Elena Giovenco
email: elena.giovenco@univ-lyon1.fr

Jean-Philippe Perrillat

Eglantine Boulard

Andrew King

Nicolas Guignot

Yann Le Godec

Quantitative 4D X-ray microtomography under extreme conditions: a case study on magma migration

Keywords: X-ray absorption microtomography, high pressurehigh temperature, melt migration

Introduction

X-ray computed tomography (XCT) is established as a powerful non-destructive method to characterize multiple properties in three dimensions [START_REF] Maire | [END_REF]. Recently, this technique has been adapted to high-pressure (HP) research (Guignot et al., 2020) either in triaxial rig (Renard et al., 2016), large volume presses (LVP) such as Drickamer (Wang et al., 2005) and Paris-Edinburgh modules (Philippe et al., 2016), or diamond anvil cells for ultra-high pressure conditions [START_REF] Liu | Proc. Natl. Acad. Sci[END_REF]Mao et al., 2019). Major constraints for high-pressure experiments come from the sample confined environment (i.e. pressure medium and anvils) and the equipment size, which makes the sample not directly accessible and prevents short sample/detector distance required for highresolution imaging. The first LVP used for tomography measurements was a modified Drickamer cell fitted in a 250-ton hydraulic press at GSECARS (Wang et al., 2005). Since, numerous improvements have been made, including the use of toroidal opposed anvils, and attenuation-XCT are routinely obtained up to 8 GPa and 2000 K in a number of scientific applications (Yu et al., 2016). To enhance equipment compactness and portability at synchrotron sources, a tomography module was also developed for Paris-Edinburgh presses (Philippe et al., 2016). The RoToPEc (Rotating Tomography Paris-Edinburgh cell) allows tomographic studies under high pressure and temperature, up to 10 GPa and 2000 K with conventional tungsten carbide anvils, either in absorption or diffraction scattering mode (Álvarez-Murga et al., 2017;Boulard et al., 2020). Both systems rely on rotating anvils supported by thrust bearings inside the load frame, and the use of X-ray transparent containment rings and cell assemblies so that the sample could be imaged over 360°. Despite the development of these techniques, the range of application is limited by the rotation speed of the anvils. Indeed, CTtomographies are typically recorded in twenty minutes or more, making tomographic reconstruction impossible if the sample undergoes plastic deformation or either structural and chemical changes during the acquisition of the projection images. Studies of dynamic processes with second to minute characteristic times are thus impossible.

To overcome this limitation, a Paris-Edinburgh press optimized for fast tomography has been developed, i.e. the UToPEc for Ultra-fast Tomography Paris Edinburgh cell (Boulard et al., 2018).

Based on a modified two-column press (Klotz et al., 2004), the UToPEc is compact (Ø 170 mm, 20 kg) and can be installed on a high speed rotation stage for continuous image acquisition. It also offers a large 165° angular opening, and hence limited blind angles that can be tolerated or corrected for by reconstruction algorithms (Turpin et al., 2020). Pressure and temperature up to 10 GPa and 2000 K can be targeted with a micrometric spatial resolution for 3D volumes recorded in less than 1s at full rotation speed.

In this paper, we present the specificity of high-pressure tomography as a practical step-by-step handbook from experimental set-up to possible results by detailing acquisition, reconstruction, segmentation, and quantification procedures. The interest of such temporal resolution will be exposed through the example of carbonate-rich melts migration in the Earth's upper mantle. This case study will illustrate fluid percolation monitoring through characterization of flow dynamic and geometry as well as morphological tracking of entities.

Experimental set up

X-ray tomography set-up at PSICHE Beamline

µ-XCT experiments were conducted on the high pressure beamline PSICHE at synchrotron SOLEIL [START_REF] King | Integrating Mater[END_REF]; Figure 1). A high-flux parallel X-ray beam with a mean energy around 45 keV is produced by filtering the polychromatic source ("pink" beam illumination), and provides a 3mm x 1.5 mm field of view and fast exposure time. Transmitted images are converted into visible light and recorded by a 100 µm thick LuAg scintillator screen, coupled by a microscope objective lens to a PCO Dimax CMOS high-speed camera (pco.dimax HS4. PCO AG, Germany) capable of recording 2000 images/s. High temperature and pressure conditions were achieved using the UToPEc press. The small size of the press allows the sample to detector distance to be reduced and hence achieve a better spatial resolution by reducing blurring due to beam divergence. Using a 7.5x optical magnification results in an effective pixel size of 1.47 m, with 4-5 micron true resolution in the reconstruction [START_REF] King | Integrating Mater[END_REF].

The UToPEc is mounted on x-y-z translational and rotational stages using rotary couplings that allows a continuous rotation of the press up to 360°/s while maintaining the electrical current and hydraulic cooling supplies (Guignot et al., 2020). To date, the hydraulic oil is not yet connected via rotary joints. Pressure must be adjusted prior to tomographies acquisition. Then, a valve seals the system while the oil pump is disconnected. The set-up is also compatible with X-ray diffraction which was used for the measurements of pressure using an hBN-based calibration (Le Godec et al., 2000).

Time-resolved XCT experiments

An experiment was designed to study the percolation of a liquid carbonate phase through an aggregate of solid silicate grains. Starting materials consisted of a 0.4 -0.6 mm thick layer of barium carbonate (BaCO 3 nano-powder from Alfa Aesar) enclosed in between layer of polycrystalline olivine Mg 0.9 Fe 0.1 Si 2 O 4 powder (Figure 1). The micron-sized ( < 100 m) olivine grains were sorted from a natural San Carlos peridotite specimen, and included sporadic iron oxides and pyroxenes impurities.

The choice of BaCO 3 heavy carbonate as the upcoming liquid was made to enhance its X-ray absorption contrast with the olivine solid matrix. Tungsten carbide spheres were also embedded within the olivine powder as positional reference markers (their necessity will be further explained in subsection 3.1). These "sandwich" samples were loaded in a classical PE assembly (Perrillat, 2008) with hBN capsule, graphite furnace, 10mm boron-epoxy gasket, and a PEEK containment ring (Figure 1). Samples were first pressurized to 2 GPa. This cold compression stage led to a strong reduction of the olivine powder initial porosity to achieve a value of 5-10 %. Temperature was then increased by steps above the melting point of BaCO 3 (i.e. T > 800°C) for CT-imaging of liquid migration. The entire process under extreme conditions lasts over one hour; after which samples were quenched and prepared for SEM observations. Table 1 summarizes P-T conditions and XCT acquisition characteristics for studied samples.

