Dr Charles Le Losq
email: charles.lelosq@anu.edu.au

Maria Rita

R Cicconi

G Neville

Neville Greaves

Dr Daniel R Neuville

Dr M R Cicconi

Prof G N Greaves

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Summary:

Silicate glasses are important cultural, societal and geological materials. Geologic glasses testify for the igneous activity of the Earth and, for instance, represented important source of tools and ornamental objects during the Paleolithic. Nowadays, silicate glasses are used to build technical materials, such as smartphone screens or glass matrix for stabilizing hazardous radioactive wastes. Therefore, silicate glasses are central to the history of the Earth and of the humanity. The compositional landscape of natural and industrial silicate glasses is vast, with various elements that all influence differently the glass properties and structure. The SiO 4 tetrahedral framework, backbone of silicate glasses, is variously influenced by the introduction of network modifier metal cations or network former aluminium cations.

Industrial and geologic silicate glasses further contain multivalent elements (e.g., Fe 2+/3+ ), rare-earth elements, and volatile elements (H, C, S, Cl, F, I) that play different roles on the glass structure and properties. This chapter proposes to review the link between the structure, the properties and the chemical composition of silicate glasses.

Silicate glasses: Historical and industrial importance

The origin of the first silicate glass is a vast question. The first glass tools actually were manufactured by breakage and date approximately of 10000 BCE, as shown by obsidian arrow heads of this age found in Turkey for example. Manufacture of silicate glasses dates back to the earliest antiquity; it follows the control of fire, and is synchronous with the Bronze Age which itself varies geographically. The first objects made by melting date of ~6000 BCE. Hazard was probably the first factor in this melting manufacturing. Henrivaux [START_REF] Henrivaux | Le verre et le cristal[END_REF] proposed that the appearance of glass should be contemporary with the manufacture of bricks cooked by fire and of certain ceramics. Indeed, a plausible hypothesis is that brick and ceramic manufacturers were the first glass manufacturers because various materials subjected to the action of an intense fire may present the first symptoms of vitrification in the form of a veneer or surface glaze. This hypothesis may explain the Mesopotamian glazes observed on several ceramics and located at Suse between 7000 and 5000 BCE. However, this hypothesis contradicts with the story reported by Pline the Elder . Indeed, in his Natural History [2], Pline reported that it would be Phoenician merchants who, cooking their food on the banks of the river Belus in pots supported by blocks of Natron, would have seen an unknown substance flow: "The story is, that a ship, laden with nitre, being moored upon this spot, the merchants, while preparing their repast upon the sea-shore, finding no stones at hand for supporting their cauldrons, employed for the purpose some lumps of nitre which they had taken from the vessel. Upon its being subjected to the action of the fire, in combination with the sand of the sea-shore, they beheld transparent streams flowing forth of a liquid hitherto unknown: this, it is said, was the origin of glass" This observation is unlikely when one knows that temperatures close to ~ 1000°C are necessary to observe the flow of silicate melts, conditions difficult to achieve using campfires. Pliny's account thus probably is a legend, and current historical knowledges suggest that the formation of glass as a byproduct of mettalurgic and ceramic activities is more plausible [e.g., see the review of 3]].

Regardless of the origin of its discovery, glass was considered as precious during the antiquity. This is shown, for instance, by the Hebrew term that designates glass, ִית" ִוֹכ ֹכ " (pronounced "zkhourhit"), which comes from the Hebrew word "זכְך" that means pure. Glass thus remained an expensive material during antiquity. As such, it was reserved for noble objects as jewelry and amulets (Fig. 1), competing with precious metals such as gold or silver for such uses. [START_REF] Henrivaux | Le verre et le cristal[END_REF].

From 5000 to 3000 BC, objects partly made of glass are characterized by a faience coating placed on the surface of a ceramic material. Then, as the furnaces of the age of bronze and copper appeared, the work of the glass became easier, allowing the manufacture of colored glass bead for instance. Core-molding and cast glass methods, using molds for shaping glass objects, were subsequently developed in the ~ 1500-500 BCE period in Mesopotamia and Egypt. Some sources attribute the invention of glass-blowing to Syrian glassmakers around 300 BCE [e.g.,[START_REF] Rasmussen | How Glass Changed the World[END_REF], but this disagrees with the representation of glassblowing in Egyptian tombs [START_REF] Gandy | The Romance of Glass-making[END_REF], as for instance in a tomb from the fifth dynasty at Sakkarah or the painting at Beni-Hassan (Fig. 2) that dates from the reign of Usertessen I. (2758( -2714 BCE) BCE). Reproduced from [START_REF] Henrivaux | Le verre et le cristal[END_REF] "Le Verre et le cristal" Vicq-Dunaud Editors, Paris [START_REF] Henrivaux | Le verre et le cristal[END_REF].

