Povilas Bertasius

Sebastien Schaefer

Jan Macutkevic
email: jan.macutkevic@gmail.com

Juras Banys

Algirdas Selskis

Vanessa Fierro

Alain Celzard

Dielectric properties of PDMS composites filled with SrTiO 3 nanoparticles

This paper deals with the dielectric properties of PDMS nanocomposites filled with SrTiO 3 nanoparticles. The investigations were performed over a very broad range of frequencies (20 Hz -3 THz). Almost no dielectric dispersion was observed in all the composites at room temperature over the entire range of measurement frequencies, and the dielectric losses were also very low under these conditions (less than 1.9). The dielectric dispersion was observed at lower temperatures (below 280 K), due to relaxation at the PDMS/SrTiO 3 interface and in the bulk polymer. The relaxation time for both cases followed the Vogel-Vulcher law, while the freezing temperature was substantially lower for relaxation at the PDMS/SrTiO 3 interface. SrTiO 3 , dielectric permittivity, polydimethylsiloxane

INTRODUCTION

New materials with special linear and non-linear dielectric properties are required in modern industry, people's life and environmental protection. For the progress of flexible electronics, new polymeric composite systems are desired [1]. Polydimethylsiloxane (PDMS) is a widely used elastic transparent polymer [2]. In addition, PDMS has excellent gas impermeability, biocompatibility, UV resistance, heat and oxidation stability, making it an important prospective matrix for polymer composites [3]. However, PDMS has low mechanical properties, low electrical conductivity and low dielectric permittivity values [3]. Nevertheless, these properties can be improved by the appropriate incorporation of nanoparticles [4][5][6]. PDMS composites are widely used in flexible bioelectronics, as sensors, coatings and batteries, and also for 3D-printing [7][8][9]. SrTiO 3 is a well-known quantum paraelectric [10][11]. No ferroelectric phase transition occurs in this material down to the lowest temperatures, but the dielectric permittivity decreases sharply on cooling. Moreover, the main dielectric dispersion is observed in the terahertz and infrared frequency ranges, while at lower frequencies the dielectric permittivity is almost independent of the frequency. Therefore, it is applicable in various electronic fields where high dielectric permittivity and low dielectric losses are required over a broad frequency range. In particular, the dielectric tunability of SrTiO 3 by electric field, light and temperature is observed at terahertz frequencies [12]. Therefore, it is possible to make various devices operating in the terahertz frequency range, such as high-speed electronic modulators, photonic crystals and metamaterials [13]. In electronics, SrTiO 3 is also applicable as wide gap semiconductor with a bandgap of 3.2 eV. SrTiO 3 composites are widely investigated as cooling materials [14], for dielectric capacitors and energy storage applications [15], or for photocatalytic water splitting for hydrogen production [16]. The dielectric properties of SrTiO 3 in various polymer matrices have been mainly investigated at low frequency [17,18]. It has been established that the dielectric permittivity of composites based on nano SrTiO 3 can be quite high at room temperature (about 60 for polyethylene with 12% SrTiO 3 of volume fraction) and is strongly dependent on the distribution of SrTiO 3 particles in the polymer matrix, being more important for aggregated SrTiO 3 particles [19]. It has also been shown that the dielectric relaxation in polymer composites with SrTiO 3 particles is mainly due to polymerrelated relaxation and interfacial relaxation [20]. The dielectric properties of polymeric composites with SrTiO 3 particles can be tuned by the electric field [20]. However, research on composites containing SrTiO 3 nanoparticles in the microwave and terahertz frequency ranges is rather rare [21].

The objective of this paper was to study the dielectric properties of SrTiO 3 /PDMS composites in wide frequency (including microwave and terahertz frequency ranges) and temperature ranges (100-300 K, where PDMS is stable [18]). EXPERIMENTAL SrTiO 3 with particle sizes of 100 nm was purchased from US Research Nanomaterials, Inc (USA), while the PDMS matrix was purchased from Farnell (France) under the reference Sylgard 184 Silicone Elastomer (Dow Corning®).

Prior to any synthesis, PDMS was degassed under reduced pressure (4 000 Pa, 30 min) at room temperature. For each composite, the corresponding amount of SrTiO 3 was dispersed in isopropanol (IPA) and under inert atmosphere (N 2 ) to avoid any potential oxidation of silver. The IPA-based suspension containing SrTiO 3 nanoparticles was then sonicated for 3 h in an ultrasonic bath (VWR USC 1200 TH, 600 W), and for 5 min using a sonotrode (VWR DIGITAL, 450 W, with a 13 mm diameter probe) at 20% of its maximum power. The suspension was then poured over the corresponding amount of PDMS and was then sonicated using the same procedure. In order to evaporate the IPA, the IPA/SrTiO 3 /PDMS blend thus obtained was placed overnight in a ventilated oven at 60°C. The resultant PDMS/SrTiO 3 paste was sonicated (ultrasonic bath) once more for 1.5 h.

