Olivier Barge
email: olivier.barge@mom.fr

Bérengère Perello

Emmanuelle Régagnon

Desert kites and aggregated cells of Mount Aragats (Armenia): spatial coincidences?

Keywords: dating, functions, spatial extension, morphology, survey, GIS, 1. Introduction

The aggregated cells were discovered during the fieldworks about desert kites conducted on the western slopes of Mount Aragats between 2011 and 2015, which is not surprising after all: the two categories of constructions share some logics of location in the landscape and it turns out that their respective extension areas, in Armenia, are very similar. Moreover, if the questions asked by the functions found only partial explanations, it seems that they imply animals in both cases. Could we advance the hypothesis of a coexistence of these two types of constructions, or even of their functional complementarity? The chronology, tricky to establish in the case of kites and still preliminary in that of the aggregates, could strengthen the idea of a possible contemporaneity. However, some rare cases of superposition make probable the anteriority of the aggregated cells.

and a comparison of the geographic distribution of both types of construction on the slopes of Mount Aragats. The coexistence of aggregated cells and kites outside Armenia will also be examined, where relevant. We will then undertake a comparison of the functions of these constructions, as the function of kites has been clearly established and can at least be discussed for aggregates. Finally, although data defining the time frame for kites are still approximate, we will nonetheless examine the absolute and relative chronologies of these constructions.

2. Methodology Both types of construction can be identified on the high-definition satellite images available on online platforms (Google Earth, Bing Maps). Field trips were conducted to monitor these observations, but also to enhance our interpretation of the images and provide new information. The combined fieldwork/image approach is very advantageous; it was widely used for the study of kites as part of the Globalkites project [START_REF] Crassard | Addressing the Desert Kites Phenomenon and Its Global Range Through a Multi-proxy Approach[END_REF] and led to the implementation of a multi-scalar approach, taking account of construction, the regional scale and the overall distribution area. The Aragats area is one of the regional "windows" studied in this programme. During fieldwork in Armenia between 2011 and 2015, 49 kites were visited, 11 of them were mapped and archaeological test pits were carried out at six of them [START_REF] Barge | Hunting with kites in Armenia[END_REF]. Today, abundant data is available on the Aragats kites, completed if necessary by the work of an Israeli-Armenian team [START_REF] Nadel | New insights into desert kites in Armenia: the fringes of the Ararat Depression[END_REF][START_REF] Malkinson | Seasonal use of corrals and game traps (desert kites) in Armenia[END_REF]. Mostly, the study of kites in other regions using the same methodology (Abu Azize & Tarawneh., 2015; Barge et al., 2016b) led to the detection of common points and underlined regional specificities [START_REF] Barge | Unity and diversity of the kite phenomenon: a comparative study between Jordan, Armenia and Kazakhstan[END_REF]Barge et al., 2016a). A comparable approach was set up for the aggregated cells of the Aragats, which also enabled us to avail of previously acquired data (topography, hydrography, geology). The first fieldwork observations in 2012 characterized the form, surface and geographic installation of these sites. Their signature on high-resolution satellite images subsequently led to the identification of numerous other aggregated cells and an inventory was drawn up. The largest cells and the layout of each construction were recorded, so that it was possible to delimit their extension. After the 2017 fieldwork mission, 121 aggregated cells had been recorded. The vectorization of the extension of these aggregates led to an estimation of their surface areas and the measurement of slope orientations. The primary aim of fieldwork was to monitor the validity of observations based on satellite images. Out of 26 visited sites, the existence of an aggregated cells was confirmed in each case. Ground observations showed that the somewhat rough estimation of their extension was nonetheless reliable. In addition, the existence of subsequent constructions partly covering the aggregates, recognized on the images, was confirmed in most cases. The second aim was to enhance the characterization of aggregated cells morphology. To this end, indepth studies were carried out for 11 sites, based on the observation of the structures and the search for surface material, the identification of frequent subsequent constructions in the same place and detailed mapping.

The following fieldwork was conducted as part of the survey of kites and aggregated cells: -Mapping of the built structures with a differential GPS, mounted on a backpack, with decimetric accuracy, -aerial photographs taken with a kite. The photos were then photogrammetrically processed, using reference points recorded with the DGPS, enabling us to obtain Digital Surface Models (DSM) and orthophotographs with spatial resolution ranging between 1 and 10 cm, depending on the sites, and accuracy of less than 5 cm. For the mapping, contour lines were generated based on the DSM; subsequent constructions and contextual elements were vectorized after identification on the orthophotographs. All of these data were used to provide a general picture of aggregates, bearing in mind the diversity of these constructions. The last aim of fieldwork was to find relative chronological markers for aggregated cells and other archaeological remains, in particular kites, based on the potential overlaps identified beforehand on satellite images.

3. Morphology of aggregated cells Aggregated cells consist of irregular and coalescent cells, delimited by dry stone walls, generally with only one facing, or by simple alignments of blocks (Annexes 1 to 7, The letter J for "Jellyfish", nomenclature used at the beginning of the program by analogy with the Jordanian structures. This analogy subsequently appeared to be erroneous to us, but the letter J was kept in the inventories.). On the surface, in some places, we can sometimes observe elevations of two, or exceptionally three rows of stones, but generally, there is only one layer of stones. The stones used were not squared but the most regular edges were frequently used for alignments. The size of the stones varies drastically, from stones about twenty centimetres long to imposing blocks reaching 1.5 or 2 metres. The overall structure of the aggregated cells is built by the relatively regular juxtaposition of large cells with a roughly constant size ranging from 10 to 20 metres (figure 1.a). These large cells seem to form the framework of the aggregate, and in some cases, only these large cells are present (J18, central part of J38, northern part of J31, …). But we frequently observe that smaller cells, or arrangements that are difficult to identify, are interposed in the layout. The case of the western part of aggregate J31 is totally representative of general aggregated cells morphology (figure 2). The large cells 1, 2, 3, 4, 5 and 6 outline the general framework, but we observe that smaller areas overlap with the latter. The diameter of cells 7 and 8 is 6 to 7 metres, whereas area 9 includes subdivisions that are difficult to read, and which may correspond to circulation areas, small closed constructions of several square metres, or to unidentified structures, in terms of shape. We also note that large cells were sometimes subdivided (cell 1). As indicated above, aggregated cells are often located on rocky slopes. The upper cells are on even steeper slopes (between 10° and 20°, even 25°), which decrease gradually towards the lower part (between 10° and 0°). Towards the top, the first cells were frequently built immediately below rocky scarps (which can be almost vertical). In these places, we clearly observe that blocks were extracted from the scarp, and we assume that these extracted blocks were used for the construction of cells. We also observe, at the base of the extraction, the presence of small platforms resting on and delimited by large blocks (figure 3). It is difficult to interpret these small areas due to the size of the materials and the irregularity of the walls from which the blocks were extracted. However, their recurrent presence suggests that they represent rustic but intentional structures. Lower down, we observe the progressive disappearance of the aggregated cells, in such a way that in most of the studied cases, it is impossible to identify a precise limit (J18 and J77 are exceptions). The walls of the cells clearly recorded further up give way to segments, then to alignments of blocks, and finally to isolated blocks at the bottom. The latter suggest that the aggregate continued but that it is no longer possible to formally identify it on the surface. These progressive disappearances towards the base can be explained by two factors which could have acted in different ways from case to case: -colluviation, which is clearly recorded by the presence of a sedimentary prism systematically formed further up from walls perpendicular to the slope, undoubtedly covered a lot of the structures at the base of slopes.

-we note that places where aggregated cells are preferentially implanted were also used at much later periods. Very often, we observe that other very characteristic constructions, which have been identified as medieval sheepfold [START_REF] Barge | Desert-kites et constructions apparentées : découvertes récentes et aire d'extension géographique[END_REF], overlap the lower part of aggregated cells, partially destroying them and probably reusing their materials (J9, J26, J31, J38, J56). Aggregated cells sometimes consist of a single complex (J9, J18, J54, J56, J77), but they can also be subdivided into two or three groups located several dozen metres away from each other (J31, J38, J78). In this case, it is not impossible that these groups may have had distinctive functions, with complexes consisting of large homogenous cells (central part of J38, northern part of J31) and others with less extensive and less regular subdivisions (west of J31, eastern part of J38).

