L Nègre

H Stünitz

H Raimbourg
email: hugues.raimbourg@univ-orleans.fr

A Lee

J Précigout

P Pongrac
email: petar.pongrac@natur.cuni.cz

P Jeřábek

Effect of pressure on the deformation of quartz aggregates in the presence of H 2 O

Keywords: quartz deformation, quartz rheology, H 2 O weakening, dynamic recrystallization

Quartzite samples of high purity with a grain size of ∼200 μm have been experimentally deformed by coaxial shortening in a solid medium apparatus at 900°C and at confining pressures ranging from 0.6 to 2 GPa. Most samples have been shortened by ∼30% with 0.1 wt.% added H 2 O. The samples deformed dominantly by crystal plasticity (dislocation creep), and there is a systematic decrease of flow stress with increasing confining pressure. Strain rate stepping tests yield stress exponents of n∼1.4. The strain determined from individual grain shapes matches that determined from bulk shortening. In addition to plastic strain, mode I cracks developed in all samples, principally in the grain boundary regions. Recrystallized material, visible through cathodoluminescence colours, forms by two mechanisms:

(1) progressive subgrain rotation and (2) cracking, nucleating small new grains. After high-angle boundaries have been established, grain boundary migration takes place, and a distinction of new grains nucleation origin (subgrain rotation or cracking) is impossible. At higher pressure, there is more recrystallized material forming in the deformed samples, and it is inferred that the inverse pressure dependence of flow stress is caused by enhanced grain boundary migration at higher pressure, consistent with previous studies.

Introduction

Despite a long history of research since the early discovery of the effect of H 2 O on quartz rheology by [START_REF] Griggs | Quartz: Anomalous Weakness of Synthetic Crystals[END_REF], many aspects of H 2 O weakening in quartz are yet unresolved. One of these aspects is the clearly observed dependence of the H 2 O weakening on pressure: it had been suggested by [START_REF] Paterson | The role of water in quartz deformation [+ Discussions[END_REF], [START_REF] Tullis | Pressure dependence of rock strength : implications for hydrolytic weakening[END_REF], [START_REF] Blacic | Water diffusion in quartz at high pressure: Tectonic implications[END_REF] and [START_REF] Mainprice | Experimental studies of the role of water in the plasticity of quartzites[END_REF] that the confining pressure has an enhancing effect on the H 2 O weakening effect in quartz, speculating that pressure may positively affect the diffusive uptake of H 2 O. The seminal work by [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] clearly demonstrated and quantified the increasing weakening of quartzite with increasing confining pressure in the presence of H 2 O. However, not much later it has been shown by [START_REF] Kronenberg | Solubility and diffusional uptake of hydrogen in quartz at high water pressures: Implications for hydrolytic weakening[END_REF] and [START_REF] Gerretsen | The uptake and solubility of water in quartz at elevated pressure and temperature[END_REF] that the diffusion of H 2 O into quartz occurs at rates far too slow (or not at all) to play a role in deformation experiments, and that the infiltration of H 2 O into quartz is achieved by microcracking in experiments. Thus, the effect of pressure on deformation of quartz in the presence of H 2 O had been demonstrated but its cause was not very clear. [START_REF] Tullis | Hydrolytic weakening of quartz aggregates: The effects of water and pressure on recovery[END_REF] have presented a study of annealing deformed quartz crystals at different pressures in the presence of H 2 O and have shown that recovery and recrystallization are enhanced by higher pressures.

In more recent studies of fine grained quartz material Rutter and Brodie (2004a,b) have determined stress exponents of n ≈ 3 and n = 1 and have demonstrated grain size sensitive flow in quartz. These n-values are lower than previous n-values of n = 4 determined by [START_REF] J O U R N A L P R E -P R O O F Paterson | Quartzite rheology under geological conditions[END_REF] and [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF] for dislocation creep. [START_REF] Fukuda | Deformation of Fine-Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep[END_REF] and [START_REF] Richter | The brittle-to-viscous transition in polycrystalline quartz: An experimental study[END_REF] have determined nvalues of 1.7 to 1.9, respectively. These values were partly interpreted as a combination of dislocation and diffusion creep mechanisms. As the experiments of J o u r n a l P r e -p r o o f [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] have been carried out using fine grained novaculite, and as this material has also been used in the experiments by [START_REF] Fukuda | Deformation of Fine-Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep[END_REF], it appears likely that the pressure dependence of deformation has been determined in material partially deformed by diffusion creep processes in the presence of H 2 O.

The solubility of quartz in supercritical H 2 O increases non-linearly with increasing pressure [START_REF] Manning | The solubility of quartz in H2O in the lower crust and upper mantle[END_REF][START_REF] Manning | Fluids of the deep crust: Deep is different[END_REF], so that solution-precipitation processes may be expected to be enhanced at high pressures. Diffusion creep in the presence of H 2 O will involve dissolution and precipitation and therefore is expected to be pressure dependent. The pressure dependence of quartz rheology could therefore arise from enhanced dissolution at higher pressures. For this reason, we have revisited the pressure dependence of quartz deformation using a coarser grained quartzite (∼200 μm grain size) as starting material in order to diminish the role of diffusion creep processes and to test whether the dependence of quartz strength on pressure is the same as in fine grained material and to study the processes of weakening in more detail.

Methods

Deformation experiments

Coaxial shortening deformation experiments of natural quartzite (for the characterization of the starting material see the results-section) have been performed in two types of solid medium apparatus (a modified Griggs apparatus at University of Tromsø, Norway and a new generation solid medium apparatus at ISTO, Orléans, France). NaCl was used as the confining medium in both sets of experiments. The preparation procedure followed for samples deformed in Orléans corresponds to the one described by [START_REF] Précigout | Highpressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus[END_REF]. For samples deformed in Tromsø, assemblies differ in size (smaller diameter and length) and use a single thermocouple instead of two.

J o u r n a l P r e -p r o o f

Cylindrical samples (diameter 6.35 mm for samples in the conventional Griggs apparatus in Tromsø and 8 mm for the new rig in Orléans) were cored from the starting material (without any preferential orientation), with ends ground flat and plane-parallel to ∼0.001 mm tolerance. They were dried at 110°C for one day (minimum), then weighed, wrapped with two layers of nickel foil (0.025 mm thickness), inserted into platinum jacket (0.15 mm thickness) and weld-sealed after addition of 0.1 wt.% of distilled water.

For deformation experiments at 2 GPa confining pressure, the sample assembly was slightly modified. The top piston and top inner salt piece were separated into two parts and a disc of compressed salt (of approximately 2.6 mm thickness and 13 mm diameter) was inserted in between. In this way, the deformation column was able to compact as P and T were increased to the final P-T conditions of the experiment without applying much deviatoric stress on the sample when advancing the pistons.

Before this modification of the sample assembly, several experiments failed as the hit-point was reached during the pumping stage and the sample started to deform earlier than expected.

All deformation experiments have been performed to approximately 30% coaxial shortening (total strain of samples is between ∼26 and 33%, except for the highstrain OR56 sample of ∼74%) at a temperature of 900°C and constant strain rate of approximatively 10 -6 s -1 -corresponding to a constant displacement rate of 1.5 x 10 -5 mm.s -1 (Table 2). The strain rate of experiments in the rig at Orléans was slightly lower (by ∼30%) than in the Tromsø rig. However, for a power law solid, this difference in strain rate should lead to only a subtle difference in flow stress.

Confining pressures were 600, 700, 800, 1000, 1250, 1500 and 2000 MPa (Table 2).

In the new type of solid medium apparatus, the pressure is regulated by a hydraulic pump and remains constant throughout the experiment, whereas in the conventional J o u r n a l P r e -p r o o f

Griggs apparatus, it is not regulated and typically increases towards the end of the experiment (the increase is corrected in the mechanical record).

One sample (OR56) was deformed at 2000 MPa at a faster strain rate of ∼10 -5 s -1 (1.5 x 10 -4 mm.s -1 ) and shortened by 70%. As the hit point was reached during the pumping phase, the strength of this sample could not be determined. Two strain rate stepping experiments have been performed in order to determine the n-exponent of the flow law. During these experiments, the pressure (2000 MPa for OR68 and 800 MPa for OR79) and temperature (900°C) conditions were kept constant but the strain rate was changed. For both experiments, the strain rate sequence was ∼1 x 10 -5 , 10 -7 , 10 -6 and 10 -5 s -1 . The n-exponent was then defined for each experiment as the slope between the log of the strain rates at the end of each strain rate step and the log of the differential stresses calculated by linear regression.

Processing of the mechanical data was carried out with a MATLAB program [START_REF] Pec | Semi-brittle flow of granitoid fault rocks in experiments[END_REF] adapted by J. Précigout following the routines of Heilbronner (https://micro.earth.unibas.ch). Finite strain of the deformed samples was calculated from mechanical record and from direct measurements of samples lengths before and after the experiments.