The real-time monitoring of BaCO 3 liquid migration was limited over time by the capacity of the onboard memory of the CMOS camera and the duration of data transfer to the storage network. For the field of view needed in this experiment, i.e. the whole gap between the anvils, a maximum of approximately 15 000 projections (1500*1500 pixels) could be recorded, corresponding to about 15 CT images. The data transfer of the projections corresponding to a single CT image to the storage network took approximately 1 min. In order to capture the motion of carbonate liquid, with second to minute resolutions, we defined a sequence of 12-15 CT scans of 1s duration with a 15s interval between each tomogram. Data were downloaded from the camera after each sequence (transfer took about 10-15 min). Dark and flat field images were recorded at the beginning and end of each sequence as spatial and temporal inhomogeneity of the incident beam, scintillator, and CMOS response are negligible in such a short period (< 4 min). Three such cycles were performed for each sample (see Table 1). Pressure was calculated from h-BN cell parameters and the equation of state of Le Godec et al. (2000). Temperature was estimated by power temperature relation curve determined in a previous experiment using a thermocouple.

Analysis methods

CT image reconstruction and pre-treatment

Each tomogram consisted of 900 projections recorded over 180° rotation in 1.035 s. Volume reconstruction was performed via standard filtered backprojection using PyHST2 (Mirone et al., 2014), and applying flat field correction and Paganin phase retrieval (Paganin et al., 2002). The presence of 15° missing angles did not produced noticeable artefacts affecting the volume quality as already observed by Urakawa et al. (2010) and Boulard et al. (2018).

After reconstruction, data correspond to a stack of XY-slices in 32bits-float data format. These data were converted into 8bits-integer format to reduce memory requirements and facilitate their analysis.

This conversion was performed with ImageJ using the automatically optimisation of brightness and contrast based on image histogram. Display range values were determined on tomography slices within the olivine matrix to enhance interstitial carbonate visibility and were kept the same for all tomographies. Small amount of pixels was allowed to become saturated (0 or 255) as visible later on the resulting 8bits histogram used for thresholding. Representative subvolumes were then extracted to reduce calculation time during segmentation and post-processing with dimensions of 1275x1325x435 voxels (i.e. ≈ 1875x1948x639 µm) for BaCarb1 and 1300x1250x402 voxels (i.e. ≈ 1911x1838x591 µm) for BaCarb3 (see Figure 2 for an illustration).

Figure 2

Tomographies cross-sections with studied sub-volume representation. Figured crosssections are from the last CT-images of cycle 3 for both samples BaCarb1 and BaCarb3 (cf Table 1 for more details).

In order to make quantitative comparisons between successive tomographies, the 3D datasets must be spatially aligned. Inherent issues from the high-pressure experiments must be addressed. (i) First, at high temperature, despite the PEEK containment ring, the experimental assembly flows and induces a translation of the sample along the vertical-axis as well as a reduction of the gap between anvils. We used WC sphere markers embedded in the olivine sample to correct this absolute motion. These benchmarks also confirm that plastic deformation did not occur within the polycrystalline aggregate under HP-HT since distances between markers remained constant. (ii) Moreover, due to the continuous rotation of the press and the delay between successive CT-scans, an angular jitter is observed between tomographies within the same acquisition cycle and between different cycles. This misalignment results in different absolute rotation stage position for each dataset that can reach 20°.

To correct this offset, 3D volumes are rotated to one another using a Python script that involves the barycentre (i.e. center of mass of entity associated voxels) of the markers. After these corrections, subvolumes can be overlapped and are thus suitable for subsequent segmentation and quantification.

CT image segmentation

After conversion to 8bit-integer format, each voxel in the subvolume is characterized by a grey level value, from 0 to 255, that reflects the local X-ray attenuation coefficient. Here highly absorbent elements, such as BaCO 3 , appear brighter on CT slices relative to silicate grains (Figure 3b). The segmentation enables the isolation of voxels with particular intensity values, and their assignment to a phase, either carbonate or olivine silicate. This segmentation step was performed with the Thermo Scientific Avizo © software, using a user-controlled hysteresis thresholding. It consists of a dual thresholding operation, where the first threshold (upper value) determines high-confidence areasany pixel value above it will be undeniably associated with carbonate -while the second threshold (lower value) consists of an extension of those areasareas above this threshold are considered to be carbonate if they are connected to high confidence areas. Both threshold values were determined from the grey scale histogram (Figure 3c), and were constant for each tomography sequence.

The choice of these threshold values is the main source of uncertainty on estimates of carbonate vs silicate volumes, since the projection grey-level can slightly fluctuate between CT-images. We assess this uncertainty by running multiple segmentations with similar first threshold value but varying the second threshold by  2 grey levels. This range corresponds to the possible values for the extension of the high-confidence limit as above +2 some carbonate information is not taken into account and below -2 segmentation induced noise and tomographic default enhancement. In subsection 4.1 those uncertainties will be represented as envelopes and will be use to select CT-scan to be compared.

After segmentation, slices are binary images where 0 corresponds to the silicate matrix and 1 to carbonate elements. Segmented entities not related to the BaCO 3 liquid migration, like WC-markers or the carbonate source layer, that are far bigger than target melt pockets are removed using a filter based on a volume limit. For each carbonate entity in the subvolume, identified as labelled-blobs, we computed position properties and shape characteristics (volume, Feret distances (length and thickness), flatness and orientation) using Avizo© predefined functions (BaryCenterX, BaryCenterY, BaryCenterZ, Volume3d, Length3d, LengthOrientTheta, LengthOrientPhi, Width3d, WidthOrientTheta, WidthOrientPhi).

Using positional barycentre information, cylindrical regions of interest (ROI) within subvolumes were defined to avoid edge defects (e.g. liquid flow along the edges of the capsule). All entities whose barycentre is included in the cylinder will be kept in its entirety, so that blobs located at the boundary of ROI are not cropped. The ROI characteristics for BaCarb1 and BaCarb3 are 294 µm height -588 µm radius and 367.5 µm height and 441 µm radius respectively (Figure 3e). µm 3 and 6656 voxels to ~21 000 µm 3 ). The left axis displays the absolute volume associated to the voxel count and the right axis represents its comparison to the ROI volume. In this example 1% of total volume is segmented as carbonate.

Object-based analysis

To better constrain flow geometrical characteristics, 3D data can be studied regarding each segmented entity. Within cylindrical ROI, the number of carbonate melt pockets varies between 100 and 300.

They were investigated in term of volume, shape and inclination statistics, as well as entity tracking.

Upcoming paragraphs and Figure 5 describe briefly the calculation of these parameters.

Shape analysis

Blob shape was characterized using Feret minimal and maximal diameter. The Feret diameter is a measure of an object size along a specified direction. It can be defined as the distance between two parallel tangents to the contour of the object. Distances were computed along with a series of orientations, Θ and φ varied from 0 to 180° and -90 to 90°, respectively, with an interval of 1°. Feret minimal and maximal distances characterize entities' thickness (shortest distance) and length (longest distance), respectively. In term of aspect ratio, entity flatness can be computed from , such that 0 corresponds to a sphere and 1 to a plane.

Entities inclination

Orientation statistics were obtained on elongated BaCO 3 blobs (aspect ratio above 2:1) by measuring their dip angle relative to the X-Y plane of the subvolume. Inclination statistics are represented by rose diagrams (Figure 10), and reveal the orientation of melt pockets between solid grains.