The required amount of curing agent specified by the supplier was then added. The resultant mixture was then gently stirred by hand for 10 min. In order to remove air bubbles that may have been trapped during this step, the final mixture was degassed under reduced pressure (4 000 Pa, 2 min). Depending on the viscosity of the final mixes, the composites were cast or manually pressed into moulds before curing. The composites were finally cured for 2-3 h at 90°C in a ventilated oven.

Visually, the color of all investigated composites is white, they are not transparent in optical frequency range. Composites with 30 vol.% SrTiO 3 is flexible, while composites with bigger SrTiO 3 concentrations are completely hard.

Scanning electron microscopy (SEM) images were obtained with a JSM 6460 LV electron microscope. Broadband measurements were performed using several techniques. At low frequencies (20 Hz -1 MHz), the complex dielectric permittivity was obtained from the complex capacitance, which was measured by a HP4824 LCR meter. The measurements accuracy in this frequency range was better than 10%. In the microwave frequency range, from 8 GHz to 50 GHz, the reflectance and transmission of a thin dielectric rod placed inside a waveguide were studied. A custom-made waveguide spectrometer was used in this frequency range [START_REF] Grigas | Microwave dielectric spectroscopy of ferroelectric and related materials[END_REF]. The typical value for the rod diameter was several hundred micrometres. The best measurements accuracy in this frequency range was in the middle of the band i.e. close to 30 GHz, in this case it is better than 10%. In the terahertz frequency range (from 100 GHz to 3 THz), a terahertz time domain spectrometer (Ekspla Ltd) based on a femtosecond laser was used for the measurements. The spectrometer is based on a femtosecond laser fibre (wavelength 1 μm, pulse duration less than 150 fs) and a GaBiAs photoconductive terahertz emitter and detector. The signal-to-noise ratio was as high as 60 dB at a frequency of 0.5 THz. The complex effective permittivity was calculated according to the Fresnel equation [START_REF] Pupeza | [END_REF]:

, ( 1
)
where N=n-ik=(ε * ) 0.5 is the complex refractive index, ε * is the complex dielectric permittivity, d is the sample thickness, c is the light velocity and m labels number of reflections in the sample. These reflections are experimentally resolved and form separate pulses in the measured signal, so that the value of the coefficient m can be easily determined.

The measurement accuracy was better than 1% at frequency 0.5 THz (where a signal to noise ratio is highest). At low frequencies (20 Hz -1 MHz), the measurements were also performed in the temperature range of 100 to 300 K. Silver paste was used to make electrical contacts with the samples. The real part σ' of the complex electrical conductivity was calculated as σ' = ω ε 0 ε",

where ω is the angular frequency, ε 0 is the permittivity of vacuum, and ε" is the imaginary part of the complex dielectric permittivity.

RESULTS AND DISCUSSION

SEM images of PDMS-based composite materials filled with SrTiO 3 nanoparticles are presented in Fig. 1. The SrTiO 3 nanoparticles were well dispersed in composites with different filler concentrations, as all areas studied in the composites with the same filler concentrations were similar.

The temperature dependence of complex dielectric permittivity for PDMS composites filled with 30 vol.% SrTiO 3 nanoparticles is presented in Fig. 2. The main dielectric anomaly was observed at about 175 K. It is related to the glass transition (α relaxation) in pure PDMS [24]. The α relaxation is due to a large-scale collective motion of many backbone segments in the amorphous phase of PDMS. The additional dielectric anomaly was clearly observed as the maximum of dielectric losses in the temperature range 200-250 K (depending on the measurements frequency)

and the change in the slope of temperature dependence of the dielectric permittivity. The additional anomaly is related to the glass transition in the polymer-filler interface (α' relaxation) [25,26]. Both relaxations are related with the orientation polarization [25,26]. Dielectric properties of pure PDMS and composites filled with SrTiO 3 nanoparticles at low frequencies (not higher than 1 MHz) are quite similar. The difference is only in the appearance of dielectric dispersion related with α' relaxation (which is related to the glass transition in polymer-filler interface) in SrTiO 3 /PDMS composites, the α' relaxation is completely absent in pure PDMS.

The α' relaxation becomes stronger with increasing SrTiO 3 concentration (will be shown below).

where k b is the Boltzmann constant, ν 0 is the attempt frequency and T 0 is the glass transition temperature of the polymer when the cooling rate becomes infinitely slow, E is the activation energy .

Fig. 3 Measurement frequency versus the temperature of dielectric losses maximum for SrTiO 3 /PDMS composites.

The parameters obtained are summarised in Table I. It can be seen that there is no clear dependence of E and T 0 on concentration. However, the activation energy for α' relaxation was substantially higher than the activation energy for α relaxation, while the freezing temperature was lowest for α relaxation. Two mechanisms have an impact on the freezing temperature in polymeric composites: the interaction between polymer molecules and nanoparticles increases the freezing temperature, while the appearance of free volume at the polymer/nanoparticle interface decreases the freezing temperature [27]. It can be concluded that both mechanisms are important in the composites under study. Moreover, the free spaces are located closer to the nanoparticles. Both relaxation mechanisms are related with orientation polarization.

