S Jacques

A Guette

F Langlais

X Bourrat

CHARACTERIZATION OF SiC/C(B)/SiC MICROCOMPOSITES BY TRANSMISSION ELECTRON MICROSCOPY

Uniform or composition graded C(B) interphases in SiC/SiC model microcomposites were characterized by transmission electron microscopy after tensile tests and thermal ageing in air. A specific method was developed to prepare thin longitudinal sections of the tested specimens.

Deflection of matrix cracks occurs within the uniform C(B) interphase as long as its anisotropy remains high enough (i.e. when the boron content is not too high). It takes place close to the most anisotropic layer (i.e. that containing 8 at. % of boron) in composition graded interphases. In both cases, crack deflection path does not reach the fiber, a feature which is consistent with the good mechanical properties. After ageing in air under tensile loading beyond the proportional limit (600 °C; σ = 800 MPa), the composition graded interphase (made of five sublayers in which the boron content increases from 0 at. % near the fiber to 33 at. % near the matrix) was observed to act as a glass forming protection, the pyrocarbon sublayer (at the fiber surface) remaining unoxidized.

INTRODUCTION

The thermomechanical behavior of ceramic matrix composites (CMCs) can be controlled by depositing on the fiber a thin film referred to as the "interphase" prior to the infiltration of the matrix. An understanding of the micromechanics involved during mechanical loading or under oxidizing conditions can be achieved by using transmission electron microscopy (TEM) [START_REF] Droillard | Strong Interface in CMCs, Condition for Efficient Multilayered Interphases[END_REF][START_REF] Frety | Oxidizing ageing effects on SiC/SiC composites[END_REF] (i.e. by observation of the crack propagation modes).

In the present study a single-filament-test-specimen was used (microcomposite). A 50 mm-long single fiber was successively coated by two layers, first a thin film of interphase and then a thicker layer of matrix. This kind of specimen, which can be easily prepared by CVD, has been recently used to study the mechanical properties [START_REF] Lamon | Determination of Interfacial Properties in Ceramic Matrix Composites using Microcomposites Specimens[END_REF][START_REF] Lamon | Microcomposite Test Procedure for Evaluating the Interface Properties of Ceramic Matrix Composites[END_REF] or to develop and characterize new kinds of interphases [START_REF] Jacques | High temperature lifetime in air of SiC/C(B)/SiC microcomposites prepared by LPCVD[END_REF][START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF]. A method for making thin longitudinal sections of microcomposites was developed and successfully applied to SiC/SiC microcomposites.

The aim of the present contribution is to report TEM characterization which has been performed on uniform or composition graded C(B) interphases (CGIs) developed in the companion paper [START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF] in order (i) to confirm the nature of the successive layers with different compositions constituting the CGIs, (ii) to link their mechanical characteristics to the crack deflection paths and (iii) to observe their evolution when submitted to oxidation conditions.

EXPERIMENTAL

In the direct ion thinning technique of a longitudinal section of a microcomposite (or a fiber), the thinning occurs circumferentially which sharpens the fiber. So, the thin area is obtained close to the fiber core and not near its external surface or the interphase. Berger and Bunsell have proposed, for simple fibers, to align and set them in contact with each other on a copper ring [START_REF] Berger | Thin foil preparation of small diameter ceramic or glass fibres for observation by transmission electron microscopy[END_REF]. Thus, each fiber surface is protected from the Ar + beams by adjacent fibers and thus the chance to obtain thin section of the fiber surface is increased (Fig. 1). Unfortunately, it was very difficult to use this method because of the space left between microcomposites, leading to a sharpening of the microcomposite tip. Thus, a simple and rapid method was developed in the case of specimen sparseness.

A few microcomposites (at least three) were laid parallel, not necessarily in contact with each other, on a silicone slab. Each microcomposite was at least 3 mm long. A drop of epoxy resin 1 was then carefully deposited so that microcomposites keep aligned on the slab as shown in figure 2.a. The microcomposites and the resin were then covered with a second silicone slab. The whole sample submitted to a slight pressure was heated in a drying oven at 160° C during two hours (Fig. 2.b).

After curing, the two silicon slabs were removed yielding a thin hard resin sheet which contained the microcomposites, with a total thickness of about 20 µm, i.e. the microcomposite diameter (Fig. 2.c). Then, it was sticked on the TEM slot copper grid (1 mm wide 2 mm long) (Fig. 2.d). The soprepared sample was then ion-milled 2 at room temperature. This method enabled to fill in totally the spaces between two adjacent microcomposites with resin which protects the side surfaces from a too rapid ion beam milling.

This technique was applied to SiC/SiC microcomposites after tensile test, performed at room temperature up to failure. The microcomposites were those prepared and tested as reported in reference [START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF]. The interphases were made of C(B) materials with different uniform boron contents (I: pyrocarbon, II: 8 at. % B and IV: 20 at. % B) or CGIs A and A'.

In the A-type CGI the interfacial sequence contained four sublayers in which the boron content increases by steps, between 0 at. % B near the 1 Micro-Measurements-Wishay adhesive, Reference M-Bond 610. 2 Dual ion mill 600 from Gatan.

fiber to 20 at. % B near the matrix. In the A'-type CGI an extra sublayer with about 33 at. % B was added near the matrix. Matrix crack deflections within interphases were observed by TEM3 according to the contrasted bright-field (BF) mode. These cracks are not artefacts due to thin foil preparations, since such cracks have never been observed within not tensile tested microcomposites prepared in the same way. Moreover, the resin selected for that preparation was usually observed within the matrix cracks, demonstrating that they were pre-existing before the sampling.

Microcomposites with interphase A' were also thinned and observed by TEM after thermal ageing in air at 600°C under load (applied stress: 800 MPa), using a previously described procedure [START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF]. A parallel electron energy loss spectrometer (PEELS) 4 was used with an electron probe size of about 20 nm for chemical elemental analyses of the oxidized interphase.

RESULTS AND DISCUSSION

Single-layered interphase

Figures 3.a. and 3.b. present typical crack deflections observed in microcomposites with uniform interphases I and II after tensile tests. In both cases, they occur within the interphase itself and not at the fiber surface. These results are consistent with the good mechanical properties observed for these microcomposites (average stress to failure: 1600 MPa and 1350 MPa respectively for microcomposites I and II) [START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF]. This feature has been reported to correspond to a "cohesive" failure mode for real 2D-SiC/PyC/SiC composites [START_REF] Droillard | Strong Interface in CMCs, Condition for Efficient Multilayered Interphases[END_REF]. It is produced by a strong bonding of the interphase with the fiber. On line is the very low matrix crack spacing observed in that case (Fig. 3.a: three matrix cracks observed in an area 10 µm long) (the large crack opening is an ion-milling artefact). These behaviors (i.e. cohesive failure mode, low crack-spacing) are the micromechanical evidences of a matrix cracking-based toughening. This is an alternative interfacial behavior to the debond/sliding mechanism in which the interface first debonds ("adhesive" failure) and where the major contribution to toughness involves sliding of the fibers along the debonded interfaces [8].

Figure 3.c. shows one of the very few cracks which could be observed in tested microcomposites with interphase IV. For this microcomposite, rather poor tensile characteristics were observed (average stress to failure: 985 MPa). It is assumed that the first matrix cracks that appear during the tensile test lead most of the time to failure. In figure 3.c., the crack propagates across the whole interphase and is deflected directly at the fiber surface. Here the bulk of the interphase does not play the role of matrix crack deflector. It has been shown in a previous paper [START_REF] Jacques | LPCVD and characterization of boron-containing pyrocarbon materials[END_REF] that for such a boron concentration in pyrocarbon (20 at. %) the texture is no more laminar but turned isotropic.

