Agreement of this empirical rate expression with reported measurements of quartz fracture rates suggests the model is robust. It gives a good fit to fracture rates over 6 orders of magnitude and explains increasing rates with increasing solution pH, the dependence of rate upon crystallographic direction, and thermal dependence of rate over 20° to 80°C. Findings in this study suggest that (1) fracture models based upon changes in surface free energy with solution composition are macroscopic descriptions of solvent‐surface interactions and parallel the mechanistic model presented here; (2) faster fracture rates observed in basic solutions are not facilitated by decreases in the activation barrier but are due to a transition in the solvent‐surface reaction to give a higher reaction frequency and (3) power law expressions applied to fracture rate versus stress intensity measurements may not have direct mechanistic significance since log‐linear relations describe rate data equally well. Results of the model indicate that common chemical constituents in groundwater could affect mineral reactivity in near‐surface and deeper earth environments. This quartz fracture rate model may lead to a better understanding of the time‐dependent integrity of rock and glassy materials in contact with the fluids of natural systems.