Tracking

The 3D alignment of tomograms (see subsection 3.1) enables particles tracking between successive CT-images. In this way, the morphological evolution of each entity, identified by its barycentre, can be quantified using the above-defined volume, shape and orientation parameters. Nevertheless, depending on the case of study, entities could disappear, split, or merge (either physically or due to data resolution). In consequence, this approach is limited to restricted set of particles of interest. An example, of melt pocket tracking is shown in Figure 12 and discussed in subsection 4.3.

Results & Discussion

Impregnation rate and dynamic

In both experiments BaCarb1 & BaCarb3, the liquid impregnation started as soon as the melting temperature was crossed, as evidenced by the appearance of melt pockets away from the initial carbonate layer already on the first tomography. The further CT-images allow tracking the progression of the migration front with a 16s resolution. Figure 6 shows eight reconstructions recorded for sample BaCarb1 in the first 176s of experiment and the distribution of carbonate voxels along the z-axis (where 0 represents the position of the initial BaCO 3 layer) for each CTreconstruction. The progression of the porosity infill by carbonate is clear between the 48s, 80s, 96s

and 112 s CT images to reach the top end of ROI. This way, we can estimate that initial impregnation took place over a distance of at least 115 µm between CT scans recorded at 48s and 120s that translates into an average vertical rate of 5.35 mm/h.

In sample BaCarb3, tracking of this impregnation front was made difficult by the presence of sporadic oxide impurities in the olivine powder that biases the identification of newly-formed small melt pockets. However, on the last CT-image recorded after 224s, the BaCO 3 melt is well dispersed and reached the top end of the ROI. As the sample maximal observable height was 368 µm, a mean impregnation rate of 5.91 mm/h can be estimated.

These impregnation rates can be compared with SEM observations on the quenched samples. Indeed, considering that experiments lasted about one hour over melting temperature (62 min for BaCarb1

and 42 min for BaCarb3) and that BaCO 3 liquid is observed over the entire 0.9-1mm thick olivine matrix on SEM images, leads to an average rate of 1mm/h for BaCarb1 and 1.35 mm/h for BaCarb3.

Not surprisingly, this estimate is significantly lower than the in situ measurements, highlighting, the need for in situ analyses. Where dt is the time interval between CT images, the cumulated carbonate volume within the slice (following values were obtained on ROI bases), and the volume of carbonate that passed through it.

BaCarb1 images depict the evolution of flow rate as a function of time as the temperature was constant at 890°C during all the experiment. Flow rates of 0 -13 8 1 3 (where subscript and exponent values correspond to the asymmetric errors), 1130 -3 8 8 and 0 -00 µm 3 /s were calculated between the 96s -176 s, 176 s -928 s, and 928 s -2904 s CT-images, respectively. This decrease of flow rates (Figure 8) shows that the melt impregnation became less effective with time. Conversely, in BaCarb3, temperature was increased by steps between each CT-imaging sequence. Each temperature step was associated with a boost in carbonate flow as evidenced by a quick slope increase of first cumulative curve of each series (Figure 7). Flow rates were thus calculated by difference between the first and last image of a sequence, giving flow rates of Those observed behaviours of flow rates are characteristic of capillary penetration and fluid transport through porous structures. Indeed, the progression of the wetting front and the decrease of flow rates with time reflect the typical diffusive behaviour of capillary flow (Washburn, 1921). Similarly, the increase in flow rates with temperature highlights the increased diffusivities (i.e. lower viscosities) of carbonate melts at high temperature.

Entities morphology

The evolution of the melt network during impregnation can be addressed by following carbonate entities' morphology. A sorting of BaCO 3 blobs as a function of their volumes (Figure 9) reveals a gradual rise in the number of blobs for each size-class and a larger representation of large blobs (> 12 500 m 3 ) over time, for both BaCarb1 & BaCarb3 runs. This gradual infill is consistent with an increasing saturation of porosity after the initial wetting of olivine grain boundaries by the melt front.

The melt flow is accommodated by a homogeneous growth of the melt pockets; as illustrated by the jump in pocket size-class, and the rise in small melt entities (< 1 250 m 3 ) previously under detection limit, between successive CT-images. The orientation of entities estimated from the dip angle relative to the X-Y plane do not show significant variations from the first to the last tomography, with preferred distribution at angles less than 50° as shown on rose diagrams (Figure 10). These morphological parameters are in agreement with the gradual saturation of the porosity network by BaCO 3 liquid.

Figure 10

Orientation analysis through time. Each rose diagram represents the cumulated evolution of the dip angle relative to the X-Y plane for an experiment. 90% of BaCarb1 and BaCarb3

entities have orientation value respectively under 48° and 51°.

Implication for carbonate liquid impregnation process

Knowledge of the location and transport of magmas in the deep Earth is an important step toward the understanding of geochemical and geodynamical processes at depths. It comes as primary importance for carbon-rich melt as carbonate magmas impact the deep carbon cycle, which remains highly debated. Those carbonate magmas have unique properties, clearly distinct from the widespread silicate liquids, coming from their unpolymerized ionic structure. Due to the weak cohesion of carbonate molecules, these magmas have low viscosities (<10 -2 Pa.s - Dobson et al., 1996;Kono et al., 2014). This high mobility is reinforced by wetting angles lower than 30° [START_REF] Hunter | [END_REF]) and a large buoyancy relative to surrounding mantle rocks (Dobson et al., 1996). Hence, these liquids are expected to form interconnected networks and to be efficiently extracted even at low melt fractions. On a chemical point of view, this large connectivity along grains implies an important exchange surface that makes them highly reactive agents (Green & Wallace, 1988).

Melt migration is often studied regarding buoyancy forces and external pressure gradients. However capillary forces and associated surface tension effects can also drive magma displacement over geologically relevant distances, particularly for low viscosity fluids (Stevenson, 1986). As revealed by our experiments, capillary forces caused the molten carbonate to infiltrate the polycrystalline olivine.

Melt migrated from high concentration areas (close to the carbonate source layer) to lower concentration areas, as illustrated in Figure 11. This spatial variation in the melt fraction give rise to a gradient in the effective pressure of the melt, thus providing a thermodynamic driving force for melt migration.

Figure 11

Representative sections of CT reconstructions over cycles #1 #2 #3 of BaCarb1

showing the progressive infill of the polycrystalline olivine (dark grey areas) by the carbonate melt (in white and light grey). The SEM image of the same section on the quench shows a complete wetting of the porosity with submicron carbonate films surrounding olivine grains. Considering the spatial resolution of CT only the large melt blobs are identified, nevertheless they can be tracked in-situ with a time-resolution of few seconds for dynamics studies.

