Bettina Richter

Holger Stünitz

Renée Heilbronner
email: renee.heilbronner@unibas.ch

The brittle-to-viscous transition in polycrystalline quartz: An experimental study

Keywords: brittle-to-viscous transition, grain size distribution, dislocation creep, quartz rheology, stress exponent

<250 words)

Shear experiments on quartz gouge were performed at elevated confining pressures (predominantly 1.5 GPa) and temperatures (500 °C -1000 °C) at shear strain rates of 3.5•10 -6 s -1 to 2•10 -3 s -1 to study the brittle-to-viscous transition. An unsystematic temperature dependence of strength at low temperatures changes towards a clear temperature weakening dependence above 650 °C. The transition from a pressure strengthening to a pressure weakening relationship takes place continuously between 650 °C and 800 °C. Strain rate stepping experiments reveal power-law breakdown at low temperatures (~650 °C). Between 800 °C and 1000 °C, a stress exponent of n = 1.9 ± 0.6 and an activation energy of Q = 170 ± 72 kJ/mol indicate a combination of diffusion and dislocation creep. The Goetze criterion is confirmed as the upper stress limit for viscous deformation mechanisms. Localised deformation

Introduction

The transition from fully brittle to fully viscous deformation in rocks (semibrittle field) occurs over a broad range of conditions in pressure, temperature, strain rate, and H 2 O-content with several changes in deformation mechanisms (e.g., [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF][START_REF] Scholz | The Mechanics of Earthquakes and Faulting[END_REF][START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF]. Viscous denotes temperature-and strain-rate dependent deformation here. In the lithosphere, the transition commonly takes place within the middle crust (continents) (e.g., [START_REF] Brace | Limits on lithospheric stress imposed by laboratory experiments[END_REF][START_REF] Handy | Deformation regimes and the rheological evolution of fault zones in the lithosphere: the effects of pressure, temperature, grainsize and time[END_REF][START_REF] Sibson | Earthquake faulting as a structural process[END_REF] but it may extend into the upper mantle for some rocks, e.g., below the oceanic crust (e.g., [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]. The transition region coincides with the greatest strength of rocks, and many large earthquakes nucleate in this region (e.g., [START_REF] Sibson | Earthquake faulting as a structural process[END_REF][START_REF] Scholz | The Mechanics of Earthquakes and Faulting[END_REF].

Under conditions of brittle deformation (e.g., low temperatures, high strain rates, typically shallow crustal levels), the strength of rocks primarily depends on normal stress and pore pressure [START_REF] Byerlee | Friction of Rocks[END_REF]. Fracture strength and/or friction control the rock deformation, leading to cataclastic processes (e.g., fracturing, frictional sliding) with characteristic microstructures at greater strain. The intersection M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3 of Byerlee's law [START_REF] Byerlee | Friction of Rocks[END_REF] with the Mohr-Coulomb fracture criterion marks the onset of semi-brittle deformation in most lithologies (e.g., [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]. This intersection is termed "brittle-ductile transition" and is temperature independent.

Viscous deformation at higher temperature, typically at deeper crustal levels, depends on strain rates and temperatures, and is caused by diffusion and/or dislocation creep involving recovery processes like dynamic recrystallisation (e.g., [START_REF] Poirier | Deformation induced recrystallization of minerals[END_REF]Tullis and Yund, 1977;Yund and Tullis, 1991;[START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[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]. The transition from semibrittle to viscous deformation is marked by the brittle-to-viscous-transition [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF] (BVT). The Goetze criterion has been introduced as an ad hoc approximation by [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF] to delineate this transition. It is formulated as ∆σ = Pc, i.e. the differential stress to drive viscous flow is equal to the confining pressure.

In the transitional semi-brittle zone, stresses required to create new fractures are lower than those for sliding on pre-existing faults (e.g., [START_REF] Byerlee | Brittle-ductile transition in rocks[END_REF][START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF] causing pervasive fracturing and grain-size reduction (cataclasis).

Dislocations may be generated by cracking and healing processes (e.g., [START_REF] Fitzgerald | Microstructures in water-weakened single crystals of quartz[END_REF]Tarantola et al., 2012;Trepmann and Stöckhert, 2013;Stünitz et al., 2017), but whether these dislocations become important for crystal plasticity (dislocation creep) depends on temperature and the efficiency of the recovery processes. At low temperatures, tangling dislocations and high dislocation densities produce strain hardening and greater stresses (e.g., [START_REF] Barber | Dislocations in minerals[END_REF]. Dominant crystal plasticity is achieved at higher temperatures, where dislocation climb and recrystallisation are rate controlling. For quartz, three types of dislocation creep regimes have been identified dependent on the dominance of subgrain-rotation recrystallization or grainboundary migration [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF].

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Grain size reduction by cracking may play an important role for the onset of viscous deformation by increasing the surface area and decreasing the transport distances, leading to accelerated mass-transfer processes (e.g., [START_REF] Pec | Semi-brittle deformation of granitoid gouges in shear experiments at elevated pressures and temperatures[END_REF]Trepmann and Stöckhert, 2003;[START_REF] Menegon | Evolution of quartz microstructure and c-axis crystallographic preferred orientation within ductilely deformed granitoids (Arolla unit, Western Alps)[END_REF]Van Daalen et al., 1999). As a result, deformation by diffusion creep may become the dominant mechanism should such cracking occur (e.g., Paterson, 2013, p. 91-105, and references therein).

It emerges from this brief discussion that in the transition region of brittle-toviscous deformation, several processes are competing: cracking and frictional sliding, crystal-plastic deformation, and diffusive mass transfer combined with friction-less grain-boundary sliding. This study will try to address their relative importance for deformation in quartz over a range of temperatures and confining pressures.

Quartz as one of the most abundant silicates in the Earth´s crust is often used to model and predict the mechanical behaviour of the upper lithosphere (e.g., [START_REF] Brace | Limits on lithospheric stress imposed by laboratory experiments[END_REF]. In addition, deformation mechanisms in quartz can be studied independently of chemical effects because of its simple chemistry and very limited compositional variation. Laboratory conditions (e.g., high strain rates: 10 -3 -10 -7 s -1 , high temperatures) have been extrapolated to natural conditions (e.g., low strain rates: 10 -10 -10 -14 s -1 , low temperatures) via flow laws that are applicable for viscous deformation (e.g., [START_REF] Jaoul | The effect of varying water contents on the creep behaviour 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] Paterson | Quartzite rheology under geological conditions[END_REF][START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF][START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF][START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF]Rutter and Brody, 2004a,b). However, few data exist to define the lower temperature limit of the applicability of these flow laws. Futhermore, discrepancies exist for the parameters of flow laws, so that the uncertainty for the users as to which data to use is large, calling for a better characterisation of rheological properties of quartz.

We present a series of deformation experiments on quartz in a modified Griggs

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5 apparatus to study the rheological transition from brittle-to-viscous deformation mechanisms at elevated pressures and temperatures. The goal is to determine the part of the pressure-temperature-strain rate-range of the transition accessible in the laboratory and to extrapolate it to natural conditions. Some rheological parameters determined for quartz fault-rock material in this study can be used in flow laws for quartz. The extrapolation of the conditions of the brittle-to-viscous transition to natural fault zones will be discussed, together with some applications of the newly determined parameters for the flow law.

Methods

Experimental method

The experiments were carried out on a crushed quartz crystal from a hydrothermally grown single crystal from an Alpine cleft (Aar Massif, Switzerland). Pieces of the crystal were repeatedly crushed and sieved to obtain a grain-size fraction below 100 µm, used for what will be considered the standard experiments (referred to as 'crushed'). One sample had a grain size range of 7-11 µm (referred to as 'sieved').

The single crystal contained several fluid inclusions (5-200 µm) (Tarantola et al., 2010). The quartz material itself was dry with a water content close to the detection limit of FTIR measurements (Stünitz et al., 2017). Most inclusions, especially the larger ones, cracked during the crushing procedure. The crushed material is used to represent a fault gouge. However, during the time at experimental pressure and high temperature, before deformation commenced, the crushed material was effectively hot pressed to a dense coherent crystalline material better termed "cataclasite".

