Cyprus Gabriel Ophiolite

Coelho

Yannick Branquet

Stanislas Sizaret

Laurent Arbaret

Rémi Champallier

Olivier Rozenbaum

Permeability of sheeted dykes beneath oceanic ridges: Strain experiments coupled with 3D numerical modeling of the Troodos

Introduction

In a classical layer-cake oceanic crust, infiltration metasomatism is responsible for a strong and pervasive alteration of the basaltic rocks. Two hydrodynamics regimes for hydrothermal fluids and associated alteration are generally distinguished within the oceanic crust (see the review on oceanic metasomatism by [START_REF] Bach | Metasomatism within the ocean crust[END_REF]. The regime concerns ubiquitous circulation and associated pervasive alteration, which cause subtle changes in the major element composition. With the exception of the upper crust, the fluid flux is moderate and fluid-to-rock ratio close to 1. The second regime involves localized and high fluid-flux upflow zones and subsequent venting in the vicinity of an axial ridge (Fig. 1; [START_REF] Alt | Subseafloor processes in mid-ocean ridge hydrothermal systems[END_REF]. In this case, the mass transfers are particularly drastic within the sheeted dyke complex, leading to strong and widespread chloritization and epidotization (Fig. 1).

Epidosites are strongly Ca-metasomatized and metal-depleted rocks composed of an epidote-quartz assemblage in subequal proportions with the original igneous texture being completely overprinted [START_REF] Richardson | Metal-depleted root zones of the Troodos ore-forming hydrothermal systems, Cyprus[END_REF][START_REF] Bach | Metasomatism within the ocean crust[END_REF]. Field and petrological data suggest that epidosites would correspond to the base (and likely, in part, to the source) of the ore-forming hydrothermal systems responsible for Cyprus-type volcanogenic massive sulfide deposition (e.g. [START_REF] Richardson | Metal-depleted root zones of the Troodos ore-forming hydrothermal systems, Cyprus[END_REF]. Epidosites are common and extensively studied in ophiolites as the Troodos complex, Cyprus [START_REF] Richardson | Metal-depleted root zones of the Troodos ore-forming hydrothermal systems, Cyprus[END_REF][START_REF] Schiffman | Petrology and oxygen isotope geochemistry of a fossil seawater hydrothermal system within the Solea Graben, Northern Troodos Ophiolite, Cyprus[END_REF]

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M A N U S C R I P T [START_REF] Schiffman | Petrology and oxygen isotope geochemistry of a fossil seawater hydrothermal system within the Solea Graben, Northern Troodos Ophiolite, Cyprus[END_REF][START_REF] Kelley | Development of a brine-dominate hydrothermal system at temperatures of 400~500°C in the upper level plutonic sequence, Troodos ophiolite, Cyprus[END_REF][START_REF] Bickle | Strontium alteration in Troodos ophiolite: Implications for fluid fluxes and geochemical transport in mid-ocean ridge hydrothermal systems[END_REF][START_REF] Alt | A sulfur isotopic profile through the Troodos ophiolite, Cyprus -Primary composition and the effects of seawater hydrothermal alteration[END_REF][START_REF] Booij | Pb-isotope systematics of a fossil hydrothermal system from the Troodos ophiolite, Cyprus: Evidence for a polyphased alteration history[END_REF] and Oman (e.g. [START_REF] Nehlig | Fracture and permeability analysis in magma-hydrothermal transition zones in the Samail ophiolite (Oman)[END_REF]. These rocks have also been observed in tectonically exposed mid-to lower arc crust (e.g. [START_REF] Banerjee | Discovery of epidosites in a modern oceanic setting, the Tonga forearc[END_REF]. Conversely, they are not documented in current oceanic crust as epidosites are related to supra-subduction context and not mid-ocean ridge [START_REF] Bach | Metasomatism within the ocean crust[END_REF].

As localized upflow zones within sheeted dykes are characterized by strong metasomatism and associated very high fluid flux, permeability appears to be a major controlling factor in oceanic hydrothermalism. Large-scale permeability is assumed to favor large convection cells responsible for localizing upflow zones at vents (Fig. 1). One important clue common in most active/reactive natural geosystems, is that permeability of oceanic hydrothermal systems is typically transient, even on short time scales: (i) the tectonic and magmatic activity of oceanic ridges yields significant brittle strain which may enhance permeability through faults, fractures, and microcracks; (ii) metasomatism, and, more generally, fluid/rock interactions greatly influence porosity and resulting permeability temporally, either by opening spaces (e.g. dissolution or anisovolumetric replacement) or sealing cracks by hydrothermal phase deposition. Thus, assessing permeability in such systems requires accounting for fracture emplacement, hydrothermal sealing, and alteration degree of the diabase, which constitutes the sheeted dykes.

Permeability in oceanic crust is usually measured using three main approaches:

(i) in situ bulk permeability of extrusive volcanic rocks and sheeted dykes has been measured by the Deep Sea Drilling Project/Ocean Drilling Program (DSDP/ODP). Different techniques, like drill-string packer and thermal flow meter measurements [START_REF] Becker | Measurements of the permeability of the sheeted dikes in hole 504B, ODP LEG 111[END_REF][START_REF] Fisher | Permeability within basaltic oceanic crust[END_REF][START_REF] Becker | Permeability of upper oceanic basement on the eastern flank of the Juan de Fuca Ridge determined with drill-string packer experiments[END_REF], have been used. These direct measurements indicate a wide range of permeability values (Fig. 1). A well-established result is that permeability

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decreases with depth from 10 -13 m 2 in the upper few hundred meters of the seafloor to 10 -18 m 2 at 1200 meters depth (Fig. 1; [START_REF] Becker | Permeability of upper oceanic basement on the eastern flank of the Juan de Fuca Ridge determined with drill-string packer experiments[END_REF];

(ii) inferred permeability using indirect approachs employ fracture and vein mapping of ophiolites (e.g. Cyprus, Oman). In these cases, permeability values are calculated using different methods including the parallel plate method, the matrix addition method, and the stochastic method (in the Troodos Ophiolite on Cyprus by Van Everdingen, 1995; in the Semail Ophiolite in Oman by [START_REF] Nehlig | Fracture and permeability analysis in magma-hydrothermal transition zones in the Samail ophiolite (Oman)[END_REF]. In Oman, calculated permeability values vary between 10 -11 and 10 -12 m 2 at the base of the sheeted dykes (Fig. 1; [START_REF] Nehlig | Fracture and permeability analysis in magma-hydrothermal transition zones in the Samail ophiolite (Oman)[END_REF]. In the Troodos Ophiolite, sheeted dykes have an on-axis permeability estimated between 10 -12 and 10 -8 m 2 (Fig. 1), while fractured diabase containing calcite-filled veins have an off-axis permeability of 10 -21 to 10 -18 m 2 (Van Everdingen, 1995). It is noteworthy that those inferred permeability values are dubious because they are calculated from outcrop data on the massive ophiolite scale, i.e. after weathering and stress relaxation induced by tectonic exhumation.

(iii) laboratory permeability measurements of oceanic rocks are seldom performed in the pressure/temperature conditions prevailing in oceanic crust hydrothermal systems (e.g. [START_REF] Aksyuk | The permeability of oceanic basalts and some questions of the formation of hydrothermal springs in the rift zone of the Atlantic Ocean[END_REF].

This large permeability variation range is partly explained by different the investigation depths, locations, and lithologies, however, the prevailing factor is the scale dependency of permeability measurements. This has been clearly established for the continental crust [START_REF] Brace | Permeability of crystalline and argillaceous rocks[END_REF][START_REF] Clauser | Permeabilität kristalliner Gesteine: Hannover, Niedersächsisches Landesamt für Bodenforschung (NLfB)[END_REF]Townend and Zoback;2000) and is unequivocally valid for the oceanic crust (see e.g. range of variations in Van Everdingen, 1995). In fact, laboratory measurements on centimeter-scale samples are systematically 3-4 orders of magnitude lower than large-scale measurements using in-situ or fracture mapping methods [START_REF] Brace | Permeability of crystalline and argillaceous rocks[END_REF]Townend and Zoback;2000). Moreover, small-scale laboratory permeability measurements obtained under estimated pressure and temperature conditions are not directly exploited when reconstructing or

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modeling hydrodynamics of Darcian hydrothermal systems. Thus, numerical hydro-thermal Darcian models of oceanic ridge convection cells currently use high large-scale permeability values mainly from ODP boreholes (e.g. 10 -15 to 10 -13 m 2 , [START_REF] Coumou | The dynamics of midocean ridge hydrothermal systems: Splitting plumes and fluctuating vent temperatures[END_REF][START_REF] Fontaine | Two-dimensional numerical models of open-top hydrothermal convection at high Rayleigh and Nusselt numbers: Implications for midocean ridge hydrothermal circulation[END_REF].

Laboratory measurements make it possible to estimate and quantify the micro-mechanisms (e.g. structural, textural, and mineralogical) at play that directly control the intrinsic permeability at the centimeter scale. Laboratory data are therefore essential when studying transient physical conditions of oceanic hydrothermalism subjected to fracture emplacement and hydrothermal alteration. Experimental permeability measurements of rocks under estimated in situ confining and pore pressures, temperatures, and strains are technically challenging and have not yet been performed on oceanic materials. Such experiments, which evaluate the effects of deformation on permeability, have been mostly performed on granitic rocks [START_REF] Zoback | The effect of microcrack dilatancy on the permeability of Westerly granite[END_REF][START_REF] David | Influence of stress-induced and thermal cracking on physical properties and microstructure of La Peyratte granite[END_REF]Tenthorey and Gerald, 2006), sandstones [START_REF] Tenthorey | Precipitation sealing and diagenesis. 1. Experimental results[END_REF](Tenthorey et al., , 2003;;Tenthorey and Cox, 2006), mudstones and fault gouge (e.g. [START_REF] Zhang | Enhancement of fluid permeability during shear deformation of a synthetic mud[END_REF], calcite (e.g. Zhang et al., 1994a) and serpentinites (Tenthorey and Cox, 2003;[START_REF] Hirose | Semi-brittle flow during dehydration of lizardite-chrysotile serpentinite deformed in torsion[END_REF]. Only one series of experiments (e.g. Tenthorey and Gerald, 2006) used water as pore fluid rather than argon. As water is a potentially reactive fluid, its use allows us to study the feedback between permeability and hydrothermal reactions, which may encourage the sealing of cracks and deformation.

This study reports permeability measurements conducted at temperatures, confining and fluid pressures common at the base of the sheeted dyke complex close to the reaction zone.

