domain: chim phys

text:
Odile Majérus

Adèle Munoz-Bongrand

Daniel Caurant

Optical properties and coloration of lead silicate glasses

Colored lead silicate glasses, whether bulky or thin (glazes), have generally been appreciated for the beauty of their color. In his commented translation of Neri, Dr Merret wrote in 1665: "If this species of glass had the same solidity as the "cristallin" glass, it would be superior to all the others, due to the beauty of its color" (Bontemps 1868, p. 527). Moreover, the colorless lead silicate glasses of SiO2-PbO-K2O system have been known and used since the 18 th century for their optical properties, being referred to as "flint glass" (this term, originally given in England to potassium and calcium white glass, was reserved for potassium and lead glass since the end of the 17 th century. It now designates a dispersive optical glass of high refractive index).

This chapter reviews the physical bases of the main optical properties, with an emphasis on color. Then it presents an overview of the optical properties and applications of transparent SiO2-PbO-M2O (M, alkaline) glasses that are often said to take a yellow color. Further on it discusses the color of lead glasses colored by transition ions, case of "colored transparent glazes". The colors of these glasses differ from those of alkaline glasses colored by the same ions, and hypotheses are proposed to understand the origin. This chapter does not cover opacification and coloration by lead-based pigments (lead antimonates, arsenates or stannates), which can be added to alkaline glasses and also to lead glasses, considering that it involves an opacification and coloration whose origin is external to the lead glass, properly speaking. Moreover, the opacification of lead glasses and their possible coloration by semiconductor or metallic particles will not be covered either, as they involve the same agents and mechanisms as the silicate glasses in general, lead oxide not modifying the phenomena except for the increase in the refractive index of the glass and the role that it can play in redox equilibriums.

Physical bases of optical properties and the origins of glass color

Complex refractive index and the main optical properties

When travelling through a material medium such as glass, light is partly reflected, partly refracted and transmitted, and partly absorbed if absorbing species are present in the glass. These properties of the material medium in relation to light are summarized in the complex refractive index [START_REF] Kittel | Physique de l'Etat Solide[END_REF]:

√𝜀(𝜔) = 𝑛(𝜔) + 𝑖 𝜅(𝜔)
where ε(ω) is the complex dielectric function, n(ω) is the refractive index and κ(ω) is the extinction coefficient.

Note : A homogeneous and continuous material medium is considered here, whose electron density distribution can be considered uniform at the scale of wavelengths of UV-visible-IR domain. In this case, the complex refractive index does not depend on the wave vector k of light.

The wave vector 𝑘 of light in vacuum changes into the wave vector (n + iκ)k in the medium of index 𝑛 + 𝑖𝜅. Considering the amplitude of the incident wave is Ey,inc = 𝐸 𝑖𝑛𝑐 𝑒 𝑖(𝑘𝑥-𝜔𝑡) , the amplitude of the transmitted wave is 𝐸 𝑦,𝑡𝑟𝑎𝑛𝑠 ∝ 𝑒 𝑖((𝑛+𝑖𝜅)𝑘𝑥-𝜔𝑡) which is: 𝐸 𝑦,𝑡𝑟𝑎𝑛𝑠 ∝ 𝑒 -𝜅𝑥 𝑒 𝑖(𝑛𝑘𝑥-𝜔𝑡) The refractive index 𝑛(𝜔) therefore reflects the decrease in the phase velocity of light due to the medium (𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

= 𝜔 𝑘 = 𝑐 𝑛(𝜔)
), driving a change in the direction of light when crossing the interface (refraction). The dependence of n on the frequency ω is referred to as dispersion, a term used for light dispersion by a prism, but it causes also the chromatic aberration of lenses. The extinction coefficient 𝜅(𝜔) corresponds to the amplitude attenuation of light travelling through a medium due to absorption phenomena. The two indices n and κ are also known as "optical constants" of the medium.

Under normal incidence, the amplitude of the reflected wave relative to the incident wave is:

𝐸 𝑟𝑒𝑓𝑙 𝐸 𝑖𝑛𝑐 = 𝜌(𝜔)𝑒 𝑖𝜃(𝜔) = 𝑛 + 𝑖𝜅 -1 𝑛 + 𝑖𝜅 + 1
Experimentally, the reflection coefficient is measured under normal incidence, being the square module of the amplitude ratio:

𝑅(𝜔) = 𝜌 2 (𝜔)
The phase information is therefore lost. However, Kramers and Kronig have shown that, due to the analytical form that can be given to 𝜀(𝜔) (not detailed here), it is possible to mathematically transform 𝑅(𝜔) to calculate 𝜃(𝜔). These "Kramers-Kronig relations" can therefore be used to get 𝑛(𝜔) and 𝜅(𝜔) from the quantitative measurement of the optical reflection spectrum 𝑅(𝜔).