The total surfaces covered by aggregated cells range from several thousand square metres to nearly four hectares (figure 1.b). However, small aggregated cells are more frequent than large ones, with a median surface of 0.72 hectare. Based on these field observations, completed by the observation of numerous cases on satellite images, aggregated cells reveal quite marked morphological homogeneity. In spite of specificities and adaptation to local topographic conditions, they have many points in common.

4. Installation rationales The lower part of the successive basalt flows from Mount Aragats generally presents moderate slopes, but these slopes are much sharper around the front. They are concave at the foot of flow fronts, where they shift considerably, and then become sub-horizontal, and some of them are in contact with the plain. These slopes were frequently chosen for constructing aggregated cells, which are quite regularly spaced out around slope edges (figure 4). Thus, this locally rugged topography beside flatter areas was clearly sought after. This is undoubtedly one of the elements explaining the absence of aggregated cells on the right bank of the Akhurian. The slopes of the latter are generally similar to those of the other bank, but they are relatively even, and do not present the local topographical accidents that characterize the slopes and basalt flows of Mount Aragats. Aggregated cells are almost systematically backed by steep slopes (often between 30° and 40°, or even more), formed by rocky outcrops (J9, J28, J31, J38, J56, J77). The presence of these rocky outcrops is characteristic of the western slopes of Mount Aragats and seems to have played a preponderant role in the choice of aggregated cells installation. As mentioned above, they may have been used as a convenient procurement source for the stones and blocks used for construction. They also acted as shelters, as the south-facing bases of flow fronts were clearly preferentially selected. Indeed, when we measure the orientation of all the slopes within the aggregated cell surface, we observe that more than 60% of the values are clustered in the southeast-southwest quadrant (figure 5). Only 13% are in the northern half and the circular average is close to 183° (a difference of less than 3° from the south). Thus, the building of aggregated cells backed by steep slopes combined with a southern orientation suggests that warm and sheltered conditions were a prerequisite. The topographic installation of kites has already been described in detail [START_REF] Barge | Desert-kites et constructions apparentées : découvertes récentes et aire d'extension géographique[END_REF], Barge et al., 2016a). In Armenia and elsewhere, the entrance of the enclosure at the extremity of the antennae was often built on a slope discontinuity (81% of cases). On the slopes of Mount Aragats, kite antennae are spread over the slightly sloped and relatively even surface of basalt flows; they converge at the convex slope discontinuity marking the upper part of flow fronts and the enclosure is built lower down the slope. The plan of each kite was clearly adapted to local topographic features, but the example of kite AM7 is representative of most situations (figure 6). In addition, front flows are nearly always dotted with rocky outcrops. As is the case for kite AM7, these rocky outcrops were clearly deliberately integrated into the interior of enclosures, and sometimes, as a result, walls had to be built on steep slopes whereas it would have been easier to build them on scarps. The construction of the walls outlines corridors between them and the rocky outcrops, suggesting that it was important to define preferential circulation directions in the topography of the interior of the enclosure. Therefore, the recurrence of rocky outcrops shows that they were clearly sought after for the installation of both types of construction: they acted as shelters in the case of aggregated cells, and this increased topographic complexity was propitious for the construction of kites. These rocky outcrops are particularly abundant in basalt front flows, which seem to present suitable conditions for aggregated cells and kites. The former were built on the lower part of front flows, whereas the latter were built on the upper part (figure 4).

Geographic distribution of aggregated cells and kites

The installation strategies of both types of construction rely on the same topographic elements, which explains why aggregated cells and kites are found near each other (figure 4). The median distance from aggregated cells to the nearest kite is 600 metres, whereas only one out of four is more than a kilometre away (figure 4b). Therefore, it is not surprising that both types of construction display very similar geographic distributions (figure 7a). From an overall quantitative viewpoint, the convex hull of all the aggregated cells on the map measures 1,188 km 2 , that of kites 1,321 km 2 and shared areas 1,110 km 2 . The shared part of the distribution area thus represents 93% for aggregated cells and 84% for kites. Inside these hulls, we observe that the areas where kites are absent correspond to those where aggregates are also absent. An increasing gradient from the east towards the west also exists for kites and aggregated cells, which is vey similar to the gradient of the presence of rocky outcrops, which are much more abundant in the west than in the east. These two distributions are thus surprisingly similar, but we can nonetheless perceive several variations. Aggregated cells are very abundant in the northwest, and as a result, kites are relatively under-represented in this zone, whereas in the south, aggregated cells are comparatively less present in the area of two kite alignments (figure 7b). These very similar geographic distributions are also surprising considering the observed isolation of the structures in both cases. This has already been highlighted for kites [START_REF] Barge | Desert-kites et constructions apparentées : découvertes récentes et aire d'extension géographique[END_REF], although no explanation could be advanced. In the case of aggregated cells, it is also impossible to explain this isolation. In spite of meticulous and systematic examinations of the satellite images beyond the area represented on the map (figure 7), none of these constructions could be identified in peripheral areas.