Insert Figure 1 here

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The crushed material (0.1 g) with 0.2 wt% water added was introduced between alumina (Al 2 O 3 ) forcing blocks (diameter 6.35 mm), cut at 45° (to achieve maximum shear stress), resulting in a layer of ~1 mm thickness (Fig. 1). The assembly was weld-sealed in a platinum jacket with a nickel foil insert. Sodium chloride was used as confining medium in a Griggs-type solid-medium deformation apparatus (Fig. 1). The temperature was controlled by S-type (Pt/Pt-Rh) thermocouples at T > 800 °C and by K-type (Cr-Al) thermocouples at T ≤ 800 °C. More details on the sample assembly can be found in [START_REF] Pec | Experimental investigation on the rheology of fault rocks[END_REF]. Samples were pressurised to confining pressure while the temperature was increased in 100 °C steps (at a rate of 20 °C per minute) to experimental conditions. The deformation experiments were started by applying a directional compressive force on the sample, i.e., by moving the σ 1 piston [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 42 Richter | Stresses and pressures at the quartz-to-coesite transformation in shear deformation experiments[END_REF]. The σ 1 piston had to push through a lead piece (so-called run-in) before it touched the alumina forcing block on top of the sample. At this point sample deformation started. When the motor was stopped, the temperature was decreased to 200 °C within 2-3 minutes with cooling rates between 150 °C and 300 °C per minute to quench the microstructure. Five experiments included a hydrostatic hot-pressing stage (at 1000 °C; 1.5-1.6 GPa confining pressure), where the sample was left for 20 hours before decreasing the temperature (2.5 °C per minute) to deformation conditions. These samples will be referred to as 'hot pressed'.

Two types of experiments were conducted. Experiments of type 1 were conducted at constant displacement rates. The constant displacement rate of the σ 1 piston resulted in an approximately constant shear strain rate. Type 2 experiments are strain-rate stepping experiments, where the displacement rate was decreased by about one half or one order of magnitude after reaching peak strength. When steady state was achieved for this reduced rate the displacement rate was decreased again. During

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7 the last step, the displacement rate was set again to the initial value.

Mechanical data: acquisition and processing

During the experiment, the applied force on the σ 1 piston, the displacement of the σ 1 piston, and the oil pressure of the confining pressure cylinder were recorded with a frequency of 1 Hz. These signals were converted to maximum principal stress (σ 1 in MPa), minimum principal stress (σ 3 in MPa), and axial displacement (d a in mm). Data processing and determination of differential stress (∆σ), shear stress (τ) and shear strain (γ) were performed according to [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 42 Richter | Stresses and pressures at the quartz-to-coesite transformation in shear deformation experiments[END_REF], including a correction for confining pressure build-up and piston overlap. The shear strain (γ) is calculated as the sum of incremental shear strains between recorded data points. For each data point, a reduced width of the shear zone is used by assuming a constant linear thinning of the sample for a known initial average width from hot pressing experiments and final deformed width measured in thin sections.

For the determination of the stress exponents and the activation energies, data from the strain rate-stepping experiments and some of the constant shear strain-rate experiments performed at the same deformation temperatures were used. The mean steady-state differential stress and the mean shear strain-rate of each strain-rate step and the differential stress at γ ~ 3 and the average shear strain rate of the constant shear strain rate experiments were used. The stress corrections of Holyoke and Kronenberg (2010) were not applied because they were not found to be appropriate for the shear experiments in our apparatus (Richter et al., 2017).

The friction coefficient of the samples was calculated for the 45° angle of the forcing block pre-cut using a simple Mohr Coulomb construction: µ = τ/ σ n (Fig. 1b).

During deformation, the normal stress on the sample (σ n ) increases (σ n is calculated as

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2D mean stress). Steady-state shear stress at γ = 3 was used to calculate the friction coefficient for high strain experiments. For samples only loaded to peak-strength, the maximum friction coefficient was calculated. In the strain rate-stepping experiments, the stress value before decreasing the displacement rate was used for the first step, and for the later strain rate steps the mean values at steady-state conditions were used.

Microstructure and texture analysis

For the preparation of polished thin sections, the sample jackets were cut parallel to the shear displacement direction and the samples were impregnated under vacuum with epoxy before cutting. For all subsequent microstructural analyses, the samples are viewed with a sinistral shear sense (shear zone boundary is horizontal).

All samples were analysed with light microscopy and scanning electron microscopy (SEM; for imaging: a field emission Philips XL 30 ESEM, for electron backscatter diffraction: a field emission Zeiss Merlin SEM with a Nordlys nano camera).

Electron backscatter diffraction (EBSD) was used to obtain quartz crystal orientations. Polishing and lapping for EBSD analysis was carried out with colloidal silica suspension Struers OP-U non dry for 3-6 minutes. Samples were coated with a thin carbon layer to prevent charging under high vacuum conditions. Acceleration voltages between 10 kV and 15 kV were used with step sizes of 0.1 to 0.2 µm. EBSD data were measured with AZtec software and analysed with the MTEX toolbox [START_REF] Hielscher | A novel pole figure inversion method: specification of the MTEX algorithm[END_REF]. Initial noise reduction was performed with CHANNEL 5 software by removing isolated points and replacing non-indexed points with the orientation of their neighbours (iteratively filled starting with eight similar neighbours down to six or five similar neigbours). were not considered grain boundaries. Grains had to contain at least five pixels to be considered as grains. The 2D grain diameters (d equ = diameter of area equivalent circle) were used as input for the StripStar programme [START_REF] Heilbronner | Image analysis in earth sciences[END_REF] to obtain the 3D diameters (D equ = diameter of the volume equivalent spheres).

Grain maps obtained with MTEX show individual grains separated by a

The volume weighted distributions of D equ were fitted with a Gaussian Normal, the modal value and the dispersion being given by the mean and the standard deviation.

For details on segmentation and grain size determination, see Heilbronner and Kilian (2017).

The kernel average misorientation of a grain (gKAM) is calculated from noise reduced EBSD data with a kernel of an order of 4 (see [START_REF] Kilian | Texture analysis of experimentally deformed Black Hills Quartzite[END_REF].

The 'mis2mean' value of each point of a grain is determined with MTEX. Averaging the 'mis2mean' value of a single grain yields the grain orientation spread (GOS). The GOS is normalised for the long axis (GOS la ) to account for the grain-size dependence, which is especially pronounced for highly elongated grains. Both, GOS la and gKAM, indicate the misorientation density of a grain and are therefore considered a measure for intragranular deformation (for derivations of GOS, see [START_REF] Cross | The recrystalliued grain size piezometer for quartz: An EBSD-based calibration[END_REF].

Using smoothed grain boundaries, the PARIS factor, a measure for grain boundary lobateness [START_REF] Panozzo | A simple method for the discrimination of convex and convex-concave lines[END_REF]) is used. It is defined by the difference between the length of the convex hull of a grain and that of the real perimeter.

Mechanical results

27 constant shear strain-rate experiments between 500 °C and 1000 °C (Table 1) and five strain rate-stepping experiments at shear strain rates between ~2.5 x 10 -6 s - M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 10 1 and ~2.5 x 10 -3 s -1 for ~650 °C, 800 °C, 900 °C and 1000 °C (Table 2) were conducted.

Insert Table 1 and2 here 3.1 Temperature dependence Above temperatures of ~650 °C, samples clearly weaken systematically with increasing temperature, whereas at 650 °C and below, the strength-temperaturerelationship is weak or unsystematic (Fig. 2a). Samples deformed at temperatures below 700 °C show steady-state behaviour or slight strain hardening. At 700 °C or higher, the samples deform below the Goetze criterion (∆σ = P c ) and show steadystate or minor strain weakening at high strain. The difference in strength between 650 °C and 700 °C is very large (~1300 MPa). At low temperatures, no significant stress drop or strain weakening occur after yield strength, except for 450br and 481br (see Table 1). These samples show a stress drop as a result of slip along the forcing block.

In addition, the alumina forcing blocks started to deform because of the high stresses (e.g., 415br).

The slopes of the loading curves up to temperatures of 650 °C are almost identical up to a differential stress of ~1 GPa. At temperatures above 650 °C the slope decreases with decreasing strength and shear strain rate (Figs. 2, 3 and4).

