Theoretical derivation of flow laws for quartz dislocation creep: Comparisons with experimental creep data and extrapolation to natural conditions using water fugacity corrections

We theoretically derived flow laws for quartz dislocation creep using climb-controlled dislocation creep models and compared them with available laboratory data for quartz plastic deformation. We assumed volume diffusion of oxygen-bearing species along different crystallographic axes (//c, ⊥R, and ⊥c) of α-quartz and β-quartz, and pipe diffusion of H 2 O, to be the elementary processes of dislocation climb. The relationships between differential stress (σ) and strain rate (_ e) are written as _ e∝σ 3 D v and _ e∝σ 5 D p for cases controlled by volume and pipe diffusion, respectively, where D v and D p are coefficients of diffusion for volume and pipe diffusion. In previous experimental work, there were up to ~1.5 orders of magnitude difference in the water fugacity values in experiments that used either gas-pressure-medium or solid-pressure-medium deformation apparatus. Therefore, in both the theories and flow laws, we included water fugacity effects as modified preexponential factors and water fugacity terms. Previous experimental data were obtained mainly in the β-quartz field and are highly consistent with the volume-diffusion-controlled dislocation creep models of β-quartz involving the water fugacity term. The theory also predicts significant effects for the transition of α-β quartz under crustal conditions. Under experimental pressure and temperature conditions, the flow stress of pipe-diffusion-controlled dislocation creep is higher than that for volume-diffusion-controlled creep. Extrapolation of the flow laws to natural conditions indicates that the contributions of pipe diffusion may dominate over volume diffusion under low-temperature conditions of the middle crust around the brittle-plastic transition zone.