Kites and aggregated cells outside the Aragats area

These very singular geographic distributions incited us to move out of a regional scale to a much wider scale. This investigation had already carried out based on the literature [START_REF] Kalantaryan | New insight into the Agglomerated Cells in Armenia: Arteni, Aragats massif[END_REF], but was limited to the Harrat-al-Shaam in Jordan and did not explicitly examine the possible relationship between kites and aggregated cells. It thus seemed necessary to provide additional elements. In Armenia, several sites from the region of Vardenis have been compared to aggregated cells on account of the fact that they present similar overall structures. The comparison of results from archaeological work carried out at Geghaqar and Aghbradzor (Harutyunyan and Badalyan 2008, cited by [START_REF] Kalantaryan | New insight into the Agglomerated Cells in Armenia: Arteni, Aragats massif[END_REF] with data from Arteni should enable us to identify possible parallels. However, after surface field observations at the Aghbradzor site, we concluded that these two types of sites were very different. Indeed, at the latter, the cells are larger in size and are not layered, there is often a depression inside each cell, we distinguish clear circulation areas between groups of cells and their construction reveals double-faced walls. None of these features have ever been observed in the aggregated cells of the Aragats area. The distribution area of kites is now better known (Barge et al, forthcoming). The systematic search for aggregated cells on satellite images from this area shows that outside Armenia, the latter are not at all omnipresent, and in fact are practically only present in Harrat-al-Shaam, a basaltic region along the Syrian-Jordanian border (figure 8a). Several studies have been carried out on these structures, or related structures [START_REF] Akkermans | A landscape of preservation: Late prehistoric settlement and sequence in the Jebel Qurma region, north-eastern Jordan[END_REF][START_REF] Athanassas | Optically stimulated luminescence (OSL) dating and spatial analysis of geometric lines in the Northern Arabian Desert[END_REF][START_REF] Rollefson | First chronometric results for 'works of the old men': late prehistoric 'wheels' near Wisad Pools, Black Desert, Jordan[END_REF]), yet few conclusions have been reached regarding the type and function of these sites. The most widely studied of these constructions are "wheel houses" or "jellyfish", dating from the end of the Neolithic or Chalcolithic, which present a very different morphology to the aggregated cells of Mount Aragats. In spite of widespread diversity, they are circular in shape and the cells inside the circle are organized around the centre, in such a way that they embody rays (figure 8b andc). On the other hand, we often observe other constructions on the images, which are much more morphologically similar to the aggregated cells of Armenia (figure 8d ande). They are more frequent than "wheel houses" with a much wider spatial extension. We have very little information on these structures. However, considering the preserved elevations observed in the field during the study of kites in the east of Jordan and the apparent "freshness" of the constructions on satellite images, some of them could be recent. In any event, cases where kites overlap with aggregated cells and "wheel houses" all show that kites are earlier than the other structures (figure 8f andg). This overview shows that the spatial association of aggregated cells and kites is far from systematic as the presence of kites is not associated with aggregated cells in many regions. In Harrat-al-Shaam, where this co-existence was mentioned at a very early stage, and led at times to considering these two types of constructions together [START_REF] Kalantaryan | New insight into the Agglomerated Cells in Armenia: Arteni, Aragats massif[END_REF], elements indicating their relative chronology seem to rule out their contemporaneity. What about any possible functional link between these structures? 7. Functions Up until now, most authors have suggested that the function of kites was for hunting (among others, Helms and Betts, 1987; [START_REF] Berg | Desert-kites of the Hemma Plateau (Hassake, Syria)[END_REF][START_REF] Holzer | Desert kites in the Negev desert and northeast Sinai: their function, chronology and ecology[END_REF][START_REF] Bonacossi | The early history of the western Palmyra desert region. The change in the settlement patterns and the adaptation of subsistence strategies to encroaching aridity: a first assessment of the desert-kite and tumulus cultural horizons[END_REF]. However, the possibility of a pastoral use has also often been mentioned, or even asserted [START_REF] Svizzero | Desert kites: were they used for hunting or for herding? A review of the recent academic literature[END_REF], particularly for the kites of Armenia [START_REF] Malkinson | Seasonal use of corrals and game traps (desert kites) in Armenia[END_REF][START_REF] Hovsepyan | Archaeobotanical data from an 'agglomerated cells' type site: Plant macroremains from Arteni-1 (Armenia)[END_REF], in spite of strong criticism [START_REF] Rosen | The function of 'desert kites' -hunting or livestock husbandry?[END_REF]. Both of these hypotheses were explored together during the course of work on the Globalkites programme; leading to the rejection of the pastoral hypothesis, in particular in Armenia [START_REF] Barge | Hunting or pastoralism ? Comments on 'seasonal use of corrals and game traps (desert kites) in Arménia[END_REF] and to the conclusion that kites were used for hunting (Crassard et al, forthcoming). The main argument for this is based on the systematic existence of cells in the plan of kites, an element that has not generally been taken into account up until now and which was often considered to be a surveillance position or a lookout post. In reality, these cells are the key element of the kite and acted as a killing stratagem. Indeed, wherever they were excavated (8 in Armenia, 14 in Kazakhstan, 6 in South Jordan, 31 in Harat-al-Shaam, and 7 in Saudi Arabia), these cells turned out to be deep pits (figure 9) into which animals were thrown. The identification of the final trapping process enabled us to coherently interpret other recurring morphological details of kites, and provided elements for understanding the overall functioning of the structures. In this way, all the projections built into the enclosure, whether they are inflections, angles or points (particularly frequent in Armenia), systematically end in a cell. These enclosure shapes made it easier to drive the animals towards the pits. The latter were often hidden from the interior of the enclosure behind slope discontinuities, which were also used to conceal the entrance of the enclosure when approached from between the antennae. This clever use of slope discontinuities explains the fact that complex topographies were chosen in most cases for constructing the enclosure and in particular in Armenia, where rocky outcrops seemed to play an important role in masking obstacles or marking out circulation paths. Finally, the orientation of kites (the direction in which the antennae point) on a regional scale is partly determined by the topography of sites, but also presents a highly dominant direction which, in cases where it could be studied, such as in Armenia [START_REF] Chahoud | Zooarchaeological approach in understanding the desert kites[END_REF], is in keeping with migratory movements of animals. All of these elements thus validate the hunting hypothesis. Furthermore, the considerable surface of kite enclosures (on average, about a hectare, with higher values in Armenia) refutes the pastoral hypothesis: it is more than ten times superior to that of the pastoral enclosures studied up until now (Crassard et al., forthcoming). Data for determining the function of aggregated cells are more limited. Based on the observation of numerous surface cases, the constant topographic features and the morphological uniformity of the constructions imply that they were functional structures. Initially, we thought of a pastoral use, where each of the large cells looks like an enclosure. The fact that aggregated cells are systematically built on steep slopes supports this hypothesis as slopes facilitate the cleaning of pastoral mountain enclosures [START_REF] Rendu | Estives d'Ossau, 7000 ans de pastoralisme dans les Pyrénées[END_REF]. Large herds may thus have been gathered in the same place and the different cells may have been used to separate the animals by species, sex, or affiliation to different (family?) groups, in order to take advantage of grazing resources. We also observed the presence of areas with reduced dimensions between the large cells forming the outline of aggregated cells or immediately below rocky scarps. Some of them may have been elementary dwellings, perhaps especially those built on the upper slopes, as they would have been more sheltered and would have leaned against the wall, making it easier to install roof cover. Others, for which the structure is less visible, could have been used for specific activities, which cannot be accurately identified solely on the basis of surface observation. The south-facing orientation suggests that warm slopes sheltered from cold winds were sought after, perhaps for seasonal use. This would exclude the warm period, from June to September, and also the winter period, when snow cover is continuous. They may thus have been used during the mid-season. For the moment, the excavation of aggregated cells is limited to the site of Arteni and unfortunately, the levels corresponding to the aggregated cells yielded little information. However, several interesting elements provide clues regarding the function of the site. Archaeobotanical data point towards a pastoral use [START_REF] Hovsepyan | Archaeobotanical data from an 'agglomerated cells' type site: Plant macroremains from Arteni-1 (Armenia)[END_REF]. Although data from the level of the aggregated cells are sparse, they reveal large quantities of coprolites (mineralized animal excrements), demonstrating the use of manure as fuel. Although they are scarce, these data point in the same direction as those from animal bone remains (Creuzieux, in: Perello et al. 2019). Indeed, data from the archaeozoological analysis show that more than 80% of the bones belong to domestic caprines (sheep/goat). In addition, the kill-off ages of young animals also point to seasonal use, and corroborate the analysis of construction orientation, suggesting occupations during intermediary periods, in spring and autumn (Perello et al. 2019, data on seasonality are only based on levels preceding aggregated cells). We could also advance the hypothesis of an agricultural function for these aggregated cells which could be considered as terraces. This is supported by the south-facing orientation and the archaeobotanical data from Arteni showing the presence of coprolites, which could be interpreted as fertiliser. These terraces may have been planted with specific seasonal cultures (tinctorial, medicinal?). The fact that they are so localized could be explained by the specific characteristics of the cultivated plant, the type of soil or cultivation method. Data pointing to the function of aggregated cells are thus tenuous and we cannot reach any firm conclusions. However, we can cautiously postulate that the pastoral function seems to be the most likely in so far as the data from three different approaches (surface morphology, archaeobotany, archaeozoology) all point towards this interpretation.