Insert Figure 2 here

Pressure dependence

At 650 ºC, the sample strength increases with increasing confining pressure, whereas at higher temperatures (700 °C and 800 ºC; Fig. 3) strength decreases with increasing confining pressure. At 800 ºC, a pressure dependence is not obvious

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11 between 1.0 and 1.5 GPa, but between 0.5 and 1.0 GPa, the weakening with increasing confining pressure is very clear (Fig. 3).

Insert Figure 3 here

Influence of initial grain size

When hot pressed at 1000 °C for 20 hours prior to deformation, samples systematically reach higher strengths compared to samples without hot pressing (Fig. 2c). The difference in flow stress is at least 500 MPa at 600 °C at γ ~ 3 (the forcing blocks start to deform in the hot-pressed sample at such high stresses). At 700 °C, the hot-pressed sample is about 900 MPa stronger and shows strain hardening, whereas the non-hot pressed sample weakens. At 800 °C, the difference is ~200 MPa and both samples show strain weakening.

One sample with a small initial grain-size fraction (7-11 µm) is deformed at 1.5 GPa, 800 °C and 2.5•10 -5 s -1 (Fig. 2c,445br). It is weaker than the experiments with a larger initial grain-size fraction (< 100 µm) performed at the same strain rate and temperature conditions. At γ ~ 3, the differential stress of 445br is less than half as high as of 388br (difference ~500 MPa). Steady-state conditions exist between a shear strain of ~0.5 to 2.5, after that the sample hardens by ~100 MPa until the end of the experiment.

Strain rate dependence

Strain rate has a pronounced effect on sample strength at temperatures above 600 °C. At 650 °C and 800 °C, increasing the strain rate by one order of magnitude shifts the flow stress from below to above the Goetze criterion (Fig. 2b). At 900 °C the same shift is achieved by increasing the strain rate by two orders of magnitude.

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12 Strain rate-stepping experiments in combination with constant displacement experiments at different rates show distinct strain rate dependence for all higher temperature experiments, except at 650 °C, where the rate dependence is only observed at very low strain rates (~10 -6 s -1 ; Fig. 4). The fastest strain rate causes the highest stresses, and lower stresses with increasing temperature and lower strain rate occur at all strain rates (Fig. 4). The strain-rate-stepping tests are plotted together with constant strain-rate tests to check the reproducibility of the results. At 900 °C and 1000 °C, the last step has slightly higher shear strain-rates than the first step (because of the thinning of the shear zone), and therefore, the differential stress is slightly higher. The experiment at 900 °C shows abrupt strain hardening at the end of the last strain rate step. This behaviour is a consequence of the sample geometry where the lower forcing block collided with the upper alumina piston. At 800 °C, the experiment failed at the slowest strain rate step.

Insert Figure 4 here

One strain-rate-stepping experiment included a hot-pressing stage prior to deformation (480br). The initial sample strength is similar to that of the hot-pressed constant-displacement experiment (419br, Fig. 4). At lower strain rates, the stresses of the hot-pressed sample are similar the sample 388br without hot pressing. At the end of the experiment, the strain-stepping sample (480br) is 200 MPa weaker than the constant rate sample (419br).

Microstructural observations

The brittle and the viscous microstructures are described in terms of being discrete Riedel surfaces without discernible shear displacement and a synthetic lowangle orientation (R) or an antithetic high-angle orientation (R´) with respect to the M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 13 shear plane are termed "Riedel surfaces". When such features have a discernible width, they are termed "shear bands" (SB, not distinguishing C or C´ orientations in the sense of [START_REF] Berthé | Orthogneiss, mylonite and non coaxial deformation of granites: the example of the South Armorican Shear Zone[END_REF]). Riedel surfaces and shear bands may occur in the same sample. Elongated quartz grains or grain aggregates typically develop a shape preferred orientation, which is termed "foliation" (F) here.

Starting material

From analyses with a laser diffraction particle size analyzer, we know that the crushed quartz powder initially has a fractal size distribution with a fractal dimension of 2.4 in the size range up to 100 µm. During the run-in of the σ 1 -piston, before the piston touches the forcing block, the samples are exposed to varying periods (up to 25 hours) of hydrostatic heat treatment. During this time, the same kind of grain growth takes place as in the healing faults described by [START_REF] Keulen | Healing microstructures of experimental and natural fault gouge[END_REF], so that the grainsize fraction <1 µm disappears (Fig. 5). Grain growth creates a normal distribution of grains at the lower size end of the fractal distribution.

A few samples were additionally hot pressed after reaching experimental conditions (20h at 1000°C). After 25 h and 800°C, the 3D mode of the grain size fraction <30 µm is ~9.1 µm, and after 20 h at 1000 °C, it is ~12.8 µm (Table 3). The initial gouge material is now fully compacted and fully cohesive. For the higher temperature samples (700 °C to 1000 °C), porosity is < 1%, whereas for lower temperature samples (500 to 600°C ) porosity is up to ~10 % (values obtained from image analysis) due to a lack of grain growth.

Insert Figure 5 here

Insert Table 3 here

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14 4.

Deformation microstructures

Low-temperature samples (T ≤ 650°C) are dominated by a complex Riedel surface geometry with synthetic R and rare antithetic R' surfaces (Fig. 6;samples 450br,479br,415br,435br). The R surfaces form at an angle of 20-30° to the direction of the applied load (σ 1 -direction) and have a predominantly brittle appearance at 500°C. The R surfaces are not connected and never transect the whole sample. These observations, in conjunction with the mechanical data, indicate that these R surfaces do not fully control the sample strength. Most original clasts are still visible but have rounded edges and corners. Undulatory extinction and discrete surfaces with small misorientation and with a high angle towards the shear zone boundary exist in several clasts at 650°C (Fig. 6; sample 435br). Tails at clasts are partly developed without resolvable small particles at the light or scanning electron microscope scale at 650°C. Deformation lamellae start to develop in clasts at 600 °C.

Shear bands are developed at 650 °C in addition to the R surfaces. At 600 °C, zones with small, equi-axed grains evolve in R surface orientation. These zones become more pronounced at higher temperatures, defining shear bands (Fig. 6; samples 479br, 435br, 493br, 419br).

Insert Figure 6 here

At higher temperatures (T ≥ 700 °C), viscous processes dominate the microstructure (Fig. 6;samples 383br,388br,412br,493br,419br). At 700 °C and 800 °C, a shear band and foliation fabric is developed (Figs. 6,7;samples 383br,388br,412br,493br,419br,452br,447br,448br,499br), and Riedel surfaces are absent. Elongated tails of recrystallized grains develop at rounded clasts. With increasing shear strain and higher temperature, the shear band and foliation fabric evolves into a single penetrative foliation of elongated clasts and recrystallised grains.

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15 Large clasts show more penetrative recrystallisation with increasing temperature of deformation and with increasing strain. At γ ~5 about 10 % clasts remain at 700 °C and 5 % clasts can be distinguished at 800 °C (Fig. 6;samples 383br,493br,388br).

Rounded clasts are predominant at 700 °C. At 800 °C, highly elongated aggregates of recrystallised grains dominate. Deformation lamellae are pronounced in clasts at 700 °C and 800 °C, but rare at 900 °C. At 900 °C and 1000 °C, the elongated aggregates of recrystallised grains give way to a more homogeneous groundmass of recrystallised grains with some clasts preserved in the recrystallised matrix (Fig. 6; samples 412br, 337br).

In samples with hot pressing (20h at 1000°C ), pre-existing cracks are anneal and barely visible. Subsequent deformation at 600 °C does not produce an obvious brittle deformation fabric of the sample (Fig. 6; sample 415br). No Riedel surfaces develop and only minor grain-boundary alignment occurs. At 700 °C and high strains, a shear band and foliation fabric is present with several remaining rounded clasts that develop tails (Fig. 6; samples 493br). At a given shear strain, the foliation angle with the shear zone boundary is clearly larger than in samples without hot pressing and the microstructure appears less deformed. At 800 °C, a pervasive foliation dominates the fabric, again with a slightly larger angle after similar shear strain than in the hot pressed sample (Fig. 6; sample 483br). More or less elongated clasts are present compared to the sample without hot pressing.