The temperature dependence of the complex dielectric permittivity for all composites studied at the frequency of 3.7 kHz is presented in Fig. 4. It can be observed that both dielectric permittivity and dielectric losses strongly increased with the concentration of SrTiO 3 . The dielectric permittivity was high (about 20 at room temperature) for the composites with the highest SrTiO 3 concentration, while the losses were low (less than 0.6). The increase of the dielectric permittivity with the SrTiO 3 concentration is related with ionic polarization of SrTiO 3 [18]. Moreover, it is possible from the data presented in Fg. 4 to separate contributions of α and α' relaxations. The α' relaxation becomes stronger with increasing SrTiO 3 concentration, while the α relaxation disappears in composites with 50 vol.%. The small increase in dielectric losses with temperature at higher temperatures (above 270 K) is related to the onset of electrical conductivity of SrTiO 3 nanoparticles [28].

Fig. 5 Frequency dependence of complex dielectric permittivity in the microwave frequency range at room temperature for SrTiO 3 /PDMS composites.

The dielectric permittivity of composites with the highest concentration of SrTiO 3 was also high in the microwave frequency range, while the dielectric losses were low (Fig. 5). Moreover, the value of dielectric permittivity at 3.7 kHz (Fig. 4) was almost equal to the value of dielectric permittivity at 39 GHz, indicating that the dielectric dispersion in the frequency range 3.7 kHz -39

GHz is very low. The small change of dielectric losses presented for composites with highest concentrations of SrTiO 3 could be related with onset of SrTiO 3 phonons, however these changes are very small and SrTiO 3 phonon frequencies are observed usually in terahertz frequency range [12], so it will be further discussed below. The transmission of composites in the terahertz frequency range decreased sharply with frequency up to a certain cut-off frequency, while at higher frequencies it was frequency-independent or even increased with frequency. The latter observation is rather an artefact related to the fact that the samples were opaque at these frequencies. The decrease in transmission with frequency in the terahertz frequency range can be explained by the decrease in complex dielectric permittivity with frequency or by the frequency-independent complex dielectric permittivity. It can be also mentioned, that the thickness of the sample has the strong impact on terahertz transmission (according to Eq. 1)

and in possible composites applications, especially for 3D printing where small deviation on the expected thickness could happens [7], the sophisticated geometries can be printed.

The frequency dependence of the complex dielectric permittivity in the terahertz frequency range is presented in Fig. 7. As at lower frequencies, the complex dielectric permittivity increased with the concentration of SrTiO 3 . In composites containing SrTiO 3 nanoparticles, the dielectric dispersion in the terahertz frequency range was very low and related to the onset of SrTiO 3 phonons [12]. The high value of dielectric permittivity of the composites in the terahertz frequency range indicates that it can be changed by external parameters and that the composites are suitable for various flexible electronics components [13].

Fig. 1

 1 Fig. 1 SEM images of SrTiO 3 /PDMS composites of different volume fractions of SrTiO 3

Fig. 2

 2 Fig. 2 Temperature dependence of the complex dielectric permittivity of PDMS composites filled

Fig. 4

 4 Fig. 4 Temperature dependence of the complex dielectric permittivity at 3.7 kHz for SrTiO 3 /PDMS

Fig. 6

 6 Fig. 6 Transmission spectra of SrTiO 3 /PDMS composites in the terahertz frequency range. The

Fig. 7

 7 Fig. 7 Dielectric spectra of SrTiO 3 /PDMS composites in the terahertz frequency range.

Table I .

 I Parameters of Vogel-Fulcher fit.

	10 vol.%	α relaxation	4.8	707	126
		α' relaxation 0.53	3637	10
	30 vol.%	α relaxation	0.24	331	147
		α' relaxation 0.53	4358	43
	40 vol.% (α' relaxation)	0.53	4054	18
	50 vol.% (α' relaxation)	0.53	4311	30
			τ 0 , ps	E, K	T 0 , K
	0 vol.% (α relaxation)	0.03	343	135


Anastassia Y Borisova
email: anastassia.borisova@get.omp.eu

Georges Ceuleneer

Nail R Zagrtdenov

Oleg G Safonov

Michael J Toplis

A R Chakhmouradian

Experimental diopsidite: Implications for natural diopsidite genesis through fluid-melt-mantle peridotite reaction

Keywords: Diopsidite, Oceanic lithosphere, Hydrated peridotite, Mantle-crust transition zone, Melt-rock reaction experiment

Occurrences of diopsidites, rocks made predominantly of gem-like diopside whose composition precludes a purely igneous origin, allow tracking the pathway of high-temperature fluids and fluid-saturated melts in the oceanic lithosphere in vicinity of the mantle-crust transition zone (the Moho) and the adjacent mantle in an oceanic setting. We have experimentally explored the origin of the mantle diopsidites by reacting serpentinite with synthetic haplobasaltic glass (corresponding to anorthite-diopside eutectic at 0.1 MPa pressure) at 900 and 1250 °C, and 0.2 GPa pressure for 120 h. At 900 °C, no reaction is observed in the sample; in contrast, in the experimental runs heated to 1250 °C, we distinguish two mineral associations (1) early Al-poor diopside [Mg# = Mg/(Mg + Fe) = 99 ± 1; Al 2 O 3 = 1.9 ± 1.6 wt%] with the diopside-hosted forsterite (Fo 99.2 ± 0.1 ) inclusions and (2) late Al-enriched diopside (Mg# = 98 ± 1; Al 2 O 3 = 3.7 ± 2.8 wt%). Our experiments confirm that mantle diopsidites can be produced at ≥ 1100 °C in response to partial melting of hydrated peridotite (serpentinite) in the presence of haplobasaltic melt and aqueous fluid at the conditions typical of the mantle-crust transition zone and the shallow mantle beneath oceanic spreading ridges.