Kinetics of melt infiltration estimated from the time-lapsed CT-images (Figure 8) exhibit the diffusive dynamics of capillary flow with a decrease of flow rates with time, and a positive dependence on temperature. The observed vertical infiltration rates of 5.3 -5.9 mm/h confirm the high mobility of carbonate liquids relative to silicate ones, as already pointed out by Hammouda & Laporte (2000). For comparison, Watson et al. (1982) reported infiltration rates of  0.05 mm/h for basaltic silicate liquids under ~1 GPa ~1300 °C, i.e. about two orders of magnitude slower. The present infiltration rates are slightly faster than the value of 2.5 mm/h reported by Hammouda & Laporte (2000) on sodium carbonate impregnation through a synthetic dunite. This may arise from the time resolution of the present in situ measurements that enables to capture the fast initial propagation front, while the infiltration rate is averaged over the duration of run in quench experiments of Hammouda & Laporte (2000). Differences in initial porosity, and carbonate melt chemistry (BaCO 3 vs Na 2 CO 3 ) may also have a significant effect.

The choice of BaCO 3 carbonate as starting material was dictated by the need to enhance the X-ray absorption contrast of the liquid with the olivine matrix. Nevertheless this led to a carbonate liquid in strong disequilibrium with solid crystals, and hence to potential chemical exchanges between the BaCO 3 melt and the matrix during the flow. This chemical reactivity was indeed observed on CTimages as rims of bright voxels surrounding specific grains (5-10 grains by average in each ROI)

subsequently identified as pyroxene impurities on SEM images. Figure 12 shows the tracking of such a reaction rim and its growth over time, and highlights the fast kinetics of chemical reaction occurring at a time scale comparable with the melt flow. This points to the need of building reactive transport models for carbonatite migration in order to address the interplay between chemical reaction and the physics of melt transport. In this perspective, the extent of 4D microtomography imaging (e.g. Dobson et al., 2016) to extreme conditions opened by the UToPEc device offers an ideal approach for imaging these mass exchange processes. Though the spatial resolution is currently limited to 4 -5m, which is significantly lower than the one achieved with electron imaging, and depends on the absorption contrasts within the studied material (Figure 11); it allows in situ observations with an unprecedented time-resolution for a quantitative understanding of reactive transport.

Figure 12

Tracking of the reaction rim surrounding a pyroxene grain in sample BaCarb1. Each caption represents the state of the process at a given time. Conditions are given in upper left corner.

Conclusion

Here, we reported the experimental set-up developed at the PSICHE beamline of SOLEIL to perform high-speed XCT in the Ultra-fast Tomography Paris-Edinburgh cell (UToPEc) up to extreme conditions of 10 GPa and 2000 K. We provided a workflow for the acquisition, visualisation and quantification of CT-scans, accounting for the specificity of working in a high-pressure and temperature environment, and showed that alignment of time-lapsed CT reconstructions allows investigation of 3D volumes, morphological statistics, and entity tracking through time. We illustrated the potential of this 4D tomography technique through the example of magma impregnation, which we were able to capture the capillary infiltration dynamics, under conditions of 2GPa and T>800°C, with micrometric resolution and characteristic times of few seconds as we tracked the melt propagation front and the gradual porosity filling, as well as fast chemical reactions. This breakthrough in 4D tomography open new perspectives to explore the dynamics of phase transformations, reaction kinetics and microstructures, as well a porosity flows under extreme conditions.

Figure 1

 1 Figure 1 UToPEc setup used in parallel pink beam XCT configuration and PE assembly with "sandwich" configuration starting sample.

Table 1

 1 Summary of experimental conditions and data acquisition. LT abbreviation is for latency time corresponding to the delay time in between cycles. Duration corresponds to the total amount time above melting point. Cycle of 12 and 15 tomographies last over ~3 min and ~4 min, respectively.

Figure 3

 3 Figure 3 Visualization of the X-ray CT data. (a) View of the BaCarb1 subvolume. (b) Representative tomography slice of the olivine polycrystals impregnated by BaCO 3 (bright area). (c) Histogram of grey scale values of the 1100x1100x325µm subvolume within the polycrystalline matrix (see squared area in (b)). Representative grayscale values of "olivine" and "carbonate" are figured. (d) Segmented carbonate blobs after hysteresis thresholding. Position and shape properties of each entity are computed. (e) Only coloured entities are studied.

  The time resolution of 16s between successive tomographies enables a real-time monitoring of porosity impregnation by BaCO 3 liquid, which starts soon after carbonate melting. A simple way to quantify this flow is to track the migration front, i.e. the maximal height where fluids are detected along the z-axis, for each CT-image. To further estimate the 3D volumetric distribution of liquid over time, the carbonate voxels for each slice were summed along the z-axis. The obtained cumulative curve (Figure4) depicts the contribution of each z-slice on the total amount of liquid. If a linear relation is observed, then the carbonate input is constant regardless of the vertical position in the sample, and the slope provides a volumetric flow rate.

Figure 4

 4 Figure 4Quantification of flow dynamics, counting every segmented voxel within the cylindrical ROI (dashed line) and studying its cumulative curve for one µCT. Both tomography slices illustrates the quantity of counted voxels (considering the 1.47 µm 3 voxel size, 2820 voxels correspond to ~9000

Figure 5

 5 Figure 5 Example of object based analysis. Upper left figure represents a carbonate entity from BaCarb3 sample. Its length can be visualised along the white arrows, its thickness along grey ones. Its dip is measured in the orthogonal system defined by the subvolume -Lower left figures illustrate its morphological evolution over time as tracked by time-lapsed CT-scans -On the right, graphs show the evolution of studied geometrics parameters along the three different temperature cycles. The increase in length and thickness of the particle depicts the growing volume of melt over time, while the dip angle and flatness parameters of the particle remain more or less constant.

Figure 6

 6 Figure 6 Visualisation of the carbonate melt impregnation front in sample BaCarb1. Vertical projections of cylindrical ROI are represented for eight tomographies over time. The carbonate source is located at the image bottom. With time, melt blobs are more numerous and located further from the initial layer. The plot on the right shows the distribution (arbitrary unit) of voxels segmented as carbonate along the ROI. Once a porosity is filled the elongation, flatness and dip of the associated pocket remain relatively constant over time, as its volume grows.

Figure 7

 7 Figure 7 Cumulative curves of carbonate voxels measured for each CT-image of successive cycle #1 (in orange), #2 (in blue) and #3 (in green) for both samples BaCarb1 and BaCarb3. In one cycle curve colours go from bright to dark as times increases. Uncertainties are by an envelope for one tomography (in black) for each cycle.

  s for cycle 2 at 955°C and 3 0 -1 83 µm 3 /s for cycle 3 at 1040°C. As expected, the flow rates increase with increasing temperature, but not linearly since the porosity is getting filled during cycles.

Figure 8

 8 Figure 8 Volumetric flow rates calculated at cylindrical ROI bottom from mass balance models.

Figure 9

 9 Figure 9 Repartition of carbonate entities in volume categories (as coloured labelled) as a function of melt content increase during experiment.

Acknowledgements

The UToPEc ongoing development program is supported by DIM OxyMORE Île de France, Synchrotron SOLEIL, and a CNRS-MITI grant. We thank G. Hamel, A.

Prat and G.Morard for their collaboration on this project.