Effect of strain rate on microstructure

Three constant shear strain-rate experiments were conducted at shear strain rates different from ~2.5•10 -5 s -1 (Fig. 2b). At 650 °C and a shear strain rate of 0.35•10 -5 s -1 several grains show more brittle deformation, and less rounded grain

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shapes at low shear strain (γ = 1.1; Fig. 7; sample 500br). Shear bands are absent and the fabric resembles samples deformed at lower temperatures at 2.5 x 10 -5 s -1 (Fig. 6; sample 479br). At 800 °C and 900 °C, faster shear strain rates (27•10 -5 s -1 and 189•10 - 5 s -1 , respectively) cause a more heterogeneous deformation, shear bands, and samples resemble those deformed at ~100 to 200 °C lower temperatures at strain rats of 2.5 x 10 -5 s -1 (Fig. 7; samples 447br, 499br).

Insert Figure 7 here

4.4 Effect of confining pressure on microstructure Samples deformed at 1.0 GPa confining pressure and 650 °C show Riedel surfaces and less commonly shear bands, very similar to samples deformed at 1.5 GPa confining pressure (Figs. 6,7;samples 494,435br). Clast shapes are less rounded than at 1.5 GPa confining pressure (cf. Figs. 6 and 7, shear strain is higher in Fig. 7; samples 494br, 435br). At 700 °C, 1.0 GPa, the samples are characterised by a larger number of shear bands and less homogeneous deformation than at 1.5 GPa (cf. Figs. 6 and7; samples 494br, 435br), whereas at 800 °C, 1.0 GPa, more clasts survive and the recrystallisation is less complete than at 1.5 GPa (cf. Figs. 6 and7; samples 448br, 388br). At 0.5 GPa confining pressure and 800 °C, deformation is localised in long synthetic R surfaces accompanied by several transgranular fractures (Fig. 8; sample 386br). Most of the displacement is accumulated along the R surfaces, where the gouge material is highly pulverised (submicron-scale) (Fig. 8b). Large clasts are slightly rounded at the edges (Fig. 8a) and microstructures resemble those of the 650°C, 1.5 GPa sample (cf. Fig. 6; sample 435br). In the series of 0.5, 1.0, and 1.5 GPa samples, more brittle deformation microstructures clearly develop with At conditions of 1.5 GPa confining pressure and shear strain rates of ~3•10 -5 s - 1 , the 3D mode of recrystallized grain size increases from 2.1 µm at 700 °C to >15 µm at 1000 °C (Fig. 9a, Table 3). The sample that was prepared with a grain-size fraction of 7-10 µm, yields a slightly larger grain size of 4.4 µm compared to the standard sample that yields 4.1 µm at the same temperature (800°) (Fig. 9b). At 1.0 GPa confining pressure, the recrystallised grain size is slightly smaller than at 1.5 GPa (1.5 versus 2.1 µm at 700 °C, and 3.3 versus 4.1 µm at 800°C). At 0.5 GPa and 800 °C, no recrystallization occurs. Shear strain rates faster than the standard value of 3•10 -5 s -1 cause smaller recrystallised grain sizes. At 800 °C and 10 times faster, the 3D mode is 2.0 µm versus 4.1 µm, at 900 °C and 100 times faster, it is 1.5 µm versus 6.1 µm (Table 3).

Insert Figure 9 here

An initial hot-pressing stage causes growth of the small grains (Fig. 5, Table 3) and the resulting grain sizes at the onset of deformation are larger. After deformation, the recrystallized grain size of these samples is similar to that of samples without hot pressing (1.6 µm compared to 2.1 µm at 700 °C, 4.8 µm compared to 4.1 µm at 800 °C; cf. Fig. 9b, Table 3).

Texture

The values of GOS and gKAM, indicators of intragranular deformation, decrease with increasing temperature between 700 °C and 1000 °C (Fig. 10) with hot Insert Figure 10 here Above 650 °C, the recrystallised matrix dominates the CPO for standard confining pressure (1.5 GPa) and standard shear strain rates (~2.5•10 -5 s -1 ). Separate pole figures are calculated for smaller and larger fractions of recrystallized grains (Fig. 11). The delimiting size between small and large grains is derived from the 3D mode of the size distribution of recrystallized grains (< 25 µm; Fig. 11). Pole figures are calculated for grains with 2D diameters (= area equivalent diameters) larger or smaller than the delimiting 3D diameter, i.e., pole figures for grains larger than the 3D mode and pole figures for grains predominantly smaller than the 3D mode. For the larger grain size fraction, the CPO is always considerably stronger. The CPO progressively evolves between 700 °C and 1000 °C. At 700 °C and 800 °C, there is one peripheral maximum of the c-axes slightly rotated with the sense of shear. At 900 °C, a peripheral and a central c-axis maximum both are established. Towards 1000 °C the CPO evolves to a single central c-axes maximum.

The pole figures of the fine-grained fraction shows a different development with increasing temperature. At 700°C, the CPO is more diffuse and the peripheral caxis maximum is less pronounced compared to that of the larger grain size. The orientation of the maximum is similar to the maximum of the larger grains. At 800 °C, the smaller grains (< 4 µm) again show a more diffuse CPO, but the c-axis maximum is rotated by 20° with the sense of shear with respect to that of the larger grains. At 900 °C, the peripheral c-axes are more dispersed and the c-axis maximum is rotated by 10° with the sense of shear compared to that of the larger grains. The central

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19 maximum of c-axes is less pronounced than that of the larger grains. The central caxis maximum at 1000 °C is present in fine grains as well as in larger grains. A rotation with the sense of shear cannot be identified.

Insert Figure 11 here

Discussion

Our series of experiments employs crushed material of natural quartz. This approach simulates a cataclasite produced by brittle deformation in nature such as seismic or aseismic movement along a fault. Such a cataclastic rock deforms dominantly by frictional mechanisms at low temperatures, high strain rates and low confining pressures, and by fully viscous mechanisms at higher temperatures, lower strain rates and higher confining pressures. The differences in the mechanical data and microstructures demonstrate that the starting material used here is adequate to study the brittle-to-viscous transition (BVT) as a function of pressure, temperature and strain rate in polycrystalline quartz rocks. Another aspect that may be studied by using such a material is how deformation mechanisms change as a function of deformation history, i.e. from a brittle precursor material to a subsequently viscously deformed material. Such a transition may occur, e.g., as a transition from seismic to postseismic creep.

Mechanical parameters of the brittle-to-viscous transition

The BVT can be defined on the basis of different parameters: mechanical data with respect to the Goetze criterion (∆σ ≈ P c ); pressure dependence of differential stress; friction coefficients and stress exponents, and microstructural transition from dominantly brittle to viscous deformation structures.

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The greatest difference in differential stress at a strain rate of ~10 -5 s -1 is observed between the 600/650 °C and 700 °C samples (Fig. 2a) where the strengths lie above and below the Goetze criterion that marks the transition from brittle (∆σ > P c ) to viscous (∆σ < P c ) deformation ("plastic" in [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]. This observation places the BVT between 650 °C and 700 °C for a strain rate of ~10 -5 s -1 in terms of the Goetze criterion.

For experiments by others at the same axial strain rates as our shear strain rates [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF], the strength of quartzite samples at 700 °C and 850 °C (at P c =1.2 GPa) shows substantial scatter, but similar average values as our samples. The deformation processes in that study were identified as semi-brittle flow (700 °C) and dislocation creep (850 °C). The similar sample strengths of the intact rock and our gouge material indicate that at higher temperatures the cataclasite is fully compacted and behaves like a normal polycrystalline material. We attribute the temperature differences for the BVT between our samples and those of [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF] to differences in the amount of total strain attained and that samples in shear are weaker than in axial compression, so that localisation in coaxially deformed samples occurs in narrower zones than in our shear zones, causing greater strain rates.

The BVT coincides with another mechanical observation in the samples: At stresses below the Goetze criterion, the slope of the loading part of the stress strain curves decreases systematically with decreasing flow stress (Figs. 2, 3 and4). The loading curve in the Griggs apparatus is not purely elastic at higher temperatures. The systematically decreasing slope at higher temperatures is the result of increasing viscous deformation processes in the samples during loading. In experiments deformed above the Goetze criterion, the slope is similar for all samples, indicating no substantial viscous deformation processes during loading.