After the experiments, all samples were cut through the centre with a diamond saw (passing through the thermocouple positions) to obtain a longitudinal section parallel to the sigma 1 direction. Thin (30 µm) and thick (90 and 150 µm) sections have been prepared from the two parts.

Cathodoluminescence

Cathodoluminescence (CL) imaging has been carried out on samples using the light microscope (LM) and the scanning electron microscope (SEM). LM-CL-images J o u r n a l P r e -p r o o f of thin sections have been recorded at ISTO (Orléans) with an OPEA cold cathode stage at approximately 10-12 kV and 120-150 µA under low-pressure Argon gas at 6.7 to 7.3 Pa. The image acquisition time was 3 to 4 s. SEM-CL-images have been recorded at BRGM (Orléans) with EDAX-Pegasus system equipped with a TESCAN CL-detector. Conditions of imaging were 5 to 15 kV and 17 to 20 mm working distance. Prior to analysis, samples were coated with 20 nm of carbon. Additional mosaic CL-images have been recorded at the University of Tromsø using a Gatan Mono-CL-system on a Zeiss Merlin Compact SEM at 15 kV and 12.5 to 13.7 mm working distance using a blue filter (380-515 nm). These images have been manually segmented and processed using ImageJ software.

Bulk sample strain analysis from sand grain shapes

Cathodoluminescence and plane polarized light microscopy allow to identify the original sand grains of the Tana quartzite and to distinguish them from the cement.

Light microscope (cross-polarized and cathodoluminescence) mosaic images of the starting material and of samples deformed at different pressures have been manually segmented to isolate original sand grains. These sand grains have been analysed using the open-source ImageJ program to obtain statistics on grain parameters (cross section area, shape, orientation) as described by [START_REF] Heilbronner | Image Analysis in Earth Sciences: Microstructures and Textures of Earth Materials[END_REF].

The sand grain size is expressed as the equivalent diameter (d eq ) calculated from the area of grains (A) as √ . The fabric is expressed as the aspect ratio (AR), the mean ratio between the long (a) and short (b) axes of the particles ( ) and their orientation. The dataset has been analysed by the SURFOR method described by [START_REF] Panozzo | Two-dimensional strain from the orientation of lines in a plane[END_REF] in ImageJ for a fabric and strain analysis.

J o u r n a l P r e -p r o o f

Electron Backscatter Diffraction (EBSD) analysis

Crystal orientations have been determined by electron backscatter diffraction (EBSD) using a Nordlys detector and an Oxford Aztec system on a Zeiss Merlin Compact FE-SEM at the University of Tromsø using a 70° tilt angle, 20 kV acceleration voltage, and 9 nA probe current. An indexing quote of 75-85% has been achieved on 4 nm carbon coated thin sections. Post-processing was performed using the MTEX v.5.2.8 program package by Bachmann et al. (2010). Orientation maps were recalculated using the 6/mmm system (hexagonal) in order to avoid displaying Dauphiné twin boundaries.

Fourier Transform Infrared (FTIR) Spectroscopy

Double-polished thick sections of 150 and 90 µm have been prepared from the starting material and Fourier transform infrared spectroscopy (FTIR) analysis has been performed at ISTO (Orléans) with Nicolet 6700 (Continµum, Thermoscientific) spectrometer and OMNIC (version 8) acquisition software.

The spectra were acquired on grain interiors, grain boundaries, and cement with 64 and 128 scans and a resolution of 4 cm -1 for a range of wave numbers from 5500 to 1500 cm -1 . A window with 40x40 µm for interior of grains and with 20x50 µm was used for grain boundary measurements (window shape and orientation was adapted to the boundaries). The background was recorded for the CaF 2 window carrying the sample and subtracted from the measured spectra. Water contents were calculated using the Beer-Lambert law and the [START_REF] Paterson | The determination of hydroxyl by infrared absorption in quartz, silicate glasses and similar materials[END_REF] calibration.

Water fugacity calculations

Assuming that during the experiments the H 2 O pressure approximatively equals the confining pressure, the water fugacity (f H2O ) can be calculated using only two parameters: the temperature and the pressure. The water fugacity has been computed

J o u r n a l P r e -p r o o f for all experimental conditions from Tony Withers' fugacity calculator (available at:

https://www.esci.umn.edu/people/researchers/withe012/fugacity.htm) based on the [START_REF] Pitzer | Equations of state valid continuously from zero to extreme pressures for H2O and CO2[END_REF] equation of state for water.

Results

Starting material

For the starting material, a very pure natural quartzite from the ELKEM quarry in Austertana, Northern Norway (N70°28´39.6´´, E28°32´30.1´´) has been used. The rock samples come from the top part (∼40 m) of the Gamasfjell formation. This sequence of late Precambrian age is approximatively 300 m thick and its top part is composed of grey to white quartzite [START_REF] Pevik | Geological and Mineralogical Characterization of the Upper Part of the Gamasfjell Quartzite at the Vaggecearu Mountain[END_REF]. The uppermost part of the formation is described as very pure (> 99% of silica), and used by the aluminium, silicon, and ferrosilicon industry [START_REF] Aasly | Advanced methods to characterize thermal properties of quartz[END_REF]. Chemical analysis (from ICP-EOS) published in [START_REF] Pevik | Geological and Mineralogical Characterization of the Upper Part of the Gamasfjell Quartzite at the Vaggecearu Mountain[END_REF] indicate major oxide values (apart from SiO 2 ) of 3547 ± 1083 ppm Al 2 O 3 , 441 ± 365 ppm Fe 2 O 3 , and 207 ± 37 ppm TiO 2 .

The Tana quartzite underwent high grade diagenesis to very low grade metamorphic conditions and is weakly deformed in a large open antiform [START_REF] Pevik | Geological and Mineralogical Characterization of the Upper Part of the Gamasfjell Quartzite at the Vaggecearu Mountain[END_REF]. However, no internal deformation on the micro-scale, no schistosity, and no lineation have been identified in the sampled rock. The blocks of the starting material collected were not oriented. The quartzite is composed of quartz grains and crystalline authigenic SiO 2 cement (99%, Fig. 1a) and very few accessory minerals (< 1%) such as sheet silicates (sericite, pyrophyllite, kaolinite), iron oxides (hematite), zircons, apatite, xenotime, monazite, rutile, and very rare feldspars. Due to filling of the pore space by authigenic SiO 2 cement, no visible porosity was detected in the light microscope or SEM.

Microstructural analysis and CL-imaging show that the quartz grains forming the J o u r n a l P r e -p r o o f

Tana quartzite are composed of (1) cores of equant and rounded detrital quartz sand grains, with various CL-colours and -intensity, and (2) a non-or dark-luminescent cement between the grains (Fig. 1c,d). The cement is in crystallographic continuity with the sand grains on which it grows epitaxially (Fig. 1a). Grains appear undeformed as they do not show any undulatory extinction, except for rare sand grains showing inherited recrystallized microstructures. A few pressure-solution contacts due to burial of the sediment are sometimes observed.

The size distribution of quartz grains composing the quartzite was obtained by image analysis using both polarized light and light microscopy (LM)-CL-images. The mean grain size is 204 µm for quartz grains and 186 µm for original sand grains (Table 1). The quartz grain sizes are larger than those of sand grains because they include the surrounding cement. The calculated mean aspect ratio (AR) is 1.56 for quartz grains and 1.55 for sand grains, indicating that grains are somewhat elongated. However, no preferred orientation of the long axes of the grains can be detected. For this reason, samples have been cored without reference to any specific orientation.

Electron Backscatter Diffraction (EBSD) measurements of grains from starting material Tana quartzite (one point per grain, n=500) confirm a random fabric (Fig. 1b, with J=1.33 and M=0.027), close to a random distribution [START_REF] Bunge | Texture analysis in materials science-mathematical methods[END_REF][START_REF] Skemer | The misorientation index: Development of a new method for calculating the strength of lattice-preferred orientation[END_REF]. The dislocation density of the material was characterized by transmission electron microscopy (TEM) as 6 x10 12 m -2 , which is a typical, low dislocation density of relatively undeformed natural silicates [START_REF] Mclaren | Transmission Electron Microscopy of Minerals and Rocks[END_REF].

The mean water content calculated is 1659 H/10 6 Si for grain interiors and 2120 H/10 6 Si for grain boundaries.

J o u r n a l P r e -p r o o f

3.2 Mechanical data

Stress strain curves

The samples show a systematic decrease in strength with increasing confining pressure (Fig. 2): the maximum final differential stress is nearly 600 MPa for a sample deformed at 600 MPa confining pressure, whereas for the sample deformed at 2000 MPa it is ∼100 MPa. This behaviour is reproducible for the two different apparatus (considering a + 30 MPa accuracy of the solid medium apparatus;

Holyoke and Kronenberg, 2010) used for a confining pressure of 1000 MPa (samples 546LN and OR32; the strain rate is slightly lower in OR32) whereas for lower pressure at 600 MPa, the sample deformed in Orléans (OR60) is slightly stronger than the one in Tromsø (542LN), despite the slightly slower strain rate.

