Mohammed Reda Zaki

David Hamani
email: david.hamani@unilim.fr

Maggy Dutreilh-Colas

Jean-René Duclere

Jonathan De Clermont-Gallerande

Tomokatsu Hayakawa

Olivier Masson

Philippe Thomas

Jean-René Duclère

Structural investigation of new

Keywords: Tellurite glasses, Glass structure, Raman spectroscopy, Optical linearity, Optical nonlinearity

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction.

Tellurium oxide (TeO 2 )-based glasses have been widely investigated as promising materials for specific optical applications, and this mostly due to their excellent nonlinear optical properties [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF][START_REF] Dimitrov | Linear and nonlinear optical properties of simple oxides. II[END_REF][START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF][START_REF] Jha | Review on structural, thermal, optical and spectroscopic properties of tellurium oxide based glasses for fibre optic and waveguide applications[END_REF]. Furthermore, such specific applications of tellurite glasses are related to their interesting thermal properties (low glass transition temperatures) and their capacity to be drawn into classical core/clad optical fibers [START_REF] Massera | Processing and characterization of core-clad tellurite glass preforms and fibers fabricated by rotational casting[END_REF], or even specialty fibers dedicated for the generation of broad supercontinuum [START_REF] Savelii | Suspended core tellurite glass optical fibers for infrared supercontinuum generation[END_REF]. Other potential applications for tellurite bulk glasses and fibers, still in connection with the large third order optical nonlinearity, will be Raman amplification [START_REF] Stegeman | Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica[END_REF][START_REF] O'donnell | Tellurite and fluorotellurite glasses for fiberoptic Raman amplifiers: glass characterization, optical properties, Raman gain, preliminary fiberization, and fiber characterization[END_REF][START_REF] Suzuki | Computational and Raman studies of phospho-tellurite glasses as ultrabroad Raman gain media[END_REF], ultra-fast optical switches or electro-optic modulators [START_REF] Shi-An | Femtosecond laser-induced transient grating in CeO 2 -doped 75TeO 2 -20Nb 2 O 5 -5ZnO glass[END_REF][START_REF] Gao | 100-nanosecond-level square-pulse generation in a ring cavity with a tellurite single-mode fiber[END_REF]. Finally, recent works also demonstrate the potentiality of rare-earth doped tellurites to be employed as laser fibers beyond 2 μm [START_REF] Muravyev | Dual-band Tm 3+ -doped tellurite fiber amplifier and laser at 1.9 μm and 2.3 μm[END_REF][START_REF] Denker | 2.3 μm laser action in Tm 3+ -doped tellurite glass fiber[END_REF].

The structural origin of this large optical nonlinearity of TeO 2 -based glasses derives mainly from the existence of the Te 4+ electronic lone pair [START_REF] Fargin | Optical non-linearity in oxide glasses[END_REF][START_REF] Jeansannetas | Glass structure and optical nonlinearities in thallium(I) tellurium(IV) oxide glasses[END_REF][START_REF] Suehara | Non-linear optical properties of TeO 2 -based glasses: ab initio static finite-field and time-dependent calculations[END_REF][START_REF] Suehara | Localized hyperpolarizability approach to the origin of nonlinear optical properties in TeO 2 -based materials[END_REF][START_REF] Roginskii | Comparative Analysis of the Electronic Structure and Nonlinear Optical Susceptibility of α-TeO 2 and β-TeO 3 Crystals[END_REF] and characteristic Te-O-Te bridges [START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF][START_REF] Mirgorodsky | Ab initio study of the nonlinear optical susceptibility of TeO 2 -based glasses[END_REF][START_REF] Soulis | Local molecular orbitals and hyper-susceptibility of TeO 2 glass[END_REF][START_REF] Smirnov | Quantum mechanical study of pre-dissociation enhancement of linear and nonlinear polarizabilities of (TeO 2 ) n oligomers as a key to understanding the remarkable dielectric properties of TeO 2 glasses[END_REF]. According to the literature, adding transition-metal oxides, such as niobium oxide Nb 2 O 5 or tungsten oxide WO 3 , may increase or at least maintain constant the linear and nonlinear optical indices of TeO 2 -based glasses [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF]. Contrarily, it has been shown that adding modifier oxides, such as alkali oxides, curtails such properties [START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF][START_REF] Berkaïne | Structure and dielectric properties of tellurium oxide-based materials[END_REF]. This transformation is commonly referred to as 'structural depolymerization' of the TeO 2 -rich network since it diminishes the network crosslinking density via breaking the Te-O-Te bridges. From the short-range structural viewpoint, it corresponds to the transformation of TeO 4 disphenoids into TeO 3 trigonal pyramids via TeO 3+1 distorted disphenoids [START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF][START_REF] Sekiya | Raman spectra of MO 1/2 -TeO 2 (M = Li, Na, K, Rb, Cs and Tl) glasses[END_REF][START_REF] Mclaughlin | The structure of alkali tellurite glasses[END_REF].

A great deal of effort has been devoted to the study of the binary (100-x)TeO 2 -xWO 3 glassy system uncovering its glass-forming domain with a WO 3 content ranging between 5 and 40 mol.% [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF][START_REF] Sekiya | Structural study of WO 3 -TeO 2 glasses[END_REF][START_REF] Shaltout | Structural studies of tungstatetellurite glasses by Raman spectroscopy and differential scanning calorimetry[END_REF][START_REF] Blanchandin | New investigations within the TeO 2 -WO 3 system: phase equilibrium diagram and glass crystallization[END_REF][START_REF] Charton | TeO 2 -WO 3 glasses: Infrared, XPS and XANES structural characterizations[END_REF][START_REF] Upender | Glass transition temperature-structural studies of tungstate tellurite glasses[END_REF][START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF]. It has been demonstrated that incorporating WO 3 in the TeO 2 -rich glass network progressively enhances both thermal and optical (linear and nonlinear) properties [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF][START_REF] Blanchandin | New investigations within the TeO 2 -WO 3 system: phase equilibrium diagram and glass crystallization[END_REF][START_REF] Shen | Tungsten-tellurite-a host glass for broadband EDFA[END_REF].

Several studies have been conducted on the binary (100-x)TeO 2 -xNbO 2.5 glassy system uncovering its glass-forming domain with a maximal NbO 2.5 content of 33.4-40 mol.% according to different authors [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF][START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF][START_REF] Berthereau | Nonlinear optical properties of some tellurium (IV) oxide glasses[END_REF][START_REF] Blanchandin | Equilibrium and non-equilibrium phase diagram within the TeO 2 -rich part of the TeO 2 -Nb 2 O 5 system[END_REF][START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF][START_REF] Villegas | Physical and structural properties of glasses in the TeO 2 -TiO 2 -Nb 2 O 5 system[END_REF][START_REF] Lin | Crystallization of TeO 2 -Nb 2 O 5 glasses and their network structural evolution[END_REF][START_REF] Hayakawa | Nonlinear optical properties and glass structure for MO-Nb 2 O 5 -TeO 2 (M=Zn, Mg, Ca, Sr, Ba) glasses[END_REF]. It has been shown that adding NbO 2.5 to the TeO 2 -rich glass network enhances both the linear and nonlinear optical properties [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF] and increases the thermal stability [START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF][START_REF] Berthereau | Nonlinear optical properties of some tellurium (IV) oxide glasses[END_REF] which is a crucial requirement in some optical glass manufacturing processes, e.g., optical fiber drawing [START_REF] Senthil Murugan | TeO 2 -BaO-SrO-Nb 2 O 5 glasses: a new glass system for waveguide devices applications[END_REF]. An improvement of the network reinforcement and mechanical strength was also reported [START_REF] Dai | The spectroscopic properties of Er 3+ -doped TeO 2 -Nb 2 O 5 glasses with high mechanical strength performance[END_REF]. The structural features of these glasses have been extensively investigated by various techniques: X-ray and neutron diffraction (see e.g., [START_REF] Hoppe | Structure of zinc and niobium tellurite glasses by neutron and x-ray diffraction[END_REF]), X-ray absorption spectroscopy [START_REF] Berthereau | Determination of local geometries around tellurium in TeO 2 -Nb 2 O 5 and TeO 2 -Al 2 O 3 oxide glasses by XANES and EXAFS: Investigation of electronic properties of evidenced oxygen clusters by ab initio calculations[END_REF], IR and Raman [START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF][START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF][START_REF] Saddeek | Thermal analysis and infrared study of Nb 2 O 5 -TeO 2 glasses[END_REF] spectroscopies. It is accepted among the previous investigators that adding NbO 2.5 leads to a structural depolymerization [START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF][START_REF] Lin | Crystallization of TeO 2 -Nb 2 O 5 glasses and their network structural evolution[END_REF][START_REF] Berthereau | Determination of local geometries around tellurium in TeO 2 -Nb 2 O 5 and TeO 2 -Al 2 O 3 oxide glasses by XANES and EXAFS: Investigation of electronic properties of evidenced oxygen clusters by ab initio calculations[END_REF]. According to Berthereau et al. [START_REF] Berthereau | Determination of local geometries around tellurium in TeO 2 -Nb 2 O 5 and TeO 2 -Al 2 O 3 oxide glasses by XANES and EXAFS: Investigation of electronic properties of evidenced oxygen clusters by ab initio calculations[END_REF], the predominant units in (100-x)TeO 2 -xNbO 2.5 glasses (x = 9.5, 18.2, 26.1, 33.4 mol.%) are TeO 4 and TeO 3+1 and the proportion of the latter increases upon adding NbO 2.5 as suggested from the extended X-ray absorption fine structure (EXAFS) results. Hoppe et al. [START_REF] Hoppe | Structure of zinc and niobium tellurite glasses by neutron and x-ray diffraction[END_REF] investigated the structure of (100-x)TeO 2 -xNbO 2.5 (x = 11.4, 18.2 and 30.5 mol.%) glasses and argued that a structural transition from network-modifying (x ≤ 18.2 mol.%) to network-forming behavior (x > 18.2 mol.%) takes place upon adding NbO 2.5 with the formation of Nb-O-Nb bridges. By means of Raman spectroscopy, Soulis et al. [START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF] argued that the bond networks of (100-x)TeO 2 - [START_REF] Lin | Crystallization of TeO 2 -Nb 2 O 5 glasses and their network structural evolution[END_REF] and Kaur et al. [START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF] agree with the previously described role of NbO 2.5 in reducing the connectivity of Te-O-Te bond network by transforming the TeO 4 into TeO 3+1 and TeO 3 units. This work is a part of an investigation on TeO 2 -based glasses containing two transition-metal oxides. After dealing with the (100-x-y)TeO 2 -xTiO 2 -yWO 3 glassy system [START_REF] Zaki | Synthesis, thermal, structural and linear optical properties of new glasses within the TeO 2 -TiO 2 -WO 3 system[END_REF], we have embarked on investigating the (100-x-y)TeO 2 -xNbO 2.5 -yWO 3 system (labeled TNxWy). To the best of our knowledge, aside from few investigations on the specific compositions given below, there is no reported systematic study within this ternary glass system. Carreaud et al. [START_REF] Carreaud | Lasing effects in new Nd 3+ -doped TeO 2 -Nb 2 O 5 -WO 3 bulk glasses[END_REF] and Dai et al. [START_REF] Dai | TeO 2 -based glasses containing Nb 2 O 5 , TiO 2 , and WO 3 for discrete Raman fiber amplification[END_REF] recorded the Raman spectra of 75TeO 2 -20NbO 2.5 -5WO 3 and 72TeO 2 -18NbO 2.5 -10WO 3 glass compositions respectively along with their thermal and linear optical properties; Muñoz-Martín [START_REF] Munoz-Martín | TeO 2 -based film glasses for photonic applications: structural and optical properties[END_REF] measured the linear and nonlinear optical properties of the 80TeO 2 -5Nb 2 O 5 -15WO 3 glass composition. In addition, Er 3+ and Yb 3+ doped TeO 2 -Nb 2 O 5 -WO 3 glass compositions have been investigated as potential candidate materials for broadband amplifiers [START_REF] Xu | Broadband 1.5-μm emission of erbium-doped TeO 2 -WO 3 -Nb 2 O 5 glass for potential WDM amplifier[END_REF][START_REF] Wang | Investigation of thermal stability and spectroscopic properties in Er 3+ /Yb 3+ codoped niobic tungsten tellurite glasses[END_REF]. A high linear optical response was measured from these glasses with refractive indices in the order of ~2.1.

