T Skopak

F Calzavara

Y Ledemi

F Célarié

M Allix

E Véron

M Dussauze

T Cardinal

E Fargin

Y Messaddeq

Properties, structure and crystallization study of germano-gallate glasses in the Ga 2 O 3 -GeO 2 -BaO-K 2 O system

Mid-infrared transparent germano-gallate glasses (with gallium oxide as main component) have been studied following the composition law (100-x) ]-xKO1/2 (with x = 0, 5, 10, 13, 17 mol%). All prepared glasses are transparent from approximately 280 nm up to 5.5 μm, with a measured linear refractive index and density decreasing respectively from 1.72 to 1.67 (at 1538 nm) and 4.79 to 4.34 g/cm 3 with increasing potassium oxide content. As expected, the increase of potassium oxide content also results in a decrease of the glass transition temperature (698 to 671 °C) and the viscosity in the softening regime whereas the thermal expansion coefficient increases (4.8 to 10.3 × 10 -6 K -1 ). These results are related to the depolymerization of the 3D interconnected glass network which has been studied by Raman spectroscopy. Large thermal stability criteria (difference between onset of crystallization and glass transition temperatures) ranging from 182 to 199 °C have been measured by DSC for the compositions containing potassium oxide, suggesting strong potential for fiber drawing from glass preforms. The 40.1GaO3/2-26.7GeO2-16.2BaO-17KO1/2 glass composition (in cation mol.%, which corresponds to 28Ga2O3-37GeO2-23BaO-12K2O in mol.%) was then selected for further investigation. Its mechanical properties (Young and shear moduli, Poisson's ratio, hardness) were measured, showing values close to those reported for well-known barium gallo-germanate (BGG) glasses. A thorough crystallization study was then carried out using DSC (Marotta's method), X-Ray diffraction and electron microscopies (TEM and SEM) to better understand the unexpected surface crystallization issues observed during the glass preform fiber drawing process. The potential of using such germano-gallate glasses to produce mid-infrared optical fiber of high mechanical strength is discussed.

Introduction

The development of optical materials transmitting in the mid-infrared region up to 5 μm is of first interest for many applications in defense and security, health and environment, for instance [START_REF] Tao | Infrared fibers[END_REF]. Most of the pollutant molecules' fingerprint are indeed located in this spectral region [START_REF] Schliesser | Mid-infrared frequency combs[END_REF], whereas it also includes the second band of the atmospheric transmission window (3-5 μm). Among them, vitreous materials like chalcogenide, fluoride or tellurite glasses are widely studied for their infrared transmission and also their relatively low-cost manufacturing, ease of shaping, optics molding or fiber drawing, by opposition to crystalline materials (e.g. Ge single-crystal, sapphire, etc.). However, chalcogenide, fluoride and tellurite glass-based optics and fibers, despite their unique infrared optical properties, possess relatively poor chemical, thermal and/or mechanical resistance as well as long-term chemical durability that strongly limit their utilization in a large number of practical applications. Remarkably, germanate glasses, whose main constituent is the glass-former germanium dioxide GeO2, are recognized for their superior mechanical, chemical and thermal resistance that has permitted their implementation in specific applications where materials robustness is critical. One can cite for instance the BaO-Ga2O3-GeO2 (so-called BGG) glass windows developed by the US Naval Research Laboratory for defense applications [ [START_REF] Bayya | BaO-Ga2O3-GeO2 glasses with enhanced properties[END_REF], [START_REF] Bayya | Infrared transparent germa-nate glass-ceramics[END_REF], [START_REF] Bayya | VIS-IR transmitting windows[END_REF], [START_REF] Bayya | Germanate glass as a window for high energy laser systems[END_REF], [START_REF] Bayya | Optical Transmission of BGG Glass Material[END_REF]]. The other well-known GeO2-based glass system is the lead-germanium oxide GeO2-PbO whose optical fibers transmitting up to 3 μm are commercially available for dentistry or laser surgery applications [START_REF] Jha | Rare-earth ion doped TeO2 and GeO2 glasses as laser materials[END_REF][START_REF] Wang | Fabrication and optical properties of lead-germanate glasses and a new class of optical fibers doped with Tm3+[END_REF]. Gallate glasses, whose infrared transparency is expected to be close to that of germanate glasses because of the close phonon energy of Ga O and Ge O bonds (~500 cm -1 ), may offer an interesting alternative to the above cited systems in terms of higher rareearth ions solubility and polarizability, for example. Gallium oxide is an intermediate oxide acting similarly to alumina in silicate glasses. It can either be a network modifier in silicate [START_REF] Shelby | Alkali and alkaline-earth galliosilicate glasses[END_REF] or germanate [START_REF] Jewell | Alkaline-earth gallogermanate glasses[END_REF][START_REF] Szu | Structure of properties of lanthanum galliogermanate glasses[END_REF] glasses or a network former or co-former in gallate, germano-gallate or gallo-phosphate glasses for instance [ [START_REF] Lapp | Gallium oxide glasses[END_REF], [START_REF] Skopak | Structure and properties of gallium-rich sodium germano-gallate glasses[END_REF], [START_REF] Hee | Properties and structural investigation of gallophosphate glasses by Ga-71 and P-31 nuclear magnetic resonance and vibrational spectro-scopies[END_REF]]. Relatively few studies have been reported on glasses having gallium oxide as principal glass component [12,13,[15], [START_REF] Murthy | Properties and structure of glasses in system M2O-Ga2O3-GeO2 (M = Li, Na, K)[END_REF], [START_REF] Baynton | Gallium oxide glasses[END_REF], [START_REF] Whichard | Glass-formation and properties in the gallia-calcia system[END_REF], [START_REF] Fukumi | Structure of alkali or alkaline-earth metal gallate glasses[END_REF], [START_REF] Balewick | Properties of calcium, strontium, and barium galliosi-licate glasses[END_REF], [START_REF] Hwa | Optical and physical properties of lanthanum gal-logermanate glasses[END_REF]], even though they may show good optical, mechanical and thermal properties for potential application from the visible to the mid-infrared (mid-IR) range. For better readability, a particular glass denomination formalism should be proposed to distinguish properly gallate glasses from gallate-based glasses. On one hand, gallate glass should stand only for glass compositions containing gallium oxide as single network former. On the other hand, when two network co-formers are involved, like in germano-gallate or gallio-silicate glasses for example, both network formers should be mentioned with the second term corresponding to the major glass constituent. To the best of our knowledge, there is no report in the literature of successful fabrication glass optical fiber from gallate glasses or any other glasses with gallium oxide as main constituent (like germano-gallate), despite the large thermal stability against crystallization that may be observed for some compositions. Gallio-silicate glass-ceramics fibers and lead-bismuth-gallium oxide glass photonic crystal fibers have been reported by Pinckney et al. [START_REF] Pinckney | Transparent gallate spinel glass-ceramics[END_REF] and by Buczynski et al. [START_REF] Buczynski | Two octaves super-continuum generation in Lead-bismuth glass based photonic crystal fiber[END_REF], respectively. But in neither case gallium oxide is the glass main component. In our previous works, GaO3/2-GeO2-NaO1/2 germano-gallate glasses have been investigated [START_REF] Skopak | Mixture experimental design applied to gallium-rich GaO3/2-GeO2-NaO1/2 glasses[END_REF][START_REF] Skopak | Structure and properties of gallium-rich sodium germano-gallate glasses[END_REF]. A thermal stability against crystallization criterion (difference between onset of crystallization and glass transition temperatures) well-above 120 °C was measured for several glass compositions, suggesting a strong potential for glass thermal shaping, including fiber drawing. However, unwanted crystallization was observed during glass thermal processing, probably related to the mobility of sodium cations at high temperature. In this work, sodium oxide has been replaced by potassium and barium oxides. Germano-gallate glasses (100-x)[48.3GaO3/2-32.2GeO2-19.5BaO]-xKO1/2 with x = 0, 5, 10, 13, 17 mol% have been studied in order to evaluate their potential for further bulk and/or fiber applications from the visible to mid-IR range. Their thermal stability, transmission window, refractive index, viscosity, linear thermal expansion coefficient, and glass structure by Raman spectroscopy are investigated. Finally, a thorough crystallization study relying on thermal analysis and electron microscopies is carried out on the most promising germano-gallate glass composition for future fiber drawing potential testing.