Multi layered interphase.

Figure 4 shows an observation of the CGI A' made of five C(B) sublayers with different boron contents. The successive sublayers can be easily distinguished owing to the different contrasts resulting from their different textures [START_REF] Jacques | LPCVD and characterization of boron-containing pyrocarbon materials[END_REF]. After tensile tests most of the microcomposites exhibited an extensive debonding at layer 2 / layer 3 interface. This debonding may be due to thermal residual stress after the CVD preparation at 950 °C. Layer 2, which is rather highly anisotropic, is assumed to exhibit distinct thermal expansion coefficients depending on the direction (lower along the fiber axis than perpendicularly). Conversely, layer 3, whose anisotropy is much lower, may have different thermal expansion coefficients. As a consequence, radial and/or shear stresses may occur at that interface. These internal stresses release when the matrix is cracking. This relaxation allows to deflect matrix cracks, as shown in figure 5. In that case, deflection occurs far from the fiber surface, before they reach layer 1 (pyrocarbon), which is favorable for a good oxidation resistance. With regard to the ultimate performance it was seen that this interfacial behavior resulted in high strength and strain to failure (average stress to failure : 1340 MPa) [START_REF] Jacques | C(B) materials as interphases in SiC/SiC model microcomposites[END_REF]. For interphase A (average stress to failure : 1490 MPa), we could observe a crack multideflection at different levels of the multilayer (Fig. 6). Thus, arrangement of the different layers can control the crack deflection path within the interphase. This is very favorable, since multideflection is energy absorbing and thereafter participates to toughening as previously demonstrated [START_REF] Droillard | Strong Interface in CMCs, Condition for Efficient Multilayered Interphases[END_REF].

Uncontrolled crystal growth

During TEM observations in BF mode of microcomposite thin longitudinal sections, dark areas appeared in interphase II (Fig. 7) or in layer 2 of the CGIs (Fig. 5). This particular phase is systematically present in the C(B) material containing about 8 at. % of boron [START_REF] Jacques | LPCVD and characterization of boron-containing pyrocarbon materials[END_REF] However, the content of this phase in the C(B) layer is rather low. The selected area diffraction (SAD) pattern over an area containing this phase (Fig. 8) reveals clearly the existence of submicrometric polycrystalline structures. High resolution TEM observations and PEELS chemical analyses have not been possible owing to a difficult thinning of such a heterogeneous material.

Inter-reticular distances d calculated from the SAD pattern and a tentative index linking in the face-centered cubic (FCC) lattice (with a lattice parameter of 358 pm) are given in Table 1. Figure 9 shows a microdiffraction pattern (electron probe diameter: 10 nm) with a four-fold symmetry axis corresponding to the FCC lattice. Such a lattice does not correspond to any boron carbide usually deposited by CVD (B 4 C, B 13 C 2 , B 50 C 2 ...) [START_REF] Ploog | Composition and structure of boron carbides prepared by CVD[END_REF][START_REF] Vandenbulke | Composition and structural changes of boron carbides deposited by chemical vapour deposition under various conditions of temperature and supersaturation[END_REF][12] nor pure boron [12]. Figure 10 gives a SAD pattern obtained with the incident electron beam along the [110] direction. Such a diagram could be related to a diamond structure with {111} planar defects, (twins) but also irregular stacking faults as asserted by streaky spots occurrence in the [111] direction. This was already reported by many authors for small diamond crystal size obtained at high nucleation rate [START_REF] Ma | Electron microscopic characterization of diamond films grown on Si by bias-controlled chemical vapor deposiiton[END_REF][START_REF] Suzuki | Electron microscopy studies of dislocations in diamon synthesized by a CVD method[END_REF][START_REF] Zhu | Structural imperfections in CVD diamond films[END_REF][START_REF]Diamond films and coatings[END_REF]. The presence of a diamond structure phase is unexpected because external excitations such as high-temperature filament or plasma or flame were not present. Nevertheless, diamond formation could be explained by the presence of halogens and boron in the reactional H 2 -rich mixture, in accordance with previous works [START_REF]Synthetic diamond : Emerging CVD science and technology[END_REF][START_REF] Patterson | Diamond growth with thermal activation of carbon-hydrogen-halogen systems and growth enhancement with the addition of oxygen[END_REF].

Ageing treatment in air

Observations of interphases A' after ageing treatment in air reveal areas where the interphase remains entirely intact and others where it is partially oxidized as shown in figure 11. It has been difficult to correlate these observations with the presence of matrix cracks because thin areas were not extended enough. In figure 11, layers 3, 4 and 5 have been replaced by an amorphous material (as shown by a diffuse SAD pattern) made of silica, as proved by PEELS analysis (Fig. 12). On location of layers 1 and 2, carbon is still present (Fig. 13). This preferential oxidation can be attributed to the path of matrix cracks. It is supposed that cracks allow oxygen diffusion to layers 3, 4 and 5 but not to layers 1 and 2 because the deflection occurs between layers 2 and 3. Furthermore, oxide has probably protected the first two layers from air: the glass forming-based protection of the three external sublayers appears efficient. The absence of boron in the oxide after ageing can be explained by the great sensitivity of B 2 O 3 towards air moisture resulting in volatile boric acid formation [START_REF] Litz | Oxidation of Boron Carbide by Air, Water, and Air-Water Mixtures at Elevated Temperatures[END_REF][START_REF] Mckee | Borate treatment of carbon fibers and carbon/carbon composites for improved oxidation resistance[END_REF][START_REF] Kobayashi | Formation and oxidation resistance of the coating formed on carbon material composed of B4C-SiC powders[END_REF]. This phenomenon might be enhanced (even at room temperature) for TEM samples due to their very low thickness.

CONCLUSION

A method for making thin longitudinal sections of microcomposites has been developed in order to characterize by TEM interphases in SiC/C(B)/SiC. The matrix crack deflection paths after tensile tests of these microcomposites were observed. It was confirmed that good mechanical properties are due to a matrix crack deflection within the bulk of the interphase before reaching the fiber. This method allowed to evidence by TEM the occurrence of a particular nano-crystallized phase which is embedded in a C(B) material with 8 at. % of boron. On the basis of measurements from SAD patterns and their index linking, this phase was found to correspond to diamond structure with planar defects.

Finally, in the composition graded interphases, an ageing in air results in a consumption of the boron-rich layers close to the matrix yielding a silica containing phase, which seems to protect the low boron content layers close to the fiber. Fiber surface Fiber core Fiber surface Fiber core

Figure 1 :

 1 Figure 1: Ion thinning of fibers in longitudinal sections according to Berger and Bunsell [7]: (a) Isolated fibers are ion thinned circumferentially and the fiber surface is removed. (b) The surface of the fiber in the middle is protected from the ion beam by the adjacent fibers and is still present on the observable thin regions.

Figure 2 :Figure 3 :

 23 Figure 2: Method for making thin longitudinal sections of microcomposites

Figure 4 :

 4 Figure 4: Bright-field image of matrix crack deflection (arrows) in compositional gradient interphase A'. (F: fibre; M: matrix; the numbers relate to the five different sublayers involved in the interphase.)