Figure 4.1 provides the indices n and κ as a function of the wavelength λ of light from UV to IR for the silica glass. Absorptions take place in far UV (towards 150 nm) and in IR (towards 9 µm). The nature of these absorptions varies: electronic for UV and vibrational for IR. They cause strong variations of the indices: as these absorptions occur, reflection and dispersion are both strong. However, in the extended visible domain (between 1 µm and 0.3 µm), the index κ is zero and the index n is quasi-constant around 1.5. The silica glass is therefore a perfectly transparent and little dispersive medium in the visible, near UV and near IR domains.

Colorless and transparent glasses are the glasses that contain no species absorbing in the visible and no diffusing species. Their use for optical applications requires more precise information on their refractive index and their dispersion. As already mentioned in chapter 1, several characteristic optical properties can be defined, among which are the following:

-Main refractive index nd is the refractive index measured at 587.56 nm (He spectral line);

-Reciprocal dispersive power or Abbe number 𝜈 𝑑 , is the ratio:

𝜈 𝑑 = 𝑛 𝑑 -1 𝑛 𝐹 -𝑛 𝐶
where nF and nC are the refractive indices measured respectively at 486.13 nm (H spectral line) and at 656.27 nm (another spectral line of H). The lower the Abbe number, the higher the dispersive power. (Lentes 1998, p. 23) Colored glasses contain species absorbing in one part of the visible spectrum. The absorption phenomenon takes out from the light a part of the visible spectrum, the transmitted light is no longer "white" but colored. The color that is finally perceived depends on the spectrum of the illuminating light (it is not always white light), on its absorption by the glass and on eye sensitivity. These data are gathered in the three colorimetric coordinates calculated from the transmission spectrum or from the reflection spectrum, by postulating a standard illumination and a standard sensitivity for the human eye. There are various systems of colorimetric coordinates, each combining in three numbers the three perceptions, namely the hue, the lightness and the saturation (related to the existence of very dominant absorptions).

When the extinction coefficient κ remains small at least in one part of the visible domain, and in the absence of any diffusing species, the colored glass is referred to as "colored transparent". For a massive glass (object, stained glass, etc.), the color is perceived in transmission. For an enamel or a transparent glaze, light is first transmitted, then reflected in a more or less diffuse manner by the substrate (a metal or ceramic surface), then once again transmitted and gets out of the glass reaching our eye. The reflection by the substrate is therefore added to the perceived color. When trying to measure the colorimetric coordinates from a reflection spectrum, attention should be paid to choosing a perfectly reflective or perfectly diffusive substrate, meaning that it does not absorb in the visible.

Glass is no longer transparent when the extinction coefficient κ is very high in all the visible domain (case of chalcogenide glasses, for example) or when heterogeneities inside it cause the phenomenon of diffusion. Indeed, particles of index differing from that of glass and of size a that is very small or close to visible wavelengths will behave as diffusing objects, the complete behavior being given by the Rayleigh theory (a << λ) or by Mie theory (a ~ λ). Depending on the size of these particles and on the difference between their index and that of glass, the intensity and the spectrum of diffused light varies from pale bluish (very small sizes of the order of 1-10 nm, diffused intensity varying with 1 𝜆 4 ⁄ ), to "white" (larger sizes, 0.1-10 µm, the diffused intensity no longer varies with the wavelength). It can then be said that these glasses are opalescent or opacified, respectively.

Coloring species in glasses

The visible domain corresponds to the energies of the valence electrons. The absorptions in the visible are therefore always related to resonant electron excitations at the level of the most external electrons. These excitations can be of various natures and are related to various species.

d-d or f-f transitions

Transition ions, whose valence level is a partially filled d level (3d, 4d, etc.), are the most common species for glass coloration since ancient times (iron, copper, cobalt, manganese ions). Under the effect of the nonspherical symmetry of the electrical field generated by the oxygen neighbors (negatively charged), the level d is split into several levels. This splitting is due to the "crystalline field". The electron-electron interactions inside the d configuration add an additional splitting term. These splittings and the energies of various levels are described by the Tanabe Sugano diagrams for each configuration d n (n = 1 to 9) placed in a crystalline field of octahedral or tetrahedral symmetry, depending on the force of the crystalline field and on the electron-electron interactions. The energy differences between the higher d levels and the lowest d level are in the visible and near IR: visible light can therefore be absorbed by the transition of a d electron to a higher d level, which is referred to as "d-d transition". The absorption bands of d-d transitions are not intense, as they are forbidden by Laporte rule that imposes a change of parity between the departure orbital and the arrival orbital. On the other hand, they are very large, both because of the vibronic coupling related to the contribution of d orbitals to the metal-oxygen chemical bond, and because of the distribution of environment and therefore of crystalline field in the glasses.