The aim of the present paper is to report, for the first time, the glass-forming domain within the TNxWy system and the measured properties from the prepared glasses, namely, their thermal characteristics, structural features by means of Raman spectroscopy, linear optical properties using UV-Vis-NIR spectroscopy and spectroscopic ellipsometry, and nonlinear optical response from Z-scan measurements. The focus is laid on the evolution of these properties as a function of NbO 2.5 and WO 3 contents.

Experimental details.

New glasses were prepared within the ternary TNxWy system by the conventional meltingquenching technique using α-TeO 2 (99.99%), Nb 2 O 5 (99.99%) and WO 3 (99.8%) from Alfa Aesar. In appropriate proportions, the raw dried powders have been ground for 40 min using agate mortar and pestle, and melted in Pt crucibles at 850 °C for 1 h. Under these experimental conditions, seventeen glass samples in the form of pellets were prepared from batches weighing 2 g, stirred three times during melting and quenched into a brass ring put over a preheated brass block at 150 °C. After cooling down to room temperature from 150 °C, the pellets were systematically annealed at 15 °C below their glass transition temperatures for 12 h at heating/cooling rates of 2 °C/min in order to release the mechanical stresses resulting from the thermal quenching. Serving as a reference sample in the structural study of TNxWy glasses, we have prepared TeO 2 glass by the fast-quenching of a pure TeO 2 melt from 850 °C down to approximately -11 °C (using an ice bath containing NaCl and ethanol) after 1 h spent inside the furnace during which the melt was stirred three times.

The amorphous state of the samples was checked by means of powder X-ray diffraction using Bruker D8 Advance diffractometer with Bragg-Brentano geometry (Cu K α1 wavelength of 1.5406 Å, 2θ range of 10-70° with a step of 0.02° and 1 s per step). The glass samples were analyzed by energy dispersive X-ray microanalysis (EDS) using a Quanta FEG-450 scanning electron microscope. The elemental analysis results suggested a good agreement between the experimental and theoretical glass compositions. The characteristic glass transition (T g ) and onset crystallization (T O ) temperatures of the glass samples were measured by heat flux differential scanning calorimetry (DSC) using NETZSCH STA 449 F3 Jupiter equipment.

The measurements were performed on glass fragments of about 25 ± 5 mg using Pt pans under N 2 atmosphere between room temperature and 720 °C at a heating rate of 10 °C/min. Densities of glass powder samples weighing 150 ± 20 mg were measured by helium pycnometry using Accupyc II 1340 Micromeritics pycnometer.

The Raman spectra were recorded at 514.5 nm and a laser power of 30 mW using T64000 Horiba Jobin-Yvon spectrophotometer operating in triple subtractive configuration (1800 grooves/mm) and equipped with a CCD detector. The objective lens x50LWD was used to record the spectra along the 15-1100 cm -1 wavenumber range with a spectral resolution of 2.5 cm -1 and acquisition time of 10 s. Three spectra from each sample have been recorded from three different spots. No baseline correction treatments were performed on any of the measured spectra, and the as-recorded intensities of each spectrum were divided by its total area. Using Focus 1.0 program [START_REF] Sousa Meneses | Software utility for the creation of optical function (FOCUS)[END_REF], the total-area averaged Raman spectra were decomposed in the entire wavenumber range (15-1100 cm -1 ) using a log-normal distribution for the boson peak (labeled band A hereafter) and twelve Gaussian functions for the rest (labeled bands B-M). The recomposed spectra match well with the experimental ones, with chi-square reliability values less than 0.05.

The optical transmission of TNxWy glasses was evaluated by measuring the UV-Vis-NIR spectra from double side polished pellets of 1.44-1.47 mm in thickness in the 300-3300 nm range using the Varian Cary 5000 spectrophotometer. From the same samples, the refractive indices were recorded by spectroscopic ellipsometry using Horiba Jobin-Yvon UVISEL ellipsometer with a fixed 60° incidence angle.

The third-order nonlinear susceptibilities χ (3) were measured from TNxWy double-side polished glasses employing the Z-scan technique, and using a comparative route in respect with the data collected for a reference fused silica plate [START_REF] Duclère | Third order nonlinear optical properties of a paratellurite single crystal[END_REF]. Pulses from regenerative Ti:sapphire laser (Spectra Physics, Hurricane) at 800 nm were used at a repetition rate of 1 kHz and with ~90 fs pulse duration. A lens (f = 200 mm) was positioned along the optical path (Z axis), and the glass samples were moved forward and backward from the focal point (Z = 0 mm), namely along the Z range between -25 mm and +25 mm at intervals of 0.5 mm. At each step, the optical transmittance was measured with the optical power meter system (Newport 2930-C/818-SL silicon photodiodes in the close and open configurations [START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF]). The Z-scan measurement from each glass sample was repeated three times. Each consists in four measurements: two at 250 nW and two at 2 nW. The measured value from pure SiO 2 glass (≈0.15 *10 -13 esu at 800 nm reported by Milam [START_REF] Milam | Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica[END_REF]) was considered in order to extract the χ (3) values for TNxWy glasses. For a reliable comparison with other TeO 2 -based glasses in the literature, we had to adjust the state-of-the-art values (those extracted by considering a value of 0.28 *10 -13 esu at 1.9 µm reported by Kim et al. [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF]) by dividing them by 1.87 which is the factor between the values reported by Kim et al. [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF] and Milam [START_REF] Milam | Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica[END_REF] respectively. Such argumentation is developed in detail in [START_REF] Duclère | Third order nonlinear optical properties of a paratellurite single crystal[END_REF]. Applying this factor to the pure TeO 2 glass leads to an adjusted χ (3) value of 7.54 *10 -13 esu based on the reported value of 14.10 *10 -13 esu [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF]. We have obtained the real part of the third-order nonlinear susceptibility from TNxWy glasses; more details can be found in the literature (e.g., [START_REF] Linda | Optical properties of tellurite glasses elaborated within the TeO 2 -Tl 2 O-Ag 2 O and TeO 2 -ZnO-Ag 2 O ternary systems[END_REF]) and lead to the following expression:

( With Δϕ corresponding to self-phase modulation which is proportional to the difference ΔT p-v (ΔT p-v ≈ 0.406 Δϕ for small apertures [START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF]) between the maximum T p (p for peak) transmittance and the minimum T v (v for valley) transmittance. I 0 represents the intensity of the incident laser beam, L eff the effective thickness of the sample and n the linear refractive index measured by spectroscopic ellipsometry.

3. Results and discussion.

Glass-forming domain

The amorphous state of TNxWy samples was analyzed using X-ray powder diffraction in order to determine the glass-forming domain given in Fig. 1(a)). The longest compositional lines extend from x = 5 to 25 mol.% in NbO 2.5 and from y = 5 to 25 mol.% in WO 3 . In total, seventeen melt compositions have yielded transparent yellowish glasses that shifted to honey-brown with increasing WO 3 molar content and remained practically unchanged upon adding NbO 2.5 (cf. Fig. 1(b)). In partially crystallized TNxW30 samples, we detected the presence of WO 2.83 (or W 6 O 17 ) crystals [START_REF] Sundberg | The crystal and defect structures of W 25 O 73 , a member of the homologous series W n O 3n-2[END_REF]. At relatively high NbO 2.5 content, crystals of Nb 6 TeO 17 [56] are detected in TN15W25, TN20W15, TN25W10 and TN30W5 samples.

Density and thermal properties

In general, the measured densities ( min = 4.51 g.cm -3 and  max = 5.15 g.cm -3 ) increase with the addition of WO 3 and slightly decrease with larger amounts of NbO 2.5 (cf. Table 1). The density increase extent upon adding WO 3 at constant NbO 2.5 content varies from one series of samples to the other. For instance, an increase by ~10% is recorded from TN5W5 (4.67 g.cm -3 ) to TN5W25 (5.15 g.cm -3 ) and by ~4% from TN10W5 (4.87 g.cm -3 ) to TN10W25

(5.06 g.cm -3 ). On the other hand, the density's compositional dependence upon adding NbO 2.5

shows a peculiar behavior in TeO 2 -rich compositions as it first increases for instance by ~4% from TN5W5 (4.67 g.cm -3 ) to TN10W5 (4.87 g.cm -3 ) before decreasing by ~7% to TN25W5 (4.51 g.cm -3 ). This unexpected behavior in the TeO 2 -richest compositions could be explained by their positions at the boundary of the glass-forming domain. In general, it can be argued that the compositional dependence of density follows the additive density rule: densities of raw oxides NbO 2.5 , TeO 2 and WO 3 are respectively 4.55, 6.13 and 7.16 g.cm -3 . Thus, we assign the glass density increase upon adding WO 3 to the higher molar mass of WO 3 (231.8

g.mol -1 ) compared to that of TeO 2 (159.6 g.mol -1 ); and the decrease upon adding NbO 2.5 from 10 to 25 mol.% to its lower molar mass of 132.9 g.mol -1 .

The thermal properties of TNxWy glasses were measured to evaluate the compositional dependence of their glass transition temperatures T g and thermal stabilities ΔT (cf. Table 1 for TNxWy glasses and Fig. 2 for TNxW5 glasses). The T g increases linearly upon adding either The recorded sequence of exothermic peaks from the DSC curves of TNxW5 glasses (Fig. 2) is in relatively good agreement with the binary TeO 2 -NbO 2.5 glasses (cf. Fig. 3 in [START_REF] Blanchandin | Equilibrium and non-equilibrium phase diagram within the TeO 2 -rich part of the TeO 2 -Nb 2 O 5 system[END_REF]); the exothermic peaks of the former are broader, probably due to a more disordered glass network, manifested by the presence of additional W-O coordination polyhedra. Therefore, the crystallizing phases from TNxW5 glasses can be assigned in agreement with those crystallizing from the binary glasses, i.e., δ-, γ-and α-TeO 2 and then Nb 2 Te 4 O 13 depending on the NbO 2.5 content.