Figure 5 :Figure 6 :

 56 Figure 5: Bright-field images of matrix crack deflection gradient interphase A'. The dark areas in layer 2 reveal the presence of polycrystalline structures.

Figure 7 :

 7 Figure 7: Bright-field image of a microcomposite with interphase II. The dark areas in the interphase correspond to the polycrystalline structures.

Figure 8 :

 8 Figure 8: An electron SAD pattern from the polycrystalline phase evidenced in figures 5 and 7.

Figure 9 :

 9 Figure 9: Microdiffraction pattern of a single crystal which belongs to one of the dark areas of interphase II evidenced in figure 7.

Figure 10 :

 10 Figure 10: SAD pattern from a single crystal which belongs to one of the dark areas of interphase II evidenced in figure 7. This pattern is typical of a twinned and faulted diamond structure.

Figure 11 :Figure 12 :Figure 13 :

 111213 Figure 11: Bright-Þeld images of a microcomposite with compositional gradient interphase A' after ageing in air at 873 K under load.

Table 1 :

 1 Miller indices and inter-reticular distances d calculated from the SAD patterns of the polycrystalline phase evidenced in figures 5 and 7.

Philips CM 30 ST.

Gatan.

ACKNOWLEDGEMENTS

This work has been supported by CNRS and SEP through a grant to S. J. The authors wish to thank M. Alrivie for her contribution to sampling techniques and R. Naslain for fruitful discussion.


Tatiana I Lappi

Yakov M Gaifulin

Vadim V Yanshole

Stephane Cordier

Nikolay G Naumov
email: naumov@niic.nsc.ru

Evidences of the non-stoichiometry and control of the composition of the cluster-based solid solution K6[Re6-xMoxS8(CN)5] (x=2.75-3.63)

Keywords: Octahedral cluster, Solid state chemistry, Rhenium, Molybdenum, Metal Sulfides

published or not. The documents may come

Introduction

Octahedral chalcogenide and halide clusters built on face-capped {M6X8} cluster core represent a large and practically important class of inorganic compounds [1][2][3][4][5][START_REF] Sokolov | Comprehensive Inorganic Chemistry II[END_REF] . They are widely studied and demonstrate promising catalytic, magnetic and photophysical properties (selected references are: [START_REF] Kumar | [END_REF][8][9][10][11][12] ). The eight faces of the M6 cluster are coordinated by inner ligands forming the cluster cores {M6(3-X)8} m+ (M = Mo, W, X = Cl, Br, I, S, Se, or Te; M = Tc, Re, X = S, Se, or Te). With a few exceptions, cluster compounds generally consist of similar [M6X8L6] building blocks and crystallize as phases of stoichiometric composition. Formation of non-stoichiometric phases is quite rare in the chemistry of clusters. Heterometallic clusters represent a special type of cluster compounds containing different metal atoms within the core [13][14][15][16][17][18][19][20][21][22][23] . The introduction of another metal atom makes it possible to change the properties of cluster compounds in a controlled manner, and can also lead to interesting optical properties due to a decrease of the symmetry of the cluster core. A few detailed studies of heterometallic clusters have shown that they may crystallize as non-stoichiometric compounds containing cluster cores with different metal-to-metal ratio and their properties are closely related to the composition of the cluster core [18,[21][22][23] . Such co-crystallization occurs as a result of high-temperature synthesis. The presence of cluster cores with different metal-to-metal ratio in the lattice of the resulting compounds was confirmed by their dissolution and investigation by spectroscopic methods (UV-Vis, NMR), mass spectrometry, chemical separation and crystallization of different species. For example, compound K2[Re3Os3Se8Cl6][Re4Os2Se7Cl7], which was obtained by reaction between Re, Os, Se, ReCl5 and KCl, is a solid solution [22] . Cluster anions with {Re3Os3Se8} and {Re4Os2Se7Cl} cores were detected using electrospray mass spectrometry of the aqueous solution of this compound.

Heterometallic clusters with {Re3Mo3S8} cores were synthesized using high-temperature reaction between ReS2, MoS2 and KCN. It was shown that the resulting polymeric phase K6[Re3Mo3S8(CN)5] comprises {Re3Mo3S8} based cluster [18] . A closer examination of this reaction and in particular the Re/Mo ratio in the final product revealed that despite the loaded composition was "K6[Re3Mo3Se8(CN)5]" in all experiments, the true final composition corresponds to the non-stoichiometric K6[Re6-xMoxS8(CN)5]. The x value depends on the experimental conditions. In order to clarify the nature of non-stoichiometry of the K6[Re6-xMoxS8(CN)5] phase, we investigated the dependence of the composition as a function of two parameters: 1) the synthesis temperature of the ReS2 and MoS2 used as reagents and 2) the temperature of interaction of sulfides with KCN. The molar ratio of ReS2:MoS2:KCN loaded composition was fixed to 3:3:14 in all experiments. We found that both parameters affect the composition and consequently, the resulting phase is composed of cluster anions of different core composition, namely, {Re4Mo2S8}, {Re3Mo3S8} and {Re2Mo4S8} co-existing in the crystal lattice in different ratio.

Experimental

Materials and methods

Elementary rhenium and molybdenum were annealed under H2 flow to reduce the traces of oxides. Water and other solvents were purged with Ar before use. Metal disulfides MS2 were obtained in silica ampoules from corresponding metals and sulfur taken in stoichiometric amounts at temperatures (T1) specified in Table 1. The syntheses were carried out for 48 h; ampoules have been recovered after the oven has cooled to room temperature. The particle size of the obtained metal sulfides was estimated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) with a Libra 120 (Zeiss, Germany) at an acceleration voltage of 60 kV, as well as by the Scherer formula from powder X-ray diffraction data (PXRD). Other reagents were purchased from commercial sources and used without further purification.

The crystals were analyzed using a JXA-8100 (JEOL, Japan) Electron Probe Microanalyzer equipped with a wavelength-dispersive spectrometer. Elemental intensities for K, Re, Mo and S were determined relative to single crystal standards using metallic Re for Re, metallic Mo for Mo and MoS2 for S. About 20 points of quantitative data were collected for the major phase of each crystal and converted to crystal-chemical formulas by assuming 26 atoms per formula unit.

Averages and standard deviations were calculated to be ±0.04, which were consistent with the 3s criteria.

Electrospray ionization mass spectrometric (ESI -MS) analysis was performed on a Bruker maXis 4G high-resolution ESI-q-TOF spectrometer. The mass spectra were recorded under the following conditions: registration mode of negative ions from m/z = 600 Da to 4000 Da, voltage +2500 V, pressure on the nebulizer 0.8 bar, drying gas flow 4 l/min, drying gas temperature 180 °C.

Preparation of K6[Re6-xMoxS8(CN)5]

For the preparation of K6[Re6-xMoxS8(CN)5], ReS2 (1.02 g, 4.0 mmol) and MoS2 (0.65 g, 4.0 mmol) were thoroughly grounded and placed in a silica ampoule with KCN (1.68 g, 25.0 mmol). Ampoule was evacuated and sealed. The reaction was carried out at the temperatures T2 (given in Table 2) for 8 days and ampoule was slowly cooled to the room temperature. Resulting product was washed with EtOH/H2O mixture to remove soluble by-products. The sample contained octahedral black crystals with an admixture of unreacted metal sulfides, which were separated by sonication in EtOH with subsequent decantation. Black crystals of K6[Re6-xMoxS8(CN)5] were filtered and dried in argon atmosphere. The analysis of the PXRD pattern of K6[Re6-xMoxS8(CN)5] revealed that it is isostructural with the reported compound K6[Re3Mo3S8(CN)5] [18] . The yields and mean chemical compositions of K6[Re6-xMoxS8(CN)5] x = 2.75-3.63 are given in Table 2. The x values were taken from the EDS. Several crystals were selected from each synthesis, where points were measured the content of each metal, ranging from 10 to 15 points.