8. Chronology A radiocarbon date from the site of Arteni places the aggregated cells level at the beginning of the Late Bronze Age (1431-1283 Cal BC). This date is in keeping with the objects found in this level. The pottery is characterized by comb treatment on the interior and exterior surfaces and decoration consisting of layers of marks made by fingernails (Perello et al. forthcoming). This type of pottery is known in the central part of the South Caucasus in Armenia and Georgia, where it is characteristic of the transition phase between the Middle Bronze Age and the Late Bronze Age (Trialeti-Vanadzor culture), that is to say, the middle of the second millennium BC [START_REF] Avetisyan | The pottery traditions of the Armenian Middle to Late Bronze Age 'Transition' in the context of the Bronze and Iron Age Periodization[END_REF]. Data for the absolute dating of kites are sparse [START_REF] Barge | Desert-kites et constructions apparentées : découvertes récentes et aire d'extension géographique[END_REF][START_REF] Barge | Hunting with kites in Armenia[END_REF]. As a result, here, we will simply place their construction in a wide chronological timeframe extending from the Late Bronze Age to the first centuries of our era, although their dating is more likely to be constricted to the Iron Age. In this way, the absolute dates would probably position the existence of kites after aggregated cells, but the temporal resolution of kite dating does not formally exclude the fact that these two types of construction could have been used at the same time over a short period. We saw above that aggregated cells are often located near kites: there are even two cases where we observe an overlap, thereby providing information on the relative chronology of the structures. The case of kite AM94, where the construction partially destroyed aggregated cell J2 has already been presented [START_REF] Barge | Desert-kites et constructions apparentées : découvertes récentes et aire d'extension géographique[END_REF]. It is clear that the aggregated cell came before the kite: the wall of the kite enclosure is continuous whereas those of the aggregated cells are interrupted near the kite wall. In the southern part of the overlap, we even perceive the former layering of the aggregated cells on the high resolution DSM, while the probably dismantled walls have disappeared (figure 10). A second case of overlap provides the same information, i.e., a kite post-dating an aggregated cell. Aggregated cells J28, which must originally have consisted of about twenty cells, was classically constructed at the base of the southern face of a rocky outcrop. A proximal pointed cell of kite AM78 was positioned on the west part of the aggregated cells, and the enclosure wall crosses, then goes around the rocky outcrop (figure 11a). This kite cell appears very clearly on the DSM while the aggregated cells is more blurred (figure 11b). The cells have totally disappeared from this place and the blocks and stones were probably reused for the construction of the kite cell. It is possible that the terrace effect that we distinguished immediately to the west of the pointed kite cell is the trace of a former cell on which the kite was built.

Conclusion

We have demonstrated that aggregated cells and kites display astonishing spatial unity. The spatial distribution of these constructions is very similar, although not totally identical. It seems as though this unit of space does not correspond to a unit of time. Relative chronology shows that kites were built after aggregated cells, and absolute chronological elements also tend to point in the same direction, placing kites after aggregated cells. However, this conclusion is still somewhat tenuous as there are only two cases where both types of structures overlap and it is still difficult to establish an absolute chronology. Therefore, we cannot totally rule out the fact that aggregated cells and kites may be contemporaneous in other places. If both types of construction turned out to be contemporaneous, we would have to assess their functional compatibility. We can now affirm that kites are hunting traps, in Armenia and elsewhere. There is no longer any doubt as to the role played by pit cells as a killing device and as an element for identifying kites in relation to other structures with convergent antennae. Furthermore, numerous other elements support this assertion. The pastoral interpretation of aggregated cells is less firmly established as the corresponding levels at the site of Arteni have yielded little archaeological material. However, markers pointing to a pastoral use are independent. In view of this, it is difficult to see how traps intended to kill animals could be functionally associated with structures designed to enclose them, without even taking the types of animal species into consideration. The coexistence of two types of independent constructions, with different functions, is thus very unlikely. In spite of the inaccuracy of temporal data and some functional data that prevent us from reaching a firm conclusion, it would be very risky to associate, in one way or another, aggregated cells and kites. In addition, outside Armenia, the coexistence of these constructions is far from systematic, and when it occurs, kites and aggregated cells do not seem to be contemporaneous. On the slopes of Mount Aragats, the observed spatial proximity between these types of construction can be explained by the fact that they rely on the same geomorphological features. The motives for their localization are closely linked to topography. For distinct reasons, the fronts of basalt flows, and in particular the rocky outcrops in these flows, were sought after in both cases. For the time being, with currently available data, the most probable explanation is thus spatial coincidence. (Annexes 1 to 7) Acknowledgements The GLOBALKITES project was financed by the French National Research Agency (No. ANR-12-JSH3-0004-01). Excavation in Arteni was carried out by the Franco-Armenian Mission "Caucasus", directed by B. Perello and funded by the Ministry for Europe and Foreign Affairs. We warmly thank colleagues from the Institute of Archaeology and Ethnography for extremely helpful assistance in Armenia. Captions:

  Figure 1: a) histogram of the diameter of cells forming the framework of aggregated cells, b) histogram of the surfaces of aggregated cells.

Figure 2 :

 2 Detailed plan of the west part of aggregated cell J31.

Figure 3 :

 3 DSM hillshade: upper part and contact with the rocky outcrop of aggregated cells J9.

  Figure 4: a) Topographic context of the installation of kites and aggregated cells: example of the basalt flow front in the northeast of Aragatsavan. b) Distance from aggregated cells to the nearest kite (box plot).

Figure 5 :

 5 Orientation of slopes with aggregated cells: distribution of the orientation of each pixel of the SRTM DEM included in the area of an aggregated cells.

Figure 6 :

 6 Topographic installation of kites: the example of kite AM7. a) oblique aerial photograph, b) interpretative approach.

  Figure7: a) Geographic distribution of the aggregated cells and kites of Armenia; b) difference in the densities of kites and aggregated cells: the density of both types of construction was calculated independently based on point features of both feature class (radius of research = 1,500 m), then subtracted from each other. In spite of the fact that kites are more numerous than aggregated cells, the discretization of the values using the Jenks algorithm spatially underlines the relative overrepresentation of one or the other construction.

Figure 8 :

 8 Figure 8: a) Presence and absence of aggregated cells in the distribution area of kites; examples of "wheel houses" (b and c), aggregated cells (d and e) and overlapping with kites (f and g) observed on high resolution satellite imagery in Harrat-al-Shaam. Figure 9: Examples of cells during excavation work filled with an accumulation of run-off sediments after being abandoned, with dry-stone lining reaching various depths, but which is often deep, a) cross section of AM14-cell1 in Armenia b) on the Ustyurt Plateau in Kazakhstan, c) in Harrat-al-Shaam in Jordan, Figure 10: Overlap of kite AM94 and the aggregated cells J2; a) DSM hillshade, b) Plan of the kite, plan of the aggregated cells and reconstruction proposal for the aggregated cells.Figure 11: a) Plan of the aggregated cells J28 and overlapping of kite AM78, b) DSM hillshade centred on the overlap. Annexes 1 to 7 (to be placed at the end of the article): Plan of the aggregated cells J9, J18, J31, J38, J54, J56 and J77 (

Figure 9 :

 9 Figure 8: a) Presence and absence of aggregated cells in the distribution area of kites; examples of "wheel houses" (b and c), aggregated cells (d and e) and overlapping with kites (f and g) observed on high resolution satellite imagery in Harrat-al-Shaam. Figure 9: Examples of cells during excavation work filled with an accumulation of run-off sediments after being abandoned, with dry-stone lining reaching various depths, but which is often deep, a) cross section of AM14-cell1 in Armenia b) on the Ustyurt Plateau in Kazakhstan, c) in Harrat-al-Shaam in Jordan, Figure 10: Overlap of kite AM94 and the aggregated cells J2; a) DSM hillshade, b) Plan of the kite, plan of the aggregated cells and reconstruction proposal for the aggregated cells.Figure 11: a) Plan of the aggregated cells J28 and overlapping of kite AM78, b) DSM hillshade centred on the overlap. Annexes 1 to 7 (to be placed at the end of the article): Plan of the aggregated cells J9, J18, J31, J38, J54, J56 and J77 (

  Figure 8: a) Presence and absence of aggregated cells in the distribution area of kites; examples of "wheel houses" (b and c), aggregated cells (d and e) and overlapping with kites (f and g) observed on high resolution satellite imagery in Harrat-al-Shaam. Figure 9: Examples of cells during excavation work filled with an accumulation of run-off sediments after being abandoned, with dry-stone lining reaching various depths, but which is often deep, a) cross section of AM14-cell1 in Armenia b) on the Ustyurt Plateau in Kazakhstan, c) in Harrat-al-Shaam in Jordan, Figure 10: Overlap of kite AM94 and the aggregated cells J2; a) DSM hillshade, b) Plan of the kite, plan of the aggregated cells and reconstruction proposal for the aggregated cells.Figure 11: a) Plan of the aggregated cells J28 and overlapping of kite AM78, b) DSM hillshade centred on the overlap. Annexes 1 to 7 (to be placed at the end of the article): Plan of the aggregated cells J9, J18, J31, J38, J54, J56 and J77 (