Structural properties

The recorded spectra from TNxWy glasses are jointly presented in Fig. 3. Since the same structural evolutions are observed from TNxWy (y = 5, 10, 15, 20 and 25 mol.%) sets of samples, we suggest to focus on the set of TNxW5 to highlight the effect of adding NbO 2.5

since it corresponds to the set with the lowest WO 3 influence. For a more accurate structural analysis, we used the conventional spectral decomposition technique based on the addition of bands of which the position (wavenumber), width (more precisely the full-width at half maximum, FWHM) and intensity can be either assigned fixed values or left free (unconstrained). In wavenumber regions where band shift and/or broadening are observed with increasing NbO 2.5 (or WO 3 ) content, we kept the introduced function's wavenumber and/or FWHM respectively parameter-free. Thus, the bands A, H and 2 for a detailed band assignment). The basis of the vibrational mode assignment of distorted WO 6 octahedra is a bilateral analysis of the vibrational (Raman spectra) vs.

structural features that we conducted on a large number of tungsten-containing oxides (metal tungstates for the most part). A similar approach has been previously undertaken on few tungstates by Sekiya et al. [START_REF] Sekiya | Structural study of WO 3 -TeO 2 glasses[END_REF]. The obtained decomposition results (calculated parameters for the inserted bands) were used to evaluate the areas of each band in all of the decomposed spectra. Then, the normalized intensity of each band was calculated by dividing the band area by the molar content(s) of the oxide(s) of which the constituent ionic species are responsible for that vibration.

Structural effect of adding NbO 2.5

The recorded Raman spectra from TNxW5 glasses are provided in Fig. 4. At first glance, one can notice the important change in the ~535-725 cm -1 range with a noticeable intensity increase of the bands G and H from TN5W5 to TN25W5. Slight increasing of Raman intensity is observed within ~200-400 cm -1 and ~850-950 cm -1 regions. On the other hand, in the low-wavenumber region (< 100 cm -1 ), an intensity decrease of the boson peak is recorded along with an insignificant red-shift of ~6 cm -1 from TN5W5 to TN25W5. As explained in the introduction of section 3. Let us now focus on the decomposition results as a function of NbO 2.5 content from the midto high-wavenumber range 400-1000 cm -1 .

 In the 400-550 cm -1 region:

As can be seen in the inset of [START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF]). 2. Wavenumbers and vibrational assignments of the inserted bands. Raman bands arising from TeO 2 network and their assignments are highlighted in bold typeface. In the spectral decomposition process, the wavenumbers of A, F, H, L and M bands were unconstrained and are given herein as wavenumber ranges from the set of TNxW5 glasses with increasing x.

 In the 550-800 cm -1 region:

The normalized intensities of bands G and H increase by ~20% and ~45% respectively upon adding NbO 2.5 (Fig. 5). To appropriately interpret the structural trend based on the evolution of these two bands, it is important to consider the shape of the corresponding Raman band (within the range of 535-725 cm -1 , cf. Fig. 3). A simple visual analysis indicates that its intensity increases upon adding NbO 2.5 with no apparent band shift. From the viewpoint of the TeO 2 -rich network in TNxW5 glasses, the fact that this large band does not red-shift might renounce any significant structural depolymerization. In the opposite case, i.e., when a modifier oxide such as Tl 2 O with a weak modifier cation Tl + is added to the TeO 2 -rich network, a significant red-shift of this band is observed due to the simultaneous intensity decrease of the Raman band assigned to Te-O bond vibrations in TeO 4 units (in the ~607-772 cm -1 range) and increase of the one assigned to Te-O bond vibrations in TeO 3 units (in the ~660-715 cm -1 range) [START_REF] Noguera | Dynamics and crystal chemistry of tellurites. II. Composition-and temperaturedependence of the Raman spectra of x(Tl 2 O)+(1-x)TeO 2 glasses: evidence for a phase separation?[END_REF]. It is important to note that the stretching vibrations of Nb-O-Nb bridges are also observed in the 535-725 cm -1 range (cf. Raman spectrum of H-Nb 2 O 5 in Fig. 3). Regarding the evolutions of bands I and J, their normalized intensities show marginal and stronger upward (increase by ~23%) trends respectively (Fig. 5). Therefore, we argue that the From the evolution of the Nb-O-Nb bond network, increasing the NbO 2.5 content from 5 to 25 mol.% results in an increase of the number of NbO 2.5 -rich regions until the crystallization of Nb 6 TeO 17 [56] at 30 mol.% of NbO 2.5 . The structure of this compound has not been determined yet; however, given the high NbO 2.5 :TeO 2 ratio (6:1), one can predict the predominant contribution of Nb-O-Nb bridges in its crystal lattice. This shifting behavior of NbO 2.5 from a network modifier towards a network former as manifested by the presence of NbO 2.5 -rich regions is in agreement with the obtained results from TeO 2 -NbO 2.5 glasses by Hoppe et al. [START_REF] Hoppe | Structure of zinc and niobium tellurite glasses by neutron and x-ray diffraction[END_REF].

 In the 800-1000 cm -1 region:

It should be noted that the intensity of the "shoulder" centered at ~880 cm -1 (cf. Fig. 3) which is due to stretching vibrations of the shortest (terminal) Nb-O bonds increases but very moderately with NbO 2.5 . This means that its expected normalized intensity must rather decrease since adding twice more NbO 2.5 (e.g., from 5 to 10 mol.%) does not yield twice more intense response in this region. This suggests that less and less terminal Nb-O bonds exist at the expense of Nb-O-Nb (bands G and H) and Te-O-Nb (band E) bridges. This is in total agreement with the previously discussed evolution of these two varieties of bridges, i.e., their number increase upon adding NbO 2.5 . We omitted in Fig. 5 the evolution of the normalized intensity of this shoulder centered at ~880 cm -1 for the two following reasons: (i) the shoulder is strongly overlapping with the surrounding bands L and M, and (ii) due to the influence of the band M (also due to the asymmetric stretching vibrations of W-O bonds) of which the normalized intensity changes as a function of the molar ratio of TeO 2 to WO 3 [START_REF] Zaki | Synthesis, thermal, structural and linear optical properties of new glasses within the TeO 2 -TiO 2 -WO 3 system[END_REF].

To sum up, we argue that the structural effect of NbO 2.

Structural effect of adding WO 3

The recorded Raman spectra of TNxWy glasses with increasing WO 3 content are presented in Fig. 7. The evolving band features are in agreement with the reported studies on TeO 2 -based glasses containing WO 3 by Raman spectroscopy [START_REF] Sekiya | Structural study of WO 3 -TeO 2 glasses[END_REF][START_REF] Kaur | Optical, thermal, and structural properties of Nb 2 O 5 -TeO 2 and WO 3 -TeO 2 glasses[END_REF][START_REF] Upender | Structure, physical and thermal properties of WO 3 -GeO 2 -TeO 2 glasses[END_REF], i.e., three additional bands at ~360, ~860 and ~925 cm -1 appear at the Raman spectra and increase in intensity upon adding Lastly, regarding the evolution of the band A (boson peak), the position of its maximum intensity insignificantly red-shifts accompanied with an intensity decrease with addition of NbO 2.5 or WO 3 contents (Fig. 3 and Fig. 7). According to literature [START_REF] Sokolov | Medium-range order in glasses: Comparison of Raman and diffraction measurements[END_REF][START_REF] Kalampounias | A temperature dependence Raman study of the 0.1 Nb 2 O 5 -0.9 TeO 2 glass-forming system[END_REF], the evolution of boson peak's position and intensity in TNxWy glasses could suggest a slight crosslinking density increase in the glass network at the medium-range scale. This behavior is in agreement with the continuous increase of the glass transition temperature upon adding NbO 2.5 or WO 3 . We recorded the optical transmission spectra from TNxWy glass pellets over a wide wavelength range extending from 300 to 3300 nm (Fig. 9). The optical transmission spectra of 16 out of 17 glass samples show a transparency over 75% in the 800-2600 nm range. The exception is the sample TN5W5 showing a slightly lower transparency of ~73%, which might be due to its peculiar composition (richest in TeO 2 ) at the boundary of the glass-forming domain. The absorption band onsetting at 2800 nm corresponds to the stretching mode of bound hydroxyl groups (R-OH), and symmetric and asymmetric stretching modes of water molecules [START_REF] Efimov | Water-related bands in the IR absorption spectra of silicate glasses[END_REF]. The transmission percentage is neither enhanced nor reduced upon adding NbO 2.5 but rather fluctuates within a relatively narrow range of less than 2% (Fig. 9). This is also the case with increasing WO 3 content (cf. Fig. 10 for TN5Wy glasses). The linear refractive indices were extracted from the optical transmission data at λ = 1.5 µm using the following equation: T = 2n/(n 2 +1). The refractive indices n 1.5 are listed in Table 1.

Optical properties

Generally, the obtained results suggest a practically constant behavior of the refractive index upon adding either NbO 2.5 or WO 3 with high values ranging approximately from 2.06 to 2.12.

It should be stressed that because of the Fresnel reflection at the air-glass interface, the above equation slightly underestimates the actual refractive index value, which will then be provided from ellipsometric measurements. The UV absorption edge slightly shifts towards longer wavelengths within the range of 410-415 nm upon adding NbO 2.5 in TNxW5 glasses (Fig. 9), implying a gradual slight decrease of the optical band gap energy E g . Upon adding WO 3 (Fig. 10), a stronger red-shift is observed within a larger wavelength range (400-437 nm). The color evolution of glasses (cf. section 3.1) is in agreement with the noticed shift of the absorption edge.

Both the optical band gap E g and Urbach E U energies were extracted from the UV absorption edges of TNxWy glasses. Based on the wavelength-dependence of the approximate absorption coefficient α (estimated using the expression α(λ) = (1/d) ln(T max /T(λ)), where T is the transmission percentage and d is the sample thickness), we plotted (αhν) ½ versus the incident photon energy hν (commonly known as Tauc plot) to estimate E g (Fig. 11). The E g values lie in the range of 2.77-2.92 eV (Table 1 The extracted values of Urbach energy E U lie in the range 0.104-0.114 eV for all the compositions. E U remains fairly stable with increasing WO 3 content (e.g., 0.109 eV in TN5Wy glasses). However, a slight decrease from 0.114 to 0.105 eV is observed upon adding NbO 2.5 from TN5W5 to TN25W5. E U is characteristic of the width of the band-tails thus estimating the density of localized states [START_REF] Urbach | The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids[END_REF]. A highly disordered glass network is characterized by a higher density of localized states and thus having a high E U value. These values are very close to those reported in literature for NbO 2.5 -and WO 3 -containing TeO 2based glasses (ranging between 0.096 and 0.114 eV, see e.g., [START_REF] Munoz-Martín | TeO 2 -based film glasses for photonic applications: structural and optical properties[END_REF]). Therefore, it can be argued that adding NbO 2.5 might slightly lessen the overall structural disorder of the glass network.

Refractive index dispersion by spectroscopic ellipsometry

We measured the wavelength-dispersion of the refractive index from TNxWy glass pellets in the range of 350-830 nm (cf. Fig. 12 for TNxW5 glasses), and derived the refractive indices n ∞ (Table 1) extrapolated to infinite wavelength using Sellmeier's dispersion formula [START_REF] Sellmeier | Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen[END_REF][START_REF] Ghosh | Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses[END_REF]: n = (A + B/(1-C/λ 2 ) + D/(1-E/λ 2 )) 1/2 where A-E are fitting constants specific to each sample.

An excellent fitting quality was achieved as demonstrated by the R 2 coefficients ranging between 0.9970 and 0.9999. The studied glasses collectively exhibit high n ∞ indices with an average of ~2.13 (n ∞(min) = 2.12 and n ∞(max) = 2.15) which is ~1.5 times higher than the refractive index of SiO 2 glass (1.439 at 1.9 µm [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF]) and practically equal to that of TeO 2 glass (2.121 at 1.9 µm [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF]).

The dependence of n ∞ on the WO 3 content suggests a constant behavior with an average value of ~2.14 in TNxW5 and TNxW25 glass series. Likewise, it seems that n ∞ remains practically constant upon adding NbO

Nonlinear optical properties

As described in the experimental section, the third-order nonlinear susceptibilities χ (3) have been measured using the Z-scan technique at λ = 800 nm. From the measured Z-scan transmittance curves, the extracted peak-valley transmittance change ΔT p-v (example of TN15W20 in Fig. 13) is used to derive the χ (3) values from the TNxWy glass pellets (cf. Table 1, with χ (3) min = 4.75 *10 -13 esu and χ (3) max = 6.38 *10 -13 esu). Interestingly, the average χ (3) value of 5.48 *10 -13 esu among TNxWy glasses is ~37 times higher than the χ (3) value of SiO 2 glass (0.15 *10 -13 esu [START_REF] Milam | Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica[END_REF]) and slightly lower than that of pure TeO 2 glass (7.54 *10 -13 esu). The compositional dependence of χ (3) values in TNxWy glasses upon adding NbO 2.5 or WO 3 can be found in Fig. 14. Their evolution upon adding NbO 2.5 suggests a fairly constant behavior from ~5.2 *10 -13 esu in TN5Wy to ~5.1 *10 -13 esu in TN25Wy. Likewise, adding WO 3 seems to maintain the χ (3) values practically stable. It is worthwhile to mention that the binary (100-x)TeO 2 -xNbO 2.5 glasses exhibit higher χ (3) values ranging from 7.540 *10 -13 esu (x = 10 mol.%) to 9.037 *10 -13 esu (x = 30 mol.%) [START_REF] Kim | Nonlinear optical properties of TeO 2 -based glasses: MO x -TeO 2 (M= Sc, Ti, V, Nb, Mo, Ta, and W) binary glasses[END_REF].

The overall evolution of the nonlinear response of TNxWy glasses upon substituting TeO 2 with either NbO 2.5 or WO 3 is shown in Fig. 15. This positive contribution could be explained by the possible influence of empty d-orbitals of each of Nb 5+ and W 6+ cations via virtual electronic transitions to d-orbitals and to the conduction band sp-orbitals as reported by Lines [START_REF] Lines | Influence of d orbitals on the nonlinear optical response of transparent transition-metal oxides[END_REF]. Nevertheless, it is very important to keep in mind that these derived values and discussed evolutions could be tempered considering the significant error bars of ~20% in average for the χ (3) responses: in concrete terms, the χ (3) evolutions could be regarded as practically steady as well. Generally, the evolution of the nonlinear optical performance of TNxWy glasses is consistent with the structural interpretations established in section 3.3.1 suggesting that only relatively slight modifications occur throughout the glass network with addition of either NbO 2.5 or WO 3 . The steady evolution of χ (3) values upon adding NbO 2.5 or WO 3 highly suggests the absence of any striking structural depolymerization of the Te-O-Te bond network.

Conclusions.

A systematic study within the (100-x-y)TeO 2 -xNbO 2.5 -yWO [START_REF] El-Mallawany | Tellurite glasses handbook: physical properties and data[END_REF]  Adding WO 3 results, at low WO 3 contents, in uniformly dispersed WO 6 octahedra throughout the glass network, and at higher WO 3 contents, in amorphous "WO 3 -rich" regions that continuously grow prior to the crystallization of WO 2.83 in TNxW30 samples. This idea is in agreement with the one proposed by Sekiya et al. [START_REF] Sekiya | Structural study of WO 3 -TeO 2 glasses[END_REF] and recently highlighted in the TeO 2 -TiO 2 -WO 3 glassy system [START_REF] Zaki | Synthesis, thermal, structural and linear optical properties of new glasses within the TeO 2 -TiO 2 -WO 3 system[END_REF].

The revealed structural properties are consistently correlated to the measured optical (linear and nonlinear) properties. The studied TNxWy glasses exhibit high linear refractive indices (n ∞(min) = 2.12 and n ∞(max) = 2.15) with an average n ∞ of 2.13 which is ~1.5 times higher than the refractive index of SiO 2 glass. It is found that the measured n ∞ values remain practically constant upon adding either NbO 2.5 or WO 3 .

The extracted third-order nonlinear susceptibilities χ (3) values are very high (χ (3) min = 4.75 *10 -13 esu and χ (3) max = 6.38 *10 -13 esu) with an average of 5.48 *10 -13 esu that is ~37 times stronger than the reported χ (3) value for SiO 2 glass. Moreover, they are found to remain practically steady with addition of NbO 2.5 and WO 3 : from TN5Wy (5.22 *10 -13 esu) to TN25Wy (5.05 *10 -13 esu), and from TNxW5 (5.40 *10 -13 esu) to TNxW25 (5.59 *10 -13 esu)

respectively. Generally, the extracted χ (3) values from TNxWy glasses are higher than those reported from other TeO 2 -based systems and particularly those where a significant structural depolymerization takes place (e.g., ZnO-or alkali-containing glasses).

xNbO 2 .

 2 5 (x = 9.5, 18.2, 26.1, 33.4 and 40 mol.%) glasses contain three types of linkages, namely Te-O-Te, Te-O-Nb and Nb-O-Nb bridges. More recently, two more studies by Lin et al.

Fig. 1 .

 1 Fig. 1. (a) Glass-forming domain obtained in the (100-x-y)TeO 2 -xNbO 2.5 -yWO 3 system (labeled TNxWy) surrounded by the yellow frame. Blue and green colored squares and spots correspond to partially crystallized samples in WO 2.83 and Nb 6 TeO 17 respectively. (b) Photograph of the obtained glass pellets in their polished state.

NbO 2 .

 2 [START_REF] Massera | Processing and characterization of core-clad tellurite glass preforms and fibers fabricated by rotational casting[END_REF] or WO 3 (T g(min) = 333 °C and T g(max) = 403 °C). It increases by ~21% from TN5W5 (333 °C) to TN25W5 (403 °C) and by ~15% from TN5W5 to TN5W25 (381 °C). We could assign the T g increase predominantly to the fact that W-O and Nb-O bonds have higher dissociation energies compared to Te-O bonds, namely, 720, 726.5 and 377 kJ.mol -1 respectively[START_REF] Luo | Comprehensive handbook of chemical bond energies[END_REF].It is worth pointing out that the thermal stabilities (T= T O -T g ) of TNxWy glasses which reflect the ability of the glass network to resist against devitrification upon heating above T g , are fairly moderate (ΔT min = 45 °C and ΔT max = 70 °C) with an average of ~60 °C. It appears that adding NbO 2.5 or WO 3 does not significantly impact on ΔT from one TNxWy composition to another. By comparison, the thermal stabilities of TNxW5 samples are relatively lower than those reported for binary TeO 2 -NbO 2.5 glasses with values ranging between ~43 and ~98 °C according to Blanchandin et al.[START_REF] Blanchandin | Equilibrium and non-equilibrium phase diagram within the TeO 2 -rich part of the TeO 2 -Nb 2 O 5 system[END_REF].

Fig. 2 .

 2 Fig. 2. DSC curves of TNxW5 glasses with the glass transition T g and onset crystallization T O temperatures given in bold and non-bold typefaces respectively.

Fig. 3 .

 3 Fig. 3. Evolution of total-area averaged Raman spectra of TNxWy glasses as a function of NbO 2.5 content. The low-wavenumber (boson peak) and mid-to high-wavenumber regions are supplied apart for more clarity. The Raman spectrum of H-Nb 2 O 5 is reproduced from Fig. 34 in [34].

M

  were fully unconstrained, while bands F and L were introduced with fixed FWHM values and bands D and J with fixed wavenumbers values. The remaining bands B, C, E, G, I and K were introduced with fixed wavenumber and FWHM values. The origins of bands associated with vibrations of Te-O bonds (bands E-J) are supported by pioneer works on the vibrational and structural properties of the three TeO 2 polymorphs (α [58], β [58] and γ [59]). The origins of the bands involving vibrations of Nb-O bonds (bands E, G, H and M) are based on the structural studies of Nb 2 O 5 and binary TeO 2 -Nb 2 O 5 crystals (cf. Table

Fig. 4 .

 4 Fig. 4. Total-area averaged Raman spectra of TNxW5 glasses. The labels A-M correspond to the inserted bands for the spectral decomposition. Inset: zoom of the region 375-540 cm -1 .

3 ,

 3 we have calculated, for each TNxWy composition, the normalized intensities of bands E, G and H by dividing their areas by the sum of TeO 2 and NbO 2.5 molar contents; those of bands F, I and J by dividing their areas by TeO 2 content. The compositional dependence of the normalized intensities in TNxW5 glasses is plotted in Fig. 5. Similar band evolutions are observed in other sets of TNxWy samples at constant WO 3 content and increasing NbO 2.5 content.

Fig. 4 ,

 4 the intensities of the two bands E and F seem to evolve in opposite directions. It can be seen from Fig. 5 that while the normalized intensity of band E slightly increases by ~10%, the band F remains practically constant. Taking into account the compositional evolutions of the two bands E and F, we argue that continuous adding of NbO 2.5 results in an increase of the number of Te-O-Nb and/or nearly symmetric Te-O-Te bridges (as in γ-TeO 2 ).

F 1  9  5 

 195 Asymmetric stretching vibrations in nearly symmetric Te-O-Te bridges (as in γ-TeO 2 )[START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ-and δ-phases[END_REF][START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF]. Stretching vibrations of highly asymmetric and almost terminalTe-O---Nb linkages[START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF].  Stretching vibrations of Nb-O in Nb-O-Nb bridges (as in H-Nb 2 O 5[START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF]). Asymmetric stretching vibrations in asymmetric Te-O-Te bridges[START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ-and δ-phases[END_REF][START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF]. Stretching vibrations of highly asymmetric and almost terminalTe-O---Nb linkages[START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF].  Stretching vibrations of Nb-O in Nb-O-Nb bridges (as in H-Nb 2 O 5[START_REF] Soulis | Structure et propriétés optiques non linéaires des verres à base d'oxyde de tellure : approche cristallochimique et calculs ab-initio[END_REF]). Asymmetric stretching vibrations in asymmetric Te-O-Te bridges[START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ-and δ-phases[END_REF][START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF].  Symmetric stretching vibrations in W-O-W bridges (as in -WO 3 )[START_REF] Daniel | Infrared and Raman study of WO 3 tungsten trioxides and WO 3 , xH 2 O tungsten trioxide hydrates[END_REF].J 772 (fixed) Asymmetric stretching of essentially covalent Teeq O bonds[START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ-and δ-phases[END_REF][START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF].K 820(fixed)  Asymmetric stretching vibrations in W-O-W bridges (as in -WO 3 ) [62]. L 852.3 -845.Stretching vibrations of W-O bonds in W-O-W bridges. M 920.4 -898.Asymmetric stretching vibrations of W-O bonds [62].  Stretching vibrations of the shortest Nb-O bonds [34]. Table

:Fig. 5 .

 5 Fig. 5. Compositional dependence of the normalized intensities of inserted bands for spectral decomposition of TNxW5 glasses. The areas of bands E, G and H were divided by the sum of TeO 2 and NbO 2.5 contents; those of bands F, I and J by the TeO 2 content.

I n c r e a s e b y 8 . 8 %

 8 evolution of bands G-J probably suggests both a slight structural depolymerization of the Te-O-Te bond network and/or increasing number of Nb-O-Nb and/or Te-O-Nb bridges. It is relevant to assess the evolution of Raman band ratios corresponding to the two ultimate TeO 4 and TeO 3 structural units. In this spirit, Ghribi et al. [64] suggested to gauge the depolymerization extent (ratio of TeO 3 /TeO 4 ) as a function of ZnO content in TeO 2 -TiO 2 -ZnO glasses by calculating the following ratio of normalized intensities: (I H + I I )/(I G + I H + I J )where the numerator holds the sum of intensity relative to bands due to stretching vibrations of Te-O in TeO 3 units, and denominator to those in TeO 4 units. We have calculated this ratio in TNxW5 glasses and the obtained results are illustrated in Fig.6. It is important to stress that the ratio values do not quantitatively reflect the ratio of TeO 3 /TeO 4 but rather a qualitative evolution. This can be explained by the following reasons: (i) the Raman intensity is proportional to both the number of vibrating entities and the extent of the polarizability change; and (ii) it is complicated to sharply distinguish TeO 3 from TeO 3+1 and TeO 4 units as there are no clear-cut boundaries due to a large panel of slightly distinct intermediate units demonstrating broad distributions of Te-O bond lengths.Ghribi et al.

Fig. 6 .

 6 Fig. 6. Evolution of the ratio of normalized intensities (I H + I I )/(I G + I H + I J ) in TNxW5 glasses. Inset: evolution of the same ratio in (95-y)TeO 2 -5TiO 2 -yZnO glasses as a function of ZnO content as reported by Ghribi et al. [64].

  5 is simultaneously manifested by (i) the weak structural depolymerization of Te-O-Te bond network and (ii) the existence of NbO 2.5 -rich regions upon adding NbO 2.5 through increasing Te-O-Nb and Nb-O-Nb bridges.

WO 3 .Fig. 7 .Fig. 8 .

 378 Fig. 7. Evolution of total-area averaged Raman spectra of TNxWy glasses as a function of WO 3 content. The Raman spectrum of -WO 3 is reproduced from Figure 2 in [62].

3. 4 . 1 .

 41 Linear optical properties 3.4.1.1. Refractive index, optical band gap and Urbach energies by UV-Vis-NIR spectroscopy

Fig. 9 .

 9 Fig. 9. UV-Vis-NIR spectra of TNxWy glasses. Insets for TNxW5: (a) Zoom-in plot of the UV absorption edge. (b) Compositional dependence of the refractive index n 1.5 calculated at 1.5 µm.

Fig. 10 .

 10 Fig. 10. UV-Vis-NIR optical transmission spectra of TN5Wy glasses. Insets: (a) Zoom-in plot of the UV absorption edge. (b) Compositional dependence of the refractive index n 1.5 calculated at 1.5 µm.

Fig. 11 .

 11 Fig. 11. (a) Evolution of the approximate absorption coefficient α as a function of the incident wavelength in TNxW5 glasses. (b) Tauc plot for the optical band gap energy E g derived from the absorption coefficient in TNxW5 glasses.

Fig. 12 .

 12 Fig. 12. Wavelength dispersion of the refractive index dispersion for TNxW5 glasses. Each dispersion curve corresponds to the average of three measured curves from different spots on the same glass pellet. Insets: Compositional dependence of the refractive index.

Fig. 13 .

 13 Fig. 13. Example of a measured Z-scan curve from the TN15W20 glass sample.

Fig. 14 .Fig. 15 .

 1415 Fig.[START_REF] Fargin | Optical non-linearity in oxide glasses[END_REF]. Evolution of normalized χ(3) values as a function of (a) NbO 2.5 and (b) WO 3 contents.

  glassy system has been established for the first time. The glass-forming domain, density, thermal, structural and optical (linear and nonlinear) properties of these glasses have been investigated and analyzed as a function of NbO 2.5 and WO 3 contents. The explored glass-forming domain holds seventeen compositions and extends from x = 5 to 25 mol.% in NbO 2.5 and y = 5 to 25 mol.% in WO 3 . The studied TNxWy glasses exhibit moderate thermal stabilities (ΔT (min) = 45 °C and ΔT (max) = 70 °C) and glass transition temperatures that increase with addition of NbO 2.5 and WO 3 (T g(min) = 333 °C and T g(max) = 403 °C). Based on the undertaken structural analysis established from full-scale Raman spectral decomposition, we report the following trends:  The structural effect of incorporating NbO 2.5 is manifested in both (i) a weak structural depolymerization of the Te-O-Te bond network accompanied by an increasing number of Te-O-Nb and/or Nb-O-Nb bridges and (ii) existence of NbO 2.5 -rich regions upon continuous addition of NbO 2.5 until the crystallization of Nb 6 TeO 17 compound which corresponds to a high NbO 2.5 :TeO 2 ratio of 6:1.

Table 1 .

 1 Thermal properties, densities, linear and nonlinear optical properties of TNxWy glasses. * Refractive indices obtained at λ= 1.5 µm from transmission spectra. § Refractive indices derived from ellipsometric dispersion curves using Sellmeier's equation.

	esu)

  Symmetric stretching vibrations of Te-O-Nb bridges (as in Nb 2 Te 4 O 13 and Nb 2 Te 3 O 11

	Inserted band	Wavenumber (cm -1 )	Raman band assignments
	A	36.0 -39.8	 The boson peak, ascribed to an excess density of vibrational states [60].
	B	146.9 (fixed)	 Intra-chain vibrations of Te-Te bonds (as in amorphous t-Te) [61].
	C	243.6 (fixed)	 Bending vibrations of WO 6 octahedra (as in -WO 3 ) [62].
	D	351 (fixed)	 Bending vibrations of distorted WO 6 octahedra [62].
	E	425 (fixed)

 Symmetric stretching vibrations in nearly symmetric Te-O-Te bridges (as in γ-TeO 2 )

[START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ-and δ-phases[END_REF][START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF]

. 

  ). Adding NbO 2.5 from 5 to 25 mol.% in TNxW5 glasses results in a steady evolution of E g from 2.92 eV to 2.89 eV. On the other hand, adding WO 3 induces a slight decrease of 5% from TN5W5 (2.92 eV) to TN5W25 (2.78 eV). These evolutions of E g upon adding NbO 2.5 and WO 3 are in agreement with the literature on the TeO 2 -Nb 2 O 5 , TeO 2 -ZrO 2 -WO 3 and TeO 2 -BaO-Nb 2 O 5 systems[START_REF] Berthereau | Nonlinear optical properties of some tellurium (IV) oxide glasses[END_REF][START_REF] Yousef | Optical and acoustic properties of TeO 2 -WO 3 glasses with small amount of additive ZrO 2[END_REF][START_REF] Umair | Effects of increasing tungsten on structural, elastic and optical properties of xWO 3 -(40-x)Ag 2 O-60TeO 2 Glass System[END_REF].

		90									16
	) -1 (cm coefficient absorption Approximate	10 20 30 40 50 60 70 80			TN5W5 TN10W5 TN15W5 TN20W5 TN25W5 (a)	E g	2.920±0.020 eV 2.913±0.020 eV 2.904±0.020 eV 2.897±0.020 eV 2.892±0.020 eV		(b)	4 6 8 10 12 14	-1 ) 1/2 (eV.cm 1/2 (h)
		0
		400	450	500	550	600	2.7	2.8	2.9	3.0	3.1
		Incident wavelength (nm)			Photon energy (eV)

  2.5 with average values of ~2.13 in TN5Wy glasses and ~2.15 in

					2.19
	n index	2.35 2.40 2.45		∞ n index Refractive	2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18	5	10 Average value: 2.138 15 20 NbO 2.5 content (mol.%)	25		TN5W5 TN10W5 TN15W5 TN20W5 TN25W5
	Refractive	2.25 2.30								n	∞	2.145±0.011 2.129±0.019 2.125±0.005 2.142±0.008 2.149±0.022
		2.20
		2.15
		350	400	450	500		550	600	650	700	750	800
						Wavelength (nm)
	TN25Wy (corresponding to the unique TN25W5 sample). A similar steady evolution of the
	refractive index in binary (100-x)TeO 2 -xWO 3 and (100-x)TeO 2 -xNbO 2.5 glasses was reported
	[45] with values in the ranges of 2.21-2.19 and 2.21-2.22 with increasing WO 3 and NbO 2.5
	contents from 10 to 30 mol.%, respectively. With an average of 2.13 for TNxWy glasses, the
	n ∞ value is ~3% lower than those reported for the above binary glasses and that extracted
	from TeO 2 -TiO 2 -WO 3 glasses (n ∞(average) of 2.192) [43]. It is important to stress that the n ∞
	values reported here are higher in comparison to other binary or ternary systems where a more
	consequential structural depolymerization occurs upon modifying the glass network (e.g., less
	than 2.100 in TeO 2 -TiO 2 -ZnO glasses [64]).

Finally, the steady evolutions of the extracted refractive indices for TNxWy glasses from both optical transmission (n 1.5 ) and ellipsometry (n ∞ ) measurements are in good agreement.

Acknowledgements.

M.R. Zaki gratefully acknowledges the financial support from Conseil Régional du Limousin.

The authors acknowledge the financial support from the CNRS via the "Projet International de Coopération Scientifique (PICS)" No. 7257 and would also like to thank Dr. J. Cornette and Dr. R. Mayet for their valued technical assistance in data acquisition of Raman spectra and XRD patterns respectively.


David Hamani
email: david.hamani@unilim.fr

A Plat

M Colas

J Cornette

O Masson

A P Mirgorodsky

P Thomas

Origin of the strong optical nonlinearity of tellurium oxide-based compounds: the specific case of BaTe2O6

Keywords: tellurium (IV) oxide, tellurium (VI) oxide, optical nonlinearity, lattice dynamics, ab initio Highlights

 Vibrational analysis of the BaTe2O6 phase reported for the first time.

 Exceptional TeO 2+ fragment situated in the Te IV O5 coordination sphere.

 Relevant relationships between the long Te IV -O bonds and the χ (3) susceptibility.

Introduction

The 'structure-properties' problem aims at understanding the relationships between fundamental physical characteristics of crystal lattices and the nature of their interatomic bonding. It always remains an intriguing point for the crystal chemistry and fundamental material science. The present paper focuses on the peculiarities of the atomic arrangement and the extraordinarily high nonlinear optical characteristics of tellurium oxide-based materials, more specifically in the BaTe 2 O 6 (BaTe IV Te VI O 6 ) crystal lattice. From the point of view of solid state chemistry, the peculiarity of BaTe 2 O 6 is the electronic structure of the coordination spheres of the Te IV atoms, which can be at the origin of extraordinary polarization properties.

Historically, it was revealed about twenty years ago that the χ (3) susceptibility for pure TeO 2 glass is about fifty times as high as that for SiO 2 [START_REF] Kim | Linear and nonlinear optical properties of TeO 2 glass[END_REF] (and was recently confirmed for their crystalline forms as well [START_REF] Ben Yahia | Theoretical third-order hyperpolarizability of paratellurite from the finite field perturbation method[END_REF][START_REF] Berkaïne | Nonlinear optical properties of TeO 2 crystalline phases from first principles[END_REF]). This fact has aroused considerable interest in the relevant studies which initially were only slightly or not at all concerned with the question: where does this high nonlinear susceptibility come from? It was generally accepted that the Te IV lone electron pairs (always present in those compounds) account for such a property [START_REF] Suehara | Localized hyperpolarizability approach to the origin of nonlinear optical properties in TeO 2 -based materials[END_REF]. However, the results of subsequent quantum chemistry ab initio considerations of different TeO 2 cluster models have shown that it is not the case [START_REF] Mirgorodsky | Ab initio study of the nonlinear optical susceptibility of TeO 2 -based glasses[END_REF][START_REF] Soulis | Local molecular orbitals and hyper-susceptibility of TeO 2 glass[END_REF][START_REF] Smirnov | Quantum mechanical study of pre-dissociation enhancement of linear and nonlinear polarizabilities of (TeO 2 ) n oligomers as a key to understanding the remarkable dielectric properties of TeO 2 glasses[END_REF], and the origin of those properties should be attributed to specific Te-O linkages occurring in the TeO 4 polyhedra which build up the molecular polymers or the crystal lattices of TeO 2 . In every polyhedron, there are two weak linkages having length of about 2.1 Å, while the rest two (about 1.9 Å in length) form a TeO 2 molecular-like unit whose geometry is close to that of the isolated molecule. So, the last mentioned fact allows regarding the TeO 2 lattices (three polymorphs α- [START_REF] Thomas | The crystal structure and absolute optical chirality of paratellurite, α-TeO 2[END_REF], β- [START_REF] Beyer | Refinement of the crystal structure of tellurite, the orthorhombic TeO 2 , Z. Für Krist[END_REF] and γ-TeO 2 [START_REF] Champarnaud-Mesjard | Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO 2[END_REF]) as molecular crystals in which the long linkages are intermolecular bonds.

According to the ab initio calculation results, in which the total nonlinear polarizability values of TeO 2 -made clusters were separated into intramolecular and intermolecular contributions, the weak intermolecular Te-O bonds represent the main source of the extraordinarily high χ (3) susceptibility for solid forms of TeO 2 .

Generally, TeO 2 -based complex oxides are constituted of TeO 4 and/or TeO 3+1 and/or TeO 3 polyhedra which depend on the nature and quantity of the added modifier oxide (see Figure 1 and for example [START_REF] Neov | A model for structural recombination in tellurite glasses[END_REF][START_REF] Sekiya | Raman spectra of MO 1/2 -TeO 2 (M = Li, Na, K, Rb, Cs and Tl) glasses[END_REF][START_REF] Himei | Coordination change of Te atoms in binary tellurite glasses[END_REF][START_REF] Becker | Crystal structures of potassium tetratellurite, K 2 Te 4 O 9 , and potassium ditellurite, K 2 Te 2 O 5 , and structural trends in solid alkali tellurites[END_REF][START_REF] Mclaughlin | Modeling glasses using the reverse Monte Carlo algorithm: addition of nuclear magnetic resonance and expanded coordination number constraints[END_REF]). Very little information on the presence of Te IV coordination spheres other than the above-mentioned can be found in the literature. One example was evidenced in the Cs 2 Te 4 O 12 (Cs 2 Te IV Te VI 3 O 12 ) crystal lattice [START_REF] Loopstra | The structures of four caesium tellurates[END_REF] in which the Te IV atom is centred in a regular Te IV O 6 octahedron formed by six Te-O bonds (2.10 Å, see Figure 1). The vibrational spectroscopy study complemented by the lattice dynamics analysis [START_REF] Hamani | Crystal chemistry peculiarities of Cs 2 Te 4 O 12[END_REF] allowed to conclude that the Te 4+ ion has no localized lone pair and, jointly with the Cs + ions, play the role of quasi-isolated cations, implying that this compound is a tellurate (but not tellurite) with a complex [Te VI 3 O 12 ] 6-anion. Another unusual type of polyhedron is found in the BaTe 2 O 6 (BaTe IV Te VI O 6 ) crystal lattice [START_REF] Koçak | Barium hexaoxoditellurate(IV,VI): oxygen coordination number 5 at tetravalent tellurium[END_REF]: it contains a particular Te IV O 5 symmetric tetragonal pyramid in which the Te IV atom forms one exceptionally short Te-O bond (1.83 Å) in the opposite direction of the Te IV lone electron pair, and four much longer equivalent Te-O bonds (2.13 Å) (Figure 1). The longest Te-O separations can be readily specified by a mainly electrostatic attraction, the shortest bond has an essentially covalent nature and therefore can be considered as a quasi-isolated molecular-like TeO 2+ entity, which provokes a special interest to the BaTe 2 O 6 crystal chemistry study.

It will be shown in this paper that the peculiarities of the BaTe 2 O 6 structure offers a possibility to clarify in direct manner the contribution of the different Te-O bond types on the nonlinear optical properties. Therefore, as a starting step of this work, the crystal structure of the BaTe 2 O 6 compound was reinvestigated by single crystal X-ray diffraction. This study was coupled with the analysis of the vibrational spectra (Raman and infrared spectra are presented for the first time) obtained from the experiment and interpreted by using the relevant firstprinciples and empirical calculations.

The results obtained for the BaTe 2 O 6 compound were interpreted from the crystal chemistry point of view in focusing our attention on the TeO 2+ fragment situated in the TeO 5 coordination sphere around Te IV atoms. These data were used to discuss the central subjects of this study: the relationships between the structural peculiarities of this coordination sphere in the BaTe 2 O 6 phase and the linear and nonlinear optical characteristics, namely the tensors of linear and second-order nonlinear susceptibilities (χ (1) and χ (3) , respectively) which were obtained by means of quantum chemistry ab initio calculations. Indeed, the calculations counterbalance the lack of experimental measurements due to the difficulty of growing large single crystals suitable for optical measurements.

The present paper is organized in the following manner. The experimental and calculation methods are exposed in part 2. The results are presented and discussed in parts 3 and 4 respectively, and concluding remarks are given in part 5.

Experimental and calculation methods

Synthesis

First, the basic material, TeO 2 , was prepared by decomposing a commercial ortho-telluric acid H 6 TeO 6 (Aldrich, 99.9%) at 550 °C for 24 h. A mixture was then obtained by adding stoichiometric amounts of commercial BaCO 3 (Aldrich, 99+%) to TeO 2 . Single crystals of BaTe 2 O 6 phase were synthesized, by melting the mixture under air atmosphere at 710 °C for 10 h in a gold crucible. The melt was first slowly cooled down at 1 °C.h -1 to 645 °C and then at 10 °C.h -1 to room temperature. A single crystal suitable for structural determination using X-ray diffraction was selected using a polarized light optical microscope.

Structural characterization

Intensity data were collected using a Bruker-Nonius KappaCCD area-detector diffractometer (Mo K α radiation). The crystal data, data collection, refinement conditions and computing details are pointed out in Table 1.

The phase was analysed by Raman and infrared spectroscopy as well. The Raman spectrum was recorded at ambient conditions in the 30-900 cm -1 range using a spectrometer (Jobin-Yvon Horiba T64000) equipped with an Ar + laser (514.5 nm exciting line) and a CCD detector in a backscattering geometry. A good signal/noise ratio required two scans of 20 seconds each. The focalization was done through a microscope (x50 LWD) and the diameter of the laser spot focused on the sample was about 1 µm. Measurements were performed at a power of 200 mW of the exciting line. The spectral resolution was about 2.5 cm -1 at the exciting line (1800 grooves.mm -1 grating). The infrared spectrum was recorded in the absorbance mode on a Fourier transform spectrophotometer (Thermo Fisher Nicolet 6700) using the polyethylene and CsI pressed technique in the 80-500 and 500-900 cm -1 ranges, respectively.

The modelling consists in calculating the vibrational spectra of the structure (i.e. the wavenumbers and the types of vibrations) in order to assign the experimental bands. Firstprinciples calculations were carried out using the CRYSTAL06 software [START_REF] Dovesi | CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals[END_REF][START_REF] Dovesi | CRYSTAL06 User's anual[END_REF] to obtain self-consistent information about the structure, wavenumbers, symmetry, eigenvectors and infrared intensities (but not Raman intensities) of the zone centre vibrations of BaTe 2 O 6 , as well as about the Te-O interatomic overlap population in various TeO 2and TeO 3 -based compounds using the same ab initio routine. The computational technique was based on the density functional theory (DFT) using the Becke's three-parameter hybrid nonlocal exchange functional [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] combined with the Lee-Yang-Parr gradient-corrected correlation functional B3LYP [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF]. The number of k-points used to describe the irreducible part of the Brillouin zone was chosen to be 27. The LADY program [START_REF] Smirnov | LADY: software for lattice dynamics simulations[END_REF] was used to perform an empirical lattice dynamical model treatment of the BaTe 2 O 6 structure in order to interpret its vibrational spectrum. This program provides the information about the wavenumbers and eigenvectors of normal modes of crystal vibrations. The experimental crystallographic data (space group, lattice parameters, and atomic coordinates) were used jointly with the data on the force constants of the relevant interatomic bonds using the Valence Force Field (VFF) model.

These data are in the form of an empirical curve displaying the dependence of the bond force constant values on the interatomic distance [START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γand δ-phases[END_REF].

Optical properties

Ab initio method was used in order to tackle the problem that unfortunately no experimental measurement was adapted due to the insufficient size (the tenth of millimetre) of the synthesized single crystals. Density functional first-principles simulations based on a numerical atomic orbital method [START_REF] Berkaïne | Nonlinear optical properties of TeO 2 crystalline phases from first principles[END_REF][START_REF] Plat | Huge susceptibility increase within the (1-x) TeO 2 + x TeO 3 crystal system: Ab initio calculation study[END_REF] were thus executed to calculate the tensor elements of the linear χ (1) susceptibility and of the second-order nonlinear χ (3) susceptibility. Calculations were carried out using the SIESTA code [START_REF] Soler | The SIESTA method for ab initio order-N materials simulation[END_REF] within the generalized gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF][START_REF] Perdew | Errata: Generalized gradient approximation made simple[END_REF] to simulate the electronic exchange and correlation. Core electrons were replaced by ab initio norm-conserving pseudopotentials generated with the Troullier-Martins scheme [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations[END_REF] in the Kleinman-Bylander fully nonlocal separable representation [START_REF] Kleinman | Efficacious form for model pseudopotentials[END_REF].

Results

The BaTe 2 O 6 phase crystallizes in the orthorhombic space group n°63 (Cmcm, D 2h 17 point group) with the unit cell parameters: a = 5.562(2) Å, b = 12.773(5) Å, c = 7.318(3) Å, V = 519.9(3) Å 3 and Z = 4 (cf. Figure 2 (a)). In addition to Table 1, structural characteristics (atomic coordinates, displacement parameters and interatomic distances) obtained from single crystal X-ray diffraction are presented in Table 2. These results are in agreement with those of Koçak et al. [START_REF] Koçak | Barium hexaoxoditellurate(IV,VI): oxygen coordination number 5 at tetravalent tellurium[END_REF]. The calculation of the bond valence sums from the interatomic distances, using the Adams' constants [START_REF] Adams | Relationship between bond valence and bond softness of alkali halides and chalcogenides[END_REF][START_REF] Adams | soft BV (version 0.96)[END_REF], emphasizes the existence of barium II (1.8 valence unit), tellurium IV (4.2 v.u.) and tellurium VI (6.1 v.u.).

The experimental Raman and infrared spectra are given in Figure 3 Raman-active (7A g + 7B 1g + 3B 2g + 7B 3g ) and 23 u-modes are IR-active (8B 1u(z) + 8B 2u(y) + 7B 3u(x) ) (the 4A u modes are IR-inactive). Since the Te VI atoms occupy inversion centres, their displacements are absent in the g-modes.

The Figure 5 presents the Te-O interatomic overlap population versus the experimental length obtained by ab initio calculations for several TeO 2and TeO 3 -based compounds (taken from [START_REF] Hamani | Crystal chemistry peculiarities of Cs 2 Te 4 O 12[END_REF]) and is completed with the calculated data for the BaTe 2 O 6 compound. The results for the χ (1) and χ (3) susceptibilities obtained by ab initio calculations are given in Table 4. For the χ (1) tensor, the xx-, yy-and zz-elements have close values (respectively 4.2, 2.3 and 3.4), traducing an isotropy of this physical quantity. The remarkable point is revealed for the χ (3) tensor: the values of the xxxx-and zzzz-elements (30.0 × 10 -13 esu and 44.3 × 10 -13 esu) are of the same order of magnitude than those for α-TeO 2 [START_REF] Berkaïne | Nonlinear optical properties of TeO 2 crystalline phases from first principles[END_REF] and are about ten times higher than that of the yyyy-element (3.2 × 10 -13 esu). The former characterize the induced polarization along the x-and z-direction respectively while the latter characterizes it along the ydirection.

Discussion

Structural analysis from vibrational spectra

In the above-presented structural description, by using pure geometrical criteria, all the O atoms are mentioned as bridging ones. Now, to perform a qualitative analysis of the vibrational modes related to the Te-O bonds, we address ourselves mainly to their chemical nature. Let us look at the experimental Raman spectrum presented in Figures 3 and4. It is dominated by two A g bands above 600 cm -1 related to the stretching modes of the Te IV -O [START_REF] Ben Yahia | Theoretical third-order hyperpolarizability of paratellurite from the finite field perturbation method[END_REF] and Te VI -O (3) terminal bonds and one A g band near 515 cm -1 related to the bending mode of the Te VI -O (1) -Te VI bridges. Such spectrum is inherent to a lattice containing chain like fragments [START_REF] Soulis | The role of modifier's cation valence in structural properties of TeO 2 -based glasses[END_REF].

To verify the objectivity of such attributions, and to make our analysis more definitive and more quantitative, we turn our attention to the results of the empirical model lattice dynamical treatment. Taking into account the argumentation relating to the nature of the axial bonds (having the length of 2.12 Å) in the TeO 4 polyhedra in the paratellurite α-TeO 2 lattice [START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γand δ-phases[END_REF],

we state our belief that the interatomic Te-O separations longer than 2.1 Å should be omitted from our analysis as being electrostatic contacts rather than covalent bonds. Two kinds of treatments were carried out to model the Raman spectrum: a 'full-lattice' treatment considering all the interatomic force constants including the Te IV -O (3) contacts of length of 2.12 Å (Figure 4 (a)) and a second one without using the Te IV -O (3) force constants i.e. these contacts are considered as weak interactions and are in that case simply ignored (Figure 4 (b)). The relevant data are given in Table 3. Firstly, the 'full-lattice' modelled spectrum is in accordance with the experimental spectrum, the main bands above 400 cm -1 being well reproduced. Secondly, the two modelled spectra are very similar: without considering the Te IV -O (3) contacts, wavenumbers are only slightly shifted towards the low wavenumbers.

Thus, the modelling consequently emphasizes the presence of quasi-isolated [Te IV Let us approximately estimate the bond orders using the overlap populations noticed in Figure 5. For the Te IV O 4 polyhedron in α-TeO 2 , the overlap population is equal to 0.141 for each of the two short equatorial bonds (1.88 Å) and 0.043 for each of the two long axial bonds (2.12 Å) so a total overlap population of 0.368. In an isolated TeO 2 molecule, the order of each Te-O bond (1.83 Å [START_REF] Krasnov | Молекулярные постоянные неорганических соединений[END_REF]) is equal to 2 and it can be thought that the initial cloud of 8 (4x2) electrons forming the two bonds of the isolated molecule is divided in the α-TeO 2 lattice between the intramolecular and the intermolecular clouds in the same proportion than that of the overlap populations. Thus the intramolecular clouds would contain 6 (3x2) electrons (so a bond order of 1.5), and 2 (1x2) electrons would belong to the intermolecular clouds (so a bond order of 0.5), this result being consistent with those of Yakovlev et al. [START_REF] Yakovlev | Nonempirical calculation of linear and nonlinear polarizability of TeO 2 -based molecular clusters and piezoelectric properties of crystalline tellurium oxide[END_REF].

Reasoning in the same manner for the Te IV O 5 polyhedron in BaTe 2 O 6 , we notice an overlap population of 0.229 for the short Te-O (2) bond and 0.042 for each of the four long Te-O [START_REF] Berkaïne | Nonlinear optical properties of TeO 2 crystalline phases from first principles[END_REF] bonds so a total overlap population of 0.397. In the virtual isolated TeO 2+ molecule, the bond order is equal to 3 and we can think that the cloud of 6 bonding electrons would be distributed in the TeO 5 polyhedron of the BaTe 2 O 6 lattice in such a way that 3.5 electrons should be attributed to the intramolecular bond (so a bond order of 1.8) and 2.5 electrons (0.625x4) would be given to the intermolecular bonds (so a bond order of 0.3).

Thus, in α-TeO 2 and BaTe 2 O 6 , the intermolecular Te-O bonds seem to keep their individual electronic features. Consequently, one may expect that these bonds should be the main source of the χ (3) lattice, all the TeO 2+ ions lie strictly along the y axis, and the longest Te-O (3) linkages lie practically in the xz-plane. Keeping in mind this fact, we direct our attention to the results of the χ (1) and χ (3) susceptibilities of the BaTe 2 O 6 compound.

Optical properties particularities

The corner stone of the next consideration is the conception of localized dipoles associated with the chemical bonds, which should allow us to connect the χ (1) and χ (3) -tensor particularities directly with the BaTe 2 O 6 geometry features. The most noticeable particularity of the χ (3) -tensor is that its xxxx-and zzzz-elements are more than ten times as large as the yyyy-elements (Table 4). The Te VI O 6 octahedra and the Ba 2+ ions are quasi-isotropic and thus cannot be responsible for a huge difference of those elements, which however is apparently attributable to the sharp anisotropy of the electron cloud distribution inside the Te IV O 5 tetragonal pyramid. This clarifies why the nonlinearity of a polarization effect in the xz-plane is so much larger than that in the y-direction: the dipole moments of the four weak bonds lie practically in that plane, thus playing a primary role in the effect under consideration. As to the role of the TeO 2+ entity, its contribution is localized in the y-direction polarization, whose nonlinearity is quite humble. These results are the first obvious confirmation of the strong superiority of the nonlinear polarizability of the weak intermolecular Te-O contacts over that of the strong molecular Te-O bonds, which is revealed here not for virtual molecular clusters [START_REF] Mirgorodsky | Ab initio study of the nonlinear optical susceptibility of TeO 2 -based glasses[END_REF][START_REF] Soulis | Local molecular orbitals and hyper-susceptibility of TeO 2 glass[END_REF][START_REF] Smirnov | Quantum mechanical study of pre-dissociation enhancement of linear and nonlinear polarizabilities of (TeO 2 ) n oligomers as a key to understanding the remarkable dielectric properties of TeO 2 glasses[END_REF] but for a real crystal lattice. As an intriguing point, we wish to note that in contrast to the χ (3) -tensor, the χ (1) -tensor elements of that lattice contain nothing extraordinary and have no noticeable anisotropy. Now let us discuss on how the above-mentioned peculiarities can be explained within a classic dipole oscillator model. We use a model approximation taking into consideration the simplest version of the anharmonicity of the oscillator potential well, which can qualitatively clarify the factors accounting for the origin of the nonlinear contribution to the polarization mechanism. The model considers an E-field induced dipole P = Zx produced by the displacement x of a charge Z which is initially placed in a minimum x = 0 of a potential well in the monodimensional space. The curvature of the well, i.e. the oscillator force constant K, depends on the charge displacement x, and the model parameter σ = dK(x)/dx characterizes such a dependence. The x value induced by the electric field E can be derived from the equilibrium between the electric and mechanical forces applied to the charge: ZE = Kx;

x = ZE/K. This means that dx/dE = Z/K, and the expressions for the linear α and the two first nonlinear β and γ polarizabilities of the oscillator are of the following form:

 α = dP/dE = (dP/dx) (dx/dE) = (Z)(Z/K) = Z 2 /K (Eq. 1)  β = dα /dE = (dα /dK) (dK/dx) (dx/dE) = (-Z 2 /K 2 )(σ)(Z/K) = -σZ 3 /K 3 (Eq. 2)  γ = dβ/dE = (dβ/dK) (dK/dx) (dx/dE) = (3σZ 3 /K 4 )(σ)(Z/K) = 3σ 2 Z 4 /K 5 (Eq. 3)
Let us remind that the α polarizability, a microscopic quantity, is the homolog of the χ (1) susceptibility, a macroscopic quantity (as β for χ (2) and γ for χ (3) ).

The absence of noticeable anisotropy for the elements of the χ (1) -matrix (Table 4) seems to be explicable: they do not depend on the σ parameter. It readily follows from Eqs. 1-3 that the potential well anharmonicity represents the source of the dipole nonlinearity: within our model, this occurs only when the σ parameter is introduced into consideration. This fact allows us to attribute the high values of the χ (3) xxxx and χ (3) zzzz susceptibilities to the specific constitution of the molecular orbital related to the weak Te IV -O bonding. Note that the occurrence of the molecular TeO 2+ entity is indicative of the sp y hybridization of the Te IV atom. This implies that the formation of the four other bonds should result from the complementary p xz 2 d 2 hybridization and would be mainly assured by the overlap between the 'long range' d-orbitals of the Te IV atom with the atomic orbitals of O atoms at 2.12 Å.

Furthermore, since the spatial variability of the d-orbitals is high among those which assure the formation of covalent bonds, the σ parameter should be high when the d-orbitals play the central role in the bonding. Such a situation can be expected for the heavy element oxides, which in particular can explain why the hyperpolarizability of the long Te-O bonds should be extraordinarily high.

Conclusion

The results of this study improve the understanding of the specific role of the Te IV atom d-orbitals in the structural and dielectric properties of crystalline complex tellurium oxides.

The BaTe 2 O 6 crystal structure presents two types of Te coordination polyhedron: one quasiisotropic Te VI O 6 octahedron and one highly anisotropic Te IV O 5 tetragonal pyramid composed of one exceptionally short molecular bond (1.82 Å) oriented along the y axis and four long and weak bonds (2.12 Å), lying practically in the xz-plane. The quantitative polarizability characteristics of such bonds can thus be separately estimated from the diagonal elements of the relevant tensors (taking into account that the contribution from the Te VI O 6 polyhedra should be isotropic). To the best of our knowledge, such a possibility was never found for any other crystalline structure. The tensors of the linear χ (1) and second-order nonlinear χ (3) susceptibilities show the following features:

 No strong distinctions occur between the diagonal elements of the χ (1) tensor, pointing to the fact that the magnitudes of the linear polarizabilities of both types of bond do not differ dramatically. With a simple polarizability model considering only three physical values, namely the Z, K and σ parameters, it implies that the first two of these parameters are not capable of producing strong anisotropy of the polarizability tensor.

 The xxxx-and zzzz-components of the χ (3) tensor are about ten times as high as the yyyy-component, evidencing that the magnitude of the second-order nonlinear polarizability of the long bonds is much higher than that of the short one. The physical aspect of such a difference may lie in the fact that the anharmonicity of the potential wells of the Te-O dipoles related to the long bonds is much stronger than that related to the short one. We venture the opinion that the chemical aspect of such a situation is determined by the nature of the contribution from the Te IV atomic orbitals to those bonds: the long bonds correspond to the p 2 d 2 hybridization whereas the short bond corresponds to the sp hybridization.

Let us underline that the stability of Te-O bonds of length of about 2.1 Å is mainly assured by the d-orbitals contribution which vanishes for a length superior to 2.4 Å, causing the bonds to break [START_REF] Smirnov | Quantum mechanical study of pre-dissociation enhancement of linear and nonlinear polarizabilities of (TeO 2 ) n oligomers as a key to understanding the remarkable dielectric properties of TeO 2 glasses[END_REF]. Consequently, the long Te-O bonds (2.12 Å) in the BaTe 2 O 6 lattice can be considered in a 'precritical' state. The very low stability of the Te IV sp 3 d 2 hybridization at normal conditions seems to be in the state of 'degradation' and begins to collapse with the occurrence of the alternative sp 3 d hybridization implying a Te IV O 4 coordination sphere of lower energy.

Besides the case of BaTe 2 O 6 , these conclusions confirm the dominating role of the axial Te-O bonds in the high χ (3) hypersusceptibility of α-TeO 2 , and are in line with the ideas clarifying the nature of the huge nonlinearity of the TeO 3 crystal lattice polarization [START_REF] Plat | Huge susceptibility increase within the (1-x) TeO 2 + x TeO 3 crystal system: Ab initio calculation study[END_REF]. Therefore, to our belief, these conclusions can have more universal validity for a wide group of heavy element oxides in which the chemical bonding is assured by the d-orbitals contribution, and in particular can clarify why the materials demonstrating extraordinary hyperpolarizability (and hypersusceptibility) have quite ordinary characteristics for the linear part of the polarization. Table 4. χ (1) and χ (3) susceptibilities tensors of the BaTe 2 O 6 compound obtained by ab initio calculations (with SIESTA). (1 esu = 1.3982 × 10 -8 m 2 .V -2 ) 1.9234 [START_REF] Neov | A model for structural recombination in tellurite glasses[END_REF] x 2 χ (1) tensor elements no unit χ (3) tensor elements ×10 -13 [START_REF] Loopstra | The structures of four caesium tellurates[END_REF])

  and completed with ab initio calculations. The Raman spectrum obtained by the empirical lattice dynamical model is shown in Figure 4 for two cases: a 'full-lattice' treatment (Figure 4 (a)) and another without taking into account the contribution of the long Te IV -O (3) contacts (2.12 Å) (Figure 4 (b)). The relevant wavenumber positions are reported in

4. 1 .

 1 Structural analysis from X-ray diffraction data The mixed BaTe 2 O 6 structure can be described at first sight as a layered structure. Every layer is made of infinite linear chains of Te VI O 6 octahedra linked by vertices, two chains being linked by Te IV O 5 tetragonal pyramids. Every Te VI O 6 octahedron presents two Te VI -O (1) bridging bonds with two other octahedra and four Te VI -O (3) bridging bonds with four Te IV O 5 polyhedra. The barium atoms lie between the layers. The Te IV atom presents a pentacoordinated environment of O atoms with a short Te IV -O (2) bond (1.82 Å) and four equivalent long Te IV -O (3) bonds (2.12 Å), the Te IV lone electron pair being opposed to the direction of the short bond. The Te VI atom is placed at the centre of a slightly deformed octahedron of O atoms with four equivalent Te VI -O (3) bonds (1.91 Å) and two equivalent Te VI -O (1) bonds (1.92 Å) (Figure 2 (b)). Thus the structure presents symmetric Te VI -O (1) -Te VI bridges (with a bridge angle of 143.7°) and asymmetric Te IV -O (3) -Te VI bridges (with a bridge angle of 121.0°). The Ba atom is at the centre of a deformed 10-coordinated polyhedron of O atoms with two equivalent Ba-O (2) distances (2.86 Å), four equivalent Ba-O (3) distances (2.98 Å) and four other equivalent Ba-O (3) distances (3.01 Å) (Figure 2 (c)).

Figure 1 .

 1 Figure 1. Possible Te IV environments in TeO 2 -based materials according to the nature and

Figure 2 .

 2 Figure 2. Displays of the BaTe 2 O 6 structure. (a) Atomic arrangement of the unit cell. (b) Structural fragment around Te IV and Te VI atoms. (c) Structural fragment around a Ba atom. Te IV atoms are labelled as Te1 and Te VI atoms as Te2. Interatomic distances are given in Å.

Figure 3 .

 3 Figure 3. Experimental spectra of powder-like sample of BaTe 2 O 6 complemented by ab initio

Figure 4 .

 4 Figure 4. Experimental and empirically modelled (with LADY) spectra of the BaTe 2 O 6 crystalline phase (a) with (b) without including the contribution of the Te IV -O (3) interactions.

Figure 5 .

 5 Figure 5. Te-O interatomic overlap population in various TeO 2and TeO 3 -based compounds

Figure_1

  Figure_1

Figure_2

  Figure_2

Figure_3

  Figure_3

Figure_4

  Figure_4

Table 3

 3

	2h	17 point

in which the overall calculated values are close to the experimental ones. The primitive cell of the BaTe 2 O 6 lattice contains 18 atoms (two formula units). Correspondingly, 51 optical vibrational modes related to the Γ-point of the Brillouin zone are distributed among the irreducible representations of the D

  Te VI -O (1) -Te VI bridges (1.92 Å) and Te IV -O (2) bonds (1.82 Å) are thus found in the lattice. Our revision of the BaTe 2 O 6 crystalline structure indicates that the interatomic distance within the TeO 2+ entity (1.82 Å) is, to the best of our knowledge, the smallest of all those occurring for Te-O bonding. It represents a unique molecular-like entity in which the interatomic bonding is the strongest among Te-O contacts. To clarify its chemical nature, the Te IV O 5 polyhedron must be considered with more details. One contact corresponds to the TeO 2+'molecule' and the rest four, representing the longest and weakest Te-O chemical linkages in the BaTe 2 O 6 lattice, are intermolecular bonds whose length (2.12 Å) is equal to that in the α-TeO 2 lattice which is the fundamental structure of crystalline TeO 2 having quasi-molecular constitution. Let us recall that the extraordinarily high χ(3) susceptibility of TeO

	O] 2+
	molecular ions.
	Consequently, the more adequate form of the crystal formula should be Ba (Te IV O) Te VI O 5 ,
	defining an oxytellurate of Ba 2+ and Te 4+ . It implies that the anionic part is comprised of
	[Te VI O

5 ] 4-infinite chain-like tellurate anions built up from Te VI O 6 octahedra. The cationic part consists of isolated Ba 2+ ions and [Te IV O] 2+ molecular ions. Terminal Te VI -O (3) bonds (1.91 Å), 2 -based materials is attributed to those intermolecular bonds [5-7]. In this connection, it is interesting to look at the key features of valence electronic cloud distributions in the two just mentioned lattices within the framework of the 'molecule in lattice' approach. 4.3. Chemical aspect of the Te-O bonding: bond orders in α-TeO 2 and BaTe 2 O 6

  susceptibility of BaTe 2 O 6 . It is important to underline that, in contrast to the α-TeO 2 lattice in which the Te-O bonds are always oriented in general directions, in the BaTe 2 O 6

Table captions Table 1 .

 captions1 Crystal data, data collection, refinement conditions and computing details for the BaTe 2 O 6 compound.

Table 2 .

 2 Atomic coordinates, displacement parameters and interatomic distances for the BaTe 2 O 6 compound (esd are given in brackets).

Table 3 .

 3 Experimental band positions (in cm -1 ) of the Raman spectrum of the BaTe 2 O 6 compound compared with the results of ab initio (with CRYSTAL06) and empirical (valence force field model with LADY) calculations.

  Atomic coordinates and isotropic or equivalent isotropic displacement parameters (in Å 2 )

	Atom Ox. Wyck. Sym. x	y	z	U eq	Site occupancy
	Ba	+2 4c	m2m 0.	0.71847(2) 0.75	0.01217(6) 1.
	Te IV	+4 4c	m2m 0.5	0.91413(2) 0.75	0.00482(6) 1.
	Te VI	+6 4a	2/m.. 0.	0.	0.5	0.00361(6) 1.
	O (1)	-2	4c	m2m 0.	0.0465(2)	0.75	0.0112(6) 1.
	O (2)	-2	4c	m2m 0.5	0.7714(2)	0.75	0.0087(5) 1.
	O (3)	-2	16h	1	0.7635(3) 0.89498(10) 0.54382(19) 0.0093(2) 1.
	Interatomic distances (Å)
	Te IV -O (2) Te IV -O (3) Te VI -O (3) Te VI -O (1)		1.823(3) 2.1176(15) x 4 x 1 1.9059(14) x 4		Ba-O (2) Ba-O (3) Ba-O (3)	2.8621(12) x 2 2.9785(16) x 4 3.0149(17) x 4

Table_1 (revised)

Acknowledgments

Calculations were performed on the CALI (Calculateur en Limousin) computer cluster of the Université de Limoges, funded by the Région Limousin, the XLIM, IPAM, GEIST institutes and the Université de Limoges. We are grateful to the Conseil Régional du Limousin for financial support.

Δρ min = -1.592 e.Å -3 , Δρ max = 1.382 e.Å -3 Computing details Data collection: COLLECT [START_REF] Dovesi | CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals[END_REF]; absorption correction: SADABS [START_REF] Dovesi | CRYSTAL06 User's anual[END_REF]; cell refinement: DirAx/LSQ [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF]; data reduction: EVALCCD [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF]; program used to solve structure: SHELXS97 [START_REF] Smirnov | LADY: software for lattice dynamics simulations[END_REF]; program used to refine structure: SHELXL-2014/7 [START_REF] Smirnov | LADY: software for lattice dynamics simulations[END_REF]; molecular graphics: Diamond [START_REF] Mirgorodsky | Dynamics and structure of TeO 2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γand δ-phases[END_REF]; software used to prepare material for publication: publCIF [START_REF] Plat | Huge susceptibility increase within the (1-x) TeO 2 + x TeO 3 crystal system: Ab initio calculation study[END_REF]