Lanthanide ions, whose valence level is the partially filled f level, give rise to f-f transitions in the visible, not intense and very thin, as the f levels are core levels that participate to a little extent to the chemical bond and therefore to vibrations. The use of these ions for glass coloration appeared in the 20 th century (see chapter 7).

Optical gap transitions and charge transfer transitions

Light may excite the valence electrons of ligands (anions of oxides, sulfides, etc.) and place them in the lowest unfilled orbitals of metallic centers. In the solid, depending on the overlapping degree of valence orbitals, there may be a charge transfer transition (little or no overlapping) or an optical gap transition between the valence band and the conduction band (strong overlapping, electron delocalization). These transitions are fully authorized and the absorptions are therefore very intense.

In the pure silica glass, the absorbance in far UV (towards 150 nm) corresponds to the optical gap transition between the top of the valence band, mainly formed of the 2p level of oxygen, and the bottom of the conduction band, mainly formed of the 3s-3p hybrid level of silicon.

In the alkaline silicate glasses, the introduction of non-bridging oxygens (denoted by NBO in what follows) isolated the ones from the others creates filled 2p levels above the valence band. The transition from these 2p levels leads to an absorbance in near UV (towards 350 nm).

In the alkaline silicates glasses that contain transition ions, these ions have their d levels below the lowest of the conduction band. The electron transition of the 2p levels of non-bridging oxygens towards the unfilled d levels of the metal ion to which these oxygens are linked is not an optical gap transition, as these levels are localized. It is properly speaking a ligand charge transfer transition towards the metallic center, as in a coordination complex.

Generally, the charge transfer transitions between the ligands and the d orbitals of the transition ions are in the near UV, but they can extend in the visible. A yellow coloration may then appear (case of glasses very rich in TiO2, for example). The oxoanions are isolated molecular entities formed between very charged metal ions and their oxygen ligands: chromates, vanadates, etc. In these entities, the charge transfer transition is located in the visible and causes very intense colorations (yellow for chromate or vanadate oxoanions). Moreover, the sulfide anions can also be bound to metal ions substituting oxide anions. The charge transfer of S 2-towards the metal ion is itself shifted in the visible. It causes for example the amber coloration of glasses containing Fe 3+ -S 2-chromophore formed by reduction of sulfate ions in glass melting [START_REF] Chopinet | L'importance des phénomènes d'oxydo-réduction dans le verre[END_REF].

It is important to note here that the color of crystalline pigments, such as the lead-based ones (lead antimonates, arsenates, stannates) or metal chalcogenides (CdS, CdSe, etc.) results from the optical gap transition in these particles, to which the diffusion effect should be added.

Plasmon resonances

Plasmon resonances are collective resonant excitations of the free electrons at the surface of metal nanoparticles (gold, silver, colloidal copper). These resonances cause thin and strong absorptions in the visible, the domain of absorbed wavelengths depending on the size of the nanoparticles. This phenomenon is for example at the origin of copper red (Cu 0 nanoparticles) or silver yellow (Ag 0 nanoparticles) of stained glasses.

Optical properties and color of transparent SiO2-PbO-M2O glasses

SiO2-PbO-M2O glasses form a very ancient family of transparent glasses used in optics, referred to as "flint". Their general optical properties are a high refractive index and a strong dispersion in the visible domain (rather low Abbe number) (see chapter 1). The high electron density of Pb 2+ ions and the polarizability of their 6s orbital filled by two electrons explain the high refractive index. As for the strong dispersion, it is related to the existence of an absorbance in the near UV due to the O(2p) → Pb(6p) transition where the O(2p) level is modified by the overlapping with the 6s level of lead. It is the nature of this absorbance and the yellow color that it confers in the presence of metal impurities that will be briefly described in this section. A more detailed discussion of the literature is presented in (Majérus et al. to be published).

Electronic structure and color of lead oxides PbO

The colors of lead oxides result from the optical gap absorption between the top of the valence band and the bottom of the conduction band. Experimentally, the optical gap is indeed given at 1.9 eV for litharge α-PbO, red, and 2.5 eV for massicot β-PbO, yellow [START_REF] Radhakrishnan | Sensitization of photoconductivity in tetragonal lead monoxide[END_REF]. The electronic structure of PbO and the orbital composition of the valence and conduction bands were the subject of many studies and debate in the literature. It was less a matter of understanding the color, but rather the nature of the free pair whose stereochemical activity manages to distort the environment of Pb 2+ ion in these oxides. A first interpretation was to assign the optical gap to a transition between the hybridized 6s-6p levels of lead, slightly overlapping with 2p orbitals of oxygens. These hybridized levels responsible for the optical gap were associated with the free pair. Their more or less significant overlapping in the direction z of the structure explained the different color in α-PbO and in β-PbO.