Strain rate stepping experiments

Two strain rate stepping experiments were performed at high (OR68, 2000 MPa) and low (OR79, 800 MPa) pressures to determine the n-value, or the stress exponent, of the flow law. Both experiments were conducted at 900°C with 0.1 wt.% water added and with a strain rate sequence of ∼10 -5 , ∼10 -6 , ∼10 -7 then again ∼10 -5 s -1 . The stress-strain-curves are presented in Fig. 3a and flow stresses for each step are reported in Table 3.

The initial step at ∼10 -5 s -1 has been repeated at the end of the experiments for a test of reproducibility. The flow stresses associated to that rate are systematically higher during the final step and steady state has not really been reached for the lower confining pressure experiment. For the steps at ∼10 -7 s -1 , both samples show an unstable and variable behaviour, probably due to the low sample strength, so that possibly some friction effects at the pistons start to play a role. In addition, at such low strain rates the initial "friction" of the run-in curve is partially recovered, so that the recorded stresses may be too low (see explanation of this effect in Tarantola et

J o u r n a l P r e -p r o o f al., 2012, appendix). In the next generation Sanchez apparatus, very low oil flow is injected by the hydraulic pump (0.0007 mL/min) in order to obtain this strain rate, this variation may partially reflect changes in the ambient conditions (daily variations recorded for the force, influenced by room temperature or cooling temperature variations).

The n-exponent is defined as the slope of the linear regression in the log-log plot of the flow stresses vs. strain rate (Fig. 3b).

Microstructures

Light microscopy

The local strain distribution in all samples is inhomogeneous. Typically, the centre and/or bottom parts of the samples are more strongly deformed (Fig. 4). The partitioning of deformation typically is detected by more elongated grain shapes in the higher strained regions (Fig. 4b). The greater elongation of individual quartz grains usually is accompanied by an increase in the amount of recrystallized material. Original quartz grains in deformed samples show evidence for plastic deformation, such as undulatory extinction, deformation lamellae and, in some places, development of subgrains (observed in the LM; Fig. 4c). Some of the progressive subgrain rotation leads to the formation of core-mantle structures (Fig. 4b,c).

This strain gradient is slightly more pronounced for samples deformed in the J o u r n a l P r e -p r o o f

conventional Griggs apparatus at Tromsø (where more of the deformation is localized at the lower part of the samples) than for those deformed in the new apparatus in Orléans (where more of the deformation is located in the central part of the sample). This type of strain localisation is common in samples deformed in the solid medium apparatus (e.g., [START_REF] Heilbronner | Analysis of bulk fabrics and microstructure variations using tesselations of autocorrelation functions[END_REF][START_REF] Heilbronner | The effect of static annealing on microstructures and crystallographic preferred orientations of quartzites experimentally deformed in axial compression and shear[END_REF][START_REF] Stünitz | Water redistribution in experimentally deformed natural milky quartz single crystals-Implications for H2O-weakening processes[END_REF] and is related to the temperature gradient in the sample. The thermocouple position indicates the highest temperature of the sample (< 90°C temperature difference between sample ends and the hot zone = thermocouple position) and this region typically corresponds to the higher strain regions.

Cathodoluminescence

SEM-CL and LM-CL images show that in all deformed samples the original sand grains can still be identified by the same variation of luminescence and tints as in the starting material (Figs. 1 & 5). The sand grains in the more highly deformed parts of the sample show a more elongated shape with the long axis at a large angle or normal to the shortening direction. In the cemented area between the original sand grains, the darker luminescent cement is clearly observable. However, in the deformed samples, a new material with a bright luminescence appears in CL-images (Figs. 5 & 6). This bright luminescence material invariably has a blue colour, so that a blue filter was used in SEM-CL images to enhance its presence. The blue luminescence is not short-lived but permanent.

Morphology of the bright luminescent material

The bright luminescence material in deformed samples is often concentrated in the boundary regions of grains, so that these bright regions appear predominantly in the cement at the grain boundaries of quartz grains. In some cases the bright luminescing material cuts across original sand grains (Fig. 6a,b). In the low strain parts of the samples, the brightly luminescing zones follow a clear crack morphology J o u r n a l P r e -p r o o f Figs. 5 & 6). The bright luminescent material occurs in the cracks that cut through both, sand grains and cement. This is observed in samples deformed at low confining pressure (e.g., OR42, 800 MPa, Fig. 6a) and at higher confining pressure (546LN, 1000 MPa, Fig. 6b). In samples deformed at low confining pressure, cracks are subparallel to the loading direction and appear to have been dilatant, mode I cracks, before new quartz material has filled the cracks. The inner parts of these cracks can be filled with non-luminescent material (Fig. 6a). From the boundaries of the healed mode I cracks, very thin cracks extend perpendicular to the mode I cracks, i.e., in an orientation typical for unloading cracks (Fig. 6a). The appearance of such cracks has first been observed in samples deformed in the Griggs-type apparatus by [START_REF] Gerald | Microstructures in water-weakened single crystals of quartz[END_REF], and these features have been termed "stepladder cracks". In all deformed samples, many thin cracks with bright luminescence in a direction perpendicular to the shortening direction extend from grain boundaries and cracked regions and have formed as unloading cracks during decompression of the samples (e.g., Fig. 6b).

(
In samples deformed at higher confining pressure, cracks tend to be thinner, more irregular, and are distributed more pervasively across the samples (Fig. 5e,f). They often (but not necessarily) follow the grain boundaries (intergranular cracks). For all the cracks in the samples, no or very little displacement has been observed along the cracks.

The brightly luminescing material sometimes forms overgrowths with crystal faces on pre-existing large grains or filling intergranular spaces (Fig. 6c,d). EBSD maps performed on these areas indicate that these faceted overgrowths are in crystallographic continuity with the parent grain. The faceted crystals can be surrounded by non-luminescent material in pore spaces (Fig. 6c,d).

J o u r n a l P r e -p r o o f

Larger regions of bright luminescent material consist of aggregates of many small new grains (Fig. 6d). Many of the small grains are brightly luminescent throughout but others have a darker luminescent core with a bright rim of variable thickness (Fig. 6d). Comparison between bright luminescent zones and the corresponding regions under crossed polarizers indicate that all of these regions consist of small grains, luminescing in blue, but not all luminescent regions consist of small grains. The amount of brightly luminescent material increases substantially with increasing strain (see also below). In a sample deformed to 74% strain (OR56) the original grains are strongly elongated and are embedded in a matrix of 30% luminescent material (Figs.

5f & 12).

Evolution of luminescent regions as a function of pressure and sample strain

For four samples (546LN, OR42, OR57 and OR56), SEM-CL longitudinal transects have been recorded from the top to the bottom (example for OR57 sample on Fig. 7). All transects were segmented manually in order to separate the original sand grains and cement from the bright luminescent material. The segmented images were then processed with the ImageJ software in order to quantify the amount of bright luminescence regions in samples.

Domains with higher finite strain show a higher proportion of brightly luminescent areas. This relationship can be observed at the scale of a given sample, between the top -relatively undeformed part -and the bottom part -where deformation is much more intense (OR62, Figs. 5e & 8a). The relationship can also be observed in samples deformed to different amounts of total strain (e.g, OR56; Fig. 5f). There is a relationship between the amount of brightly luminescent material and confining pressure demonstrated for the three samples strained up to 30% (OR42, 546LN and OR57). The amount of brightly luminescent material increases in the middle to J o u r n a l P r e -p r o o f bottom part of the samples (more deformed regions; Fig. 8a): 9.88% for sample OR42 (800 MPa), 10.72% for sample 546LN (1000 MPa), 15.08% for sample OR57 (2000 MPa; Fig. 7). Thus, there is a trend of increasing amount of brightly luminescent material with increasing confining pressure and with strain (Fig. 8b).

Strain analysis from fabric and grain shapes

The starting material and samples deformed at 700, 1000, 1500 and 2000 MPa confining pressure have been studied for their grain shapes and fabric by image analysis. The goal of the analysis was to compare the bulk sample strain determined from the mechanical record and from measuring sample lengths with an analysis based on strain of individual quartz grains. Such an analysis is difficult in normal quartz grain aggregates because the regions of dynamic recrystallization make it difficult to identify original grain shapes as passive markers. The outlines of original sand grains in the Tana quartzite represent true strain markers for the deformed samples, because dynamic recrystallization typically affects the grain boundary region first (e.g. formation of "core and mantle" structures), i.e. the cement regions.

However, the sand grain outlines are located inside the original quartz grains and are only rarely affected by the bright luminescence regions. Furthermore, they present passive markers because the cement overgrowth is in crystallographic continuity with the original sand grains. In addition, the orientation of long axes of the sand grains and their fabric are more or less random in the starting material (Table 1).