Preparation of (Ph4P)5[Re6-xMoxS8(CN)6]

Samples for the ESI-MS analyses were prepared by quantitative precipitation of (Ph4P)5[Re6-xMoxS8(CN)6]. To dissolve K6[Re6-xMoxS8(CN)5], the technique reported in [18] was used: KCN (10 mg, 0.16 mmol) and H2O (5 ml) were added to K6[Re6-xMoxS8(CN)5] (250 mg, 0.16 mmol). The solution of Ph4PCl (300 mg, 0.8 mmol) in H2O (5 ml) was added to the solution of cluster complex, causing immediate precipitation of (Ph4P)5[Re6-xMoxS8(CN)6]. After centrifugation and washing, the obtained salt was dissolved in CH3CN (3 ml) and the resulting solution was investigated by ESI-MS.

Results and discussion

According to [18] , the reaction of ReS2 and MoS2 with KCN at elevated temperature resulted in formation of cluster-based phase K6[Re3Mo3S8(CN)5] by reaction:

3ReS2 + 3MoS2 + 14 KCN = K6[Re3Mo3S8(CN)5] +9/n(CN)n +4K2S
During investigation of the "K6[Re3Mo3S8(CN)5]" phase we have discovered that its precise composition and in particular the Re/Mo ratio, depends on the synthesis temperature of both cluster phase and MS2 precursors. This results in a phase stoichiometry deviation from the ideal K6[Re3Mo3S8(CN)5]. To understand the non-stoichiometry of the K6[Re6-xMoxS8(CN)5] phase, we investigated the dependence of the composition on i) sulfide sintering temperature (T1) and ii) the synthesis temperature of K6[Re6-xMoxS8(CN)5] phase (T2). The comparison of XRD patterns (Figure 1) of binary sulfides sintered at different temperatures expectedly showed that the increase of sintering temperature leads to the increase of the average particle size (Table 1) and narrowing the XRD reflections. Estimation by the Scherrer equation showed a trend in the average size of crystals, and the broadening of the diffraction peaks confirms the change. The increasing of particles size was confirmed by SEM and TEM studies (Fig S2 -S3). Determination of the average size has been challenging due to the ability of metal sulfides to form agglomerates and due to high aspect ration of crystallites.The effect of sintering temperature on the peak broadening and average particle size is well known for metal sulfides.

Scherer formula

In order to reduce the number of parameters to be changed, we fixed the ratio of rhenium and molybdenum sulfides, the amount of KCN in the ampoule, the synthesis time (8 days) and the isolation procedure described in the Experimental part. Table 2 summarizes the product yield and ratio of heavy atoms according to EDS analysis. It should be noted that in some cases, a temperature higher than 850 о С leads to the degradation of ampoules, and lower temperatures resulted in by-products. 2, for the reaction with KCN carried out at a temperature of 700°C, the total amount of rhenium in the reaction product increases from 2.37 to 3.16 with rising temperature preparation of metal sulfides. In the case of syntheses carried out at higher temperatures, the content of rhenium in the product changes insignificantly with changing of the precursors. There is a slight increase in the Re content from To confirm the complex nature of solid solutions, we used high-resolution electrospray mass spectrometry. As it was shown in [18] , the K6[Re3Mo3S8(CN ] and [Re2Mo4S8(CN)6] cluster anions with a 6charge (Figure 3). The ratio of these anions in different samples varies strongly depending on the sintering temperature T1 and the synthesis temperature T2. Table 3 graphically represents the mole ratios between the anions [Re6-nMonS8(CN)6], n= 2, 3 and 4 based on the mass-spectrometry data. anion. These data are in agreement with the EDS data (Table 2). Thus, mass-spectrometry reveals that K6[Re6-xMoxS8(CN)5] phase is built up from 3 different cluster-based units with {Re2Mo4S8}, {Re3Mo3S8}, {Re4Mo2S8} cluster cores in different amounts which leads to x values ranging from 2.75 to 3.63. The presence of different anions with integer content was also observed earlier in the selenide phase K6[Re6-xMoxSe8(CN)5] [19,21] . Apparently, the formation of solid solution substitution at non-isovalent substitution is a common feature of heterometallic clusters.

T1 (MS2

Conclusion

In this work, we described the effect of the synthesis temperature, as well as the sintering

Fig. 1 .

 1 Fig. 1. Dependence of XRD for the ReS2 (a) and MoS2 (b) from the temperature T1.

3.13 to 3 .

 3 23 for reaction carried out at 750 °C, and at 850 °C the Re/Mo ratio in the samples is practically insensitive to the MS2 synthesis temperature.Analysis of the EDS results showed that the metal ratio can vary even within one crystal of the K6[Re6-xMoxS8(CN)5] phase (Fig.2). It has been observed that the edges of the crystal have different Re/Mo ratio in comparison with the area closer to the crystal center. Each crystal was investigated in several measuring points, including its edges and center. For example, for a sintering temperature T1 equal to 600 o C and a synthesis temperature T2 equal to 750 o C, the Re/Mo ratio in the center of the crystal and at the edge was 2.74:3.26 and 3.69:2.31, respectively. Similar gradient of composition was observed for many crystals in all syntheses.

Fig. 2 .

 2 Fig. 2. Image of a crystal of compound 1 obtained at sintering temperature T1 equal to 600 o C and synthesis temperature T2 equal to 750 o C.

) 5 ]

 5 phase can be dissolved in aerated KCN solution giving [Re3Mo3S8(CN)6] 5-anion. To clarify the nature of non-stoichiometry of K6[Re6-xMoxS8(CN)5] solid solutions, we have dissolved them in a similar way and analyzed all prepared samples by ESI-MS analysis. The dissolution of K6[Re6-xMoxS8(CN)5] resulted in formation of [Re6-xMoxS8(CN)6] 5-anions which were precipitated as tetraphenylphosphonium salts. Acetonitrile solution of (Ph4P)5[Re6-xMoxS8(CN)6] was used for registration of ESI-MS spectra. Regardless the composition of K6[Re6-xMoxS8(CN)5] samples, all mass spectra reveal the presence of [Re4Mo2S8(CN)6], [Re3Mo3S8(CN)6

Fig. 3 .*Table 3 .

 33 Fig. 3. Isotopic distributions of cluster adducts presented in CH3CN solution of (Ph4P)5[Re6-xMoxS8(CN)6] salt prepared at different T1 (600, 800, 1000 o C) and T2 (700, 750, 850 o C) (top). Bottom: calculated isotopic distributions for corresponding adduct. Signals corresponds to the adducts {(Ph4P)[Re3Mo3S8(CN)6]*H2O} 2-(m/zcalcd= 808.758 Da), {(Ph4P)[Re4Mo2S8(CN)5]} 2-(m/zcalcd= 831.276 Da), {H2[Re2Mo4S8(CN)4]*H2O*CH3CN} 2- (m/zcalcd= 1220.399 Da) left to right, correspondingly).

3 or 4 .

