Julien Gasc
email: gasc@geologie.ens.fr

Sylvie Demouchy

Fabrice Barou

Sanae Koizumi

Patrick Cordier

Creep mechanisms in the lithospheric mantle inferred from deformation of iron-free forsterite aggregates at 900-1200 °C

Keywords: olivine, deformation, grain boundary sliding, upper mantle, high pressure

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The lithospheric mantle can be subject to temperatures as low as 500 °C. Experimental deformation of mantle rocks at such low temperatures is a major challenge in mineral and rock physics, since the strain rates necessary to achieve steady state dislocation creep are too low to be performed in the laboratory. Consequently, deformation experiments that provide insights into the "cold" rheology of olivine, are performed at high stresses without achieving geologically relevant steady state and the strain rate dependence is difficult to assess [START_REF] Druiventak | Low-temperature plasticity of olivine during high stress deformation of peridotite at lithospheric conditions -An experimental study[END_REF][START_REF] Mei | Experimental constraints on the strength of the lithospheric mantle[END_REF]. Typically, little to no rate-dependence is observed because it is impossible to activate ductile flow, which leads to seemingly large stress exponent values in the flow law [START_REF] Druiventak | Low-temperature plasticity of olivine during high stress deformation of peridotite at lithospheric conditions -An experimental study[END_REF].

For decades, the flow law of [START_REF] Evans | The temperature variation of hardness of olivine and its implication for polycrystalline yield stress[END_REF], which uses an exponential expression to account for the Peierls stress control over dislocation motion, has been used to model the lowtemperature rheology of the olivine-rich rocks composing the uppermost mantle. Nevertheless, recent experimental studies have shown that the uppermost mantle is likely much weaker than previously expected from extrapolations of high-temperature rheology flow laws to upper mantle temperatures (e.g., [START_REF] Demouchy | Experimental deformation of olivine single crystals at lithospheric temperatures[END_REF][START_REF] Burnley | The importance of stress percolation patterns in rocks and other polycrystalline materials[END_REF], 2014, Boioli et al., 2015a, 2015b;[START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF][START_REF] Gouriet | Dislocation Dynamics modelling of the power-law breakdown in olivine single crystals: toward a unified creep law for the upper mantle[END_REF].

A solution to these issues, is to identify the physical deformation mechanisms at play (e.g., dislocation slip systems) and to implement them in numerical dislocation dynamics models (Boioli et al., 2015a, 2015b[START_REF] Gouriet | Dislocation Dynamics modelling of the power-law breakdown in olivine single crystals: toward a unified creep law for the upper mantle[END_REF]. Although this approach gives valuable insights into single crystal plasticity, it does not fully describe the creep behavior of polycrystalline rocks, which may arise from a variety of interacting deformation mechanisms. Therefore, to grasp the complexity and better constrain the low-temperature rheology of mantle rocks, and despite the issues mentioned above, experiments on olivine aggregates are still needed.

The incorporation of iron, hydrogen and titanium in the atomic structure of olivine is known to induce a weakening effect (iron: e.g., [START_REF] Zhao | Effect of iron content on the creep behavior of olivine: 1. Anhydrous conditions[END_REF]Zhao et al., , 2018;;[START_REF] Bollinger | Deformation of forsterite polycrystals at mantle pressure: Comparison with Fe-bearing olivine and the effect of iron on its plasticity[END_REF][START_REF] Hansen | The influence of microstructure on deformation of olivine in the grain boundary sliding regime[END_REF] hydrogen: e.g., [START_REF] Mackwell | The role of water in the deformation of olivine single crystals[END_REF][START_REF] Mei | Influence of water on plastic deformation of olivine aggregates 2. Dislocation creep regime[END_REF][START_REF] Tasaka | Evolution of the rheological and microstructural properties of olivine aggregates during dislocation creep under hydrous conditions[END_REF][START_REF] Tielke | Hydrolytic weakening in olivine single crystals[END_REF]titanium: e.g., Faul et al., 2016;Cline II et al., 2018). To avoid adding complexity to the olivine plasticity due to its dependence upon point defects (i.e., vacancy concentrations), it was thus chosen here to restrict the deformation experiments to hydrogen-free, iron-free fine-grained forsterite-rich aggregates.

We used a two-phase aggregate material, mostly composed of forsterite (with minor amounts of enstatite), which has previously been used in several deformation studies at low pressure and high temperature, in the diffusion creep regime [START_REF] Tasaka | Influence of mineral fraction on the rheological properties of forsterite plus enstatite during grain-size-sensitive creep: 2. Deformation experiments[END_REF][START_REF] Nakakoji | Diffusion creep and grain growth in forsterite + 20 vol% enstatite aggregates: 1. High resolution experiments and their data analyses[END_REF]. The aim of the present study is to assess the creep mechanisms of this fully equilibrated fine-grained aggregate under conditions more relevant to the uppermost mantle, i.e., under significant confining pressure and colder temperatures. In particular, we focus here on a temperature range that encompasses the transition from power law flow (high temperature, T > 0.6 Tm, where Tm is melting temperature; for Fo100, Tm=1890 °C) to exponential law flow ("cold" temperature, 0.3-0.6 Tm). In addition to the mechanical data, the microstructures are analyzed with state-of-the-art techniques to provide valuable information regarding deformation mechanisms.

Materials and Methods

Starting material

The samples used in this experimental study were produced from synthetic nano-sized powders at the Earthquake Research Institute (Tokyo, Japan), following a sintering procedure previously described in details by [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF], which we only briefly outline here. Starting nano-sized powders of forsterite and enstatite were first synthesized from high purity SiO2 and Mg(OH)2, then pre-pressed into the desired cylindrical shape in carbide dies, and pressed under hydrostatic conditions at 200 MPa. The resulting cold-pressed specimens were then annealed under vacuum at 1260 °C for 2-3 hours, which yields a fully dense aggregate (< 1 % porosity) and ensures complete dehydration [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF]. The chemical composition of the starting material was analyzed by X-ray fluorescence with a Philips® PW 2400 spectrometer (see Supp. Mat. Table S1). Iron content is under 10 ppm. This new type of high-quality sintered aggregate has proven to be an excellent material for rheology studies [START_REF] Hiraga | Comparison of microstructures in superplastically deformed synthetic materials and natural mylonites: Mineral aggregation via grain boundary sliding[END_REF][START_REF] Tasaka | Influence of mineral fraction on the rheological properties of forsterite plus enstatite during grain-size-sensitive creep: 2. Deformation experiments[END_REF]. The microstructure of the starting material was characterized by scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The EBSD map in Figure 1 shows that the biminerallic aggregate is composed of pure forsterite with an average equivalent diameter of 2.8 µm.

It also contains ~2-3 % of orthoenstatite homogeneously distributed across the aggregate with a smaller grain size than forsterite (1.8 µm on average), which prevents it from impacting the bulk rheological properties [START_REF] Huet | The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data[END_REF][START_REF] Wang | Bulk flow strength of forsterite-enstatite composites as a function of forsterite content[END_REF]. The EBSD maps also provide statistical data on the microstructure, as reported in Table 1. The starting material shows equilibrated textures, with ubiquitous triple junctions and straight grain boundaries (Figure 1), as already described by [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF]. Due to the very fine grain size, initial porosity is difficult to assess from SEM images since it is difficult to differentiate between actual residual pores from sample sintering and newly formed cavities caused by grain plucking during cross section preparation. Nevertheless, porosity has been characterized in previous studies and is estimated to be significantly less than 1 % in volume [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF]. As observed on Figure 1, the grains are nearly equiaxed.

Their aspect ratio is found here to be 1.9, whereas previous studies using the same material have reported a value of 1.3-1.4 [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF]. The aggregate starting material has a measurable shape preferred orientation (SPO), most likely inherited from the cold press stage of the samples synthesis [START_REF] Koizumi | Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders[END_REF]. The samples used for deformation consisted in cylinders with diameters ranging from 4.5 to 4.8 mm, and lengths varying between 7.25 and 10.55 mm (Table 1).

Deformation experiments

Eight deformation experiments were carried out using a high-resolution gas-medium highpressure high-temperature apparatus [START_REF] Demouchy | Low strength of Earth's uppermost mantle inferred from tri-axial deformation experiments on dry olivine crystals[END_REF][START_REF] Demouchy | Viscoplasticity of polycrystalline olivine experimentally deformed at high pressure and 900 degrees C[END_REF][START_REF] Paterson | Rock Deformation Experimentation[END_REF][START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF] at Geosciences Montpellier (University of Montpellier, France). An additional static annealing test was carried out without deformation to assess the importance of grain growth during our experiments (NF_1000-0, Table 1). All experiments were performed under a confining pressure of 300 MPa using argon gas. Constant piston-displacement uniaxial deformation was performed under constant temperatures ranging from 900 to 1200 °C (Table 1). The samples were placed between alumina and zirconia pistons and fitted in metal sleeves (e.g., [START_REF] Mei | Influence of water on plastic deformation of olivine aggregates 2. Dislocation creep regime[END_REF][START_REF] Demouchy | Viscoplasticity of polycrystalline olivine experimentally deformed at high pressure and 900 degrees C[END_REF]. The nature of the metal sleeve was chosen depending on the temperature of each experiment, to avoid melting of the sleeve while keeping its strength as low as possible (Table 1). Silver, copper and nickel sleeves were used for experiments at <1000 °C, 1000-1050 °C, and >1050 °C, respectively (Table 1). All parts were encapsulated in an iron jacket thin enough to transmit the confining pressure.

Axial force values were obtained from an internal load cell during deformation. Flow laws for Cu, Fe, Ni, and Ag from [START_REF] Frost | Deformation mechanism maps: the plasticity and creep of metals and ceramics[END_REF] were used to determine the contributions of the iron jacket and the metal sleeve to the measured load. Sample stress as a function of time was then retrieved by calculating the evolution of the sample surface corresponding to a shortening with constant volume. Strain was corrected using the apparatus stiffness, which was calibrated beforehand (~83 kN mm -1 ). The stress-strain data were further processed (smoothed) to accurately identify the yield point and the apparent Young moduli at yield point (see Supp. Mat. for details, Figures S1 andS2).

For each experiment, constant displacement rate was set based on the initial length of the sample to yield a stress plateau with a strain rate of 10 -5 s -1 . All samples were deformed, at least, until the maximum stress was achieved. Below 1050 °C, axial shortening was stopped if a significant stress decrease-indicative of brittle failure of the sample-was observed. At temperatures > 1050 °C, a plateau with constant stress was obtained and more extensive deformation was performed. Finite strain ranged from 2.8 to 12.4 % (Table 1).

Scanning electron microscopy and electron backscattered diffraction

The recovered samples were kept in the metal sleeve and jacket and cross sections were cut either normal or parallel to the compression direction for SEM and EBSD. The sample sections were prepared using a standardized polishing protocol [START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF]. A final chemomechanical polishing step using colloidal silica on a vibrating plate was necessary to achieve a highquality polish for EBSD. The SEM and EBSD analyses were performed with a CamScan X500FE Crystal Probe equipped with an EBSD system at Geosciences Montpellier (University of Montpellier, France). The geometry of the Crystal Probe-EBSD was previously detailed in [START_REF] Demouchy | Forsterite to wadsleyite phase transformation under shear stress and consequences for the Earth's mantle transition zone[END_REF]. Operating conditions were 15-18 kV, ~6 or 10 nA (for exposure times of 48 and 24 ms, respectively) and a working distance of 24-25 mm. Low vacuum conditions (4 Pa of gaseous nitrogen), carbon coating and copper-carbon tape were used around the studied area to avoid charging of the specimen. Several EBSD maps were collected on each sample section, including on the starting material (undeformed), as well as on the statically annealed sample.

The dimensions of the area mapped by EBSD typically varied from a few tens to several hundreds of microns, which corresponds to hundreds to several thousands of grains, thus allowing satisfying statistical analysis in terms of grain size, shape grain and crystallographic orientation. The step size was set either to 0.2 or 0.4 µm depending on the size of the analyzed area.

The data were acquired using Oxford instrument's HKL Aztec2 software. Data were first processed to remove wild spikes (isolated pixels that have eight similar neighbors) and fill nonindexed pixels that had seven neighbors with identical orientations, then treated with the MTEX MATLAB toolbox [START_REF] Bachmann | Texture Analysis with MTEX -Free and Open Source Software Toolbox[END_REF][START_REF] Hielscher | A novel pole figure inversion method: specification of the MTEX algorithm[END_REF][START_REF] Mainprice | Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components[END_REF].

Grain boundaries are usually detected using a critical misorientation angle of 10-15° [START_REF] Mainprice | Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components[END_REF]. Here, grain boundaries were detected using a threshold misorientation angle of 13°.

Variations of this critical threshold angle between 10 and 15° does not impact the microstructure results significantly (see Supp. Mat., Table S2). Grains were filtered to a minimum of 1.44 µm 2 (i.e., 9 or 36 pixels, according to the step size). Similarly, subgrains were identified as neighboring pixels with misorientations of 2-13°. The density of the orientation distribution function was calculated using an axially symmetric de la Vallee Poussin kernel, with a half-width of 10° (bandwidth of 28 in spherical harmonic coefficients). Crystal preferred orientations (CPO) and texture J-index were calculated [START_REF] Bunge | Texture Analysis in Materials Science: Mathematical Methods[END_REF]. The texture J-index is a measurement of the texture strength calculated as the integral of the square of the orientation distribution function, and is calculated using one data point per grain to avoid overestimating the contribution of large grains [START_REF] Mainprice | Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components[END_REF].

Densities of pole figures were normalized to a uniform distribution and contoured at intervals of 0.06 × uniform.

Transmission electron microscopy

Transmission electron microscopy (TEM) was also used to characterize the microstructures after the deformation experiments. Three deformed samples (NF_950-1, NF_1050-1 and NF_1200-1) were selected for this investigation from which doubly polished thin sections (30 µm thick) were prepared. Sample NF_1200-1 was cut parallel to the deformation axis, and NF_950-1 and NF_1050-1 perpendicular to the deformation axis. They were glued on a Cu grid and ion milled at 5 kV under a low beam angle of 15° until electron transparency was reached. The foils were subsequently covered with a thin layer of carbon. TEM observations were carried out at the University of Lille (France) using a FEI® Tecnai G2-20 TWIN microscope operating at 200 kV.

Results

Mechanical data

The stress-strain curves from each deformation experiment are shown in Figure 2. Stress data for experiment NF_1110-1 appear noisier than other experiments due to a temporary grounding issue of the internal load cell during the deformation, which resulted in apparent stress fluctuations (Figure 2a). Maximum stresses range from 480 to 1870 MPa, for temperatures varying from 1200 to 900 °C, respectively. The mechanical values reported in Table 1 thus define an expected inverse dependence with increasing temperature. At temperatures ≤1000 °C, stress increases until it reaches a maximum, then starts decreasing upon further straining. Sample failure was observed for NF_900-1. For experiments NF_950-1, NF_1000-1 and NF_1000-2, deformation was stopped after observing a significant stress decrease, indicative of possible imminent failure. In contrast, at higher temperatures (>1000 °C), stress reaches a constant value (plateau) and samples could be further deformed in an apparent (quasi-) steady state. We note however, that, for all experiments, the stress increases above the confining pressure (> 300 MPa) and is upheld without immediate failure over non-negligible amounts of strain, i.e., several percent after apparatus stiffness correction.

From 900 to 1110 °C, yield stress values are close to ~600 MPa, regardless of temperature.

Yield stress is only significantly lower in experiment NF1200-1, performed at the highest temperature (Figure 2b). In contrast, aside from experiment NF1110-1, we observe a consistent decrease in the apparent Young modulus with temperature, from 112 GPa at 900 °C to 32 GPa at 1200 °C (Table 1).

Microstructures

Results from EBSD analyses on the deformed aggregates are summarized in Table 1. Average grain size, aspect ratio and shape factor (i.e., measured perimeter/perimeter of the circle with equivalent area) values obtained for the largest map in each sample, are shown as a function of finite strain and temperature in Figure 3. For the sake of readability, a full statistical report is provided in the supplementary material, where results from the two largest maps for each sample are given along with corresponding minimum, maximum and standard deviation values (Table S3).

We note that values of aspect ratio are somewhat larger than expected. This is attributed to a slight drift of the electron beam (often observed when working with non-conductive samples) when collecting EBSD maps, which results in a minor artificial elongation of the grains.

From the EBSD maps, average grain sizes of 2.7-3.3 µm are found. Therefore, both in the static annealing test NF_1000-0 and in the deformation experiments, grain size remains essentially unchanged from the value measured in the starting material. Only a slight decrease (-15 %) in grain size is observed in the deformed samples (Table 1, Figure 3). Nevertheless, one finds no correlation between grain size and temperature or strain over the entire data set (Figure 3), consistently with the results of [START_REF] Tasaka | Influence of mineral fraction on the rheological properties of forsterite plus enstatite during grain-size-sensitive creep: 2. Deformation experiments[END_REF], who reported only minor grain growth, even at temperatures as high as 1260 °C. Based on the low temperatures and short durations of the present experiments, static growth is therefore negligible here (Table 1, Figure 3). SEM images displayed in Figure 4, show the preservation of equilibrium texture features, such as triple junctions and straight boundaries in the samples deformed at 950-1000 °C. Visually, textures from samples deformed more extensively and at greater temperatures (1050-1200° C) show more curved grain boundaries (Figure 4g,h). This is confirmed by the values of shape factor and aspect ratio, which remain essentially unchanged, when compared to the starting material, for the samples deformed at 900-1000 °C, as well as for NF1110-1 (all of which experienced less than 10 % strain), but are slightly larger for the three samples deformed by at least 10 % strain at 1050-1200 °C (Table 1, Figure 3). In the low-temperature samples, many grain boundaries are open (Figure 4), a feature that seems much less common at 1000-1110 °C and which is not observed at 1200 °C.

In addition, at low temperature, many grains appear with strong topology in the SEM images (Figure 4b), which is due to out-of-plane motion (vertical offsets) between adjacent grains in the imaged plane. At 1050 °C, voids created by the opening of grain boundaries are still observed.

Typical cases where grains have slid relative to each other and created a void due to insufficient ductility of adjacent grains can be seen in Figure 4d.

In all samples deformed at 1050 °C and 1100 °C, grain boundaries are serrated in a pervasive way as shown in Figure 4. At 1050 °C, the scale of the serration (its wavelength) is at the limit of the observation capability of the SEM, i.e., in the order of tens of nanometers, at most. We note that, due to the relatively small scale at which this change occurs, it is not measurable in terms of shape factor (which increases with grain boundary tortuosity, Figure 3) since EBSD data are collected with much larger step sizes than the serration scale. Nevertheless, the wavelength of the serration seems to increase with temperature and decreasing stress; as also suggested by TEM images of samples NF_950-1 and NF_1050-1 (see below for details). At 1110 °C, the samples show no evidence of major grain boundary sliding but the serration of grain boundaries is ubiquitous and occurs at the scale of a few tens to hundreds of nanometers. Several large grains exhibit important intracrystalline contrast variations, typical of subgrain boundaries (Figure 4f). This results from distortions of the crystal lattice and/or from defect concentrations and therefore highlights active intracrystalline plastic deformation. At 1200 °C, all grain boundaries remained closed and many display incipient bulging, with wavy boundaries at the scale of hundreds of nanometers to a micron (Figure 4h). Neither gaping, nor grain boundary sliding is observed.

The distribution of the long-axis direction of the grains is shown in Figure 5. A strengthening of the initial SPO (i.e., present in the undeformed sample) is observed upon deformation (Figure 5 and Table S3). Indeed, the long-axis of the grains tend to align normal to the compression axis, which is the same as during the compaction stage of the samples, prior to sintering. We note that for samples NF_1110-1 and NF_1110-2, shortened by 12.4 and 5 %, respectively, the long axis orientation distribution is very similar, which implies that most of the SPO formed during the early stages of the axial deformation.

By definition, grain orientation spread (GOS) defines the variations in local crystallographic orientation inside a given grain. Therefore, in an ideal unstrained crystal lattice, GOS is theoretically nil and its actual value only reflects EBSD measurement uncertainty. This is the case for the undeformed samples, which have an average GOS of 0.2-0.21° (Table 1 andFigure 3). Larger GOS values can reflect plastic deformation due to the presence of internal strain heterogeneities of the crystal lattice, which can originate from residual elastic strains (although unlikely here, in the case of a free surface) or more generally from the presence of geometrically necessary dislocations (GND). In the EBSD maps, GOS increases with the amount of strain to reach a maximum of 1.375° at 1100 °C. The largest values are obtained for samples NF_1110-1 and NF_1050-1 (Figure 3), which reveal substantial intracrystalline plasticity. At higher temperature, increasing temperature seems to have the opposite effect since lower values of GOS (0.705°) were obtained for sample NF_1200-1, deformed by about the same amount (Table 1). A comparison between two EBSD maps collected on samples that have experienced different temperatures and finite strains is shown in Figure 6. Similar to undulose extinction in optical microscopy, Misorientationto-Mean (Mis2Mean), which represents angular variations in crystal orientation inside a grain relative to the grain's average crystallographic orientation, allows the spatial strain heterogeneity distributions of the crystal lattice to be visualized. When finite strain is the largest, Mis2Mean values, and therefore GOS, often exceed 5°, as evidenced by the brighter areas in Figure 6b, Mis2Mean values > 5° are more common in coarser grains, where subgrains often formed. We note that, in Figure 6a, yellow-saturated grains are a consequence of neighboring grains being incidentally positioned in crystallographically close orientations and therefore identified as single grains with large Mis2Mean values, whereas the actual maximum value is ~1°.

Pole figures obtained for the starting material, the annealing test and the deformation experiments are displayed in Figure 7 and show near-random crystal orientations, as pointed out by their very low J-indexes ranging from ~1.01-1.11. However, in many cases, analysis over a large number of grains (> 10,000) detected slight but meaningful deviations from a random distribution.

As expected, the starting material shows no significant CPO. Samples deformed from 900 to 1000 °C experienced small amounts of finite strain and do not show any significant CPO either.

Only sample NF_950-1 displays a possibly meaningful pattern, where the [001] axis forms a girdle normal to the compression axis. This very weak CPO pattern may also be present in other samples but was probably only detected in NF_950-1 due to the large EBSD map size, which allowed better statistics (over 14,000 grains analyzed). We note, indeed, that J-indexes are consistently higher for smaller EBSD maps, which is an artifact of poorer statistics generating greater local maxima. In the present case, the very weak texture described above was likely present in the sample prior to deformation and preserved due to very low finite strain.

In contrast, three out of four samples deformed between 1050 and 1200 °C (≥ 10 % strain), NF_1050-1, NF_1110-1 and NF_1200-1, show a weak CPO characterized by an alignment of the [010] axis parallel to the compression direction. The distribution of [001] axes defines a girdle normal to the shortening direction in NF_1050-1, whereas it displays maxima at ~45° of the shortening direction in NF_1110-1, and is nearly random for NF_1200-1. Similarly, [100] axes have local maxima at 45° of the compression direction in NF_1050-1 and NF_110-1. We note that these features appear fainter for sample NF_1200-1. In addition, this CPO is not observed for sample NF_1110-2, which, consistently with its low finite strain, shows a texture similar to that of the starting material and the low temperature samples.

In summary, deformation-induced CPOs are characterized by a concentration of [010] axes parallel to the compression direction, while the other axes tend to form girdles and point maxima, which are normal and at ~45° with respect to the compression direction, respectively. These patterns are characteristics of the A-fiber texture, where the [100] and [010] axes are parallel to the shearing (lineation) and principal stress directions, respectively [START_REF] Mainprice | Pressure sensitivity of olivine slip systems and seismic anisotropy of Earth's upper mantle[END_REF][START_REF] Michibayashi | Natural olivine crystal-fabrics in the western Pacific convergence region: A new method to identify fabric type[END_REF][START_REF] Ohuchi | In situ observation of crystallographic preferred orientation of deforming olivine at high pressure and high temperature[END_REF][START_REF] Tommasi | Viscoplastic self-consistent and equilibrium-based modeling of olivine lattice preferred orientations: Implications for the upper mantle seismic anisotropy[END_REF]. Similar textures have also been reported for iron-bearing olivine using the same experimental setup at 900 °C and are indicative of co-existing

[100](010), [001](010) and possibly [001]{110} slip systems [START_REF] Demouchy | Experimental deformation of olivine single crystals at lithospheric temperatures[END_REF]Demouchy et al., 2014;[START_REF] Phakey | Transmission Electron Microscopy of Experimentally Deformed Olivine Crystals[END_REF][START_REF] Raleigh | Mechanism of plastic deformation of olivine[END_REF].

Intracrystalline plasticity was identified in the EBSD maps of the deformed samples via the analysis of misorientation within the grains determined by MTEX. At 1050-1200 °C, many subgrains were observed (misorientations of 2-13°) and statistics on those subgrains could be extracted (Figure 8, Figures S3 andS4). At 900-1000 °C, however, little intragranular plasticity and few subgrains are present. Intracrystalline plasticity was therefore investigated by analyzing targeted grains that showed a GOS > 1° and where deformed areas larger than 10 pixels could be analyzed (Figure 8 and Figure S5). Subgrains can form twist or tilt walls in the grains. Figure 8 (and Supp.

Mat. Figures S3 andS4) illustrates the types of subgrains identified in all three samples that have experienced major deformation; i.e., NF_1050-1, NF_1110-1 and NF_1200-1. Subgrains are mostly found in large grains (>~4 µm) and correspond to modest misorientations, typically lower than 5° (Figure S3). Detailed analysis reveals that the majority of subgrain boundaries are tilt walls, i.e., with the rotation axis oriented nearly parallel to the subgrain wall. The most common subgrain types for those three samples (deformed at 1050-1200 °C) are illustrated in Figure 8, where the distribution of subgrain rotation axis is plotted in inverse pole figures. These plots reveal clustering mostly around the [001] and [1 10] directions. Subgrain rotation around [1 10] is more prominent at 1050 °C than at 1110 and 1200 °C. At 1200 °C, subgrain rotations around the [1 10] direction are negligible and rotations around [001] dominate, associated with a slightly larger contribution from subgrain rotations around the <0kl> directions and around the [010] axis.

At 900-1000 °C fewer grains were analyzed. It is therefore difficult to identify specific rotation axes as clearly as in the high-temperature samples (Figure S5). However, a similar trend is observed, particularly for larger misorientation values (which present a lower uncertainty), with rotation axes located near the [1 10] and [011] directions. We note that, unlike at 1050-1200 °C, those latter rotations seem to be favored over those around the [001] axis.

At 1050-1110 °C, the high concentration of subgrain rotations around [001] probably reflects the appearance of tilt walls as a result of dislocations of screw and edge character in the [001](010) and [100](010) slip systems, respectively, consistently with the CPOs described above. However, other rotations, such as those around [1 10] and [011] observed throughout the entire 900-1200 °C temperature range investigated (Figures S3 andS4), may simply reflect the presence of GNDs. Those rotations can result from [001]{110} and [100]{011} dislocations, as already identified in previous studies [START_REF] Cordier | Disclinations provide the missing mechanism for deforming olivine-rich rocks in the mantle[END_REF][START_REF] Demouchy | Viscoplasticity of polycrystalline olivine experimentally deformed at high pressure and 900 degrees C[END_REF][START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF][START_REF] Wallis | Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction[END_REF]. Conclusively, misorientation may be used as a proxy for dislocation density in general, but does not necessarily represent the density of mobile (free) dislocations accommodating most of the strain.

The three samples investigated by TEM exhibit very distinctive microstructures, as shown in Figure 9. At 950 °C (NF_950-1), consistently with the stress drop observed at high stress, one observes mostly indication of a brittle response (Figure 9a). Although some intragranular microcracks can be occasionally observed, brittleness results predominantly from grain boundary cracking as seen in Figure 9b. In most cases, the grain boundary microcracks are straight and cleavage-like. However, some exhibit serration, suggesting a different behavior before rupture (Figure 9b, Figure S6a), characteristic of ductile cracks [START_REF] Ponson | Statistics of ductile fracture surfaces: the effect of material parameters[END_REF]. The intragranular microstructure is very heterogeneous. Many grains are pristine, but dislocation activity can be observed in some grains, probably related to microplasticity (i.e., plastic deformation by dislocation motion occurs locally, while the bulk material remains essentially in the elastic/brittle field).

At the highest temperature investigated (NF_1200-1), the microstructure is also very heterogeneous (Figure 9). Several grains are still dislocation free, however clear dislocation activity is observed in many of them and, consistently with SEM observations, the grain boundaries are perfectly cohesive (Figure 9h, Figure S6d). The most striking observations come from the sample deformed at 1050 °C (NF_1050-1). Very marked grain boundary openings are ubiquitous (Figures 9c-f). Contrary to NF_950-1, damage at grain boundary does not result from purely brittle cleavage-like micro-fracturing. The shape of surfaces formed by crack opening clearly suggests some ductile processes (Figure 9e, Figures S6b andS6c). As a result, some cohesion could be maintained during crack opening. This is probably what explains the ductility exhibited by this sample despite very strong damage. Another characteristic of this sample is the presence of dislocation activity in almost all grains (Figure 9f), which is consistent with the GOS evolution observed among samples (Figure 3). Although dislocation activity might be related to the ductile processes suggested by the crack morphologies, no clear correlation could be evidenced.

Discussion

Brittle to ductile transition mechanisms

Between 900 and 1000 °C, no steady state could be achieved (Figure 2). Stress almost immediately reached a yield point, beyond which deformation occurred in a semi-brittle manner, via micro-cataclastic processes (intergranular cracks and sliding). As shown by the images of recovered samples (Figures 4 and9), for this range of temperature, the stress drop observed beyond the stress maximum likely corresponds to the coalescence and propagation of pervasive microcrack networks. In the brittle field and across the brittle-ductile transition here, when grains slide relative to each other (GBS), strain incompatibilities develop (usually at triple junctions), which can lead to the formation of voids. In some cases, these voids further develop under local tensile stresses and fully open grain boundaries (Figure 4, Figure 9d). Although these openings can be seen as mode-I cracks in the brittle sample at 900 °C, an involvement of ductile processes in their development is clearly identified at 950-1110 °C (Figures 4 and9d,e), where they therefore correspond to "ductile cracks" [START_REF] Idrissi | Low-temperature plasticity of olivine revisited with in situ TEM nanomechanical testing[END_REF][START_REF] Ponson | Statistics of ductile fracture surfaces: the effect of material parameters[END_REF]. The presence of pervasive gaping grain boundaries indicates indeed that deformation involved a significant contribution of GBS at the sample scale [START_REF] Ree | Grain boundary sliding and development of grain boundary opening in experimentally deformed octachloropropane[END_REF][START_REF] Langdon | Grain boundary sliding revisited: Developments in sliding over four decades[END_REF]. This is well illustrated by the relative motion of grains in Figure 4d and Figure 9c. The damage (i.e., cavitation) caused by this mechanism is a direct consequence of the moderate confining pressure conditions (0.3 GPa) relative to stress levels and the low temperature (~0.54-0.59 × Tm for Fo100), which, for our experimental durations, prevents diffusion from filling the areas in tension as the grains are pulled apart (e.g., [START_REF] Ree | Grain boundary sliding and development of grain boundary opening in experimentally deformed octachloropropane[END_REF].

Indeed, creep by diffusion would occur if characteristic diffusion lengths were greater than the grain size of the aggregate. This criterion can be assessed using Si diffusivity since it is the slowest diffusing species in silicates. For 900-1000 °C, data from [START_REF] Fei | High silicon self-diffusion coefficient in dry forsterite[END_REF] predict lattice diffusivities of 1.4 × 10 -25 to 3.7 × 10 -24 m 2 s -1 and corresponding characteristic diffusion lengths of ~0.07 to 0.3 nm for the durations of our experiments, which excludes a significant contribution from diffusion creep (e.g., Nabarro-Herring creep). Additionally, theoretical strain rates for diffusion creep can be calculated from the diffusion coefficients mentioned above and using the maximum (or steady-state) stress measured for each experiment [START_REF] Raj | On grain boundary sliding and diffusion creep[END_REF][START_REF] Tasaka | Influence of mineral fraction on the rheological properties of forsterite plus enstatite during grain-size-sensitive creep: 2. Deformation experiments[END_REF].

Using a grain size of 3 µm, representative of our samples, these calculations yield strain rates of the order of 10 -13 -10 -10 s -1 and therefore confirm the unlikely dominance of diffusion creep in our experiments.

Interestingly, these low-temperature samples (< 1000 °C) sustained major strain hardening without reaching failure and largely exceeded the Goetze criterion, i.e., differential stress exceeded confining pressure [START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF]. Transient violation of the Goetze criterion has been previously reported in similar deformation experiments on fined-grained iron-bearing olivine [START_REF] Demouchy | Experimental deformation of olivine single crystals at lithospheric temperatures[END_REF][START_REF] Demouchy | Viscoplasticity of polycrystalline olivine experimentally deformed at high pressure and 900 degrees C[END_REF][START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF]. In the present case, the Goetze criterion should only be seen as a condition that predicts the nucleation of cracks (i.e., cavitation), but without necessarily resulting in macroscopic failure.

Interestingly, SEM images of our low-temperature samples show more pronounced surface relief than samples deformed at > 1100 °C (Figure 4b). These features are very similar to the outof-plane grain displacements on free surfaces reported by [START_REF] Bollinger | Intragranular plasticity vs. grain boundary sliding (GBS) in forsterite: microstructural evidence at high pressures (3.5-5.0 GPa)[END_REF] at 3.5-5 GPa (1000-1200 °C, 2 × 10 -5 s -1 ), as well as to those evidenced on samples deformed by GBS creep at 1 atm [START_REF] Watanabe | High temperature intergranular fracture enhanced by grain boundary migration in the alpha iron-tin alloy[END_REF]Maruyama andHiraga, 2017a, 2017b;[START_REF] Masuda | Mantle region accommodating two-dimensional grain boundary sliding in ODS ferritic steel[END_REF][START_REF] Masuda | Two-dimensional grain boundary sliding and mantle dislocation accommodation in ODS ferritic steel[END_REF]. Although, the physical explanation for the appearance of these displacements on free-surfaces created after the experiments remains elusive. It is suspected that this late relative grain motion occurs as a relaxation process at grain boundaries in response to large residual stress heterogeneities due to stored elastic energy. This relaxation is made possible by the decohesion of a significant fraction of the grain boundaries. The present study and those of Maruyama and Hiraga (2017a) and [START_REF] Bollinger | Intragranular plasticity vs. grain boundary sliding (GBS) in forsterite: microstructural evidence at high pressures (3.5-5.0 GPa)[END_REF] thus show the possible activation of GBS under a wide range of confining pressure (0.3-5 GPa). We argue that, under relatively low temperature, rapid laboratory stain rates generate heterogeneous stress concentrations, which can locally be at least equal to the confining pressure, even under several gigapascals of pressure [START_REF] Druiventak | Low-temperature plasticity of olivine during high stress deformation of peridotite at lithospheric conditions -An experimental study[END_REF][START_REF] Burnley | The importance of stress percolation patterns in rocks and other polycrystalline materials[END_REF]. These stress concentrations either create openings (cavitation), as in our case, or, at high temperature, drive ionic diffusive fluxes towards low-pressure areas (e.g., [START_REF] Wheeler | The effects of stress on reactions in the Earth: Sometimes rather mean, usually normal, always important[END_REF].

Grain boundary mediated deformation at low strain

The apparent Young moduli (Figure 2b, Figure S2) provide valuable information about the deformation behavior of the aggregates at low strain. Both yield stresses and corresponding apparent Young moduli are reported in Figure 10 as a function of temperature. Our results describe a linear temperature dependence of -263 MPa/°C. This value is too large to be explained by forsterite elasticity only, as shown by the comparison with the values of [START_REF] Suzuki | Elastic Properties of a Single-Crystal Forsterite Mg2SiO4, up to 1,200 K[END_REF], which yield a temperature derivative of -32 MPa/°C (Figure 10a). These results corroborate the recent study of [START_REF] Burnley | Elastic plastic self-consistent (EPSC) modeling of San Carlos olivine deformed in a D-DIA apparatus[END_REF] on iron-bearing olivine aggregates. It is unclear what percentage of the strain is accommodated elastically or plastically at this stage of the deformation curves. This deviation from purely elastic behavior observed upon modest amounts of strain may reflect a contribution of GBS, accordingly with TEM images, which evidence an involvement of ductile processes in the grain boundary network. In any case, these data suggest a major rheological impact of the grain boundaries with increasing temperature. Since grain boundary mediated deformation is activated at lower temperatures than crystal plastic mechanisms, it may play a key role in the mantle at low temperature and/or high stress conditions, typical of the brittle-ductile transition.

Flow mechanisms and comparison to previous rheological laws

In the 900-1000 °C range, there is no deformation-induced CPO pattern (Figure 7), accordingly with the low amounts of strain experienced by the samples. At the TEM scale, dislocation activity is observed in NF_950-1, but is likely related to microplasticity, and coexists with pervasive microfracturing (Figure 9a). As discussed above, in this temperature range, deformation is transiently ductile at the sample scale, and shortening results from the propagation of micro-cracks at the grain (micrometric) scale, together with minor dislocation activity (glide of [100] and [001] dislocations), as previously proposed by [START_REF] Druiventak | Low-temperature plasticity of olivine during high stress deformation of peridotite at lithospheric conditions -An experimental study[END_REF]. Consequently, the maximum stresses obtained in this temperature range correspond to a semi-brittle regime and lie largely above previously established low temperature flow laws, as shown in Figure 11. We note, as pointed out by previous studies (e.g., [START_REF] Demouchy | Experimental deformation of olivine single crystals at lithospheric temperatures[END_REF][START_REF] Burnley | The importance of stress percolation patterns in rocks and other polycrystalline materials[END_REF], 2014[START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF], that extrapolations from power law flow yield overestimated stress values for the present temperature range and strain rates. At, or above, 1050 °C, apparent steady state was achieved over the strain range investigated (Figure 2) and two observations stand out: (1) GOS values are the highest at 1100 °C, then decrease at 1200 °C (Figure 3). Therefore, the increase in GOS from 900 to 1100 °C, associated with the appearance of numerous subgrain boundaries (Figure 8), reflects an increasing contribution of intracrystalline plasticity with temperature, whereas the lower value obtained at 1200 °C likely indicates a contribution of diffusive mechanisms. (2) In addition, grain boundary sliding, opening and serration are also commonly observed (Figure 4, and Figures 9c-e), indicative of grain boundary mediated plasticity. Thus, deformation in the 1050-1110 °C range corresponds to a transitional regime where both plastic and cataclastic deformation mechanisms are active.

At 1200 °C, a quasi-steady state is achieved rapidly, after only 3 % of strain. The microstructure is noticeably different, with almost no grain pluck out, no evidence of grains sliding relative to each other, no out-of-plane motion, and less grain boundary serration, when compared to samples deformed at 1050 and 1110 °C. Grain boundaries are preserved and appear more curved than at lower temperature; and boundary bulging is clearly identified (Figure 4h). Together with a small decrease in GOS and weaker olivine CPO patterns, these observations suggest further activation of recovery mechanisms (subgrain boundary formation, grain boundary migration, ionic diffusion) than at lower temperature. This is consistent with recent values of Si diffusion in forsterite [START_REF] Fei | Si and O self-diffusion in hydrous forsterite and iron-bearing olivine from the perspective of defect chemistry[END_REF], which, at 1200 °C, predict a strain rate of ~10 -5 s -1 for a grain size of 1 µm and a stress of ~500 MPa [START_REF] Raj | On grain boundary sliding and diffusion creep[END_REF]. Therefore, as already observed by [START_REF] Tasaka | Influence of mineral fraction on the rheological properties of forsterite plus enstatite during grain-size-sensitive creep: 2. Deformation experiments[END_REF] under the same pressure, temperature and strain rate conditions, our experiment at 1200 °C also points to a transitional regime where both dislocation-accommodated grain boundary migration and diffusive mechanisms are active.

Conclusively, our results report a mechanical continuum from low temperature (i.e., semibrittle) to high temperature plasticity. The temperature dependence of stress obtained at ≥ 1050 °C (Figure 11) is in agreement with that calculated from power law flow (e.g., [START_REF] Hirth | Rheology of the upper mantle and the mantle wedge: a view from the experimentalists[END_REF][START_REF] Ohuchi | In situ observation of crystallographic preferred orientation of deforming olivine at high pressure and high temperature[END_REF]. Below 1050 °C, however, the temperature-dependence is greater than that calculated from exponential laws either from experimental studies (e.g., [START_REF] Evans | The temperature variation of hardness of olivine and its implication for polycrystalline yield stress[END_REF][START_REF] Demouchy | Low strength of Earth's uppermost mantle inferred from tri-axial deformation experiments on dry olivine crystals[END_REF][START_REF] Faul | Dislocation creep of fine-grained olivine[END_REF] or numerical modeling (Boioli et al., 2015b). As detailed in the above, this is due to the occurrence of a variety of deformation mechanisms at play throughout the temperature range investigated.

Effect of iron on olivine strength

The stress values obtained in the present study are slightly larger (~17 and 50 % at 1000 and 1200 °C, respectively) than those reported for San Carlos olivine (Fo90) aggregates in [START_REF] Thieme | Stress Evolution and Associated Microstructure During Transient Creep of Olivine at 1000-1200°C[END_REF] using the same apparatus, under identical PT and strain rate conditions and with a comparable grain size (Figure 11), which is qualitatively consistent with the notorious weakening effect of iron on olivine [START_REF] Bollinger | Deformation of forsterite polycrystals at mantle pressure: Comparison with Fe-bearing olivine and the effect of iron on its plasticity[END_REF][START_REF] Zhao | Effect of iron content on the creep behavior of olivine: 1. Anhydrous conditions[END_REF]. The compositional effect observed here is weaker than the one reported by [START_REF] Zhao | Effect of iron content on the creep behavior of olivine: 1. Anhydrous conditions[END_REF] at identical PT conditions, which predicts at least an order of magnitude increase in stress. However, their iron-content dependent rheology law was based on Fo00-Fo90 compositions and the chosen expression is mathematically unfit to predict stress/strain values for Fo100 (strain rate nil for Fo100). A direct rheological comparison between ion-bearing and iron-free olivine at high pressure (3.1-8.1 GPa) by [START_REF] Bollinger | Deformation of forsterite polycrystals at mantle pressure: Comparison with Fe-bearing olivine and the effect of iron on its plasticity[END_REF] has also reported weaker effects of iron incorporation. Following the approach of [START_REF] Bollinger | Deformation of forsterite polycrystals at mantle pressure: Comparison with Fe-bearing olivine and the effect of iron on its plasticity[END_REF] see their equation 3), i.e., using a power flow law and assuming constant activation energies and pre-exponential terms; the difference observed at 1200 °C can be explained by a stress exponent decrease from 3.5 for Fo90 olivine to only ~3.25 for Fo100 forsterite, whereas an exponent of 2.3 was found by [START_REF] Bollinger | Deformation of forsterite polycrystals at mantle pressure: Comparison with Fe-bearing olivine and the effect of iron on its plasticity[END_REF] at 1100-1300 °C and ~5 GPa. The present results thus point to a small rheological effect of iron (between Fo100 and F90) on GBS in very fine-grained olivine aggregates.

Implications for the lithospheric mantle

In summary, the GBS observed in our samples in the brittle-ductile transition field (950-1050 °C) upon modest amounts of strain (<2 %), is first transiently accommodated elastically and then viscously. Upon further strain, GBS eventually produces significant cavitation. This reflects specific experimental conditions, namely (i) relatively low temperatures (T/Tm ≤ 0.68), (ii) fast strain rates (10 -5 s -1 ) and (iii) sub-micron grain-sized and well annealed polygonal microstructures, which are all prerequisites to generate high macroscopic differential stress relative to confining pressure and induce cavitation without immediate failure of the samples. Such conditions may be achieved in mantle shear zones with peculiar settings, such as in tectonically exhumed mantle, where deformation at crustal pressure and temperatures may locally allow stress to exceed lithostatic pressure and, in turn, lead to GBS and gaping as observed in our experimental study.

Under the present dry conditions, high local differential stresses are needed for cavitation to generate unpressurized voids [START_REF] Burnley | The importance of stress percolation patterns in rocks and other polycrystalline materials[END_REF]. However, cavitation may occur with lower stress levels if pressurized aqueous fluids or reactive melts are present [START_REF] Précigout | Evidence of phase nucleation during olivine diffusion creep: A new perspective for mantle strain localization[END_REF].

In addition, the predominance of diffusion creep or GBS over dislocation creep in mylonitic shear bands in peridotites is still debated based on field and microstructural evidences. It strongly depends on stress and strain rate evolution upon grain size reduction (Platt and Behr, 2011). On the other hand, the recent review of [START_REF] Vauchez | Faults (shear zones) in the Earth's mantle[END_REF] suggests that, in most instances, the dominant mechanism remains dislocation creep, associated to grains sizes of typically ~200 µm. In any case, in the lithospheric mantle, GBS and cavitation might be transient mechanisms occurring in incipient mantle shear zones in response to large stresses. Eventually, lower strain rates and stresses will likely allow ionic diffusion, rather than cavitation, to accommodate deformation. (172 GPa), calculated using the data of [START_REF] Suzuki | Elastic Properties of a Single-Crystal Forsterite Mg2SiO4, up to 1,200 K[END_REF], is also shown next to the data of NF_900-1, for which the apparent Young modulus is 112.2 GPa.

Conclusions

FiguresFigure

  Figures

  Figure 1: (a) SEM image (Forward scattered electrons) of the starting material used for the deformation experiments. (b) EBSD map collected on the same starting material showing phase distribution and grain boundaries determined with MTEX (black lines, see text for details).

Figure 2 :

 2 Figure 2: Stress-strain curves for axial deformation experiments. Each curve is colored as a function of temperature, according to the appended color scale. (a) Mechanical curves after data treatment (see section 2.2 for details). (b) Smoothed stress-strain curves (up to 5% strain) used to retrieve yield points, indicated by squares (see supp. mat. for details). As a guide to the eye, the Young modulus of forsterite at 900°C

Figure 3 :

 3 Figure 3: Grain size, shape parameters (shape factor and aspect ratio) and grain orientation spread (GOS) as a function of temperature and finite strain. The leftmost datum point at room temperature and no strain corresponds to the starting material. The other nine data points correspond to the static annealing test (1000 °C, no strain) and the axial deformation experiments.

Figure 4 :

 4 Figure 4: SEM images (forward scattered electrons) of samples deformed at various temperatures. Scale bar is 5 µm on all images. The direction of the deformation (either horizontal or in-plane) is given by the

Figure 5 :

 5 Figure 5: Polar histograms displaying the normalized orientation distribution of the longest axis of forsterite grains. Samples length, and therefore axial compression direction, is horizontal. (a) Starting material (black line) and sample NF_900-1 (grey bars), deformed to a finite strain of 3.9 %. (b) Samples NF_1110-2 (black line) and NF_1110-1 (grey bars) deformed by 5 and 12.41 % of finite strain, respectively.

Figure 6 :

 6 Figure 6: EBSD maps showing grain boundaries and Mis2Mean angles (°) within each grain. (a) Sample NF_900-1 (3.9 % finite strain). Very limited grain plasticity is observed, as shown by Mis2Mean values, which rarely exceed 1°. (b) Sample NF_1110-1 (12.41 % finite strain), which presents the largest GOS values observed in our samples. Note that the color scale maximum in (b) is five times larger than in (a).

Figure 7 :

 7 Figure 7: Pole figures of forsterite obtained for the starting material, the annealing experiment and each axial deformation experiment. Densities were obtained from the largest EBSD map collected on each sample and reduced to one point per grain. Densities were contoured with a 0.06 interval. The color scale given beside the starting material pole figures is the same on all figures. The number of grains used, N, and the corresponding J-index are provided in each case. The direction of axial compression deformation is vertical for all figures, except for sample NF_900-1, where orientation was lost due brittle failure of the sample.

Figure 8 :

 8 Figure 8: Intracrystalline plasticity at 1050-1200 °C. (a)-(e) Misorientation analysis in sample NF_1050-1. (a) EBSD map showing Mis2Mean values, grain boundaries (black lines) and subgrain boundaries (thick colored lines). (b) Reference forsterite crystal habitus used in (c), (d) and (e). In addition to principal axes, specific axes, corresponding to 110 and [011] subgrain rotations, are shown and colored according to the inverse pole figure colors given in the inset. (c)-(e) Detailed views of grains (and subgrains) marked by a star in (a).The bars on top of the subgrain boundaries represent the orientation of the subgrain rotation axis; their length is a function of their dipping angle (i.e., they are shorter when the rotation axis sticks out of plane).

Figure 9 :

 9 Figure 9: TEM images of samples deformed at 950-1200 °C. (a)-(b) Sample NF_950-1. (a) Grains show few to no dislocation. Gaping grain boundaries are straight, typical of brittle failure. (b) Several grain boundaries are serrated at the scale of a few tens of nanometers (thick arrow) and intragranular cracks are also present (thin arrow). A higher magnification image of these features is provided in the supplementary material

Figure 10 :

 10 Figure 10: (a) Apparent Young modulus at yield point as a function of temperature. Young modulus of forsterite as a function of temperature from Suzuki et al. (1983) is shown for comparison. Values of grain boundaries apparent elasticity for iron-bearing olivine from Burnley and Kaboli (2019) are also reported. (b)Yield stress as a function of temperature from the mechanical curves displayed in Figure2b(see Supp Mat for details, FigureS2).

Figure 11 :

 11 Figure 11: Comparison of iron-bearing olivine strength from the literature with the mechanical data from this study obtained on forsterite. All data are for a strain rate of 10 -5 s -1 . The data points were colored as a function of temperature, according to same color scale used in Figure 2.

(1)

In the present experiments, several deformation mechanisms are at play with their respective contributions varying with temperature, and stress levels. We document a transition from micro-cracking to grain boundary sliding, and then to dislocation creep at around 1050-1100 °C; with a potential important contribution of ionic diffusion at 1200 °C.

(2)

The transition results in subtle changes in SPO and CPO, but is evident in the recovered microstructures in SEM and TEM. Moreover, in our experiments, as well as in previous experimental studies, grains slide against their neighbors towards areas where, local tensile stresses have been generated by large stress heterogeneities. This is possible under moderate confining pressure in laboratory, where the Goetze criterion can be violated in a transient way.

(3) Given the experimental high-stress conditions, our results may not directly apply to the deformation of the Earth's mantle at large scale. Nevertheless, our results highlight that the grain boundary network in forsterite aggregates is an agent of deformation that is activated at lithospheric temperatures (< 1100 °C), before intracrystalline deformation.

Acknowledgments

The authors wish to thank Franck Nono, Manuel Thieme and Nicolas Marino for their


J Greffier
email: joel.greffier@chu-nimes.fr

A Larbi

J Frandon

P A Daviau

J P Beregi

F Pereira

Influence of iterative reconstruction and dose levels on metallic artifact reduction: a phantom study within four CT systems

Keywords: Metallic artifact reduction (MAR), Computed tomography (CT), Image quality, Iterative reconstruction CT: Computed tomography FBP: Filtered back projection iMAR ® : iterative metal artifact reduction IR: Iterative reconstruction MAR: Metallic artifact reduction O-MAR ® : Metal artifact reduction for orthopedic implants ROI: Region of iInterest Single energy metal artifact reduction Smart-MAR ® : Smart metallic artifact reduction

Purpose: To compare metallic artifact reduction (MAR) algorithms proposed by four vendors according to the delivered dose and iterative level using a phantom study.

Methods: Four CT systems (Revolution GSI ® , Ingenuity Elite ® , Somatom Edge ® , and Aquilion Prime ® ) equipped with MAR algorithms (Smart MAR ® , O-MAR ® , iMAR ® , and SEMAR ® ) were compared. Acquisitions were performed with CIRS Phantom technology containing a titanium rod core insert using 120 kV and two dose levels (3 and 7mGy). Images were reconstructed with and without MAR algorithms using standard "soft tissue" kernel for filtered back projection (FBP) and intermediary iterative level. Artifact propagation was assessed by counting the number of pixels containing an HU outside a defined threshold interval (> 100HU and < -80 HU). Artifact correction was evaluated by computing the differences between images with and without MAR.

Results: Accuracy of N CT values increased significantly using MAR algorithms, IR, and high dose levels (P<0.001). Image noise reduced -31±15 (SD) % (range: -50% ;-14%) with Smart-MAR ® , -28 ± 3 (SD) % (range -31%; -25%) with O-MAR ® , -32 ± 7 (SD) % (range: -40%; -24%) with iMAR CN ® , -52 ± 8 (SD) % (range: -60%; -42%) with iMAR TH ® and -29 ± 6 (SD) % (range: -37%; -23%) with SEMAR ® . The number of pixels outside the threshold interval was also reduced using MAR algorithms. Each MAR algorithm corrected in distinct patterns, with satisfactory artifact correction for all MAR algorithms.

Conclusion:

This study demonstrates that artifact correction using MAR algorithms differs according to the main manufacturers, although corrections are satisfactory for all systems.

Corrections also improved by using IR and increasing the dose level.

Introduction

Computed tomography (CT) image quality is degraded in patients with metallic material because of disruptions known as metallic artifacts [START_REF] Barrett | Artifacts in CT: recognition and avoidance[END_REF]. These artifacts hinder or even prevent radiologists from evaluating the interface between metallic materials and adjacent tissues.

Metallic artifacts result when structures induce profound nonlinearity between measured attenuation projections and attenuation line integrals, leading to beam hardening and photon starvation [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Morsbach | Reduction of metal artifacts from hip prostheses on CT images of the pelvis: value of iterative reconstructions[END_REF]. When a photon beam interacts with metal, low-energy photons are more attenuated than high-energy photons. By contrast, high attenuation leads to insufficient photon quantities reaching the detector). These quantum phenomena distort calculations during the image reconstruction process, resulting in higher image-noise and the presence of dark streaks around the metallic device.

Several simple techniques have been used to reduce metallic artifacts, such as increasing kV or mAs, using softer reconstruction kernel, using iterative reconstructions (IR), using thinner slices, and adapting windowing [START_REF] Barrett | Artifacts in CT: recognition and avoidance[END_REF][START_REF] Lee | Overcoming artifacts from metallic orthopedic implants at high-field-strength MR imaging and multi-detector CT[END_REF][START_REF] Nakae | Clinical evaluation of a newly developed method for avoiding artifacts caused by dental fillings on X-ray CT[END_REF]. However, these techniques have a limited impact on artifact reduction and may require an increased delivered dose or a reduction of spatial resolution. Another strategy to reduce metallic artifact consists of using extrapolated mono-energetic images obtained with dual-energy CT [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Bamberg | Metal artifact reduction by dual energy computed tomography using monoenergetic extrapolation[END_REF][START_REF] Lewis | Reducing the effects of metal artefact using high keV monoenergetic reconstruction of dual energy CT (DECT) in hip replacements[END_REF][START_REF] Meinel | Metal artifact reduction by dual-energy computed tomography using energetic extrapolation: a systematically optimized protocol[END_REF]. However, dual energy CT-scanners are not widespread, datasets are usually acquired prospectively, and postprocessing is time-consuming. Recently, metal artifact reduction (MAR) algorithms have been proposed [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Morsbach | Reduction of metal artifacts from hip prostheses on CT images of the pelvis: value of iterative reconstructions[END_REF][START_REF] Hu | Value and clinical application of Orthopedic Metal artifact reduction algorithm in CT scans after orthopedic metal implantation[END_REF][START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF][START_REF] Jeong | Usefulness of a metal artifact reduction algorithm for orthopedic implants in abdominal CT: phantom and clinical study results[END_REF][START_REF] Kidoh | Reduction of dental metallic artefacts in CT: value of a newly developed algorithm for metal artefact reduction (O-MAR)[END_REF][START_REF] Yasaka | Single-energy metal artifact reduction for helical computed tomography of the pelvis in patients with metal hip prostheses[END_REF]. MAR aims to reduce artifacts caused by beam hardening and photon starvation. Algorithms are split in two groups: sinogram completion methods such as projection-based MAR, and model-based iterative algorithms [START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Giantsoudi | Metal artifacts in computed tomography for radiation therapy planning: dosimetric effects and impact of metal artifact reduction[END_REF]. In both, metal objects are segmented in raw-data space (sinogram) and replaced by approximated or interpolated data [START_REF] Yasaka | Single-energy metal artifact reduction for helical computed tomography of the pelvis in patients with metal hip prostheses[END_REF][START_REF] Hauswald | Reducing mater artifacts in a patient with dental fillings[END_REF][START_REF] Ge Healthcare | Smart metal artifact reduction (MAR)[END_REF][START_REF]Philips Healthcare -Philips CT Clinical Science: metal artifact reduction for orthopedic implant (O-MAR)[END_REF][START_REF] Teixeira | Total hip prosthesis CT with single-energy projection-based metallic artifact reduction: impact on the visualization of specific periprosthetic soft tissue structures[END_REF]. MAR algorithms can be used with single or dual energy CT systems.

Many studies have demonstrated the clinical contribution of these algorithms on artifact reduction [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Morsbach | Reduction of metal artifacts from hip prostheses on CT images of the pelvis: value of iterative reconstructions[END_REF][START_REF] Hu | Value and clinical application of Orthopedic Metal artifact reduction algorithm in CT scans after orthopedic metal implantation[END_REF][START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF][START_REF] Jeong | Usefulness of a metal artifact reduction algorithm for orthopedic implants in abdominal CT: phantom and clinical study results[END_REF][START_REF] Kidoh | Reduction of dental metallic artefacts in CT: value of a newly developed algorithm for metal artefact reduction (O-MAR)[END_REF][START_REF] Yasaka | Single-energy metal artifact reduction for helical computed tomography of the pelvis in patients with metal hip prostheses[END_REF]. However, the majority of these studies were performed using a single MAR algorithm. Other studies compared different MAR algorithms for the same dose level and type of reconstruction (filtered back projection [FBP] or IR). Therefore, an important emerging question is how MAR algorithms influence metallic artifact corrections with respect to dose reduction and use of IR algorithms.

The purpose of this study was to compare MAR algorithms proposed by four vendors according to the delivered dose and iterative level using a phantom study.

Materials and methods

CT examinations

Datasets were acquired using four distinct CT systems including Revolution GSI ® (GE Healthcare), Ingenuity Elite ® (Philips Medical Systems), Somatom EDGE ® (Siemens Healthineers) and Aquilion Prime ® (Canon Medical Systems). The CT units were equipped with the following MAR algorithms: Smart-MAR ® (GE Healthcare), SEMAR ® (Canon Medical Systems), iMAR ® (Siemens Healthineers) and O-MAR ® (Philips Medical Systems).

The basic principle of the first two MAR algorithms relies on projection-based MAR whereas the last two rely on model-based iterative algorithms.

Phantom features

The model 062M electron density phantom (CIRS) was used. This phantom has two nested disks (head and abdomen) made of Plastic Water ® in which 17 different inserts with 30-mm diameter can be used to simulate human tissue or medical objects. The titanium rod core insert was employed to assess MAR algorithms. This cylindrical insert has a diameter of 6.35mm and a high electron density (12.475x10 23 electrons/cm 3 ). These characteristics are similar to a coil employed for cerebral or abdominal embolization. Positions of 17 inserts are shown in Figure 1a. Titanium insert was placed in the lateral part of the abdomen disk (Figure 1b), configuration employed for all acquisitions.

Parameters of acquisition and reconstruction

Acquisitions were performed with rotation time of 0.5s/rot and tube current modulation was disabled. Tube voltage was 120kV and tube current (mAs) was adjusted to obtain a volume computed tomography dose index (CTDIvol) determined for a 32 cm-diameter reference phantom of 3.0 and 7.0mGy, corresponding to the delivered dose in our institution for thoracic and abdominal-pelvic acquisitions, respectively. Acquisitions were performed on helical mode with a pitch factor close to 1, which corresponds to the intermediary pitch factor between thoracic and abdominal-pelvic acquisitions. Raw data were reconstructed using "soft tissue" kernel, with FBP and intermediate iterative level of IR algorithm available on each system and used in clinical practice (Asir-V ® for GE Healthcare, iDose 4® for Philips Medical Systems, ADMIRE ® for Siemens Healthineers and AIDR 3D ® for Canon Medical Systems). Hybrid or statistical IR algorithms were used in all systems, except for Somatom Edge ® . ADMIRE ® corresponds to a partial model-based iterative reconstruction.

Images were reconstructed with and without MAR algorithms, with a field-of-view of 350mm and slice thickness close to 1mm. For Somatom Edge ® , seven types of artifact correction were available with iMAR ® algorithms. Neuro coils (iMAR NE ® ) and thoracic coils (iMAR TH ® ) were evaluated in this study. These two types of algorithms are usually used to correct metal artifacts generated by cerebral, thoracic and abdominal coils. Acquisition and reconstruction parameters are shown in Table 1. The total number of reconstructed data sets evaluated was 36, corresponding to eight for each system assessed, except for Somatom Edge ® [START_REF] Jeong | Usefulness of a metal artifact reduction algorithm for orthopedic implants in abdominal CT: phantom and clinical study results[END_REF].

Raw images were stored in 12 bits except for Aquilion Prime ® , which had data stored in 16 bits. The scale of HU values can be represented with 4096 gray levels for 12 bits and 65536 gray levels for 16 bits.

CT-number and image-noise

Image-quality evaluations were performed using in-house MATLAB ® routines. Two square regions-of-interest (ROI) were centered in the titanium rod core insert (Figure 1c): a ROI of 11x11 pixels surrounds the insert (ROI Insert ) and a ROI of 45x45 pixels includes the Plastic Water ® and the titanium insert (ROI Tot ). A third ROI (ROI Tot-Insert ) was defined by using all pixels contained in ROI Tot except the pixels inside the ROI Insert . This ROI Tot-Insert was composed only with Plastic Water® (N CT ≈ 10HU). Average and standard deviation of the pixel values were computed in ROI Tot-Insert . The former corresponds to the mean of CTnumber (N CT ) and the latter to the image-noise (standard deviation of N CT value).

values within ROI Tot-Insert .

Horizontal and vertical profiles

Artifact propagation

Two assessments were conducted to evaluate artifact dispersion and impact of MAR algorithms. First, two threshold values were employed to catch disturbance of N CT values targeting to HU extreme values. Pixels with values higher than 100HU and lower than -80HU in the ROI Tot were recovered and quantified. Threshold interval was defined using mean and standard deviation of N CT measured in the ROI Tot-Insert for all CT-scans (10 ± 90 HU). Similar approaches were employed in preceding studies [START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF]. Second, the difference between 'with' and 'without' MAR was computed using ROI Tot. Hot-colors indicate N CT values in the MAR image that are higher than without MAR. Cold-colors were assigned for the opposite.

Statistical analysis

The

Results

A test for normality (KS) indicated that the data of this study do not fit normal distribution.

Therefore, a non-parametric test (i. e., Conover squared-ranks test) was employed to examine dispersion of N CT values in ROI Tot-Insert .

Mean CT-Number and image-noise

N CT accuracy within ROI Tot-Insert increased when MAR algorithms were used. Similarly, improved accuracy was found in IR faced to FBP and at 7 mGy compared to 3 mGy. These patterns were found for all CT systems except for Aquilion Prime ® , where accuracy reduction was a function of dose delivered (Figure 2).

The median of N CT values was negative for images without iMAR ® but positive for images using iMAR ® independent of dose level and reconstruction type. In addition, the median of N CT values was higher using iMAR NE ® than iMAR TH ® . The median of N CT values was negative for images without SEMAR ® but positive using SEMAR ® for images reconstructed with FBP, and the opposite was true using IR.

The dispersion of pixel values in ROI Tot-Insert using MAR algorithms were significantly different (P-corrected<0.001) from without using MAR algorithms, independently of dose level and reconstruction type. Additionally, data dispersion had significant differences (Pcorrected <0.001) for 3 mGy versus 7 mGy and for FBP versus IR, independently of employing MAR algorithms.

Image-noise in ROI Tot-Insert decreased using MAR algorithms, IR, and high dose (Figure 3). Smart-MAR ® algorithm reduced image-noise, and this reduction was greater at 3mGy than 7mGy with IR rather than FBP (-27% for FBP/3mGy, -14% for FBP/7mGy, -50%

for IR/3mGy and -35% for IR/7 mGy). O-MAR ® algorithm reduced image-noise similarly for dose level and reconstruction type, achieving a mean of -28±3 (SD) % (range: -31%; -25%).

SEMAR ® algorithm reduced image-noise and this reduction was greater at 7mGy than 3mGy and with IR rather than FBP (-23% for FBP/3mGy, -29% for FBP/7mGy, -28% for IR/3mGy and -37% for IR/7 mGy). For Somatom Edge ® , a similar pattern was found and image noise reduction was more evident with iMAR TH ® (-42% for FBP/3mGy, -49% for FBP/7mGy, -57% for IR/3mGy and -60% for IR/7 mGy) than iMAR NE ® (-24% for FBP/3mGy, -31% for FBP/7mGy, -34% for IR/3mGy and -40% for IR/7 mGy).

Horizontal and vertical profiles

For images not using MAR algorithms, measured diameters were higher than actual insert diameters in Revolution GSI ® , Ingenuity Elite ® and Somatom Edge ® , but lower in Aquilion Prime ® (Table 2). Vertical diameter was slightly higher (from 4 to 8%) than horizontal diameter for Revolution GSI ® , Ingenuity Elite ® and Somatom Edge ® independently of MAR algorithm usage. Additionally, for the Revolution GSI ® , both diameters were reduced using Smart-MAR ® (-15% for horizontal and -18% for vertical diameter) compared to no MAR, resulting in a smaller insert image than real one. For other CT systems, diameter variations were less noticeable using MAR algorithms (≤ ±2%).

Artifact propagation

The number of pixels below -80HU or above 100HU decreased using MAR algorithms except for iMAR TH ® , in which the number of pixels was similar with no MAR (Figure 4). For the Somatom Edge ® with iMAR ® , reduction of pixel numbers below -80HU was greater than pixels above 100HU. Moreover, the number of pixels within the interval decreased from IR to FBP and from 7mGy versus 3mGy, with the exception of Aquilion Prime ® , where the number of pixels was higher at 7mGy than at 3mGy.

Discussion

Metallic artifacts are a major concern for radiologists because they complicate or even prevent radiological evaluation. Image evaluation of the interface between the metallic materials and adjacent tissues is particularly problematic [START_REF] Barrett | Artifacts in CT: recognition and avoidance[END_REF]. MAR algorithms have emerged as important tools to reduce metallic artifacts without increasing delivered dose or decreasing spatial resolution [START_REF] Barrett | Artifacts in CT: recognition and avoidance[END_REF][START_REF] Lee | Overcoming artifacts from metallic orthopedic implants at high-field-strength MR imaging and multi-detector CT[END_REF][START_REF] Nakae | Clinical evaluation of a newly developed method for avoiding artifacts caused by dental fillings on X-ray CT[END_REF]. Preceding studies have assessed the impact of these algorithms on phantoms and on clinical practice [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF][START_REF] Morsbach | Reduction of metal artifacts from hip prostheses on CT images of the pelvis: value of iterative reconstructions[END_REF][START_REF] Hu | Value and clinical application of Orthopedic Metal artifact reduction algorithm in CT scans after orthopedic metal implantation[END_REF][START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF][START_REF] Jeong | Usefulness of a metal artifact reduction algorithm for orthopedic implants in abdominal CT: phantom and clinical study results[END_REF][START_REF] Kidoh | Reduction of dental metallic artefacts in CT: value of a newly developed algorithm for metal artefact reduction (O-MAR)[END_REF][START_REF] Yasaka | Single-energy metal artifact reduction for helical computed tomography of the pelvis in patients with metal hip prostheses[END_REF]. However, few studies have compared distinct MAR algorithms according to dose levels and using FBP and IR. Additionally, radiological studies evaluating whether and how artifacts are created from coil devices are lacking. This experimental study aimed to objectively evaluate image-quality of MAR algorithms in GE Healthcare ® , Philips Medical systems ® , Siemens Healthineers ® and Canon Medical Systems ® as a function of dose level and reconstruction type.

Although accuracy of N CT values depends on material density, MAR algorithms improve such metric and reduce image-noise in ROI Tot-Insert . These findings are significantly more pronounced for IR versus FBP and when dose increases in all but Aquilion Prime ® .

Similar results were published regarding N CT accuracy and image-noise reduction [START_REF] Andersson | Metal artefact reduction in CT imaging of hip prostheses-an evaluation of commercial techniques provided by four vendors[END_REF][START_REF] Morsbach | Reduction of metal artifacts from hip prostheses on CT images of the pelvis: value of iterative reconstructions[END_REF][START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF][START_REF] Yasaka | Single-energy metal artifact reduction for helical computed tomography of the pelvis in patients with metal hip prostheses[END_REF]. However, these studies were carried out with orthopedic or dental implants of different size and/or composition.

Insert deformation was evaluated as a function of reconstruction type, dose levels and MAR algorithms. For Revolution GSI ® , Somatom Edge ® and Aquilion Prime ® , inserts were distorted with and without MAR algorithms. Moreover, vertical diameter was higher than the horizontal diameter. MAR algorithms had no impact on measured insert diameters, except in the instance of GE, where Smart-MAR ® reduced insert diameter in both axes. Similar results were found by Huang et al. [START_REF] Huang | An evaluation of three commercially available metal artifact reduction methods for CT imaging[END_REF]. Furthermore, insert was not distorted using IR or when dose decreases.

Artifact propagation and prevalence of bright/dark streaks were assessed. MAR algorithms reduced pixel count outside of the -80HU to 100HU threshold range, except for iMAR ® TH with N CT < -80HU. Bolstad et al. [START_REF] Bolstad | Metal artifact reduction in CT, a phantom study: subjective and objective evaluation of four commercial metal artifact reduction algorithms when used on three different orthopedic metal implants[END_REF] presented similar results for titanium inserts thresholded at 500HU using Smart-MAR ® , iMAR ® (in hip implant) and SEMAR ® .

The visual impact of MAR algorithms on metal artifact correction and image quality is shown in Figure 5 and Figure 6. Smart-MAR ® and SEMAR ® typically reduce dark streaks thereby increasing pixel values around the insert, although some pixel values were reduced forming a "black circle". The effect of having a "black circle" around the insert improves transition between solid water and metal. For SEMAR ® , pixel values increased around the insert whereas those in periphery reduced. For Ingenuity Elite ® system, increasing and reducing pixel values had equal rates.

Decreased values around the insert were also observed. With iMAR ® , the pixel values on the periphery of the insert reduced. Corrections were more pronounced with iMAR TH ® than iMAR NE ® , but the image-quality appears higher with iMAR NE ® . Berger et al. found that iMAR NE ® presented better results than iMAR TH ® in correcting artifacts due to metal residues [START_REF] Berger | Retained bullets in the head on computed tomography -Get the most out of iterative metal artifact reduction[END_REF].

This study has some limitations. First, raw-data were reconstructed using a single kernel and one iterative level. Second, it was carried out on a 6.35mm titanium insert that could have similar features of brain or abdominal coil. This study hypothesized that metallic artifact produced by this insert would be comparable to those produced by these coils.

However, this hypothesis needs to be validated in a clinical study. Third, only phantom was employed, thus the same study should be performed on patients. Finally, spatial resolution was not assessed.

In conclusion, our results suggest that MAR algorithms correct artifacts generated by an insert similar to cerebral or abdominal coils. Correction improves accuracy of N CT and bright/dark streaks, but also modifies the insert. Moreover, correction patterns differ across manufacturers. In addition, the efficiency of MAR algorithms improves using IR and decreases when the dose decreases. Dark/bright streaks around the metal device were found in images without MAR algorithms. Bright streaks were globally corrected using MAR algorithms. The dark circle surrounding the insert was found using Smart-MAR ® . A blurred zone was created using iMARNE ® and dark streaks appeared on either side of the insert using iMARTH ® . For Aquilion Prime ® system, images were smoothed using IR.

Figure 6. Difference between images in ROITot of 45×45 pixels with and without MAR algorithms of four manufacturers as function of the dose and the reconstruction type. Hot colors were assigned to all pixels having NCT values in MAR image higher than image without MAR. Cold colors were assigned for the reverse situation. This figure illustrates differences between images with and without MAR. Red streaks, corresponding to pixels with higher values in MAR images than without MAR images, were found for all manufacturers. Blue streaks, corresponding to pixels with lower values in MAR images than without MAR images, were observed in images using O-MAR ® and iMARTH ® . Lastly, pixel values on the insert borders decreased using MAR algorithms. Both red and blue colors had greater intensity with iMARTH ® than iMARNE ® .

Table 1. Acquisition and reconstruction parameters used on each CT unit.

Table 2. Differences in percentage between the unique diameter of the titanium rod core insert (6.35 mm) and the horizontal and vertical diameters obtained for dose levels and reconstruction types.

  Horizontal and vertical profiles were defined as the pixel values extracted from horizontal and vertical lines passing through the center of the insert. Full-width at half-maximum (FWHM) was used to estimate insert diameters. Profile baseline values were defined according to the mean value of N CT in the ROI Tot-insert that correspond to the mean HU values out of the insert depicted in the bottom line of the profile. Profile maximum values were obtained from the mean of N CT within the ROI Insert that correspond to the mean HU values in the insert depicted in the top line of the profile. Differences in percentage between the real and measured diameters were computed.

Figure 1 :

 1 Figure 1: a. Positions of the 17 inserts in the two nested disks; b. CT image of the phantom with its 17 inserts; c. ROIs used in this study. Red corresponds to the ROITot of 45×45 pixels; yellow to the ROIInsert of 11×11 pixels. ROITot-insert corresponds to the pixels within the red square excluding the yellow.

Figure 2 .

 2 Figure 2. Accuracy of NCT values was computed in ROITot-Insert for images with/without MAR algorithms of four manufacturers as function of the dose and the reconstruction type. Bars are defined by means of the lower box end (1st quartile: Q1, the margin of the lower and upper box (median and the upper box line (3rd quartile: Q3. The expected NCT value of Plastic Water is approximatively 10HU.

Figure 3 .

 3 Figure 3. Image-noise values computed in ROITot-Insert for images with/without MAR algorithms of four manufacturers as function of the dose and the reconstruction type.

Figure 4 .

 4 Figure 4. Number of pixels with NCT values inferior to -80HU or superior to 100HU for images with/without MAR algorithms of four manufacturers as function of the dose and the reconstruction type.

Figure 5 .

 5 Figure5. Image-quality in ROITot of 45×45 pixels centered on the titanium insert for images with/without MAR algorithms of four manufacturers as function of the dose and the reconstruction type. The window and level were fixed to 350 HU and 50 HU, respectively. This figure illustrates artifact propagation before correction and respective artifact reduction. Dark/bright streaks around the metal device were found in images without MAR algorithms. Bright streaks were globally corrected using MAR algorithms. The dark circle surrounding the insert was found using Smart-MAR ® . A blurred zone was created using iMARNE ® and dark streaks appeared on either side of the insert using iMARTH ® . For Aquilion Prime ® system, images were smoothed using IR.

  Kolmogorov-Smirnov (KS) test was used to test data normality. Conover squared-ranks test, a non-parametric test primarily used to identify differences on variability between groups, was used to examine data dispersion (equality of variance). N CT values in ROI Tot-Insert with and without MAR algorithms for each dose level and reconstruction type were independently compared. The same assessment was employed for 3 mGy versus 7 mGy, for FBP versus IR, and for iMAR NE ® versus iMAR TH

®

. The Bonferroni test was used correct for multiple comparisons and only P values < 0.001 were considered significant.

Conflict of interests

The authors have no conflicts of interest to disclose regarding this article. Results are expressed as mean ± standard deviation. Numbers in brackets are ranges.