Historical glass compositions are based on the use of silica, lime and soda. The compositions of historical glasses remain in a tight chemical domain. They are still close to those of present glasses (Fig. 3), illustrating that the optimization of glassmaking processes was achieved early in the history of human glass manufacture. An interesting fact is that early glass makers already aimed at controlling the color of translucent or slightly opaque glasses through the addition of metals such as copper (red and blue-red), iron (black, brown and green), antimony (yellow), cobalt (blue) or tin (white). Such coloring substances were already identified and known before the age of glass manufacturing, as several of them were used as pigments [6]. Early glass manufacturers probably had access to raw materials presenting variable quality. Production was therefore subject to many hazards, against which they could only contrast empirical knowledge. (lunar glass, dunite, peridotite, tephrite, basalt, phonolite, andesite, trachyte, rhyolite, tektite, obsidian), industrial (Optical fiber, Window glass, Glass E, Nuclear Glass, Refiom, Pyrex 1912, Actual window glass) and historic (Roman glass Embiez 200y,Flint,Egyptian,Babylonians,Tour,Chartres,Rouen,Germanique,Boheme) glasses [7][START_REF] Kurkjian | Perspectives on the history of glass composition[END_REF][START_REF] Brill | L'épave Ouest-Embiez 1, Var : le commerce maritime du verre brut et manufacturé en Méditerranée occidentale dans l'Antiquité[END_REF][10].

Around the 15 th century BCE, improvements of the furnaces allowed higher working temperatures. As a result, fusion quality improved, leading to a technological transformation as the first translucent glasses were produced. Glass objects presenting a large variety of shape appeared, such as bottles and containers used to preserve ointments, perfumes, food or beverages, for instance. For instance, to form small containers, core-molding technics were used: a rather viscous silicate melt was spread on a core, made for example of a mixture of clay and manure; the core was then removed from the inside of the new piece. Other shaping methods were developed, and, from that time, glasses were decorated. In addition, technological glasses appeared, as for instance millefiori glasses (Fig. 4a) composed of many glass filaments embedded in a transparent glass, forming a unique piece. Thin glaze films covering various objects were also formed using silicate melts rich in lead oxide and, hence, presenting low viscosity at working temperature. Towards the 4 th century BCE, this new process improved greatly potteries, making them waterproof. From its Mesopotamian-Egyptian origin, the art of glass spread to neighboring countries. Pearls made at the end of the second millennium were found from Italy to Central Asia and China (Fig. 4b). Glass containers were found in Greece, Italy and China, respectively dating from the 13th, 8th and 5th centuries BCE. The availability and quality of the raw materials may have determined the abundance and interest in producing glass at such time. Indeed, glass transparency requires using raw materials with high purity during the glass-forming process. In particular, the starting materials should be very poor in iron oxide, one of the main glass colorant that is abundant on Earth surface. As such pure raw materials were easily found in Palestina and Egypt, for instance, this may explain the abundance of glasses made in these areas. The use of glass blowing during the Roman empire (Fig. 2) gave birth to a veritable industrial revolution.

This process allowed fast, easy and thus cheap shaping of the glass. The size and shape of the pieces were also less limited than with previous methods. Whether intended for utilitarian or decorative purposes, glass was able to find its place in all homes under the Roman empire. Even the deceased benefited of such technological evolution as their ashes were preserved in glass urns. Glasses dating from the Roman empire cover a small chemical composition domain. This suggests a form of globalization of the glass market at that time, with the production of glass concentrated in various factories located along the syro-palestinian costline [11]. This concentration probably resulted from the abundance of local deposits of pure sand and natron, giving this region a great competitive advantage. From there, glass was exported in the form either of finished products or of glass ingots, which could be re-melted in small furnaces at their destination to shape the final objects. For instance, the Ouest-Embiez ship wreck found in the Mediterranean Sea testifies for the occurrence of this trade [11].

The decline of the Roman Empire followed by the Arab conquests probably led glass trading routes to be cut off [START_REF] Rasmussen | Reinventing an Old Material: Venice and the New Glass[END_REF]. As a result, starting at the beginning of the Middle Ages (5 th -15 th century BCE), glasses had to be produced locally in Western Europe, with the available resources on the spot. The local cullet was used together with ashes to help melting local sands in order to produce glass. Using ashes helped compensating the absence of natron. Figure 5 represents the composition of ashes obtained from different plant and tree species. In Europe, ash from beech, oak and fern were mostly used in glass making processes. Such ashes are rich in potassium (Fig. 5), such that potash-lime glasses were produced in northern Europe. Unfortunately, potassium is not an element ensuring the stability of the glass in regards of alteration, explaining why potash-lime glasses from the early Middle Ages are not well preserved.