Ab-initio calculations with DFT method [START_REF] Terpstra | Electronic Structure of the Lead Monoxides: Band-Structure Calculations and Photoelectron Spectra[END_REF][START_REF] Watson | Origin of the Lone Pair of α-PbO from Density Functional Theory Calculations[END_REF] have recalled into question the nature of the free pair and the contribution of various orbitals in the valence band. Indeed, internal 6s-6p hybridization did not allow understanding why the environment of Pb 2+ is distorted in PbO, while it is perfectly spherical in PbS. The anion had to play a role [START_REF] Du | Microscopic Origin of Stereochemically Active Lone Pair Formation from Orbital Selective External Potential Cal-culations[END_REF].

According to these calculations, which were experimentally validated in the 2000s [START_REF] Payne | Electronic Origins of Structural Distortions in Post-Transition Metal Oxides: Experimental and Theoretical Evidence for a Revision of the Lone Pair Model[END_REF], the top of the valence band in PbO oxide is mainly formed of 2p levels of oxygens, with a very small contribution of 6s and 6p orbitals of lead. The optical gap is therefore assimilated to a O(2p) → Pb(6p,6s) transition, where the O(2p) level is slightly overlapping with 6s and 6p orbitals of lead (figure 4.2). This information is important for understanding the electronic transitions at the UV limit of the spectrum in glasses containing PbO. [START_REF] Watson | Origin of the Lone Pair of α-PbO from Density Functional Theory Calculations[END_REF].The orbitals contributing to the top of the valence band, which can be assimilated to the "free pair" presenting a stereochemical activity, are represented in violet, the other orbitals in blue. In these calculations, the top of the valence band is essentially formed of 2pz orbitals of oxygens, with a minor contribution of 6s and 6pz of lead. VB = valence band. CB = conduction band. e -= valence electrons.

Electronic structure, optical properties and color of SiO2-PbO(-M2O) glasses

The studies dedicated to the electronic structure of binary SiO2-PbO glasses or to alkaline lead ternary glasses are relatively few. While the silica glass does not absorb below 9 eV, absorptions appear at about 6.7 eV, 5.3 eV and 4.2-4.6 eV when PbO is added to the silica [START_REF] Ellis | The Electronic Band Struc-ture and Optical Properties of Oxide Glasses II. Lead Silicates[END_REF]. The absorptions explain the significant increase of the refractive index and of the dispersion of these glasses with respect to the silica glass in the near UV domain of the spectrum.

These energy electronic transitions in the UV domain have been mainly explained by the internal 6s → 6p transition of Pb 2+ in the studies published between 1970 and the beginning of 2000 [START_REF] Bourdillon | The reflection spectra of lead glass[END_REF][START_REF] Ellis | The Electronic Band Struc-ture and Optical Properties of Oxide Glasses II. Lead Silicates[END_REF][START_REF] Robertson | Electronic Structure of Lead Glasses and Resonant Covalence in Glasses[END_REF][START_REF] Gubanov | Electronic States Spectrum for Lead Silicate Glasses with Different Short-Range Order Structures[END_REF][START_REF] Weinstein | Effects of Structural Disorder and Urbach's Rule in Binary Lead Silicate Glasses[END_REF]). To our knowledge, these interpretations were not resumed and recalled into question until present. However, in the light of recent results on the electronic structure of PbO already mentioned, and of knowledge on the local order around Pb 2+ in glasses, it is likely that these transitions have in reality a O(2p) → Pb(6p) character predominant over Pb(6s) → Pb(6p). Indeed, the local environment of Pb 2+ ions in SiO2-PbO glasses is close to the one in oxides (see chapter 3, section 3.3.3.2.). These environments of low coordination number and distorted reflect the strong interactions due to the overlapping of 6s and 6p orbitals of lead with the 2p orbitals of oxygens, similar to PbO oxide (figure 4.2). A simplified electronic structure is therefore proposed for these glasses inspired from the PbO oxide in figure 4.9a.