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Higher confining pressures cause greater sample strength for frictional sliding [START_REF] Byerlee | Friction of Rocks[END_REF] and cracking [START_REF] Paterson | Experimental rock deformation -the brittle field[END_REF] and references within), whereas the viscous creep strength of wet quartz decreases with increasing confining pressure (Tullis et al., 1979;[START_REF] Kronenberg | Flow Strengths of Quartz Aggregates: Grain Size and Pressure Effects due to Hydrolytic Weakening[END_REF]. The observed strengthening of samples with increasing pressure at low temperatures (650 °C, Fig. 3) is consistent with frictional or brittle behaviour (cf. [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF]. The lowering of flow-stress with increasing pressure observed at T > 650 °C (Fig. 3) indicates the onset of viscous deformation. At a first glance, the difference in flow stress between samples deformed at 1.0 and 1.5 GPa P c (453br and 437br) does not appear significant (Fig. 3), but when seen with respect to the Goetze criterion, the difference is well defined: The sample at 1.5 GPa (437br) barely reaches the Goetze criterion, whereas the sample at 1.0 GPa (453br) is clearly above it. The difference in flow stress is clearly established at low P c between 0.5 GPa and 1.0 GPa (Fig. 3). A very similar trend was observed in novaculite by [START_REF] Kronenberg | Flow Strengths of Quartz Aggregates: Grain Size and Pressure Effects due to Hydrolytic Weakening[END_REF]: a smaller stress dependence at P c ≥ 1.0 GPa and a distinct pressure dependence at lower confining pressures. The decreasing peak stress with increasing pressure is related to increased water fugacity and its enhancing effect on crystal plasticity (Tullis et al., 1979;[START_REF] Kronenberg | Flow Strengths of Quartz Aggregates: Grain Size and Pressure Effects due to Hydrolytic Weakening[END_REF][START_REF] Paterson | Quartzite rheology under geological conditions[END_REF][START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF].

The pressure dependence delineates the BVT also in the range of 650 °C to 700 °C for ~10 -5 s -1 .

Coefficient of friction

To delineate the BVT better, mechanical properties such as friction coefficient and stress exponent can be used. Frictional deformation should be rather temperature insensitive up to 440 to 500 °C (Paterson and Wong, 2005, p. 172), whereas viscous

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22 deformation is by definition temperature dependent. Viscous flow laws imply a strong positive stress dependence for the strain rate [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 41 Orowan | Problems of plastic gliding[END_REF][START_REF] Kohlstedt | Constitutive equations, rheological behaviour, and viscosity of rocks[END_REF], whereas in frictional deformation the strain rate at slow sliding rates (as employed in this study) are assumed to be weakly dependent or strain-rate independent as a first approximation [START_REF] Byerlee | Friction of Rocks[END_REF][START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]Paterson and Wong, 2005, p. 178, and references therein). To better use the mechanical data for defining the BVT, we determined the friction coefficients and stress exponents for many of our experiments, even if these mechanical properties are outside the range of conditions for which brittle deformation would be expected.

At 1.5 GPa and below 700 °C, the friction coefficient (µ ~ 0.45; Fig. 12) is somewhat less than normal rock friction values (0.6; [START_REF] Byerlee | Friction of Rocks[END_REF]. The temperature dependence is very small up to 650 °C. From 700 °C to 1000 °C, the friction coefficient shows a systematic temperature dependence. At 1.5 GPa confining pressure and a strain rate of 2.5•10 -5 s -1 , the friction coefficient µ ~ 0.3 to 0.05, at a strain rate of 2.5•10 -4 s -1 , µ ~ 0.35 to 0.16. At strain rates of ~10 -6 s -1 , the friction coefficients become very small (µ < 0.02). Low confining pressures cause greater friction coefficients between 650 °C and 800 °C (Fig. 12b): At 0.5 GPa and 800 °C, the greatest friction coefficient occurs (µ = 0.53), which is twice the value at 1.0 GPa.

A distinct jump in the values occurs for the friction coefficient between 650 °C and 700 °C for a strain rate of 2.5 x 10 -5 s -1 , coinciding with the Goetze criterion (Fig. 12).

Insert Figure 12 here

Frictional deformation in quartz and granite, in general, is only weakly temperature-dependent below 350-400 °C [START_REF] Blanpied | Frictional slip of granite at hydrothermal conditions[END_REF][START_REF] Chester | Multimechanism friction constitutive model for ultrafine quartz gouge at hypocentral conditions[END_REF], so that the smaller friction coefficients and the strong temperature dependence at T > 650 °C also indicate a change in deformation mechanism to viscous behaviour.

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The pronounced strain rate dependence of strength between 650 °C and 900 °C (Figs. 2b,4,12a) is present down to temperatures as low as 650 °C (Fig. 4). This behaviour emphasises the contribution of viscous deformation processes, and thus a semi-brittle character at these low temperatures. It is remarkable that in one sample (500br) at temperatures of 650 °C, the flow stress can be below the Goetze criterion.

However, in that sample, steady state was not achieved because at the low strain rate of ~10 -6 s -1 only a small total strain was attained (Figs. 2b and4). Strain rates of ~10 -4 s -1 are required to achieve sample strengths above the Goetze criterion and realistic friction coefficients at T = 800 °C, whereas a strain rate of ~10 -3 s -1 is required at T = 900 °C (Figs. 2b,12a). These results can be used to extrapolate the BVT to lesser strain rates (see below).

Stress exponent and activation energy

Based on a power-law creep relationship, the stress and strain rate data can be used to derive a stress exponent and an activation energy (Fig. 13):

(Eq. 1)

where ẏ [s -1 ] is the shear strain rate, A [MPa -n •s -1 ] is a material-dependent constant, ∆σ [MPa] is the differential stress, n is the stress exponent, Q [J/mol] is the activation energy, R [J•mol -1 •K -1 ]
is the ideal gas constant and T [K] is the temperature. At low temperatures (~650 °C), the n-value is high (n = 6.4 ± 1.3). The stress exponent of high-temperature experiments (800-1000 °C) is 1.9 ± 0.6 (Fig. 13a) and shows little variation with temperature. For high temperature experiments, the activation energy is determined to be ~170 ± 72 kJ/mol (Fig. 13b).

The highest stress values at 900 °C (499br at ~10 -3 s -1 ) and 800 °C (447br, fast step of 488br at ~10 -4 s -1 ; Fig. 4) are not included in the determination of the stress exponent

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24 and the activation energy because steady state is not indicated by the mechanical data.

Insert Figure 13 here

The calculated stress exponents confirm the transition from brittle-dominated to viscous-dominated deformation at temperatures of 650 / 700 °C, and strain rates of ~10 -5 s -1 . The stress exponent of ~6.4 of samples deformed at low temperatures (Fig. 13) is too high for dislocation creep deformation with typical values of n = 3-5 (e.g., [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 40 Karato | Geodynamic significance of seismic anisotropy of the upper mantle: new insights from laboratory studies[END_REF][START_REF] Paterson | Materials science for structural geology[END_REF][START_REF] Kohlstedt | Constitutive equations, rheological behaviour, and viscosity of rocks[END_REF], thus indicating the beginning of the power-law breakdown, i.e., the lack of rate-controlling viscous deformation at T < 700 °C. On the other hand, the n-values of 1.8 to 2 derived for samples deformed at T > 700 °C (Fig. 13) are too low for dislocation creep, yet rather high for diffusion creep.

Our determined Q-value of 168 to 170 kJ/mole is very similar to values determined by [START_REF] Jaoul | The effect of varying water contents on the creep behaviour of Heavitree quartzite[END_REF] and lies in the range of other experimentally determined values for dislocation creep (Table 4). Activation energies for diffusion creep vary considerably and the values are highly dependent on the involved material (silicon or oxygen diffusion) and the controlling process (transport or reaction) (e.g., 137-178 kJ/mol for silicon diffusion in Farver and Yund, 2000; 142-243 kJ/mol for oxygen diffusion in [START_REF] Giletti | Oxygen diffusion in quartz[END_REF]220 kJ/mol in Rutter and Brodie, 2004a).

