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

Abstract

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 H2O, to be the elementary processes of dislocation climb. The relationships between differential stress (σ) and strain rate ( trueε˙) are written as trueε˙∝σ3Dv and trueε˙∝σ5Dp for cases controlled by volume and pipe diffusion, respectively, where Dv and Dp 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.

Deformation of Fine‐Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep

“… Note . In a theory by Fukuda and Shimizu (), μ is the shear modulus of quartz (42 × 10 3 MPa), b is the burgers vector (5 × 10 −10 m), k is the Boltzmann constant (1.381 × 10 −23 J/K), D 0 is the preexponential factor for diffusion of oxygen‐bearing species parallel to the c axis in α quartz by Farver and Yund () taking into account the effect of water fugacity in Fukuda and Shimizu () (5.8 × 10 −7 m 2 /s MPa − r with r = 1), and Q is its activation energy. GSI = grain‐size‐insensitive creep; GSS = grain‐size‐sensitive.…”

“…Quartz grain size paleopiezometers (shown by dashed lines) by St06 + H&K10 (Stipp et al, , with the stress correction in Holyoke and Kronenberg, ) for regime 1 [steeper in (a)] and regimes 2 and 3 [gentler in (a) and this is shown only in (b) for three grain sizes for simplicity], Sh08 (Shimizu, ). Flow laws by L&P92 (Luan & Paterson, ); L&P92 + F&S17 (Luan & Paterson, , redetermined by Fukuda & Shimizu, ); R&B04a, b (Rutter & Brodie, , ); H01 + H&K13 (Hirth et al, , revised by Holyoke & Kronenberg, ); and F&S17 (Fukuda & Shimizu, ; Theory).…”

“…In the stress‐grain size relationship (Figure a), the lowest differential stresses predicted by flow laws for quartz dislocation creep are given by the Luan and Paterson () flow law revised by Fukuda and Shimizu (; shown with a “plus, +” hereafter for original and revised papers and in Figure ). The flow law by Hirth et al () is based on experimental results of Luan and Paterson () and Gleason and Tullis () and results for naturally deformed quartzites, and these flow laws are included in “other GSI creep” in Figure a.…”

“…These flow laws, however, were obtained in the β ‐quartz field. Fukuda and Shimizu () theoretically calculated dislocation creep flow laws controlled by volume diffusion coefficients of oxygen bearing species which were different between α ‐ and β ‐quartz. Their theoretical calculations indicate that flow stress for α ‐quartz in most natural conditions can be ~1 order of magnitude higher than that for β ‐quartz, while it becomes opposite in experimental conditions where temperature is usually larger than 900°C, meaning the flow stress for α ‐quartz is lower than that for β ‐quartz.…”

Experimental Determination of Eutectic Liquid Compositions in the MgO‐SiO2System to the Lowermost Mantle Pressures

“…The present experiments found that MgSiO 3 bridgmanite is the liquidus phase of melts with a wider range of SiO 2 /(MgO + SiO 2 ) ratios than previously predicted by ab initio calculations and thermodynamic modeling. (Fukuda & Shimizu, 2017); while SiO 2 stishovite is more viscous than MgSiO 3 bridgmanite (Xu et al, 2017), quartz usually includes water and is thus a weak phase.…”