Let us now consider the effect of these transitions on the color. It was often noted that beyond a certain lead content, SiO2-PbO or SiO2-PbO-M2O glasses have in their thickness a yellow coloration [START_REF] Hampton | Colour of Heavy Lead Silicate Glass[END_REF][START_REF] Stroud | Optical Absorption and Color Caused by Selected Cations in High-Density, Lead Silicate Glass[END_REF][START_REF] Cohen | Optical and Electrical Properties of Lead Silicate Glasses[END_REF]. The origin of this coloration was debated, in the attempt to establish whether it was intrinsic and resulted from a shift and a thermal widening of near UV transitions, or it was related to impurities. By showing that a lead flint glass with a refractive index of 1.90 is colorless over 5 cm thickness if it is quite pure, Hampton settled the argument and established the essential role of impurities [START_REF] Hampton | Colour of Heavy Lead Silicate Glass[END_REF]. These impurities can be d transition ions (typically Fe 3+ ) and also platinum if the glass is elaborated in platinum crucible.

The very significant sensitivity of lead glass coloration to the presence of impurities is however remarkable and not equivalent to that of alkaline glasses, as it was very clearly established by Stroud in a study related to 10 coloring species (V 5+ , Cr 6+ /Cr 3+ , Mn 3+ /Mn 2+ , Ni 2+ , Cu 2+ /Cu + , Ce 4+ /Ce 3+ , U 6+ ions and Rh, Pd, Pt metals with their ionized species) [START_REF] Stroud | Optical Absorption and Color Caused by Selected Cations in High-Density, Lead Silicate Glass[END_REF]. Moreover, Cohen et al. noted that the cutoff wavelength in near UV increases regularly with the PbO content: in other terms, lead glasses are all the more yellow (UV absorbance extending towards violet) as their PbO content increases. They therefore suggest that "the presence of variable concentrations of metal ion impurities is not the only source of yellow color in PbO-rich glasses" [START_REF] Cohen | Optical and Electrical Properties of Lead Silicate Glasses[END_REF].

The "mystery" therefore persists, as clearly formulated by Stroud and Cohen, on this yellow coloration that seems to originate both in the presence of impurities and in PbO content.

This point will be discussed in further detail in section 4.3 related to the color of SiO2-PbO(-M2O) glasses colored by transition ions.

SiO2-PbO-M2O glasses colored by transition ions

A remarkable property of lead glasses is their color in the presence of transition elements, and this is presented in most chapters of this book. Lead glazes have warm and intense colors, unlike their soda lime or alkaline borosilicate analogues colored with the same transition ions.

This fact is well known by the potters of varnished terracotta who desperately try to reproduce, with leadless commercial glazes, the ochre-yellow (with Fe 3+ ) and sap green (with Cu 2+ ) colors so characteristic of their ceramic art (figure 4.3). In contrast, the same ions in the borosilicate glazes offer pale and cold substitutes to these colors, at best creamy-white and blue-green. The color of lead glass is stronger and greener (with Cu 2+ ) or more "honey-like" (with Fe 3+ ) than the soda glass. The study of these glasses by optical absorption spectroscopy and electron paramagnetic resonance (EPR) presented below can be used to propose an origin to this color change1 .

Optical absorption spectroscopy and origin of color changes

As a first step, the optical absorption spectra of colorless glasses are presented in figure 4.6. As these glasses do not contain any coloring species (except for impurities visible by the small band at 27 000 cm - 1 in NaI glass), their absorbance remains close to zero throughout the visible domain and it strongly increases in the near UV under the effect of the optical glass transition (top of the valence band, in fact constituted of isolated levels of NBO → bottom of the conduction band. It is important to note that rigorously speaking the term "optical gap" is not suitable to a glass, due to the disorder that prevents the orbital overlapping throughout the solid). When Na2O is substituted by PbO, this optical gap transition strongly shifts towards the visible. The shift is of about 5 800 cm -1 (table 4.1 and figure 4.6). In the leadonly glass (PbI), absorption extends towards 450 nm, which explains the yellow coloration of this glass. The optical absorption spectra of the colorless soda glass (NaI) and of iron-colored glasses (NaFe, NaPbFe and PbFe) are represented in figure 4.7. First of all, the comparison between the spectrum of NaI glass and the spectrum of NaFe glass makes it possible to identify the transitions related to the iron oxide introduced in the glass and attributable to the two degrees of oxidation of iron, namely Fe 2+ (wide absorption band at 10 000 cm -1 ) and Fe 3+ (several absorption bands between 20 500 and 27 000 cm -1 ). These absorption bands extending largely in the visible are due to d-d transitions whose attribution is indicated in the figure (for the details on these attributions, see [START_REF] Vercamer | Spectroscopic and Structural Properties of Iron in Silicate Glasses. Propriétés Spectroscopiques et Structurales du Fer dans les Verres Silicatés[END_REF][START_REF] Majérus | Origin of the yellow color of lead silicate glasses[END_REF]). They are at the origin of the yellow-green color of the soda NaFe glass. Besides these d-d transitions, another effect of the addition of Fe2O3 is the shift of the optical gap absorption from UV to near UV and visible. This shift reflects the appearance of unfilled levels below the conduction band of the glass: unfilled d levels of Fe 2+ and Fe 3+ ions. The nature of the absorption in near UV therefore changes, passing from an optical gap transition in the colorless glass to a charge transfer transition in the complex formed by the transition ion and its oxygen ligands in NaFe glass (O(2p) → Fe(3d) transition).