MD Benjamin Leroy Freschini

MD Eric Ouvrard

MD Elhocine Triki

MD, PhD Alessio Imperiale
email: a.imperiale@icans.eu

Prof Alessio Imperiale

Ovarian metastases of ileal neuroendocrine tumor

Keywords: ovary, ovarian metastasis, neuroendocrine tumour, carcinoid, 18 F-FDOPA PET

A 55-year-old menopausal woman with history of breast carcinoma was referred for recurrent abdominal pain, without diarrhea. Physical examination, routine biological investigation and serum CA15-3 were normal. Abdominal contrast-enhanced computed tomography (CT) found a 15-mm ileal hyper vascularized lesion with mild intestinal dilation and a mesenteric mass of about 20-mm. Both ovaries were moderately enlarged without radiological overt signs of malignancy. CT findings were consistent with ileal neuroendocrine tumor (ileal-NET) with mesenteric invasion. Serum value of chromogranin A was normal. 18 F-Fluorodihydroxyphenylalanine ( 18 F-FDOPA) PET/CT was added to the preoperative work-up 1 and distinctly identified the primary ileal-NET with the mesenteric involvement. Moreover, intense and pathological 18 F-FDOPA uptake was showed in both ovaries and 1 peritoneal nodule of few millimeters in the Douglas space (Fig 1A), suggesting ovarian metastases with peritoneal carcinomatosis. Surgical exploration found the primary tumor and the mesenteric lesion that were removed by a 20-cm ileal resection and mesenteric lymphadenectomy.

Intervention was completed by bilateral salpingo-oophorectomy, omentectomy, and multiple peritoneal biopsies (Fig 1B). Postoperative course was uneventful, and pathology confirmed a 20-mm well-differentiated grade-2 ileal-NET (Ki-67: 4%) with mesenteric invasion, ovarian bilateral spread, and pelvic peritoneal metastases as small as a few millimeters in size (pT4N2M1, UICC 2016).

The rate of neuroendocrine metastasis to the ovary seems significantly higher than previously assumed, and the small intestine is often the primary tumor site [START_REF] Limbach | Neuroendocrine metastases to the ovaries are significantly associated with small bowel neuroendocrine tumors and carcinomatosis[END_REF] . At the time of diagnosis of ileal-NET, only a low percentage of patients have ovarian metastases that are often associated with peritoneal carcinomatosis [START_REF] Limbach | Neuroendocrine metastases to the ovaries are significantly associated with small bowel neuroendocrine tumors and carcinomatosis[END_REF][START_REF] Angelousi | Neoplastic metastases to the endocrine glands[END_REF] .

Neuroendocrine ovarian lesions may not be detected by conventional investigations, and PET/CT imaging with 18 F-FDOPA or 68 Ga-DOTATOC should be considered in the diagnostic work-up of NET patients [START_REF] Ouvrard | Intra-individual comparison of 18 F-FDOPA and 68 Ga-DOTATOC PET/CT detection rate for metastatic assessment in patients with ileal neuroendocrine tumours[END_REF] . However, intraoperative examination of the ovaries remains recommended especially in patients with small bowel NETs and peritoneal carcinomatosis.

COI/Disclosure:Figure 1 .

 1 Figure 1. (A) Preoperative 18 F-FDOPA PET/CT investigation (anterior maximum intensity projection PET image) showing pathologic uptake in both primary ileal tumor and adjacent mesenteric lesion, bilateral ovarian metastases and peritoneal carcinomatosis in Douglas space. (B) Pelvic surgical exploration showing bilateral ovarian metastasis of ileal-NET.


A Guediche
email: amira.guediche@cea.fr

F Compoint

C Boscher

C Stelian

And H Piombini
email: herve.piombini@cea.fr

Indentation hardness and scratch tests for thin layers manufactured by sol-gel process

Keywords: nano-indentation, nano-indenter, thin film, PDMS, polymeric silica, elastic modulus, hardness, nano scratch test, self-healing

Indentation hardness and scratch tests are common techniques used in industries and laboratories to determine the mechanical properties of thin films. Here, we propose to determine a relative value of the elastic modulus and hardness of thin films composed of a mixture of polydimethylsiloxane and polymeric silica with elastic properties and selfhealing effects. For this study, a homemade nano-indenter and nano scratch tester has been designed with a microscope and a scanning stage allowing the carrying out of measurements on transparent materials having a weak elastic modulus and the possibility to identify a self-healing effect of these films.

Introduction

Indentation and scratch tests are used in laboratories and industries to determine the mechanical properties of thin films and adhesion. Generally, a diamond indenter with a specific geometry (spherical, pyramidal or conical) is used to impress its shape on the film surface by using a known load [START_REF] Oliver | Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology[END_REF][START_REF] Oliver | An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments[END_REF].

However, the measured hardness differs as a function of the indenter shape (Brinell, Vickers, Rockwell, Shore… hardness) and associated parameters (duration, load…). The typical problems encountered with the indentation in the field of thin films are linked to their weak thickness and more particularly, for the sol-gel films, to their high porosity. The aim is to study films with elastic properties that could absorb shocks induced by the power laser beam absorption. Indeed, these shockwaves can increase the size of previously produced laser damage [START_REF] Yu | Laser-Induced Damage Initiation and Growth of Optical Materials[END_REF]. The absorption processes due to laser beams by a thin film are numerous and complex. The aim of this paper is limited to having better knowledge of the mechanical properties of elastic layers to improve studies on laser-matter interaction with elastic layers. As such, the effects of the power laser beam absorption on the layers are not developed in this paper. This study is part of the LMJ (Laser MégaJoule) project. It is a key component of the simulation program of the Commissariat aux Energies Atomiques et aux énergies renouvelables. Its purpose is to study, on a very small scale, the behavior of materials under extreme conditions like those reached during the operation of nuclear weapons. The LMJ officially became operational in October 2014, with the weapon physics experiments. It was designed to achieve inertial confinement fusion. It will deliver in a few billionths of a second more than one million joules of light energy on a target measuring a few millimeters in diameter. The optical components of laser channels working in transmission are produced by a sol-gel process on which laser-damage appears from time to time. We hope that the introduction of an elastic layer will help reduce the amplitude of the mechanical waves generated by the weak absorption of the laser pulse and so decrease the risk of further laser damage (Fig. 1). Indeed, as the propagation of shock waves depends on the material elastic modulus E (the sound velocity Csound is equal to ⁄ with ρ the density), one way to control it is by developing layers with weak elastic modulus to cover the optical components made of fused silica (Csound ≈ 5 km.s -1 [START_REF] Sugiura | Dynamic response of fused quartz in the permanent densification region[END_REF][START_REF] Ayouch | Elasticity of an Assembly of Disordered Nanoparticles Interacting via Either van der Waals-Bonded or Covalent-Bonded Coating Layers[END_REF] in fused silica while Csound ≈ 1.7 km.s -1 in our solgel films [START_REF] Compoint | Sol-gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems[END_REF]).