An example of the segmentation of the OR62 sample (2000 MPa) is shown in Fig. 9. Sand grains are manually separated from surrounding cement in LM-CL-images.

In this way, only the original sand grains and their internal plastic deformation are considered for this strain analysis.

Sand grain size and parameters calculated from the analysis of mosaic LM J o u r n a l P r e -p r o o f cathodoluminescence images are presented in Table 4. The number of analysed grains varies with the grain sizes (sample size for 546LN is smaller). The equivalent diameter of sand grains varies with the layers in the starting material and is not a function of deformation. The aspect ratio of individual grains increases for deformed samples (from 1.55 to 2.05) in comparison to the starting material. No correlation emerges between confining pressures and equivalent diameters or aspect ratios neither with sample bulk strain (calculated or measured).

The SURFOR program facilitates the calculation of the sample strain/fabric anisotropy from the particle outlines of the starting material and deformed samples.

The results are presented in Table 5 and shown in Fig. 10. The difference between the minimum and maximum of the projection curves corresponds to the global strain value (from 0 to 1). The angular difference between the maximal and minimal position of the projection curve should be 90° (corresponds to the angle between shortening and extension direction), and the value of the minimum corresponds to the shortening direction.

For the starting material (TQ) the minimum of the curve is 0.965 for α=70°, indicating a very slight flattening of the grains. However, as the studied thin section was not oriented in a particular way and the cores for experimental samples were not made in the same orientation, this value indicates the general fabric anisotropy of the starting material but does not correspond to the orientation of this material in the apparatus. Yet, we should consider the ± 3.5 % anisotropy as a mean error for strained samples.

For deformed samples, the bulk shortening for the grain fabric calculated by the SURFOR analysis is between 22.9 and 37.2%. For the samples OR52, OR64 and OR62 the values are very close to the ones calculated from mechanical data and J o u r n a l P r e -p r o o f measured on thin sections and are within the error range (± 3.5%). However, for 546LN, the shortening value is underestimated and overestimated for OR32

(difference up to > 8%).

EBSD maps and misorientation calculations

Two regions were selected for detailed EBSD analysis: (1) a low strain region with limited recrystallization and formation of discrete luminescence in response to cracking (546LN), and (2) a high strain region affected by more extensive recrystallization/luminescent material (OR56).

In region ( 1) the cracks are visible in the SEM-CL image, cutting through original quartz sand grains as well as cement (Fig. 11a). The corresponding EBSD map of this region shows small new grains (clasts) that make high angle boundaries with the larger quartz grains in the traces of the cracks. In addition, some low angle boundaries also separate the small clasts from the host quartz grains (Fig. 11b). The size of the clasts (new grains) can be as small as 1-2 μm and as large as ∼10 μm (Fig. 13). Low angle new grains (in Fig. 13 marked as "subgrains") and the high angle new grains (in Fig. 13 marked as "recrystallized grains") do not show different size distributions, only high angle new grains are more frequent (Fig. 13). On the scale of the EBSD maps, the smaller and larger clasts all have more or less rounded shape (Fig. 6c,d). This is the case in light microscope images, too (Fig. 4). The clasts typically have a bright blue luminescence colour. The clasts with low angle boundaries (< 10°) only show a weakly preferred misorientation axis in [0001],

whereas the larger angle boundaries are misoriented with axes in [0001] and [-12-10].

In the high strain region (2), the original quartz grains appear bright in the SEM-CL image, and the recrystallized matrix is medium grey (blue luminescence; Fig. 12).

Some relict parts of original quartz grains are present as porphyroclasts with bright J o u r n a l P r e -p r o o f luminescence surrounded by a matrix of recrystallized grains (separated mostly with high angle boundaries). The corresponding EBSD map shows a large number of recrystallized grains of 1-2 μm size with high angle boundaries in the matrix (Fig. 13).

The two large relict quartz grains (labelled 1744 and 3542 in Fig. 12) show a number of subgrains with low angle boundaries (< 10° misorientation from the large quartz porphyroclast) forming regions of subgrains between the porphyroclast and the recrystallized matrix. The subgrains do not show different luminescence from their host grains. The two large grains show different distributions of misorientation axes for their subgrains: [0001] (in 1744) and no preferred axis (in 3542). The high angle grain boundary misorientations (Fig. 12c,d) have rotation axes of [1-100] (in 3542) and axes between and [-12-10] (in 1744). The subgrain sizes are in the same range as the sizes of small recrystallized grains (Fig. 13).

The sizes of relict grains do not differ between the two microstructures (Fig. 13 and Table 6). Relict grains are those grains that are located in a matrix of recrystallized grains. The original large porphyroclasts of the starting material typically are too large to be included completely in the EBSD maps. They are cut off at the margins of the map and therefore are not counted. The proportion of subgrains and recrystallized grains is much higher in the high strain sample OR56 than in the lower strain sample 546LN (Fig. 13).

Discussion

Deformation processes

We observe two deformation processes that operate in all deformed samples:

Cracking and crystal plastic deformation. Crystal plastic deformation is visually dominant in the microstructures, and the fact that the bulk sample strain can be calculated from the particle strain of original sand grains within a few percent error (Fig. 10, Tables 2 &5) documents that most of the bulk shortening of the samples is 4 & 12) observed in the quartz grains are consistent with this observation. Thus, the dominant process of deformation in all samples is crystal plastic deformation, i.e.

dislocation creep, as it has been documented previously for quartz under these P-, T-, strain rate conditions (e.g., [START_REF] J O U R N A L P R E -P R O O F Griggs | Hydrolytic Weakening of Quartz and Other Silicates*[END_REF][START_REF] Jaoul | The effect of varying water contents on the creep behavior of Heavitree quartzite[END_REF][START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF][START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF].

Despite the dominance of plasticity, cracking takes place in all samples (Figs. 5 & 6). Even though the crack morphology changes with confining pressure, there is one feature that is common to all observed cracking: the cracks accommodate very little displacement, so that the cracks do not contribute significantly to the finite strain.

Furthermore, the highest stresses attained in these experiments are all (except sample OR60) below the Goetze criterion (Δσ < Pconf). This criterion defines the upper differential stress limit of plastic or viscous deformation (brittle-plastic transition; [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]. In the presence of a pore fluid, this criterion has to be considered with some care [START_REF] Hirth | The role of fluid pressure on frictional behavior at the base of the seismogenic zone[END_REF][START_REF] Hirth | The role of fluid pressure on frictional behavior at the base of the seismogenic zone[END_REF]. The effect of pore pressure at high pressure and temperature conditions and small amounts of pore fluid is poorly investigated, but recent results by [START_REF] Okazaki | Rheology of the Fluid Oversaturated Fault Zones at the Brittle-Plastic Transition[END_REF] indicate that at the porosity of our experiments (0.12 vol%, using the density of H 2 O from data by [START_REF] Larrieu | Measurements of the pressure-volume-temperature properties of fluids to 20 kbar and 1000°C: A new approach demonstrated on H2O[END_REF]), the potentially expected reduction of differential stress by pore pressure effects should be in the range of experimental error (± 30 MPa; [START_REF] Holyoke | Accurate differential stress measurement using the molten salt cell and solid salt assemblies in the Griggs apparatus with applications to strength, piezometers and rheology[END_REF]. Thus, the effective pressure coefficient α in σ eff = σ n -αP (see [START_REF] Hirth | The role of fluid pressure on frictional behavior at the base of the seismogenic zone[END_REF] should be close to zero, so that dominant viscous deformation can be concluded from the mechanical data for all of the samples, consistent with the dominant deformation mechanism in the microstructures.

J o u r n a l P r e -p r o o f

The observed mode I cracks (Fig. 6a) have geometries typical of those formed at low confining pressures (P conf ), (e.g. Paterson and Wong, 2005) and their occurrence in samples deformed at the lowest P conf is not surprising. We expect that such cracks in the higher pressure samples have formed during early stages of the experiments, by processes described previously in quartz experiments in the solid medium apparatus [START_REF] Gerald | Microstructures in water-weakened single crystals of quartz[END_REF][START_REF] Chernak | Effect of aqueous and carbonic fluids on the dislocation creep strength of quartz[END_REF]Tarantola et al., 2010;[START_REF] Stünitz | Water redistribution in experimentally deformed natural milky quartz single crystals-Implications for H2O-weakening processes[END_REF]. These stepladder cracks (Fig. 6a,b) form as the result of a sequence of initial cracking and subsequent crack healing, during which dislocations are produced, followed by the glide of some of these dislocations. As a consequence, there is a zone of plastically shortened material that forms immediately adjacent to the crack. During unloading of the sample at the end of the experiment this zone expands and develops unloading cracks [START_REF] Gerald | Microstructures in water-weakened single crystals of quartz[END_REF][START_REF] Stünitz | Dislocation generation, slip systems, and dynamic recrystallization in experimentally deformed plagioclase single crystals[END_REF][START_REF] Stünitz | Water redistribution in experimentally deformed natural milky quartz single crystals-Implications for H2O-weakening processes[END_REF]. In this way the stepladder cracks document the initiation of crystal plastic deformation in which local brittle processes and healing of cracks play an important role. The CL observations document that cracking is a ubiquitous feature during the dominant plastic deformation of quartz at high temperatures of 900°C. At higher confining pressures cracks tend to have a different geometry, but the interaction of cracking, crack healing, and plastic deformation is not expected to change. The microstructures also document that cracking without major displacement and thus without major kinematic contribution to strain accommodation may be common at high temperatures when the sample strain is dominantly accommodated by plastic mechanisms and flow stresses are low, especially at high confining pressure (Fig. 2).