Hence, the range of previously determined activation energies and the precision of our determination are inadequate to conclude decisively about the nature of the process causing it. Rutter and Brodie, 2004a,b are the only studies that have determined activation energies for both processes, and the values are very similar (Table 4). Based on this evidence and our observations of a constant stress exponent of n ~2 between 800 °C to 1000°C, we would like to maintain the idea that the activation energies of contributing diffusion creep and dislocation creep mechanisms should be similar.

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Insert Table 4 here

A stress exponent (n ~ 2) has been derived for deformation by dislocationaccommodated grain-boundary sliding by, e.g., [START_REF] Kohlstedt | Constitutive equations, rheological behaviour, and viscosity of rocks[END_REF].

However, the rather strong CPOs occurring in our samples argue against grain boundary sliding (GBS). Although evidence exists for strong CPOs produced by GBS (e.g., [START_REF] Schmid | Simple shear experiments on calcite rocks: rheology and microfabric[END_REF][START_REF] Gomez Barreiro | Preferred orientation of anorthite deformed experimentally in Newtonian creep[END_REF][START_REF] Hansen | Grain boundary sliding in San Carlos olivine: Flow law parameters and crystallographic-preferred orientation[END_REF], the general consensus is that dominant GBS should produce weak CPOs (e.g., [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 38 Edington | Superplasticity[END_REF][START_REF] Bell | An investigation of grain-boundary sliding during creep[END_REF]. A possible explanation is a combination of deformation processes, where dislocation creep produced strong CPOs and n-values of 3 to 5, in tandem with grain-size-sensitive diffusion creep, including grain boundary sliding, which produced weak CPOs. Both together yield n-values of ~2.

To derive a grain-size exponent, we used samples 388br (standard), 419 (hot pressed) and 445br (sieved to 7-11µm), which were all deformed at 800 °C, 1.5 GPa and 10 -5 s -1 , but yielded significantly different differential stresses. The grain size exponent p = m / n, where m is the slope of the linear fit in the log(stress) versus log(grain size) diagram (Fig. 13c) and n is the average stress exponent of 1.9. The correlation coefficient for this fit is very low (R=0.258), and the value of p = 1.08 is not well constrained. While our database is far too small for a reliable determination of the grain size exponent, it is nevertheless interesting to note that similar uncertainty is present in published data (Rutter and Brodie, 2004a).

Microstructure development at the brittle-to-viscous transition

The microstructural changes correspond to the transition conditions inferred from the mechanical data. At strain rates of ~10 -5 s -1 , the samples at T ≥ 700 °C show features of dynamic recrystallisation, whereas at lower temperatures, Riedel fractures and7). The transition between brittle and viscous microstructures is clearly visible between 650 °C and 700 °C at the strain rate of ~10 -5 s -1 and confining pressures of 1.0 and 1.5 GPa. This observation is in excellent agreement with the transition defined by mechanical data discussed above. The effect of confining pressure becomes obvious in the microstructures at low confining pressure of 0.5 GPa, where samples at 800 °C show predominantly brittle microstructures (Fig. 8). The strain rate effect is not as clearly expressed in the microstructure: At 650 °C, deformation at a strain rate of ~10 -6 s -1 produces similar microstructures as a strain rate of ~10 -5 s -1 (cf. Figs. 6,7). But at ~10 -5 s -1 , clasts are more rounded, and Riedel surfaces and shear bands are more pronounced. These differences may well be due to the less total strain of the sample for a slower strain rate. The faster strain rates at 800 °C and 900 °C yield microstructures that resemble a mixture of microstructures at a strain rate of ~10 -5 s -1 between 600 °C and 700 °C (for high shear strain): several remaining large clasts coexist with clusters of recrystallised grains in a fabric dominated by shear bands (below referred to as "transitional").

At stresses above the Goetze criterion, typical regime 1 stress-strain curves with pronounced weakening after peak stress [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF] are only observed at 800 °C and a strain rate of ~2.5•10 -4 s -1 (Fig. 2). Bulging recrystallisation concentrates along shear bands producing small new grains. After sufficient recrystallisation, strain partitioning and weakening occur while mechanical and microstructural steady state are not achieved. Below the Goetze criterion, generally at higher temperatures and slower strain rates, minor strain weakening occurs, except at 1000 °C where steady state is attained (Fig. 2). The associated microstructure is dominated by a pervasive shape foliation of recrystallised grains and the development of a CPO. Hence, mechanical steady state is approached, but not perfectly realised,

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27 and this result is consistent with incomplete recrystallisation (Fig. 6), a switch from one deformation mechanism to the next, or simultaneous operation of two mechanisms.

5.5 Texture and grain size at the brittle-to-viscous transition

Misorientation density

So as to distinguish recrystallised grains from potential survivor grains of the original quartz material on the basis of some intragranular misorientation density, the grain kernel average misorientation (gKAM) and the grain orientation spread normalised with respect to the long axis (GOS la ) were measured. We initially assumed that low intragranular misorientation densities are characteristic of newly recrystallised, recovered grains, whereas high misorientation densities are typical for the original crushed material. However, it was found that recrystallising grains continue to accumulate intragranular strain as the overall shear deformation continues.

Accordingly, the gKAM remains high and rather reflects grain-scale strain [START_REF] Kilian | Texture analysis of experimentally deformed Black Hills Quartzite[END_REF]. A correlation of high gKAM with small (recrystallized) grain size has also been noted (Heilbronner and Kilian, 2017). In other words, the gKAM, or any other measure of internal misorientation density, does not reflect recovery, and therefore cannot be used to distinguish recrystallized grains from relict grains.

However, gKAM and GOS la do vary as a function of temperature: The higher the deformation temperature, the smaller the intragranular misorientation density (Fig. 10). Pre-deformation hot pressing or sieving does not significantly influence this trend. At lower temperatures, large grains with high PARIS factors (more lobate grains) have higher gKAM and GOS la values than the small grains with low PARIS factor (fully convex grains). In other words, large grains tend to have high

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28 misorientation densities while small grains display the full spectrum of misorientation density, from fully recovered to highly strained. This distinction becomes progressively smaller with increasing temperature, until, at 1000 °C, all grains, irrespective of shape and size, have very small misorientation densities, i.e., appear fully recovered.

CPO of diffusion and dislocation creep

To investigate if diffusion creep and dislocation creep are grain-size selective, we consider the textures of the small and the large grain-size fractions separately (Fig. 11). Small and large grain-size fractions are delimited by the 3D mode which as a result the number of grains in the smaller and larger fraction differ considerably. Pole figures are therefore weighted by the area of the evaluated grains to avoid artefacts.

We also checked by comparing number-weighted pole figures that were calculated for the large grain-size fraction and for the same number of randomly selected small At 700 °C, the weaker texture of the small grains is attributed to processes such as solution precipitation and nucleation. At 800 °C and 900 °C, textures of the small grains are not only weakened but also the c-axis maxima are rotated with respect to those of the large grains. For 800 °C and 900 °C, the rotation is 20° and 10°, respectively, clockwise in the sense of the applied shear, compatible with grainboundary sliding and a stiff rotation of grains. At 1000 °C, the difference between the pole figures of the smaller and larger grain size fractions is the texture strength, not in the texture type. As the rotation axis of the applied shear is parallel to the (strong) c-

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29 axis maximum, a potential rotation is difficult to discern.

Comparing the experimental quartz deformation analysed here with results derived from naturally or experimentally deformed quartzites, we find that the CPO evolution of the larger grain-size fraction (Fig. 11) is consistent with observations where high temperature deformation produces a central c-axis maximum, whereas low temperature deformation (or small shear strains in experiments) produces peripheral maxima (e.g., [START_REF] Schmid | Complete fabric analysis of some commonly observed quartz c-axis patterns[END_REF]Stipp et al., 2002;Heilbronner andTullis, 2002, 2006). In terms of the three microstructural regimes identified in nature, the 700 °C and the 800 °C experiments would coincide with BLG (bulging), the 900 °C sample with SGR (subgrain rotation) and the 1000°C sample with GBM (grain boundary migration). In a more recent study by [START_REF] Kilian | Texture analysis of experimentally deformed Black Hills Quartzite[END_REF], it was found that the textures of Black Hills quartzite (BHQ) deformed in the dislocation creep regimes 1, 2, and 3, develop from a peripheral c-axis maximum towards a central c-axis maximum as the result of a transition from dominant nucleation / bulging recrystallisation to dominant subgrain rotation recrystallisation.