The layers studied here can also have self-healing properties to heal the potential damage that could appear under laser flux [START_REF] Harreld | Self-healing organosiloxane materials containing reversible and energy-dispersive crosslinking domains[END_REF][START_REF] Harreld | Self-healing organosilixane materials containing reversible and energy-dispersive crosslinking domains[END_REF][START_REF] Colombani | Attempt toward 1D cross-linked thermoplastic Elastomers: Structure and Machanical porperties of a new sysem[END_REF][START_REF] Colombani | Selective synthesis of non-symmetrical bis-ureas and their self-assembly[END_REF] as shown in section 3.3. They are composed of cocondensation between polydimethylsiloxane (PDMS, formula HO[Si(CH3)2O]nH) [START_REF] Mackenzie | Rubbery Ormosils and their Applications[END_REF][START_REF] Mackenzie | Mechanical properties of ormosils[END_REF] and tetraethylorthosilicate [START_REF] Mackenzie | Rubbery Ormosils and their Applications[END_REF][START_REF] Huang | Ceramers: Hybrid Materials Incorporating Polymeric/Oligomeric Species with Inorganic Glasses by a Sol-Gel Process[END_REF][START_REF] Huang | Structure-Property Behavior of New Hybrid Materials Incorporating Oligomeric Species into Sol-Gel Glasses. 3. Effect of Acid Content, Tetraethoxysilane Content, and Molecular Weight of Poly(dimethylsiloxane)[END_REF][START_REF] Huang | Structure-Property Behaviour of Hybrid Materials Incorporating Tetraethoxysilane with Multifunctional Poly(tetramethylene oxide)[END_REF][START_REF] Mark | Polymer-modified silica glasses I. Control of sample hardness[END_REF]. The resulting nanocomposites demonstrate tunable elastic properties and a possible self-healing effect thanks to the incorporation of PDMS into the SiO2 network. To optimize these films, we have used various techniques to identify the optical characteristics [START_REF] Voarino | High-precision measurements of reflectance[END_REF][START_REF] Piombini | Apparatus designed for very accurate measurement of the optical reflection[END_REF][START_REF] Piombini | New device to measure the reflectivity on steeply curved surface[END_REF][START_REF] Piombini | Guided wave measurements for characterization of sol-gel layers[END_REF], measure their stress level [START_REF] Piombini | Stress measurement of elastic sol-gel layer by photoelasticimetry -comparison with Stoney[END_REF] and determine their elastic modulus [START_REF] Ayouch | Elasticity of an Assembly of Disordered Nanoparticles Interacting via Either van der Waals-Bonded or Covalent-Bonded Coating Layers[END_REF][START_REF] Compoint | Sol-gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems[END_REF][START_REF] Fall | Surface acoustic wave characterization of optical sol-gel thin layers[END_REF]. In this paper, we used a homemade nano-indenter built from a microscope equipped with an x*y motorized stage. It makes measurements on transparent elastic materials with weak elastic moduli that are deposited upon a substrate as thin film. The possible self-healing effect of our transparent materials is also checked. In the future, we wish to increase the laser damage threshold of our components by reducing mechanical shock waves thanks to a viscoelastic layer (Fig. 1).

Experimental setup and characterization

Experimental setup and calibration

Hardness measurements were carried out with a laboratory-built nanoindenter/scratch tester that can be modified based on experimental needs.

Nano scratch test measurements were performed with various associated parameters [START_REF] Heavens | Some factors influencing the adhesion of films produced by vacuum evaporation[END_REF][START_REF] Benjamin | Measurement of adhesion of thin films[END_REF][START_REF] Laugier | The development of the scratch test technique for the determination of the adhesion of coatings[END_REF]. The experimental setup is given in Fig. 2.

This laboratory-built indenter was designed with a Leica DMR microscope equipped with x&y scanning stages (Multicontrol 2000) with a range of 47.3*74.4 mm² and a 1 µm resolution, a V500 digital camera with a 640x480 pixel chip for imprint observation [START_REF] Avice | Quantitative estimation of crazing in sol-gel layers by automated optical microscopy analysis[END_REF], a conical diamond indenter (Fig. 3), a microscope with objectives ranging from X5 to X100, operable in brightfield (BF), darkfield (DF) and differential interference contrast (DIC). This equipment was computer-driven by a LabVIEW program that controlled microscope focusing. Z-axis resolution was 50 nm. The setting and acquisition of camera settings used (gamma, gain, shutter…), the scanning stage movements (acceleration, speed, courses along x and y) and the necessary corrections of slope and concentricity defects caused by objectives used were monitored by the computer. The sample illumination was defined by the integration of the luminous flux reflected by a reference sample (polished silica substrate). To ensure the measurement reproducibility, this light intensity adjustment was better by 1 % compared to our reference intensity.

The indenter and its holder were fixed on a rail (Fig. 2) positioned above a scanning stage that held the tested sample. The conical diamond indenter had a 61.3° angle and seemed satisfactory when observed through an optical microscope (Fig. 3).

Scanning Electron Microscope (SEM) photography showed that the indenter is more spherical than conical (Fig. 4) for our application, with a tip radius estimated at 20 µm. In section 2.3 further details will be developed about the indenter shape to consider.

Motorized stages enabled the adjustment of the indenter location along the y-axis. The z-axis was fitted with the microscope to see the mark left by the indenter in the camera field. Correction of the slope coming from either the parallelism defects of the substrate or the stage displacement can be done thanks to the previous acquisition of some images' heights located at three extreme spots of the measurement surface (nevertheless the samples, being optically polished, should be flat). This correction was done during the indenter displacement by adjusting the z-position. The z-position at which focalization was satisfactory was determined using a reference image on which the focalization had been correctly adjusted. Before each measurement, an initial set of images corresponding to future locations of either the imprints or the scratches were displayed and stored to consider possible local defects of the analyzed layer. After indentation tests, images showing the change of either the indentation matrix or the scratch state were recorded to follow their evolution and determine the appropriate self-repairing kinetic. Microscope focus was adjusted with the vertical displacement of its stage, enabling control over the load applied on the sample. The indentation or scratch force was calibrated thanks to an accurate weighing scale (accuracy = 0.1 mg). This calibration method only gives a relative value of the load. Indeed, the scale can be modeled as a spring and the indentation or scratch force, when applied on the surface of the scale, gives a result of the load applied relative to the stiffness of the scale and of the layer. This explains why a β coefficient is used for the F load applied. The indenter was attached to the motorized translation stage with a 0.1 µm resolution. Indenter placement was adjusted to be in contact with the weighing scale tray. The weight was then recorded according to displacement. The curve is given in Fig. 5 with a slope of 0.324 mN.µm -1 . As the microscope sensitivity along the z-axis was equal to z = 50 nm for its displacement, the load sensitivity was equal to 1.65 mg, so approximatively 16 µN. For more details on illustrations and calibration of the system, please refer to reference [START_REF] Compoint | Sol-gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems[END_REF]. Moreover, according to the indentation images taken, it has been possible to determine the aspect of a satisfactory indentation.

Evaluation of contact stiffness

In the context of a typical indentation, indenter resistance to elastic and plastic deformation is much greater than that of the surface layer. A schematic diagram of the indenter is shown in Fig. 9.

The indenter can be described as a column with an extremity composed of a linear-elastic element with a given spring stiffness. The stiffness of the k indentation system after contact with the surface layer is related to the spring and contact stiffness (the elements are in series):

1 k = 1 k s + 1 k t (1)
The stiffness ks of the spring is given by:

k s = E s . A s L s (2)
With Es the elastic modulus of the indenter column, AS the cross-sectional surface and Ls the length of the column (Ls = b -a). This latter is made of steel, so Es = 200 GPa [START_REF] Oyen | Handbook of Nanoindentation: With Biological Applications[END_REF], and knowing the column to be a 5 mm circular rod of diameter 1.07 mm we find ks ≈ 36.10 6 N.m -1 .

The contact stiffness kt is given by [START_REF] Oyen | Handbook of Nanoindentation: With Biological Applications[END_REF] (for a circular contact): kt = 2.r.M, where M is the indentation modulus of tip-surface. It considers deformation in both the tip and the surface during contact and is equal to:

1 M = 1 M tip + 1 M Surface layer (3)
With Mtip the indentation modulus of the tip and MSurface layer the indentation modulus of the layer. Supposing the material to be elastically isotropic, we obtain the following relation:

M Surface layer = E sl 1-ν sl 2 (4)
Here, the layer considered is a hybrid silica-PDMS with an E sl elastic modulus and νsl Poisson's ratio. As Esl = 50 GPa (if we take the higher valueobtained with 10 wt. % of PDMS [START_REF] Fall | Surface acoustic wave characterization of optical sol-gel thin layers[END_REF]) and = 0.5, it gives MSurface layer ≈ 67 GPa. Moreover, for a typical diamond indenter used in nano-indentation [START_REF] Oyen | Handbook of Nanoindentation: With Biological Applications[END_REF],

Mtip = 1,150 GPa. Thus, the indentation modulus is M ≈ 63 GPa. Then, the contact stiffness, for a nano-indentation contact radius of r = 20 µm is kt ≈ 2.5

MN.m -1 . The contact stiffness is less than the spring stiffness kt < ks, so most of the indenter displacement is taken up by the contact and we have negligible deformation of the spring (a << b). Additionally, the value of the surface indentation modulus is less than the indenter modulus: MSurface layer < MTip.