Recrystallization processes

Recrystallized material in all samples is marked by blue luminescence. The blue luminescence colour is caused by a re-working (recrystallization) of quartz involving

J o u r n a l P r e -p r o o f

an interaction with the aqueous fluid facilitating an exchange of trace elements or producing defects during crystal growth (e.g. [START_REF] Ramseyer | Cathodoluminescence Colours of α-Quartz[END_REF][START_REF] Götze | Origin, spectral characteristics and practical applications of the cathodoluminescence (CL) of quartz -a review[END_REF]. The blue luminescence is and has been attributed to Ti-incorporation into quartz [START_REF] Spear | The eastern Tonale fault zone: a 'natural laboratory' for crystal plastic deformation of quartz over a temperature range from 250 to 700°C[END_REF][START_REF] Bestmann | Ti distribution in quartz across a heterogeneous shear zone within a granodiorite: The effect of deformation mechanism and strain on Ti resetting[END_REF]. It is unclear how Ti-incorporation could have been achieved in the deformed samples in our experiments, because a major Ti-source is lacking (although minute amounts of Tiphases (rutile) are present in the starting material) and Ti-incorporation during recrystallization has been demonstrated to be slow and not producing homogeneous equilibrium compositions easily [START_REF] Negrini | The effect of deformation on the TitaniQ geothermobarometer: an experimental study[END_REF]. A detailed analysis of the trace element exchange that causes the luminescence was not attempted here because it is beyond the scope of this study. However, as a potential origin of luminescence by deformation-induced defects is very unlikely -these defects in quartz typically show red luminescence colours [START_REF] Hamers | Distinction between amorphous and healed planar deformation features in shocked quartz using composite color scanning electron microscope cathodoluminescence (SEM-CL) imaging[END_REF][START_REF] Hamers | Scanning electron microscope cathodoluminescence imaging of subgrain boundaries, twins and planar deformation features in quartz[END_REF], and this type of luminescence disappears after some electron beam irradiation (Bestmann, pers. Comm.) -it is inferred that luminescence is caused by an interaction of the quartz with an aqueous fluid during the reconstitution of the material. Therefore, it is concluded that the luminescence observed in our samples is the result of exchange of trace elements with a fluid during recrystallization of quartz (facilitated by boundary migration). This makes luminescence a useful tool to trace recrystallized material in the deformed samples.

Some of the recrystallization takes place by progressive subgrain rotation as documented by EBSD maps (Figs. 11 & 12). Subgrains with misorientation angles of < 10° are dominantly rotated around the [c]-axis. Such rotations can be produced by tilt walls made up of edge dislocations in the prism planes with <a> Burgers vectors or by twist boundaries in the basal plane made up of screw dislocations with <a> Burgers vectors (e.g., [START_REF] Trépied | Subgrain boundaries in quartz theoretical analysis and microscopic observations[END_REF][START_REF] Kilian | Analysis of crystallographic preferred orientations of experimentally deformed Black Hills Quartzite[END_REF]. Thus, this J o u r n a l P r e -p r o o f constitutes evidence for prism <a> or basal <a> slip. For misorientations > 10°, rotation axes are parallel to [-1100] or between [-1100] and [-12-10], consistent with basal <a> or combined basal <a> and prism <c> slip. However, it is difficult to infer slip systems accurately for larger misorientation angles, because misorientations may partially be produced by grain boundary sliding processes once high angle boundaries are established. The microstructures of subgrain boundaries within original quartz porphyroclasts and the immediately adjacent grains with high angle boundaries exhibit core-mantle structures (Fig. 12) and indicate progressive subgrain rotation as the dominant recrystallization mechanism for such grains. Subgrains with low angle boundaries and recrystallized grains with high angle boundaries do not differ systematically in size (Fig. 13). The P-, T-, strain rate conditions of deformation of the samples are those of regime 2 creep according to [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF],

where rotation recrystallization is dominant. In these microstructures, the luminescence of the porphyroclasts and their subgrains does not change, so that non-recrystallized parts of porphyroclasts with subgrains still maintain the original luminescence of the porphyroclasts (Fig. 12a). This observation is consistent with the process of fluid exchange discussed by [START_REF] Negrini | The effect of deformation on the TitaniQ geothermobarometer: an experimental study[END_REF]: formation of subgrain boundaries is a climb process, which does not a priori involve any grain boundary mobility and thus no interaction or exchange with a fluid phase. Once high angle boundaries are established, grain boundary mobility may lead to exchange with a fluid, producing different luminescence colours of these recrystallized grains.

A completely different process can form new grains in the deformed samples, too.

Local cracking produces small new grains, especially at grain boundaries and in local cracks cutting through original quartz grains (Figs. 5,6 & 11). Some new grains show high angle misorientation relationships, whereas others show low angle relationships along the same zones of cracks (Fig. 11). The CL images indicate that in some J o u r n a l P r e -p r o o f cases, inner parts of clasts can still show the original luminescence of old grains, whereas rims and small grains nearby show the blue luminescence typical of reconstituted material (Figs. 6d,[START_REF] Richter | The brittle-to-viscous transition in polycrystalline quartz: An experimental study[END_REF]16). From these microstructures, it is inferred that the small clasts in cracks have mobile boundaries that migrate and can produce a reconstitution (recrystallization) of the quartz and exchange trace elements to produce the different luminescence. Local grain boundary migration processes have been inferred in previous studies (Stipp et al., 2002a(Stipp et al., , 2002b)), where the migration process is inferred to be the first step. A second type of process is subsequently required to produce isolated new grains, because the local migration itself cannot isolate small new grains. This second step can be subgrain formation and/or local cracking (Stipp et al., 2002a(Stipp et al., , 2002b)). In this study, we can observe the dominance of cracking in certain locations of the sample, where new grains form (Figs. 4 & 5). The sequence in this study is reversed: the cracking occurs first, followed by boundary migration to exchange with the fluid. It is proposed here that cracking and local boundary migration operate to produce microstructures that are consistent with what is termed "bulging recrystallization" in the literature (e.g., [START_REF] Bailey | The recrystallization process in some polycrystalline metals[END_REF]Stipp et al., 2002aStipp et al., , 2002b;;[START_REF] Stipp | Dynamic recrystallization near the brittle-plastic transition in naturally and experimentally deformed quartz aggregates[END_REF]. Local bulging may occur in these samples, too, so that probably not all of the bulging recrystallization microstructures are induced by cracking.

The brittle origin of new grains in quartz and other silicates during plastic for dilatant sites that act as small local reservoirs of fluids. These microstructures testify to the fast precipitation in dilatant sites and to the fact that there is excess H 2 O in these samples (so that a H2O = 1). Thus, the samples deformed at different confining pressures show two types of recrystallization that takes place during deformation: (1) progressive subgrain rotation, and (2) crack-related local grain boundary migration that appears to be a type of bulging recrystallization. Both operate at the same time in samples, although the geometry of some cracks indicates an early origin of these. here are lower than n = 3 to 5, too, and therefore inconsistent with typical n-values for pure dislocation creep (Fig. 3b).

Dislocation creep and stress exponent

The starting material in the samples of this study is coarse grained, so that diffusion creep in the starting material is unlikely. However, some of the recrystallized material (in particular the cracked material in bulging-type microstructures) is fine grained, and some diffusion creep in the recrystallized material is conceivable. In addition, extensive exchange with aqueous fluid in the recrystallized material is observed in our samples, so that diffusive mass transfer processes are evident.

Thus, it is inferred that the low n-values of n∼2 in our samples may also be explained by a combination of dislocation and diffusion creep processes. A potential explanation of dislocation accommodated grain boundary sliding (disGBS), as it is inferred in olivine (e.g., [START_REF] Hansen | The influence of microstructure on deformation of olivine in the grain-boundary sliding regime[END_REF] is unlikely, because it would require the whole material to consist of fine grain sizes.

As diffusion creep is grain size dependent, its contribution to the deformation process is expected to increase with an increase of fine grained material or decrease with grain growth. In most of our samples, steady state deformation is observed (Fig.