Experimental details

Glass synthesis

The glass samples were prepared by traditional melt and quenching technique according to the composition law (100-x)[48.3GaO3/2-32.2GeO2-19.5BaO]-xKO1/2 with x = 0, 5, 10, 13, 17 mol%. The starting materials used were gallium oxide Ga2O3 (Strem Chemical, 99.99%), germanium oxide GeO2 (Strem Chemical, 99.999%), barium carbonate BaCO3 (ACS Merck, 99%) and potassium carbonate K2CO3 (Sigma Aldrich, 99%). After weighing, the powders were intimately mixed and placed in a platinum crucible for a pre-sintering treatment at 1200 °C for 1 h30 and then melted under ambient atmosphere at 1300-1400 °C for 30 min. The melted mixtures (up to 30 g) were then quenched in the ambient air before being ground. Small glass pieces were taken from each composition prepared to carry out DSC analysis to determine their corresponding glass transition temperature Tg. Then the remaining glass powders were melted a second time in order to increase their homogeneity. The resulting glasses were finally annealed at Tg -40 °C for 4 h and slowly cooled down to room temperature. All the resulting glasses were colorless, transparent and bubble free. Samples of different sizes and shapes, including glass rods of 10 mm diameter and 40 mm length, were produced. Glass slices of thickness ranging from 1 to 8 mm were then cut and polished on both parallel faces for further characterizations.

Thermal, physical and structural characterizations

The nominal stoichiometry was verified by quantitative microanalysis (Wavelength Dispersive Spectroscopy (WDS)) with an Electron Microprobe Cameca SX 100, with a deviation of ±2 mol%. The amorphous state of the samples was verified by Powder X-ray diffraction (XRD) patterns which were collected on a PANalitycal X'pert PRO MPD diffractometer used in a Bragg-Brentano θ-θ geometry and equipped with a secondary monochromator and X'Celerator multi-strip detector. Each measurement was performed within an angular range of 2θ = 8-80°. The Cu-Kα radiation was generated at 45 kV and 40 mA (λ = 1.5406 Å). XRD was also used to identify the crystalline phases formed during the crystallization study. The density, ρ, was obtained from the average of two measurements per sample by Archimedes' method by immerging a glass chunk in diethyl phthalate at room temperature on a Precisa XT 220A weighing scale with an estimated error of 0.005 g/cm 3 . Thermal properties which include the glass transition temperature (Tg), the onset of crystallization (Tx) and the maximum of crystallization (Tc) were measured on a Netzsch DSC Pegasus 404 F3 apparatus with glass chunks in a Pt pan at a heating rate of 10 °C/min with a precision of ±2 °C. The thermal stability (ΔT = Tx -Tg) was also calculated. The crystallization was also investigated more specifically on a selected glass composition by using the DSC method from Marotta [START_REF] Marotta | Nucleation in glass and differential thermal analysis[END_REF]. More details about the used method are given in Section 3.4.2. The linear thermal expansion coefficient (TEC) was determined by thermal mechanical analysis (TMA) on a Netzsch TMA 402 F1 between 25 and 750 °C with a heating rate of 5 °C/min. Silica spacers were used on cylindrical samples of 5 to 8 mm height with a 5 mm diameter. The linear TEC was determined for each composition from the slope of the TMA signal between 30 and 300 °C. The dilatometric glass transition temperature (Tgd) and the dilatometric softening point (Td) were determined as well. The viscosity in the interval of 10 10 to 10 7 Poise was recorded on a Theta US parallel plate viscometer, on 10 mm diameter and 6 to 8 mm height cylindrical samples placed between two silica spacers. The samples, under a 300 g charge, were heated up to 650 °C with a heating rate of 4 °C/min and then up to 795 °C with a heating rate of 2 °C/min. The potential fiber drawing temperature was estimated for a viscosity of 10 7 Poise by a simple linear extrapolation of the viscosity curve with an approximated error of ±5 °C. In this approach, we assumed a linear behavior of the viscosity-temperature curve in this regime of viscosity, which was found to be an acceptable approximation in anterior works by Galstyan et al. [START_REF] Galstyan | Role of io-dine in the solubility of Tm3+ ions in As2S3 glasses[END_REF]. Nonetheless, it is worth noting that the Vogel-Fulcher-Tammann and Avramov-Milchev equations are generally employed to account for the viscosity evolution of glassy materials as a function of temperature [START_REF] Avramov | Effect of disorder on diffusion and viscosity in condensed systems[END_REF][START_REF] Mauro | Viscosity of glass-forming liquids[END_REF]. The refractive index was measured by prism coupling on a M-line 2010/M Metricon apparatus at 532, 633, 972, 1308 and 1538 nm with an estimated error of ±0.005. The transmission spectra in the UV-Visible-NIR and the IR ranges were respectively obtained from Agilent Cary 5000 (UV-Visible-NIR) and Bruker Equinox 55 (FTIR) spectrometers. The short wavelength cut-off (λUV) and the multiphonon cut-off (λIR) were determined from the recorded spectra using the Beer-Lambert law for an absorption coefficient of 10 cm -1 . Regarding the mechanical properties, the Young's modulus (E), shear modulus (G) and Poisson's ratio (νpoisson) were estimated from the average of 4 measurements by ultrasound echography with a JSR Ultrasonics DPR300 pulser/receiver on two cylindrical samples of 1.1 cm height and 1 cm diameter at room temperature using 10 MHz piezoelectric transducers. The elastic modulus are given by the formula (in agreement with the ASTM E494 -15 procedure):

where Vl and Vt are the longitudinal and transversal wave speeds. The Meyer's hardness (HM) measurements were obtained from 10 indentations at 250 mN and 10 indentations at 1 N with an Instrumented Vickers diamond indenter setup (Fischerscope H100C) on the samples used for the ultrasound echography. These measurements were carried out with a 20 s increase in charge followed by a hold at maximum force (250 mN and 1 N) for 5 s before releasing the charge. Note that these mechanical characterizations were carried out only on the glass composition selected as the best candidate for future glass fiber drawing potential. The Raman spectra were obtained using a Horiba Jobin-Yvon XploRA Raman spectrometer with a spectral resolution of 2 cm -1 , equipped with a 532 nm laser and a confocal microscope objective (x 50). The obtained spectra were normalized at their main peak intensity around 500 cm -1 . Samples for transmission electron microscopy (TEM) were prepared from powder dispersed in absolute ethanol, and deposited onto a holey carbon film supported by a copper grid. Bright field images were carried out with a TEM (Philips CM20) operating at 200 kV and equipped with an Oxford energy dispersive spectrometry (EDS) analyzer. Scanning electron microscopy (SEM) was carried out with a Philips ESEM XL40 apparatus equipped with an Oxford EDX detector for elementary analysis. Samples were observed and analyzed by SEM under high vacuum. To prevent the accumulation of electrostatic charge, an ultrathin coating of carbon was deposited on the glass sample surface.

Results and discussion

Physical-chemical properties of the GGBKx glasses

The different nominal compositions (100-x)[48.3GaO3/2-32.2GeO2-19.5BaO]-xKO1/2 with x = 0, 5, 10, 13 and 17 mol%, labelled GGBKx, are reported in Table 1 along with the experimental glass compositions obtained by WDS quantitative analysis. The experimental (K + 2Ba)/Ga molar ratio, corresponding to the (KO1/2 + 2•BaO)/GaO3/2 M ratio, represents the ratio between the amount of alkali ions charges and the amount of gallium and is reported for each composition in Table 1. The nominal stoichiometry of the mixtures appears to be maintained during glass synthesis and the (K + 2Ba)/Ga ratio increases from 0.81 (for the GGBK0 glass) up to 1.23 (for the GGBK17 glass).

Regarding the thermal properties, the onset of glass transition temperature Tg and the onset of crystallization temperature Tx were determined from the DSC trace from the tangents crossing, as depicted in Fig. 1. The maximum of crystallization temperature Tc, as well as the calculated thermal stability against the crystallization ΔT = Tx -Tg, were also determined by DSC and are listed in Table 2 whereas the thermograms are presented in Fig. 1. On can note an expected decrease of Tg with the addition of potassium oxide due to the depolymerization impact of the modifier oxides addition in the glass network. The thermal stability, which is considered as an indicator of potential formability of glasses regarding bulk shaping or fiber drawing, is above 150 °C for all glass compositions and does not show significant variations with the addition of KO1/2. Moreover, one can note on the thermograms shown in Fig. 1 that the crystallization peak shape is evolving from a two-component intense and narrow peak (GGBK0) toward a broadened and weak peak for the GGBK13 and GGBK17 glasses. This behavior, resulting from the addition of potassium oxide into the GGB vitreous network, can be considered as favorable for further fiber drawing experiments. It is indeed preferable to avoid a sharp and intense crystallization peak to maximize the temperature working range for possible thermal shaping.