This explains why it is reasonable to neglect the indenter column stiffness.

However, it is planned to properly determinate its value in further experiments.

Determination of the contact area

The experimental scratch test is given in Fig. 10. It makes scratches, i.e.

lateral displacement of the tip with a controlled depth on the layer surface in order to penetrate the thin film and inflict damage on the scale of its thickness.

The scratches have a maximum target depth of half the film thickness.

Each image (Fig. ImageJ software [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF] to measure the contact surface Aimprint, also called projected area or surface. A portion of the image presenting the indentation was selected. Then, an analysis of particles was applied to the selected portion of the image. The indentation surface was given by the main surface defect.

The pixel sizes of the camera were standardized with a calibrated target for each microscope objective. In this way, the hardness H (H = F/Aimprint) was determined with the known β.F load applied. The visualized indent surfaces (a few square microns cf. Fig. 11) are nearer to a spherical indenter imprint than the one made by conical indenter. One way to determine which shape of the indenter was leading is to calculate the himprint indentation contact depth from the projected area. The relationship between projected surface AImprint and penetration or indentation contact depth hImprint for a spherical indenter is given by: AImprint = -π.himprint 2 + 2π.R.himprint (5.1)

and for a conical indenter:

AImprint = π.himprint 2 .tg 2 θ (5.2)
For a layer of 1.4 mm thickness with Aimprint = 4.5 µm 2 , θ = 30.65° and R = 20 µm, from the Eq. 5.1 and Eq. 5.2 one obtains hImprint = 36 nm for a spherical indenter and hImprint = 2 µm for a conical indenter. Yet, 2 µm is greater than the layer thickness, which is not possible in this case because the tip displacement was 800 nm at most. Thus, the himprint obtained for a conical indenter is incompatible with the layer thickness and with the h tip displacement, which confirms the SEM photography analyze (Fig. 4). For the scratches, the relationship becomes:

Spherical indenter A Imprint =2 .L. R 2 -2.h.R+ℎ ( 6
)
where L is the length of the scratch measured experimentally on photograph taken with the microscope.

Another way to verify the accuracy of assimilating the indenter shape to a spherical shape is to calculate the himprint/R ratio, where himprint is 0.2 µm for its highest value (determined from the highest measure of AImprint and from the Eq. 5.1). One should find ≤ 1 -"#$ & [START_REF] Chen | Influence of indenter tip roundness on hardness behavior in nanoindentation[END_REF], with & half the angle of the indenter equal to 30.65°. This gives himprint/R = 1.10 -2 . The inequality is verified. Thus, the determination of the hardness, in particular the projected area AImprint was done by considering the indenter with a spherical shape.

Manufactured sample and results

Sol-gel layer used

The sol-gel layers were deposited by spin-coating technique with a hybrid silica-PDMS solution on a 50 mm diameter and 5 mm thickness silica polished substrate. The material synthesis is made from tetraethylorthosilicate and a PDMS reagent that leads to a silica-PDMS ormosil formulation via a sol-gel reaction [START_REF] Compoint | Sol-gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems[END_REF]. The substrate is then coated with the ormosil solution.

The spin coating technique [START_REF] Birnie | Spin coating technique, Sol-gel Technologies for glasses producers and users[END_REF] consists of putting a few drops of the sol-gel solution on a substrate while it is rotating at high speed. The rotation caused the solution to spread approximatively uniformly on the substrate and the thickness was controlled with the solution viscosity and the rotation speed.

The spinning speeds used to make our layers were between 1,500 and 4,000 rpm and were maintained for 20 seconds, with an acceleration rate of 1,000 rpm.s -1 . The substrates were coated at room temperature. An appropriate heat treatment was carried out at 120°C during 1.5 hours with pre-heating steps (Fig. 12) to avoid the apparition of thermal stress inducing cracks in the coating.

This thermal treatment eliminated solvents and undesirable products obtained from the chemical reaction and still there. Moreover, it also activated the chemical bounds between the surface silanol groups (Si-OH) of the substrate and the sol-gel species of the layer to increase layer hardness. The main parametric studied concerned the variation in mass (expressed in wt. %) of PDMS (from 10 to 40 wt. %) in the polymeric silica, the pattern number n of the PDMS chain The film thickness was measured thanks to a spectrophotometer Perkin-Elmer after thermal treatment [START_REF] Avice | Controlling the Nanocontact Nature and the Mechanical Properties of a Silica Nanoparticle Assembly[END_REF][START_REF] Mouchart | Détermination des Constantes Optiques n et k de Matériaux Faiblement Absorbants[END_REF]. Two types of PDMS were used, one with a viscosity of 0.25 St and a molar mass estimated around 550 g.mol -1 according to the supplier Sigma-Aldrich, the other between 18 and 22 St and a molar mass measured around 14,234 g.mol -1 . The difference in viscosity is related to the difference in the length of the PDMS chain (n) that we measured by using an exclusion chromatography (see Table 1) [START_REF] Pietrzyk | Separations: Introduction to Chromatography[END_REF].

                - -

Determination of the hardness and elastic modulus

The curves of loading versus contact depth given in Fig. 13 show the differences in hardness of hybrid silica-PDMS layers. For a same value of load, the himprint contact depth is higher for the formulations with a lesser PDMS ratio. For example, in the case of the PDMS with a molar mass of 550 g.mol -1 and a viscosity of 0.25 St, the layer silica-PDMS at 40 wt. %, for a same value of load, has a lesser residual penetration of the tip than the one with 30 wt. % PDMS and this latter has also a lesser residual penetration than the one with 40 wt. % PDMS. Experimentally, we only have access to the value of the plastic deformation, and thus the residual tip penetration as we determined himprint from the image of the contact surface Aimprint. For small values of load (less than 35 µN), the behavior of the hybrid at 10 wt. % and 30 wt. % PDMS is similar. So, having a penetration depth lower when the ratio of PDMS increases in the hybrid silica-PDMS, for a given value of load (higher than 35 µN) is explained by the difference in elasticity of the hybrids caused by the introduction of the PDMS in the rigid polymeric silica matrix [START_REF] Sugiura | Dynamic response of fused quartz in the permanent densification region[END_REF][START_REF] Ayouch | Elasticity of an Assembly of Disordered Nanoparticles Interacting via Either van der Waals-Bonded or Covalent-Bonded Coating Layers[END_REF]. Indeed, for a higher value of the PDMS ratio, the material is less rigid, as the PDMS is an elastomer. Thus, the elastic response of the hybrid increases with the PDMS ratio, explaining why the residual penetration depth measured is lower with 40 wt. % PDMS. So, when the tip lowers, once positioned at the contact surface, the elasticity of the layer allows the tip to vertically displace from a certain distance before penetrating the layer and thus, damaging it. It is the surface displacement around the contact surface due to the elastic response of the layer. As we only have access to the residual penetration depth, the more himprint value is high, the more the layer is rigid for a given tip displacement. Moreover, the influence of the viscosity is also visible on the Fig. 13. The layers with PDMS at 22 St in viscosity show a deeper penetration of the tip for a given load compared to the other layers made with the PDMS at 0.25 St. As expected, viscosity and elastic properties are two important parameters that influence the hardness of layers.