Grain size distributions in diffusion and dislocation creep

In a mixed mode of diffusion creep and dislocation creep, as inferred here from the stress exponents of n ~ 2, diffusion creep is expected to be more efficient in small grains while dislocation creep, which is grain-size insensitive, should be more active in larger grains [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]. An estimate for the upper grain-size limit of grain-size-sensitive creep is given as <1 µm (Rutter and Brodie, 2004a), whereas [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF] estimate the upper size limit to be ~20µm. The recrystallised grain size measured for our experiments at T = 800 -1000 °C, is well within these limits: Recrystallised grain sizes range from <1 µm up to 25 µm, with modal values (3D mode) of ~4, ~6 and ~10 µm for 800 °C, 900 °C and 1000°C, respectively (Fig.

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ACCEPTED MANUSCRIPT 30 9). As was shown, the partitioning of deformation mechanisms into smaller and larger grain size fractions takes place in our samples for grain size below and above these modal values as a threshold. Our threshold values are closer to the transition limit of [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF] for dislocation and diffusion creep.

Before reaching the hit point, the original fractal grain-size distribution has been modified by grain growth. We can estimate from the analysis of two hotpressed samples that the very smallest size fraction has been obliterated in a manner described by [START_REF] Keulen | Healing microstructures of experimental and natural fault gouge[END_REF] for healed faults. However, we do not know how far grain growth proceeded during pressurization and heating, and what the smallest grain size may be at the start of the experiment. In contrast, when the starting material consists of a grain-size fraction of 7-11 µm (sample 445br), we know that any grain smaller than 7 µm must have formed during deformation, possibly by a process such as bulging recrystallisation, nucleation [START_REF] Kilian | Texture analysis of experimentally deformed Black Hills Quartzite[END_REF], or creep cavitation (Precigout and Stunitz, 2016). Comparing samples 445br (sieved), 388br (standard) and 419br (hot pressed), we note that the grain sizes and stress do not follow a piezometric relation. Grain sizes (3D modes) of 4.4, 4.1 and 4.8 µm were measured for flow stresses of 309, 791 and 1016 MPa, respectively.

Rather than decreasing with grain size, stress seems to increase (cf. Fig. 13c). In other words, the piezometer relation does not hold and pure dislocation creep can be excluded, suggesting that a substantial contribution of diffusion creep has to be inferred.

Using the Griggs apparatus for the derivation of stress exponents

As mentioned above, for dislocation creep in quartz, stress exponents of n = 3-5 are often given in the literature [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF] [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF], despite the fact that lower values were determined experimentally (n < 2.5) in many cases (e.g., [START_REF] Jaoul | The effect of varying water contents on the creep behaviour 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] Paterson | Quartzite rheology under geological conditions[END_REF]Rutter and Brodie, 2004b, see Table 4). For some earlier data acquired with solid-medium apparatus, a large uncertainty is attributed to imprecise stress measurements in the solid-medium deformation apparatus (e.g., [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF]. However, a large part of the lack of precision and accuracy of the solid medium apparatus is caused by friction and errors associated with the hit point determination. Strain-rate-stepping experiments should not be affected by this error, because all data within a single experiment is determined with respect to the same hit point, and only a slope is fitted to the data, regardless of the absolute values of stresses. In addition, a recent study indicates good accuracy for stresses derived from Griggs apparatus [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 42 Richter | Stresses and pressures at the quartz-to-coesite transformation in shear deformation experiments[END_REF]. Furthermore, the lack of evidence for partial melting in our samples would be consistent with expected low values for stress exponents as suggested by [START_REF] Jaoul | The effect of varying water contents on the creep behaviour of Heavitree quartzite[END_REF]; [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF].

Stress exponents can only be correlated with deformation processes if steady state conditions are reached. Achieving this state may be especially problematic for regime 1 conditions [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF]. The required high strain conditions are difficult to achieve in coaxial compression experiments. Our shear experiments are deformed to high shear strain (up to γ ~ 5) where mechanical and microstructural steady state is more or less achieved, at least at high temperatures (800-1000 °C; Fig. 2). Hence, the low stress exponents cannot be explained by incomplete steady state conditions as suggested by [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF]. In addition, [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF] associate low stress exponents with the transition from regime 2 to regime 1 after [START_REF] Hirth | The brittle-plastic transition in experimentally deformed quartz aggregates[END_REF]. Such a temperature dependent microstructural change is

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32 not observed in our samples used for calculating stress exponents. However, the observed microstructures indicate dislocation creep and diffusion creep between 800 °C and 1000 °C. In contrast, dislocation creep was solely inferred in earlier studies (e.g., [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF][START_REF] Jaoul | The effect of varying water contents on the creep behaviour of Heavitree quartzite[END_REF]. These studies used quartzites with narrow grain-size ranges and large average grain sizes where grain-size-sensitive deformation mechanisms are unlikely. The broad grain-size range of our starting material with a pronounced fine-grained fraction enables grain-size-sensitive diffusion creep in addition to grain-size-insensitive dislocation creep resulting in mixed stress exponents.

Extrapolation to natural conditions

It is important to attempt the extrapolation of experimental results to natural conditions. As a first step, the different mechanical and microstructural criteria should be combined to delineate the BVT. In the present study, sample deformation was classified as viscous, semi-brittle, and transitional on the basis of the microstructural suites and experimental behaviour, where transitional deformation is defined by the presence of many remaining large clasts coexisting with clusters of recrystallised grains, the fabric dominated by shear bands at high shear strain. Deformation microstructures can be plotted for the same strain rate in a differential stress vs.

confining pressure diagram at a strain rate of 2.5•10 -5 s -1 (Fig. 14a). The transitional samples all plot above the Goetze criterion, so that the Goetze criterion, as to be expected, marks the upper stress limit of dominantly viscous deformation mechanisms. For high confining pressures (1.5 GPa), the BVT can be well delineated using the microstructures and strain rate -temperature relationships (Fig. 14b), although the Goetze criterion is more difficult to define at low temperatures. Using the

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33 broad division boundary (green line) from the experimental data, the BVT can be extrapolated to natural conditions of strain rate and temperature (Fig. 14c). As can be seen, the extrapolation is in fairly good agreement with the well documented BVT data point of Stipp et al. (2002a,b) for a strain rate of ~10 -12 s -1 . For the representative natural conditions (280 °C, P c = 300 MPa, ∆σ = 250 MPa), the stresses, which were determined were converted to strain rates using the flow law from [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF] and recalculated for 1.5 GPa confining pressure using the appropriate water fugacity values. The microstructures of the Stipp et al. (2002a,b) sample at 280 °C are within the viscous field at stresses just below the brittle conditions, consistent with the Goetze criterion and the extrapolation from this study. If natural conditions of 1.0 GPa confining pressures are used, our corrected results for P c = 1 GPa and the Stipp et al. (2002a,b) data are consistent, too (Fig. 14d). For 0.5 GPa confining pressure, our experiments have only one data point, but it is also consistent with the extrapolation derived from the series of experiments at higher pressure (Fig. 14d). Thus, this extrapolation should serve as a guideline to determine the BVT in quartz for a wide range of conditions between experiments and nature. For example, semibrittle microstructures in rocks at elevated temperatures in quartz could be used to infer minimum strain rates.