The measured density of the glasses is given in Table 2, showing a rapid decrease with the addition of KO1/2 from 0 to 10 mol% and then a slower decrease from 10 to 17 mol% of KO1/2. This result can be readily explained by the lower molar weight of KO1/2 vs the other glass constituents. The TMA curves of the GGBKx glasses are presented in Fig. 2 whereas the linear thermal expansion coefficient (TEC, determined from the curve slope between 30 and 300 °C), the dilatometric glass transition temperature (Tgd, determined from the tangents crossing as depicted in Fig. 2) and the dilatometric softening point (Td, determined from the maximum dilatation point as depicted in Fig. 2) are reported in Table 2.

The addition of KO1/2 implies an increase in the linear coefficient of thermal expansion, which confirms the role of the potassium oxide on the depolymerization of the network, thus leading to an increase of the TEC. Tgd decreases when KO1/2 is added, in accordance with the DSC results presented in Fig. 1. A 20 °C difference between the two Tg measurements is noticed, ascribed to distinct measurement methods and heating rates used, i.e. calorimetric with the DSC run at 10 °C/min and dilatometric with the TMA run at 5 °C/min. The evolution of viscosity as a function of temperature of the GGBKx glass samples is presented in Fig. 3 whereas Table 2 reports the estimated fiber drawing temperature (Tfib). The glass viscosity is decreasing as the potassium oxide content increases, as well as the potential fiber drawing temperature. These Tfib temperatures remain lower than the onset of crystallization temperature Tx determined by DSC. The transmission spectra of the GGBKx glass samples recorded in the short wavelength region (from 250 to 500 nm) are presented in Fig. 4a. The artefact observed at 350 nm corresponds to the source change during the spectrum acquisition. The full transmission spectrum of the GGBK17 glass sample is shown in Fig. 4b. Similar transmission spectra were recorded for all studied samples. One can notice a strong absorption band around 3 μm related to the presence of OH groups in the glass, which was expected as no special care was taken during glass synthesis here. Various methods have been proposed in the literature to eliminate water from the starting materials and the produced glasses, resulting in a strong decrease of intensity of this band [START_REF] Bayya | Germanate glass as a window for high energy laser systems[END_REF]. Then, one can observe in Fig. 4b that the short wavelength band-edge of the GGBK17 glass is located around 300 nm whereas its multiphonon band-edge is located around 5.5-6 μm. The same broad transmission window was observed on all the samples and is similar to that reported in BGG glasses [START_REF] Bayya | Germanate glass as a window for high energy laser systems[END_REF]. Furthermore, as one can see from Fig. 4a and from the calculation of the short wavelength cut-off λUV of each glass composition for a given linear absorption coefficient of 10 cm -1 , a small decrease from 293 to 277 nm with increasing the potassium content in the glass is observed (i.e. from GGBK0 to GGBK17). It is however difficult to explain this slight increase of the glass optical bandgap from the chemical composition evolution. Many aspects must indeed be taken into account (e.g. presence of nonbridging oxygens, transition metals impurities, etc.). It is worth reminding here that the barium and potassium carbonate precursors used here were only of 99% purity. Moreover, no effect of the glass composition was observed on their multiphonon wavelength cut-off, determined at λIR = 5.9 μm (for a given linear absorption coefficient of 10 cm -1 ) for all samples. Again, such a result was expected considering that the infrared band-edge is governed by the phonon energy of the vitreous network built on gallium and germanium oxides. The increasing concentration of barium and potassium oxide modifiers in the network (from 19.5 to 33.2 mol% in GGBK0 and GGBK17, respectively) is not sufficient to significantly change its multiphonon energy. The refractive indices of the GGBKx glasses measured at five wavelengths in the visible and near-infrared ranges are plotted as a function of their potassium oxide content in Fig. 5. A monotonous decrease of the refractive index is observed at all wavelengths when increasing the potassium oxide in the glass. For instance, at 532 nm, the measured refractive index decreases from 1.754 (GGBK0) to 1.701 (GGBK17), which is consistent with the decrease of glass density reported in Table 2. With respect to the mechanical properties, only the GGBK17 glass sample was characterized (as it corresponds to the selected composition for further fiber drawing and crystallization studies, see Section 3.4.1). Its measured Young's modulus, shear modulus, Poisson's ratio and hardness are E = 62 ± 1 GPa, G = 24.4 ± 0.5 GPa, νpoisson = 0.285 ± 0.002 and HM = 5.54 ± 0.05 GPa, respectively. These results will be discussed in Section 3.3.

Structural study

The Raman spectra were recorded on all the glass samples and are presented in Fig. 6. One can note, for all glasses, a principal band with a maximum at around 500 cm -1 and a broad band between 700 and 900 cm -1 . The addition of potassium oxide induces a shift toward lower frequencies for both bands. The latest also shows an increase of its relative intensity. The spectra are similar to the ones observed for the gallium-rich GaO3/2-GeO2-NaO1/2 glasses studied in our previous work [START_REF] Skopak | Mixture experimental design applied to gallium-rich GaO3/2-GeO2-NaO1/2 glasses[END_REF][START_REF] Skopak | Structure and properties of gallium-rich sodium germano-gallate glasses[END_REF]. The presence of a 3D interconnected network made of connected tetrahedral XO4 units (X = Ga or Ge) can be associated to the vibrations observed at 500 cm -1 . One can note that due to the similar mass of gallium and germanium, their signature cannot be distinguished by Raman spectroscopy. The shift in frequencies of the band at 500 cm -1 marks a modification of the X -O -X (X = Ga or Ge) bonds within the network. In fact, the glasses GGBK0 and GGBK5, which present a (K + 2Ba)/Ga ratio of respectively 0.81 and 0.92, cannot have a full charge compensation of the entire [GaO4] -tetrahedral units. As observed for the gallium-rich glasses in the GaO3/2-GeO2-NaO1/2 system [START_REF] Skopak | Mixture experimental design applied to gallium-rich GaO3/2-GeO2-NaO1/2 glasses[END_REF][START_REF] Skopak | Structure and properties of gallium-rich sodium germano-gallate glasses[END_REF], one can assume that some of the gallium cations, which do not find a charge compensation in tetrahedral units, may be inserted in highly coordinated gallium sites (either 5 or 6 coordination numbers) which do not require a charge compensation and the presence of a neighboring alkali. The highly coordinated gallium sites may as well generate connection by the edges or faces, leading to an increase of the Ga -O -Ga bond's strengthening. In the same time, there is creation of gallate units in 4-fold coordination having a full compensation of charge that are inserted within annular structures made of [GeO4] and [GaO4] -units, as observed in GaO3/2-GeO2-BaO glasses. This leads to the two components centered around 750 and 850 cm -1 in the broad 700-900 cm -1 band [START_REF] Mckeown | Raman spectroscopic studies of BaO-Ga2O3-GeO2 GLASSES[END_REF]. Once the ratio (K + 2Ba)/Ga is above unity, all the gallium tetrahedral oxygenated sites can be charge balanced and the creation of new Q 3 (i.e. having 3 bridging oxygens) GeO4 units can occur from the excess of alkali ions, which leads to a third component of vibration located around 800 cm -1 . One can also note that this system presents two types of alkali ions (Ba 2+ and K + ), from which the capacity to compensate negative charges in the network might differ [START_REF] Fukumi | Raman spectroscopic study of the structural role of alkaline-earth ions in alkaline-earth gallate glasses[END_REF]. In summary, the bands observed in the Raman spectra in Fig. 6 can be assigned according to McKeown et al.'s work [START_REF] Mckeown | Raman spectroscopic studies of BaO-Ga2O3-GeO2 GLASSES[END_REF], as following: (i) at 500 cm -1 : vibration X -O -X bonds with X = Ge or Ga; (ii) at 820 cm -1 : Q 3 XO4 unit vibrations with X = Ge or Ga; (iii) at 850 cm -1 : vibration of annular structure composed of [GeO4] and [GaO4] -units and; (iv) at 270-300 cm -1 : network vibration containing K + and Ba 2+ ions.