Introduction

Diopsidites were discovered in the Oman ophiolite and interpreted as crystallization products resulting from the percolation of hydrothermal fluids in mantle peridotite at high temperatures (Python et al. 2007a,b). These rocks are made up predominantly of diopside [0.95 < Mg/ (Mg + Fe) < 1] and minor Mg-rich (Fo > 95 mol%) olivine. The diopsidites form dykes hosted by peridotites in the lithospheric part of ophiolites (Python et al. 2007a;[START_REF] Akizawa | Petrology of mantle diopsidite from Wadi Fizh, northern Oman ophiolite: Cr and REE mobility by hydrothermal solution[END_REF]. Veins composed mainly of diopside with associated chromite, Fe-Ni-Co metal, silica and troilite occur in lunar soil samples collected by the Apollo 17 mission at the base of the Sculptured Hills and appear to result from intrusion and crystallization of fluid [START_REF] Irving | Lunar noritic fragments and associated diopside veins[END_REF]. The source of the fluid is considered as enigmatic. MARID suite consisting of varying proportions of mica, amphibole, rutile, ilmenite and diopside has been distinguished by [START_REF] Dawson | The MARID (mica-amphibole-rutileilmenite-diopside) suite of xenoliths in kimberlite[END_REF] within kimberlite pipes. In the oceanic mantle-crust transition zone, diopside is present as scattered crystals in dunites and as inclusions in chromites at the same setting [START_REF] Borisova | A new view on the petrogenesis of the Oman ophiolite chromitites from microanalyses of chromite hosted inclusions[END_REF][START_REF] Rospabé | Origin of the dunitic mantle-crust transition zone in the Oman ophiolite: The interplay between percolating magmas and high-temperature hydrous fluids[END_REF][START_REF] Rospabé | Multi-scale development of a stratiform chromite ore body at the base of the dunitic mantle-crust transition zone (Maqsad diapir, Oman ophiolite): the role of repeated melt and fluid influxes[END_REF]. Additionally, rare occurrences of plagioclase diopsidites, made of equal proportions of diopside and pure anorthite, have also been reported in the dunitic transition zone (Python et al. 2007a) and in the ophiolitic and modern oceanic crust [START_REF] Vanko | Hydrothermal anorthitization of plagioclase within the magmatic/hydrothermal transition at mid-ocean ridges: examples from deep sheeted dikes (Hole 504B, Costa Rica Rift) and a sheeted dike root zone (Oman ophiolite)[END_REF][START_REF] Akizawa | Crustal diopsidites from the northern Oman ophiolite: Evidence for hydrothermal circulation through suboceanic Moho[END_REF][START_REF] Akizawa | Petrology of mantle diopsidite from Wadi Fizh, northern Oman ophiolite: Cr and REE mobility by hydrothermal solution[END_REF]. Mantle diopsidites have (not foliated) metasomatic textures contrasting with igneous textures and comparable to those of metasomatic skarns or rodingites frequently present in serpentinite bodies within the ophiolitic crust. The diopsidites frequently appear as dykes, with a few mm to few tens of cm wide transitional zones, which contain high amounts of hydrous minerals, between the diopsidite and its host rock (Python et al. 2007a). The mechanism of the diopsidite rock formation was proposed to be crystallization from high temperature fluids intermediate between the silicate melts and supercritical water. These rocks were suggested to form due to high temperature circulation of seawater-derived hydrothermal or carbonated fluids at > 800 °C close to the mantle-crust transition zone (Python et al. 2007a). One argument for the hydrothermal origin of the water is the pronounced positive Eu anomaly in diopside crystals, showing that the fluid has leached gabbroic rocks en route to the Moho transition zone (Python et al. 2007a). However, the proposed mechanism requires a high waterto-rock ratio and may be unrealistic. Thus, it is still a matter of debate why predominant diopside crystallizes in the mantle to form diopsidite rocks. A revised formation mechanism of the high-Mg rock origin may now be proposed based on reactions documented at depths in the oceanic lithosphere [START_REF] Benoit | The remelting of hydrothermally altered peridotite at mid-ocean ridges by intruding mantle diapirs[END_REF][START_REF] Borisova | A new view on the petrogenesis of the Oman ophiolite chromitites from microanalyses of chromite hosted inclusions[END_REF][START_REF] Rospabé | Origin of the dunitic mantle-crust transition zone in the Oman ophiolite: The interplay between percolating magmas and high-temperature hydrous fluids[END_REF][START_REF] Rospabé | Multi-scale development of a stratiform chromite ore body at the base of the dunitic mantle-crust transition zone (Maqsad diapir, Oman ophiolite): the role of repeated melt and fluid influxes[END_REF][START_REF] Zagrtdenov | Anatomy of a chromitite dyke in the mantle -crust transition zone of the Oman ophiolite[END_REF][START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part II: Fast assimilation of serpentinized mantle by basaltic magma. Special Volume on magma-rock and magmamush interactions as fundamental processes of magmatic differentiation[END_REF][START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part I: Planetary felsic crust formation at shallow depth. Special Volume on magma-rock and magma-mush interactions as fundamental processes of magmatic differentiation[END_REF], as well as based on experimental modeling of the proposed reactions at a pressure of 0.2 GPa.