 4 temperature of starting metal sulfides precursors MoS2 and ReS2 on the content of rhenium and molybdenum in the solid solution K6[Re6-xMoxS8(CN)5] (x = 2.75-3.63). It was found that the temperature of the sintering of the starting metal sulfides affects the size of the resulting particles and subsequently the composition of K6[Re6-xMoxS8(CN)5] phase. It was determined that starting from sulfides sintered at 600 °С leads to molybdenum rich phase K6[Re2.37Mo3.63S8(CN)5] when the reaction temperature is low (700°C) . With the rise in the reaction temperature, the rhenium content in the reaction product increases. ESI-MS spectrometry reveals that the solutions prepared from these compounds contain 3 different anions cores based on the three following cluster cores: {Re2Mo4S8}, {Re3Mo3S8} and {Re4Mo2S8}. The sintering temperature of sulfides and temperature of the synthesis of K6[Re6-xMoxS8(CN)5] phase influence on the proportions of these forms. With a rise in the synthesis temperature, the amount of the {Re4Mo2S8} form increases, and the amount of the {Re3Mo3S8} and {Re2Mo4S8} forms decrease. Thus, EDS analysis and mass-spectrometry reveal that K6[Re6-xMoxS8(CN)5] phase is the substitution solid solution with the fractional indexes (x = 2.75-3.63) composed of discrete cluster cores with an integer indexes n in Re6-nMonS8, n= 2, The reported study was funded by the Russian Science Foundation (project No 22-73-10181). The research was also supported by the Ministry of Science and Higher Education of the Russian Federation. Authors thank the Microscopic Centre of the Siberian Branch of the Russian Academy of Sciences and the Shared Equipment Center ''Spectroscopy and Optics'' of the Institute of Automation and Electrometry SB RAS for the provided instrumental support.

Table 1 .

 1 The mean particle size of the obtained metal sulfides estimated by PXRD by the

Table 2 .

 2 Yield

	, o C)	600	800	1000

composition of the K6[Re6-xMoxS8(CN)5] phase. According to the Table

2

, the highest molybdenum content was observed in the sample prepared from rhenium and molybdenum sulfides obtained at low temperature (600°C). This phase has a average ratio of Re/Mo equal to 2.37/3.63. The increase of the sulfide sintering temperature and/or synthesis temperature leads to the formation of rhenium richer phases. According to data given in Table


Elina Thibeau-Sutre

Jelmer M Wolterink

Olivier Colliot

Ninon Burgos

How can data augmentation improve attribution maps for disease subtype explainability?

Keywords: Explainability, Pattern recognition and classification, Synthetic data, Subtyping, Interpretability

As deep learning has been widely used for computer aided-diagnosis, we wished to know whether attribution maps obtained using gradient back-propagation could correctly highlight the patterns of disease subtypes discovered by a deep learning classifier. As the correctness of attribution maps is difficult to evaluate directly on medical images, we used synthetic data mimicking the difference between brain MRI of controls and demented patients to design more reliable evaluation criteria of attribution maps. We demonstrated that attribution maps may mix the regions associated with different subtypes for small data sets while they could accurately characterize both subtypes using a large data set. We then proposed simple data augmentation techniques and showed that they could improve the coherence of the explanations for a small data set.

INTRODUCTION

Explaining the decisions made by deep learning models is not trivial, but could be helpful to validate their application to clinical tasks for which only few test samples are available. This is why explainability methods generating attribution maps have been developed for classifiers working on images. Many of these methods are based on gradient back-propagation. [START_REF] Simonyan | Deep inside convolutional networks: Visualising image classification models and saliency maps[END_REF] Frameworks such as weakly-supervised segmentation 2 assume that the attribution map of a convolutional neural network (CNN) performing classification is coherent with prior knowledge. In this kind of framework, a deep learning network produces a label at the image-level (for example the presence or absence of a tumor), and the assumption is that the attribution map of this decision highlights which information in the image the network used to compute its output. These attribution maps are assumed to produce the segmentation of the region needed for the classification task (for example the segmentation of the tumor). However, a recent publication 3 benchmarked a series of explainability methods derived from gradient back-propagation and assessed that they had poor localization performance. This means that they were not able to correctly segment the region of interest corresponding to the classification task. However, it remains difficult to evaluate the coherence with prior knowledge of deep learning models associated with their explainability methods, especially for clinical tasks whose ground truth varies according to clinicians. [START_REF] Saporta | Benchmarking saliency methods for chest X-ray interpretation[END_REF] This is in particular true for disease subtyping as there is often no universally accepted ground-truth for subtypes. This ground truth is even more difficult to assess when there is no consensus on the definitions of the subtypes composing the disease, as is the case for example for Alzheimer's disease, [START_REF] Ferreira | Biological subtypes of Alzheimer disease: A systematic review and meta-analysis[END_REF] Parkinson's disease, [START_REF] Thenganatt | Parkinson Disease Subtypes[END_REF] or frontotemporal dementia. [START_REF] Seelaar | Clinical, genetic and pathological heterogeneity of frontotemporal dementia: A review[END_REF] In this paper, we show that gradient back-propagation can correctly highlight ground truth patterns. We first assess that a CNN can identify latent subtypes grouped under the same label by K-means clustering on its feature maps, and then show that attribution maps can accurately highlight specific patterns of these subtypes. Additionally, we propose and evaluate simple data augmentation strategies to improve the separability of these subtypes with a limited number of samples. We work with synthetic data mimicking the patterns of a neurodegenerative disease. In such a controlled setting, we know which patterns are relevant for the classification, allowing a more reliable comparison of the evaluated techniques.

MATERIALS AND METHODS

Experiments, including data generation, network training, and attribution maps computation, were conducted with the ClinicaDL * software. [START_REF] Thibeau-Sutre | ClinicaDL: An open-source deep learning software for reproducible neuroimaging processing[END_REF]

Synthetic data

Synthetic images were used instead of real ones to ensure that the patterns identified by the network correspond to the true patterns specific to the underlying subtypes. These images are inspired from the Shepp-Logan phantom [START_REF] Shepp | The Fourier reconstruction of a head section[END_REF] that was used to develop and test neuroimaging reconstruction algorithms.

Our use case is Alzheimer's disease heterogeneity. We simulated a data set of T1-weighted (T1w) MR images of demented patients and cognitively normal participants. Three rules were used to generate the synthetic data sets. First, the disease is characterized by the atrophy (volume decrease) of specific regions of the brain. Second, the disease is heterogeneous, i.e. different atrophy patterns exist within a patient group. Third, some patients can hardly be distinguished from cognitively normal participants based on their T1w MRI.

The size of the images was fixed to 128 × 128 pixels. Three subtypes, displayed in Figure 1, were sampled by varying the size, position, orientation and contrast of the ellipses depicting simplified brain regions. A random smoothing was applied. Subtypes vary according to the size of the regions Top and Bottom. Subtype 1 has two large regions, subtype 2 has a large Top region and a small Bottom region, and subtype 3 has a small Top region and a large Bottom region. Two labels are associated with these subtypes: Control and Atrophied. The Control group comprises only images of subtype 1, whereas the Atrophied group comprises images of subtype 1 (errors), subtype 2 (typical) and subtype 3 (atypical).

As we do not know the proportion of each subtype in the Atrophied group, three training/validation data sets were sampled with different Atrophied distributions: homogeneous (500 samples per class) consists of 85% typical subtypes, 10% atypical subtypes, and 5% errors, heterogeneous (500 samples per class) consists of 65% typical subtypes, 25% atypical subtypes, 10% of errors, and large (10,000 samples per class) has the same properties as homogeneous. Finally, we generated a test set of 1,000 images in which the Atrophied group is composed of half typical and half atypical subtypes.

Baseline CNN classification

All networks (except in section 3.2.1) learn the classification task Control versus Atrophied. The subtypes are not given to the network. The chosen architecture is composed of five convolutional blocks followed by a dropout layer with probability 0.5 and a fully-connected layer. Each convolutional block is made of two convolutional layers with kernel size of 3 and padding of 1, a batch-normalization layer, a LeakyReLU activation and a max pooling layer with a kernel size and a stride of 2. Default values were used for other hyperparameters. The predicted label of the input image is the index of the output node having the maximum activation. The weights of the convolutional and fully-connected layers were initialized with the default initialization method of PyTorch. [START_REF] He | Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification[END_REF] During training, weights were updated based on the cross-entropy loss. The training continues to the end of Each training/validation data set was split into training and validation sets by performing a 5-fold crossvalidation (CV) stratified by subtype. The 5-fold data split was performed only once, thus guaranteeing that all the experiments used the same images during CV. Models were tested on the test set of 1,000 images without data augmentation. The balanced accuracy was computed to ensure that the model correctly learnt the task.

Data augmentation

Data augmentation was only applied to the training set during the training procedure. Once an image is loaded, it may be randomly altered to produce a slightly different version. The possible transformations are the following:

• CropPad samples between 0 and 10 pixels to crop the boundaries on one side and pad the opposite side;

• Erasing 11 draws a black rectangle in the image with a probability of 0.5. The default PyTorch values were used to choose the size and location of the rectangle;

• Noise adds Gaussian noise to the original image with a standard deviation sampled between 0 and 0.1;

• Smoothing smooths the image with a Gaussian kernel of standard deviation sampled between 0 and 1.

Note that we limited our search to transformations that could easily be applied to 3D volumes.

Subtype identification using attribution maps

Though many explainability methods exist, we restricted this study to attribution maps produced by gradient back-propagation, 1 as it is widely used and conceptually simple. An individual attribution map corresponds to the gradients of an output node with respect to an image. In our case, the output node is the one corresponding to the Control group. The intensities of the attribution map of an image correspond to the changes needed to transform this image into a sample of the Control group. A group attribution map is the average of the individual attribution maps of the correctly classified images of this group.

The coherence of the CNN coupled with attribution maps in identifying Atrophied subtypes and their characteristics was measured with three criteria. In the following we refer to the regions Top, Bottom and Background, where Background includes all pixels of the image which are neither in Top nor in Bottom. S X is the surface of region X and I(p) is the intensity of the saliency map at position p.

CNN subtyping ability. The ability to identify the subtypes was evaluated by clustering ten times the feature maps before the dropout layer and evaluating the mean adjusted rand index † between the true subtypes and the clusters found on the evaluation set.

Theoretical values of each criterion for a perfect or random characterization of the patterns are given in Table 1. Intensities in a region are normalized, i.e. divided by the surface of the whole region. As discussed in Section 4, one should not compare the values of the criteria between the two subtypes.

RESULTS

Baseline results

The three evaluation criteria were applied to networks trained on the homogeneous and heterogeneous data sets (Table 1). Group attribution maps of the first fold of each network series are displayed in Figure 2A. Balanced accuracy is very high (>= 0.98) for all the networks. The subtyping ability of the CNN is maximal for all the networks, the difference on homogeneous being caused by results on one fold being lower than the others. The separability and specificity of attribution maps are equivalent for both data sets. On both data sets the separability of the atypical saliency map is equivalent to a random map, even though these maps are specific.

Ideal cases

To understand how these baseline results could be improved, saliency maps obtained in two ideal cases were evaluated. In the first case, the same amount of data is used but the subtypes are actually known and used to train the network. In the second case, the labels are unknown but the data set is larger.

Known subtypes

In this section, the networks are not trained on the binary class Control vs Atrophied as in the other sections. Instead, a three-class classification is learnt based on the subtype. Results with known labels are displayed in Figure 2B and in Table 1. In this case the CNN subtyping ability was not evaluated, as the networks are actually learning to differentiate the subtypes, so it actually corresponds to the balanced accuracy evaluated on the test set. We used 100 epochs as convergence was reached sooner.

The specificity is increased when knowing the labels, i.e. regions that are not correlated with any subtype are less highlighted by the saliency maps compared to the ones correlated with the patterns. However, the separability remains low, which means that both regions of interest are highlighted for both subtypes, so it is not possible to differentiate subtypes based on their heatmaps.

Large data set

We studied the impact of the number of samples by comparing the results obtained with the large and homogeneous data sets (Table 1 and Figure 2C). For the large data set, we used 100 epochs because training was more computationally costly and convergence was reached sooner.

For the large data set, the separability and the specificity of the attribution maps are much higher than for the homogeneous data set, even when the task is to differentiate the subtypes. Moreover, the areas highlighted by the attribution maps appear more separated at visual inspection. This indicates that attribution maps may better reflect the patterns of each sample without being contaminated by the global pattern of the disease when CNNs are trained with more data. However, data sets in medical imaging tend to be small so we need to find solutions to improve the separability and specificity of our attribution maps on small data sets.

Benchmark of data augmentation strategies

We proposed to use data augmentation (see section 2.3) to improve the separability and specificity of attribution maps. Notable improvement was only observed for the heterogeneous data set. Only CropPad led to a statistical improvement according to a T-test with Bonferroni correction on the five folds of each experiment, and on atypical maps only. The two best-performing techniques were selected to be applied in the following order: CropPad and Noise. This combination led to a statistically significant improvement compared with the baseline values on the separability and the specificity of the typical subtype, and the specificity of the atypical subtype. Criterion values are summarized in Table 2 and group attribution maps obtained with the homogeneous data set are displayed in Figure 3.

CONCLUSION

We studied the ability of CNNs and attribution maps to identify subtypes composing a heterogeneous disease. Our synthetic data was made to simulate Alzheimer's disease heterogeneity, but the whole framework can be adapted to another clinical problem. We observe that even when models obtain a very high accuracy and disease subtypes are correctly identified, the attribution maps fail to represent the underlying ground truth at the subtype level on small data sets. We then studied two ideal cases: first the case in which the subtypes are actually known and learnt by the network and then a case with a larger amount of data. We observed that the saliency maps are only slightly improved by the ground truth subtypes knowledge, and that a better coherence with the ground truth patterns is obtained with a larger data set.

As medical imaging data sets are often small, we introduced different data augmentation techniques to better identify patterns with attribution maps. This improved the separability and specificity of group attribution maps on a small data set. We showed that this improvement depends on the subtype distribution. For the homogeneous data set, the increase in performance was generally smaller than for the heterogeneous data set. The reduced number of techniques reaching a statistically significant improvement compared with the baseline could also be due to the limited number of models run per technique (five, one for each fold). This analysis could be improved by running more models for each experiment.

This study is limited to the use of gradient back-propagation to generate attribution maps, but other methods exist. Comparing them using the proposed criteria would also allow assessing the reliability of these criteria, by comparing the inter-rater reliability on individual assessments of each explainability method. [START_REF] Tomsett | Sanity Checks for Saliency Metrics[END_REF] Another current limitation is the restriction to synthetic data.