2), as it is typical for the dislocation creep regime 2 as defined by [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF]. This observation suggests that an increase of recrystallized material does not increase the contribution of diffusion creep. The reason for this may be that grain growth (= migration processes) of very small grains produced by cracking takes these grains out of the diffusion creep field (producing an equilibrium recrystallized grain size). Continued microcracking may produce new very small grains, which in turn may grow. These processes appear to be in a steady state to produce steady state deformation. However, it is premature to speculate further on this aspect, and more research is required to investigate the relationship between cracking and J o u r n a l P r e -p r o o f recrystallization processes in more detail.

Effect of H 2 O and pressure

The progressive lowering of the flow stress with increasing confining pressure in our samples is consistent with the initial observations by [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] and [START_REF] Mainprice | Experimental studies of the role of water in the plasticity of quartzites[END_REF]. When the stresses (taken at 15%

shortening, where all samples reach more or less steady state flow stress) are plotted as a function of the confining pressures, a power law relationship between the flow stress and the confining pressure of the form is found (Fig. 14), similar to that of [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF]. However, in this study, a coarse grained quartzite instead of fine grained novaculite was used (as in [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF], confirming that the process of pressure-dependent weakening in quartz is not dependent on grain size of the starting material. [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF] proposed that the pressure dependence of the rheology should be expressed as a fugacity term with exponent m in the quartz flow law. The log-log plot of flow stresses vs. fugacity (Fig. 15) allows a fit of the r = m/n value, which is -0.46 for our samples. The plot in Fig. 15 shows other data from the literature together with our data, but the curve fit is only shown for data of this study.

The r = m/n value is similar to that of [START_REF] Post | Effects of chemical environment on dislocation creep of quartzite[END_REF] (-0.47), [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] (-0.5, as fitted by [START_REF] Post | Effects of chemical environment on dislocation creep of quartzite[END_REF], Chernak et al. (2009) (-0.40), and of Holyoke and Kronenberg (2013) (-0.63, for their quartzite). It should be noted that experiments by [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] and [START_REF] Holyoke | Reversible water weakening of quartz[END_REF] were performed at 800°C, those of [START_REF] Post | Effects of chemical environment on dislocation creep of quartzite[END_REF] and [START_REF] Chernak | Effect of aqueous and carbonic fluids on the dislocation creep strength of quartz[END_REF] at 900°C and 1.5 GPa. A linear regression to all existing data yields almost the same slope as our data (0.458 vs. 0.460), but with a much lower correlation coefficient (0.71 vs. 0.93). This situation confirms the validity and applicability of our new data set.

J o u r n a l P r e -p r o o f

The exponent m for the fugacity depends on the n-value of the stress exponent. In this study, a stress exponent of n∼2 is inferred, which would result in an m-value of 0.92, or m∼1. An m-value of m=1 has been determined by [START_REF] Fukuda | Deformation of Fine-Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep[END_REF] for their n-value of 1.7, quite consistent with our results. If n-values closer to n=4 are chosen, as determined by [START_REF] J O U R N A L P R E -P R O O F Paterson | Quartzite rheology under geological conditions[END_REF] and [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF] and used in [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF] and others, or n=2.7 (or n∼3, Rutter and Brodie, 2004), as proposed by [START_REF] Tokle | Flow laws and fabric transitions in wet quartzite[END_REF], the m-value would be m=1.84 or 1.24.

However, the original m-value of 1 proposed by [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF] is consistent with our results and those of [START_REF] Fukuda | Deformation of Fine-Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep[END_REF] for their m/n and n-values.

Lu and Jiang ( 2018) have proposed to correct the quartz flow law for pressure by using an activation volume term. This correction would have the opposite effect as the fugacity correction, and it is only meaningful to employ such a term once the activation energy is precisely determined. The presently existing data base of Qvalues shows a large scatter (see compilation in, e.g., [START_REF] Richter | The brittle-to-viscous transition in polycrystalline quartz: An experimental study[END_REF], so that it appears to be necessary to determine Q accurately as a first step, before an activation volume term needs to be considered. We therefore do not consider the activation volume here.

What is the cause of sample weakening with increasing pressure?

In previous studies of quartz deformation with the presence of H 2 O the weakening effect has been inferred as due to enhanced recrystallization or recovery [START_REF] Tullis | Pressure dependence of rock strength : implications for hydrolytic weakening[END_REF][START_REF] Tullis | Hydrolytic weakening of quartz aggregates: The effects of water and pressure on recovery[END_REF]. Subgrain boundary formation is enhanced in quartzites deformed with H 2 O and grain boundary migration forms dislocation-free grains during dynamic recrystallization. Both processes are faster at higher confining pressures. Our results are consistent with this interpretation. The amount of recrystallized material increases with increasing confining pressure (Fig. 8), and this is the most obvious difference in the microstructures with increasing confining J o u r n a l P r e -p r o o f pressure, apart from a different crack geometry. The recrystallization in our samples involves grain boundary migration, which, in the presence of an aqueous fluid, can be described as a process of solution and precipitation with a very short transport distance of dissolved species across the boundary region. The solubility of SiO 2 increases non-linearly with increasing pressure (e.g., [START_REF] Manning | The solubility of quartz in H2O in the lower crust and upper mantle[END_REF][START_REF] Manning | Fluids of the deep crust: Deep is different[END_REF], so that enhanced boundary migration rates are likely with increasing pressure because of enhanced solubility of quartz, provided that an efficient precipitation process can be identified. The precipitation may be favoured at local dilatant sites which may form by grain boundary sliding and in which precipitation has been observed or inferred [START_REF] Fusseis | Creep cavitation can establish a dynamic granular fluid pump in ductile shear zones[END_REF][START_REF] Menegon | Creep cavitation bands control porosity and fluid flow in lower crustal shear zones[END_REF][START_REF] Okudaira | High-temperature fracturing and subsequent grain-size-sensitive creep in lower crustal gabbros: Evidence for coseismic loading followed by creep during decaying stress in the lower crust[END_REF][START_REF] Précigout | Evidence of phase nucleation during olivine diffusion creep: A new perspective for mantle strain localisation[END_REF][START_REF] Précigout | Highpressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus[END_REF], 2019). In fine grained material, grain boundary sliding is an important mechanism to accommodate shape changes of grains induced by plastic deformation of grains (glide of dislocations) and to adjust for the plastic strain incompatibilities as a consequence of an insufficient number of slip ), but it is not easy, because J o u r n a l P r e -p r o o f their size is similar and they all show bright luminescence. It is inferred that in this material the weakening effect takes place as a consequence of increased confining pressure. The inference that the pressure-dependent H 2 O-weakening is caused by grain boundary processes is supported by the observation by [START_REF] Holyoke | Reversible water weakening of quartz[END_REF] that the pressure dependence of the flow stress in polycrystalline aggregates is greater than in single crystals. Consequently, these authors have attributed the weakening effect to recrystallization/recovery processes [START_REF] Tullis | Hydrolytic weakening of quartz aggregates: The effects of water and pressure on recovery[END_REF]) at grain boundaries, too.

The plot in Fig. 15 suggests that the pressure effect of H 2 O-weakening could be greater at low pressure than at high pressures. A potentially greater m-value may be caused by a change in n-or r-values in m = r/n. The determination of the stress exponent is not precise enough at this stage to decide whether a constant n-value would require an intrinsic effect of the H 2 O fugacity or whether the potentially changing pressure dependence of flow stress could be caused by a change in the stress exponent n.

Geological application

The lowering of quartz flow stresses with increasing confining pressures that has been documented since the study by [START_REF] Kronenberg | Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening[END_REF] -also documented in this study -suggests that in subduction channels at high pressure the strength of quartz dominated lithologies is expected to be very low. Low stresses for deformation in subduction zones have been inferred by [START_REF] Stöckhert | Low differential stress during high-pressure metamorphism: The microstructural record of a metapelite from the Eclogite Zone, Tauern Window, Eastern Alps[END_REF][START_REF] Stöckhert | Low effective viscosity during high pressure metamorphism due to dissolution precipitation creep: the record of HP-LT metamorphic carbonates and siliciclastic rocks from Crete[END_REF], [START_REF] Stöckhert | Rheology of Crustal Rocks at Ultrahigh Pressure[END_REF], [START_REF] J O U R N A L P R E -P R O O F Stöckhert | Stress and deformation in subduction zones: insight from the record of exhumed metamorphic rocks[END_REF] and [START_REF] Wassmann | Low stress deformation of garnet by incongruent dissolution precipitation creep[END_REF], partly based on different deformation mechanisms. This study confirms that even for dislocation creep, where stresses tend to be higher than for diffusion creep, flow is expected to take place at very low stresses at high confining pressures of 2 GPa and higher.