Experimental and analytical methods

To experimentally model the petrogenesis of diopsidite rocks, we have used a similar design as that of [START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part II: Fast assimilation of serpentinized mantle by basaltic magma. Special Volume on magma-rock and magmamush interactions as fundamental processes of magmatic differentiation[END_REF][START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part I: Planetary felsic crust formation at shallow depth. Special Volume on magma-rock and magma-mush interactions as fundamental processes of magmatic differentiation[END_REF] with a serpentinite cylinder in the upper part and haplobasaltic (i.e. the synthetic system of albiteanorthite-diopside, [START_REF] Barth | Theoretical petrology[END_REF] glass powder in the lower part of an Au 80 Pd 20 capsule. As starting materials, we used the synthetic haplobasalt (86.7-82.4 wt%) and natural serpentinite (13.3-17.6 wt%) (Table 1). These components have been chosen to model experimentally interaction between (i) a model silicate melt, which is formed due to partial melting of predominantly gabbroic crust enriched in anorthite and diopside, (ii) altered (hydrated or serpentinized) peridotite and (iii) an aqueous fluid. These experiments were designed to simulate the process of basaltic melt infiltration into serpentinite rock that does not necessarily reach equilibrium. Three experiments (P40, P41 and P41bis) with different basalt to serpentinite mass ratios (4.7-6.5; Table 2) were carried out at a pressure of 0.2 GPa and temperature of 900 °C (P40) and 1250 °C (P41 and P41bis) using an internally heated gas pressure vessel [START_REF] Safonov | Interaction of biotiteamphibole gneiss with H 2 O-CO 2 -(K, Na)Cl fluids at 550 MPa and 750 and 800°C: Experimental study and applications to dehydration and partial melting in the middle crust[END_REF]). The duration of experiments was 120 h for all runs. The pressure in the system was created by pure Ar gas. The experimental charge was heated in a furnace with two windings (to minimize any thermal gradient). The temperature was set and measured by a TRM-101 OVEN controller through two S-type (Pt 90 Rh 10 versus Pt 100 ) thermocouples. The thermocouples were mounted at the top and close to the bottom of the run hot spot to monitor the temperature gradient. The experiments were quenched by switching off the furnace. The pressure during the quench was kept constant down to 550 °C, and then slowly released. The cooling rate from 1250 to 1000 °C was 167 °C/min, and then 90 °C/min from 900-1000 °C down to 550 °C. After the runs, the Au 80 Pd 20 capsules were mounted in epoxy, cut in half using a diamond micro-saw, and then polished using SiC sand papers and diamond pastes.

The major experimental products (silicates and hydrous glasses) in the samples were identified using two scanning electron microscopes (SEM) JEOL JSM-6360 LV and Bruker TESCAN using energy-dispersive X-ray spectrometry (EDS). X-ray mapping of the experimental samples was performed using the electron microscopes. In order to perform the EDS mapping, the X-ray lines (Kα) have been measured for the elements Al, Si, Mn, Fe, Ca and Mg. Major and minor elements in the crystals and glasses were analyzed using a CAMECA SX-Five electron probe micro-analyser (EPMA) operated at 15 kV and 20nA; the analyzed surface area was 2 μm 2 . The following synthetic and natural reference materials were used for the EPMA calibration: albite (for Na), corundum (Al), wollastonite [START_REF] Jochum | MPI-DING reference glasses for in situ microanalysis: new reference values for element concentrations and isotope ratios[END_REF] were analyzed as unknowns to monitor the accuracy of the major and minor (Cr, Ni) element analyses. The analysis of silicate reference materials allowed us to control precision for the major and minor element analyses to be within the limit of the analytical uncertainty (related to the count statistics). The accuracy, estimated on the reference glasses, ranged from 0.5 to 3% (1σ RSD = relative standard deviation), depending on the element contents in the reference glasses.