Soda-lime glasses were also produced in regions were the local availability of saltwort was good (Fig. 5). This induced a typical geographic repartition of soda-lime and potash-lime compositions in Western and North-Eastern Europe at this time. This changed during the 11 th century, as saltwort becomes to be imported from Spain for producing glass.

In parallel to the events in Europe, the development of glass in the East took a totally different path after the fall of the Roman empire. In the Byzantine empire, glassmaking processes used during the Roman period survived, such that the glass production that characterized the Roman glasses was conserved. The rise of the Muslim Arabs see the development of new glasses. The Islamic glassmakers used their knowledge of the Roman and Byzantine glassmaking technics and their own experience to produce high quality glasses. In particular, this lead to the introduction of the Islamic soda-lime glass, introduced between the 8 th and 10 th century CE. After the first crusades in the 11 th century, glassmaking centers progressively shifted from the Islamic glassmakers to the Venice (Italy) center. Vernioles [START_REF] Vernioles | Les sites vitrifiés de France: inventaire et mode de réalisation[END_REF].

Indeed, the glassmaking knowledges acquired during the prosperous periods of the Roman empire never really died, and new contacts with the Byzantine empire following the first crusades allowed the transmission of new knowledges from the Islamic to the Venetian glassmakers. In addition, starting from the 11 th century, Venice was becoming one of the most important center of trade, commerce and arts in the Europe and Mediterranean regions. As a result of the combination of those factors, the Italian glassmaking industry started to flourish again from around 1200 CE. In 1291, the glassmaking factories moved to the Island of Murano, to keep the Venice city safe from fires. This further helped keeping the secrets of the Venetian glassmaking processes safe. By the 15 th century, Murano became one of the most important glassmaker in Europe. Venetian glassmakers continued to improve the quality of the glasses they produced, this leading to the production of the cristallo for instance, a transparent, shiny glass prepared from soda ash and quartz pebbles from Ticino (Italy). Using this glass composition that is characterized by a long working time, the Murano glassmakers manufactured thin and relatively light glass windows and mirrors that were exported all other Europe.

While the Venetian glasses were of high quality, they also were expansive. This actually pushed the birth of a French glassmaking company that is nowadays one of the largest glass and material producer in the world. Indeed, when the French king Louis XIV decided to build the Versailles castle, the price asked by the Murano glassmakers for the required large quantities of glasses was particularly depressing. This pushed Louis XIV to grant a royal privilege in 1665 to a new glass factory, which finally settled in 1693 in the village of Saint-Gobain. In 1695, it became the French Royal Glass Factory, famous for the production of flat glass through cooling and flattening the melt directly on a wood table of several meters.

This process was notably depicted in the painting "The visit of the duchess of Berry at Saint-Gobain in 1822". The process cited thereabove was a late evolution of two technics used to produce flat glass, in high demand for the construction of windows and mirrors for religious and royal edifices in Western Europe since the Middle Ages. Indeed, the first productions of flat glass were performed using either the crown or the cylindrical sleeve processes. The crown process consisted in obtaining a cylinder of flat glass from a vase, initially formed by blowing. This cylinder of flat glass can then be cut in any wanted shapes. The cylindrical sleeve process used a different approach, forming a glass sheet from a glass cylinder (Fig. 6).

Glasses formed through those processes were expansive, such that their use was reserved to religious or important edifices until the end of the 17 th century. While the brazier represented in Figure 2 is one of the first representations of a glass furnace, the one developed since the Middle Aged were highly sophisticated. An example of a furnace used at this time is given by Agricola in De Re Metallica in 1556 and later reported by Neri et al. [6]. Figure 7 shows the representation displayed in Neri et al. [6], in which we distinguish three different furnaces: -i) the first called calcaria was used to prepare oxide and carbonate powders from raw materials (shells, chalk, marls, wood, sea salt, vegetable or animal ash…); -ii) the second furnace was typically a pot furnace used to melt the materials generated with the first furnace, in order to obtain from 100 to 300 kg of glass (a bath furnace could also be used for generating large glass volume of several cubic meters); -iii) a third furnace was used for annealing the glass pieces generated by blowing the silicate melt from the second furnace.

At the end of the Middle Ages and the beginning of the Renaissance, academic societies and the renaissance savants started to make further important progress in knowledge. Such time saw the development of new glasses, and glassmaking technics. For example, the Prince Rupert started to look at some spectacular and curious properties of glass, presented to the Royal Society of London in 1661.

Indeed, dropping melts at high temperature in water, Prince Rupert noticed the formation of glass drops very resistant to violent shocks, up to a point after which they exploded suddenly and turned into fine powder. Spectacularly, these first tempered glasses, well known as the Prince Rupert's drops, illustrated the role of internal stresses that accumulate in the absence of annealing (Fig. 8). George Ravenscroft In parallel of the discovery of such new glass compositions, the fast spreading of mechanical glassmaking processes allowed lowering the price of glass, making it suitable for its use in many different areas such as food storage, building or glass lenses for instance. Following World War II, many new glass families were made and developed, and the invention of the float glass process by Sir Alastair Pilkington and Kenneth Bickerstaff between 1953 and 1957 further revolutionized the glass production processes.

Nowadays, silicate glasses still represent the largest quantity of human-made glasses. They are used in many aspects of everyday life, e.g. fiber optics, cellphone and computer screens, car windshields.

However, the importance of silicate glasses is becoming smaller, thanks to the development of new and exciting glasses, such as, for example, chalcogenide, metallic or fluoride glasses. Such new glasses have a high technological importance, with critical applications as for instance for infrared cameras, photonics or data storage.

From the previous discussion, silicate glasses used in many technical and technological applications through historical times as well as natural geologic glasses present a wide range of chemical composition (Fig. 3). Such large variations in chemical composition are associated with large differences in term of glass properties, e.g., glass transition temperature T g , density, hardness, chemical durability. For example, the T g and relative density of simple binary silicate glasses M n+ 2/n O-SiO 2 are reported as a function of the molar percentage of M n+ 2/n O in them in Fig. 9 (M=Na, K, Mg, Ca); along the M n+ 2/n O-SiO 2 binary systems, T g vary non-linearly of hundreds of degrees. In addition, glasses composed of a given amount of SiO 2 but different metal cations M present different T g (Fig. 9a). Density changes are closer to a linear trend that vary quite strongly with composition (Fig. 9b). Such changes in glass properties translate changes in the glass disordered molecular structure upon variations of the glass chemical composition. Indeed, while glasses do not present long-range order arrangement as crystals do, they still present specific molecular arrangements at short and intermediate range order. For instance, the environment at short range order of Si 4+ cations is well defined as being a SiO 4 tetrahedral units in silicate glasses. At a scale of a few SiO 4 tetrahedral units, arrangements of such tetrahedral species in rings and cages is also reported, as it will be presented in the following sections. However, one should remember that even such molecular arrangements are disordered in glasses: for instance, they can present a broad range of bond angle and bond lengths, as shown by the board distribution of the Si-O-Si bond angle in the silica SiO 2 glass [START_REF] Mozzi | The structure of vitreous silica[END_REF][START_REF] Neuefeind | Bond angle distribution in amorphous germania and silica[END_REF][START_REF] Clark | Correlated structural distributions in silica glass[END_REF][START_REF] Tucker | Refinement of the Si-O-Si bond angle distribution in vitreous silica[END_REF][START_REF] Malfait | 29Si NMR spectroscopy of silica glass: T1 relaxation and constraints on the Si-O-Si bond angle distribution[END_REF]. [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF]; T g of Li 2 O-SiO 2 glasses: [START_REF] Losq | Rôle des éléments alcalins et de l'eau sur les propriétés et la structure des aluminosilicates fondus et vitreux : implications volcanologiques[END_REF]; T g of MgO-SiO 2 and of CaO-SiO 2 glasses: [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF][START_REF] Neuville | Viscosity, structure and mixing in (Ca, Na) silicate melts[END_REF]. Density data are from [START_REF] Losq | Rôle des éléments alcalins et de l'eau sur les propriétés et la structure des aluminosilicates fondus et vitreux : implications volcanologiques[END_REF][START_REF] Neuville | Viscosity, structure and mixing in (Ca, Na) silicate melts[END_REF][START_REF] Doweidar | The density of alkali silicate glasses in relation to the microstructure[END_REF][START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF].

In the present chapter, the structure and properties of silicate glasses will be reviewed. We define silicate glasses as glasses containing dominantly SiO 2 as the glass network former oxide component that allows their vitrification. Glasses built upon the presence of other network formers in their structure will be discuss in the following chapters (see chapters XXXXX). Silicate glasses usually contain various elements such as, for example, aluminum, iron, alkali and alkaline-earth metal cations. In a first time, the structure and properties of the silica glass will be briefly reviewed in section 1.2. Then, we will add new levels of complexity by looking at the structure and properties of Al-free and Al-bearing silicate glasses in sections 1.3 and 1.4. Section 1.5 will review multivalent and rare-earth elements in silicate glasses, and redox effects will be discussed, while sec. 1.6 gives a brief overview of volatiles elements dissolved glasses.