J o u r n a l P r e -p r o o f

The recrystallization mechanism of bulging recrystallization in quartz is usually observed at low temperature conditions or the onset of crystal plastic deformation (e.g., Stipp et al., 2002aStipp et al., , 2002b)). The interaction of cracking and local grain boundary migration indicates that some new grains in this recrystallization process can be generated by cracking. One consequence of this process is that the host control in new grain nucleation will be more difficult to determine, because small rotation of new grains is likely, (e.g., [START_REF] Van Daalen | Orientation analysis of localized shear deformation in quartz fibres at the brittle-ductile transition[END_REF], but the rotation sense and misorientation relationship is not necessarily clear and is not dependent on slip systems.

Cracks are abundant in high pressure samples deformed by plastic mechanisms at high temperature, in spite of the low deviatoric stress (∼100 MPa) and the high normal stress acting on any potential fracture plane (Pc ∼2 GPa) -there is no or very little displacement on these cracks. The interaction of cracking, crack healing, and plasticity has been shown by [START_REF] Gerald | Microstructures in water-weakened single crystals of quartz[END_REF] and [START_REF] Stünitz | Water redistribution in experimentally deformed natural milky quartz single crystals-Implications for H2O-weakening processes[END_REF].

These observations suggest that in natural rocks, microcracks may play an important role in the initiation of plastic deformation and during dynamic recrystallization, even for the deep levels of the crust where high temperatures enable viscous deformation at low deviatoric stresses.

Conclusions

The deformation of quartzites in the presence of 0.1 wt.% of added H 2 O shows decreasing flow stresses with increasing confining pressure. An r-value of 0.46 can be fitted to the fugacity data, resulting in an m-value of ∼1 for the fugacity coefficient at an n-value of ∼2. In addition, the following observations have been made:

1. The dominant deformation process is crystal plasticity in original quartz grains, so that the strain analysis of quartz grains matches the bulk sample strain with an J o u r n a l P r e -p r o o f error of a few percent. Dynamic recrystallization and recovery processes are observed, too, so that the dominant deformation mechanism is dislocation creep.

Some cracking occurs during plastic deformation, but as the cracks do not display significant offset, their contribution to the bulk strain is negligible. and appears to be an important part of a process that is termed "bulging recrystallization".

3. The stress exponent n is approximately equal to 2, when some diffusive mass transfer is important during dislocation creep. This contribution is likely to be fluiddependent or fluid enhanced.

4. The amount of recrystallized material increases with increasing confining pressure. It is inferred that the increasing confining pressure has an enhancing effect on the grain boundary migration rate and thus recrystallization rate. J o u r n a l P r e -p r o o f Figure 10. SURFOR projections curves showing that the starting material TQ2 has a slight strain of 3.5% whereas deformed samples at various confining pressures have an orientation comprise between 80 and 90° for a strain comprise between 24.6% (546LN) and 34.4% (OR52). The global shortening direction for deformed samples is theoretically 90°. J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f

Figures and Tables

Figure 10. SURFOR projections curves showing that the starting material TQ2 has a slight strain of 3.5% whereas deformed samples at various confining pressures have an orientation comprise between 80 and 90° for a strain comprise between 24.6% (546LN) and 34.4% (OR52). The global shortening direction for deformed samples is theoretically 90°.

J o u r n a l P r e -p r o o f

J

  o u r n a l P r e -p r o o f produced by crystal plastic deformation of individual original quartz grains. The undulatory extinction, deformation lamellae, and progressive subgrain rotation (Figs.

  deformation has been described by[START_REF] Van Daalen | Orientation analysis of localized shear deformation in quartz fibres at the brittle-ductile transition[END_REF] in natural rocks, and by[START_REF] Stünitz | Dislocation generation, slip systems, and dynamic recrystallization in experimentally deformed plagioclase single crystals[END_REF][START_REF] Stünitz | Water redistribution in experimentally deformed natural milky quartz single crystals-Implications for H2O-weakening processes[END_REF] and[START_REF] Vernooij | Development of crystallographic preferred orientations by nucleation and growth of new grains in experimentally deformed quartz single crystals[END_REF] in experiments. The CLmicrostructures of these deformed samples indicate that the original clasts become modified by grain boundary migration processes after their initial formation by cracking. The misorientation of the small clasts with low angle boundaries shows a weak preference of c-axis rotation, whereas higher angle boundaries can be J o u r n a l P r e -p r o o f misoriented by c-, a-, or m-axis rotation (Fig.11).Grains with blue luminescence and faceted crystal shapes in open pore spaces tend to show oriented overgrowth in crystallographic continuity with original porphyroclasts(Figs. 6c & 11b) and have been described by[START_REF] Palazzin | Evolution in H2O contents during deformation of polycrystalline quartz: An experimental study[END_REF]

From

  the conclusion of crystal plasticity, the operation of climb and dislocation glide are dominant deformation mechanisms, an n-value for the stress exponent of n = 3 to 5 would be expected for climb controlled creep (e.g., Paterson, 2012). Our strain rate stepping experiments have yielded n-values of ∼1.4 or ∼2, depending on whether the slowest strain rate steps are considered or not. The variance of these values and the uncertainty of the slowest strain rate steps require more detailed investigation and a better data base to determine the stress exponent more accurately. However, the present determination of n∼2 suggests values of n < 3 and is consistent with observations of Fukuda et al. (2018) and Richter et al. (2018) in quartz aggregates. Both research groups have concluded a contribution of diffusion creep (including dissolution precipitation creep) to the viscous deformation of quartz. Richter et al. (2018) have observed weaker preferred orientation of quartz in fine grained aggregates, and the n∼2 values are explained by a combination of J o u r n a l P r e -p r o o f dislocation and diffusion creep deformation in their samples. The values obtained

  systems in silicates (compared to metals). The low n-values (Fig.3) in strain rate stepping experiments are consistent with grain boundary sliding and diffusion creep components of deformation. Grain boundary sliding and local dilatancy in the form of cavitation is likely to occur in these aggregates and may cause immediate oversaturation of the fluid and precipitation of quartz. Overgrowth of quartz seams on quartz grains is observed in larger dilatant sites (Fig.6c). Replacement of quartz material during grain boundary migration is evident from the change of CL colours in the recrystallized material, indicating boundary migration by dissolution, precipitation, and exchange of elements with a fluid.It has been pointed out above that once high angle boundaries are established, the distinction of grains formed by progressive subgrain rotation and those produced from initial cracking is possible(Pongrac et al., in prep.

2.

  Dynamic recrystallization of the deforming quartz grains takes place by progressive subgrain rotation and by local grain boundary migration. The grain boundary migration affects small clasts produced by cracking as well as former subgrains once high angle boundaries have been established. The recrystallized material acquires a different luminescence colour (blue), which can be used to track the recrystallized material in the microstructures. The processes indicate that nucleation of new grains may take place by cracking (in addition to other processes)

  Figure 1. (a) Cross-polarized microphotograph of starting material Tana quartzite

Figure 2 .

 2 Figure 2. Mechanical data for samples deformed in wet conditions (0.1 wt.% H 2 O

Figure 3 .

 3 Figure 3. (a) Stress strain curves obtained for strain rate stepping experiments at 800

Figure 4 .

 4 Figure 4. Cross polarized light images of sample OR32 deformed at 1000 MPa

Figure 5 .

 5 Figure 5. SEM-cathodoluminescence images of (a) starting material and of samples

Figure 6 .

 6 Figure 6. (a & b) SEM-CL-images of cracks in both cement and grains in sample

Figure 7 .

 7 Figure 7. Left: mosaic of OR57 sample (2000 MPa) in polarized light with associated

Figure 8 .

 8 Figure 8. Percentage of bright luminescence for SEM-CL images longitudinal

Figure 9 .

 9 Figure 9. Example of the manual segmentation made for the OR62 (2000 MPa) thin

Figure 11 .

 11 Figure 11. Cathodoluminescence (CL) image, EBSD orientation map and inverse

Figure 13 .

 13 Figure 13. Log 10 grain size distributions for samples (a) 546LN and (b) OR56. Grain

Figure 14 .

 14 Figure 14. A power-law relationship fitted to the flow stresses (at 15% strain) at

Figure 15 .

 15 Figure 15. Relationship between water fugacity and flow stresses. The slope

Figure 16 .

 16 Figure 16. Sketch of the grain assemblage evolution during deformation.

Figure 1 .

 1 Figure 1. (a) Cross-polarized microphotograph of starting material Tana quartzite showing equant grains without undulatory extinction. (b) Pole figure of random crystallographic orientation of c-axis from 500 grains measured by EBSD. (c & d) Plane polarized light microscope-cathodoluminescence images: equant and rounded sand grains of various tints are surrounded by darker cement that grows in crystallographic continuity (arrows).

Figure 2 .

 2 Figure 2. Mechanical data for samples deformed in wet conditions (0.1 wt.% H2O added) at 900°C for confining pressures between 600 and 2000 MPa. Samples …LN have been deformed in Tromsø (Norway) whereas samples OR… have been deformed in Orléans (France). The samples strengths systematically decrease with increasing confining pressure. J o u r n a l P r e -p r o o f

Figure 4 .