(ATHO-G, StHs6/80-G, T1-G, KL2-G, ML3B-G, GOR132-G, GOR128-G,

Results

Figure 1 (a-i) illustrates backscattered electron images and X-ray mapping of the diopsidite samples (P40, P41 and P41bis). The P40 sample (900 °C) contains initial starting serpentinite rock and haplobasaltic glass with no reaction zone (Fig. 1d,g), whereas the recovered P41 and P41bis samples (1250 °C) are almost monomineralic and comprise predominantly diopside (Fig. 1a-c, e-f, h-i). In the experimental diopsidites, two mineral associations were distinguished: (D1) early Al-poor diopside (Mg# = 99 ± 1; Al 2 O 3 = 1.9 ± 1.5; Cr 2 O 3 = 0.16 ± 0.10 wt%) with inclusions of forsterite (Fo 99.2 ± 0.1 ) (Fig. 1 a-c, e, h, i) and (D2) late Alrich diopside (Mg# = 98 ± 1; Al 2 O 3 = 3.7 ± 2.8 wt%) forming a well-crystallized diopsidite matrix (Fig. 1a-b, f, i; Table 3).

The size of the diopside crystals varies from 100 to several hundred µm.

Discussion

Results of the P41 and P41bis runs demonstrate that haplobasaltic melt component reacts with dehydrated serpentinite at 1250 °C at conditions of saturation with aqueous fluid, whereas temperature of 900 °C was not sufficient to initiate the reaction. Numerous bubbles in experimental samples P41 and P41bis correspond to a fluid, consistent with water fluid saturation of the haplobasaltic melt at 0.2 GPa pressure. According to [START_REF] Benne | Water solubility in haplobasaltic melts[END_REF], the saturation of haplobasaltic melt in anorthite-diopside system with aqueous fluid at 0.2 GPa requires an H 2 O content of about 5 wt% in the melt; it is likely that the water saturation of the melt was developed progressively in response to the crystallization of anhydrous mineral. The conditions created in our experimental system at 1250 °C thus were close to aqueous fluid saturation due to serpentinite dehydration, especially at the final stages of the diopsidite crystallization. The localized occurrence of Mg-rich olivine inclusions in the low-Al diopside crystals (Fig. 1) corresponds to the emplacement of the former serpentinite zone, suggesting reaction of serpentinite with haplobasaltic melt and aqueous fluid to form forsterite and Al-poor diopside according to the following equation:

where Serp is the principal serpentine mineral, HB is haplobasaltic melt component, Fo is forsterite, Di is diopside, RM is a residual silicate (melt) component and Fluid is an aqueous fluid.

From experimental works of [START_REF] Yoder | Diopside-anorthite-water at five and ten kilobars and its bearing on explosive volcanism[END_REF] and [START_REF] Yoder | Origin of basalt magmas: An experimental study of natural and synthetic rock systems[END_REF], it is well-known that higher pressures widen the crystallization field of diopside in haplobasaltic (1) systems saturated with water (Fig. 2). Similarly to the haplobasaltic experimental system, any starting composition corresponding to dry anorthite-diopside eutectic composition (Di 63 An 37 ) at room pressures (0.1 MPa) would result in crystallization of pure diopside at high pressures (≥ 0.2 GPa) if the system is water-saturated. Silicate melts of composition approaching the pure haplobasaltic systems are not common in nature, nevertheless, natural anorthitediopside associations are documented in ophiolites at Moho level as described above. The altered lower oceanic crust is regularly enriched in epidote, chlorite (chloriterich epidosite), but also anorthite and high-Ca diopside formed due to intermediate to high temperature alteration [START_REF] Seyfried | Hydrothermal alteration processes at mid-ocean ridges: Constraints from diabase alteration experiment, hot-spring fluids and composition of the oceanic crust[END_REF][START_REF] Gillis | Controls on hydrothermal alteration in a section of fast-spreading oceanic crust[END_REF]McCollum and Shock 1998;[START_REF] Vanko | Hydrothermal anorthitization of plagioclase within the magmatic/hydrothermal transition at mid-ocean ridges: examples from deep sheeted dikes (Hole 504B, Costa Rica Rift) and a sheeted dike root zone (Oman ophiolite)[END_REF][START_REF] Alt | Subsurface structure of a submarine hydrothermal system in ocean crust formed at the East Pacific Rise, ODP/IODP Site 1256[END_REF]). These altered lower crustal Ca-Al-Mg-rich rocks may be formed in the sheeted dyke complex due to hydrothermal fluid circulation through the gabbroic crust. As a result, the NaCl-bearing fluids are strongly enriched in Ca, Al and Si due to the high solubility of anorthite in hydrothermal fluids [START_REF] Seyfried | Hydrothermal alteration processes at mid-ocean ridges: Constraints from diabase alteration experiment, hot-spring fluids and composition of the oceanic crust[END_REF][START_REF] Oelkers | Experimental study of anorthite dissolution and the relative mechanism of feldspar hydrolysis[END_REF][START_REF] Oelkers | The surface chemistry of multi-oxide silicates[END_REF]. These NaCl-rich fluids (up to 5.6 wt% NaCl) represent 'hot modified seawater' described as inclusions in minerals of anorthitized rocks [START_REF] Vanko | Hydrothermal anorthitization of plagioclase within the magmatic/hydrothermal transition at mid-ocean ridges: examples from deep sheeted dikes (Hole 504B, Costa Rica Rift) and a sheeted dike root zone (Oman ophiolite)[END_REF]. Figure 2 shows an expansion of the diopside crystallization field to Ca-Al-rich compositions in the fluid-saturated systems. Thus, diopside will crystallize from haplobasaltic melt at ≥ 1100 °C and pressure below 0.5 GPa in the presence of aqueous fluid.

Mg 3 Si 2 O 5 (OH) 4 [Serp] + 2CaAl 0.74 Mg 0.63 Si 2 O 6.7 [HB] = MgSiO 4 [Fo] + CaMgSi 2 O 6 [Di] + CaAl 1.48 Mg 1.63 SiO 10.4 [RM] + 2H 2 O [Fluid]
Our model illustrated by Fig. 3 suggests that periodic partial melting of the altered (and enriched in anorthite-diopside) gabbroic crust produces a silicate melt approaching haplobasaltic Fig. 1 (a-f) Backscattered electron images of diopsidite rock experimentally produced during the serpentinite-haplobasaltic glass reaction at 0.2 GPa, 900 °C (P40) and 1250 °C (P41 and P41bis samples) for 120 h. In the experimental system at 1250 °C, the final mineral associations are represented by (i) D1: early Al-poor diopsidehosted forsterite inclusions together with (ii) D2: late Al-rich diopside composed by well-crystallized diopsidite with water fluid bubbles. HBAS = haplobasaltic glass, SERP = dehydrated serpentinite, Di = diopside, Fo = high-Mg olivine and L = residual melt. component. The haplobasaltic melt reacts and replaces the mantle peridotite with dykes and veins of forsterite-bearing diopsidites. Indeed, mantle diopsidites are regularly associated with mantle plagiogranites (M. Benoit, personal communication). In fact, the associated mantle plagiogranites have been inferred to form due to fluid-assisted melting of hydrated peridotite owing to the reaction with basaltic melt [START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part I: Planetary felsic crust formation at shallow depth. Special Volume on magma-rock and magma-mush interactions as fundamental processes of magmatic differentiation[END_REF]. The process of basaltic melt-peridotite reaction is therefore common in the mantle and the mantle-crust transition zone [START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part II: Fast assimilation of serpentinized mantle by basaltic magma. Special Volume on magma-rock and magmamush interactions as fundamental processes of magmatic differentiation[END_REF][START_REF] Borisova | Hydrated peridotite -basaltic melt interaction Part I: Planetary felsic crust formation at shallow depth. Special Volume on magma-rock and magma-mush interactions as fundamental processes of magmatic differentiation[END_REF]. The reaction between hydrated peridotite and basaltic melts may happen periodically during the oceanic lithosphere formation. The haplobasaltic melt component, thus, constitutes a missing silicate component necessary for diopside crystallization upon the reaction with peridotite at the level of the oceanic mantle-crust transition zone or even in deeper parts of the lithospheric mantle.

Conclusions

Synthetic diopsidite was produced experimentally for the first time. In the experimental system, reaction of natural serpentinite with a synthetic haplobasaltic melt (corresponding to the anhydrous anorthite-diopside eutectic at 0.1 MPa) at 1250 °C and 0.2 GPa produces two mineral associations represented by (i) Al-poor diopside with high-Mg olivine inclusions and (ii) Al-rich diopside composing well-crystallized diopsidite. We propose a model, where mantle diopsidites are formed near the oceanic mantle-crust transition zone due to reaction of haplobasaltic melt produced via efficient melting of an altered gabbroic crust rich in anorthite and diopside. The generated haplobasaltic melts react with the mantle peridotite at ≥ 1100 °C and < 0.5 GPa in the presence of high-temperature aqueous fluid to produce veins of forsterite-bearing diopsidites. The process of basaltic melt-hydrated peridotite reaction is common in the oceanic mantle and the mantle-crust transition zone. This reaction (e.g. Eq. 1) may happen periodically during the formation of the oceanic lithosphere at mid-ocean spreading centers.

  Fig.1 (a-f) Backscattered electron images of diopsidite rock experimentally produced during the serpentinite-haplobasaltic glass reaction at 0.2 GPa, 900 °C (P40) and 1250 °C (P41 and P41bis samples) for 120 h. In the experimental system at 1250 °C, the final mineral associations are represented by (i) D1: early Al-poor diopsidehosted forsterite inclusions together with (ii) D2: late Al-rich diopside composed by well-crystallized diopsidite with water fluid bubbles. HBAS = haplobasaltic glass, SERP = dehydrated serpentinite, Di = diopside, Fo = high-Mg olivine and L = residual melt. (a-c) the P41 sample; (d) P40 sample; (e-f) P41bis sample. (g-i) X-ray mapping for Al, Si, Mn, Fe, Ca and Mg of the experimental diopsidite samples. (g) P40 sample; (h) P41bis sample; mauve color corresponds to the high-Mg olivine inclusions in the D1 diopside. (i) P41 sample. Blue color corresponds to the high-Mg olivine inclusions in the D1 diopside ◂