The relative hardness measurements of the various ormosil layers are given in Fig. 14. The trend of the hardness is to increase with the length of the PDMS chain (the more the chain is long, the more the viscosity is high) and with TFS catalysis. Plus, the hardness decreases when the PDMS ratio increases, as seen above. However, when it comes to nano-indentation, a question remains: how to be sure that what is measured is not the hardness of the substrate? Usually, the Bückle rule provides a reasonable starting point [START_REF] Westbrook | The science of hardness testing and its applications[END_REF]: the indentation depth should not exceed 10% of the layer thickness if you want to measure the hardness of the layer without any substrate effect.

Otherwise, the plastic response associated with the indentation will be contained entirely within the film and the elastic response of the substrate will be negligible. In cases where the film is not too thin and the indenter not too blunt the assumption gives reasonable results. However, experimental and numerical studies on coated materials have shown the inadequacy of this rule [START_REF] Kouitat-Njiwa | Boundary element numerical analysis of elastic indentation of a sphere into a bi-layer material[END_REF]36]. According to these works, although there is no elastic deformation (on the part of the substrate), the response of the film-substrate system corresponds to the film response only for indentation depths less than 1% of the thickness. In addition, for an indentation depth beyond 2% of the film thickness, the elastic response of the coated substrate differs from the film and may account from 10% to 90% in the values measured for the deposited layer. This explains why in the experiments of this article, the tip has not been pushed more than 1% of the layer thickness (Fig. 14. a). Even though the tip penetrated the film of less than 1%, the effects of the substrate are visible on some hardness vs penetration depth curves (Fig. 14. a). Indeed, on such curves, the hardness has three areas of variation with depth of indentation: growth (at low loads), plateau and decay for large deformations [START_REF] Fischer-Cripps | Critical review of analysis and interpretation of nanoindentation data[END_REF] as shown in Fig. 13. b. The curves derived from our experiments (Fig. 14. a) follow the ones of the literature (Fig. 14. b). The value of the hardness on the plateau is attributed to the film [START_REF] Fischer-Cripps | Critical review of analysis and interpretation of nanoindentation data[END_REF]. Indeed, once we have a fully developed plastic zone, the hardness of the film should reach a constant or a plateau. At larger loads, or greater depths, the influence of the substrate will not be negligible and the hardness may increase or decrease according to the relative hardness of the film and substrate. As we used a tip that was not sharp enough, it is normal to see the influence of the substrate surface even at very small depth penetrations [START_REF] Fischer-Cripps | Critical review of analysis and interpretation of nanoindentation data[END_REF]. Indeed, if the indenter is too blunt, then most of the deformation may be elastic and the mean contact pressure so measured will not reflect perfectly the film hardness.

Knowing the displacement of the tip during the loading and the depth of penetration h after the unloading for the point matrix, we can determine the elastic modulus Et of the layer by using the relationship given by Sneddon [START_REF] Sneddon | The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile[END_REF] and the reduced modulus Ersl [START_REF] Maciejak | Mesure de dureté par nano-indentation[END_REF][START_REF] Hay | Instrumented indentation testing[END_REF]:

E ()* = 1 γ √π 2 S A(h) with 1 E ()* = 61 -υ )* 8 E )* + (1 -υ : ) E :
where: S is the contact stiffness, S = dF/dh, νsl and νt are the Poisson's ratio of the layer and the tip respectively, Et is the elastic modulus of the tip, γ is a geometrical constant of the order of unity. The contact stiffness has been calculated by determining the hs surface displacement around the contact surface due to the elastic response of the layer. It is given by: h = hs + himprint, where h is the tip displacement. The F load, even given relatively to a β coefficient (taken equal to 1 here), permits to find values of the elastic modulus very close to results coming from the commercial nano-indenter of the Anton Paar Company (Fig. 15. a). Differences appear between the results from the homemade nano indenter and those from the commercial indenter as the results from the homemade nano indenter are only relatives. However, the trend remains: the value of the elastic modulus is higher with a higher wt. % PDMS. Furthermore, the relative elastic modulus increases with TFS catalysis. It decreases with the PDMS ratio (Fig. 15. a). Thus, we find again the trends obtained by Mackenzie [START_REF] Mackenzie | Rubbery Ormosils and their Applications[END_REF] about the PDMS mass bulk (Fig. 15.

b).

Scratches: mechanism of self-healing

In Fig. 16, an evolution over time of the scratches for some layers has been observed. For example, when the PDMS (550 g.mol -1 ) ratio reached 40 wt. % with HCl catalysis, a self-healing effect of the thin film is shown. Indeed, when observed with a magnification microscope of X50, the scratches The Burgers model fit follows the experimental data. So, the scratches, observed in the Fig. 16 decreased over time thanks to the viscoelastic effects of the thin film.

Conclusion

We modified our microscope to allow the evaluation of mechanical properties in relative terms of our hybrid layers such as the determination of hardness from the imprint surface and elastic modulus thanks to the indentation matrix.

The pre-focalization made before the indentation permitted to correct the bad flatness of our silicon substrates. We were able to rank our materials in hardness from the imprint surface. The scratch tests highlighted that some of our layers had self-healing properties. Two different decay times have been identified and we found that the self-healing was linked to the layer viscosity.

Our layers show viscoelastic properties over a long time which indicates that our measurements are correct because the time put to made measurement is short when compared to the characteristic times found.

We are going to improve our device with an increasing magnification of our microscope to get a larger imprint surface recorded. We will also change our tip; this one will be fixed on a stage carrying out nano-displacements.

Moreover, the spring stiffness of the indenter system will be precisely determined. The addition of a nano-force sensor on the microscope will permit a better determination of the values of the mechanical properties of our hybrid layers, instead of having only a trend.

Another study will also be made to determine the viscosity of the solution silica-PDMS once deposited onto its layer form. Indeed, the viscosity of a liquid is not the same as the viscosity of a layer. Thus, the Burgers model will be more accurate.

Finally, the optimized layer with the smallest value of hardness is the hybrid silica-PDMS with 40 wt. % PDMS.

Microscope

Indenter holder Tip with its holder X&Y motorized stages

Fig. 6 and

 6 Fig.[START_REF] Compoint | Sol-gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems[END_REF] and Fig.7respectively describe our device operating mode for the

Fig. 8

 8 Fig. 8 is an example of two intercrossed indentation matrices with a step of 0.25 mm and a vertical motion of ∆Z = 200 or 800 nm between each line.

  11. a) of the imprint taken either in brightfield, darkfield or in differential interference contrast (DIC) was treated (Fig. 11. b) with the

  used during the synthesis: either hydrochloric acid (HCl) or triflic acid (trifluoromethanesulfonic TFS).

  decreased over time. When the PDMS ratio reached 30 wt. % with HCl catalysis, no evolution of the scratches over time is observed. Scratches at 200 nm and 500 nm depth fade clearly over time at room temperature, showing a self-repair mechanism of the layer since a large part of the damage is erased in a few hours. Having healing properties with only the 40 wt. % layer (in the case of PDMS 550 g.mol -1 ) shows that the mechanism governing the repair is largely related to viscoelastic phenomena characterized by stress relaxation leading to damage recovery.The kinetics of the surface evolution (Fig.17

  ) can be adjusted by two exponential functions that indicate two mechanisms of healing: one short-term ( τ1 is the decay time) and the other long-term (τ2 is the decay time).Our indentation measurements being made in a few minutes, the recorded surfaces stay close to indented surfaces.The evolution has been studied from a mechanical point of view leading to a Burgers model.The time-dependent viscoelastic response of the silica-PDMS film can be described by the Burgers model[START_REF] Lemaitre | Mécanique des matériaux solides[END_REF][START_REF]Mechanics of Anisotropic Materials[END_REF] (Fig.18) which corresponds to an association of the Voigt-Kelvin model with the Maxwell model by adding up the deformations of the two models and by taking the same strain for the two models.

Acknowledgments

The authors would like to thank Mr. A. Benedetto of Saint-Gobain Research Paris for his relevant comments.