Silica glass

Structural concepts

Silicate glasses inherit their names from the basic oxide component that allow their formation: silica oxide or SiO 2 . Interestingly, the possibility to quench the simple SiO 2 melt into glass indicates that Si 4+ is a network former cation, similar to other cations such as Ge 3+ or B 3+ for instance (see chapters XXX for further information). Network former elements in oxide glasses participate in building an interconnected molecular network, forming the backbone of glassy materials. Regarding the pure silica glass, it is composed of Si 4+ cations and O 2-anions arranged in SiO 4 tetrahedral units with Si 4+ at the center and O 2-at the summit. Those SiO 4 units are interconnected by their apical bridging oxygen atoms, forming a tridimensional tetrahedral network.

Because of its simple chemistry, one may think that the structure of the silica glass is simple. However, it actually exhibits such a level of complexity that there is no definitive consensus about the threedimensional arrangements of SiO 4 tetrahedral units at medium-range order. An early description of the silica glass structure was provided by Zachariasen [START_REF] Zachariasen | The atomic arrangement in glass[END_REF], who proposed the Random Network (RN) model to describe the structure of oxide AX 2 glasses (with A the network former cations and X the anions).

Following this model, Si and O structural sites are energetically equivalent, and the Si and O atoms randomly distribute between those sites following 4 rules that govern the formation of AX 2 glasses: 1) the system contains enough X anions to ensure the formation of triangle or tetrahedra of X anions around the central network former A cations;

2) those triangle/tetrahedra share the apical X anions at their summit;

3) a given X anion only link 2 A cations; 4) the triangle/tetrahedra only share their summit, and not their faces or edges.

In the silica glass, this model predicts the formation of a three-dimensional disordered network composed of rings and cages of SiO 4 interconnected tetrahedral (Fig. 10). First X-ray diffraction data of the silica glass in 1934 corroborated such description [START_REF] Warren | Direct Imaging of a Two-Dimensional Silica Glass on Graphene[END_REF], and the latest observations of thin 2-dimensional films of silica deposited on graphene further support such view [28] (Fig. 10).

Figure 10: Image linking the transition between the theoretical 2D view the structure of the silica glass as drawn by Zachariasen [26] in 1932 (on the left) and the experimental observation by Huang et al. [28] in 2012 of a thin 2D film of amorphous silica deposited on graphene (on the right), made with using annular dark-field scanning transmission electron microscopy (ADF-STEM). Reprinted with permission from Huang, P.Y., Kurasch, S., Srivastava, A., Skakalova, V., Kotakoski, J., Krasheninnikov, A.V., Hovden, R., Mao, Q., Meyer, J.C., Smet, J., Muller, D.A., Kaiser, U., 2012. Direct Imaging of a Two-Dimensional Silica Glass on Graphene. Nano Letters 12, pages 1081-1086, doi:10.1021/nl204423x. Copyright 2012American Chemical Society. Pre-1990 analysis of X-Ray diffraction data [e.g., 29] and Raman spectra [e.g., 30] of the SiO 2 glass as well as early structural calculations [e.g., 31] supported the idea that the structure of the SiO 2 glass at medium range order was composed of tetrahedral rings, but no consensus existed about the number of tetrahedral units in the rings. In the Raman spectrum of SiO 2 , the asymmetric R band centred near ~460 cm -1 , which extends from ~ 200 to ~ 650 cm -1 , is actually assigned to Si-O-Si and O-Si-O bending vibrations in such SiO 4 rings (Fig. 11).

Figure 11: Raman spectrum of the Lybian glass, a glass found in the Lybian desert that probably results from a meteoritic impact. This glass present a composition of 99% silica and 1% impurities (Al 2 O 3 , alkalis…). The Raman spectrum of this glass is very similar to that of the pure SiO 2 glass. It displays:

the Boson peak at ~65 cm -1 , that can be assignment to collective transverse acoustic vibrational modes [START_REF] Shintani | Universal link between the boson peak and transverse phonons in glass[END_REF] promoted in silicate glasses by cooperative inter-tetrahedral librations [START_REF] Bucheneau | Low-frequency modes in vitreous silica[END_REF][START_REF] Chumakov | Equivalence of the Boson Peak in glasses to the transverse acoustic van Hove singularity in crystals[END_REF][START_REF] Courtens | The vibrational modes of glasses[END_REF]; the R band, an asymmetric band with an intensity maxima near 440 cm -1 that may be assigned to O movements along the Si-O-Si intertetrahedral bonds of tetrahedral rings with 5, 6 or more tetrahedral [START_REF] Bell | The vibrational spectra of vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Bell | Bell-JPC-70-3.pdf[END_REF][START_REF] Bell | Normal mode assignments in vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Sharma | Raman investigation of ring configurations in vitreous silica[END_REF][START_REF] Mcmillan | The structures and vibrational spectra of crystals and glasses in the silica-alumina system[END_REF][START_REF] Galeener | Planar rings in glasses[END_REF][START_REF] Galeener | Planar rings in vitreous silica[END_REF][START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mcmillan | Vibrational spectroscopy of silicate liquids and glasses[END_REF][START_REF] Mcmillan | A study of SiO₂ glass and supercooled liquid to 1950 K via high-temperature Raman spectroscopy[END_REF][START_REF] Pasquarello | Identification of Raman defect lines as signatures of ring structures in vitreous silica[END_REF][START_REF] Umari | Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum[END_REF][START_REF] Rahmani | Signature of small rings in the Raman spectra of normal and compressed amorphous silica: A combined classical and ab initio study[END_REF]; the D 1 and D 2 sharp peaks, assigned to breathing vibrations of four and three membered rings, respectively [39, 41-43, 46, 48-51]; an asymmetric band near 800 cm -1 , assigned to asymmetric vibrations of SiO 4 units with both O and Si movements [START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Kalampounias | A low-frequency Raman study of glassy, supercooled and molten silica and the preservation of the Boson peak in the equilibrium liquid state[END_REF][START_REF] Galeener | Band limits and the vibrational spectra of tetrahedral glasses[END_REF][START_REF] Sen | Phonons in AX₂ glasses: From molecular to band-like modes[END_REF]; a peak near 1065 cm -1 , assigned to Si-O asymmetric stretching vibrations in SiO 4 units [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF][START_REF] Sarnthein | Origin of the High-Frequency Doublet in the Vibrational Spectrum of Vitreous SiO2[END_REF][START_REF] Spiekermann | Vibrational mode frequencies of silica species in SiO 2 -H 2 O liquids and glasses from ab initio molecular dynamics[END_REF][START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF]; and a broad band between 1100 and 1250 cm -1 that is assigned to Si-O symmetric stretching vibrations in SiO 4 units [START_REF] Bell | The vibrational spectra of vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Bell | Bell-JPC-70-3.pdf[END_REF][START_REF] Bell | Normal mode assignments in vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF]. At higher frequency, peaks at ~1060 cm -1 and ~1195 cm -1 are observed, and are assigned to Si-BO asymmetric and symmetric stretching modes of SiO 4 units, respectively [START_REF] Seifert | Three-dimensional network structure of quenched melts (glass) in the systems SiO 2 -NaAlO 2 , SiO 2 -CaAl 2 O 4 and SiO 2 -MgAl 2 O 4[END_REF][START_REF] Sarnthein | Origin of the High-Frequency Doublet in the Vibrational Spectrum of Vitreous SiO2[END_REF][START_REF] Spiekermann | Vibrational mode frequencies of silica species in SiO 2 -H 2 O liquids and glasses from ab initio molecular dynamics[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Pasquarello | Dynamic structure factor of vitreous silica from first principles: Comparison to neutron-inelastic-scattering experiments[END_REF]. Peak-fitting the ~1180 cm -1 band with Gaussian components, Seifert et al. [START_REF] Seifert | Three-dimensional network structure of quenched melts (glass) in the systems SiO 2 -NaAlO 2 , SiO 2 -CaAl 2 O 4 and SiO 2 -MgAl 2 O 4[END_REF] noticed that two peaks were necessary because this ~1180 cm -1 band is asymmetric (Insert in Fig. 11). They interpreted this splitting of the Si-O symmetric stretching in Q 4 units in two components as indicating an asymmetry of the Q 4 environments in the silica glass. This could be related to a slight asymmetry of the T-O-T inter-tetrahedral angle in SiO 2 glass (Fig. 12), as suggested by results from molecular dynamic simulations [START_REF] Tucker | Refinement of the Si-O-Si bond angle distribution in vitreous silica[END_REF][START_REF] Rino | Structure of rings in vitreous ${\mathrm{SiO}}_{2}[END_REF][START_REF] Benoit | Model of silica glass from combined classical and ab initio molecular-dynamics simulations[END_REF][START_REF] Yuan | Si-O-Si bond angle and torsion angle distribution in vitreous silica and sodium silicate glasses[END_REF], 29 Si NMR spectroscopy [START_REF] Malfait | 29Si NMR spectroscopy of silica glass: T1 relaxation and constraints on the Si-O-Si bond angle distribution[END_REF] and X-Ray absorption spectroscopy [START_REF] Mozzi | The structure of vitreous silica[END_REF][START_REF] Henderson | An x-ray scattering study of vitreous KFeSi3O8 and NaFeSi3O8 and reinvestigation of vitreous SiO2 using quasi-crystalline modelling[END_REF][START_REF] Poulsen | Amorphous silica studied by high energy X-ray diffraction[END_REF]. Seifert et al. [30] assigned this asymmetry to different puckering extents of 6-membered rings in the structure of the silica glass that yield T-O-T angle differences of ~5-10°. In line with such idea, Henderson et al. [START_REF] Henderson | An x-ray scattering study of vitreous KFeSi3O8 and NaFeSi3O8 and reinvestigation of vitreous SiO2 using quasi-crystalline modelling[END_REF] discussed the X-Ray Diffraction (XRD) data for SiO 2 as suggesting the coexistence of cristobalite-like and trydimite-like 6-membered rings in silica. Such structural models fall in the category of the crystallite network model of the SiO 2 glass, discussed by Wright [START_REF] Wright | Neutron scattering from vitreous silica. V. The structure of vitreous silica: What have we learned from 60 years of diffraction studies?[END_REF]. Mauri et al [START_REF] Mauri | Si-O-Si bond-angle distribution in vitreous silica from first-principles ${}^{29}\mathrm{Si}$ NMR analysis[END_REF] (dotted curve). Reprinted from Malfait [START_REF] Malfait | 29Si NMR spectroscopy of silica glass: T1 relaxation and constraints on the Si-O-Si bond angle distribution[END_REF], Copyright (2008), with permission from Elsevier.