We performed experiments with the three main rock types (metadiabase, chloritized metadiabase and epidosite) encountered in the sheeted dykes at Troodos Ophiolite complex (Cyprus). Moreover, applying differential stresses, we accounted for brittle deformation of rocks that occurs during oceanic crust spreading. Argon and water were used as the pore fluid

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in order to evaluate potential hydrothermal reactions (e.g. sealing of cracks) during our experiments. Finally, in order to explore effects of unloading and stress relaxation during ophiolite exhumation, we performed 3D void-space mapping numerical simulations to measure the core sample permeability after the laboratory experiments.

Experimental constant conditions

We used the well-defined stratigraphy of Troodos around Mt. Olympus (ICRDG drillholes CY1, 1a and 4;Vine and Smith, 1990) to choose our experimental conditions. The stratigraphic data indicates a thickness of rocks of about 2 km above the reaction zone (Fig. 1). A mean seawater depth above mid-ocean ridges of 3 km has been assumed. The lithostatic pressure at the base of the sheeted dyke complex is then close to 90 MPa. Since the thickness of volcanic and sedimentary rocks varies along axis for slow-spreading ridges (e.g. [START_REF] Cannat | Thin crust, ultramafic exposures, and rugged faulting patterns at the Mid-Atlantic Ridge (22°-24[END_REF], the experimental confining pressure was fixed at 100 MPa. This configuration corresponds to a hydrostatic fluid pressure around 50 MPa (Fig. 1). To a first order approximation, as in most numerical models (e.g. [START_REF] Fontaine | Two-dimensional numerical models of open-top hydrothermal convection at high Rayleigh and Nusselt numbers: Implications for midocean ridge hydrothermal circulation[END_REF], we assume a hydrostatic fluid pressure gradient. Therefore, a target pore fluid pressure at 50 MPa was chosen.

The experimental temperature was chosen using data from fluid inclusion studies. At Troodos, trapping temperatures range between 300 and 400°C [START_REF] Richardson | Metal-depleted root zones of the Troodos ore-forming hydrothermal systems, Cyprus[END_REF][START_REF] Schiffman | Petrology and oxygen isotope geochemistry of a fossil seawater hydrothermal system within the Solea Graben, Northern Troodos Ophiolite, Cyprus[END_REF][START_REF] Kelley | Development of a brine-dominate hydrothermal system at temperatures of 400~500°C in the upper level plutonic sequence, Troodos ophiolite, Cyprus[END_REF][START_REF] Kelley | Processes of brine generation and circulation in the oceanic crust: Fluid inclusion evidence from the Troodos ophiolite, Cyprus[END_REF][START_REF] Bettison-Varga | Fluid-rock interaction in the hydrothermal upflow zone of the Solea graben, Troodos Ophiolite, Cyprus[END_REF]. Similar temperatures have been estimated at the roofs of the magma chambers in other ophiolite complexes (e.g. Oman; [START_REF] Nehlig | Salinity of oceanic hydrothermal fluids: A fluid inclusion study[END_REF][START_REF] Nehlig | The root zones of oceanic hydrothermal systems: Constraints from the Samail ophiolite (Oman)[END_REF]. Considering all these studies, the experimental temperature was held fixed at 400°C.

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Starting material

We selected three representative lithologies of the Troodos sheeted dyke complex:

1) A diabase metamorphosed under greenschist facies conditions (close to the village of Askas; X= 506547.522; Y= 3866086.848; Cyprus metric grid). This sample is hereafter referred to as metadiabase. The selected sample is composed of quartz, calcic plagioclase (An64), actinolite, accessory chlorite and sparse magnetite (Fig. 2A). Microgranular doleritic texture is defined by spherulites of plagioclase and actinolite. Magnetite grains present ilmenite exsolutions. Therefore, most of the magmatic texture is preserved. Actinolite and chlorite are common to typical ocean-floor metamorphism, widespread in current oceanic floors [START_REF] Honnorez | Hydrothermal alteration vs. ocean-floor metamorphism. A comparision between two case histories: The TAG hydrothermal mound (Mid-Atlantic Ridge) vs. DSDP/ODP Hole 504B (Equatorial East Pacific)[END_REF]. Their presence is considered to result from distal alteration processes away from the focused discharge area.

2) A strongly chloritized metadiabase with little evidence of epidotization (close to the village of Galata; X= 490689.092; Y= 3875265.152). The selected sample is enriched in chlorite, the other phases being quartz, albite, actinolite, very small amount of epidote and sparse magnetite (Fig. 2B). The primary magmatic texture is less recognizable because of the intense chloritization. The degree of alteration of this sample is more intense than in the metadiabase.

3) An epidosite (from the Spilia-Kannavia epidosite zone; X= 496904.572;

Y=3869827.252). The selected sample is composed of epidote, lobate quartz, chlorite, and titanite replacing ilmenite (Fig. 2C). The texture is granoblastic. This rock underwent pervasive alteration with intense chemical replacement, from processes in focused discharges of hydrothermal fluids proximal to the ridge axis [START_REF] Honnorez | Hydrothermal alteration vs. ocean-floor metamorphism. A comparision between two case histories: The TAG hydrothermal mound (Mid-Atlantic Ridge) vs. DSDP/ODP Hole 504B (Equatorial East Pacific)[END_REF].

All specimens were cored (30 mm in length and 10 mm in diameter) from large rock samples and dried at 45°C for three days for not adding water to the pore fluid system.

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Experimental method and laboratory permeability measurements

All measurements were conducted in an internal heated Paterson gas apparatus able to independently control confining pressure (Pc), pore pressure (Pp), temperature (T), and longitudinal strain (ε) (see details in [START_REF] Paterson | A high-pressure, high-temperature apparatus for rock deformation[END_REF]. Pore fluid pressure is isolated from the argon confining medium by an iron jacket (Fig. 3) (Tenthorey and Cox, 2006). For each starting material (Table 1), two experiments were performed with either argon or de-ionized water as pore fluid to evaluate effects of potential hydrothermal phase deposition on permeability. In all experiments, the experimental procedure started by raising Pc up to the target level of 100 MPa. Then, pore pressure was progressively increased up to a value of 50

MPa. All specimens were initially heated to 500 °C for a period of 15 minutes to ensure coupling between the specimen and jacket (the jacket molds the sample at high temperature)

and prevent fluid flow outside the specimen. Just after, we lowered the temperature to 400 from 500°C and permeability was measured before, during (at different stagnant steps of differential stress) and after deformation of the specimen (e.g. Fig. 4B). At each loading step, the strain rate was constant at 8×10 -5 s -1 . Permeability was measured using the steady state flow method for Darcian flow, which consists of imposing a known pore pressure difference across the specimen (ΔP in Pa) and measuring the resultant flow rate (Q), which is proportional to permeability (k in m 2 ). Since the fluid flux at both ends of the specimen is monitored before and after a pore pressure difference is imposed, the permeability can be calculated using the following equation:

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where μ is fluid viscosity (µ = 67.990×10 -6 Pa.s for water and µ = 49.057×10 -6 Pa.s for argon at 400°C and 50 MPa; [START_REF] Kestin | Thermophysical properties of fluid H2O[END_REF][START_REF] Younglove | The viscosity and thermal conductivity coefficients of gaseous and liquid argon[END_REF], L (in m) is specimen length and A (in m 2 ) is specimen cross-sectional area.

The pore fluid system includes an upstream reservoir, the specimen column, and a downstream reservoir interconnected together by the pore fluid conduit, as described by Zhang et al. (1994b). Typical imposed pore pressure differences across the specimens during permeability measurements were 3 MPa. For this, the upstream pressure is automatically maintained at 50 MPa using a servo-controlled volumometer. The volumometer consists of a cylinder (pore fluid reservoir) and a piston device, driven by a printed armature DC servomotor through reduction gears, and has a volume of 2000 mm 3 . The piston displacement, which keeps the upstream pressure constant, is measured with a DC-LVDT over time. The downstream pressure is maintained at 47 MPa by the way of a micrometering needle valve.

Thus, Q is calculated from the volume of fluid injected into the specimen (V) by the volumometer over time (see details in the appendix).

Error bars of laboratory permeability values were determined from the derivative of ln (k):

The variations in µ, L, A and ∆P during experiments are negligible relative to Q. Q, dependent of V, may induce errors in k measurements for specimens presenting very low permeability (k < 10 -20 m 2 ) because a very small amount of fluid passes through those specimens. Thus, in this case only, the piston advances discontinuously:

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Furnace calibrations indicate that there is, at most, a 5°C variation along the length of the specimen. At the end of each experiment, specimens were unloaded with no quenching.

Confining and pore pressures were decreased in tandem. After all experiments, one third of the fractured specimen was cut to perform X-ray microtomography in order to obtain 3D images of the porous network and allow post-experiment permeability calculation. The other two-thirds of the specimen were used to make a polished thin section.

Three-dimensional images of fracture networks and numerical permeability calculation after experiment

After each experiment, 3D images of fracture networks were obtained and permeability was calculated through numerical simulations so as to compare these results with permeability measurements.

Acquisition of 3D images

Microtomography analyses were performed using an industrial CT device (Nanotom 180NF; GE Phoenix|x-ray, Wunstorf, Germany) at the ISTO. This unit has an 180kV nanofocus X-ray tube and a digital detector array (2304X1152 pixels Hamamatsu detector). A target made of tungsten was used in order to obtain high accelerating voltage. Samples were placed in the chamber and rotated by 360 degrees during acquisition. The samples (in the form of 10 mm diameter rods) were mounted and waxed on a carbon fiber rod. An operating voltage of 160 kV and a filament current of 23 µA were applied. The distance between the X-ray source and the sample and between the X-ray source and the detector was 22 and 400 mm, respectively, giving a voxel size of 5.5 µm. The 2000 projection images (angular increment of 0.18°) were acquired during rotation (with an acquisition time of 4 hours).

The resulting projections were converted into a 3D image stack using a microcluster of four PCs with the Phoenix 3D reconstruction software (filtered back projection Feldkamp algorithm; [START_REF] Feldkamp | Box-skeletons of discrete solids[END_REF]. The reconstruction software contains several different modules for artifact reduction (e.g. beam hardening, ring artefacts) to optimize the results.

Theoretically, with a monochromatic X-ray (e.g., from a synchrotron beamline), the relation between pixel value (attenuation coefficient) and the compound's mass density is well defined by the Beer-Lambert equation [START_REF] Peix | General principles[END_REF]. With a polychromatic X-ray beam, which is the case for laboratory XCT, artifacts are inevitable and difficult to remove. It is therefore difficult to lay pixel values with material densities in an absolute and quantitative manner.

Frequently encountered artifacts include: beam hardening effect (Van de Casteele et al., 2004) where an object of uniform density appears to have a thick and dense skin or ring effect [START_REF] Lumpkin | X-ray imaging of the aps storage ring beam stability effects: From the alaskan earthquake to undulator field changes[END_REF], generally caused by temporary and spurious bad pixels in the detector.

This effect can be reduced by the reconstruction software, but only to a certain extent and is less effective for a multi-component object. Using a filtered back projection algorithm, a computer reconstructed the projections to obtain cross-sectional images of the sample (tomograms). Stacking these reconstructed images forms a 3D image of the sample (volume dataset). At each space position of the resulting dataset, a grey-value corresponds to the effective X-ray attenuation coefficient. Therefore, if the principal compounds of the object are known and have a sufficient density contrast, the distribution of these compounds within the object can be easily deduced. Finally, the 16-bit 3D image was converted into 8-bit (256 grey levels) for the image analysis processing.

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Segmentation and numerical calculation of permeability

Calculation of permeability involves correctly segmenting the solid and the porous phases. Image segmentation, the process by which a greyscale image is converted into black and white voxels, was done using ImageJ (rsb.info.nih.gov/ij, accessed 01/2012). Because it was not possible to directly threshold the greyscale images we used two filters in order to obtain binary images (the fractures in black and the matrix in white). The first filter is "A Trous filter", which removes noise using wavelet-based analysis. After thresholding, the resulting binary (black and white) image was filtered with the "3D Analysis" plugin [START_REF] Iannuccelli | NEMO: A tool for analyzing gene and chromosome territory distributions from 3D-FISH experiments[END_REF]) so as to eliminate the smallest particles that correspond to noise. We visualized in 3D the fracture networks in the segmented volumes with the software Blob3D.

Single phase gas flow simulations were done through the segmented volumes using Palabos was set so as to model a single phase, isothermal, laminar flow. Constant fluid viscosity and density were set to 1/6 kg/lu/s and 1 kg/lu 3 , respectively. The symbol lu is the lattice unit length, which was set to the voxel edge length. The pressure gradient was on the order of 10 -7 kg/lu 2 /s 2 so as to ensure laminar flow (i.e., Reynolds number << 1). Darcy's law is applied with the averaged stream-wise velocity component, the imposed pressure gradient, and the fluid viscosity to solve for permeability k in nondimensional lattice units, lu 2 . This value is converted back to m 2 by multiplying it by the square of the voxel edge length. For

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each volume, one permeability value is obtained in the vertical direction. The laminar and steady-state nature of the simulated flow was tested by ensuring that the permeability values were constants at different applied pressure gradients.

Fractures are narrow and sometimes only a few voxels across. It is to be expected that sample permeability is sensitive to thresholding. This was tested by successively eroding one voxel layer of the fracture and calculating the permeability at each erosion step. The permeability of a representative sample being of 3.4×10 -13 m 2 initially, it decreased to 6.4×10 - 14 m 2 , 1.2×10 -14 m 2 , and 3.7×10 -18 m 2 for one, two, and eight successive erosions, respectively.

We consider that our thresholding is accurate to ±1 voxels, which gives us a typical uncertainty of a factor 5.

Results

Laboratory permeability measurements

Permeability evolution of metadiabase

For the first experiment on metadiabase (PP239, Table 1), argon was used as the pore fluid. Before deformation of the specimen, three permeability values were measured near 2.5×10 -20 m 2 (Fig. 4A). Then, the specimen was subjected to axial loading until macroscopic failure appeared around 1000 MPa. Just after the failure and the unloading of the specimen, permeability increased by about one order of magnitude relative to the starting isostatic conditions. Despite the inert nature of argon, permeability tended to decrease with time to 4.2×10 -20 m 2 .

For the second experiment on metadiabase (PP274, Table 1), de-ionized water was used as pore fluid. Before deformation, two permeability values were measured near 4×10 -20

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m 2 (Fig. 4B). The specimen was then progressively loaded and permeability measured at each increment of differential stress. From the first increment (100 MPa) and until the macroscopic failure, permeability tended to decrease with time. Contrary to the experiment with Argon, the failure occurred at a lower differential stress of 700 MPa. Later on, a differential stress of 250

MPa was maintained with no permeability variation. A peak of permeability appears (2.9×10 - 19 m 2 ) after the complete unloading of the specimen. The end of the experiment is characterized by a slow regular decrease of permeability to a value around 6×10 -21 m 2 .

Permeability evolution of strongly chloritized metadiabase

In the experiment with argon (PP324, Table 1), no permeability was measured, even after the macroscopic failure (Fig. 5A). In fact, no Ar was injected into the sample, which appeared to be impermeable. Therefore, the specimen would have a permeability lower than 5×10 -21 m 2 , which corresponds to the minimum permeability measurable with the steady-state flow method (GSA repository item 2003132 of Tenthorey and Cox, 2003).

Using de-ionized water (PP298, Table 1), two permeability values were measured by infiltration of water before loading at different steps of differential stress. These initial values are between 1×10 -20 and 3×10 -20 m2 (Fig. 5B). For all loading steps, no measure of permeability was possible. The macroscopic failure occurred at a differential stress of 250

MPa. After that, a differential stress of 200 MPa was maintained and permeability increased up to 2.6×10 -19 m 2 . Afterwards, permeability decreased with time to 2.5×10 -20 m 2 . Just after the unloading of the specimen, the permeability increased slightly to 3.4×10 -20 m 2 . Then, the sample had been re-shortened by 300 µm by a slip along the macroscopic fracture which accommodated most of the displacement. Just after this second deformation, a complete unloading of the specimen was performed. At this moment, permeability increased to 1.0×10 -

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measureable permeability.

Permeability evolution of epidosite

With Argon as pore fluid (PP332, Table 1), two inital permeability values were approximately 1.1×10 -18 m 2 (Fig. 6A). After the first two increments of differential stress (100 and 200 MPa), permeability decreased to 9.0×10 -19 m 2 . At the last increment of differential stress (300 MPa), permeability increased slightly to 1.0×10 -18 m 2 . Macroscopic failure occurred at a differential stress of 350 MPa. After that, a differential stress of 180 MPa was maintained and permeability remained constant around 1.6×10 -18 m 2 . Permeability was not affected by the complete unloading of the specimen and no permeability reduction was observed. Permeability remained constant until the end of the experiment.

Using water as pore fluid (PP308, Table 1), two permeability values were measured close to 6.5×10 -19 m 2 before deformation (Fig. 6B). After the first two steps of differential stress (100 and 200 MPa), permeability decreased to 4.3×10 -19 m 2 . At the last differential stress (300 MPa), permeability increased slightly to 5.4×10 -19 m 2 . The macroscopic failure occurred at a differential stress of 350 MPa. After failure, a differential stress of 160 MPa was maintained. Permeability decreased and stabilized at 2.1×10 -18 m 2 . After the complete unloading of the specimen, permeability increased to 2.5×10 -18 m 2 . Later on, permeability decreased slowly and stabilized at values close to 1.0×10 -18 m 2 .

Analysis of microstructures and numerical calculations of permeability after experiments

In this study, all analyses under scanning electron microscope (SEM) were conducted on polished thin sections using a TESCAN MIRA 3 XMU (voltage = 25 kV).

Fractured metadiabase

In both experiments (PP239 and PP274), no gouge was observed under SEM along the main fractures. The main fractures were widely opened after experiments (Fig. 7A). Opened micro fractures perpendicular to σ1 and a set of microcracks parallel to σ1 are observable (Fig. 7B). In the argon experiment, an amorphous phase was observed within microcracks (Fig. 7C). Energy dispersive spectroscopy (EDS) analyses suggest that it possibly corresponds to silica. Both experiments present abundant crack textures suggestive of self-healing within quartz grains (Fig. 7D).

The 3D fracture networks reconstructed from micro-tomographic imaging are composed of conjugate shear fractures associated with thin fractures sub normal to σ1 (Fig. 8A&B). Close observations on sectional images showed that the fractures sub normal to σ1 tends to follow curved mineral grain borders. Single phase gas flow simulations yield permeability values of 3.1×10 -13 m 2 and 3.4×10 -13 m 2 for the samples from experiments with argon (PP239) and water (PP274) respectively.

Fractured strongly chloritized metadiabase

After each experiment (PP324 and PP298), specimens were reddish colored. After the argon experiment (PP324), large quantities of water were present at the top and bottom of the sample column. Optical microscopic observations reveal that chlorite is completely redbrown, especially in experiments with argon used as pore fluid. Additionally, gouge along the main fractures is observed via SEM (Fig. 9A). The gouge contains intensely sheared minerals, in particular magnetite grains. Gouge is particularly developed where chlorite is the more abundant phase. Moreover, all of the fractures are thinner than those of metadiabase

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experiments. As for the experiments on metadiabase, in both experiments (argon and water as pore fluid) some quartz grains present crack textures suggestive of self-healing (Fig. 9B).

The 3D visualizations of the fracture networks of the two specimens (PP324 and PP298) present 3D discontinuities along the fractures (Fig. 8C&D). These discontinuities precisely match with the gouge zones. On top of that, fracture networks are simple: no conjugate fractures and no fractures normal to σ1 have been observed, contrary to the metadiabase experiments (Fig. 7). Single-phase gas flow simulations yield permeability values of about 1.6×10 -14 m 2 and 5.1×10 -15 m 2 for the samples from experiments with argon (PP324) and water (PP298) respectively. These values are lower than those for the metadiabase.

Fractured epidosite

SEM images reveal complex networks of porosity in the two specimens (PP332 and PP308). Conjugate fractures (Fig. 10A) and thin discontinuous fractures through chloritized zones are observed (Fig. 10B), in addition to an obvious initially large porosity (Fig. 10A). A specific microstructure was observed in the deformed epidosite: micro fractures localized and propagated along epidote grains boundaries (Fig. 10C). As for the fractured chloritized metadiabase, textures suggestive of self-healing in quartz grains were observed only in the experiment using water as the pore fluid (PP308) (Fig. 10D).

Because of the high initial porosity of the epidosite, from microtomographic images, it was not possible to isolate the fracture network developed during deformation in the epidosite. A single-phase gas flow simulation done through the initial porosity of epidosite before experiment yielded a permeability at 1.3×10 -19 m 2 . This calculated permeability approaches the starting permeability measured in our experiment using water as pore fluid (PP308).

A C C E P T E D M A N U S C R I P T

Discussion

Effects of deformation and lithology on laboratory permeability measurements

Our experiments show that each diabase alteration facies presents its own specific fracture pattern, independently of the pore fluid nature and the loading procedure used: i) the fractured metadiabase is characterized by conjugated shear macrofractures associated with micro-cracks sets parallel and sub-normal to σ1; ii) the fractured chloritized metadiabase presents thin, discontinuous shear macrofractures filled with gouge where chlorite is abundant in the sample; and iii) the fractured epidosite presents conjugate shear fractures, which may be discontinuous where chlorite is abundant. These fractures are associated with cracks parallel to σ1 and controlled by epidote and quartz grain interfaces. However, the geometry, the location, and the dips of macroscopic fractures may vary slightly for the same lithology. This is relevant to mechanical experimentation on natural samples in which structural and textural inheritance is not homogenous at the core sample scale.

During deformation of epidosite samples, initial loading steps trigger closure of preexisting cracks and lead to a small drop in permeability (Fig. 6). Before the macroscopic failure, permeability values increase as the result of vertical crack aperture. This compaction/dilatant evolution before failure is well known in studies dealing with granitic rocks (e.g. [START_REF] Zoback | The effect of microcrack dilatancy on the permeability of Westerly granite[END_REF]Tenthorey and Gerald, 2006) and basaltic rocks [START_REF] Fortin | Influence of thermal and mechanical cracks on permeability and elastic wave velocities in a basalt from Mt. Etna volcano subjected to elevated pressure[END_REF]. This evolution is not observed in the experiments on metadiabase and chloritized metadiabase (Fig. 4B and5B). The initial permeability drop is common to all lithologies and suggests closure of thermal cracks and micropores particularly abundant within the epidosite (see initial porosity on Fig. 10A). In contrast, absence of a dilatant stage for metadiabases suggests that these rocks accommodate part of the deformation by strain mechanism as

A C C E P T E D M A N U S C R I P T

pressure solution creep. In that sense, we interpret the fractures sub-normal to σ1 as pressure solution joints, similar to "stylolites" and reopened after the experiment. This implies transport of silica which could be associated to rock failure processes, and re-precipitation in cracks by sealing and/or healing.

After macroscopic failure, the hydrodynamics are different depending on lithology.

The macroscopic failure induces a classical peak of permeability for the chloritized metadiabase (Fig. 5B) and epidosite (Fig. 6). This is not observed for the metadiabase sample, the peak being achieved only at the complete unloading of the specimen (Fig. 4B). Therefore, we conclude that macroscopic shear fractures in metadiabase are not a major drain for fluids before unloading. Moreover, horizontal pressure solution joints (see above) might be responsible for limited vertical fluid flow.

The fact that unloading might be an important control for increasing permeability (Fig. 4B) is not described in similar experimental works (e.g. Tenthorey and Gerald, 2006). We suggest that shear fractures and associated damage zones oblique to σ1 are subject to dilation when isostatic conditions are recovered. Those fractures then constitute major pathways for fluids.

Hydrothermal reaction: healing, sealing and role of chlorite content

There is permeability reduction after failure in all experiments with the exception of the experiments on chloritized metadiabase (PP324) and epidosite (PP332) with argon. We reproduce the same exponential decrease in permeability values observed in similar experiments (e.g. Zhang et al., 1994b;[START_REF] Tenthorey | Precipitation sealing and diagenesis. 1. Experimental results[END_REF][START_REF] Morrow | Permeability reduction in granite under hydrothermal conditions[END_REF]Tenthorey and Gerald, 2006). Under hydrothermal conditions, this evolution is interpreted to be the result of gradual chemical equilibration of the pore fluid with the host rock induced by fluid-

A C C E P T E D M A N U S C R I P T

rock reactions [START_REF] Aharonov | Precipitation sealing and diagenesis: 2. Theoretical analysis[END_REF]. Most of those studies assume that this equilibration is achieved by sealing of cracks associated with mineral precipitation. In our experiments cracked quartz grains display typical self-healing textures (Fig. 7D, 9B, 10D) with micro cavity alignments as described in experiments by [START_REF] Brantley | Healing of microcracks in quartz: Implications for fluid flow[END_REF] or in natural deformed rocks by [START_REF] Labaume | Diagenesis-dependence of cataclastic thrust fault zone sealing in sandstones. Example from the Bolivian Sub-Andean Zone[END_REF]. Moreover, the fast reaction kinetics involved in our experiments (from hours to days) are coherent with processes of healing rather than sealing (e.g. [START_REF] Brantley | Healing of microcracks in quartz: Implications for fluid flow[END_REF][START_REF] Niemeijer | Velocity dependence of strength and healing behaviour in simulated phyllosilicate-bearing fault gouge[END_REF][START_REF] Niemeijer | Healing of simulated fault gouges aided by pressure solution: Results from rock analogue experiments[END_REF][START_REF] Gratier | Fault permeability and strength evolution related to fracturing and healing episodic processes (years to millennia): The role of pressure solution[END_REF].

Therefore, we conclude that a major controlling process of the time-dependent permeability reduction is healing of cracks driven by minimization of surface energy in the presence of aqueous fluids.

Nevertheless, we clearly identify an amorphous siliceous phase partially filling intergranular spaces and cracks (Fig. 7C). This kind of filling is not widespread in our experiments as it was only observed in one fractured sample (PP239). The origin of this silica is associated with fracture processes. The deposition of this amorphous phase in spaces is characteristic of a sealing process with fluid infiltration as defined by [START_REF] Ramsay | The crack-seal mechanism of rock deformation[END_REF]. The sealing of fractures by infiltration is considered to take between months and centuries [START_REF] Renard | Kinetics of crack-sealing, intergranular pressure solution and compaction around active faults[END_REF][START_REF] Gratier | Modeling fluid transfer along Californian faults when integrating pressure solution crack sealing and compaction process[END_REF][START_REF] Gratier | Fault permeability and strength evolution related to fracturing and healing episodic processes (years to millennia): The role of pressure solution[END_REF]. Thus, our experiment shows that sealing fractures with an amorphous siliceous phase is possible and faster at laboratory time scales, from hours to days. Such peculiar sealing textures (Fig. 7C) have not yet been recognized in similar experiments (400°C, a confining pressure of 100 MPa and a pore fluid pressure of 50 MPa) on natural rocks (Tenthorey and Gerald, 2006).

To summarize, our experiments clearly show that permeability reduction operates through processes of self-healing and sealing of fractures, in the presence of an aqueous fluid phase that ensure mass transport.

A C C E P T E D M A N U S C R I P T

This assumption is clearly verified with water as pore fluid for all lithologies, whereas experiments using argon as pore fluid need to be re-examined. Argon, an inert gas, was initially used to measure permeability independently of any hydrothermal reaction. However, three different permeability evolutions have been observed in the three tested diabase alteration facies. For epidosite (PP332), the permeability remained constant after macroscopic failure. This evolution was expected using an inert fluid medium, as it is observed in other studies (e.g. Tenthorey and Gerald, 2006). On the other hand: i) the experiment on the metadiabase (PP239) shows a return to the initial permeability values after the macroscopic failure; and ii) the experiment on the chloritized metadiabase (PP324), permeability never exceeded the measurement sensitivity. Closure mechanisms described above (self-healing and sealing) and the presence of water in the chloritized metadiabase sample column after the experiment, attest to the fact that water-rich fluids have been generated during experiments using argon as a pore fluid pressure. A potential source of water might be the dehydration of chlorite. Indeed, the red color of the chlorite after the experiment PP324 appears to be the result of oxidation. The mechanism of chlorite oxidation is well known to produce water (Borggaard et al., 1982) in oxidizing conditions close to our temperature and redox experimental conditions. In fact, using argon, we maximize hydrogen loss in the sample column, causing oxidation of the sample [START_REF] Hamilton | The solubility of water and effects of oxygen fugacity and water content on crystallization in mafic magmas[END_REF]. Moreover, the formation of hematite, detected by X-Ray powder Diffraction (XRD, INEL diffractometer with a curved position-sensitive detector CPS120), corroborates the oxidizing conditions prevailing during experiments with argon (Fig. 11). Borggaard et al. (1982) demonstrated that chlorite oxidation, in addition to forming water, yields structural changes like an overall expansion of the c-dimension. As a result, from the beginning of the experiment, chlorite should have expanded and partly filled the initial low porosity. This hypothesis was verified by XRD after experiment (PP324): chlorite has a larger d(001) value than before the experiment (Fig. 11).

A C C E P T E D M A N U S C R I P T

Scale and decompression effects on permeability

Our starting laboratory permeability values of metadiabase are lower than drill-string packer measurements of in situ permeability (10 -18 to 10 -17 m 2 ) in current sheeted dykes [START_REF] Becker | Measurements of the permeability of the sheeted dikes in hole 504B, ODP LEG 111[END_REF][START_REF] Fisher | Permeability within basaltic oceanic crust[END_REF][START_REF] Becker | Permeability of upper oceanic basement on the eastern flank of the Juan de Fuca Ridge determined with drill-string packer experiments[END_REF]. As mentioned in the introduction, these differences of several orders of magnitude are explained by the scale dependency of permeability measurements (e.g. [START_REF] Brace | Permeability of crystalline and argillaceous rocks[END_REF]Townend and Zoback, 2000). Our natural samples have a diameter of 10 mm and have been intentionally selected from zones where very few microcracks occurred. In contrast, borehole permeability measurements deal with large volume in situ rocks, which are intensively fractured. However, fracture development in our experiments allows increasing permeability by at least one order of magnitude. Moreover, our initial values on metadiabases approach permeability values obtained in experimental studies on oceanic crustal basalt samples [START_REF] Hamano | Physical properties of basalts from Holes 417D and 418A. Initial Rep[END_REF][START_REF] Johnson | Crack distribution in the upper oceanic crust and its effects upon seismic velocity, seismic structure, formation permeability, and fluid circulation[END_REF][START_REF] Karato | Physical properties of basalts from Deep Sea Drilling Project Hole 504B. Initial Rep[END_REF].

Basalt permeability values vary significantly in those studies (10 -22 to 10 -16 m 2 ) depending on the texture (fresh basalt vs. breccias basalt) and the diagenesis (± smectite).

It is noteworthy that our single gas flow numerical simulations performed on samples after experiments vary between 10 -13 and 10 -15 m 2 depending on tested lithologies (± chlorite and epidote). Thus, after total decompression (i.e. the confining pressure is progressively decreased to 1 bar at the end of each experiment) and preparation of samples for X-Ray tomography, simulated permeability values are 4-6 orders of magnitude higher than experimental values determined under P-T conditions. This intuitive result is well explained by the effect of the confining pressure on permeability (e.g. [START_REF] Karato | Physical properties of basalts from Deep Sea Drilling Project Hole 504B. Initial Rep[END_REF][START_REF] David | Influence of stress-induced and thermal cracking on physical properties and microstructure of La Peyratte granite[END_REF] which must be considered in permeability determinations contrary to some methods such as fracture mapping on ophiolitic outcrops [START_REF] Nehlig | Fracture and permeability analysis in magma-hydrothermal transition zones in the Samail ophiolite (Oman)[END_REF]Van Everdingen, 1995).

A C C E P T E D M A N U S C R I P T

Conclusion

Our results clearly show the intrinsic relationship between deformation and hydrothermal reaction and its impacts on transient permeability in altered oceanic rocks from sheeted dyke complex at the centimeter scale. During the loading of the specimens, laboratory permeability values are lower than the initial values due to the compaction and the closure of the low porosity. Permeability increased slightly just before macroscopic failure only in the epidosite via a coalescence of microcracks that would be favored by many large quartz grains.

Immediately following failure, permeability peaks and decreases in a few minutes using water as pore fluid. This closure of the porosity is explained by self-healing and/or sealing of microcracks. Contrary to the study of Tenthorey and Gerald (2006), our experiments using argon as the pore fluid on metadiabases show that permeability reduction is possible despite the inertia of this gas. Indeed, in chloritized samples, self-healing and/or sealing was possible using argon thanks to intrinsic water from oxidation of chlorite.

Fracture networks induced by deformation are influenced by mineralogy (chlorite content). After experiments in metadiabase, conjugate fractures, micro fractures perpendicular to σ1 and numerous microcracks parallel to σ1 in quartz grains were observed. With respect to the fractured strongly chloritized metadiabase, fracture emplacement was represented by few thin discontinuous fractures where chlorite is abundant (gouge zones).

After the laboratory experiments, the fractured samples were imaged and the permeability values modeled by numerical simulations were compared to the measured permeability values under P-T conditions. Our numerical simulations performed after experiments confirm that decompression greatly increases permeability by 4-6 orders of magnitude. Consequently, after high pressure experiments, textures studied by X-ray During stress loading, a compaction/dilatant evolution is observed only in experiments on epidosite. Failure tends to increase permeability by one order of magnitude. For example, using water as pore fluid, permeability measurements after macroscopic failure give the following variations from 4×10 -20 m 2 to 2.9×10 -19 m 2 for metadiabase, 1×10 -20 m 2 to 2.6×10 -19 m 2 for chloritized diabase and 6.5×10 -19 m 2 to 3×10 -18 m 2 for epidosite.

Textures suggestive of self-healing and sealing explain permeability reduction by hydrothermal reaction after macroscopic failure. Paradoxically, even using argon as pore fluid, hydrothermal reaction is possible in metadiabases due to dehydration of chlorite.

A C C E P T E D M A N U S C R I P T

Fig. 1. Diagram of a typical hydrothermal system within an oceanic ridge axial zone (modified from [START_REF] Alt | Subseafloor processes in mid-ocean ridge hydrothermal systems[END_REF].

Permeability data of the sheeted dyke complex are compiled from two different methods: fracture and vein mapping in ophiolites [START_REF] Nehlig | Fracture and permeability analysis in magma-hydrothermal transition zones in the Samail ophiolite (Oman)[END_REF]van Everdingen, 1995) and in situ measurements in current oceanic crusts [START_REF] Becker | Permeability of upper oceanic basement on the eastern flank of the Juan de Fuca Ridge determined with drill-string packer experiments[END_REF]. Notice that hydrothermal fluid flow (recharge area, reaction zone and discharge area) can be represented in two directions (perpendicular and parallel to ridge axis). Ophiolite using argon (A) and water as pore fluids (B). In (A), it was not possible to measure the permeability before and after macroscopic failure. So, using argon as pore fluid, permeability was certainly lower than the minimum permeability measurable by the steady-state flow method represented by blue dashes (5×10 -21 m²;

GSA repository item 2003132 of Tenthorey and Cox, 2003). In (B), it was not possible to measure the permeability during deformation before macroscopic failure. When permeability stabilized after macroscopic failure, the specimen was deformed again with a slip (Sl) of 300 µm on the fracture.

  highly parallelized lattice Boltzmann code, Palabos (see details in[START_REF] Degruyter | Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices[END_REF], running on a computer cluster at the ISTO. The segmented volumes were converted in an input file using a Matlab script where porous space is filled with a fluid and the walls of the porous medium are set to bounce-back boundary conditions. Palabos solves for the steadystate velocity field of the fluid flow caused by an imposed pressure gradient across two opposite ends of the segmented volume (the four other sides of the volume being sealed).

  have to be carefully interpreted in terms of size aperture and hydrodynamics in future experimental endeavors. Consequently, as already noticed by[START_REF] Brace | Permeability of crystalline and argillaceous rocks[END_REF], inferred permeability measured from fracture spacing and apertures in outcrop are subject to severe overestimation. Finally, the low, fracture-enhanced, centimeter-scale permeability values of different diabase alteration facies within the oceanic sheeted dyke complex are inadequate in explaining the very high fluid flux observed in localized upflow zone near and along oceanic ridges. At large scales, fluids are channelized through up to centimeter-scale connected fractures/faults network, resulting in higher large-scale permeability values, allowing free convection cells to develop. Although our short duration experiments are not designed to simulate oceanic metasomatism, micro-crack healing and sealing appear to be rapid phenomena, not favoring the physical percolation of metasomatic fluids. The volume of fluid injected into the specimen (V) is monitored over time. Thus, Q is known by linear regression as shown in the figure A (Q = 0.0024 mm 3 /s). This figure represents the first Q measurement made on the metadiabase with water as pore fluid (PP274) before deformation. We can notice that the fluid is not continuously injected by the piston because of the initial low permeability of the sample (4×10 -20 m 2 ). Whereas after failure and the complete unloading of the specimen, the fluid is continuously injected (Fig. B; Q = 0.025 mm 3 /s and k = 2.9×10 -19 m 2 ).

  achieved at 400°C, 100 MPa of confining pressure and 50 MPa of pore fluid pressure, conditions at the base of sheeted dykes. Permeability was measured by injection of water and argon before, during and after coaxial deformation. Resulting textures and mineralogy were studied by microscopy and X-ray microtomography in order to identify mineral reactions and to calculate the permeability by numerical simulation after decompression.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Photomicrographs in crossed polars of the three lithologies sampled from sheeted dikes in Troodos ophiolite. (A) Metadiabase presenting relics of doleritic texture (spherulites of actinolite and plagioclase feldspar). The magmatic texture is well preserved despite the reequilibration in the greenschist facies conditions. (B) Strongly chloritized metadiabase, spherulites of plagioclase grains are less discernible. (C) Epidosite enriched in epidote and quartz. Magmatic texture is overprinted by an intense metasomatic replacement leading to a granoblastic texture. Abbreviations: Act = Actinolite; Chl = Chlorite; Ep = Epidote; Plag = Plagioclase; Qtz = Quartz.

Fig. 4 .Fig. 5 .

 45 Fig. 4.Permeability evolutions of metadiabase from the sheeted dyke complex of Troodos Ophiolite using argon (A) and water as pore fluids (B). In (A), permeability was measured before and after macroscopic failure. In (B), permeability was measured at different steps of differential stress. The minimum permeability measurable by the steady-state flow method is fixed at 5×10 -21 m² (GSA repository item 2003132 ofTenthorey and Cox, 2003) and represented by blue dashes.

Fig. 6 .

 6 Fig.6. Permeability evolutions of epidosite from the sheeted dyke complex of Troodos Ophiolite using argon (A) and water as pore fluids (B). In (A&B), permeability was measured at different steps of differential stress.Notice that the error bars of permeability measurements are almost zero.

Fig. 7 .

 7 Fig. 7. SEM micrographs showing microstructures and typical textures after experiments on metadiabase (in all images σ1 is vertical). (A) SEM image of the top of the fractured specimen after experiment with water (PP274). Note that the lower part of the sample is missing because it has been cut for X-Ray microtomography. (B) SEM image showing microcracks parallel to σ1 and a microfracture subnormal to σ1 in the fractured specimen after experiment with argon (PP239). (C) High magnification SEM image of same specimen as in (B) showing an amorphous siliceous phase between quartz and plagioclase feldspar grains. (D) High magnification SEM image of same specimen as in (A) showing a grain of quartz presenting self-healing texture (S-H). Abbreviations for minerals: Act = Actinolite; Mag = Magnetite; Plag = Plagioclase; Qtz = Quartz.

Fig. 8 .

 8 Fig.8. 3D visualizations (using the software Blob3D) of the fracture network of one part of each specimen. σ1 is parallel to Z axis. Microcracks could not be segmented because of the resolution (the voxel size is approximately 5.5 µm). Fracture networks of metadiabase from the experiments using argon (A) and water (B) as pore fluids.Fracture networks of strongly chloritized metadiabase from the experiments using argon (C) and water (D) as pore fluids.

Fig. 9 .

 9 Fig. 9. SEM micrographs showing microstructure and typical textures after experiments on strongly chloritized metadiabase (in all images σ1 is vertical). (A) SEM image of a gouge in the water experiment (PP298). (B) High magnification SEM image of same specimen as in (A) showing a grain of quartz presenting self-healing texture (S-H). Abbreviations for minerals: Chl = Chlorite; Mag = Magnetite; Plag = Plagioclase; Qtz = Quartz.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. SEM micrographs showing microstructure and typical textures after experiments on epidosite (in all images σ1 is vertical; images from the water experiment PP308). (A) SEM image showing conjugate fractures and the initial porosity (I.P.). (B) SEM image showing a discontinuous thin fracture because of chlorite. (C) SEM image showing micro fractures along epidote grains. (D) High magnification SEM image showing a grain of quartz presenting self-healing texture (S-H). Abbreviations for minerals: Chl = Chlorite; Ep = Epidote; Qtz = Quartz.

Fig. A .

 A Fig. A. V vs. time diagram for the first Q measurement before deformation (PP274).

Fig. B .

 B Fig. B. V vs. time diagram for Q measurement after failure and complete unloading of the specimen (PP274).

Figure 3 A

 3 Figure 3

Figure 6 A

 6 Figure 6

Figure 9 A

 9 Figure 9

  Figure A

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Tenthorey, E., Cox, S.F., 2006. Cohesive strengthening of fault zones during the interseismic period: An experimental study. J. Geophys. Res. 111, doi: 10.1029/2005JB004122. Vine, F.J., Smith, G.C., 1990. Structural and physical properties of the Troodos crustal section at ICRDG drillholes CY1, 1a and 4, in: Malpas, J., Moores, E.M., Panayiotou, A.,

m 2 . Finally, permeability dropped quickly to 6.9×10 -21 m 2 , a value close to the minimum

Acknowledgements

We are very grateful to Eleni Gergiou-Morisseau (Geological Survey Department of Cyprus) for her warm welcome in Cyprus and her help in sampling. We would also like to thank Michel Pichavant and Luc Barbanson for supporting this project funded by FluxHyd, Calamine and the 3F INSU program. We counted on the expertise of Alain Burgisser on using Palabos. For the use of the computer clusters we thank Jean-Louis Rouet, Laurent Catherine and Emmanuel Le Trong (CCSC CaSciModOT).

Appendix. Flow rate

A C C E P T E D M A N U S C R I P T

Highlights  We studied relations between permeability, deformation and three alteration facies.  Permeability reduction after failure is due to self-healing and crack sealing.  Experiments using argon as pore fluid are not inert because of dehydration.  Abundance of chlorite generates gouge faults.  Numerical simulations show permeability overestimation in unloaded samples.


Yanyan Yuan

Karine Le Guen

Jean-Michel André

Christian Mény

Corinne Ulhaq

Anouk Galtayries

Jingtao Zhu

Zhanshan Wang

Philippe Jonnard
email: philippe.jonnard@upmc.fr.

Interface observation of heat-treated Co/Mo 2 C multilayers

Keywords: Co/Mo 2 C multilayer, intermixing, demixing, NMR spectroscopy, ToF-SIMS, XRD, TEM, XES

We study the interface evolution of a series of periodic Co/Mo 2 C multilayers as a function of the annealing temperature up to 600°C. Different complementary techniques are implemented to get information on the phenomenon taking place at the interfaces of the stack. The periodical structure of Co/Mo 2 C multilayer is proven by Time-of-flight secondary ion mass spectrometry (ToF-SIMS) depth profiles which demonstrate the formation of an oxide layer at both air/stack and stack/substrate interfaces. From Nuclear magnetic resonance (NMR) spectra, we observed the intermixing phenomenon of Co and C atoms for the asdeposited sample, and then at annealing temperature above 300°C Co and C atoms separate from their mixed regions. Comparison of NMR results between Co/Mo 2 C and Co/C references confirms this phenomenon. This is in agreement with x-ray emission spectroscopy (XES) measurements. Furthermore the calculation of the Co-C, Co-Mo and Mo-C mixing enthalpy using Miedema's model gives a proof of the demixing of Co and C atoms present within the stacks above 300°C. From the transmission electron microscopy (TEM) analysis, we found the presence of some crystallites within the as-deposited sample as well as the mainly amorphous nature of all layers. This is confirmed using x-ray diffraction (XRD) patterns which also demonstrate the growth of crystallites induced upon annealing.

Introduction

Multilayer systems periodically alternating (at least) two materials are widely used in the extreme ultra-violet and soft x-ray ranges. The optical performances of multilayers mirrors are usually limited by the interface and surface quality, such as intermixing, interdiffusion, interface reaction and surface oxidation. Multilayer optics may be subject to high temperatures in their applications, for instance intense synchrotron light, free electron laser or laser plasma sources. Thus the ability to withstand high-power x-ray radiation without undergoing radiation damage or interdiffusion is an important merit for an x-ray multilayer mirror.

A lot of works focused on the study of the thermal behaviour of the Mo/Si [START_REF] Stearns | Thermally induced structural modification of Mo/Si multilayers[END_REF][START_REF] Voorma | Temperature induced diffusion in Mo/Si multilayer mirrors[END_REF][START_REF] Bajt | Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers[END_REF][START_REF] Jonnard | Physico-chemical and x-ray optical characterizations of a Mo/Si multilayer interferential mirror upon annealing[END_REF][START_REF] Valkovskiy | Study of roughness in multilayer Mo-Si mirrors[END_REF], Albased [START_REF] Windt | Performance, structure, and stability of SiC/Al multilayer films for extreme ultraviolet applications[END_REF][START_REF] Zhong | The chemical characterization and reflectivity of the Al(1.0%wtSi)/Zr periodic multilayer[END_REF][START_REF] Zhong | The thermal stability of Al(1%wtSi)/Zr EUV mirrors[END_REF][START_REF] Zhong | Thermally induced structural modification in the Al/Zr multilayers[END_REF] and Co-based multilayers [START_REF] Zhu | Comparison of Mg-based multilayers for solar He II radiation at 30.4 nm wavelength[END_REF][START_REF] Le Guen | Development and Interfacial Characterization of Co/Mg Periodic Multilayers for the EUV Range[END_REF][START_REF] Li | Improved thermal stability of Mg/Co multilayer by introducing Zr barrier layer[END_REF][START_REF] Le Guen | Introduction of Zr in nanometric periodic Mg/Co multilayers[END_REF][START_REF] Hu | Investigation of the thermal stability of Mg/Co periodic multilayers for EUV applications[END_REF] have demonstrated that interface properties play an important role in the optical performances. Concerning these multilayers, single elements are usually used as a spacer and absorber layers to constitute a multilayer. However it is generally easy to form some compounds between two single elements. A possible solution to avoid or at least reduce the interdiffusion and compound formation is to build a multilayer where one or even both spacer and absorber layers consist in a stable compound. Bai et al. reported that CoMoN/CN multilayers show relatively stable interfaces [START_REF] Bai | Interdiffusion in lowtemperature annealed amorphous CoMoN/CN compound soft-x-ray optical multilayer mirrors[END_REF]. Recently, the investigation of B 4 C/Mo 2 C multilayer also demonstrated abrupt interfaces with respect to B 4 C/Mo multilayer where interlayers were detected [START_REF] Choueikani | Xray properties and interface study of B 4 C/Mo and B 4 C/Mo 2 C periodic multilayers[END_REF].

The evolution of interface structure upon annealing has been widely studied. In Mo/Si multilayers, it has been reported that the reflectivity decreases upon annealing owing to the increase of interdiffusion at interfaces [START_REF] De Rooij-Lohmann | Enhanced diffusion upon amorphous-to-nanocrystalline phase transition in Mo/B 4 C/Si layered systems[END_REF]. The Co/C multilayers showed an enhanced reflectivity at annealing temperatures lower than 250°C due to phase separation [START_REF] Bai | Enhancement of the reflectivity of soft-x-ray Co/C multilayers at grazing incidence by thermal treatment[END_REF]. Moreover a backward diffusion of two elements, from their mixtures to the pure elements, at the interfaces was also observed in the Co/Au, Co/Ag, Co/C and CoN/CN multilayers annealed up to 250°C [START_REF] Broeder | Perpendicular Magnetic Anisotropy of Co-Au Multilayers Induced by Interface Sharpening[END_REF][START_REF] Luby | Tailoring of multilayer interfaces by pulsed laser irradiation[END_REF][START_REF] Bai | Interdiffusion in Co/C soft X-ray multilayer mirrors[END_REF][START_REF] Bai | Interdiffusion in CoN/CN soft X-ray multilayer mirrors[END_REF].

In the present paper, we study the change of the interface properties of the Co/Mo 2 C multilayer with the annealing temperature. The optical properties of this series multilayers have been investigated by using hard x-ray and soft x-ray reflectivities and already reported in Ref. [START_REF] Yuan | Investigation of the x-ray reflectivity of the Co/Mo 2 C system upon thermal treatment[END_REF].

To summarize, the best reflectivity is 27% at 1.59 nm for 300°C annealed sample and decreases down to 20% following annealing at 600°C. The interface structure is studied by combining both non-destructive methods, x-ray emission spectroscopy (XES), nuclear magnetic resonance (NMR) spectroscopy, x-ray diffraction (XRD) and destructive methods, time-of-flight secondary ions mass spectroscopy (ToF-SIMS) and transmission electron microscopy (TEM). The comparison of the XES Co/Mo 2 C multilayer spectra with that of the reference samples, a Mo 2 C thin film and Co/C multilayer, is used to determine the chemical state of the C atoms within the stack. NMR spectroscopy is carried out to provide the information about the chemical state of Co atoms by describing the Co atoms distribution as a function of their resonance frequency. ToF-SIMS depth profiles determine the distribution in depth of various elements. Phase change and microstructure are studied by using XRD and transmission electron microscopy (TEM) respectively.

Experiments

All the samples are prepared following the designed parameters described in a previous paper [START_REF] Yuan | Co/Mo 2 C multilayer as X-ray mirror: Optical and thermal performances[END_REF]. Let us recall that the samples were prepared on the sliced and polished Si(100) substrate by magnetron sputtering. The based pressure was 10 -5 Pa before deposition. The sputtering gas was argon (99.999% purity) at a constant working pressure 0.1 Pa. The powers applied to sputtering target were 40 W and 60 W for Co and Mo 2 C, respectively. The aimed period is equal to 4.1 nm and the ratio of the Mo 2 C thickness to the period is 0.36, resulting in Co and Mo 2 C thicknesses of 2.6 nm and 1.5 nm, respectively. Six samples with an area of 20 x 20 mm 2 were deposited separately on the Si wafer with the same conditions. From one sample to another a small variation of the period can exist. The number of periods is 30. A 3.5 nm-thick B 4 C capping layer was deposited on top of the samples to prevent oxidation. The samples were annealed at 200, 300, 400, 500 and 600°C for 1 h under high vacuum. A reference Mo 2 C thin film, with a thickness of about 60 nm, was deposited onto a silicon substrate with the same deposition conditions as the Mo 2 C layers of the multilayer. Three Co/C multilayers with the thickness of 2.0 nm for both Co and C layers in one period were deposited on a silicon substrate using the same conditions as for the Co/Mo 2 C multilayers. Two of them were annealed at 300°C and 600°C for one hour in a furnace with a base of pressure of 3.0×10 -4 Pa.

X-ray emission spectroscopy

The X-ray emission analysis was performed in a high-resolution wavelength dispersive soft x-ray spectrometer [START_REF] Bonnelle | Instrument for research on interfaces and surfaces[END_REF] equipped with a curved etched multilayer [START_REF] Jonnard | An etched multilayer as a dispersive element in a curved-crystal spectrometer: implementation and performance[END_REF] to disperse the emitted radiation. The C Kα emission (2p -1s transition) from the Co/Mo 2 C multilayers and the reference samples (Mo 2 C thin film and Co/C multilayer) was analysed. Graphite was also used as a reference material. The Mo valence states have not been studied since the corresponding emission (Mo Lβ 2 , 4d -2p 3/2 transition), accessible with our spectrometer, is not very sensitive to the chemical state of the molybdenum atoms. The same is true with the Co atoms [START_REF] Le Guen | Characterization of EUV periodic multilayers[END_REF].

Nuclear magnetic resonance spectroscopy

In order to probe the chemical state of the Co atoms within the multilayer, the samples were analyzed by zero-field NMR spectroscopy. The NMR spectra represent the distribution of the Co atoms as a function of their resonance frequency. The NMR resonance frequency is sensitive to the local environment of the probed atoms: the number, nature and symmetry of atoms in its neighbourhood [START_REF] Panissod | NMR analysis of buried metallic interfaces[END_REF][START_REF] Panissod | Nuclear magnetic resonance investigations of the structure and magnetic properties of metallic multilayers and nanocomposites[END_REF]. The NMR spectroscopy of a Co 3 Mo disordered alloy and two Co/C multilayers (as-deposited and 600°C) were also measured as reference samples to analyse the Co/Mo 2 C spectra. To enhance the sensitivity, the measurement temperature was 2 K for all the multilayer samples and 4.2 K for the Co 3 Mo disordered alloy. All the multilayer spectra are normalized to the samples surface area.

Time-of-flight secondary ions mass spectrometry

The depth distribution of the Co/Mo 2 C multilayers was investigated using a ToF-SIMS instrument (TOF.SIMS V spectrometer, ION-TOF GmbH) working in the dual-beam mode. The sputtering was performed using a 1 keV (59 nA) Cs + ion beam, rastered over an area of 300 µm × 300 µm. A pulsed 25 keV Bi + primary ion source at a current of 1.3 pA (high current bunched mode), rastered over a scan area of 100 µm × 100 µm was used as the analysis beam. Both ion beams were impinging the sample surface forming an angle of 45° with the surface normal and were aligned in such a way that the analyzed ions were taken from the center of the sputtered crater.

Both positive and negative ions were recorded. In the present paper, only negative ions spectra are presented since they can provide sufficient information from each layer. The ToF-SIMS technique provides a qualitative chemical analysis as the intensity does not correspond directly to the number of atoms in the multilayer (the sputtering yields vary from one element to another as well as from one matrix to another).

X-ray diffraction

To further characterize the phase structure of samples annealed at different temperatures, the XRD measurements were performed by using a PANalytical X'Pert Pro diffractometer with Cu Kα radiation (0.154 nm) emitted from an x-ray tube operating at 45 kV and 40 mA. The scanning angle range is 10-80° with a step of 0.01°. For the sake of comparison, the XRD patterns of the Co/C reference multilayers were also performed. Here no refinement of procedure of the structural characterization [START_REF] Fullerton | Structural refinement of superlattices from x-ray diffraction[END_REF][START_REF] Beke | Thermal stability of amorphous and crystalline multilayers produced by magnetron sputtering[END_REF] was done.

Transmission electron microscopy

Ultra-thin cross-sectional slices were prepared using a focused ion beam (FIB). Highresolution images were obtained by the JEOL 2100F instrument operated at 200 kV with an image resolution of 0.2 nm. Scanning transmission electron microscopy (STEM) images were obtained by scanning the focused beam over the slice with an image resolution of 0.11 nm. High angle-annular dark field (HAADF) images can be collected simultaneously, which makes the STEM a good technique for materials morphological and chemical characterization of materials at the subnanometer level.

Results

X-ray emission spectroscopy

The C Kα emission bands emitted by the as-deposited and annealed at 600°C Co/Mo 2 C multilayers as well as the Mo 2 C, graphite and Co/C multilayers references (for this latter, asdeposited and annealed at 600°C), are presented in Fig. 1. The spectrum of the Co/Mo 2 C annealed at 300°C is the same as that of the as-deposited sample and is thus not shown here. The spectra of the Co/Mo 2 C annealed at 400 and 500°C are not shown here as they are the same as that of Co/Mo 2 C annealed at 600°C (Fig. 1(a)). Regarding the Co/C reference multilayers, the spectrum of the as-deposited Co/C sample should be similar to one of the amorphous carbons if no interaction takes place within the structure.

The comparison with the spectra of amorphous C from Refs. [START_REF] Galakhov | Ultrasoft X-ray spectroscopy with variation of the electron excitation energy as a method for analyzing thin films and solid/solid interfaces[END_REF][START_REF] Hosokawa | Soft X-ray emission study of nanostructured carbon[END_REF] shows that this is not the case (Fig. 1(b)). This indicates that, in the as-deposited Co/C system, some interaction exists between the

Nuclear magnetic resonance spectroscopy

NMR spectra of all Co/Mo 2 C multilayers as a function of the annealing temperature are presented in Fig. 2. It can be seen that the spectra of the as-deposited and 200°C samples consist of a wide structure without any extra feature. For the 300, 400, 500 and 600°C annealed samples, a welldefined line is observed at around 221 MHz. This line corresponds to bulk Co with an hcp-like structure [START_REF] Malinowska | The anisotropic first-neighbour contribution to the hyperfine field in hexagonal-close-packed Co: a nuclear magnetic resonance study of diluted alloys and multilayers[END_REF]. However the frequency is lower than the one expected for well crystallized hcp Co.

As suggested in Ref. [START_REF] Zoll | Influence of the growth technique on the coupling and magnetoresistance of Co/Ru sandwiches[END_REF], this is most probably due to the presence of a large amount of stacking faults within the layer. Regarding the as-deposited and 200°C annealed samples the absence of a well-defined NMR feature indicates that most of Co atoms are mixed with other atoms (Mo or C).

From 300°C, the intensity of the 221 MHz line increases with the annealing temperature while the low frequency (<220 MHz) contributions stay almost unchanged. This indicates that the total amount of ferromagnetic Co atoms as well as pure Co increase from 300°C and above. From the phase diagram of Co-Mo system showing the existence of several ordered phases, it is unlikely that annealing the samples result in a phase separation between Co and Mo. Therefore the strong intermixing revealed by the as-deposited NMR spectra is more likely to come from mixing of Co and C atoms. Since the Co carbides are not stable phases the C is likely to separate from Co-C mixing region upon annealing. This phenomenon has also been reported by H. Bai et al. [START_REF] Bai | Interdiffusion in Co/C soft X-ray multilayer mirrors[END_REF].

To check this interpretation, we measured the NMR spectrum of a reference Co 3 Mo disordered alloy, as well as the spectra of the Co/C multilayers as-deposited and annealed at 600°C, signal gives evidence of the periodic structure of the multilayer. There are only 29 periods for these three samples from the outermost period to the substrate, meaning that the 30 th period is chemically modified. At the stack/substrate interface, this period is mixed with the Si substrate and the C - profile presents a low amplitude signal at the end of the profile. The C -, Co -, O -, CoO -, B -and MoO 2 -profiles toward the air/stack and stack/substrate interfaces for the as-deposited, 300 and 600°C annealed samples are presented in Fig. 6. From the O -depth profiles, it can be deduced that oxidation took place at both interfaces. Oxidation at the air/stack interface is due to the atmospheric contamination of the surface layers during storage in air and transfer. Oxidation at the stack/substrate interface is due to the native oxide on the silicon substrate. Similar phenomena were reported in Al/Mo/SiC multilayers [START_REF] Hu | Structural properties of Al/Mo/SiC multilayers with high reflectivity for extreme ultraviolet light[END_REF]. The oxidation of the first Mo 2 C layer in the stack was also reported by Giglia et al. [START_REF] Giglia | Thermal effects on Co/Mo 2 C multilayer mirrors studied by soft x-ray standing wave enhanced photoemission spectroscopy[END_REF]. At the stack/substrate interface, the O -profile for the 300°C and 600°C annealed samples is sharper than that of the as-deposited sample. This is probably caused by the diffusion of oxygen atoms from the substrate into the stack after annealing. We did not get the information about the combination between O and Mo atoms as no difference in the MoO 2 -profile can be found when the annealing temperature is varied. The oxidation at the stack/substrate interface explains why the 30 th period is not well detected.

Furthermore, in the case of as-deposited and 300°C annealed samples, the signal of the CoO - ions at the air/stack and stack/substrate interfaces is more intense than in that of the 600°C annealed sample. For 600°C annealed sample, the signal of the CoO -ions is not detected at the air/stack interface. Firstly, this indicates that Co layers are oxidized at temperatures lower than 300°C and that the Co oxide decomposes at high temperature. The C -and B -profiles do not show any significant change in the three samples. annealed sample. The Mo -profile follows the C -profile (not shown). The C -profile displays a symmetrical shape and is almost in the opposite phase with respect to the Co -profile. The Co -depth profile displays some shoulders which correspond to the maxima in the CoMo -depth profile. This is attributed to a matrix effect since for ultra-thin layers it is not possible to reach a steady sputtering regime before the end of the period. Figure 7(b) shows the comparison of the Co -and C -ions profiles of the as-deposited and 600°C annealed samples. Both ions profiles are normalized. We cannot observe any significant changes in the Co -depth profile between as-deposited and 600°C annealed samples. The same situation is recorded for the C -depth profile except a slightly better contrast for the sample annealed at 600°C with respect to the as-deposited sample. Fig. 7 ToF-SIMS depth profiles of the Co -, CoMo -and C -ions for the 600°C annealed sample (a) and comparison of depth profiles of the Co -and C -ions for the as-deposited and 600°C annealed samples (b). ToF-SIMS depth profiles of Co -and CoMo -ions are shifted vertically for clarity.

Transmission electron microscopy

Discussion

From the preceding analysis, it suggests that the enhancement of ferromagnetic Co signal above 300°C should be primary ascribed to a separation of Co and C atoms at the interfaces. In the multilayer because of their high crystallization temperature [START_REF] Newsam | The structures of the ηcarbides Ni 6 Mo 6 C, Co 6 Mo 6 C, and Co 6 Mo 6 C 2[END_REF]. Otherwise, the XRD results show that no significant Co 3 Mo crystallites can be formed from as-deposited to 500°C annealed samples.

Therefore, we can deduce that intermixing takes place for the as-deposited and 200°C annealed samples without significant formation of Co 3 Mo compound.

Based on the Miedema's macroscopic atom model [START_REF] Das | Miedema model based methodology to predict amorphous-forming-composition range in binary and ternary systems[END_REF], we can calculate the mixing enthalpy of the Co-Mo and Co-C systems to confirm our results. According to this model, which have been developed to calculate the enthalpy values for binary alloys, the enthalpy of formation of the Co-Mo system, made of two transition metals, can be expressed as:

( ) for ordered alloy ( )

3 1 3 1 2 3 1 3 1 2 3 2 2 - -+ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - + - - = Δ
3 2 3 2 3 2 Co Co Mo Mo Mo Mo S Mo V c V c V c c + = ( ) 3 2 3 2 3 2 Co Co Mo Mo Co Co S Co V c V c V c c + = P=14.1, Q/P=9.4 V 2 /(d.u.) 2/3
Here, Co

+ ⋅ = 1 3 2 3 2 (2)
where a is a constant equal to 0.04 for Mo and 0.1 for Co [43]. For the Mo-C system, the enthalpy change can be expressed as:

( ) ( ) ( ) [ ] metal element C C ws Mo ws Mo ws C ws Mo C Mo Mo C C C Mo C C C H c n n P R n n P Q V c V c f Pc H → Δ + + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - + - - + = Δ - - 3 1 3 1 2 3 1 3 1 2 3 2 3 2 2 φ φ (3) ( ) 3 2 3 2 3 2 C C Mo Mo Mo Mo S Mo V c V c V c c + = ( ) 3 2 3 2 3 2 C C Mo Mo C C S C V c V c V c c + = P=14.1, Q/P=9.4 V 2 /(d.u.) 2/3 R/P=2.1 V 2
Here ( )

metal ment C C H → Δ
ele stands for the transformation enthalpy of C into a metallic state and the third term in the equation (3) represents a hybridization contribution and favors a tendency of phase separation. For carbon, the corresponding transformation energy equals the heat of fusion, 100 kJ/mol. To improve the agreement between predicted and experimental values, the transformation energy has been changed to 180 kJ/mol [START_REF] Niessen | The "Macroscopic Atom" Model: An Easy Tool to Predict Thermodynamic Quantities -Springer[END_REF].

As mentioned above, we need to consider the volume change of the constituents C and Mo that occurs due to charge transfer when the alloy is formed. The relation is expressed as:

( ) [ ] Mo C C Mo pure C alloy C af V V φ φ - + ⋅ = 1 3 2 3 2 (4)
where a is a constant equal to 0.04 for carbon.

The calculated mixing enthalpy of the Mo-C system is presented in Fig. 10. We can see that the value of formation enthalpy is negative at C mole fraction below 0.45 and after increases sharply. In the Co/Mo 2 C stack, the atomic fraction of Mo to C in the Mo 2 C layer is designed to be 2. That is to say, the Mo 2 C compound shows small possibility of phase separation. Moreover the thermal stability of Mo 2 C has been already demonstrated [START_REF] Choueikani | Xray properties and interface study of B 4 C/Mo and B 4 C/Mo 2 C periodic multilayers[END_REF][START_REF] Tripathi | Atom beam sputtered Mo2C films as a diffusion barrier for copper metallization[END_REF]. Regarding the results mentioned above, we infer that there is a possibility of excess C atoms existing in the multilayer. Actually, this is demonstrated by the x-ray photoemission spectroscopy results of thin film Mo 2 C, which gives the atomic ratio of 0.5 between Mo and C atoms. Based on all the described results, we conclude that the Co atoms in the Co layers are mixing with C atoms for as-deposited and 200°C annealed Co/Mo 2 C samples. After annealing at 300°C and above, Co and C atoms demix from their mixed regions. However the direction of diffusion may not follow the growth direction of thin layers but other directions, such as a direction parallel to the surface. This means that separated Co and C atoms do not necessarily go back to their original layers. This phenomenon explains the decrease of the reflectivity of the multilayer after annealing [START_REF] Yuan | Co/Mo 2 C multilayer as X-ray mirror: Optical and thermal performances[END_REF].

Conclusion

The

Fig. 1 .

 1 Fig.1. C Kα emission bands emitted by the as-deposited and annealed at 600°C Co/Mo 2 C multilayers as well as the thin film Mo 2 C, graphite (a) and by (as-deposited and annealed at 600°C) Co/C references, graphite and amorphous carbon from Refs.[32,33] (b).

C

  and Co atoms leading to intermixing between C and Co layers. The consequence is a change in the density of C (and Co) valence states and thus in the shape of the C Kα emission band. With respect to as-deposited Co/C, the spectrum of Co/C annealed at 600°C shows a significant broadening and is close to that of graphite. These results suggest that the Co and C atoms are intermixed within the as-deposited Co/C, while the annealing at 600°C induces the demixing of Co and C atoms and the "graphitization" of C layers. The spectrum of as-deposited Co/Mo 2 C is the same as that of both as-deposited Co/C and of the Mo 2 C references. Thus the chemical state of the C atoms is not distinguishable for the Co/Mo 2 C as-deposited multilayer: the carbon atoms exist either in the form of Co and C mixture or in the form of Mo 2 C compound or in both forms. Following annealing at 400°C and above, the spectra of the Co/Mo 2 C multilayers show a slight broadening towards the high photon energy side. This suggests that a slightly change of the chemical state of the C atoms takes place from 400°C.

Fig. 3 .

 3 Fig.3. The spectra of the Co 3 Mo disordered alloy and of the Co/C as-deposited multilayer show a

Fig. 2 NMRFig. 3

 23 Fig.2 NMR spectra of the Co/Mo 2 C multilayers as a function of the annealing temperature.

Fig. 4

 4 Fig.4 Diffraction patterns of the Co/Mo 2 C samples: as-deposited, annealed at 200°C, 300°C, 400°C, 500°C and 600°C (a) and of the Co/C multilayers: as-deposited, 300 and 600°C (b).

3. 4 .

 4 Time of flight-secondary ions mass spectroscopy Shown in Fig.5 are the ToF-SIMS depth profiles of C -ions of the as-deposited, 300 and 600°C Co/Mo 2 C samples. The amplitude of the signal in the middle of the profile is normalized to unity to show the relative contrast of the ion signal. Then, for the sake of clarity, the curves of 300°C and 600°C annealed samples are arbitrarily shifted. The periodic modulation of C -ions

Fig. 5

 5 Fig.5 ToF-SIMS depth profiles of the C -ions for the as-deposited, 300°C and 600°C annealed Co/Mo 2 C samples(Cs + , 1 keV, 59 nA).

Fig. 6

 6 Fig.6 ToF-SIMS depth profiles of the C -, Co -, O -, CoO -, B -and MoO 2 -ions at the air/stack and stack/substrate interfaces domains for as-deposited (a), 300 (b) and 600°C (c) annealed samples. (Colour online) Figure 7(a) shows the ToF-SIMS depth profiles of the Co -, CoMo -and C -ions of the 600°C

Figure 8 (

 8 Figure 8(a) and (b) show the HAADF and bright-field images of the Co/Mo 2 C as-deposited

Fig 8

 8 Fig 8 Transmission electron microscopy of the Co/Mo 2 C as-deposited sample: HAADF (a) and bright field image (b); high-resolution image (c) and selected-area electron diffraction (d).

  Co-C binary phase diagram, there is no stoichiometric compound resulting from the reaction between Co and C [38]. In the Co-Mo binary phase diagram, Co 3 Mo and Co 7 Mo 6 (µ and δ phase) are mentioned [39,40]. The Co-C-Mo ternary phase diagram gives two ternary compounds Mo 3 Co 3 C and Mo 6 Co 6 C but there is a small possibility for their formation in the Co/Mo 2 C

  c and Mo c are the mole fraction ( Co c + Mo c =1), o C V and Mo V are the atomic volumes of Co and Mo, respectively, φ the electronegativity and ws n the electron density at the first Wigner-Seitz boundary. The electron densities are usually given in terms of density units (d.u.), 1 d.u.=6.75×10 22 electron/cm 3 . S Co C and S Mo C are the surface densities of Co and Mo atoms, respectively. ! !" !" represents the degree to which an atomic cell of Mo is in contact with dissimilar atomic cell of Co on average within the alloy. When we calculate the atomic volume, the atomic volumes of Co and Mo atoms are approximate the same ones. In equation (1), the first term is negative and proportional to the square of difference in the electronegativity parameters and therefore the charge transfer between Co and Mo. This part shows the tendency for compound formation. The second term which is positive stands for the discontinuity in electron density at the Wigner-Seitz boundary of Co and Mo atoms. This part shows the tendency of phase separation. Another effect, which has to be considered, is the volume change of the constituents Co and Mo that occurs due to charge when the alloy is formed. The charge transfer occurring between dissimilar atomic cells depends on the difference of the electronegative parameters of Co and Mo. An empirical relationship for volume change has been established

Fig. 9

 9 Fig.9 Simulated mixing enthalpy for the Co-Mo system.The loss of the ferromagnetic Co signal in NMR could be ascribed to a disordered mixture at the

Fig. 10

 10 Fig.10 Simulated mixing enthalpy for the Mo-C system.

  interfacial and structural properties of Co/Mo 2 C multilayers with annealing were characterized by the XES, NMR, ToF-SIMS, XRD and TEM. The Co/Mo 2 C multilayers show a periodic structure, the Co and Mo 2 C layers in the stack being mainly amorphous. The formation of oxide layers at both air/stack and stack/substrate interfaces are observed by the ToF-SIMS. According to TEM results, some crystallites are present in the as-deposited samples. The C Kα emission spectra of the Co/Mo 2 C multilayers annealed at 400°C and above show a slight broadening with respect to that of the as-deposited sample, suggesting a slightly change of the carbon chemical state. The NMR spectra demonstrate a demixing phenomenon between Co and C in the multilayer stack after annealing. Comparing the NMR spectroscopy results of the Co/Mo 2 C multilayers with these of the Co/C reference multilayers, we find that Co and C mix together after deposition and then, after annealing at 300°C and above, Co and C demix from their mixed regions. The Miedema's model is used to calculate the mixing enthalpy and accounts for the phenomenon of phase separation of the Co-C system.

Table 1 .

 1 Values of φ , ws n and V for calculating the mixing enthalpy of the Co-Mo system.

	Element φ (V)	ws n (d.u.) V (cm 3 /mol)
	Co	5.10	7.00	6.7
	Mo	4.37	8.46	9.4

Table 1

 1 lists the values of φ , ws n and V used for calculating the mixing enthalpy ΔH. The calculated enthalpy of Co-Mo mixing system is shown in Fig.9. It is always negative. This indicates that the Co and Mo compounds easily form. Moreover the mixing enthalpy is negative when the mole fraction of Mo changes from 0 to 0.45. However the ratio of atomic fraction between Co and Mo in the Co/Mo 2 C multilayer stack is about 3:1 and thus the Mo atomic fraction is 0.25 (according to the designed thickness of each layer). This means that the mixing enthalpy of the Co and Mo compound always decreases even if all Co atoms react with all Mo atoms in the Co/Mo 2 C multilayer, or in other words, once Co and Mo compounds are formed and they cannot easily separate.

Acknowledgments

This work is done under the framework of the international ANR-NSFC COBMUL project (ANR #10-INTB-902-01 and NSFC #11061130549). We would like to thank Imène Estève for preparing FIB sample in IMPMC in Paris.