 4 Figure 4. Cross polarized light images of sample OR32 deformed at 1000 MPa confining pressure. Left: overview of sample showing higher strain regions near the centre of the sample. In the most strongly deformed part of the sample, clasts are elongated, and limited recrystallization is observed at grain boundaries (core-mantle structures). Right: details of the recrystallized region showing undulatory extinction, subgrains, and new grains. The shortening direction is vertical. J o u r n a l P r e -p r o o f

Figure 6 .

 6 Figure 6. (a & b) SEM-CL-images of cracks in both cement and grains in sample deformed at (a) 800 (OR42) and (b) 1000 MPa (546LN) confining pressure. (c) Crystal faces at open grain boundary region in 546LN sample (1000 MPa). (d) Crystal faces in small luminescent grains in open space between grains in OR64 sample (1500 MPa). The shortening direction is vertical for all images.

Figure 7 .Figure 9 .

 79 Figure 7. Left: mosaic of OR57 sample (2000 MPa) in polarized light with associated SEM-CL-images longitudinal transect. Right: examples of segmentation and identification of bright luminescent zones (coloured in blue). J o u r n a l P r e -p r o o f

Figure 11 .

 11 Figure 11. Cathodoluminescence (CL) image, EBSD orientation map and inverse pole figures (IPF) for sample 546LN. (a) CL image with blue (380-515 nm) optical filter to highlight recrystallized areas; (b) EBSD map of quartz orientations coloured parallel to the X direction, sample is plotted with hexagonal symmetry (6/mmm) to account for the effect of Dauphiné twins. Grain boundaries are identified by black bounding lines and subgrains are identified by white boundaries. (c) IPF's for subgrain (defined by a misorientation between 2 and 10°) boundaries and (d) grain (defined by a misorientation greater than 10°) boundaries. All IPF's are plotted in hexagonal 6/mmm symmetry with the same scale for multiples of uniform (m.u.d.) for each plot. (e) Colour key for IPF ‖ X map. J o u r n a l P r e -p r o o f

Figure 15 .

 15 Figure 15. Relationship between water fugacity and flow stresses. The slope indicates a m/n coefficient of 0.46 for the values obtained in this study for Tana quartzite. Results from published studies are included for comparison. J o u r n a l P r e -p r o o f

Table 1 .

 1 Grain parameters for starting material Tana quartzite calculated from area than the grain) and AR is the Aspect Ratio (ratio of major and minor axes of the ellipse fitting).

segmentation of both cross-polarized (CP) and cathodoluminescence (CL) light microscopy images. D eq is the equivalent diameter (diameter of a circle of the same J o u r n a l P r e -p r o o f

Table 2 .

 2 Experimental conditions of deformed samples.

Table 3 .

 3 Flow stresses obtained and corresponding strain rates for the two strain rate stepping experiments performed.

Table 4 .

 4 Results from particle analysis. The errors correspond to the standard deviation.

Table 5 .

 5 Results from SURFOR analysis. For the finite sample strain, the first column corresponds to the calculated strain and the second column to the measured strain (refer to Table2. for details).

Table 6. Grain sizes obtained from EBSD analysis on 546LN (1000 MPa) and OR56 (2000 MPa, high-strained) samples (corresponding maps in Figs.11 & 12).

Table 1 .

 1 Grain parameters for starting material Tana quartzite calculated from segmentation of both cross-polarized (CP) and cathodoluminescence (CL) light microscopy images. D eq is the equivalent diameter (diameter of a circle of the same area than the grain) and AR is the Aspect Ratio (ratio of major and minor axes of the ellipse fitting).

		d eq (µm)	AR	d eq (µm)	AR
		CP-image analysis	LM-CL-image analysis
	N	1423		2103
	Mean	203.71	1.56	186.18	1.55
	Median	198.20	1.47	178.60	1.46
	RMS	210.78	-	196.14	-
	SD	54.16	0.38	61.72	0.38
	Max	451.49	3.54	476.29	4.68
	Min	210.78	1.01	57.47	1.01

Table 2 .

 2 Experimental conditions of deformed samples.

	Sample name	Griggs apparatus	Temperature (°C)	Water added (wt.%)	Confining pressure (MPa)	Strain rate (s -1 )	Shortening calculated (%)	Shortening measured * (%)
	542LN				600	1.29E-06	33.46	30.48
	544LN	Tromsø			1500	1.37E-06	33.48	30.71
	546LN				1000	1.28E-06	31.27	28.01
	OR32				1000	9.32E-07	30.96	29.39
	OR42				800	8.12E-07	29.71	30.83
	OR48				1250	8.80E-07	28.42	27.71
	OR52				700	8.26E-07	31.98	32.12
	OR56 OR57		900	0.1	2000 2000	not determined not determined	74.43 27.76
	OR60	Orléans			600	7.33E-07	30.92	30.57
	OR62				2000	9.29E-07	30.53	29.51
	OR64				1500	9.40E-07	29.76	26.59
	OR59				1000	Hot pressed (251.7h)	0.53
	OR66				2000	Hot pressed (216.8h)	-
	OR68				2000	Strain rate stepping
	OR79				800	Strain rate stepping

*

error is estimated to be up to 0.8% for a measuring error of 0.1 mm J o u r n a l P r e -p r o o f

Table 3 .

 3 Flow stresses obtained and corresponding strain rates for the two strain rate stepping experiments performed.

	Sample	OR68	OR79
	Pressure (MPa)	2000	800
	Temperature (°C)	900
	Diff. stress at 10 -5 s -1	200.6	471.7
	Diff. stress at 10 -6 s -1	85.4	164.3
	Diff. stress at 10 -7 s -1	10.0	65.3
	Diff. stress at 10 -5 s -1	265.2	633.4

Table 4 .

 4 Results from particle analysis. The errors correspond to the standard deviation.

	Sample	Confining pressure (MPa)	Number of grains analysed	Equivalent diameter (µm)	Aspect Ratio
	TQ2	Starting material	2103	186 ± 62	1.55 ± 0.38
	OR52	700	2203	174 ± 62	1.95 ± 0.64
	546LN	1000	1116	230 ± 69	1.76 ± 0.54
	OR32	1000	1835	204 ± 69	2.05 ± 0.73
	OR64	1500	2603	172 ± 54	1.81 ± 0.55
	OR62	2000	3072	181 ± 66	1.85 ± 0.57

Table 5 .

 5 Results from SURFOR analysis. For the finite sample strain, the first column corresponds to the calculated strain and the second column to the measured strain (refer to Table2. for details).

	Sample	Confining pressure (MPa)	Minimum of the projection curve	Angle of minimum (°)	Angle(s) of maximum (°)	Fabric anisotropy (%)	Finite sample strains (%) Calc. Meas.
	TQ2	Starting material	0.965	70	160 -165	3.5	-
	OR52	700	0.656	90	0 -175	34.4	31.98 32.12
	546LN	1000	0.754	85	170 -175	24.60	31.27 28.01
	OR32	1000	0.628	90	0 -180	37.2	30.96 29.39
	OR64	1500	0.722	80	170	27.8	29.76 26.59
	OR62	2000	0.718	85	170 -175	28.2	30.53 29.51

Table 6 .

 6 Grain sizes obtained from EBSD analysis on 546LN (1000 MPa) and OR56 (2000 MPa, high-strained) samples (corresponding maps inFigs.11 & 12).

			546LN			OR56
		Relict grains	Recryst. grains	Subgrains	Relict grains	Recryst. grains	Subgrains
	Arith. Mean	7.967	3.789	3.854	9.030	3.323	2.683
	Geom. Mean	7.595	3.291	2.884	8.314	2.825	2.121
	RMS	8.613	4.282	4.879	9.853	3.824	3.871
	Median	7.930	3.450	3.230	8.091	2.968	2.252
	Mode	7 -8	3.5 -4 4.5 -5	4 -4.5	7 -9	3.2 -3.6	1.5 -1.7
	Std. Dev.	2.603	2.003	2.993	3.955	1.894	2.790

Acknowledgements

We thank Rune Stien (ELKEM) and Raoul Heilbronner for their help with the sampling of the quartzite at Austertana. We thank Ida Di Carlo for her support with SEM-cathodoluminescence, Aneta Slodczyk for her precious help with FTIR measurements, and Audrey Sauldubois for TEM support. We thank Greg Hirth and Andreas Kronenberg for their very insightful and constructive reviews. P. Pongrac J o u r n a l P r e -p r o o f

Author statement

All authors have read the manuscript and agree with its content.

J o u r n a l P r e -p r o o f acknowledges support from the grant agency of Charles University (GAUK 488119) and the Centre of Geosphere Dynamics (UNCE/SCI/006). Support from the VOLTAIRE (ANR-10-LABX-100-01) and PLANEX (ANR-11-EQPX-36) projects funded by ANR through the PIA (Programme d'Investissement d'Avenir) is gratefully acknowledged.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: