Daniel Caurant

Wallez Gilles

Odile Majérus

Roisine Gauthier

Thibault Charpentier

Structure and Properties of Lead Silicate Glasses

Introduction

As already noted in chapter 1, given their specific properties, glasses containing lead oxide have a very broad field of application. This extends from crystal glasses, enamels and glazes, to optical glasses with high refractive index, passing through glasses absorbing ionizing radiation and glasses for lowtemperature welding of metals, ceramics or glasses [START_REF] Frieser | A review of solder glasses[END_REF][START_REF] Rabinovich | Lead in glasses[END_REF][START_REF] Takamori | Solder glasses[END_REF][START_REF] Volf | Chemical approach to glass[END_REF]. For these various applications, glass composition must certainly be adapted in terms of its elaboration and forming (viscosity, expansion coefficient, glass transition temperature Tg) as well as in terms of its properties under the conditions of use (refractive index, transparency, color, chemical durability, electrical resistivity, etc.). These various properties, which concern both the liquid during its melting, forming and cooling (quenching), and the final glass, i.e. the amorphous solid resulting from the quenching of the supercooled liquid below Tg, are closely related to its structure. In the case of oxide glasses that are of interest here, this corresponds to the way in which the polyhedrons associated with the various present cationic species surrounded by oxygen O 2-anions are arranged with respect to one another inside the network that constitutes the glass structure. Unlike crystals, this network has no long-range order (figure 3.1). In the case of glasses containing lead, it is therefore particularly important to understand the way in which Pb 2+ ions are inserted in the structure of this network depending on the lead oxide content and on the glass composition (nature of the forming oxide (SiO2, B2O3, P2O5), effect of the presence of modifier oxides (alkaline and alkaline-earth oxides) and intermediate oxides ( Al2O3)) 1 and to evaluate 1. A glass former oxide can be defined as an oxide that only by melting + more or less rapid cooling (quenching) readily yields a glass particularly due to the high viscosity of the corresponding liquid in the vicinity of the melting temperature Tf and in its supercooled state (T < Tf). A glass can be defined as a solid that has no long-range order (≥ 10Å) at the level of its atomic organization (unlike crystallized materials) but has a glass transition temperature Tg (range of temperature for which the liquid solidifies when cooled and the glass tends to soften when heated). A glass can be considered a supercooled liquid that freezes during quenching. Compared to crystallized materials, glasses have therefore an excess of free energy and are in a nonequilibrium state from the perspective of thermodynamics (when heated above Tg they tend to crystallize). The main glass former oxides are SiO2, B2O3, P2O5 and GeO2 which readily lead to glasses and whose structure is a random continuous network of tetrahedrons (SiO4, PO4, GeO4) or triangles (BO3) connected only by the vertices (small surplus of free energy their impact on the structure of this network, and also on the environment, and the distribution of specific species that may be present, such as transition metal ions used for coloration (see chapter 4). (in yellow), the bridging and non-bridging oxygen atoms (in red), and the modifier ions Na + (in purple) and Ca 2+ (in green). Reproduced from [START_REF] Charpentier | Computational simulations of solid state NMR spectra: a new era in structure determination of oxide glasses[END_REF] with the permission of The Royal Society of Chemistry.

COMMENT RELATED TO FIGURE 3.1.-Representation a) of the pure silica glass showing the SiO4 tetrahedrons all interconnected by bridging oxygen atoms and b) of a soda-lime silica glass (SiO2- showing the breaking of the silicate network with the formation of non-bridging oxygen atoms connected to a single SiO4 tetrahedron. The modifier ions Na + and Ca 2+ compensate the negative charge of the non-bridging oxygen atoms.

This chapter focuses first of all on the chemistry of lead, and more specifically on the properties and stereochemistry of the Pb 2+ ion (species under which lead is present in oxide glasses), the nature of the Pb-O chemical bond and the crystalline structure of pure PbO oxide (stereochemistry and mode of connection of the polyhedrons). Then, since the lead-based oxide glasses of interest are overwhelmingly silicate glasses, the focus is on how the Pb 2+ ions get inserted in the glassy network of silica and modify its structure, first of all in the case of the simple binary SiO2-PbO system (for which the evolution of the structure of the binary crystalline phases will also be approached depending on their PbO content compared to glasses), then in the case of more complex systems such as the ternary SiO2-PbO-R2O (R: alkaline) and SiO2-PbO-Al2O3 systems. The effect of these structural evolutions on certain properties of the glass or liquid will also be discussed, with the exception of optical properties (transmission, coloration) that are presented in chapter 4. compared to the crystallized ordered state), by means of directional bonds of iono-covalent type (Zachariasen model (Zachariasen 1932)) (figure 3.1a). As for a glass modifier oxide, it can be defined as an oxide that by itself it never leads to a glass by (even extremely rapid) melting + quenching of the melting liquid, particularly due to the very low viscosity of the liquid and to the structural organization of polyhedrons with respect to one another which is difficult to maintain in a disordered state (excess of free energy between the disordered and ordered state much larger than for the glass former oxides). Higher or lower quantities of modifier oxides (particularly alkaline and alkaline-earth oxides) are however added to glass former oxides in the glasses to facilitate the melting of the mixture (role of fluxing agent), fining of the liquid (elimination of microbubbles and homogenization) and forming of objects (role of fluidizing agent), and also to act on the properties of the final glass. At the structural level, modifier oxides (present in the form of cations) by means of non-directional ionic bonds play the role of compensator in the vicinity of negative charges present in the structure, such as those resulting from breaking the iono-covalent bonds such as Si-O-Si bonds (formation of non-bridging oxygen atoms, Si-O -) (figure 3.1b) or those due to the presence of negatively charged species, such as AlO4 - or BO4 -. Like modifier oxides, intermediate oxidessuch as Al2O3never lead by themselves to glasses by melting + quenching, but at structural level they generally play a different role from that of modifiers and can enter the structure of the glass formers network. It is important to note however that in the absence of glass former oxide and in the presence of one or several modifier oxides, intermediate oxides can also lead in certain cases to glasses, as it is the case of aluminate glasses [START_REF] Pye | Aluminate Glasses -A Review[END_REF]).

Lead and lead oxides

This section focuses on the key elements facilitating the comprehension of lead chemistry in both crystallized and glassy oxides, with a particular highlight of the importance and consequences (physical and structural properties) of the existence of the free 6s 2 electron pair of the Pb 2+ ion.

Elementary lead and its specific properties

3.2.1.1. Lead oxidation states and Pb 2+ ion Lead (atomic number 82) is the heaviest stable element of column 14 of the periodic table. Due to its electron configuration ([Xe] 4f 14 5d 10 6s 2 6p 2 ), it has three common oxidation states: Pb 0 , Pb 2+ and Pb 4+ whose stability domains can be evaluated by the standard potentials of the ionization reactions in aqueous solution:

Pb 0 ⇌ Pb 2+ + 2 e -E° = -0.13 V Pb IV O2 + 4 H + + 2 e -⇌ Pb 2+ + 2 H2O E° = 1.47 V

According to these two equations, bivalent lead is therefore stable within a large potential range, which includes particularly that of the O2/O 2-pair (1.12 V). It is present in this oxidation state in the vast majority of lead-bearing minerals such as litharge, massicot (PbO) and galena (PbS) which is the main ore, as well as in various carbonates, silicates, phosphates or sulfates and in oxide glasses (silicates, borates). Tetravalent lead, much rarer, can be found in minium (Pb3O4, or Pb IV Pb II 2 O4) and plattnerite (PbO2), especially known as the material of the positive electrode of lead-acid batteries. Even rarer is metallic (or native) lead. It is therefore logical that following the example of nature, the arts of fire practiced under an oxidizing potential close to that of the atmosphere can be used for the elaboration of solids containing exclusively Pb 2+ ions, as in the case of oxide-based glasses.

With a coordination number of 8, Pb 2+ ion has a radius of 1.43 Å, comparable to that of strontium Sr 2+ (1.40 Å) [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chacogenides[END_REF]. Similar to the heavy alkaline-earth ions Ca 2+ , Sr 2+ and Ba 2+large and lightly charged -, its oxides have a basic behavior that renders them reactive in relation with acidic oxides (B2O3, CO2, SiO2, P2O5, SO3, etc.) or amphoteric oxides (H2O, Al2O3, Fe2O3, etc.) and leads to the formation of many mixed oxides. Lead oxide-based glasses, though they have no defined compositions, are part of this context. However, the outer electron configuration of Pb 2+ ion ([Xe] 4f 14 5d 10 6s 2 ) is radically different from the saturated one of the ions of the 2 nd column (alkaline-earth). It can be graphically represented as a sphere comprising 4f and 5d orbitals and whose radius corresponds to the one of Pb 4+ ion (1.08 Å) [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chacogenides[END_REF], the external residual volume (nearly 60 %) being filled by the single 6s 2 pair. Strongly screened by the inner orbitals, these two 6s electrons are both labile and very sensitive to the local electric field.

Polarizability of Pb 2+ ion

Polarizability (α), which measures the capacity of a particle to polarize under the action of an electric field E (P = α.E, P being the induced polarization), is generally proportional to the volume, for same charge ions belonging to a same column. As shown in figure 3.2, this relation is strictly followed in the alkalineearth series, but the Pb 2+ ion stands out very clearly due to the contribution of the 6s 2 pair. This high polarizability proves to be a key parameter of the physical, chemical and structural properties of the Pb 2+ ion, and more generally of the ions of elements of block p having an ns 2 np 0 outer electron configuration, such as Tl + , Bi 3+ and Te 4+ , isoelectronic with Pb 2+ .

Polarizability determines particularly the relative permittivity εr as shown by the Clausius-Mosotti relation:

𝜀 𝑟 -1 𝜀 𝑟 + 2 = 𝑁𝛼 3𝜀 0
which yields:

𝜀 𝑟 = 3𝜀 0 + 2𝑁𝛼 3𝜀 0 -𝑁𝛼
N being the number of particles per unit volume and ε0 the vacuum permittivity. One of the main technological applications of lead oxide-based ceramics is logically found in the industry of dielectric, piezoelectric, pyroelectric and ferroelectric components, whose properties are directly linked to polarizability and where Pb 2+ has gradually replaced Ba 2+ in their composition. In the range of optical frequencies, polarizability is expressed through the refractive index n (= √εr). The predominantly positive effect of lead II can be illustrated by the series of crystal compounds M II CO3 with aragonite (orthorhombic, biaxial) structure, whose average refractive index, quasi-identical (1.62) for M = Ca, Sr and Ba, reaches 1.98 for cerussite PbCO3. The shine and covering power of a pulverulent material being directly related to its refractive index, it can be readily understood why white lead (mixture of cerussite and hydrocerussite Pb3(CO3)2(OH)2) has been considered through the ages as top white pigment [START_REF] Welcomme | Classification of lead white pigments using synchrotron radiation micro X-ray diffrac-tion[END_REF][START_REF] Stols-Witlox | The heaviest and the whitest: lead white quality in northwestern European documentary sources, 1400-1900[END_REF]. Likewise, a specific effect of the introduction of lead in the composition of glasses and glazes is to increase the refractive index (chapter 1, figure 1.3).

Lead stereochemistry in oxides

The Valence Shell Electron Pair Repulsion theory (VSEPR) is particularly helpful in understanding the distortions induced by non-bonding doublets of light elements of p block and explaining the geometry of distorted molecules such as water and ammonia. A similar phenomenon can be observed in coordination complexes and crystalline structures containing heavy ions with the ns 2 np 0 configuration, whose two common crystal arrangements of PbO (litharge and massicot) are typical examples.

In litharge (tetragonal symmetry, P4/nmm, a = 4.004 Å and c = 5.071 Å), stable phase at ambient temperature, Pb 2+ ion is surrounded by eight O 2-anions like in a CsCl structure. But here, instead of a cube, the polyhedron is shaped as a very elongated parallelepiped with a square base, in which lead occupies a highly off-centered position (figure 3.3). Pb-O distances, extremely disparate (4  2.33 Å and 4  4.37 Å), reflect an imbalance in the distribution of bonding forces [START_REF] Brown | Bond-valence parameters obtained from a systematic analysis of the inorganic crystal structure database[END_REF], 99 % of which are directed towards the closest four anions. Therefore, the actual coordination number is here only 4, with a hemispherical distribution (known as "umbrella") specific to cations with ns 2 np 0 configuration, lead thus occupying the apex of a square-based pyramid. Short bonds have here the same length as a Pb 4+ -O 2-bond (2.33 Å), which shows that the four close oxygen atoms are in contact with the sphere formed by the 4f and 5d orbitals of lead. In massicot (figure 3.3), a PbO form that is stable above 490 °C, metastable at ambient temperature, the hemispherical coordination number of lead is 4, though less regular due to the orthorhombic symmetry (Pbcm, a = 5.893 Å, b = 5.490 Å and c = 4.753 Å). In both cases, the 6s 2 pair is repelled to the opposite of short bonds due to the high polarizability of Pb 2+ ion, in the apparently unoccupied part of the oxygen polyhedron ("apparently" because these two electrons, which are a far less charged and coherent source of scattering than the 78 electrons of the lead core orbitals grouped in a small volume, are difficult to observe by X-ray diffraction, and even more difficult by neutron diffraction, for which only the nuclei are "visible"). From an electrostatic perspective, the 6s 2 pair however plays an essential role, like that of a nonbonding pair in VSEPR, as its negative charge strongly repels the anions on the opposite side of strong bonds, hence the strong increase in Pb-O distance (4.37 Å) on this side of the polyhedron (figure 3.3). The dipole moment of Pb 2+ ion thus influences the geometry of its environment. The representation of ions in actual proportions in the two PbO varieties (figure 3.4) shows that it is off-centered by approximately 1 Å with respect to the nucleus and that it occupies roughly the same volume as an anion. Its presence in the apparently empty volumes of the structures makes it actually possible, with oxygen anions, to obtain pseudo-hexagonal layouts close to the ideal packing density contributing to the stability of these oxides.

Let us now focus on how the PbO4 polyhedrons are connected in the two crystal varieties of PbO. In the case of litharge, these polyhedrons are interconnected by the edges and arranged head-to-tail to minimize the electron repulsions between non-bonding doublets of the lead atoms (figure 3.5). In massicot, the pyramids are interconnected by the edges, and once more the arrangement makes it possible to minimize the electron repulsions between non-bonding doublets of Pb 2+ ions. Litharge is the most stable form, as it is stabilized by the interactions between non-binding doublets, with an antiparallel orientation between near-neighbors of the same plane (001). This orientation is partly lost in massicot due to the distortion of polyhedrons, which leads globally to the weakening of this interaction at the crystal scale; massicot is therefore less stable. The origin of the shift of 6s orbitalnormally spherical and nucleus-centeredin ions with ns 2 np 0 configuration was the subject of many experimental and theoretical works following those of Gillespie and Nyholm in the 1950s [START_REF] Gillespie | Inorganic stereochemistry[END_REF]. The widespread model is that of a simple hybridization of 6s and 6p orbitals of Pb 2+ allowing the doublet to take the shape of a protuberant lobe; however recent studies tend to prove the involvement of 2p levels of neighboring O 2-anions [START_REF] Watson | Ab initio calculation of the origin of the distortion of alpha-PbO[END_REF][START_REF] Waghmare | First-principle indicators of metallicity and cation off-centricity in the IV-VI rocksalt chalcogenides of divalent Ge, Sn and Pb[END_REF]. Whatever the mechanism, the structural distortion of a crystalline solid by a stereochemical effect of "free pair" ultimately follows a simple law: minimizing the network energy. In litharge for example, the shift of the 6s 2 pair "vacates" the opposite 4f and 5d orbitals, allowing the formation of four short Pb 4+ -O 2-bonds, which are highly covalent and directional, globally more stable than the eight bonds with high ionicity rate that would form in a symmetric structure of CsCl type. Adding that its electronegativity (1.87 on Pauling scale) is significantly higher than that of alkaline and alkalineearth elements (Na = 0.93; K = 0.82; Mg = 1.31; Ca = 1.00), it is clear that the structural role of lead in glasses is much closer to that of glass former or intermediate elements (Si = 1.9; Al = 1.61), although closer to the former due to its size. As it will be noted further on in this chapter (section 3.3.3), in oxide glasses such as silicates, the free pair of Pb 2+ ions contributes also to their incorporation in the form of polyhedrons of low coordination number (3 or 4) with the oxygen anions anisotropically distributed around lead [START_REF] Fayon | Pb 2+ environment in lead sili-cate glasses probed by Pb-LIII edge XAFS and 207 Pb NMR[END_REF][START_REF] Rybicki | The structure of lead-silicate glasses: molecular dynamics and EXAFS studies[END_REF][START_REF] Alderman | Lone-pair distribution and plumbite network for-mation in high lead silicate glass, 80PbO.20SiO2[END_REF].

The same energy contingency is however applicable sometimes to the stereochemical activity, when a stable structural form adapted to the composition makes it possible to host the cation in a steady environment. The already mentioned series of MCO3 carbonates with aragonite structure offers an example. Metastable for Ca 2+ that more often crystallizes as calcite, it is in fact perfectly adapted to larger cations, such as Sr 2+ and Ba 2+ for which it is the stable form. However, the structure of cerussite PbCO3 [START_REF] Chevrier | Neutron single-crystal refinement of cerussite, PbCO3, and comparison with other aragonite-type carbonates[END_REF]) is quasi-identical with that of SrCO3 [START_REF] Pannhorst | ZurKristallstruktur von Strontianit, SrCO3[END_REF], with an environment of Pb 2+ whose regularity (2.65 < Pb-O < 2.76 Å) proves the absence of stereochemical activity of the 6s 2 pair. However, the absence of permanent polarization of Pb 2+ ion does not impede the previously mentioned strong polarizability. Moreover, it is important to note that the stereochemical activity of the free pair of Pb 2+ ion depends also on the nature of neighboring anions. Hence, unlike in PbO, the free pair of Pb 2+ ions is stereochemically inactive in PbS due to the anion-cation orbital interactions that differ for the two phases [START_REF] Walsh | The origin of the stereochemically active Pb(II) lone pair: DFT calculations on PbO and PbS[END_REF]. The stereochemical activity of the 6s 2 pair is therefore not systematic in the crystal structures containing lead II, but it is however frequent (it is the case of crystallized lead silicates, as it will be seen in section 3.2), though sometimes less marked than in the two varieties of PbO. Pb 2+ has for this reason an intermediate behavior between those of its isoelectronic neighbors, the stereochemical activity being rarer and less marked for Tl + and quasisystematic and strong for Bi 3+ , undoubtedly for reasons of size and charge.

In the biological domain, the effect of the free pair widely contributes to lead toxicity, as it replaces cations that are essential to the metabolic functioning, such as Ca 2+ , Zn 2+ or Fe 2+ inside the structures of enzymes and complexes. This substitution is on the one hand easy and almost irreversible, as the stereochemical activity of the 6s 2 pair allows the formation of strong bonds with the ligands, and on the other hand it is harmful, as it modifies the symmetry to the point of disrupting the functioning [START_REF] Gourlaouen | Is an electronic shield at the molecular origin of lead poisoning? A computational modeling experiment[END_REF], which renders lead ingestion particularly toxic (lead poisoning, chapters 13 and 14) [START_REF] Patrick | Lead toxicity, a review of the literature. Part 1: Exposure, evaluation, and treat-ment[END_REF].

Crystal phases and glasses of the SiO2-PbO system

In lead oxide-based silicate glasses used both in the industry and in the crafts and art (massive glasses, glazes, enamels), SiO2 and PbO are the majority of oxides forming the glass structure. Hence in the crystal glass, the sum SiO2 + PbO is generally about 85 % of its mass (the rest being mainly alkaline oxides K2O and Na2O) while in transparent lead glazes deposited on the surface of ceramics, this sum commonly reaches over 90 % in mass (the rest being then mainly constituted of alumina most of the time [START_REF] Tite | Review arti-cle. Lead glazes in antiquity -methods of production and reasons for use[END_REF]) (chapter 10). Though the binary glasses of the SiO2-PbO system have actually no practical use as there is almost always an addition to their composition of other glass former, modifier or intermediate oxides (boron oxide, alkaline oxides, alumina, etc.) depending on the considered applications [START_REF] Rabinovich | Lead in glasses[END_REF]), it appears particularly important to properly understand the structure of these simple glasses depending on their PbO content and especially the manner in which the Pb 2+ ion is inserted in the structure of the silicate glassy network for both low and highest PbO contents, if the objective is to apprehend the structure of more complex lead silicate glasses. This explains the rich literature related to the structural study of glasses of the SiO2-PbO system published for nearly 85 years [START_REF] Bair | The constitution of lead oxide-silica glasses: I, atomic arrangement[END_REF])! Despite the increasingly advanced and various methods of investigation and simulation implemented in order to explore the environment of lead, silicon and oxygen in these simple glasses, there are still many questions related to the way the Pb 2+ ions are incorporated in these glasses and particularly for the highest PbO contents, as it will be seen here. But before focusing on the glassy system (the supercooled liquid frozen during quenching, which is in a nonequilibrium state), let us first examine the binary system at thermodynamic equilibrium depending on temperature and its composition, and also on the structure of mixed crystal phases existing in this system and more specifically on the manner in which the Pb 2+ ions are incorporated in their crystal network.

The binary SiO2-PbO system at equilibrium

Given the importance of this system, phase diagrams were proposed for the binary SiO2-PbO system since the 1930s [START_REF] Geller | The system PbO-SiO2[END_REF], which were subsequently completed and refined using new experimental results and calculations. To our knowledge, the most recent one belongs to Shevchenko and Jak [START_REF] Shevchenko | Experimental phase equilibria studies of the PbO-SiO2 system[END_REF], combining calculations and experimental results (figure 3.6).

As indicated in chapter 1, this diagram shows the very clear fluxing effect of PbO when added to SiO2 (strong decrease of the green curve corresponding to the liquidus of the system). However, it can be noted that for PbO contents ranging between 40 and 80 mol%, the liquidus temperature (Tliquidus) does not change much and ranges between 730 and 750 °C, but it has a small increase when getting close to the pure PbO phase (massicot, Tmelting = 886 °C). This diagram also contains in full line the phase diagram calculated by the same team in a previous study [START_REF] Jak | Thermodynamic optimization of the systems PbO-SiO2, PbO-ZnO, ZnO-SiO2 and PbO-ZnO-SiO2[END_REF].

As long as the PbO content is below 50 mol%, the only stable crystal phases susceptible to form inside the system are the various crystal varieties of silica (cristobalite, tridymite, quartz) and lead metasilicate PbSiO3 (alamosite) with congruent melting. Therefore, there is no stable mixed crystal phase with less than 50 mol% of PbO. It is important to note that contrary to the predictions of the calculations of Jak et al. [START_REF] Jak | Thermodynamic optimization of the systems PbO-SiO2, PbO-ZnO, ZnO-SiO2 and PbO-ZnO-SiO2[END_REF]) (black curve, figure 3.6), the experimental curve of liquidus exhibits no stable demixing dome indicating the existence of phase separation phenomena inside the liquid (T > Tliquidus). However, the specific S-shape of the liquidus curve (green curve, figure 3.6) suggests that a metastable demixing may occur in the supercooled liquid (T < Tliquidus) [START_REF] Calvert | Liquidus behavior in the silica-rich region of the system PbO-SiO2[END_REF] as in the SiO2-BaO system [START_REF] Seward | Phase separation in the system BaO-SiO2[END_REF]). The diagram shows that several mixed crystal phases may form in this system besides PbSiO3 for PbO contents above 50 mol%:

-at high temperature, near the liquidus curve: Pb2SiO4 (lead cyclosilicate, with congruent melting), Pb11Si3O17 (with congruent melting) and Pb5SiO7 (with incongruent melting). The Pb4SiO6 phase shown in older phase diagrams (Smart and Gasser 1974) would not be stable [START_REF] Hirota | Phase Relations in the System PbO-PbSiO3[END_REF];

-at lower temperature, in the solidus domain: Pb7Si6O19 and Pb3Si2O7 (these two phases decompose before melting).

Crystal phases of the binary SiO2-PbO system

This section presents the evolution of the structure of mixed crystal phases mentioned in the previous section depending on the lead oxide content according to the data in the literature2 (mol% PbO): alamosite PbSiO3 (50 %) [START_REF] Boucher | The crystal structure of alamosite, PbSiO3[END_REF]), Pb7Si6O19 (53.8 %) [START_REF] Siidra | Structural complexity of lead silicates: Crystal structure of Pb21[Si7O22][Si4O13] and its comparison to hyttsjöite[END_REF], Pb3Si2O7 (60 %) [START_REF] Petter | Die Kristallstruktur von Blei-Barysilit, Pb3Si2O7[END_REF], Pb2SiO4 (66.6 %) [START_REF] Dent Glasser | The structure of lead orthosilicate, 2PbO. SiO2[END_REF]), Pb11Si3O17 (78.6 %) [START_REF] Hirota | Phase Relations in the System PbO-PbSiO3[END_REF][START_REF] Kato | Die Kristallstruktur des Bleisilicats Pb11Si3O17[END_REF]. Three of these structures are represented in figure 3.7. Pb5SiO7 (83.3 %), which is stable only at high temperature [START_REF] Hirota | Phase Relations in the System PbO-PbSiO3[END_REF], is the only one whose structure remains unsolved. The focus is here on the effect of PbO addition to the silicate network and on the manner in which Pb 2+ ions are incorporated in this structure (type of occupied sites, existence of connections between them and with the silicate units). The absence of mixed crystalized oxides with a PbO content below 50 mol% (or 79 mass%) is a tendency found among the known complex silicates (exception: margarosanite PbCa2Si3O9 has a 43 mol% PbO rate). Therefore, the estimation of the structural behavior of crystal glasses and lead glazes (with PbO contents of the order of 10 and 30 mol%, respectively) based on the crystal phases will only be possible by extrapolation, or interpolation with the pure SiO2 pole. However, as it will be seen in section 3.3.3.1, binary glasses of the SiO2-PbO system with up to 83 mol% PbO content can be obtained, therefore for PbO contents that are as high as those of crystal phases (figure 3.7). An examination of the crystal structures shows that the 6s 2 pair of Pb 2+ is systematically active from stereochemical perspective, thus the average number of short bonds (dPb-O < 2.5 Å, with a bond valence above 0.35 v.u.3 ) varies only from 2.3 to 3.0 per Pb 2+ ion, no correlation with the PbO rate being noted. As it disperses SiO4 tetrahedrons, PbO addition is expected to mechanically reduce their cross-linking.

Hence the silicate network, formed of infinite meta chains in PbSiO3 evolves towards disilicate units in Pb3Si2O7, following the same tendency as for the addition of CaO. For these two families, the rate of bridging oxygen atoms (involved in the Si-O-Si bonds) evolves in line with the theoretical model following a law in (2 -3x)/(2 -x), with x = M II /(M II + Si) which explains the depolymerization of the silicate network (figure 3.8). The same is applicable to Pb7Si6O19, whose more complex structure expands in Pb21(Si7O22)2(Si4O13). The analysis of crystal structures suggests that in lead glasses and glazes (0.1 < x < 0.3), lead oxide has a depolymerizing effect similar to that of a standard modifier. For x = 2/3, theoretical threshold of total depolymerization (figure 3.8), silicate tetrahedrons become effectively independent in Ca2SiO4 (calcium orthosilicate), but its lead homologue has a radically different structure, of oxy-cyclosilicate type (Pb2OSiO3, figure 3.7) due to which Si-O-Si cross-linkages (cycles of 4 tetrahedrons) persist. The same is valid for Pb11Si3O17 (Pb11O6(Si2O7)(SiO4)), which has an even higher lead rate and contains silicate dimers (figure 3.7). This singularity is very likely explained by the stereochemistry of the 6s 2 pair, which allows the establishment of strong bonds in the opposite direction of silicate units, certain anions being thus grabbed by three or four Pb 2+ cations and isolated from the silicate network (figure 3.7); the latter can therefore maintain a certain degree of polymerization, for example in the form of cycles or dimers (figure 3.7).

The strong Pb-O bonds (with O 2-ions that are not bound to silicon) are at the origin of a second form of cross-linking, which does not exist with alkaline or alkaline-earth modifiers. It is however more difficult to define than that of silicate network, due to the irregularity of the lead environment. Taking into account only the Pb-O bonds whose length is below 2.5 Å, the formation of Pb-O-Si and Pb-O-Pb crosslinkages can be noted, their evolutions being represented in figure 3.9. The separation of lead, which occurs beyond x = 0.66 generates a significant decrease of the former, to the benefit of the latter. In the domain of glasses and glazes (0.1 < x < 0.3), the interpolation between SiO2 and the nearest crystallized lead silicates suggests the existence of a significant primary cross-linking, of about 0.2 to 0.7 "strong" Pb-O-Si cross-linkages per oxygen. On the other hand, the Pb-O-Pb cross-linkages are of about three to four times rarer (figure 3.9). Within the lead-rich crystal phases of SiO2-PbO system (≥ 50 mol% PbO, figure 3.6), the connection between the polyhedrons occupied by Pb 2+ ions is generally done by the edges (figure 3.7). This approach based on the comparison with known crystal structures, though weakened by their high PbO rates ( 50 mol%) for the crystal glasses and lead glazes (≤ 30 mol% PbO), but more realistic for PbOricher glasses having contents within the same range as crystal phases (section 3.3.3.1), therefore suggests that lead contributes to the depolymerization of the silicate network similarly to calcium. However, thanks to the stereochemical activity of the 6s 2 pair, it allows the formation of Pb-O-Si cross-linkages based on strong Pb-O bonds. The strong Pb-O-Pb cross-linkages would be marginal for crystal glasses and lead glazes but would have a significant and increasing contribution for glasses with much higher PbO contents (figure 3.9).

Glasses of the binary SiO2-PbO system

Overview of glasses of the binary SiO2-PbO system

After the crystal phases of lead silicates, let us now focus on the impact of adding increasing quantities of PbO to the well-known glass former oxide which is vitreous silica SiO2 and more particularly on its structure and the manner in which Pb 2+ ions are incorporated in it 4 and also on the evolution of certain physical properties. The study of the structure of these glasses and of the structure-properties relations is particularly important from both fundamental and applied perspectives, as SiO2 and PbO are the two predominant oxides in most of the lead oxide-based silicate glasses (crystal glass industry, glazes and enamels, optics, etc.). Moreover, the very wide domain of vitrifiable composition in this system compared to other binary systems, such as alkaline or alkaline-earth silicates is still the subject of many questions in terms of their structure and the role of lead particularly for the PbO-richest compositions. Indeed, it is possible to obtain binary SiO2-PbO glasses by melting--quenching up to PbO contents of over 83 mol% 5 (95 mass%) [START_REF] Feller | A multispectroscopic structural study of lead silicate glasses over an extended range of compositions[END_REF]) while for the SiO2-R2O systems (R: alkaline) it is increasingly difficult to obtain glasses above 55 mol% R2O [START_REF] Imaoka | Studies of the glass-formation range silicate systems. Investiga-tions on the glassformation range 2[END_REF] due to the very strong tendency to 4. As mentioned above (section 3.2.1.1), lead is overwhelmingly present in the form of Pb 2+ ions in oxide glasses. The presence of Pb 4+ ions would only step in for highly lead-rich glass compositions melted under highly oxidizing atmosphere. This is in line with the evolution of the stability of lead oxides with temperature (PbO2 < Pb3O4 < PbO). 5. Binary glasses with PbO contents above 90 mol% were sometimes mentioned in the literature [START_REF] Ellis | The electronic band struc-ture and optical properties of oxide glasses[END_REF]), but due to the lacking results of chemical analysis, such data must be carefully considered given the strong evaporation tendency of PbO for lead-rich compositions (> 70-80 mass% PbO) [START_REF] Andersen | The volatilization of lead oxide from lead silicate melts[END_REF][START_REF] Volf | Chemical approach to glass[END_REF]. Moreover, melting liquids that are very rich in PbO (> 90 mass%) have a very strong crystallization tendency (Faivre and Weiss 1963, p. 587).

crystallize of the corresponding supercooled liquids during cooling, associated both with a decrease in their viscosity and with the very strong depolymerization of the silicate network 6 . In the lead system, for compositions very rich in PbO, the amorphous structure of the liquid can be stabilized by quenching, even though SiO2 is in a minority. This implies a different structural behavior of Pb 2+ ions compared to that of alkaline and alkaline-earth ions in these glasses and particularly for high PbO (which is in agreement with the comparison of crystal phases of alkaline-earth and lead silicates, figure 3.8), though, like them, its gradual addition to SiO2 induces both a strong decrease of the liquidus temperature of the system (figure 3.6) and of the viscosity of the liquid (figure 3.10). It is important to note that even if the liquid is still homogeneous for T > Tliquidus (figure 3.6), the compositions rich in SiO2 (> 65 mol%) have a demixing tendency (metastable, therefore sub-liquidus) during the cooling of the liquid [START_REF] Calvert | Liquidus behavior in the silica-rich region of the system PbO-SiO2[END_REF][START_REF] Vogel | Glass chemistry[END_REF]). However, the tendency towards phase separation in these binary glasses is suppressed when K2O is added (as it is the case in the crystal glass), which can be explained by the quasi-absence of demixing tendency in the binary SiO2-K2O [START_REF] Charles | Metastable Liquid Immiscibility in Alkali Metal Oxide-Silica Systems[END_REF]) due to the low field strength 7 of K + cation (F  0.14 Å -2 ) compared to Pb 2+ cation (F  0.36 Å -2 ) [START_REF] Vogel | Glass chemistry[END_REF]. The substantial tendency of binary glasses SiO2-PbO with low PbO content to demixing coupled with their very high liquidus temperature (figure 3.6) requiring melting temperatures of about 1 600-1 700 °C explains the small number of studies in the literature on the compositions of lead silicates very rich in silica [START_REF] Bair | The constitution of lead oxide-silica glasses: I, atomic arrangement[END_REF][START_REF] Calvert | Liquidus behavior in the silica-rich region of the system PbO-SiO2[END_REF]. A certain number of studies have also been conducted on the crystallization of binary SiO2-PbO glasses with or without nucleating agent (such as P2O5) but will not be developed here (Carr andSubramanian 1982a, 1982b;[START_REF] Lippmaa | High resolution 29 Si NMR study of the structure and devitrification of lead-silicate glasses[END_REF][START_REF] Neiman | Crystallization kinetics of lead metasilicate[END_REF][START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF][START_REF] Pena | In-situ Raman spectroscopy unveils metastable crystallization in lead metasilicate glass[END_REF]. Hence, according to Kaur et al. [START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF], as long as the PbO content < 50 mol%, glasses resist well to crystallization at heating, while when the PbO content  50 mol%, the majority crystallization of phases such as PbSiO3 and Pb2SiO4 was evidenced. Before going further into the structural details and in particular on the manner in which Pb 2+ ions are inserted in the vitreous structure and how they react to the silicate network (section 3.3.3.2), it is interesting to 6. For binary SiO2-R2O glasses, assuming the gradual formation of SiO4 Q n entities with a decreasing number n of bridging oxygen atoms (figure 3.1b) when R2O is added (Q n represents the SiO4 tetrahedrons counting n bridging oxygen atoms), it appears that between 50 and 60 mol% R2O there are only highly depolymerized entities Q 2 and Q 1 (binary model). Beyond 66.6 mol% R2O, the glass would only be constituted of completely depolymerized Q 0 (SiO4 present the effect of the gradual addition of PbO to the silica on certain physical properties of the glass and of the liquid [START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF]).

Besides the above mentioned effect on the viscosity of the melting liquid (strong decrease with the PbO content, figure 3.10), highlighting the fluxing effect of the lead oxide as it is the case for alkaline oxides and boron oxide, the incorporation of increasing PbO contents to the silica leads to a decrease in the glass transition temperature, of the electrical resistivity of glasses and of the surface tension of associated liquids. Moreover, the molar volume tends also to decrease to 60 mol% PbO, then slightly increases [START_REF] Shelby | Property/structure relationships in lead silicate glasses[END_REF][START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF][START_REF] Ben Kacem | Du cristal au plomb jusqu'aux déchets domestiques : rôle du plomb dans les verres et les[END_REF]. The effect of the lead content on the mechanical properties of binary SiO2-PbO glasses has also been studied, showing for example a tendency of their hardness and of their Young's modulus to decrease when PbO concentration increases [START_REF] Yoshihoto | The effect of composition on crack propagation in lead silicate glas-ses[END_REF][START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF]. The increase in density and in the refractive index presented in chapter 1 is simply explained by the high atomic mass of lead compared to silicon and oxygen (density) and by the strong polarizability of the Pb 2+ ion and its high atomic mass (refractive index). Furthermore, it is important to note that the coefficient of thermal expansion of binary SiO2-PbO glasses increases linearly with their molar content in PbO [START_REF] Greenough | Thermal expansion of lead silicate glasses[END_REF][START_REF] Shelby | Property/structure relationships in lead silicate glasses[END_REF]) but remains below that of binary SiO2-Na2O glasses [START_REF] Scholze | Le verre. Nature, structure et propriétés[END_REF], this property being important particularly for glazes (crazing problem). The chemical durability in aqueous medium of the glasses containing lead oxide was briefly addressed in chapter 1 (section 1.1.8) and is presented in detail in chapter 13 for industrial glasses containing both lead and alkaline ions (crystal glass), therefore it will not be covered here. However, related to the binary SiO2-PbO glasses without alkaline ions, it is important to note the study conducted by El-Shamy and Taki-Eldin (El Shamy and Taki-Eldin 1974) on the chemical durability of glasses depending on pH, which shows a nonmonotonic evolution of their tendency to leaching depending on their PbO content. It is also important to mention the more recent works of Mizuno et al. [START_REF] Mizuno | Leaching of lead and connectivity of plumbate networks in lead silicate glasses[END_REF] on the durability of binary SiO2-PbO glasses conducted in an acid medium. which the authors tried to link to the distribution of lead-based structural units PbOn in the vitreous structure as a function of lead concentration.

Structure of the glasses of the binary SiO2-PbO system

According to certain works in the literature (Sorokina et al.1996), the structural role of lead in the binary silicate glasses evolves with the PbO content, passing from modifier to glass former oxide, which might explain the larger expansion of the vitreous field of lead silicates compared to alkaline silicates as mentioned above (section 3.3.3.1). Before presenting more precisely these works and also other studies stating that the structural role of lead would not evolve fundamentally as a function of its concentration [START_REF] Smets | The structure of glasses and crystalline compounds in the system PbO-SiO2, studied by X-ray photoelectron spectroscopy[END_REF][START_REF] Mizuno | Leaching of lead and connectivity of plumbate networks in lead silicate glasses[END_REF]Ben Kacem et al. 2017) and proposing various structural models, let us focus only on lead oxide PbO and its capacities, or lack thereof, to lead to a glass by melting--quenching.

It is important to note first of all that PbO is not a glass former oxide, since unlike silica, for example, it does not lead by melting + quenching to the formation of a glass. This may be due to several reasons. First of all, the very low viscosity of liquid PbO in the vicinity of its melting temperature (  0.01 Pa.s (0.1 P) [START_REF] Sinn | Measurement of the shear viscosity in garnet high temperature solutions by a cylin-drical rotation viscometer[END_REF])) which is higher only by a factor of 10 than that of water at ambient temperature (  0.001 Pa.s (0.01 P) [START_REF] Korson | Viscosity of water at various temperatures[END_REF]) and significantly lower than that of melted silica in the vicinity of its melting temperature (  10 6 Pa.s (10 7 P) [START_REF] Martlew | Viscosity of molten glasses. Dans Properties of glass-forming melts[END_REF])) explains the ease of PbO crystallization from the liquid by the strong mobility of species and therefore the difficulty to maintain the latter in supercooled state and consequently to obtain a glass by quenching. Moreover, from a structural point of view, according to Zachariasen rules related to glass former oxides MxOy [START_REF] Zachariasen | The atomic arrangement in glass[END_REF]), these must be such that on the one hand the MOn polyhedrons are loosely coordinated (3 or 4)which corresponds to small highly charged cations M +2y/x such as Si 4+ , B 3+ and P 5+and connected with one another only by the vertices (not by the edges or the faces) allowing a significant flexibility in the structural arrangement, without getting a too high increase in the free energy of the system. According to the same rules and for the same reasons, it is stipulated that the oxygen anions should not connect more than 2 MOn polyhedrons. The coordination number of Pb 2+ ions being 4 in crystal PbO, as already seen above (figures 3.3 and 3.5), the coordination number of O 2-ions should also be 4, to have electroneutrality. This explains why the PbO4 units are connected by the edges and not by the vertices, which is contrary to Zachariasen's rules. Being relatively constrained locally, this structure may seem unfavorable to accepting significant disorder at the level of polyhedral layout without this leading to a significant increase in its free energy 8 . From a thermodynamic point of view, this should be in favor of the crystallized state compared to the vitreous state, and could explain structurally why PbO is not a forming oxide. Likewise, according to Dietzel's theory [START_REF] Dietzel | Structure and properties of glass[END_REF]) connecting the cationic field strength F and the structural role of oxides in glasses, it appears that Pb 2+ ion has a field strength of approximately 0.36 Å -2(9) , which would put PbO in the class of modifier oxides for which F ranges between 0.1 and 0.4 Å -2 (F ranges between 1.5 and 2.0 Å -2 for glass former oxides). However, it is important to recall here that due to its strong polarizability (section 3.2.1.2), from the point of view of its bonds with the nearest neighbor oxygen ions, the Pb 2+ ion can be considered as a Pb 4+ ion with a higher field strength F = 0.48 Å -2 . This would put PbO in the class of intermediate oxides (F ranging between 0.5 and 1.0 Å -2 ) with quite directional Pb-O bonds, which are ionocovalent and asymmetrically arranged in its environment (figures 3.3 and 3.5). This type of Pb-O bond is therefore very different from the one existing between alkaline and alkaline-earth cations and O 2-anions in the crystallized oxides (ionic bonds distributed quite symmetrically around cations).

It can be then understood that the mode of incorporation of Pb 2+ ions in a silicate glass may be very different 10 from the one of traditional modifier cations (Na + , K + , Ca 2+ , etc.) which are far less polarizable 11 and for which the bonds with the oxygen anions are weaker, ionic and therefore nondirectional. Relying on the crystal structure of PbO and assuming that the environment of Pb 2+ ions in SiO2-PbO glasses was also very asymmetrical with quite strong directional bonds due to their very strong polarization by O 2-anions, Fajans and Kreidl (Fajans and Kreild 1948) proposed in the 1940s that this particular type of lead environment was at the origin of the largest stability of the liquids of SiO2-PbO system in terms of crystallization (and therefore of their easier vitrification) compared to alkaline silicate compositions for which the crystallization processes are facilitated by the easier reorganization of species in the corresponding liquids (weaker and non-asymmetric bonds between alkaline cations and O 2-anions) 12 . However, the study of the structure of binary SiO2-PbO glasses had started about ten years earlier, in 1936, by X-ray scattering [START_REF] Bair | The constitution of lead oxide-silica glasses: I, atomic arrangement[END_REF], only one year after the well-known works of Warren and Loring on the X-ray scattering study of the structure of soda silicate glasses [START_REF] Warren | X-ray diffraction study of the structure of soda-silica glass[END_REF] and 4 years after the famous Zachariasen's publication on the structure of oxide glasses [START_REF] Zachariasen | The atomic arrangement in glass[END_REF]. However, the model proposed by Bair for lead silica glasses [START_REF] Bair | The constitution of lead oxide-silica glasses: I, atomic arrangement[END_REF], based on his processing of Xray scattering data, was very close to the structural model of soda silicate glasses of Warren and Loring (random continuous silicate network with homogeneous distribution of Pb 2+ ions near non-bridging oxygen atoms of SiO4 tetrahedrons). Since these first works aimed at clarifying the structure of binary SiO2-PbO glasses, many studies have been conducted using various structural investigation methods such as X-ray and neutron scattering, X-ray absorption (EXAFS 13 and XANES 14 ), XPS 15 , multinuclear NMR 16 ( 207 Pb, 29 Si, 17 O), Raman and IR spectroscopies, as well as molecular dynamics. These studies confirmed the hypothesis of Fajans and Kreidl of a very asymmetric environment of Pb 2+ ions in the 8. It is important to note however that due to the two-dimensional character of the crystalline structure of PbO (litharge and massicot, figure 3.6), it may probably easier accept local constraints due to disorder than three-dimensional crystalline structures such as those of alkaline and alkaline-earth oxides, whose role as modifier oxides is well established. 9. Calculation made according to the crystalline PbO structure and Shannon's ionic radii [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chacogenides[END_REF]) (rPb 2+ = 0.98Å, rO 2-= 1.38Å). 10. Indeed, as noted in section 3.3.2, for crystallized lead silicates the environment of Pb 2+ ions is also strongly asymmetric. 11. Indeed, according to Kordes, the values of polarizability (in Å 3 ) are the following: Na + (0.175) < Ca 2+ (0.469) < K + (0.821) < Pb 2+ (3.623) [START_REF] Dimitrov | An interpretation of optical properties of oxides and oxide glasses in terms of the electronic polarizability and average single bond strength (review)[END_REF]. 12. It is interesting to signal that according to Vogel [START_REF] Vogel | Glass chemistry[END_REF], the fact that the vitrifiable domain of the P2O5-PbO system is less extended than that of SiO2-PbO system (66 mol% compared to 83 mol%) could be explained by the very strong polarization exerted by the P 5+ ions on the O 2-anions of the phosphate network, which would have a weaker polarizing effect on the Pb 2+ ions than in the case of silicate glasses (Si 4+ ion having a weaker field strength than P 5+ ion), thus leading to weaker Pb-O bonding forces and a higher coordination number for Pb 2+ ions with the oxygen atoms associated with phosphorus [START_REF] Hoppe | Environments of lead cations in oxide glasses probed by X-ray diffraction[END_REF]. For further information on the structure and properties of the glasses of the binary P2O5-PbO system, please see the references [START_REF] Dayanand | Structural investigations of phosphate glasses: a detailed infrared study of the x(PbO)-(1-x) P2O5 vitreous system[END_REF][START_REF] El-Egili | Structure and some physical proper-ties of PbO-P2O5 glasses[END_REF]Matori et al. 2013) silicate glasses, such as the study of [START_REF] Mydlar | X-ray diffraction study of lead sili-cate glasses[END_REF][START_REF] Mydlar | X-ray diffraction study of lead sili-cate glasses[END_REF]. Nowadays all the authors agree that in lead silicate glasses the majority of Pb 2+ ions are found in very asymmetric environments like in the PbO and lead silicates crystals (figures 3.3, 3.5 and 3.7) having also a sterochemically their active 6s 2 pair 6s 2 (sections 3.2.2 and 3.3.2). However, the authors still diverge on the structural role of lead, its type of environment and its evolution as a function of PbO content in glass. A part of these structural works on binary SiO2-PbO glasses was the object of past [START_REF] Rabinovich | Lead in glasses[END_REF] or more recent [START_REF] Alderman | The structure of vitreous binary oxides: silicate, germanate and plumbite networks[END_REF]) bibliographic syntheses. Based on some of these studies, and particularly on the more recent ones, the following sections of this chapter focus on the manner in which the silicate vitreous network is affected by the addition of increasing quantities of lead oxide. Then the structural role of Pb 2+ ions and the evolution of their environment and of their distribution in the vitreous network will be examined.

Vitreous silicate network

Prior to any lead oxide addition, the structure of pure silica glass is exclusively formed of SiO4 tetrahedrons connected to one another by their vertices forming a continuous network, as seen at the beginning of this chapter (figure 3.1a). In this case each SiO4 tetrahedron has four bridging oxygen atoms. In order to introduce the classification of various types of SiO4 tetrahedrons present in the glasses composed of silica and one or more other oxides such as PbO, let us consider the well-known case of binary SiO2-Na2O glasses. When Na2O is added to the silica glass, Si-O-Si bonds are broken (Na2O has the role of modifier oxide): the vitreous silicate network becomes partially depolymerized and non-bridging oxygen atomswhose negative charge is locally compensated by Na + ionsare formed (figure 3.1b). To account for the gradual depolymerization of SiO4 tetrahedrons depending on Na2O content, the notation Q n is introduced, representing the SiO4 tetrahedrons counting n bridging oxygen atoms. A pure silica glass thus contains only Q 4 units, and for binary glasses a Q 3 unit corresponds to a SiO4 -tetrahedron, a Q 2 unit to a SiO4 2- tetrahedron, a Q 1 unit to a SiO4 3-tetrahedron and a Q 0 unit to a SiO4 4-tetrahedron that is completely isolated from the rest of the silicate network. The more Q n units with low n, the more difficult it becomes to vitrify the liquid, as it is increasingly fluid and is readily organized in the form of crystals. Using this notation, the chemical equation corresponding to the introduction of Na2O in a pure silica glass is: 2Q 4 + Na2O → 2Q 3 . It is in fact an acid-base reaction (in the sense of oxo-acidity [START_REF] Flood | The acidic and basic properties of oxides[END_REF])) between the basic oxide Na2O giving O 2-anions and the acidic oxide SiO2 that accepts them. Moreover, in the melting liquid there is an equilibrium (disproportionation reaction) between Q n units (2Q n ↔ Q n-1 + Q n+1 ) that can be found in the glass obtained after quenching [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF]. The description of the silicate network involves particularly the study of its degree of polymerization, hence following-up the evolution of the proportions of various units Q n that compose it. In the case of simple silicate compositions, this can be done, for example, using 29 Si NMR and Raman [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF][START_REF] O'shaughnessy | The influence of modifier cations on the Raman stretching modes of Qn species in alkali silicate glasses[END_REF]) spectroscopies, while the follow-up of the evolution of the proportions of the various types of oxygen atoms (bridging, non-bridging or not connected to the silicate network) can be achieved by 17 O NMR (after glass enrichment in 17 O) 17 and XPS spectroscopies, for example [START_REF] Dalby | Resolution of bri-dging signals from O 1s spectra of silicate glasses using XPS: Implications for O and Si specia-tion[END_REF][START_REF] Lee | Probing metal-bridging oxygen and configurational disorder in amor-phous lead silicates: insights from 17 O solid-state nuclear magnetic resonance[END_REF].

In the case of interest here, several studies focused on the evolution of the structure of the silicate network of lead silicate binary glasses and clearly highlight the fact that the introduction of PbO leads to an increasing depolymerization of the silicate network. For example, Bessada et al. [START_REF] Bessada | 29 Si MAS-NMR in lead silicates[END_REF]), Fayon et al. [START_REF] Fayon | 29 Si and 207 Pb NMR study of local order in lead silicate glasses[END_REF]) and Fayon [START_REF] Fayon | Caractérisation du rôle structural du plomb dans des matrices vitreuses : approche par RMN haute résolution solide mono et bidimensionnelle[END_REF]) have used 29 Si NMR to compare the spectra of glasses to those of crystalline phases and to quantify the Q n units present in the glasses containing 31 to 73 mol% PbO (figures 3.11and 3.12). [START_REF] Fayon | Caractérisation du rôle structural du plomb dans des matrices vitreuses : approche par RMN haute résolution solide mono et bidimensionnelle[END_REF]). 7 T magnetic field, 10 kHz rotational frequency (with the kind permission of F. Fayon)

It has thus been shown that from 31 mol% up to approximately 40 mol% PbO, the Q 3 units were predominant and the proportion of Q 2 units increased mainly to the detriment of Q 4 units [START_REF] Fayon | Caractérisation du rôle structural du plomb dans des matrices vitreuses : approche par RMN haute résolution solide mono et bidimensionnelle[END_REF][START_REF] Fayon | 29 Si and 207 Pb NMR study of local order in lead silicate glasses[END_REF]) (figure 3.12). Then Q 1 units appear and their proportion increases with the PbO content mainly to the detriment of Q 3 units and become predominant beyond 60 mol% PbO. Finally, the Q 0 units appear and are the predominant units with Q 1 units beyond 72 mol% PbO (figure 3.12). This structural evolution was more recently confirmed over a more extended range of PbO contents (33-83 mol%) by Feller et al. [START_REF] Feller | A multispectroscopic structural study of lead silicate glasses over an extended range of compositions[END_REF] who showed that the glass prepared with 83 mol% PbO contained almost exclusively Q 1 species (24 %), entities composed of only two SiO4 tetrahedrons connected by a vertex, and Q 0 species (72 %), namely SiO4 tetrahedrons with no connection to another SiO4 tetrahedron, thus confirming for binary SiO2-PbO compositions the possibility to obtain a vitreous state in the absence of an extended silicate vitreous network. The comparison of 29 Si chemical shifts of Q n units between binary glasses and crystalline phases of the same composition has on the other hand evidenced a number of Pb 2+ ions second nearest neighbors of silicon atoms more significant for the glasses [START_REF] Bessada | 29 Si MAS-NMR in lead silicates[END_REF]. Furthermore, it is interesting to note that the equilibrium constants of 2Q n ↔ Q n-1 + Q n+1 reactions (disproportionation) in the overmelted liquid and frozen in the glass during the quenching and which were determined by 29 Si NMR from proportions of various Q n units in the glasses (figure 3.12) have an order of magnitude above that of alkaline silicate glasses [START_REF] Fayon | 29 Si and 207 Pb NMR study of local order in lead silicate glasses[END_REF], which tends to show a more significant clustering tendency of Pb 2+ ions compared to alkaline ions. The persistence of Q 2 and Q 1 units far beyond 66 mol% PbO (threshold beyond which only Q 0 units should remain if PbO fully transferred these O 2-anions to the silicate network by acidic-basic reaction) suggests that an increasing fraction of oxygen atoms in the structure are only connected to Pb 2+ ions, the rest being present in the form of bridging oxygen atoms (Si-O-Si) and non-bridging oxygen atoms (Si-O-Pb). This has been directly confirmed by 17 O NMR for PbOrich (60-71 mol%) glasses enriched in 17 O (figure 3.13) [START_REF] Lee | Probing metal-bridging oxygen and configurational disorder in amor-phous lead silicates: insights from 17 O solid-state nuclear magnetic resonance[END_REF]. C 119, 748-756, 2015). Copyright (2020) American Chemical Society.

COMMENT ON FIGURE 3.13.-a) The peaks marked by asterisks are rotational bands. b) The PbO/SiO2 molar ratios are indicated in the figures and correspond to 60 (1.5:1), 66 (2:1) and 71 (2,5:1) mol% PbO. The various types of oxygen atoms evidenced are: bridging oxygen atoms ( [4] Si- [2] O- [4] Si), non-bridging oxygen atoms ( [n] Pb- [m] O- [4] Si) and oxygen atoms bound only to lead ( [n] Pb- [m] O- [n] Pb). (Kohara, S., Ohno, H., Takata, M., Usuki, T., Morita, H., Suzuya, K., Akola, J., Pusztai, L., Phys. Rev. B, 82, 134209, 2010). Copyright (2020) by the American Physical Society.

COMMENT ON FIGURE 3.14.-The structural models have been obtained by the reverse Monte Carlo method from X-ray and neutron scattering results. The distribution of Q n (n = 0, 1, 2, 3, 4) units determined for various glasses from these models is also presented in the form of histograms [START_REF] Kohara | Lead silicate glasses: Binary network-former glasses with large amounts of free volume[END_REF].

Other authors have used Raman spectroscopy to follow up the evolution of the structure of lead silicate glasses and try to quantify the Q n units by sometimes drawing comparisons with the crystalline phases [START_REF] Furukawa | The structure of lead silicate glasses determined by vibrational spectroscopy[END_REF][START_REF] Feller | A multispectroscopic structural study of lead silicate glasses over an extended range of compositions[END_REF][START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF]Ben Kacem et al. 2017). Similar to 29 Si NMR, a very strong evolution of Raman spectra with the PbO content was observed in conjunction with an increasing depolymerization of the silicate network. Moreover, in line with the 17 O NMR results (figure 3.13), the joint formation of Pb-O-Pb bonds was evidenced, reflecting an increasing tendency of Pb 2+ ions to bind to one another (clusterization). The studies conducted by XPS (O 1s) on binary SiO2-PbO glasses have also evidenced a strong decrease in the proportion of bridging oxygen atoms with the PbO content, however the resolution of spectra is insufficient to separate the contribution of oxygen atoms from that of oxygen atoms that are not bound to silicon [START_REF] Smets | The structure of glasses and crystalline compounds in the system PbO-SiO2, studied by X-ray photoelectron spectroscopy[END_REF][START_REF] Sorokina | X-ray electron spectroscopy investigation of the structure of double lead silicate glasses[END_REF][START_REF] Dalby | Resolution of bri-dging signals from O 1s spectra of silicate glasses using XPS: Implications for O and Si specia-tion[END_REF]). However, some of these studies highlight the persistence of bridging oxygen atoms i.e. Si-O-Si bonds-in the most PbO-rich compositions [START_REF] Smets | The structure of glasses and crystalline compounds in the system PbO-SiO2, studied by X-ray photoelectron spectroscopy[END_REF][START_REF] Dalby | Resolution of bri-dging signals from O 1s spectra of silicate glasses using XPS: Implications for O and Si specia-tion[END_REF] in agreement with the 29 Si NMR studies (figure 3.12). Finally, it is important to mention the studies conducted by X-ray and neutron scattering combined with structural modeling using the reverse Monte Carlo method [START_REF] Suzuya | A reverse Monte Carlo study of lead metasilicate glass[END_REF][START_REF] Kohara | Lead silicate glasses: Binary network-former glasses with large amounts of free volume[END_REF]) which led to a distribution of Q n units as a function of composition (figure 3.14) consistent with 29 Si NMR results (figure 3.12). On the other hand, the structural models obtained by molecular dynamics and which do not take into account the polarizability of Pb 2+ ions that leads to anisotropic local environments yield average results, these works using symmetric interaction potentials (Ribycka et al. 1999).

All these results related to the evolution of the silicate network of SiO2-PbO glasses are therefore qualitatively close to at least the evolution of the structure of crystalline phases of lead silicates presented in section 3.2 (figures 3.7 to 3.9). Indeed, both cases show a strong depolymerization of the silicate (vitreous and crystalline) network with the persistence of SiO4 tetrahedrons bound to one another for the highest PbO contents (figures 3.7, 3.8 and 3.12): Q 1 and Q 2 units for glasses, and Si4O12 rings and Q 1 units respectively for Pb2SiO4 (66 mol% PbO) and Pb11Si3O17 (78 mol% PbO) crystalline phases. In both cases there is a significant proportion of oxygen atoms exclusively bound to lead (Pb-O-Pb bonds) (figures 3.9 and 3.13).

Environment, distribution and structural role of lead

Various techniques can be used to extract information on the lead environment in glasses. Some of these techniques make it possible to specifically probe the lead, such as NMR18 , EXAFS and XANES and XPS, while other techniques such as X-ray and neutron scattering, though providing very useful information on the environment of Pb 2+ ions (coordination number, Pb-O distance), probe also other elements that are present in the vitreous network. The studies published in the literature on lead environment and incorporation using these investigation techniques are numerous and sometimes contradictory, so that the structural role of lead in silicate glasses is still under debate. However, the majority of authors agree nowadays that Pb 2+ ions are inserted in the structure of binary silicate glasses with their free pair 6s 2 stereochemically active in the form of very asymmetric PbOn polyhedrons with low coordination number (n = 3 -4), of pyramidal type with short Pb-O bonds with strong covalent character: lead would therefore have a local environment close to the one occupied in the crystalline phases of lead silicates and in the pure lead oxide (sections 3.2.2 and 3.3.2). Moreover, for high PbO contents, PbOn units would tend to bind to one another in order to form increasingly larger percolating domains until building the main frame of the vitreous network including increasingly depolymerized silicate units (Q 1 , Q 0 ), similar to crystallized lead silicates (figure 3.7). The existence of such domains is in agreement with 17 O NMR-evidenced increasing proportion of oxygen atoms exclusively bound to lead (Pb-O-Pb bonds, figure 3.13). These conclusions rely, among others, on X-ray absorption (EXAFS, XANES) and X-ray and neutron scattering studies.

The X-ray and neutron scattering studies allow the extraction of radial distribution functions concerning the various pairs of atoms present in the structure and from which it is possible to find the interatomic distances and coordination numbers (figure 3.15). Hence Hoppe et al. [START_REF] Hoppe | Environments of lead cations in oxide glasses probed by X-ray diffraction[END_REF] and [START_REF] Takaishi | Structural study on PbO-SiO2 glasses by X-ray and neutron diffraction and 29 Si MAS NMR measurements[END_REF] find the Pb-O distances of the order of 2.30 Å for the nearest oxygen atoms with a coordination number of 3, these distances and coordination numbers varying relatively little with the PbO content in glasses (figure 3.15).

Based on their X-ray and neutron scattering results, and particularly on the Pb-Pb distance that remains quasi-constant (3.83-3.86 Å) for all the studied glasses (25-89 mol%), Takaishi et al. proposed a structural model of SiO2-PbO glasses employing Pb2O4 units constituted of two trigonal pyramidal PbO3 connected by an edge and oriented in opposite directions in order to minimize the repulsion between the free pairs 6s 2 of the two Pb 2+ ions, these Pb2O4 units having a zero global charge (figure 3.16) [START_REF] Mizuno | Leaching of lead and connectivity of plumbate networks in lead silicate glasses[END_REF][START_REF] Takaishi | Structural study on PbO-SiO2 glasses by X-ray and neutron diffraction and 29 Si MAS NMR measurements[END_REF]. These entities would be present starting with the lowest PbO contents by the authors (25 mol%). According to this model, lead behaves as a forming element starting with the lowest lead concentrations. Based on their scattering results and on a structural model obtained with reverse Monte Carlo simulation method for glasses with PbO contents between 30 and 65 mol%, Kohara et al. [START_REF] Kohara | Lead silicate glasses: Binary network-former glasses with large amounts of free volume[END_REF] did not confirm the existence of Pb2O4 dimeric units in lead silicate glasses, but a lead environment predominantly in the form of distorted PbO4 units of square-based pyramidal type (figure 3.17). Such an environment is close to that of lead in the crystalline forms of PbO (figures 3.3 and 3.5) and in the crystalline phases of lead silicates (figure 3.7). A number of PbOn units connected to one another strongly increasing with the lead content were evidenced in the structure of these glasses. The same authors have also presented a compared evolution of the silicate network and of the lead network depending on the lead oxide percentage, which clearly shows the predominance of the lead network starting from at least 50 mol% PbO (figure 3.17). An equivalent study conducted by Suzuya et al. [START_REF] Suzuya | A reverse Monte Carlo study of lead metasilicate glass[END_REF]) on the 50 mol% PbO composition also led these authors to propose a lead environment in the form of irregular PbO4 pyramids; these units are assumed to form rings constituting the lead network. These models employing an increasing connectivity of PbO4 units to the detriment of the silicate network are close to the one proposed by several other authors [START_REF] Bessada | 29 Si MAS-NMR in lead silicates[END_REF][START_REF] Wang | Structural role of lead in lead silicate glasses derived from XPS spectra[END_REF].

Figure 3.17. Local and extended structure of lead silicate glasses (30 -65 mol% PbO) according to X-ray and neutron scattering results and reverse Monte Carlo simulation method (RMC) [START_REF] Kohara | Lead silicate glasses: Binary network-former glasses with large amounts of free volume[END_REF].

COMMENT ON FIGURE 3.17.-a) Distorted PbO4 pyramidal unit resulting from RMC simulations. b) (up) Compared evolution depending on the lead content of silicate networks (blue) and lead networks (red) constituted respectively of SiO4 and PbOx interconnected units, the proportion of SiO4 and PbOx units that do not participate to these networks is represented in yellow, green and pink. (down) Evolution of the lead network with lead content (The interconnected PbOx units are represented in red, and the rest in yellow, the SiO4 tetrahedrons are not represented). Reproduced with permission from (Kohara S., Ohno H., Takata M., Usuki T., Morita H., Suzuya K., Akola J., Pusztai L., Phys. Rev. B, 82, 134209, 2010). Copyright ( 2020) by the American Physical Society.

Alderman et al. [START_REF] Alderman | The structure of vitreous binary oxides: silicate, germanate and plumbite networks[END_REF][START_REF] Alderman | Lone-pair distribution and plumbite network for-mation in high lead silicate glass, 80PbO.20SiO2[END_REF]) have more recently proposed a more convincing structural description of lead silicate glasses (0 -80 mol% PbO) also based on X-ray and neutron scattering results, but using a structural refinement of their experimental data employing empirical interatomic interaction potentials 19 (figures 3.18 and 3.19). Their modeling was optimized particularly by considering Pb 2+ ions as dipoles to better account for the specific stereochemistry of the sites occupied by these ions, induced by the non-bridging 6s 2 doublet of lead. These authors note first of all, as for crystals, an increase with the PbO content of the average Si-O distance ascribed to the evolution of the silicon coordination sphere, and more particularly an increase of the average number of 19. This technique referred to as EPSR (Empirical Potential Structure Refinement) was implemented for the study of the local environment around Pb 2+ ions, the way in which PbOn polyhedrons are connected and the layout of free 6s 2 pairs. This method, which takes into account the strong polarizability of Pb 2+ ions is therefore more suitable than the simple reverse Monte Carlo method implemented in other studies on lead silicate glasses. Pb 2+ ions around the non-bridging oxygen atoms. The authors also note a slight evolution of the lead environment between 35 and 80 mol% PbO: the short Pb-O distances (≤ 2.7 Å) tend to become shorter and more numerous around the Pb 2+ ions until reaching four bonds. Conversely, the number of long Pb-O distances (between 2.7 and 3.27 Å) tends to decrease. The environment of Pb 2+ ions tends therefore to evolve towards that of litharge (figure 3.5) when the lead oxide rate increases and therefore when the silicon number in the second sphere of coordination of lead decreases. Consequently, the oxygen environment evolves strongly with the lead oxide rate passing from a OSi2 environment to an increasingly lead-rich environment as lead oxide is added, tending to a OPb4 environment on average, as noted in the crystals. This is reflected by the presence, in all glasses, of PbOn polyhedrons connected by edges, which makes it possible to effectively have several Pb 2+ ions compensating a given non-bridging oxygen atom and to have more than two non-bridging oxygen atoms around a Pb 2+ ion, as it is the case in crystals. However, the presence of the Pb2O4 unit proposed by Takaishi et al. [START_REF] Takaishi | Structural study on PbO-SiO2 glasses by X-ray and neutron diffraction and 29 Si MAS NMR measurements[END_REF] as a basic unit of the lead network independently of the PbO content (figure 3.16) was not observed in this study. Finally, an important conclusion of these works is the emphasis of the formation of areas deficient in silicate species in the lead oxide-rich glasses, due to the organization of non-bridging doublets of Pb 2+ ions (figure 3.19). This organization of non-bonding doublets of lead is found in lead-rich crystallized lead silicates such as Pb11Si3O17 (figure 3.7), litharge and massicot (figure 3.5) that form channels in the crystalline structure. These areas of deficiency (voids) are not present in glasses with low lead oxide content (figure 3.18) whose structure is closer to that of alamosite PbSiO3 (figure 3.7).

Summary of the structural evolution of binary SiO2-PbO glasses and the role of lead

All the structural results published on the binary SiO2-PbO glasses presented in this chapter tend to highlight that the structural role of lead does not change essentially with the PbO content and that it is closer to the role of a glass former oxide. Its short distance environment is very asymmetric, of deformed pyramidal type with triangular or square base (PbO3, PbO4) with lead at the and in all the cases the free 6s 2 pair of Pb 2+ ions stereochemically active, similar to the PbO crystalline phases (massicot and litharge) and lead silicates (sections 3.2.2 and 3.3.2). The lead environment would therefore slightly evolve as a function of PbO content, with only a light reinforcement of short distance PbO bonds, more tetracoordinated (PbO4) environments and the increasing presence of Pb-O-Pb connections with bonds by vertices and edges between the PbOn polyhedrons forming an increasingly significant lead network, as in the case of crystalline phases (figures 3.7 and 3.9). Similar to the latter (figures 3.7 and 3.8), a substantial evolution of the silicate network with the PbO content is observed, with gradual depolymerization (Si-O-Si bonds disappear to the benefit of Si-O-Pb bonds, figures 3.12 and 3.14), silicon atoms having an increasing number of Pb 2+ ions as second neighbors. However, for PbO contents above that of lead oxy-cyclosilicate (Pb2SiO4, 60 mol% PbO) from which complete depolymerization of the silicate network was expectedas it is the case for alkaline silicate systems, for examplewith only isolated SiO4 units (Q 0 ), small-size units having Si-O-Si bonds are still present even for the lead-richest compositions (figures 3.12, 3.13 and 3.14). The presence of these units in the lead network for lead-rich compositions as well as the existence of an environment distribution for Pb 2+ ions and Pb-O-Pb and Pb-O-Si connections in the structure of glasses (and thus of corresponding liquids at the melting moment and before quenching) must therefore contribute to slowing down the crystallization of the supercooled liquid during quenching and therefore make it easier to obtain a glass. On the other hand, in the case of alkaline and alkaline-earth cations that are bound to O 2-anions only by ionic and non-directional bonds and that have quite spherical environments in the silicate glasses, it is clear that the reorganization of the liquid leading to crystals is facilitated and therefore it is not possible to vitrify silicate liquids for high alkaline and alkaline-earth oxide contents. All these structural results can be used to explain to a large extent the variation of physical properties of the binary SiO2-PbO glasses as a function of PbO content, as mentioned in section 3.3.3.1. Hence the depolymerization of the silicate network, the fact that the average force of the bonds between oxygen and its Si and Pb neighbors decreases with the lead content (Pb-O bonds being weaker than Si-O bonds) and the strong polarizability of Pb 2+ ions (and therefore their strong deformability) explain the decrease with the PbO content of the liquid viscosity, of the vitreous transition temperature and of the electrical resistivity (figure 3.10). Likewise, the increase of the thermal expansion coefficient of SiO2-PbO glasses with the PbO content can be explained by a decrease of the average force of bonds, like for the alkaline silicate glasses; however, the Pb-O bonds having a ionocovalent character, unlike the bonds between alkaline R + ions and the O 2-anions, which are purely ionic, the expansion coefficient of alkaline silicate glasses remains higher than that of lead silicate glasses for the same R2O and PbO molar content [START_REF] Scholze | Le verre. Nature, structure et propriétés[END_REF]. Finally, the decrease in the molar volume of SiO2-PbO glasses when lead concentration increases for the lowest PbO contents [START_REF] Shelby | Property/structure relationships in lead silicate glasses[END_REF][START_REF] Kaur | Structure-property correlations in lead silicate glasses and crystalline phases[END_REF]Ben Kacem et al. 2017) might be explained by the decrease in the free volume existing in the silicate glasses rich in SiO2 following the gradual breaking of the Si-O-Si bonds. While the stabilization of the free volume, and even its reincrease from 50 mol% PbO, could be explained by the formation of an increasingly extended lead network and by the presence of an increasing number of free 6s 2 pairs associated with lead creating deficient area (voids) in the structure (figure 3.19). It is important to note that the strong polarizability of Pb 2+ ion and the existence of the free 6s 2 pair stereochemically active may be at the origin of the significantly higher solubility of metallic oxides such as Cr2O3 in silicate glasses containing lead oxide compared to classical silicate glasses containing alkaline and alkaline-earth oxides and in which the chromium oxide is little soluble [START_REF] Ashour | Study of crystallization of chromium oxide in glass (chrome aventurine)[END_REF][START_REF] Volf | Chemical approach to glass[END_REF].

3.4. Glasses of SiO2-PbO-R2O system (R= Na, K)

Overview of ternary SiO2-PbO-R2O glasses

After the binary SiO2-PbO glasses, let us focus on the structure and properties of ternary SiO2-PbO-R2O glasses, where R represents an alkaline element such as Na or K. These ternary glasses have many applications in fields such as luxury glassmaking (crystal glass making), glazes and enamels and glasses absorbing the ionizing radiation, as already mentioned in chapter 1. Hence the crystal glass belongs to the ternary SiO2-PbO-K2O system with molar contents for example of about 77 % SiO2, 11 % K2O and 10 % PbO (with, according to productions, a little bit of Na2O, Al2O3 and traces of fining agents such as Sb2O3), which leads to PbO mass contents of about 28 % in this case. While, for example, tin-opacified lead alkaline mixed heritage glazes have mass contents of about 20-40 % PbO and 5-12 % Na2O + K2O, compared to contents of about 45-60 % PbO and less than 2 % Na2O + K2O for lead transparent glazes (Tite et al. 1998, chapter 10). In the case of crystal glass, there is a multiple interest of adding lead to the binary glass of potassium silicates (melting, forming, machining, optical properties, napping of glazes, see chapter 1). In parallel, the addition of K2O to the binary SiO2-PbO glass makes it possible to reduce the demixing tendency of lead silicate glasses having low or moderate PbO contents (< 35 mol%) (section 3.3.3.1) [START_REF] Calvert | Liquidus behavior in the silica-rich region of the system PbO-SiO2[END_REF][START_REF] Vogel | Glass chemistry[END_REF]) and also facilitates the melting of the vitrifiable mixture. Given the importance both at industrial and heritage levels of the ternary SiO2-PbO-R2O glasses, many studies related to their hydrolytic resistance in submerged medium or in humid atmosphere were conducted with a twofold purpose: sanitary [START_REF] Angeli | Structure and chemical dura-bility of lead crystal glass[END_REF] and conservation [START_REF] Palomar | Hydrolytic resistance of K2O-PbO-SiO2 glasses in a-queous and highhumidity environments[END_REF]. The alteration of this type of glasses is widely dealt with in chapter 13.

Structure of ternary SiO2-PbO-R2O glasses

The structure of binary SiO2-PbO glasses as a function of their PbO content was largely presented in section 3.3.2. This section focuses on the effect on the structure of the glass and the lead environment of the simultaneous presence of PbO and an alkaline oxide (such as Na2O or K2O). The alkaline oxides are well known for their modifier role in the binary SiO2-R2O silicate glasses, leading to a more or less marked depolymerization of the silicate network as a function of the R2O content [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF]. It is interesting to consider here the way in which the structure of the binary lead silicate glasses is affected when a modifier oxide (here R2O) is added to their composition and particularly on the way in which the environment and the distribution of Pb 2+ ions can be modified. However, unlike the structural studies conducted on binary lead silicate glasses, which are particularly abundant in the literature, those related to ternary SiO2-PbO-R2O glasses are less numerous, despite the important industrial applications of these glasses. Several spectroscopy methods were implemented for the study of these glasses, such as Raman, IR and XPS spectroscopies.

At the same time, while the crystalline phases of the PbO-SiO2 system were the object of a quasi-systematic structural study (section 3.3.2), very little is known on more complex crystalline compounds, such as those of ternary SiO2-PbO-R2O systems. Thus, despite the considerable number of possible compositions, crystallized lead silicates containing alkaline or alkaline-earth cations were the object of structural studies only as part of both rare and ancient works related to K2Pb2Si2O7 disilicate [START_REF] Mcmurdie | K2Pb2Si2O7[END_REF] and its isotype K2Pb2Ge2O7 [START_REF] Bassi | Structure du pyrogermanate de plomb potassium K2Pb2Ge2O7[END_REF], the cyclosilicate PbCa2Si3O9 or margarosanite [START_REF] Freed | Determination and refinement of the crystal structure of margaro-sanite PbCa2Si3O9[END_REF] and the oxy-monosilicate Li10PbO2(SiO4)2 [START_REF] Brandes | Li10Si2Pb II O10 = Li20[(SiO4)4(OPbO2PbO)] -Daserste "gemischte" Silicat-Plumbat(II)[END_REF]. Despite different lead contents, these structures show that the depolymerizing effect of alkaline and alkaline-earth oxides -at various degrees depending on their content -support, similarly to binary lead silicates, asymmetric environments for Pb 2+ ions (free 6s 2 pair stereochemically active) and strong Pb-O-Pb cross-linkages. This effect is particularly prominent for the crystalline phase Li10PbO2(SiO4)2 which has infinite -Pb-O-chains thanks to its exceptionally high rate alkaline elements that fully depolymerize the silicate network.

The silicate vitreous network

There are several studies on ternary SiO2-PbO-R2O glasses in the literature varying the relative proportions of three oxides. Thus, by adding increasing Na2O contents to a glass of composition 50 SiO2 -50 PbO (mol%) or increasing PbO contents to a glass composition 75 SiO2 -25 Na2O (mol%), studies conducted by 29 Si NMR [START_REF] Shrikhande | 29 SiMAS NMR and microhardness studies of some lead silicate glasses with and without modifiers[END_REF][START_REF] Shrikhande | Photoluminescence and structural studies on Na2O-PbO-SiO2 glasses[END_REF] have clearly highlighted a depolymerization of the silicate network, i.e. a decrease of the proportion of bridging oxygen atoms connecting the silicon atoms, as it is the case when increasing PbO contents are added to SiO2 (figure 3.12). A similar structural evolution has been observed during the gradual substitution of SiO2 by PbO (up to 50 mol%) in an industrial crystal glass whose composition is close to 77.9 SiO2 -10.7 PbO -11.4 K2O (mol%), as presented in figure 13.1. For this latter glass, 29 Si NMR has shown that it was essentially constituted of Q 3 units (59 %) and Q 4 units (41 %), which corresponds to 25.7 % of non-bridging oxygen atoms and is in perfect agreement with what is obtained by calculation from its composition assuming that K2O and PbO fully transfer their O 2-anions to the silicate network [START_REF] Angeli | Structure and chemical dura-bility of lead crystal glass[END_REF]) (complete acid-base reaction). This may suggest that these two oxides have similar effects on the silicate network and a similar structural role. However, for higher PbO contents (> 30 mol%), there is an increasing disagreement between the result of the calculation of the proportion of non-bridging oxygen atoms based on the glass composition and the NMR results (chapter 13). This strongly suggests that for quite high lead contents, a part of the oxygen brought by PbO is in the form of Pb-O-Pb bonds, as it is the case of leadrich binary SiO2-PbO glasses (section 3.3.3.2). A study conducted by XPS (O 1s) on ternary glasses by gradually substituting PbO by Na2O also confirms this [START_REF] Gee | Atomic environments in binary lead silicate and ternary alkali lead silicate glasses[END_REF].

Environment and distribution of lead and alkaline elements in the vitreous network

To our knowledge, unlike the binary SiO2-PbO glasses, there is no EXAFS, XANES, or X-ray or neutron scattering or 207 Pb NMR data available in the literature for the ternary SiO2-PbO-R2O glasses that may bring direct information on the lead environment in these glasses. The situation is therefore different from the binary SiO2-PbO glasses for which it was highlighted by these techniques that lead in the form of Pb 2+ ions (with its stereochemically active free 6s 2 pair) was localized in very asymmetric sites connected to the silicate network by quite strong Si-O-Pb bonds, with the possibility that these sites are also connected to one another for high PbO contents. However, by analogy with the above mentioned ternary crystalline phases of alkaline or alkaline-earth lead silicate, it is highly probable that in the ternary glasses of the same systems the Pb 2+ ions are also located in asymmetric environments with their stereochemically active free 6s 2 pair. Moreover, a recent study conducted by NMR on ternary SiO2-PbO-K2O glasses enriched in 17 O brought abundant information on the way in which Pb 2+ ions are distributed with respect to K + ions in the vitreous network structure depending on the PbO content (substituted for SiO2) (figure 3.20) [START_REF] Angeli | Structure and chemical dura-bility of lead crystal glass[END_REF]. This study comes close to the one of [START_REF] Lee | Probing metal-bridging oxygen and configurational disorder in amor-phous lead silicates: insights from 17 O solid-state nuclear magnetic resonance[END_REF] conducted on binary SiO2-PbO glasses (figure 3.13) and is presented in detail in chapter 13 (figure 13 COMMENT ON FIGURE 3.20.-Reproduced with permission from (Angeli, F., Jollivet, P., Charpentier, T., Fournier, M., Gin, S., Environ. Sci. Technol., 50, 11549-11558, 2016). Copyright (2020) American Chemical Society.

It is important to note that for these PbO contents the presence of oxygen atoms isolated from the silicate network in the form of Pb-O-Pb bonds is not observed, which shows that PbO oxide fully reacts with SiO2, in agreement with the above mentioned 29 Si NMR results. On the other hand, when the PbO content increases up to at least 30 mol%, all the K + ions share the non-bridging oxygen atoms with the Pb 2+ ions. It is only for higher PbO contents (> 30 mol%) that are highlighted Pb-O-Pb connections, as suggested by 29 Si NMR and (O 1s) XPS studies mentioned in section 3.4.2.1. This is consistent with increasing clusterization of PbOn entities and the gradual formation of a lead network as for the binary lead silicate glasses and is in agreement with the structure of the above mentioned ternary crystalline phases of leadrich alkaline or alkaline-earth silicates. This was confirmed by a molecular dynamic study and adjustment of the NMR results by reverse Monte Carlo method (chapter 13, figure 13.4). Moreover, Si-O-Pb connections without K + ions in their nearest neighborhood should be increasingly abundant. The significant change of the environment of potassium ions with the lead content highlighted for these glasses is in agreement with the clear evolution of the (Na 1s) XPS spectrum observed with the lead content for 70 SiO2 -x PbO -(30-x) Na2O (mol%) glasses [START_REF] Gee | Atomic environments in binary lead silicate and ternary alkali lead silicate glasses[END_REF]). These structural evolutions, and particularly the formation of mixed Si-O-(Pb,K) bonds to the detriment of simple Si-O-K bonds, explains the effect of the partial substitution of SiO2 by PbO on the electrical resistivity (increase) of alkaline silicate glasses [START_REF] Scholze | Le verre. Nature, structure et propriétés[END_REF], the large Pb 2+ ions impeding on the mobility of alkaline ions.

3.5. Glasses of SiO2-PbO-Al2O3 system

Overview of ternary SiO2-PbO-Al2O3 glasses

Though the glasses of the ternary SiO2-PbO-Al2O3 system have ancient applications, such as glazes deposited on the surface of ceramic objects20 [START_REF] Tite | Review arti-cle. Lead glazes in antiquity -methods of production and reasons for use[END_REF]) and much more recently as materials containing rare earth ions for optics and dosimetry [START_REF] Bhargavi | The structural influence of aluminium ions on emission characteristics of Sm 3+ ions in lead aluminium silicate glass system[END_REF][START_REF] Bhargavi | Thermal Lu-minescence of Ho2O3-PbO-Al2O3-SiO2 Glasses Exposed to Gamma Radiation[END_REF][START_REF] Bhargavi | γ-Ray induced thermoluminescence characteristics of the PbO-Al2O3-SiO2:Pr 3+ glass system[END_REF][START_REF] Rao | The de-clustering influence of aluminum ions on the emission features of Nd 3+ ions in PbO-SiO2 glasses[END_REF][START_REF] Rao | Influence of indu-ced structural changes on thermoluminescence characteristics of γ-ray irradiated PbO-Al2O3-SiO2: Dy 3+ glasses[END_REF], as well as for the protection against ionizing radiation [START_REF] Singh | Comparative study of gamma ray shielding and some properties of PbO-SiO2-Al2O3 and Bi2O3-SiO2-Al2O3 glass systems[END_REF], only a limited number of works have been published on the glasses of this system. It is particularly the case of studies conducted on their structure and on the impact of the presence of alumina on the environment of Pb 2+ ions in the vitreous network, compared to the extent of the studies conducted on binary SiO2-PbO glasses (section 3.3.3). Some examples are essentially the recent studies conducted by Bhargavi et al. [START_REF] Bhargavi | The structural influence of aluminium ions on emission characteristics of Sm 3+ ions in lead aluminium silicate glass system[END_REF][START_REF] Bhargavi | Thermal Lu-minescence of Ho2O3-PbO-Al2O3-SiO2 Glasses Exposed to Gamma Radiation[END_REF][START_REF] Bhargavi | γ-Ray induced thermoluminescence characteristics of the PbO-Al2O3-SiO2:Pr 3+ glass system[END_REF], Rao et al. [START_REF] Rao | The de-clustering influence of aluminum ions on the emission features of Nd 3+ ions in PbO-SiO2 glasses[END_REF][START_REF] Rao | Influence of indu-ced structural changes on thermoluminescence characteristics of γ-ray irradiated PbO-Al2O3-SiO2: Dy 3+ glasses[END_REF] and Ben Kacem (Ben Kacem 2017) using vibrational or optical spectroscopies, by Roisine (Roisine 2018) using NMR and Raman spectroscopies and X-ray and neutron scattering, and the more ancient ones of Prabakar and Rao [START_REF] Prabakar | MAS NMR studies of ternary silicate glasses[END_REF] using NMR spectroscopy and of Roy [START_REF] Roy | Infrared spectroscopy of lead and alkaline-earth aluminosilicate glasses[END_REF]) using infrared spectroscopy. It is important to note however that other structural studies have been conducted on more complex glasses of the SiO2-PbO-Al2O3-B2O3 system containing boron besides aluminum, but they are not covered here [START_REF] Sawvel | Local structure of amorphous (PbO)x[(B2O3)1z(Al2O3)z]y(SiO2)y dielectric materials by multinuclear solid state NMR[END_REF][START_REF] Saini | Structure-property correlations in lead borate and borosilicate glasses doped with aluminum oxide[END_REF]Falconeri et al. 2012). Though the extension of the vitrifiable domain in the ternary SiO2-PbO-Al2O3 system has not been reported in the literature, it can however be stated that the Al2O3 content of the studied glasses never exceeds 30 mol% (Ben Kacem 2017) and that glasses with only 10 mol% SiO2 (10 SiO2 -80 PbO -10 Al2O3) could be obtained by classical melting-quenching [START_REF] Prabakar | MAS NMR studies of ternary silicate glasses[END_REF]. It is interesting to note that hyperquenching can be used to prepare binary Al2O3-PbO glasses without silicon and with PbO contents ranging between 50 and 95 mol% [START_REF] Kantor | Preparation of iron sesquioxide glasses by ultra-fast quenching from the melt ("splat-cooling[END_REF][START_REF] Morikawa | Glass forming ability and crystallization in the PbO-Al2O3 system[END_REF]. There is a multifaceted interest in adding aluminum to the composition of lead silicate glasses due to the significant effect of this element on their properties. Hence, Al2O3 is assumed to increase the mechanical resistance of binary glasses of the SiO2-PbO system and to decrease their crystallization tendency [START_REF] Mylyanych | Study of glass structures and crystalline phases in the PbO-Al2O3-SiO2 system[END_REF]. Moreover, according to the phase diagram of the SiO2-PbO-Al2O3 system [START_REF] Chen | Experimental study of phase equilibria in the PbO-Al2O3-SiO2 system[END_REF], the introduction of alumina in the binary SiO2-PbO system would reduce the demixing tendency of the liquid. However, the liquidus temperature tends to significantly increase, particularly for the lead-richest compositions corresponding in particular to the domain of lead glazes, which may pose melting problems and therefore limits the amount of alumina that can be added. Moreover, for this type of PbO-rich compositions, the glass transition temperature and the viscosity of the liquid increase rapidly with the alumina rate (figures 3.21 and 3.22).

It is also important to note the existence of a large number of ternary crystalline phases (11 phases according to Chen et al. [START_REF] Chen | Experimental study of phase equilibria in the PbO-Al2O3-SiO2 system[END_REF]) in this domain of composition that may contribute, besides the strong increase in viscosity of the melting liquid, to facilitate its vitrification during cooling according to the "frustration" principle [START_REF] Mysen | Silicate glasses and melts[END_REF]. Finally, the positive effect of the presence of aluminum in lead silicate glasses containing rare earth ions is worth mentioning, as it leads to a better dispersion of the latter in the vitreous structure (destruction of clusters) [START_REF] Rao | The de-clustering influence of aluminum ions on the emission features of Nd 3+ ions in PbO-SiO2 glasses[END_REF]. Similar to the above-mentioned ternary systems of alkaline or alkaline-earth lead silicates (section 3.4.2), the known structures of ternary Pb-Si-Al-O oxides are very few and come down to lead feldspar PbAl2Si2O8 [START_REF] Benna | The structure of ordered and disordered lead feldspar (PbAl2Si2O8)[END_REF] and other structures of zeolite type [START_REF] Ronay | Crystal structures of Pb6-A and Pb9(OH)8(H2O)3-A. Zeolite A ion ex-changed with Pb 2+ at pH 4.3 and 6.0 and evacuated[END_REF][START_REF] Yeom | Crystal structure of zeolite X exchanged with Pb(II) at pH 6.0 and dehydrated: (Pb 4+ )14(Pb 2+ )18(Pb4O4)8Si100Al92O384[END_REF]. However, unlike the crystalline phases of SiO2-PbO, SiO2-PbO-R2O and SiO2-PbO-R'O (R: alkaline and R': alkaline-earth) systems, in these structures the lengths of Pb-O bonds are relatively regular. Their environment in PbAl2Si2O8 is thus very similar to that of Sr 2+ ions in the equivalent feldspar highlighting the absence of stereochemical activity of the lead 6s 2 pair in this very aluminum-rich phase. This is likely explained by the force of the aluminosilicate skeleton and its maximal cross-linking.

Bridging two SiO4 and AlO4 tetrahedrons, an oxide anion has available only about 0.25 u.v. to share with the neighboring Pb 2+ ions, which forbids the formation of strong bonds, and hence the highly structuring Pb-O-Pb cross-linkages observed in the depolymerized silicates of SiO2-PbO, SiO2-PbO-R2O and SiO2-PbO-R'O systems. In this type of aluminum-rich crystalline structure, Pb 2+ ions compensate the charge of the AlO4 -tetrahedral units, unlike the previous systems considered in this chapter.

Aluminosilicate vitreous network and the lead environment

Since the earliest structural studies conducted on ternary SiO2-Al2O3-PbO glasses (Prabakar et Rao 1991), 27 Al NMR revealed that aluminum was incorporated in their structure essentially in the form of AlO4 - tetrahedral entities and that a part of the Pb 2+ ions present in the structure acted as charge compensators of these entities, for Al2O3 contents of 10 mol% and PbO contents ranging between 30 and 80 mol%. Concerning the silicate network, the studies conducted more recently on various series of ternary glasses by Raman and 29 Si NMR have shown that the addition of alumina or its partial substitution to PbO in the binary SiO2-PbO glasses led in all cases to a strong evolution of their structure (Ben Kacem 2017; Roisine 2018) (figures 3.23 and 3.24).

It can be observed that, by adding increasing quantities of alumina to lead silicate glasses, there is a shift towards low energies and a change in the shape of Raman band between 800 and 1 200 cm -1 associated with elongation vibrations of T-O bonds of tetrahedral entities TO4 (T = Si, Al) (figure 3.23). The evolution of this band can only be explained by the gradual incorporation of aluminum in the form of AlO4 -units in the silicate network and not by a depolymerization of the latter according to 17 O NMR results (figures 3.25 and 3.26) and the evolution of physical properties (strong increase of Tg and viscosity, figures 3.21 and 3.22). Indeed, it is known for other silicate glasses without lead that the presence of 4-fold coordinated aluminum in the silicon environment (as a second neighbor) leads to a shift of the elongation vibration bands of Q n towards low energies [START_REF] Rossano | Raman spectroscopy applied to earth sciences and cultural heritage[END_REF]. The evolution of the 29 Si NMR signal towards the higher values of the chemical shift with the Al2O3 content (figure 3.24) can be similarly explained, the chemical shift of Q n units increasing when a growing number of AlO4 -tetrahedrons are present as second neighbors of SiO4 units [START_REF] Kirkpatrick | Solid-state nuclear magnetic resonance spectroscopy of minerals[END_REF]. The low energy region (100-200 cm -1 ) of Raman spectracorresponding to Pb-O vibrations (Ben Kacem 2017)has also a strong evolution with the content of alumina added to the binary SiO2-PbO glasses (figure 3.23). A strong evolution in this region of the spectrum has also been observed if PbO is gradually replaced by Al2O3 with constant SiO2 content [START_REF] Ben Kacem | Du cristal au plomb jusqu'aux déchets domestiques : rôle du plomb dans les verres et les[END_REF]. This shows a significant change of local environment of Pb 2+ ions, which may be explained by the gradual disappearance of quite strong Pb-O-(Pb,Si) bonds to the benefit of weaker Pb-O-Al bonds associated with the role of charge compensator of AlO4 -units played by an increasing number of Pb 2+ ions. Indeed, the direct study of the aluminum environment by 27 Al NMR in these glasses (figure 3.27) shows that it is still predominantly present in the form of AlO4 -(and therefore necessarily locally compensated by Pb 2+ ions, which are the only cations susceptible to play this role in ternary glasses), with the increasing but sill minority contribution of AlO5 units highlighted by 27 Al MQMAS NMR for the highest alumina contents (> 15 mol% Al2O3) [START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF].

Concerning the oxygen atoms in the structure, the 17 O NMR study of 17 O -enriched ternary glasses also confirms a strong evolution of the lead environment following the addition of alumina in the binary SiO2-PbO glasses (figures 3.25 and 3.26). Indeed, a strong decrease of the contribution of Si-O-Pb bonds to the benefit of Si-O-Al bonds can be noted, thus showing a strong repolymerization of the vitreous network (strong decrease of the proportion of non-bridging oxygen atoms). Moreover, the small number of Pb-O-Pb bonds present in the binary glass seems to disappear in the ternary glass (figure 3.25), which may suggest a better dispersion of lead in the aluminosilicate network, in agreement with the results obtained by Raman spectroscopy (region of low-frequency spectra). However, additional studies conducted on the same glasses by X-ray scattering did not reveal a significant evolution of the average Pb-Pb distance during the addition of alumina to the binary SiO2-PbO glasses [START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF]. According to the structural results concerning the stereochemistry of Pb 2+ in Al2O3 -rich crystalline phases such as PbAl2Si2O8 (section 3.5.2.1) for which the free 6s 2 pairs are stereochemically inactive, it may be thought that the same is valid for ternary SiO2-Al2O3-PbO glasses at least for Pb 2+ ions playing the role of charge compensator of AlO4 -units, excess Pb 2+ ions being likely to preserve their 6s 2 pair active, similar to the binary SiO2-PbO glasses.

Conclusion

Given its high polarizability and its specific electron configuration (free 6s 2 pair), Pb 2+ ion has a unique stereochemistry, which leads to obtaining binary SiO2-PbO silicate glasses that may contain very high PbO contents, significantly higher in particular than the quantity of alkaline R2O oxides that can be introduced in the binary glasses of alkaline silicates (SiO2-R2O). Though the first structural studies conducted on binary glasses of lead silicates date back over 80 years, there are still unanswered questions on the structural role of PbO in silicate glasses and on the evolution of the distribution of Pb 2+ ions as a function of the lead concentration. However, the implementation of many investigation methods coupled with numerical simulation methods led to many publications and to an increasingly precise knowledge on the structure of these glasses. Hence, for the binary glasses of the SiO2-PbO system, it appears that -as for the PbO crystalline phases and lead silicates -Pb 2+ ions are located in very asymmetrical sites of low coordination (3,4) with their stereochemically active free 6s 2 pair. Though the addition of PbO leads to a depolymerization of the silicate network, the structural role of Pb 2+ ions is very different from that of bivalent ions, such as the alkaline-earth ions. Indeed, on the one hand, significantly stronger bonds are established starting with the low PbO contents between the Pb 2+ ions and the non-bridging oxygen atoms of the silicate network, and on the other hand for high PbO contents an increasing proportion of O 2-ions are found connected only to Pb 2+ ions gradually forming an increasingly extended lead network. Nevertheless, even for the strongest PbO contents, a significant proportion of SiO4 units remain connected to one another thus contributing to the stabilization of the lead network in relation to crystallization. On the other hand, the structural studies conducted on other lead-rich systems are significantly fewer, but however very instructive. Hence, in the alkaline silicate glasses, for low lead contents Pb 2+ ions tend to get incorporated in area containing alkaline ions where they associate with non-bridging oxygen atoms, while for high PbO contents, Pb-O-Pb connections appear, as a signature of the formation of an increasingly extended lead network. In these glasses, Pb 2+ ions preserve their stereochemically active free 6s 2 pair and are located in very asymmetric sites by analogy with crystalline phases. On the other hand, in the case of lead aluminosilicate glasses, Pb 2+ ions tend to play the role of charge compensator of the AlO4 -units and are likely losing the stereochemical activity of their 6s 2 pair. However, questions still remain on the evolution of the lead network as a function of Al2O3 content in these glasses.

Figure 3 . 1 .

 31 Figure 3.1. Examples of three-dimensional representation of pure silica glass (a) and of a soda-lime silica glass (b)showing the SiO4 tetrahedrons (in yellow), the bridging and non-bridging oxygen atoms (in red), and the modifier ions Na + (in purple) and Ca 2+ (in green). Reproduced from[START_REF] Charpentier | Computational simulations of solid state NMR spectra: a new era in structure determination of oxide glasses[END_REF] with the permission of The Royal Society of Chemistry.

Figure 3 . 2 .

 32 Figure 3.2. Representation of polarizability α of Pb 2+ ion and of alkaline-earth ions (Shannon and Fischer 2016) as a function of the cube of radius with a coordination number of 6

Figure 3 . 3 .Figure 3 . 4 .

 3334 Figure 3.3. Oxygenated environment of the Pb 2+ ion and Pb-O distances in two varieties of PbO: litharge (a) and massicot (b). Pb (in black) and O (in red)

Figure 3 . 5 .

 35 Figure 3.5. Crystal structures of two PbO polymorphs: litharge (a) and massicot (b). Pb (in black) and O (in red)

Figure 3 . 6 .

 36 Figure 3.6. Phase diagram of the PbO-SiO2 system (mol%) above 500 °C[START_REF] Shevchenko | Experimental phase equilibria studies of the PbO-SiO2 system[END_REF].Massicot: PbO phase stable at high temperature, for mixed crystal phases: P = PbO and S = SiO2

Figure 3 . 7 .

 37 Figure 3.7. Crystal structures of three lead silicates (in-depth representation of 1/2 unit cell) in ascending order of PbO content from left to right(50, 66.6 and 78.6 mol%) showing the various modes of connection between SiO4 tetrahedrons (in yellow) as well as the asymmetry of the coordination polyhedron for PbOn. Pb (in black) and O (in red).

Figure 3 . 8 .

 38 Figure 3.8. Evolution of Si-O-Si cross-linkage rate per oxygen atom depending on the molar ratio M II /(M II + Si) for M = Pb and Ca in crystallized lead silicates (•) or calcium silicates (▲)

Figure 3 .

 3 Figure 3.10. Evolution as a function of PbO content of the temperature corresponding to viscosities of 10 2 and 10 13 Poise for liquids of the SiO2-PbO system (according to Martlew data (Martlew 2005)). It can be noted that the temperature corresponding to a given viscosity decreases with the PbO content, which shows its fluxing effect.

Figure 3 . 11 .

 311 Figure 3.11. Evolution of 29 Si MAS NMR spectra of lead silicate glasses depending on their PbO content[START_REF] Fayon | Caractérisation du rôle structural du plomb dans des matrices vitreuses : approche par RMN haute résolution solide mono et bidimensionnelle[END_REF]). 7 T magnetic field, 10 kHz rotational frequency (with the kind permission of F.Fayon)

Figure 3 . 12 .

 312 Figure3.12. Evolution of the relative proportions of Q n units determined from29 Si MAS NMR spectra of lead silicate glasses (figure3.11) as a function of their PbO content (the dotted curves serve only as a guide)[START_REF] Fayon | Caractérisation du rôle structural du plomb dans des matrices vitreuses : approche par RMN haute résolution solide mono et bidimensionnelle[END_REF]) (with the kind permission of F. Fayon).

Figure 3 . 14 .

 314 Figure 3.14. Evolution of the silicate vitreous network (only SiO4 tetrahedrons are represented) of lead silicate and pure silica glasses depending on their PbO content. Reproduced with permission from(Kohara, S., Ohno, H., Takata, M., Usuki, T., Morita, H., Suzuya, K., Akola, J., Pusztai, L., Phys. Rev. B, 82, 134209, 2010). Copyright (2020) by the American Physical Society.

Figure 3 . 15 .

 315 Figure 3.15. Radial distribution functions calculated from the neutron scattering data for glasses of composition (1-x)SiO2 -xPbO (x in mol%)[START_REF] Takaishi | Structural study on PbO-SiO2 glasses by X-ray and neutron diffraction and 29 Si MAS NMR measurements[END_REF]

Figure 3 .

 3 Figure 3.16. Structural model of lead silicate glasses proposed by Takaishi et al.[START_REF] Takaishi | Structural study on PbO-SiO2 glasses by X-ray and neutron diffraction and 29 Si MAS NMR measurements[END_REF] based on the X-ray and neutron scattering results

Figure 3 . 18 .

 318 Figure 3.18. Structural model proposed by Alderman for the 35PbO -65SiO2 (mol%) glass. Reproduced with the permission of O. Alderman from (Alderman 2013)

Figure 3 .

 3 Figure 3.19. Structural model proposed by Alderman for 80PbO -20SiO2 glass. To the right of the vertical separation line (yellow), the non-bonding doublets of Pb 2+ ions are omitted, while to the left they are represented (pink spheres). The green triangle is a SiO3 defect resulting from the calculation. Reproduced with the permission of O. Alderman from (Alderman 2013).

  .2). It shows the evolution of the proportion of various types of connections between Si, Pb, O and K in the glass structure depending on its lead content: Si-O-Si, Si-O-K, Si-O-Pb, Si-O-(Pb,K) and Pb-O-Pb. It appears that for the lowest PbO contents such as that of crystal glass ( 11 mol%), Pb 2+ ions share with a part of the K + ions the non-bridging oxygen atoms of the structure in the form of mixed Si-O-(Pb,K) bonds, a significant part of K + ions remaining however connected only to non-bridging oxygen atoms in the form of Si-O-K bonds (figure 3.20).

Figure 3 .

 3 Figure 3.20. 17 O MQ-MAS spectrum of a crystal glass (77.1 SiO2 -10.6 PbO -11.3 K2O -0.8 Na2O -0.2 Sb2O3 mol%) in blue showing the contribution of oxygen atoms of Si-O-Si, Si-O-K and Si-O-(Pb,K) bonds (Angeli et al. 2016). The position of the contribution of Si-O-Pb and Pb-O-Pb bonds obtained by Lee et al. (Lee et al. 2014) for PbO-rich binary SiO2-PbO glasses is represented in black.

Figure 3 . 21 .

 321 Figure 3.21. Evolution of the glass transition temperature Tg adding increasing Al2O3 contents to the 40SiO2 -60PbO (mol%) composition (according to the data of Roisine (Roisine 2018))

Figure 3 . 22 .

 322 Figure 3.22. Evolution of viscosity  (in poiseuilles Pl) as a function of temperature after adding increasing Al2O3 contents to the 40SiO2 -60PbO (mol%)composition[START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF]

Figure 3 . 23 .

 323 Figure 3.23. Evolution of Raman spectra of ternary SiO2-Al2O3-PbO glasses obtained by adding increasing Al2O3 contents (0 -25 mol%) to the binary 60 SiO2 -40 PbO (mol%) glass[START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF]

Figure 3 .

 3 Figure 3.25. Comparaison of 17 O MAS NMR spectra of 60 SiO2 -40 PbO et 51 SiO2 -34 PbO -15 Al2O3 (mol%) glasses enriched in 17 O (*: rotational band) (Roisine 2018)

Figure 3 .

 3 Figure 3.26. 17 O MQMAS NMR spectra of 60 SiO2 -40 PbO and 51 SiO2 -34 PbO -15 Al2O3 glasses in mol% enriched in 17 O[START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF]

Though most of the structural studies conducted on the binary crystal phases of SiO2-PbO system involved X-ray diffraction, NMR studies conducted on 29 Si and 207 Pb nuclei allowed the correlation of the chemical shift changes to the evolution of the environment of silicon and lead in the structure of crystals, thus providing very useful data for understanding the evolution of the environment of these same species in glasses[START_REF] Bessada | 29 Si MAS-NMR in lead silicates[END_REF][START_REF] Fayon | Empirical cor-relations between 207 Pb NMR chemical shifts and structure in solids[END_REF]).

v.u.: unit of bond valence.

207 Pb is the only stable isotope of lead (natural abundance 22.1 %) having a nonzero nuclear spin (I = ½), it can therefore be studied by NMR. However, given its high polarizability, the NMR signals obtained are large and poorly resolved.

In the case of highly lead-rich lead glazes, the origin of the alumina in their composition (< 10 % Al2O3 mass)[START_REF] Tite | Review arti-cle. Lead glazes in antiquity -methods of production and reasons for use[END_REF][START_REF] Roisine | Céramiques glaçurées de Bernard Palissy : à la recherche des secrets d'un maître de la Renaissance[END_REF]) may be either the raw materials deposited at the surface of ceramic objects before firing, or the partial dissolution in the thin layer of melting liquid rich in SiO2 and in PbO of a fraction of alumina initially present in the paste constituting the objects.