J P Perrillat

R Bonjan

Y Le Godec

F Bergame

J Philippe

M Mezouar

G Garbarino

A King

N Guignot

A new high-pressure technique for the measurement of low frequency seismic attenuation using cyclic torsional loading

We report a new technique for torsional testing of materials under giga-pascal pressures, which uses a shearing module in a large volume Paris-Edinburgh press in combination with highresolution fast radiographic X-ray imaging. The measurement of the relative amplitude and phase lag between the cyclic displacement in the sample and a standard material (Al2O3) provides the effective shear modulus and attenuation factor for the sample. The system can operate in the 0.001 to 0.01 Hz frequency range, and up to 5 GPa and 2000 K; although hightemperature measurements may be affected by grain growth and plastic strain. Preliminary experimental results on San Carlos olivine are in quantitative agreement with previously reported Q -1 factors at lower pressure. This cyclic torsional loading method opens new directions to quantify the viscoelastic properties of minerals/rocks at seismic frequencies and in pressure-temperature conditions relevant to the Earth's mantle, for a better interpretation of seismological data.

INTRODUCTION

The Earth's materials are viscoelastic solids characterized by a continuous change from elastic behavior at high frequencies and/or low temperatures to viscous behavior at low frequencies and/or high temperatures (e.g. Jackson, 2008). This anelastic behavior of rocks is evidenced by seismic attenuation that manifests through the decrease in amplitude and energy of seismic waves as they propagate inside the Earth (e.g. [START_REF] Aki | Quantitative Seismology, theory and Methods[END_REF]. This viscoeleastic relaxation is responsible for dispersion, i.e. the frequency dependence, of seismic wave velocities. It is generally quantified in seismology by the quality factor Q (or its reciprocal loss factor Q -1 ) defined as Q = 2E/E, where E is the energy of seismic wave and E is the energy change per cycle [START_REF] Knopoff | Q[END_REF]. The relaxation processes in rocks are controlled by the temperature, composition, grain size, melt/volatile content, and a number of other physical and chemical factors of the rocks (e.g. [START_REF] Karato | Defect microdynamics in minerals and solid-state mechanisms of seismic wave attenuation and velocity dispersion in the mantle[END_REF][START_REF] Cooper | Seismic Wave Attenuation: Energy Dissipation in Viscoelastic Crystalline Solids[END_REF]Jackson, 2008). For this reason, seismic attenuation is a potential rich source of information about the Earth's interior, complementary to seismic velocities. Over the last decade, seismologists have made striking progress in mapping seismic attenuation, parametrized in terms of the quality factor Q, either at the regional [START_REF] Stachnik | Seismic attenuation and mantle wedge temperatures in the Alaska subduction zone[END_REF][START_REF] Pozgay | Seismic attenuation tomography of the Mariana subduction system: implications for thermal structure, volatile distribution, and slow spreading dynamics[END_REF] or global scale [START_REF] Gung | Q tomography of the upper mantle using three component longperiod waveforms[END_REF][START_REF] Adenis | Attenuation tomography of the upper mantle[END_REF]. However, attempts to translate Q values into meaningful quantitative physico-chemical parameters have been hampered by the lack of experimental data on the anelasticity of rocks at the relevant high pressure-temperature (P-T) conditions and low frequencies of teleseismic waves (mHz-Hz).

Laboratory measurements of attenuation Q -1 involves cyclic-loading methods that measure the dynamic mechanical response of a material to an applied stress (e.g. [START_REF] Guéguen | Introduction to the physics of rocks[END_REF]. These involve either axial or torsional forced-oscillation tests, where the sample and an elastic standard of known modulus and negligible dissipation are connected in series and subjected to a low-frequency sinusoidal time varying stress. For the elastic standard the resulting strain is in phase with the applied stress with an amplitude inversely proportional to its elastic modulus. Similarly, for the investigated sample, except that its viscoelastic behaviour is manifest in a phase lag () of strain behind stress. Thus the measurement of the relative amplitudes and phases of the cyclic displacements in standard and sample provides the elastic modulus, and the strain energy dissipation (Q -1 = tan()) respectively, for the sample.

The measurements must be performed in the linear domain (i.e. where the stress response is linearly proportional to strain) so that the elastic modulus and internal friction Q -1 are independent of strain amplitude. The upper limit of strain in the linear region depends on materials, for example, 10 -2 for alumina [START_REF] Ota | Anelastic and plastic relaxation in polycrystalline alumina and singlecrystal sapphire[END_REF]. Therefore, for mm-size sample, the displacement strain to be observed is usually of the order of few microns.

Torsion pendulum devices have been successfully applied at high-temperature and room pressure to explore the anelastic properties of minerals (Guéguen et al., 1981, Gribb and[START_REF] Gribb | Low-frequency shear attenuation in polycrystalline olivine: grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology[END_REF], and solid or partially molten rocks (Berckhemer et al. 1982, Bagdassarov and[START_REF] Bagdassarov | Frequency dependent rheology of vesicular rhyolite[END_REF]. However, these early measurements suffered from the creation of porosity through thermal microcracking and the complex behavior of interfaces within the experimental assembly. To overcome these limitations, [START_REF] Jackson | A high-pressure high-temperature apparatus for studies of seismic wave dispersion and attenuation[END_REF] implemented the forcedoscillation technique in an internally heated gas-charged pressure vessel. In this device, a pair of electromagnetic drivers housed within the pressure vessel provides for the generation of the This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. torque, and the twist of the assembly is measured above and below the elastic standard by pairs of parallel plate capacitance transducers. The frequency-dependence of the shear modulus and dissipation has been determined in this device in a variety of polycrystalline materials like olivine [START_REF] Jackson | Grain-size-sensitive seismic wave attenuation in polycrystalline olivine[END_REF], MgO [START_REF] Webb | Anelasticity and microcreep in polycrystalline MgO at high temperature: an exploratory study[END_REF] or titanate perovskites [START_REF] Webb | Viscoelasticity of the titanate perovskites CaTiO3 and SrTiO3 at high temperature[END_REF]. However, the maximum accessible pressure within this device is 0.3 GPa, which is a major limitation to the application of attenuation data to the Earth's mantle.

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The effect of pressure on a general anelastic response is manifested by an activation volume that might be significant at giga-pascal pressures. Furthermore, pressure commonly induces structural changes in minerals which act to modify mechanical properties, both elastic and anelastic. Such properties clearly need to be understood at the high P-T conditions of stability of the phases involved. The challenge in applying the cyclic loading method in the giga-pascal pressure domain is the need of a technique for measuring stress and strain with sufficient precision, and with sufficiently short measurement time, while the sample is embedded in a high-pressure vessel. Recently, several studies demonstrated these difficulties can be overcome by the use of synchrotron radiography. [START_REF] Li | Effect of phase transitions on bulk dispersion and attenuation: implications for the earth[END_REF] and [START_REF] Yoshino | Short-period cyclic loading system for in situ Xray observation of anelastic properties at high pressure[END_REF] reported axial-forced oscillation measurements of Q -1 for San Carlos olivine specimen up to 5 GPa and 2000 K in the D-DIA, a large-volume press with capabilities of advancing / withdrawing the top and bottom rams. Change of strain and elastic properties with time is directly observed by X-ray radiography at a specific oscillation frequency. Use of synchrotron X-ray gives an opportunity to determine not only strain but also confining pressure and phase identification. A limitation of this axial-loading method is that it provides the Young's modulus (E). The shear modulus (G) must be converted from the measured Young's modulus using a value for the bulk modulus (K) or the Poisson's ratio () either assumed or from literature data, and the following equations: G = 3.K.E / (9K-E) or G = E / 2.(1+), respectively.