It is now interesting to compare the spectra of the three glasses doped with Fe2O3. These spectra are normalized to the thickness and to the concentration of Fe ions in the glass, so that their ordinate corresponds to the linear and molar extinction coefficient ε (linked to the above mentioned linear extinction coefficient κ by the relation 𝜅 = 𝜀 × 𝑐 where c is the concentration in mol.L -1 of ions in the glass). In the PbFe glass compared to the glass, the d-d band of Fe 2+ ions at 10 000 cm -1 strongly decreases in absorbance and very slightly shifts towards high energies (shift of about + 300 cm -1 , not visible in figure 4.7). But most of all, the charge transfer band shifts very strongly towards the visible, by about 5 500 cm -1 (table 4.1 and figure 4.7). It extends this time up to over 600 nm, explaining the marked "honey-like" color of PbFe glass.

Finally, figure 4.8 summarizes the spectra of NaI glass and of three glasses doped with CuO. These spectra show a d-d absorption band attributed to the 2 E → 2 T2 transition of Cu 2+ ions in octahedral symmetry towards 12 500 cm -1 , and the charge transfer absorption in near UV. The d-d band is slightly asymmetric due to the Jahn-Teller effect, which causes an axial deformation of the octahedral complex CuO6 and splits the transition into several sub-transitions. Here too, when Na2O is replaced by PbO, this band shifts very lightly towards high energies (near + 500 cm -1 ). But above all, the charge transfer band shifts strongly towards the visible, by about 5 500 cm -1 as in the PbFe glass. These shifts towards the visible cause the modification of color between lead glasses and soda glasses, as the violet to blue parts of the spectrum become absorbed, which introduces a prominent yellow-orange component in the perceived color. The d-d bands vary very little and do not explain the change of color.

In any case, the spectrum of the mixed soda and lead glass is between the two other spectra and shows that these changes are related to the gradual substitution of Na2O by PbO. The shifts towards the visible of near UV absorptions have been evaluated by the energy for which the absorbance normalized to thickness takes the value A = 10 cm -1 (transmission of 10 -10 ). These energies are summarized in table 4.1 and the shifts by total substitution of Na2O by PbO are calculated by difference in the last column. In the PbFe and PbCu glasses, these shifts, of 5 500 cm -1 , can be due either to the reduction of energy of the first unfilled d levels of the metal ion, or to the increase in the energy of donor levels of ligands O(2p), or to the two combined effects. As there is such a shift also in the non-doped PbI glass (5 800 cm -1 ), this proves that it is, in fact, due only to the energy increase of donor levels. The diagrams of the energy levels in figure 4.9 summarize these conclusions. In figure 4.9, the terms "conduction band" (CB), "valence band" (VB) and "optical gap" are given in quotation marks to highlight the fact that these terms rigorously designate delocalized levels that do not actually exist in the glasses (because of the disorder, the electronic levels are rather localized). However, these terms are used by direct analogy with the crystals, as the nature of transitions is similar (same types of departure and arrival orbitals). In the diagram of the PbI glass, the donor level of the optical gap transition is formed of orbitals of NBO modified by the overlapping with the 6s level of Pb, denoted by "NBO 6s", and the acceptor level is formed of 6p orbitals of Pb modified by the overlapping with O(2p), as in the PbO crystal. Let us therefore consider that in PbI glass with 38 %mol in PbO, the local order around Pb 2+ ions and the Pb-O chemical bond are similar to those in PbO (see figure 4.2). This is justified by the structural results presented in detail in section 3.3.3.2 and by the comparative examination of the optical absorption spectra conducted here. In the diagram of NaCu glass, the Cu 2+ ions introduce their 3d levels under the "CB" so that the first absorption in UV is a charge transfer absorption between NBO(2p) and Cu(3d) in the quasi-molecular CuO6 complex. In the diagram of PbCu glass, the charge transfer takes place this time between the NBO levels modified by the presence of lead (denoted by "NBO 6s" and represented in violet) and the Cu(3d) levels. The energy difference with respect to the same charge transfer in NaCu is of -5 500 cm -1 , pushing this transition the violet-blue part of the visible spectrum. These positions relative to the energy levels can be interpreted as follows at molecular scale. In the glass, Cu 2+ ions are bound to 6 NBO, forming a quasi-molecular CuO6 complex. This complex has excess negative charge of -4 (Cu 2+ surrounded by 6 NBO carrying each a formal negative charge). This charge excess is compensated by alkaline ions or Pb 2+ that are near the complex, so that the following formal equations can be written:

in NaCu: 𝐶𝑢𝑂 + 2 𝑁𝑎 2 𝑂 [𝑆𝑖𝑂 2 ] → (𝐶𝑢𝑂 6 4-, 4 𝑁𝑎 + ) 𝑆𝑖𝑂2 glass in PbCu: 𝐶𝑢𝑂 + 2 𝑃𝑏𝑂 [𝑆𝑖𝑂 2 ] → (𝐶𝑢𝑂 6 4-, 2 𝑃𝑏 2+ ) 𝑆𝑖𝑂2 glass
In these equations, CuO and Na2O or PbO oxides are considered as modifiers of silica: each of their oxygens reacts with silica and forms two non-bridging oxygens. In the resulting quasi-molecular complex, these non-bridging oxygens are bound at the same time to the Cu 2+ center and to the compensating Na + or Pb 2+ ions. These complexes are schematically represented in figure 4.10, where the NBO brought by Na2O, PbO or CuO are drawn each in a different color.

The charge transfer transition is the transition between the 2p level of these NBO having the highest energy (donor level) and the unfilled 3d level with the lowest energy of Cu 2+ . In the (𝐶𝑢𝑂 6 4-, 2 𝑃𝑏 2+ ) complex, the antibonding overlapping of O(2p) and Pb(6s) orbitals (as in PbO, figure 4.2) forms a donor level denoted by "NBO 6s" that is significantly higher in energy than in the 𝐶𝑢𝑂 6 4-, 4 𝑁𝑎 + complex and is represented in violet in the diagrams of figures 4.2 and 4.9.

The same conclusions are obviously drawn for Fe 3+ ions.

Variation of the local environment of Cu 2+ ions depending on the type of glass

The local environment of Cu 2+ and Fe 2+ is slightly modified in the lead glass compared to the soda glass, as proven by the slight shift towards high energies of their d-d absorption band (for Fe 3+ , the d-d transitions are in the charge transfer band of PbFe glass and therefore impossible to observe). This high energy shift reflects a stronger interaction between the 3d orbitals and the NBO ligands, i.e. an increase of the crystalline field. In diagram c) of figure 4.9, it was represented by an increase of 2 T2 level, which is the one interacting the most with the ligands.

Cu 2+ ion has a d 9 configuration with a total electronic spin S = ½, which makes it a paramagnetic species that can be studied by electron paramagnetic resonance (EPR).

The EPR-based study of Cu 2+ ions in the two types of glass is presented in detail in (Majérus et al. to be published). The symmetry of the CuO6 complex is slightly modified in the lead glass compared to the soda glass, but the crystalline field is slightly stronger and the Cu-O bond more covalent. These conclusions are also those of a recent study on the Cu 2+ ions in various lead matrices [START_REF] Andreev | Influen-ce of macroand microcomponent content on the color of M2O-PbO-SiO2 (M = Li, Na, K, Rb, Cs) glasses doped with copper[END_REF].

In summary, in this study related to two transition ions (Fe 3+ and Cu 2+ ), it appears that the warmer and more intense colors of lead glasses are due to the prominent absorption of the violet-blue component of the visible spectrum in the presence of both lead and metal ion. In the quasi-molecular complex formed by the metal ion, its oxygen ligands and its charge compensators Pb 2+ , the charge transfer transition is clearly shifted in the visible. This is due to the hybridization of 2p orbitals of oxygen ligands with the 6s orbital of Pb 2+ ions that increases the energy of the donor level. There is a stronger interaction of this level with the d orbitals, which is reflected by a slightly stronger crystalline field and a more covalent metal-oxygen bond.

The conclusions of this study are confirmed by the recent results on the electronic structure in PbO presented in section 4.2.1, which show that the top of the valence band (comparable to the donor level here) is constituted by 2p orbitals of the oxygen in antibonding overlapping with Pb(6s) orbital. They are consistent with the studies of Hampton, Stroud and Cohen highlighting both the role of impurities and the PbO content in the yellow coloration in transparent lead glasses.

Figure 4 . 1 .

 41 Figure 4.1. Refractive index and extinction coefficient of the silica glass measured by optical reflection. Figure extracted from(Lentes 1998, p. 23)

Figure 4

 4 Figure 4.2. a) Very simplified diagram of the chemical bond in PbO compound according to the partial densities of states calculated by ab-initio method (DFT) for α-PbO by Watson et al. represented in b)[START_REF] Watson | Origin of the Lone Pair of α-PbO from Density Functional Theory Calculations[END_REF].The orbitals contributing to the top of the valence band, which can be assimilated to the "free pair" presenting a stereochemical activity, are represented in violet, the other orbitals in blue. In these calculations, the top of the valence band is essentially formed of 2pz orbitals of oxygens, with a minor contribution of 6s and 6pz of lead. VB = valence band. CB = conduction band. e -= valence electrons.

Figure 4 . 3 .

 43 Figure 4.3. Two varnished terracotta jugs by Agnès Cabaret, ceramist in Sarthe. The green and ochre colored glazes are based on a lead glazing mixture and copper oxide (green) and iron oxide (ochre). The transparent lead glaze covering the jugs is slightly colored in yellow by a little iron oxide.

Figure 4 .

 4 Figure 4.4. a) Glass elaboration process with two meltings at temperatures T1 and T2, summarized in table b). Soda glasses being more viscous than lead glasses, these temperatures had to be increased

Figure 4 . 5 .

 45 Figure 4.5. Nominal molar compositions and photographs of nine glasses prepared in the laboratory, their names being specified in bold. The compositions were analyzed in the laboratory by EDX, and they are very close to these nominal compositions (deviation below 1% molar for each oxide).

Figure 4 . 6 .

 46 Figure 4.6. Absorption spectra of three "colorless" glasses NaI, NaPbI and PbI, showing the shift of 5 800 cm - 1 towards the visible of the charge transfer band when Na2O is substituted by PbO. This shift is at the origin of the slightly yellow color of the PbI glass. The band at 27 000 cm -1 visible on the spectrum of NaI and NaPbI glasses is attributed to impurities. The dashed, dotted and continuous lines refer to the spectra of NaI, NaPbI and PbI glasses respectively.

Figure 4 . 7 .

 47 Figure 4.7. Molar extinction coefficient ε of iron-doped glasses and comparison with the normalized spectrum of non-doped NaI glass. The dotted-dashed, dashed, dotted and continuous lines refer to the spectra of NaI, NaFe, NaPbFe and PbFe glasses respectively.

Figure 4 . 8 .

 48 Figure 4.8. Molar extinction coefficient ε of copper-doped glasses and comparison with the normalized spectrum of non-doped NaI glass. The dotted-dashed, dashed, dotted and continuous lines refer to the spectra of NaI, NaCu, NaPbCu and PbCu glasses respectively.

Figure 4 . 9 .

 49 Figure 4.9. Schematic energy level diagrams, using the transition energies experimentally determined on the optical absorption spectra of PbI (a), NaCu (b) and PbCu (c) glasses and summarized in table 4.1

Figure 4 .

 4 Figure 4.10. Schematic representation of quasi-molecular CuO6 complexes of octahedral symmetry formed in the a) NaCu and b) PbCu glass. Each "O -" is a NBO playing the role of ligand and binding the Cu 2+ ion to the silicate network. The bond between Pb 2+ and O -is represented by a line to indicate its covalent character related to the interaction between O(2p) and Pb(6s, 6p).

Table 4 .

 4 1. Wavenumbers (in cm -1 ) for which the absorbance normalized to thickness reaches A = 10 cm -1 for each of the glasses. The four values in blue are used for the energy level diagram in figure4.9

		Pb	NaPb	Na	Na -Pb Difference
	Cu 2+	24	28 000	31 000	5 500
	Fe 3+	23 000	26 300	28 500	5 500
	/	28 400	31 200	34 200	5 800

All the optical absorption spectra are presented here either in the form of absorbance normalized to the thickness of the glass slide (unit cm - 1 ), or in the form of absorbance normalized to the thickness and to the nominal molar concentration of coloring ion (unit L.mol -1 .cm -1 ). A baseline was subtracted from all the spectra before normalization. For each glass composition, this baseline was established from the difference spectrum between the spectrum of a thick slide and the spectrum of a thinner slide of glass, following the procedure described in[START_REF] Vercamer | Spectroscopic and Structural Properties of Iron in Silicate Glasses. Propriétés Spectroscopiques et Structurales du Fer dans les Verres Silicatés[END_REF][START_REF] Majérus | Origin of the yellow color of lead silicate glasses[END_REF].