Structure-properties relationship

As KO1/2 acts in the glass network as a modifier oxide, it induces a depolymerization of the glass network through the decrease of connected gallate octahedral sites from (2Ba + K)/Ga ratio of 0.81 to 1.03 and then the formation of new Q 3 units (characterized on Raman spectra by the band component at 800 cm -1 , Fig. 6). This depolymerization of the network by the addition of potassium oxide, observed for a ratio above unity, induces a decrease of the density, the glass transition temperature, the viscosity and an increase of the thermal expansion coefficient (Table 2, Fig. 1, Fig. 2, Fig. 3). The increase in the KO1/2 content, which is less polarizable than the other components of this glass system (GeO2, GaO3/2 and BaO), combined to the decrease of the density, leads to an expected decrease of the refractive index values (Fig. 5). As mentioned earlier, a small decrease of the short wavelength cut-off is observed for K + Ba/Ga ≥ 1. As the potassium oxide introduction generates the formation of new Q 3 units in the glassy matrix, an increase of λUV could have been expected due to the creation of new non-bonding molecular orbitals in the upper level of the valence band. However, one should keep in mind that the short wavelength cut-off is also influenced by the presence of impurities (transition metal ions in particular) within the raw materials, making the discussion more complex. The Young's modulus was estimated by the ultrasound echography study for the glass composition GGBK17 to be at 62 GPa. This value appears to be higher than the Young's modulus obtained for chalcogenide glasses (for example E = 16.5 GPa for an As2S3 glass [START_REF] Rouxel | Elastic properties and short-to medium-range order in glasses[END_REF]) and even fluoride glasses (as for the ZBLAN glass, E = 54.3 GPa [START_REF] Rouxel | Elastic properties and short-to medium-range order in glasses[END_REF]). The Young's modulus of the GGBK17 glass composition seems to be closer to the values measured for silicate glasses (with E = 50 to 100 GPa depending on the glass composition [START_REF] Rouxel | Elastic properties and short-to medium-range order in glasses[END_REF]). The hardness of the GGBK17 glass, which is of 565 kg/mm 2 (or 5.54 GPa) is higher than the value observed by Bayya et al. [ [START_REF] Bayya | BaO-Ga2O3-GeO2 glasses with enhanced properties[END_REF], [START_REF] Bayya | Infrared transparent germa-nate glass-ceramics[END_REF], [START_REF] Bayya | VIS-IR transmitting windows[END_REF], [START_REF] Bayya | Germanate glass as a window for high energy laser systems[END_REF]]; [ [START_REF] Lapp | Gallium oxide glasses[END_REF], [START_REF] Skopak | Structure and properties of gallium-rich sodium germano-gallate glasses[END_REF], [START_REF] Hee | Properties and structural investigation of gallophosphate glasses by Ga-71 and P-31 nuclear magnetic resonance and vibrational spectro-scopies[END_REF], [START_REF] Murthy | Properties and structure of glasses in system M2O-Ga2O3-GeO2 (M = Li, Na, K)[END_REF]] for BaO-Ga2O3-GeO2 and BaO-In2O3-Ga2O3-GeO2 glasses (showing respectively a hardness between 385 and 455 kg/mm 2 (or 3.77 and 4.46 GPa)). The latest being studied in the germanium oxide rich portion of the system, it can be suggested that the addition of gallium oxide tends to increase the hardness of the glasses.

Crystallization study

Composition selection and preliminary crystallization test

Regarding the thermal and optical properties, the most suitable glass for further thermal shaping like fiber drawing is the GGBK17 sample whose nominal composition is 40.1GaO3/2-26.7GeO2-16.2BaO-17KO1/2 (in cation mol.%, which also corresponds to 28Ga2O3-37GeO2-23BaO-12K2O in mol.%). This glass presents a high ΔT (191 °C), a weak and broad crystallization peak on the DSC measurements (Fig. 1), a refractive index of 1.701 at 532 nm and a large transmission window (from 277 to 5900 nm, Fig. 4). One should also keep in mind that the higher the potassium content is, the easier it is to melt and shape the glass at lower temperature due to lower viscosity (Fig. 3) and the temperature compatibility with molding materials (for example stainless steel). In order to get preliminary crystallization information regarding the GGBK17 glass, a heat treatment was performed on bulk and powder at a temperature T1 between Tfib = 819 °C and Tx = 832 °C. To do so, one bulk and one powder samples were heated up in 5 min from ambient temperature to the temperature T1 = 825 °C, hold for 30 min at T1 and then cooled down to room temperature. The powder XRD patterns (see Fig. 7) were then recorded to determine the observed crystalline phases on both bulk and powder samples. The bulk sample presents one crystalline phase which can be indexed with either KGaGeO4 (JCPDS 052-1595) or BaGa2O4 (JCPDS 046-0415). Both phases are isostructural and exhibit very close cell parameters, which prevents clear assignation from XRD. The powder sample shows two crystalline phases being for the main one KGaGeO4 (JCPDS 052-1595) or BaGa2O4 (JCPDS 046-0415) and α-BaGa2O4 (JCPDS 049-0890) a high temperature polymorphism of the previous BaGa2O4 phase. These different results demonstrate the existence of a surface crystallization mechanism.

Nucleation-growth curves determination

The nucleation-like curve is determined with the DSC method proposed by Marotta et al. [START_REF] Marotta | Nucleation in glass and differential thermal analysis[END_REF]. It consists in measuring the variation of the maximum of the crystallization peak Tp after a thermal treatment at a potential nucleation temperature TN. According to the following equation:

where I0 represents the nucleation rate at the temperature TN, Tp 0 (respectively Tp) the maximum of crystallization obtained on the thermal analysis of the glass without any heat treatment (respectively after a heat treatment of 30 min at TN), EC the crystallization activation energy and C a constant that cannot be determined, plotting (1/Tp -1/Tp 0 ) as a function of TN will provide a qualitative information on the nucleation rate variation. Then the nucleation-like curve only shows the qualitative evolution of the nucleation rate with the temperature. Experimentally, one glass bulk piece (40 -55 mg) is placed in a Pt crucible and into a DSC apparatus. A first DSC measurement is run with a slope of 20 °C/min from room temperature to a temperature above crystallization (TFC), providing the thermal profile reference of the studied glass. Then, several glass samples are tested following the heat treatment represented in Fig. 8a. A displacement of the maximum of crystallization will occur depending on TN, as represented in Fig. 8a. In fact, if many nuclei are formed during the isothermal plateau, the crystallization will occur at a lower temperature compared to the original DSC curve of the non-treated glass. The growth-like curve is then also determined from DSC method, as proposed by Ray et al. [START_REF] Ray | Determining crystal growth rate-type of curves in glasses by differential thermal analysis[END_REF]. In this case, the glass sample is considered to already contain nuclei, and the applied heat treatment only induces their growth, as represented in Fig. 8b. As crystallization appears as an exothermic phenomenon on the DSC curves, the variation of the crystallization peak area will provide information on the growth mechanism, as represented in Fig. 8b. The plot of the growth-like curves is ruled by the potential growth temperature (TG) as follows:

where A0 (respectively At) is the exothermic peak area for the glass sample which is not heat treated at TG (respectively for the glass sample treated at TG). In order to stay similar to the nucleation-like curve, the heat treatment slope is maintained at 20 °C/min and the mass of the analyzed bulk piece is between 40 and 75 mg. The nucleation and growth profiles were both acquired, and thus the measurement were realized on glass chunks. The obtained curves are presented in Fig. 9. The maximum nucleation and maximum growth temperatures, respectively TNmax and TGmax, are determined from these curves respectively at 710 °C and 880 °C. One can observe that the nucleation and growth curves show a huge overlap, with the presence of two maxima for the growth curve. In fact, the first maximum at around 750 °C could be associated to the surface crystallization when the second, and major maximum at 860 °C may be related to the volume crystallization. From this, it can be deduced that no control on the nucleation and growth of the volume can be managed. Actually, the surface crystallization may always grow while the volume nucleates. One can note that the first maximum at 750 °C is lower than the estimated fiber drawing temperature (Tfib = 819 °C) and might generate problematic surface crystallization during fiber drawing.

Crystallization at the maximum of nucleation and phase determination

Crystallization tests were realized on bulk samples at TNmax = 710 °C for 5 and 72 h. The powder XRD patterns recorded are presented in Fig. 10. For the sample heat-treated 72 h, diffraction peaks corresponding to the same crystalline phases above mentioned are clearly observed, as well as the presence of a glassy phase. On the other hand, the sample heat-treated 5 h appears to be essentially glassy. A small peak is however arising at around 28° which can indicate the apparition of first crystals. TEM observations were then performed in order to detect a possible phase separation in the glass (pristine and treated at TNmax for 5 and 72 h). The TEM micrographs acquired in bright field mode and the electron diffraction patterns recorded on selected areas are presented in Fig. 11. Note that electron diffraction patterns were recorded here to detect the presence of crystals in the samples rather than identify their nature. All the analyzed pristine samples appear homogenous and do not present phase separation. However, the glass heat-treated for 5 h at TNmax shows some dispersed crystallized areas (see Fig. 11b) with corresponding electron diffraction pattern presented in inset) while the sample heat-treated for 72 h at TNmax exhibits numerous nanocrystals (Fig. 11c) and corresponding electron diffraction pattern in inset). These observations are in agreement with the XRD patterns presented in Fig. 10. As the crystalline phase could not be determined accurately from XRD, the surface of one sample treated at 710 °C for 72 h was studied by SEM-EDX. A first observation of the surface of the sample, as presented in Fig. 12b). The EDX analyses of the dendrites presented in Fig. 12d and Table 3 indicate a mixed composition between KGaGeO4 and BaGa2O4, suggesting a K1-xBaxGa1+xGe1-xO4 solid solution with a x = 0.27 composition. This result almost corresponds to a 3:1 combination of KGaGeO4 and BaGa2O4 phases. Moreover, an analysis of the residual glassy phase in between the dendrites shows a deficit in the potassium content, which tends to increase when measuring its concentration in depth of the glass sample. This can be explained from a lower concentration of potassium in the crystal compared to the pristine glass.

In summary, the crystallization behavior described here on the GGBK17 glass composition shows that surface crystallization issues are expected during further fiber drawing experiments from a glass preform, despite the fact that this composition possesses a very large thermal stability against crystallization, as determined by DSC (ΔT = 191 °C). Preliminary tests of fiber drawing from GGBK17 glass preforms (40 mm length and 10 mm diameter) were conducted in parallel, confirming these surface crystallization issues. To illustrate this result, Fig. 13 shows a typical GGBK17 preform neck-down obtained after conventional drawing at 805 °C, even after optical polishing of the preform surface. Last, as mentioned in the introduction, the initial approach here was to replace sodium cations in the germano-gallate vitreous network by less mobile barium and potassium cations in order to limit surface crystallization issues occurring during fiber drawing from preform (as observed in our anterior work on sodium germano-gallate glasses). It appears however from the results presented here that surface crystallization still constitutes a limiting factor for fiber drawing from glass preforms. Three directions may therefore be considered to circumvent this problem. The first one is related to the fiber fabrication process with the implementation of the crucible technique for instance. In such an approach, the glass fiber is indeed produced during cooling of the glass brought to its liquid state within a crucible, limiting therefore the risk of crystallization that occurs here upon glass preform heating. The second direction consists in modifying the glass composition and eventually replaces the alkali oxides by other components whereas the third one would be a combination of the first two. Efforts are currently ongoing in order to produce crystal-free optical fibers from these mid-infrared transparent germano-gallate glasses. Their superior thermal and mechanical properties (vs heavy metal oxide or fluoride glasses for instance) indeed make them promising candidates for robust and durable mid-infrared optical materials in general.

Conclusion

Germano-gallate glasses (i.e. with gallium oxide as the main component) of compositions (100-x)[48.3GaO3/2-32.2GeO2-19.5BaO]-xKO1/2 (with x = 0, 5, 10, 13, 17 mol%) have been investigated in order to determine most appropriate composition for preform fiber drawing. The obtained glasses are transparent from approximately 280 nm up to 5.5 μm. When the potassium oxide content is increased, the measured linear refractive index and density decrease respectively from 1.72 to 1.67 (at 1538 nm) and 4.79 to 4.34 g/cm 3 ; the glass transition temperature decreases (698 to 671 °C), as well as the viscosity in the softening regime whereas the thermal expansion coefficient increases (4.8 to 10.3 × 10 -6 K -1 ). These expected results are related to the depolymerization of the 3D interconnected glass network studied by Raman spectroscopy. Slightly superior mechanical properties (Young and shear moduli, Poisson's ratio, hardness) vs well-known BGG glasses have been measured on the glass composition, 40GaO3/2-27GeO2-16BaO-17KO1/2 (in mol.%, which corresponds to 28Ga2O3-37GeO2-23BaO-12K2O), selected as the most promising one for optical fiber production. A thorough crystallization study combining DSC method with XRD, SEM and TEM analyses has been conducted on this glass composition to better understand the unexpected surface crystallization issues observed during the glass preform fiber drawing process. Surface crystallization of mixed KGaGeO4 and BaGa2O4 phases has been evidenced, suggesting the formation of a K1-xBaxGa1+xGe1-xO4 (x = 0.27) solid solution. The obtained results provide better insight of the surface crystallization behavior observed in this germano-gallate glass, which is somewhat representative of that observed in Ga2O3-GeO2-based glasses, independently of their germanium and gallium oxides relative content.

As such crystallization behavior under heating treatment constitutes a serious limiting factor to glass thermal processing like fiber drawing from a preform, alternative avenues have to be explored to produce germano-gallate glass optical fibers transmitting in the mid-infrared.

Fig. 1 .

 1 Fig. 1. DSC thermograms of the GGBKx glass samples recorded at 10 °C/min. Traces were vertically translated for better reading.

Fig. 2 .Fig. 3 .

 23 Fig. 2. TMA curves recorded on the GGBKx glass samples.

Fig. 4 .

 4 Fig. 4. (a) Transmission spectra in the short wavelength range of the GGBKx glass samples. Samples thickness is about 1 mm. (b) Transmission window of the GGBK17 glass sample (thickness is about 5 mm).

Fig. 5 .

 5 Fig. 5. Variation of refractive index measured at different wavelengths of the GGBKx glass samples as a function of their nominal potassium oxide content (KO1/2 in mol.%).

Fig. 6 .

 6 Fig. 6. Raman spectra of the studied GGBKx glasses normalized at their main peak intensity (~ 500 cm -1 ).

Fig. 7 .

 7 Fig. 7. Powder XRD diffraction patterns recorded on GGBK17 glass powder and bulk samples annealed at 825 °C for 30 min, with the peak positions related to the KGaGeO4, BaGa2O4 and α-BaGa2O4 crystalline phases.

Fig. 8 .

 8 Fig. 8. Representations of the heat-treatment applied on the GGBK17 glass with the corresponding effect on the DSC curve for: a) the nucleation-like curve determination, and b) the growth-like curve determination.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Volume nucleation (black curve) and growth (red curve) curves for the GGBK17 glass obtained on one or two glass pieces with the isothermal technique. TNmax is the maximum nucleation temperature and TGmax is the maximum growth temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 11 .

 11 Fig. 11. TEM micrographs and electron diffraction patterns (in inset) of GGBK17 glass pieces: a) without heat-treatment, b) treated at 710 °C for 5 h, and c) treated at 710 °C for 72 h.

Fig. 12 .

 12 Fig. 12. SEM observations: a) in Back Scattered Electron mode of the GGBK17 glass surface after a heat-treatment at 710 °C for 72 h; b-c) of the section of the GGBK17 glass treated at 710 °C for 72 h at two different magnifications with the localization of the EDX analysis spots and the corresponding spectra (d).

Fig. 13 .

 13 Fig.[START_REF] Lapp | Gallium oxide glasses[END_REF]. Photograph of a GGBK17 preform neck-down after a conventional fiber drawing at 805 °C.

Acknowledgements

This research was conducted in the framework of the Laboratoire International Associé (LIA) LuMAQ and supported by the Canadian Excellence Research Chair program (CERC) in Photonics Innovations and the Aquitaine Region. The authors are also grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fonds de Recherche Québecois sur la Nature et les Technologies (FRQNT) and the Canadian Foundation for Innovation (CFI) for the financial support. The authors thank the ICMN Laboratory (Orléans, France) for TEM access. Steeve Morency is also acknowledged for his technical assistance.

Mobilities were supported by grants of the French Consulat in Québec (by the Frontenac Program), the association of Campus France and Mitacs Globalink as well as grants of the Agence Nationale de la Recherche (ANR) with the program "Investissement d'avenir" number ANR-10-IDEX-03-02 and ANR-17-CE08-0042-01, and the French Region Nouvelle Aquitaine, with the program n° 2016 -1R10107.


Mathieu G Faure-Brac

François Pelissier

Jorge Cubo

The influence of plane of section on the identification of bone tissue types in amniotes with implications for paleophysiological inferences Running title : Assessment of bone tissue types

Keywords: anisotropy, bone histology, isotropy, parallel-fibered bone, woven bone

We show that the presence of canaliculi running radially from large irregular osteocyte lacunae, and general isotropy at tissue scale, but local anisotropy at cellular scale, offer reliable characters for diagnosing woven bone in amniotes.

Introduction

In vertebrate paleontological studies, bones constitute the large majority of fossilized remains.

The histological analysis of skeletal elements allows to infer bone growth rates [START_REF] Botha-Brink | Osteohistology of the Triassis Archosauromorphs Prolacerta, Porterosuchus, Eparkeria, and Erythrosuchus from the Karoo Basin of South Africa[END_REF][START_REF] Cubo | Paleohistological estimation of bone growth rate in extinct archosaurs[END_REF][START_REF] Padian | Dinosaurian growth rates and bird origins[END_REF][START_REF] Padian | Growth in small dinosaurs and pterosaurs: the evolution of archosaurian growth strategies[END_REF], lifestyle [START_REF] Houssaye | Bone histology of aquatic reptiles: What does it tell us about secondary adaptation to an aquatic life?[END_REF][START_REF] Houssaye | Bone histology of aquatic reptiles: What does it tell us about secondary adaptation to an aquatic life?[END_REF][START_REF] Laurin | Bone microanatomy and lifestyle : A descriptive approach[END_REF], biomechanical constraints [START_REF] Cubo | First Reported Cases of Biomechanically Adaptive Bone Modeling in Non-Avian Dinosaurs[END_REF] or metabolic rates [START_REF] Cubo | Bone histology of Azendohsaurus laaroussii: Implications for the evolution of thermometabolism in Archosauromorpha[END_REF][START_REF] Fleischle | Quantitative histological models suggest endothermy in plesiosaurs[END_REF][START_REF] Legendre | Palaeohistological Evidence for Ancestral High Metabolic Rate in Archosaurs[END_REF][START_REF] Olivier | First palaeohistological inference of resting metabolic rate in an extinct synapsid , Moghreberia nmachouensis (Therapsida: Anomodontia)[END_REF]. Traditionally, bone paleohistology was based on the analysis of transverse sections (e.g., all the references cited above). Paleohistologists defined two characters using this material. The first one concerns bone matrix organization and has three states: presence of woven-fibered bone matrix (WB), presence of parallel-fibered bone matrix (PFB) and presence of lamellar bone matrix (LB) [START_REF] Francillon-Vieillot | Microstructure and Mineralisation of Vertebrate Skeletal Tissues[END_REF]. The second one is based on the organization of bone as a tissue and has two states: presence of lamellar-zonal bone (LZB) and presence of fibro-lamellar bone (FLB) [START_REF] Francillon-Vieillot | Microstructure and Mineralisation of Vertebrate Skeletal Tissues[END_REF]. [START_REF] Prondvai | Development-based revision of bone tissue classification: The importance of semantics for science[END_REF] proposed a development-based nomenclature in which LB is a particular type of PFB and FLB is a particular case of woven-parallel complex.

According to [START_REF] Francillon-Vieillot | Microstructure and Mineralisation of Vertebrate Skeletal Tissues[END_REF], two osteohistological features can be used to identify WB and PFB: (1) collagen fiber orientation (inferred from the presence or absence of birefringence under cross-polarized light) and (2) morphology and spatial distribution of osteocyte lacunae. Under cross-polarized light, a highly organized matrix with fibers running parallel (oriented in the same direction; PFB) is anisotropic and appears bright (birefringent) when fibers are perpendicular to the axis of light propagation and it appears dark when fibers are aligned along the axis of light propagation [START_REF] Bromage | Circularly Polarized Light Standards for Investigations of Collagen Fiber Orientation in Bone[END_REF]. Thus, in transverse thin sections, collagen fibers parallel to the main axis of a long bone appear dark. At low 4 magnification (at tissue scale), the poorly organized matrix of woven bone shows intermediate brightness values [START_REF] Bromage | Circularly Polarized Light Standards for Investigations of Collagen Fiber Orientation in Bone[END_REF]), or "general isotropy" (Francillon-Vieillot et al., 1990) from all cutting directions. However, at high magnification (on cellular scale), considering that WB collagen fibers are parallel in former osteoblast secretory territories ("microlamellar arrangement"), they are anisotropic and they appear bright where they are perpendicular to the axis of light propagation [START_REF] Kerschnitzki | The organization of the osteocyte network mirrors the extracellular matrix orientation in bone[END_REF]. The other osteohistological feature, the morphology and spatial distribution of osteocyte lacunae, reflects (i.e., is correlated to) the extracellular matrix organization [START_REF] Kerschnitzki | The organization of the osteocyte network mirrors the extracellular matrix orientation in bone[END_REF].

In PFB the longitudinal axis of osteocyte lacunae is parallel to collagen fiber direction whereas canaliculi are perpendicular to it [START_REF] Kerschnitzki | The organization of the osteocyte network mirrors the extracellular matrix orientation in bone[END_REF]. In contrast, in WB there is no alignment between osteocytes and canaliculi run radially from osteocyte lacunae [START_REF] Kerschnitzki | The organization of the osteocyte network mirrors the extracellular matrix orientation in bone[END_REF]. Stein & Prondvai (2014) drew attention to the fact (known previously but neglected before 2014) that WB, and PFB with fibers parallel to the main axis of the long bone, both appear dark in transverse thin sections. Considering that the proportion of WB to PFB has been extensively used to infer bone growth rates and resting metabolic rates of extinct organisms, mismeasure of WB content in transverse sections may have important paleophysiological consequences. The aim of this study is to test in a variety of amniotes the null hypothesis that WB content is not significantly different in the transverse and the longitudinal section planes.

Material and Methods

We analyzed femoral mid-diaphyseal transverse and slightly metaphyseal longitudinal thin sections of 14 extant and extinct taxa including five synapsids, three lepidosaurs, two testudines and four archosauromorphs. The transverse sections of most of them were prepared and used by [START_REF] Montes | Relationships between bone growth rate , body mass and resting metabolic rate in growing amniotes: a phylogenetic approach[END_REF]: Chelodina oblonga (Gray, 1841), Crocodylus niloticus 5 (Laurenti, 1768), Gallus gallus (Linnaeus, 1758), Pelodiscus sinensis (Wiegmann, 1835), Varanus exanthematicus (Bosc, 1792), Varanus niloticus (Linnaeus, 1766) and Zootoca vivipara (Von Jacquin, 1787). We prepared the corresponding longitudinal thin sections using the remaining slightly metaphyseal bone samples that were conserved embedded in epoxy resin. Vivian de Buffrénil kindly shared with us the femur of a growing Caiman crocodilus (Linnaeus, 1758), that was embedded in epoxy resin and cut both transversally and longitudinally. The transverse sections of four (of the five) synapsids were prepared and used by [START_REF] Olivier | First palaeohistological inference of resting metabolic rate in an extinct synapsid , Moghreberia nmachouensis (Therapsida: Anomodontia)[END_REF]: Capreolus capreolus (Linnaeus, 1758), Lepus europaeus (Pallas, 1778), Lystrosaurus sp., and Oudenodon bainii Owen 1860. We used the remaining slightly metaphyseal bone samples (conserved embedded in epoxy resin) to perform the corresponding longitudinal thin sections. Transverse and longitudinal sections of the fifth synapsid of the sample (Clepsydrops collettii Cope 1875) and of the archosauromorph Azendohsaurus laaroussii Dutuit 1972 were prepared and used respectively by Laurin & Buffrénil (2016) and by [START_REF] Cubo | Bone histology of Azendohsaurus laaroussii: Implications for the evolution of thermometabolism in Archosauromorpha[END_REF]. For further information on the ontogenetic stage of the specimens, see Supplementary file 1. It is expressed as % of adult body mass in extant species and inferred from bone histology in extinct ones. To check whether WB can be diagnosed in a reliable way we used a sample including different ontogenetic stages, different thermometabolic regimes (endotherms and ectotherms), and extant and extinct species of diverse amniote clades.

Transverse sections were available because they have been used in previous studies (see above). The corresponding longitudinal thin sections, 100 ± 10µm thick, were obtained from slightly metaphyseal samples of the same specimens using the protocol described by [START_REF] Montes | Relationships between bone growth rate , body mass and resting metabolic rate in growing amniotes: a phylogenetic approach[END_REF]. Thin sections were photographed using a Nikon Eclipse E600POL microscope under linearly polarized light and cross-polarized light with lambda wave plate. Thin sections were deposited at the vertebrate hard tissues histological collection of the French National 6 Museum of Natural History (MNHN), where they are available upon request to the curator (accession numbers of the thin sections analyzed in this study are given in Supplementary file 1). Bone histology nomenclature follows [START_REF] Francillon-Vieillot | Microstructure and Mineralisation of Vertebrate Skeletal Tissues[END_REF] with addenda from [START_REF] Prondvai | Development-based revision of bone tissue classification: The importance of semantics for science[END_REF].

For each taxon included in this study transverse sections were analyzed first. In transverse sections, bone matrix appearing yellow/orange or blue under cross-polarized light with lambda wave plate, or bright without lambda wave plate, is composed of PFB with fibers perpendicular to the main axis of the long bone. In these transverse sections, at low magnifications (at the tissue level), bone matrix appearing red under cross-polarized light with lambda wave plate, or black without lambda wave plate, is composed of either WB or PFB with fibers parallel to the main axis of the long bone. Please note that at high magnifications (at the cellular level), woven bone is anisotropic because of the presence of microlamellar arrangement in former osteoblast secretory territories (fibers appear yellow/orange or blue where they are perpendicular to the axis of light propagation; white arrow in Figure 1). We encircled WB areas in transverse sections and measured these areas using ImageJ when we observed: (a) a bone matrix showing general isotropy at low magnification (at tissue scale);

(b) an anisotropic microlamellar arrangement at high magnification (on cellular scale); (c) no alignment between osteocytes, and (d) canaliculi running radially from large irregular osteocyte lacunae. Longitudinal sections were analyzed likewise in a second time. Please note that the channels herein referred to as vascular cavities are known to not be exclusively filled with corresponding veins and arteries but accommodate a few more tissues as well such as nerves and lymphatic vessels [START_REF] Starck | Bone microstructure and developmental plasticity in birds and other dinosaurs[END_REF].

We tested the null hypothesis suggesting that the proportion of WB (expressed in percentage: WB area / Total matrix area) is not significantly different in transverse and in longitudinal sections. For this first we performed Shapiro-Wilk normality tests for the proportion of WB in 7 transverse and in longitudinal sections in R (R Development Core Team, 2008). Second, we tested the null hypothesis using a Wilcoxon signed-rank non-parametric paired test in R (R Development Core Team, 2008) because the proportions of WB in transverse and in longitudinal sections are not normally distributed.

Results

We analyzed qualitatively and quantitatively femoral transverse and longitudinal bone thin sections of the fourteen taxa of the sample in order to test whether the quantified amount of WB is the same in both section planes. First we provide detailed qualitative histological descriptions of six species of the sample: two extant endotherms (Capreolus capreolus and Gallus gallus, Figure 2), two extant ectotherms (Crocodylus niloticus and Zootoca vivipara, 2B). In these areas collagen fibers can be either woven or longitudinally organized parallel to the long axis of the bone (and so cut transversally). The small size of the osteocyte lacunae of these areas (Figure 2B, black arrowhead) suggests that it is composed of PFB cut transversally. Finally, under cross-polarized light with lambda wave plate, we always observe bluish stripes (Figure 2B, white arrow) equidistant from two consecutive vascular cavities. The large size and irregular shape of osteocyte lacunae of these areas suggest that it is composed of WB (Figure 2B, white arrow). The bluish aspect of these stripes (Figures 1 and2B, white arrows) may be linked to the microlamellar arrangement of collagen fibers in WB at cellular scale [START_REF] Kerschnitzki | The organization of the osteocyte network mirrors the extracellular matrix orientation in bone[END_REF]). The analysis of the corresponding longitudinal section (Figure 2C,D) is congruent with this interpretation because the entire section but the WB area (Figure 2D, white arrow) is strongly anisotropic. Note however that the WB area (Figure 2D, white arrow) is not entirely red but rather dark purple under cross-polarized light with lambda wave plate because of the microlamellar arrangement. The LB (Figure 2D, white arrowhead) is composed of alternating anisotropic layers of fibers oriented either parallel to the main axis of the bone (appearing blue because they are perpendicular to the axis of light propagation), or perpendicular to the main axis of the bone and parallel to the axis of light propagation (appearing as black lines). The PFB is anisotropic and appears bright blue under cross-polarized light with lambda wave plate in longitudinal section (Figure 2D, black arrowhead) because collagen fibers run parallel to the main axis of the bone (and so are perpendicular to the axis of light propagation). It contains spindle shaped osteocyte lacunae (Figure 2D, black arrowhead). In summary, there is a scaffold of WB trabeculae containing large primary osteons formed by a peripheral thick layer of PFB and a inner thin layer of LB around the vascular cavities (Figure 2 A-D).

The femoral transverse section of Gallus gallus is characterized by a radial pattern of vascular cavities (Figure 2E,F). These ones are lined by anisotropic PFB (Figure 2F, black arrowhead). Between these layers of PFB, we can observe areas of isotropic bone matrix (Figure 2F, white arrow). The large size and irregular shape of osteocyte lacunae of these 9 isotropic areas suggests that it is composed of woven bone. The analysis of the corresponding longitudinal section (Figure 2G,H) is congruent with this interpretation. We can observe areas of WB (Figure 2H, white arrow) and areas of PFB (Figure 2H, black arrowhead).

The femoral transverse section of Crocodylus niloticus is organized into three regions (white bar in Figure 3B). It contains longitudinal vascular canals without anastomoses (Figure 3A,B). Some of them are surrounded by an anisotropic tissue (blue and yellow under crosspolarized light with lambda wave plate in Figure 3B, white arrow) indicating the presence of PFB forming primary osteons. Others are simple vascular canals (Figure 3B, black arrow) and are preferentially located in the outer half of the cortex. The inner region is formed by a layer of endosteal bone around the medullary cavity (Figure 3B, D white arrow-heads). This endosteal layer is anisotropic in the longitudinal section (Figure 3D, white arrow-head), whereas it appears blue and red in the transverse section (Figure 3B, white arrow-head), indicating that it is probably composed of spiraling PFB at low angle to the bone's long axis.

In the central region (in between the endosteal bone and the outer half of the cortex), in between primary osteons, the bone matrix is isotropic. It contains irregular large osteocyte lacunae (Figure 3B, black arrow-heads) suggesting that this matrix is composed of WB. The bone matrix of the outer half of the cortex appears blue at some locations, indicating that it is composed of PFB, and red at other locations, suggesting that it is formed by either WB or by PFB with fibers oriented parallel to the main axis of the bone. The small size of the osteocyte lacunae suggests that the second interpretation is correct. The longitudinal section was prepared from a slightly different (more metaphyseal) region and it contains only the endosteal layer and an outer region corresponding to the outer half of the cortex observed in the transverse section (bar in Figure 3D). The layer of endosteal bone is anisotropic (see above), suggesting that it is formed by PFB. The bulk of the cortex contains simple vascular canals (Figure 3D, black arrow) that appear elongated because they are parallel to the main The bone matrix of this region is anisotropic, suggesting that it is mainly composed of longitudinal PFB (Figure 3D). Note, however, that it may contain a few transversally oriented collagen fibers relative to the main axis of the long bone because bone matrix appears partly blue in the transverse section; Figure 3B).

The femoral transverse section of Zootoca vivipara (Figure 3E,F) is completely avascular. It contains an endosteal layer of PFB (Figure 3F, white arrow-head) and an outer periosteal region that is also composed of PFB according to overall birefringence under cross-polarized light with lambda wave plate. The longitudinal section also shows birefringence (Figure 3H). These observations suggest that the PFB forming the periosteal bone cortex probably contains spiraling fibers at about 45° to the bone's long axis.

The femoral transverse section of Lystrosaurus sp. is characterized by a pattern of longitudinal vascular cavities (Figure 4A,B). These ones are lined by anisotropic PFB forming primary osteons (Figure 4B, white arrowheads). These primary osteons are separated by areas of isotropic bone matrix (Figure 4B, white arrows). The large size and irregular shape of osteocyte lacunae in these isotropic areas suggests that it is composed of WB. The analysis of the longitudinal section shows that the vascular canals have an elongated aspect aligned to the main axis of the bone (Figure 4C,D). These cavities are lined by PFB forming primary osteons (Figure 4D, white arrowheads). In between these primary osteons we can see isotropic areas composed of WB (Figure 4D, white arrows).

Transverse and longitudinal femoral sections of Oudenodon bainii (Figure 4E-H) show a pattern similar to that described for Capreolus capreolus : there is a scaffold of trabeculae containing WB (Figure 4F, H, white arrows) and, in-between two layers, there are primary osteons (vascular cavities lined by LB; Figure 4F,H Quantifications of proportion of WB in transverse and longitudinal sections are given in Table 1. Shapiro-Wilk normality tests showed that the proportion of WB was not normally distributed neither in transverse (p-value = 0.02398) nor in longitudinal (p-value = 0.04465) sections. A Wilcoxon signed-rank non-parametric paired test did not reject the null hypothesis suggesting that the proportion of WB (expressed in percentage: WB area / Total matrix area) is not significantly different in transverse and in longitudinal sections (p-value = 0.9056). In other words, the Wilcoxon signed-rank non-parametric paired test did not detect a significant difference in the WB content of the two section planes. Discussion 12 Stein & Prondvai (2014) analyzed the bone histology of sauropod dinosaurs using transverse and longitudinal sections and concluded that the amount of woven bone has been overestimated in previous studies that used only transverse sections. They suggested that this is because, under cross-polarized light, WB and PFB with fibers parallel to the main axis of the long bone, both appear isotropic (dark) in transverse thin sections. Considering that the proportion of WB to PFB has been widely used to perform paleobiological inferences of bone growth rates and resting metabolic rates (see below), the bias put in evidence by Stein & Prondvai (2014) in sauropod dinosaurs, if proven by comparative data in other taxa, may have important paleophysiological consequences. First, we elaborate on why quantifying the proportion of WB is relevant in paleobiology by analyzing the relationships between this feature and bone growth rates and resting metabolic rates. Afterwards we test the null hypothesis that WB content is not significantly different in the transverse and the longitudinal section planes. Finally, we propose recommendations and a workflow based on our findings.

WB is formed by the process of static osteogenesis: mesenchymal cells differentiate into stationary osteoblasts oriented randomly, which differentiate into osteocytes in situ [START_REF] Cubo | Static osteogenesis does not precede dynamic osteogenesis in periosteal ossification of Pleurodeles (Caudata, Amphibia) and Pogona (Squamata, Lepidosauria)[END_REF][START_REF] Ferretti | Static and dynamic osteogenesis : two different types of bone formation[END_REF][START_REF] Marotti | Static and dynamic osteogenesis[END_REF][START_REF] Palumbo | Osteocyte Dendrogenesis in Static and Dynamic Bone Formation: An Ultrastructural Study[END_REF]. PFB is formed by the process of dynamic osteogenesis: mesenchymal cells differentiate into osteoblasts that are all oriented in the same direction and move back as they secrete osteoid, forming a migrating lamina of osteoblasts [START_REF] Cubo | Static osteogenesis does not precede dynamic osteogenesis in periosteal ossification of Pleurodeles (Caudata, Amphibia) and Pogona (Squamata, Lepidosauria)[END_REF][START_REF] Ferretti | Static and dynamic osteogenesis : two different types of bone formation[END_REF][START_REF] Marotti | Static and dynamic osteogenesis[END_REF][START_REF] Palumbo | Osteocyte Dendrogenesis in Static and Dynamic Bone Formation: An Ultrastructural Study[END_REF]. We will consider the relationships between WB and bone growth rate at three levels: tissue, cellular and ultrastructural (see Stein & Prondvai, 2014, for a detailed review). At the tissue level, during the initial growth stages, a number of amniotes form an initial scaffold made of WB that includes large cavities and produces a rapid volume expansion of the cortex (e.g. [START_REF] Castanet | Periosteal bone growth rates in extant ratites ( ostriche and emu ). Implications for assessing growth in dinosaurs[END_REF], in the long bones of ratites and [START_REF] De Margerie | Assessing a relationship between bone microstructure and growth rate: a fluorescent labelling study in the king penguin chick ( Aptenodytes patagonicus )[END_REF], in the long bones of the king penguin). In other amniotes, the initial expansion of the cortex by appositional growth is made of PFB including, if any, smaller cavities, and producing a slow volume expansion of the cortex (e.g., Castanet, 1978, in squamates). As a consequence, for the same quantity of osteoid produced, static osteogenesis and WB are associated to a higher rate of bone accretion (at the tissue level) than dynamic osteogenesis and PFB. At the cellular level, considering that in static osteogenesis stationary osteoblasts are oriented randomly, the WB matrix formed is highly porous (Stein & Prondvai, 2014). In contrast, in dynamic osteogenesis, osteoblasts are all oriented in the same direction and produce PFB, a much more compact matrix (Stein & Prondvai, 2014). Again, for the same quantity of osteoid produced, static osteogenesis will produce a higher rate of volume expansion than dynamic osteogenesis.

At the ultrastructural level, the absolute growth rates at which WB and PFB are formed depend on the osteoid secretion rate of, respectively, static osteogenesis osteoblasts and dynamic osteogenesis osteoblasts (Stein & Prondvai, 2014). Considering that no ultrastructural differences have been observed between static and dynamic osteoblasts [START_REF] Marotti | Static and dynamic osteogenesis[END_REF], we expect to find similar osteoid secretion rates (Stein & Prondvai, 2014).

The formation of a scaffold of WB incorporating large cavities at high rates and the perimedullary resorption of bone tissue by osteoclasts at high rates are both energy consuming [START_REF] Montes | Relationships between bone growth rate , body mass and resting metabolic rate in growing amniotes: a phylogenetic approach[END_REF]. Thus, these mechanisms are only possible in taxa characterized by high resting metabolic rates [START_REF] Fleischle | Quantitative histological models suggest endothermy in plesiosaurs[END_REF][START_REF] Legendre | Palaeohistological Evidence for Ancestral High Metabolic Rate in Archosaurs[END_REF][START_REF] Olivier | First palaeohistological inference of resting metabolic rate in an extinct synapsid , Moghreberia nmachouensis (Therapsida: Anomodontia)[END_REF].

According to [START_REF] Padian | Typology versus transformation in the origin of birds[END_REF] "the types of tissue deposited in the bones of extinct animals are the most direct evidence of basal metabolic rates, because they directly reflect growth rates […]. The sustained deposition of fast-growing bone tissues, as displayed by mammals, birds and other dinosaurs, must reflect sustained high basal metabolic rates." This hypothesis was supported by the results obtained by [START_REF] Montes | Relationships between bone growth rate , body mass and resting metabolic rate in growing amniotes: a phylogenetic approach[END_REF]: the variation of bone growth rates significantly explains the variation of resting metabolic rates in a sample of 14 extant amniotes. In conclusion, precise quantifications of the proportion of WB is a key factor for performing reliable paleobiological inferences of both bone growth rates and resting metabolic rates.

Is WB content significantly different in the transverse and the longitudinal section planes? Qualitatively, when a stripe or a patch of WB was identified in a transverse section, the corresponding stripe or patch of WB was always found at the same location in the corresponding longitudinal section (please find in supplementary file 2 pictures of all the analyzed thin sections where WB areas, PFB areas and vascular canals were encircled).

Quantitatively, the proportion of WB is not significantly different in transverse and in longitudinal sections (i.e., the Wilcoxon signed-rank non-parametric paired test did not reject the null hypothesis suggesting that the proportion of WB is not significantly different in transverse and in longitudinal sections).

Considering that traditional bone histology is a destructive method, and that performing longitudinal sections (in addition to the transverse sections) involves the destruction of supplementary volume of material, we recommend a three steps workflow to efficiently establishing the proportion of WB in the diaphysis of an appendicular bone: (a) a careful analysis of transverse sections to propose hypotheses of the presence of WB when we observe the presence of canaliculi running radially from large irregular osteocyte lacunae, and general isotropy at tissue scale, but local anisotropy at cellular scale; (b) performing and analyzing longitudinal sections only in cases where an ambiguity remains; and (c) reanalyzing the corresponding transverse sections.

Author contributions

Figure 3 )

 3 Figure3) and two extinct taxa (Lystrosaurus sp. and Oudenodon bainii, Figure4). The

Faure

  long bone (they appear rounded in the transverse section; Figure3B, black arrow).

  , white arrowheads). Please note that in 11 the transverse section of Oudenodon vascular cavities are not as regularly circumferentially parallel to the periosteum as in Capreolus. The analysis of the six taxa described above, and of the remaining taxa (shown in supplementary file 2: Azendohsaurus laaroussii, Caiman crocodilus, Chelodina oblonga, Clepsydrops collettii, Lepus europaeus, Pelodiscus sinensis, Varanus exanthematicus and Varanus niloticus) reveals no incongruences between what is observed in the transverse sections and what is observed in the longitudinal ones. When the presence of a) general isotropy, b) a microlamellar arrangement in former osteoblast secretory territories, c) no alignment between osteocytes, and d) canaliculi running radially from large irregular osteocyte lacunae, suggested the presence of a patch or a stripe of WB in a transverse section, the analysis of the corresponding longitudinal section confirmed the presence of such stripe or patch of WB at the same relative location. Please find in supplementary file 2 pictures of all transverse and longitudinal sections analyzed in this study where WB areas, PFB areas and vascular canals were encircled.

Figure 1 .Figure 2 .

 12 Figure 1. Transverse thin sections of the femur of Capreolus capreolus observed in cross

Figure 3 .

 3 Figure 3. Transverse (A, B, E, F) and longitudinal (C, D, G, H) thin sections of the femora of

Figure 4 .

 4 Figure 4. Transverse (A, B, E, F) and longitudinal (C, D, G, H) thin femoral sections of

Acknowledgments

We thank Hayat Lamrous for having prepared the thin sections, Vivian de Buffrénil for sharing his material on Caiman crocodilus and Damien Germain, curator of the vertebrate hard tissues histological collection of the MNHN, for including the thin sections produced in this study in that collection. We thank Edina Prondvai and two anonymous reviewers for their constructive comments.

15

JC conceived and designed the study, MFB wrote a first draft of the manuscript and performed quantifications and statistical tests. All three authors analyzed thin sections and wrote the final version.