As an alternative, we developed a new high-pressure technique to directly measure the shear modulus (G) dispersion and shear attenuation (QG -1 ) by cyclic torsional loadings [START_REF] Jackson | Progress in the experimental study of seismic wave attenuation[END_REF]. In this paper, we fully describe the experimental set-up that combines a Paris-Edinburgh press with rotating anvils capabilities and synchrotron X-rays. We detail the technical and analytical protocol to determine the anelastic properties from the X-ray monitoring of the sample/standard strain, and discuss the attenuation factor resolution this method can resolve at high P-T and low frequencies. To demonstrate the potential of this new technique, we present a pilot study on strain energy dissipation in polycrystalline San Carlos olivine.

EXPERIMENTAL METHODS

The forced-oscillation high P-T device

To perform the forced-oscillation mechanical testing under high P-T conditions we modified a Paris-Edinburgh cell, a large-volume press based on opposed anvil geometry [START_REF] Besson | Neutron powder diffraction above 10-GPa[END_REF], to allow for the controlled rotation of the top or bottom anvil under load.

Using an X-ray transparent gasket, this geometry offers a large window in the equatorial plane for the in situ radiography and diffraction measurements. A detailed mechanical description of this so-called RoToPEc device (for Rotational and Tomography Paris-Edinburgh cell) has been given by Philippe et al. (2016). A schematic drawing is shown in Figure 1. In brief, the two opposed anvils can rotate independently under load, with no limitation in the rotation angle, through two sets of gear reducers and thrust bearings located at the end of each anvil. The accurate rotation of the anvils is monitored by stepper motors and encoders, with an angular resolution of 0.02°. After pressurization, a sinusoidal stress and strain can be produced on the assembly by rotating the top anvil while the bottom one is held fixed. A Labview software allows to configure the desire sine wave profile by defining the rotation amplitude (in degrees), period (in seconds) and number of cycles. A frequency range from 0.001 to 0.01 Hz and a rotation amplitude from 1 to 5 degrees have been tested so far, and produced resolvable strain on the sample. This cyclic torsional loading system can operate up to 5 GPa and 2000 K for millimeter-size sample (using 10 mm boron-epoxy gasket with tungsten carbide anvils), the main limitation to operate at higher pressure being the reduction of the X-ray window due to the gasket flow under high P-T.

Cell assembly

The configuration of the cell assembly used for the forced-oscillation measurements is shown in Figure 2. It consists of a biconical boron epoxy gasket of outer diameter of 10 mm and a cylindrical graphite furnace, both transparent to high-energy X-rays. To ensure a transmission of the torque and avoid slippage at interfaces, the sample and elastic standard are directly stacked in between two MgO rods. The sintered polycrystalline specimen and the elastic reference, a dense Al2O3 rod (Alfa Aesar TM Al23), are 0.5-0.8 mm in length and 2.9 mm in diameter, both prepared with flat faces polished to mirror quality to be perfectly parallel. The length of MgO rods is adjusted to place the sample and reference material in the center of the X-ray window. A tungsten rod (=90 m) is positioned vertically along the outer diameter of the sample/Al2O3 for measuring the twist angle by X-ray absorption. The tungsten rod is actually inserted in a thin groove, made with a diamond file, along the sample/Al2O3 cylinder, to ensure a good mechanical coupling between the rod, the sample and the elastic standard.

Gold wires (=25 m) are also placed on the top and bottom sides of the sample and alumina reference to measure their lengths during the cycling torsional loadings. The pressure on the sample is derived from the MgO unit-cell volume measured using X-ray diffraction along with the thermoelastic data of [START_REF] Speziale | Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volume-temperature equation of state[END_REF]. Temperature is estimated by a powertemperature relation curve determined in a previous experiment using a thermocouple and identical cell configuration.

In situ strain measurements

The force-oscillation technique relies on the time-resolved measurement of the twist angles of the sample and elastic reference in response to the sinusoidal imposed torque. The attenuation factor (QG -1 ) of the sample is determined from the phase lag of strain relative to the standard, while the strain amplitude ratio provides a comparative determination of the effective shear modulus (G). A difficulty of the technique is that, in order to be independent of strain amplitude (i.e. in the linear viscoelastic domain), extremely small strain variations as 10 -3 to 10 - 6 depending on the investigated material need to be detected. The use of synchrotron X-ray radiography gives the opportunity to monitor such small displacements, with high precision (micron to sub-micron) and at short periods, by following the motions of strain markers.

In practice, a large X-ray beam illuminates the cell assembly through the transparent gasket. The absorption contrast between the assembly parts, sample, Al2O3 reference, and strain markers is converted into visible light by a phosphorous YAG single-crystal set in the transmitted beam on the downstream side of the press. A 45° mirror reflects the visible contrast into a high-speed CCD camera, and the image is focused by an objective lens (Figure 1). In this study, measurements have been obtained during two sessions performed at beamline ID27 of ESRF (Mezouar et al., 2005) and beamline PSICHE of Synchrotron SOLEIL [START_REF] King | Tomography and imaging at the PSICHE beamline of the SOLEIL synchrotron[END_REF]. At ID27, the monochromatic 33 keV beam has a field of view of 2.0 and 2.7 mm in the vertical and horizontal directions, respectively. The CCD camera is a CoolSNAP HQ2 (Photometrics) which allows the acquisition of 745 x 413 pixel images at time intervals down to 100 ms. The magnification of the imaging system leads to a pixel size of 2.2 m. At PSICHE, a pink beam with an average energy of 45 keV is collimated to 2.5 mm and 4.5 mm in the vertical and horizontal directions, respectively. The objective lens of a Hamamatsu ORCA Flash4.0 sCMOS camera gives an effective pixel size of 2.45 m. For a region of interest of 1500 x 900 pixels the acquisition time can achieved 10 ms.

The experimental protocol is first to cold compress the cell to the target pressure. Due to compaction of the assembly parts, the strain markers may then appear deformed or tilted on the X-ray image, but without effect on the further strain monitoring (Figure 2). Afterward, temperature is raised by steps, and oscillations are applied according to the sine wave profile configuration. The usual settings for torsional loadings are 1 to 5 degrees for the top anvil rotation, over 100 to 1000 s sine wave period, and between 5 to 20 successive cycles.

Meanwhile, radiographic images are recorded at high frequencies, producing an image sequence of thousands of frames that traces the motion of the sample/alumina strain markers as a function of time.