The idea of different 6-membered rings coexisting in the structure of the silica glass is still presently plausible, as no consensus has been reached on the structure of the silica glass. For instance, Huang et al. [START_REF] Huang | Tailoring structure and properties of silica glass aided by computer simulation[END_REF] recently followed such idea, showing with the help of Molecular Dynamic simulations that the mixing in different quantities of two types of 6-membered rings, presenting shapes close to those found in a-cristobalite and b-cristobalite, may account for variations of the SiO 2 bulk modulus and density with pressure. However, most Monte Carlo and Molecular Dynamic simulations [e.g., [START_REF] Tucker | Refinement of the Si-O-Si bond angle distribution in vitreous silica[END_REF][START_REF] Umari | Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum[END_REF][START_REF] Umari | Modeling of the Raman spectrum of vitreous silica: concentration of small ring structures[END_REF][START_REF] Rino | Structure of rings in vitreous ${\mathrm{SiO}}_{2}[END_REF][START_REF] Van Ginhoven | Silica glass structure generation for ab initio calculations using small samples of amorphous silica[END_REF] indicate that, at medium range order, the structure of the silica glass is composed of a distribution of rings with different numbers of SiO 4 units, with 5-, 6-and 7-membered rings tending to be dominant (Table 1). Therefore, as rings with different number of tetrahedral units present different T-O-T angles [START_REF] Galeener | Planar rings in vitreous silica[END_REF][START_REF] Rino | Structure of rings in vitreous ${\mathrm{SiO}}_{2}[END_REF],

Si-O stretching frequency in SiO 4 units should vary as a function of the ring statistic in the SiO 2 glass.

For instance, signals assigned to Si-O stretching in SiO 4 units in the main 6-and 7-membered rings will give signals at different frequency because they present different Si-O-Si bond angles and Si-O bond lengths [START_REF] Galeener | Band limits and the vibrational spectra of tetrahedral glasses[END_REF][START_REF] Sen | Phonons in AX₂ glasses: From molecular to band-like modes[END_REF][START_REF] Rino | Structure of rings in vitreous ${\mathrm{SiO}}_{2}[END_REF]. Therefore, a repartition of SiO 4 units in mostly 5-, 6-and 7-membered rings, as suggested by results from simulations, may actually explain the asymmetry observed in the Raman data.

In all cases, the asymmetry of the R band further agrees with considering the structure of the SiO 2 glass as containing a distribution of rings with 3 to more than 8 tetrahedral units. In particular, two sharp peaks at ~590 and ~606 cm -1 in Raman spectra of SiO 2 glasses (Fig. 11) can be assigned to minor fractions of 4-and 3-membered rings in the glass structure, respectively [39, 41, 42, 45-49, 51, 52, 68]. Such observation thus support results from simulations that tends to predict low concentrations of such rings in the glass structure [e.g., [START_REF] Pasquarello | Identification of Raman defect lines as signatures of ring structures in vitreous silica[END_REF][START_REF] Umari | Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum[END_REF][START_REF] Rahmani | Signature of small rings in the Raman spectra of normal and compressed amorphous silica: A combined classical and ab initio study[END_REF][START_REF] Umari | Modeling of the Raman spectrum of vitreous silica: concentration of small ring structures[END_REF]. The vibrational decoupling of such rings from the remaining part of the glass network allow them to contribute significantly to the glass Raman spectra [49]. Overall, the picture of the structure of the silica glass still is incomplete, but advances in simulations and spectroscopic technics may bring further determining pieces of information in a near future.