Contrary to [3], we assessed that an explanation method in association with the deep learning network it explains could be coherent with prior knowledge. As we found that the coherence of our setup could be improved using the same deterministic explanation method by changing the training of the CNN, we conclude that the poor localization utility that they observed in their study is not due to the explanation methods as they hypothesize, but to the CNNs which were not able to learn the clinical relevant features and relied instead on confounding variables. These findings support our previous study on the lack of robustness of CNNs trained on neuroimaging data. [START_REF] Thibeau-Sutre | Visualization approach to assess the robustness of neural networks for medical image classification[END_REF] This analysis also shows a limitation of semi-supervised segmentation frameworks described in the introduction, in which the number of samples may not be sufficient to highlight the diversity of regions necessary to characterize a label learnt at the level of the image, even if the labels are accurate and homogeneous.

Figure 1 :

 1 Figure 1: Display of the three subtypes. Regions Top and Bottom are framed in blue and orange, respectively. Subtype 1 has two large regions, subtype 2 has a large Top region and a small Bottom region, and subtype 3 has a small Top region and a large Bottom region.

Figure 2 :

 2 Figure 2: Group attribution maps obtained for the first fold of the 5-fold CV without data augmentation (A) with unknown subtypes, (B) with known subtypes and (C) with a large data set of unknown subtypes.

Figure 3 :

 3 Figure 3: Group attribution maps obtained for the first fold of the 5-fold CV with the homogeneous data set and different data augmentation strategies (CropPad, Noise and their combination), for both the typical and atypical subtypes.

Table 1 :

 1 Baseline performance for each data set. The first two rows indicate the theoretical values for a perfect or a random characterization of the patterns. Unless stated otherwise, only the networks trained with 1,000 epochs are presented. The final model is the one that obtained the lowest validation loss during training. The loss of the model is evaluated at the end of each epoch. By default there is no data augmentation.

	Data set	Task	CNN subtyping ability	typical subtype separability specificity separability specificity atypical subtype	balanced accuracy
	perfect		1.00	+∞	+∞	+∞	+∞	N/A
	random		0.00	1.0	1.0	1.0	1.0	N/A
	homogeneous Control versus Atrophied	0.95	12.3	5.3	1.6	4.2	0.98
	heterogeneous Control versus Atrophied	1.00	8.6	5.1	0.9	4.6	0.98
	homogeneous subtype classification	N/A	9.3	6.6	1.1	7.9	1.00
	heterogeneous subtype classification	N/A	9.8	7.3	1.1	7.8	1.00
	large	Control versus Atrophied	0.99	102.5	12.3	12.9	13.7	1.00
	a pre-defined number of epochs (100 or 1,000).

  Attribution maps separability. The ability to distinguish patterns of typical vs atypical subtypes was evaluated by comparing the sum of the absolute values of the normalized intensities in the regions Top and Bottom.Attribution maps specificity. The specificity was evaluated by computing the ratio between the sum of the absolute values of the normalized intensities in the regions Top and Bottom and in the Background.

	separability typical =	p∈T op |I(p)| p∈Bottom |I(p)|	*	S Bottom S T op	separability atypical =		p∈Bottom |I(p)| p∈T op |I(p)|	*	S T op S Bottom
									(1)
	specif icity typical = specif icity atypical =	p∈T op∪Bottom |I(p)| p∈Background |I(p)|	*	S Background S T op∪Bottom

Table 2 :

 2 Benchmark of data augmentation techniques on the homogeneous and heterogeneous data sets. * denotes a statistical difference with the baseline values assessed using a T-test (p<0.05) with Bonferroni correction.

	Experiment	CNN subtyping ability	typical subtype separability specificity separability specificity atypical subtype	balanced accuracy
	CropPad	1.00	13.2	4.7	2.0	5.1	0.99
	Erasing	1.00	19.6	5.6	1.8	4.0	0.99
	Noise	1.00	18.4	9.1	2.3	5.5	0.99
	Smoothing	1.00	10.4	2.9	1.1	4.3	0.99
	CropPad + Noise	1.00	19.1	6.4	4.2	7.1	1.00
	None (baseline)	0.95	12.3	5.3	1.6	4.2	0.98
		(a) Homogeneous data set
	Experiment	CNN subtyping ability	typical subtype separability specificity separability specificity atypical subtype	balanced accuracy
	CropPad	1.00	20.6	5.8	2.6*	7.3*	1.00
	Erasing	1.00	13.7	6.3	2.0	5.2	0.99
	Noise	1.00	17.3	8.1	2.3	5.4	0.99
	Smoothing	1.00	12.1	5.1	1.3	3.9	0.99
	CropPad + Noise	1.00	41.8*	7.6*	3.7	8.2*	1.00
	None (baseline)	1.00	8.6	5.1	0.9	4.6	0.99
		(b) Heterogeneous data set

† the mean adjusted rand index measures the similarity of two clusterings, corrected for chance

ACKNOWLEDGMENTS

The research leading to these results has received funding from the French government under management of Agence Nationale de la Recherche as part of the "Investissements d'avenir" program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute) and reference ANR-10-IAIHU-06 (Agence Nationale de la Recherche-10-IA Institut Hospitalo-Universitaire-6). We also acknowledge funding from the 4TU Precision Medicine program supported by High Tech for a Sustainable Future, a framework commissioned by the four Universities of Technology of the Netherlands. The authors have no relevant financial or non-financial interests to disclose.

https://github.com/aramis-lab/clinicadl


         𝑆 𝑀 𝑀 ⃗⃗ 𝑀 𝑠 𝑀 ⃗⃗ 𝑑𝑀 𝑑𝑡 ⃗⃗⃗⃗⃗⃗ = -𝛾𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ + 𝛼 𝑀 𝑠 𝑀 ⃗⃗ × 𝑑𝑀 𝑑𝑡 ⃗⃗⃗⃗⃗⃗ Eq. 1 𝛾 𝛼 𝑀 ⃗⃗ ∝ 𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ ∝ 𝑀 ⃗⃗ × 𝑑𝑀/𝑑𝑡 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ∝ 𝑀 ⃗⃗ × 𝑀 ⃗⃗ × 𝐻 ⃗ ⃗ 𝛾𝐻 𝛼𝛾𝐻, 𝐻 𝐻 𝑑𝑀/𝑑𝑡 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝛼 𝛼 < 1
i. ii. iii. AOS in combined ferri and ferromagnetic heterostructures Fig. 7 iv. ii. THz spin injection iii. Spintronic THz emission Fig.

AOS in ferrimagnetic materials

AOS in ferromagnetic materials

AOS in fully ferromagnetic spin-valves

1 .

 1 Introduction ........................................................................................................................................... 2. Short bio ................................................................................................................................................ 3. Curriculum Vitae .................................................................................................................................... 4. Research work ..................................................................................................................................... a. Manipulating spins and speed limits ............................................................................................... b. All-optical magnetization switching (AOS) .................................................................................

Fig. 1

 1 Fig. 1

Fig. 1 :

 1 Fig. 1: Magnetization pattern after a single 4.4 ps magnetic field pulse. Because the magnetic field is non homogeneous (stronger in the center) a bull's eye pattern appears, where the magnetization has turned by 180° in the black outer ring, then 360°, 540°, and do on. Figure extracted from Ref 4 .

Fig. 2

 2 Fig. 2

Fig. 2 :

 2 Fig. 2: Schematic of first demonstration of the all-optical switching, without any magnetic field assistance. The laser writes magnetic domains of alternating polarization by using the helicity of the light. Figure extracted from ref 15 .