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Estimation of anelastic properties

The image sequence is analyzed with an automated ImageJ routine that outputs the sinusoidal curves of the twist angle of the sample (s) and reference (ref) as a function of time, during the cyclic loading. The image processing scheme is depicted in Figure 3. It first includes, for each frame, the determination of the horizontal offset of the tungsten rod in the sample (ws) and reference (wref) obtained by fitting a Gaussian function along the absorption profile. The round shape and the diameter of 90 m of the tungsten generate a strong absorption signal on the X-ray images which helps this profile fitting. The offset defines sine waves of few pixels amplitude superimposed to a non-linear baseline that is further subtracted by a second order polynomial fit. This non-linear motion comes from a translation of the whole assembly relative to the X-ray beam as a result of gasket extrusion. The lengths of the sample (ls) and reference (lref) as defined by the location of the gold wires markers are also measured. Actually, we did not observed any resolvable change in lengths whatever the rotation angle of the anvils, meaning that the applied torque generates only simple shear. The twist angles of the sample and reference are then calculated according to s = atan (ws/ls), and ref = atan (wref/lref), respectively.

These two curves are finally fitted to a sinusoidal equation s(ref) = As(ref) sin (t + s(ref)) where

A is the amplitude, t is time, and  is a phase angle. The shear attenuation factor (QG -1 ) is determined from the phase angle lag s-ref between the sample and reference according to QG - 1 = tan(). The shear modulus is obtained from the Aref/As amplitude ratio and the elastic modulus of the reference material. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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RESULTS AND DISCUSSION

Calibration of the forced-oscillation apparatus

In order to check the integrity of the present forced oscillation technique, it is necessary to investigate any contamination of the relative amplitudes and phases of the twist angle sinusoids. Potential sources of errors include (i) any mechanical interaction between the specimen/standard set and the boron-epoxy pressure medium, (ii) sliding along the MgO rods, specimen and standard interfaces, or (iii) some image artefacts affecting the location of strain markers. We therefore conducted initial tests at the ESRF synchrotron in which the specimen was replaced by a cylinder of Al2O3 of the same composition and dimensions as the one used for the elastic standard. We carried out two sets of measurements under 3.1 GPa pressure, at ambient temperature and 800°C, respectively. For each P-T point, the mechanical testing was performed at conditions of 2 degrees rotation angle -200 s period, and 1 degree rotation angle -100 s period.

The twist angle versus time curves are shown in Figure 4. The values of the twist angles for the top and bottom Al2O3 rods correspond to a 10 -3 magnitude of strain. These twist angles are consistent with the expected amount for the 2 degrees torsion of a 6.5 mm long assembly (i.e. the length of the sample plus reference and MgO rods); meaning that the rotation of the anvils is transmitted to the sample assembly with no loss at the anvil-gasket interface. For some runs, the position of both the top, middle and lower interfaces exhibit some non-sinusoidal spikes (see Figure 3c) that translate into similar artefacts on the twist angle curves (Figure 4). These features are reproducible over cycles which seems to rule out an origin from sliding on an interface. Instead, they appear to be somehow associated with reversing direction of rotation, being more pronounced whit increasing load, when the rotation angle is larger or when the oscillating period is longer, so that we suspect some slack in the gearbox to be their cause.

Being reproducible, these parasitic motions do not significantly affect the sine wave fitting of the twist angle curves, and hence the determination of the QG -1 and G parameters. In all runs, the top and bottom Al2O3 sinusoids are in phase with amplitude ratio close to one, providing compelling evidence that there is no compliance associated with the interfaces, nor any significant effect of the pressure medium and/or graphite furnace. These findings validate the synchrotron imaging method to quantify oscillation strain and the image processing scheme to retrieve the mechanical properties. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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Preliminary measurements on San Carlos olivine aggregates

To demonstrate the capabilities of the present forced-oscillation technique, we carried out experiments on San Carlos polycrystalline olivine. This phase is one of the most abundant minerals in the mantle, so that the knowledge of its elastic and anelastic properties are critical parameters to understand and model the Earth's interior. Several previous studies have investigated the viscoelastic behavior of olivine both under ambient (Guéguen et al., 1989;[START_REF] Gribb | Low-frequency shear attenuation in polycrystalline olivine: grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology[END_REF] or high pressures [START_REF] Jackson | Grain-size-sensitive seismic wave attenuation in polycrystalline olivine[END_REF]Li and Weidner, 2007;[START_REF] Yoshino | Short-period cyclic loading system for in situ Xray observation of anelastic properties at high pressure[END_REF] to compare with our preliminary measurements. The starting material consisted of natural San Carlos (Fe0.1Mg0.9)2SiO4 crystals, powdered and hot-pressed at 4 GPa -1000°C for 24 hours to achieve a fine 1-10 m grain size and a low porosity. Cylindrical samples, respectively 0.48 mm in length and 2.9 mm in diameter were loaded in series with the Al203 (Alfa Aesar TM -Al23) reference. In a first loading, the cell assembly was cold compressed and then heated by steps at 1020 K, 1380 K and 1490 K for the mechanical tests. In a second loading, pressure was first increase to 1.6 GPa at 300 K, with subsequent heating at 1130 K, 1430 K and 1560 K. For all P-T points, the forced-oscillation measurements were performed at This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Figure 6 displays the twist angle vs. time curves for each P-T point, and the fits to sinusoids for the olivine and alumina reference. Figure 7 shows an enlarged view of these curves for the 0.9 GPa -1380 K data, as well as the corresponding plot for the specimen twist angle against the alumina reference. In such a graph, the deviation from linearity, i.e. the appearance of an elliptic shape, is a manifestation of anelasticity, and the surface of this loop represents the amount of energy dissipated (e.g. [START_REF] Tisato | Attenuation at low seismic frequencies in partially saturated rocks: Measurements and description of a new apparatus[END_REF]. The twist angle vs. time curves show the presence of a visible phase lag, and hence attenuation, for temperatures above about 1300 K, along with a marked decrease of the shear modulus. This dispersion of the modulus results from the increase of shear attenuation with temperature.