Insert Figure 14 here

If creep conditions of laboratory data for quartz are to be extrapolated to natural conditions, a power-law behaviour (Eq. 1) is always assumed. Existing and commonly used flow laws assume pure dislocation creep with a relatively high stress exponent, typically n = 4 [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF][START_REF] Paterson | Quartzite rheology under geological conditions[END_REF]. Our flow law parameter of a stress exponent of n = 1.9 (Table 4) introduces combined (mixed mode) deformation mechanisms of dislocation and diffusion creep. It should be

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34 pointed out that the stress exponent for silica gel in the experiments by [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF] also show a value of n = 2.3, the data by [START_REF] Jaoul | The effect of varying water contents on the creep behaviour of Heavitree quartzite[END_REF] show n = 1.4 to 2.4, and [START_REF] Kronenberg | Flow Strengths of Quartz Aggregates: Grain Size and Pressure Effects due to Hydrolytic Weakening[END_REF] show n = 2.5 for novaculite. Thus, several studies have determined stress exponents of n ≈ 2, independently from each other. The reason why these stress exponents have been questioned in the past is that either impurities [START_REF] Luan | Preparation and deformation of synthetic aggregates of quartz[END_REF] or melt [START_REF] Jaoul | The effect of varying water contents on the creep behaviour of Heavitree quartzite[END_REF] may have affected the rheology of the samples. In our case, no melt was detected, and we can demonstrate the effect of smaller and larger grain-size fractions for the activation of different deformation mechanisms. Our value for the activation energy is greater than those of [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF] and [START_REF] Kronenberg | Flow Strengths of Quartz Aggregates: Grain Size and Pressure Effects due to Hydrolytic Weakening[END_REF] and less than those of Rutter and Brodie (2004) and [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF], but the range of values is consistent with previous determinations (Table 4).

When our data are extrapolated to low temperatures at natural strain rates, the BVT in terms of temperature, strain rate, and pressure will very much depend on the grain size, where small sizes that are very common at low temperatures will favour the operation of diffusion creep mechanism, which are part of the inferred deformation mechanisms in this study. In nature, the expected deformation process probably is solution precipitation creep. It is an important result of this study that the BVT in quartz is not simply a transition from cracking to crystal-plastic deformation, but, instead, it involves grain-size dependent diffusion-creep processes, too.

Cataclasis is a very efficient process to reduce grain size, so that our simulated cataclasite is an appropriate starting material for studying the deformation history dependent transition from cracking to viscous deformation. The results clearly show that cataclasites are very likely candidates for subsequent viscous deformation. This interplay of brittle and viscous deformation processes is particularly applicable to high -Geological Society, London, Special Publications 200, 171-190. Stünitz, H., Thust, A., Behrens, H., Kilian, R., Tarantola, A., FitzGerald, J. D. (2017)

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT Sample T [°C] Pc [GPa] γ̇ [10 -5 • s -1 ] Width [px] Height [px]
Step size [µm] No. of grains

2D mean 1) [µm] 2D median 2) [µm] 2D RMS 3) [µm] 3D mode 4) [µm]
3D st.dev.

  10°. Dauphine twin boundaries (misorientation of 60 ± 5°)

  similar values to samples without hot pressing. For individual grains, neither PARIS factors, indicating high lobateness, nor grain size correlate with GOS and gKAM values.

  figures of smaller grains are weaker than those for larger grains. The weaker textures

;

  Luan and Paterson,

  such as seismically active deformation zones. Catclasis will provide the fine-grained material, which helps to accommodate aseismic creep in interseismic periods, i.e., postseismic creep deformation.6. ConclusionsA set of shear experiments performed on quartz material under elevated confining pressures (predominantly 1.5 GPa) and temperatures (500 °C -1000 °C) at intermediate to fast shear strain rates (3.5•10 -6 s -1 to ~2•10 -3 s -1 ) documents the transition from (semi)-brittle to viscous deformation. The Goetze criterion (∆σ > P c ) is confirmed to delineate the upper limit of differential stress for viscous deformation.Samples above the Goetze criterion are characterised by Riedel fractures or shear bands at high shear strain, normal geological friction coefficients, and n-values too high for dislocation creep. At low temperatures, increasing confining pressure causes increasing strength, as is to be expected for fracturing and frictional deformation. A somewhat unsystematic temperature-dependence of stress is observed under these conditions. Cataclastic flow partly accompanied by stress-induced dissolution precipitation is suggested as the dominating deformation process at temperatures just below the transition to viscous deformation (650°C) for a strain rate of 2.5 x 10 -5 s -1 , indicated by a power-law breakdown with a stress exponent of n = 6.4 ± 1.3.Below the Goetze criterion (∆σ < P c ), viscous deformation dominates, as demonstrated by weakening of samples with increasing pressure and temperature. The microstructure is dominated by a pervasive foliation at high shear strain accompanied by an increasing recrystallised grain size with increasing temperature, only partially dependent on flow stress. Presence of different CPO´s in different grain-size fractions exponents (n = 1.9 ± 0.6) indicate a combination of diffusion creep and dislocation creep. It is argued that diffusive mass transfer and grain-boundary-sliding prefer the small grain-size fraction while dislocation creep is more effective in large grains. The constant stress exponent between 800 °C and 1000 °C suggests no change in the rate-limiting factor and a similar activation energy for the diffusion and dislocation creep mechanism.From these results, it can be inferred that the brittle to viscous transition with increasing temperature in nature may occur as a combination of diffusion and dislocation creep. The combination favours the viscous deformation to occur in fine grained aggregates likely to have formed by previous cataclastic deformation. Such a sequential transition in time elegantly explains the alternation of episodic seismic (brittle) and aseismic deformation in high stress, seismically active zones.

Figure 1 :

 1 Figures and tables

Figure 2 :

 2 Figure 2: Stress-strain curves for constant shear strain rate experiments.

Figure 3 :

 3 Figure 3: Stress-strain curves to demonstrate the influence of confining

Figure 4 :

 4 Figure 4: Stress-strain curves for strain rate stepping experiments.

Figure 5 :

 5 Figure 5: Starting material.

Acknowledgments

We would like to thank Rüdiger Kilian for extensive stimulating discussions and help with the MTEX toolbox. Furthermore, we wish to thank Willy Tschudin for preparing excellent thin sections, Hans-Rudolf Rüegg for supplying equipment in the deformation lab, Trine Merete Dahl for preparing thin sections for EBSD, and the team of the Nano Imaging Lab and Tom Ivar Eilertsen for support with the SEM. Raw data and samples can be acquired at the corresponding author. Constructive and insightful reviews of 2 anonymous reviewers and Raphael Gottardi and he very constructive input by the editor William Dunne have substantially improved the manuscript. Funding by the Swiss National Science Foundation grant no. 200021-

Two measures for misorientation density at the grain scale are evaluated for samples deformed at temperatures from 700 °C to 1000 °C; gKAM = grain kernel average misorientation (Heilbronner and Kilian, 2017); GOS la = grain orientation spread, normalised for long axis (see text); for each data point, the PARIS factor is colour coded and the symbol size is related to the equivalent diameter. Friction coefficient is calculated from shear and normal stress on sample: µ = τ / σ n (Figure 1). (a) Different shear strain rates at constant confining pressure of 1.5 GPa. (b) Different confining pressures at constant shear strain rate of 2.5•10 -5 s -1 .

Figure 13: Derivation of stress exponent and activation energy.

(a) At 650 °C, the stress exponent n ~ 6.4. For 800 °C -1000 °C, the average of the stress exponent is determined: n = 1.9±0.6. (b) From experiments at strain rates of 10 -4 s -1 and 10 -5 s -1 , the activation energy is derived: Q ~ 170 kJ/mol. (II) indicates the second measurement of stress at a given strain rate in strain rate stepping experiments (cf. Table 2). (c) At 800°C, 1.5 GPa and 10 -5 s -1 , and for a stress exponent n = 1.9, the grain size exponent p is 1.08; m = slope of liner fit. Samples used: 388br = standard starting material; 419br = hot pressed at 1000°C; 445br = sieved to (7 ≤ d ≤-11µm). d) Same extrapolation as in (c) using additional data points recalculated for 1.0 GPa (orange) and 0.5 GPa (blue) confining pressure; filled circles -using flow law after [START_REF] Hirth | An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks[END_REF]; open circles -using flow law of this study.

Table 1: Experimental conditions for constant shear strain rate experiments. 1) Pre-treatment: Hot pressed = 20 hours at 1000°C and 1.5-1.6 GPa. Sieved = powder sieved to grain size fraction (7 ≤ d ≤ 11 µm).

2) Friction coefficient determined at peak stress. 2) Approximate value due to power failure.

3) Sample hot pressed for 20 hours at 1000°C and 1.5-1.6 GPa.

4) Hardening at end of experiment due to contact of forcing blocks. (1) New large data set defines brittle to viscous transition in quartz

(2) Low stress exponent of n = 1.9 + 0.6 between 800C and 1000C for viscous (5) Goetze criterion is confirmed as upper stress limit of viscous deformation