Fig. 3

 3 Fig. 3

Fig. 3 :

 3 Fig. 3: Simulation of temperature evolution of electrons and phonons for various switching conditions (𝛥𝑡 being the pulse duration) using a 1D 3 temperature model (spin temperatures not plotted). Figure extracted from ref21.

Fig. 4 Fig. 4

 44 Fig.4

Fig. 4

 4 Fig. 4

Fig. 5

 5 Fig.5

Fig. 5 :

 5 Fig. 5: Schematic of model for MCD driven AOS. (a-c) state of magnetic cells before and (d-f) after excitation with a circularly polarized laser pulse. (a,d) Shows the distribution of magnetic states. (b,c) shows the energy barriers as a function of temperature, and the temperature of up and down cells. (c,f) represent the well barrier and hopping time for non-excited (c), as well as hot and cold cells (f). Figure extracted from ref 28 .

Fig. 6

 6 Fig.6

Fig. 6

 6 Fig. 6

Fig. 6 :Fig. 7 :

 67 Fig. 6: (left) GdFeCo/Cu/[Co/Pt] structure indicating a polarized current in the Cu spacer (as yellow circled electrons) and (right) magnetization state observed by a MOKE microscope after a series of single laser shot. The large amplitude optical pulses switch the GdFeCo layer AND makes the Co/Pt layer parallel P (P- P+ or P-P+). The lower amplitude pulses switch only the GdFeCo layer (for ex: P+AP+ or P-AP-). Figure extracted from ref 40 .

42 . 42 Fig. 7

 42427 Fig. 7: The demagnetization of the GdFeCo layer (left) induces a spin current in the direction of the Gd spins that can reverse the Co/Pt layer (right). The image on the right in a magneto-optical image of the reversed domain by the laser pulse. Figures extracted from ref42.42

Fig. 7 Fig. 7 ‡ 22 Fig. 7

 77227 Fig. 7

Fig. 8

 8 Fig.8

Fig. 8

 8 Fig.8

Fig. 8

 8 Fig.8

Fig. 1Fig. 9 Fig. 1Fig. 9 Fig. 8 :

 998 Fig. 1Fig.

Fig. 9 ≫

 9 Fig.9

Fig. 9

 9 Fig.9

Fig. 9 :

 9 Fig. 9: Magnetization dynamics obtained from TR-MOKE. a) Magnetization dynamics for a Cu thickness of 10 nm measured for several fluences starting from a P configuration. Utilizing a quarter wave-plate enables separating the signal from the free layer and from the reference layer. An external magnetic field larger than the coercive field of the reference layer is applied during the measurement. b) Magnetization dynamics for a Cu thickness of 80 nm starting from the P+ (green) and AP+ (purple) states with F = 10.4 mJ/cm2. An external magnetic field (H) whose magnitude lies between the coercive fields (HC) of free layer and the reference layer (HC of free layer < H < HC of reference layer) is applied during the measurement

Fig. 10 ~4Fig. 10 𝑔Fig. 10 :

 101010 Fig. 10

62 . 29 Fig. 11

 622911 Fig. 10: Top left) a) Schematic of experiment and sample b) image of photoconductive switch c) image of magnetic device. Top right) demagnetization 10ps after arrival of electrical pulse as a function of the peak current within the pulse. Bottom left) polar MOKE response after a 2.6 ps optical pulse. Bottom right) polar MOKE response after a 5.5 ps electrical current pulse. Figures extracted from ref62.

Fig. 11 :

 11 Fig. 11: Fast electronic heating induced toggle switching of the magnetization in a GdFeCo sample, unsing a) optical pulses and b) 9 ps wide electrical pulses. Figure extracted from ref 65 .

Fig. 12

 12 Fig.12

Fig. 12 :

 12 Fig. 12: Picosecond current pulse generation platform with photoswitch, coplanar waveguide and ferromagnet. The ferromagnet stack used here experiences spin-orbit torques due to the spin Hall effect. The THz pump -optical probe configuration allows the investigation the dynamics of the magnet. Figure extracted from ref 70 .

Fig. 13

 13 Fig. 13

Fig. 13 :

 13 Fig. 13: Normalized change in the out-of-plane component of the magnetization 𝛥𝑀 𝑧 /𝑀 𝑠 (probed via time resolved polar MOKE) after excitation by a 3.8 ps wide electrical current pulse (shown in the inset). Current and in-plane field polarities are shown in the labels. Figure extracted from ref 70 .

Fig. 14

 14 Fig. 14

Fig. 14

 14 Fig.14

Fig. 14 :

 14 Fig. 14: Evolution of the out-of-plane component of the magnetization of a Pt/Co/Cu/Ta film after injection of a ~6 ps current pulse. A) starting with a magnetization pointing up, and for two current polarities b) starting with a magnetization pointing down and for two current polarities. The in-plane magnetic field is also flipped between these experiments.

Fig. 15

 15 Fig.15

Fig. 15

 15 Fig. 15

Fig. 15 𝜆Fig. 15 :Fig. 16 :

 151516 Fig. 15

Fig. 17 :

 17 Fig. 17: Beam array configuration. The various kinematic mirrors allow to select any beam as a probe or pump for any of the two setups (right top, bottom left). Both PHAROS and CHAMELEON lasers are fed into the matrix.

Fig. 17

 17 Fig. 17

Fig. 17

 17 Fig.17

  Fig.18

Fig. 19

 19 Fig.19

Fig. 18 :

 18 Fig. 18: Labview Control Unit used in the optics labs by all PCs. It contains a message list, a single counter identifier for experiments, some logging fields (user, samples, laser type and conditions…), which are all stored in a digital logbook. This interface also gives access to open access to instruments and programs (jobs or loops), see right panels.

Fig. 19 :Fig. 20 :

 1920 Fig. 19: Labview typical interface, with various windows opened that enable control of the sample stage, delay line and lock-in,as well as a pump-probe program that communicates with the delay line and lock-in.

Fig. 21

 21 Fig. 21

Fig. 21 :

 21 Fig. 21: Average number of users per month from January 2021 to July 2022.

Fig. 22 Fig. 23 :

 2223 Fig. 22 Home page with sponsors, team presentation, news, twitter feed, calendar…

  ..... Experimental developments ............................................................................................................... 6. Mentoring of students......................................................................................................................... 7. Responsibilities and other works ........................................................................................................

	.....................
	iii. Spintronic THz emission ..............................................................................................................
	d. Ongoing / Future work ....................................................................................................................
	e. Active collaborations .......................................................................................................................
	5.

i. AOS in ferrimagnetic materials ................................................................................................... ii. AOS in ferromagnetic materials .................................................................................................. iii. AOS in combined ferri and ferromagnetic heterostructures ...................................................... iv. AOS in fully ferromagnetic spin-valves ........................................................................................ c. THz spintronics ................................................................................................................................ i. THz spin heating .......................................................................................................................... ii. THz spin injection ...................................................................................................8. References ........................................................................................................................................... * See ordinance: arrêté de 23 novembre 1988 † See circular: circulaire relative au doctorat et à l'habilitation à diriger des recherches (ministère de l'éducation nationale et de la culture 27 Octobre 1992) 7 8 10  32

https://www.inp.cnrs.fr/fr/cnrsinfo/accelerer-la-vitesse-decriture-surmemoire-magnetique, see bottom of Fig.20https://engineeringcommunity.nature.com/posts/exploring-pico-spintronics of Fig.20of Fig.20

Acknowledgments 5