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The attenuation factors (QG -1 ) obtained at 0.9 GPa -1380 K and 1.6 GPa -1430 K fall within the range of previous estimates for olivine at ambient and high pressures (Figure 8) using either axial or torsional loading techniques [START_REF] Gribb | Low-frequency shear attenuation in polycrystalline olivine: grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology[END_REF][START_REF] Tan | High temperature viscoelasticity of fine-grained polycrystalline olivine[END_REF][START_REF] Jackson | Grain-size-sensitive seismic wave attenuation in polycrystalline olivine[END_REF][START_REF] Yoshino | Short-period cyclic loading system for in situ Xray observation of anelastic properties at high pressure[END_REF]. The temperature dependence of attenuation for the present 0.005 Hz measurements is in broad agreement with literature data obtained at 0.01 Hz on polycrystalline olivine; although a more precise comparison would require to investigate in details the grain size and frequency dependence of the attenuation. We could not determine the This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0055549 attenuation for temperature beyond 1430 K since the strain curves did not follow anymore the sinusoidal torsion imposed by the anvils. This may point to the onset of plastic strain in the sample or alumina, or any sliding at interfaces. Grain growth is also efficient at high temperature and may affect the attenuation factor for samples where the strain energy dissipation is controlled by grain-boundary sliding processes. These preliminary data demonstrate that forced-oscillations in the RoToPEc device combined with synchrotron X-ray imaging is an effective method to study the anelastic properties of materials under extreme conditions, and quantify the effect of temperature, pressure, frequency and grain size on energy dissipation. To date, this method can operates up to 5 GPa within a frequency range from 0.001 to 0.1 Hz. The magnitude of strain achieved is about 10 -3 while the upper limit of strain to stay in the linear regime domain may be as low as 10 -4 for some minerals (Guéguen et al., 1989). Further developments to achieve 10 -4 strain will involve the increase of sample length, the reduction of rotation angle and improvement of Xray radiography resolution. The use of sintered diamond anvils and/or toroidal gaskets (Kono et al., 2015) will also enlarge the X-ray window available for CT imaging in order to expand the technique to higher pressure. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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  DOI:10.1063/5.0055549

Figure 1 -

 1 Figure 1 -3D view of the 450 ton V7 Paris-Edinburgh press with the RoToPEc module, and picture of its installation on beamline ID27 of the ESRF.

Figure 2

 2 Figure 2 -(left) Cell assembly used for the forced-oscillation measurements, and (right) representative X-ray radiograph through the sample and alumina standard. Highly absorbing features are the gold and tungsten strain markers.

Figure 3 -

 3 Figure 3 -Principle of the forced-oscillation technique to measure strain energy dissipation. (a) Schematic drawing of the motion of the strain markers during oscillation, and (b) corresponding X-ray radiograph from which the position of the gold foils and tungsten rod are monitored over time. (c) Position of the W rod marker as a function of time (i.e. image number) at the sample and alumina interfaces, and (d) estimated twist angle in degrees for the alumina reference and sample. Represented data are from an olivine specimen and alumina reference at 0.9 GPa and 300 K (see below).

  DOI:10.1063/5.0055549

Figure 4 -

 4 Figure 4 -Twist angle vs. time curves for Al2O3-Al2O3 test experiments at 3.1 GPa and 300 K-1173 K, and 100 -200 s oscillation periods, respectively

  DOI:10.1063/5.0055549 conditions of 2 degrees rotation angle -200 s period, and X-ray images were recorded at 1 Hz. A SEM image of the recovered sample is shown in Figure 5.

Figure 5 -

 5 Figure 5 -Electron backscattered images of the sample charge after experiment showing (a) the assembly parts: MgO rod, Al2O3 reference, Olivine specimen, Gr. Graphite furnace; and (b) the microstructure of the olivine specimen with 1 -10 m grain sizes.

Figure 6 -Figure 7

 67 Figure 6 -Twist angle vs. time curves for the San Carlos olivine sample (green dots) and Al2O3 reference (orange dots) at specified PT conditions. The forced-oscillation were performed at conditions of 2 degrees rotation angle -200 s period. Attenuation factors (Q -1 ) and shear moduli (G) are determined from the phase lag and amplitude ratio estimated from the sinusoid fits to strain curves (dark green and red lines for the olivine sample and alumina reference fits, respectively).

Figure 8 Figure 1 -

 81 Figure 8 -(a) Attenuation factor (log QG -1 ) vs. temperature and (b) shear modulus (G) vs. temperature for olivine aggregates at frequency of 10 -5 mHz and pressures between 1 atm to 1.6 GPa, as determined by Gribb & Copper (1998) for 3 m grain-size Balsam Gap olivine, Tan et al. (2001) for 30 m grain-size San Carlos olivine, Jackson et al. (2002) for 3-12 m grain-size Fo90 olivine, Yoshino et al. (2016) for 3 m grain size San Carlos olivine, and the present study for 1-10 m grain-size San Carlos olivine

Figure 2 -

 2 Figure 2 -(left) Cell assembly used for the forced-oscillation measurements, and (right) representative X-ray radiograph through the sample and alumina standard. Highly absorbing features are the gold and tungsten strain markers.

Figure 3 -

 3 Figure 3 -Principle of the forced-oscillation technique to measure strain energy dissipation. (a) Schematic drawing of the motion of the strain markers during oscillation, and (b) corresponding X-ray radiograph from which the position of the gold foils and tungsten rod are monitored over time. (c) Position of the W rod marker as a function of time (i.e. image number) at the sample and alumina interfaces, and (d) estimated twist angle in degrees for the alumina reference and sample. Represented data are from an olivine specimen and alumina reference at 0.9 GPa and 300 K (see below).

Figure 4 -

 4 Figure 4 -Twist angle vs. time curves for Al2O3-Al2O3 test experiments at 3.1 GPa and 300 K-1173 K, and 100 -200 s oscillation periods, respectively.

Figure 5 -

 5 Figure 5 -Electron backscattered images of the sample charge after experiment showing (a) the assembly parts: MgO rod, Al2O3 reference, Olivine specimen, Gr. Graphite furnace; and (b)the microstructure of the olivine specimen with 1 -10 m grain sizes.

Figure 6 -

 6 Figure 6 -Twist angle vs. time curves for the San Carlos olivine sample (green dots) and Al2O3reference (orange dots) at specified PT conditions. The forced-oscillation were performed at conditions of 2 degrees rotation angle -200 s period. Attenuation factors (Q -1 ) and shear moduli (G) are determined from the phase lag and amplitude ratio estimated from the sinusoid fits to strain curves (dark green and red lines for the olivine sample and alumina reference fits, respectively).

Figure 7 -

 7 Figure 7 -(a) Detailed view of the twist angle vs. time curve for the olivine-Al2O3 reference at conditions of 0.9 GPa -1380 K and sinusoidal loading with period of 200 s; and (b) the corresponding hysteresis loop. The elliptic shape is a manifestation of anelasticity, and results in a Q -1 factor of 0.104.

Figure 8 -

 8 Figure 8 -(a) Attenuation factor (log QG -1 ) vs. temperature and (b) shear modulus (G) vs. temperature for olivine aggregates at frequency of 10 -5 mHz and pressures between 1 atm to 1.6 GPa, as determined by Gribb & Copper (1998) for 3 m grain-size Balsam Gap olivine, Tan et al. (2001) for 30 m grain-size San Carlos olivine, Jackson et al. (2002) for 3-12 m grain-size Fo90 olivine, Yoshino et al. (2016) for 3 m grain size San Carlos olivine, and the present study for 1-10 m grain-size San Carlos olivine.

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ACKNOWLEDGMENTS

We acknowledge the European Synchrotron Radiation Facility and Synchrotron SOLEIL for the allocation of beamtimes. We are grateful to S. Bauchau, H. Cardon, J.P. Deslandes, and S. Peuble for technical support during the experiments. This work was financially supported by the French 'Réseau Hautes Pressions', a CNRS-MITI grant 'Instrumentation aux limites', and the CNRS-INSU PNP program.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.