Fig. 2 Fig. 3

 23 Fig. 2 Diopside (Di)-anorthite (An) phase diagram demonstrating eutectic compositions for three experimental systems (i) anhydrous haplobasaltic melt at P = 0.1 MPa pressure (marked as P = 0.1 MPa);(ii) hydrous system at 0.5 GPa pressure under fluid saturated conditions (P H 2 O = 0.5 GPa) and (iii) hydrous system at 1.0 GPa pressure under fluid saturated conditions (P H 2 O = 1 GPa) according to[START_REF] Yoder | Diopside-anorthite-water at five and ten kilobars and its bearing on explosive volcanism[END_REF] and[START_REF] Yoder | Origin of basalt magmas: An experimental study of natural and synthetic rock systems[END_REF]. Expansion of the diopside crystallization field to Ca-Al-rich compositions is remarkable in the fluidsaturated systems

Table 1

 1 Compositions (wt%) of the starting materials

	Sample *	BAS	SERP
	SiO 2	50.34	40.69
	TiO 2	-	bdl
	Al 2 O 3	15.38	0.88
	Fe 2 O 3 **	-	7.53
	MnO	-	0.11
	MgO	10.80	38.24
	CaO	23.48	0.06
	Na 2 O	-	bdl
	K 2 O	-	bdl
	P 2 O 5	-	0.05
	LOI	-	11.55
	Total	100.00	99.1
	H 2 O total		11.91
	BAS haplobasaltic powder,
	SERP serpentinite rock (TSL-
	19), BDL values below detec-
	tion limits. LOI loss on ignition
	** Total Fe quoted as Fe 2 O 3

*

Table 2

 2 Experimental sample description SERP serpentinite rock, BAS haplobasaltic powder, T temperature and P pressure

	Sample	Conditions	Starting proportions*	BAS melt to	Final phases**
				SERP rock
				ration
		T (°C), P (GPa)	SERP / BAS (wt%)	-
	P40	900, 0.2	16.9 / 83.1	4.93	Dehydrated serpentinite and haplobasaltic glass
	P41	1250, 0.2	13.3 / 86.7	6.50	Diopside, Mg-rich olivine: D1 and D2
	P41bis	1250, 0.2	17.6 / 82.4	4.69	Diopside, Mg-rich olivine: D1 and D2
	** The final mineral associations are represented by (i) D1: early Al-poor diopside-hosted forsterite inclusions together with (ii) D2: late Al-rich
	diopside composed by well-crystallized diopsidite with water fluid bubbles

*

Table 3

 3 Chemical composition of mineral and glass phases in the experimental diopsidites produced at 0.2 GPa and 1250 °C Errors are quoted at 2σ level (standard deviation); Mg# = Mg/(Mg + Fe); bdl -below detection limit Fo forsterite, Wo wollastonite, En enstatite, Fs ferrosilite, bdl values below detection limits * Bracketed numbers correspond to the numbers of EPMA points (P41 and P41bis samples) Average = average value

	Associatio	Mineral association D1			Mineral association D2
	Phase	Olivine (15)*	Diopside 1 (30)*	Diopside 2 (75)*	Residual glass
								(4)*
		Average Error	Average Error	Average Error	Average Error
	Major and minor oxides (wt%)	43.50	0.87	54.70	1.07	53.40	2.00	42.28	10.85
	SiO 2	bdl	-	bdl	-	bdl	-	bdl
	TiO 2	bdl	-	1.91	1.61	3.70	2.84	19.30	10.93
	Al 2 O 3	0.76	0.12	0.41	0.20	0.55	0.34	1.59	0.56
	FeO	bdl	-	bdl	-	bdl	-	bdl	bdl
	MnO	55.16	1.50	18.80	0.70	17.97	1.20	12.62	4.65
	CaO	1.04	0.70	24.46	0.27	24.65	0.48	18.44	4.62
	Na 2 O	bdl	-	bdl	-	bdl	-	bdl	-
	K 2 O	bdl	-	bdl	-	bdl	-	bdl	-
	Cr 2 O 3	bdl	-	0.16	0.10	0.06	0.12	bdl	-
	NiO	0.21	0.06	bdl	-	bdl	-	bdl	-
	Total	100.86	1.01	100.57	0.37	100.45	0.77	94.75	5.50
	Mineral and members (mo1%)
	Fo	99.23	0.14	-	-	-		-	-
	Wo	-	-	48.02	-	49.22	-	-	-
	En	-	-	51.35	-	49.94	-	-	-
	Fs	-	-	0.63		0.84	-	-	-
	Mg #	99.23	0.14	98.76	0.62	98.27	1.21	93.34	1.25

Acknowledgements

The experiments were carried out using an internally heated gas pressure vessel at the Korzhinskii Institute of Experimental Mineralogy (Chernogolovka, Russia). Major element analyses of minerals and glasses and the sample imaging were performed at the Géosciences Environnement Toulouse laboratory (GET) and at the Centre de Microcaractérisation Raimond Castaing (Toulouse, France). Authors thank two anonymous reviewers and journal editor Anton Chakhmouradian for numerous suggestions, which significantly improved the manuscript. This work was supported by the Institut national des Sciences de l'Univers (INSU) foundation, France.

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