Value References

Si-O bond distance 1. 59 -1.61 Å [18, 67] Si-O-Si bond 146° -151° [START_REF] Clark | Correlated structural distributions in silica glass[END_REF][START_REF] Tucker | Refinement of the Si-O-Si bond angle distribution in vitreous silica[END_REF][START_REF] Malfait | 29Si NMR spectroscopy of silica glass: T1 relaxation and constraints on the Si-O-Si bond angle distribution[END_REF] % of 3-membered rings 0.0 -0.7 % [START_REF] Tucker | Refinement of the Si-O-Si bond angle distribution in vitreous silica[END_REF][START_REF] Umari | Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum[END_REF][START_REF] Umari | Modeling of the Raman spectrum of vitreous silica: concentration of small ring structures[END_REF][START_REF] Rino | Structure of rings in vitreous ${\mathrm{SiO}}_{2}[END_REF] % of 4-membered rings 0.0 -7.7 % % of 5-membered rings

Properties of Silica

The precedent section depicted the structure of the silica glass as consisting of a tri-dimensional arrangement of SiO 4 tetrahedral units connected by their summit and forming ring structures in the glass.

Such interconnected, polymerized structure yields the highest known glass T g , equal to 1480 K according to the calorimetric measurements of Richet and Bottinga [START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF] (Fig. 13). , predicted from the viscosity data of Leko et al. [70] assuming that log(h) = 12 Pa s at T = T g .

For comparison, the calorimetric T g of Richet and Bottinga [69] is also reported as a black empty square.

Silica actually is the strongest know liquid, in the strong-fragile denomination of liquids that was introduced by Angell [START_REF] Angell | Spectroscopy simulation and scattering, and the medium range order problem in glass[END_REF][START_REF] Angell | Relaxation in liquids, polymers and plastic crystals-strong/fragile patterns and problems[END_REF]. A strong liquid is characterized by a linear or nearly-linear relationship between the logarithm of its viscosity and the T g /T ratio, while fragile liquids present strong departure from this linearity. The fragility m of liquids, equal to the slope of the log(h) vs Tg/T curve at T g , allows one to quantify such deviations. m tends toward ~20 for strong liquids such as SiO 2 , and to much higher values for fragile liquids, such as B 2 O 3 for instance. The unique interconnexion of the silica tetrahedral network makes the silica glass properties very sensitive to the presence of impurities. For instance, the addition of OH or Na 2 O in the silica glass produces a dramatic reduction of hundreds of degrees of the silica glass transition temperature T g (Fig. 13). Another example is the thermal diffusivity of the silica glass, which varies between 0.795 and 0.870 mm 2 s -1 at 298K depending on the impurities present in the glass [73; see Another parameter needs to be taken into account when looking at the link between the structure and the properties of the silica glass: the fictive temperature T f . Indeed, T g is usually defined as the temperature corresponding to the glass transition upon cooling the melt at a given laboratory cooling rate of ~ 10°/sec.

However, cooling the glass much faster or slower that the latter value yields different temperatures for the glass transition. Those different values are referred as the fictive temperature, T f . As silica is extremely viscous even at high temperatures, changes of hundreds of degrees of T f can be obtained easily by varying the cooling rate from hundreds of degrees per seconds to ~ 1° per second. This leads to small variations in the glass density or refractive index, for instance (Table 2). Such variations in the glass density are linked to changes in the silica glass structure: glasses presenting higher T f also present high concentrations of three-and four-membered rings, as shown by the increasing signals of those rings in the Raman spectra of fast-quenched glasses [START_REF] Heili | The dependence of Raman defect bands in silica glasses on densification revisited[END_REF]. However, such causal relationships between T f , glass structure and properties is complex and depend on the glass composition. For instance, the analysis of a glass with a 75%-25% mixture of SiO 2 -GeO 2 revealed an opposite correlation between the glass T f , density and the ring statistic [START_REF] Heili | The dependence of Raman defect bands in silica glasses on densification revisited[END_REF].

Value Remarks References

Density 2.2002-2.2060 g cm -3 depends on T f [START_REF] Brückner | Properties and structure of vitreous silica. I[END_REF] Molar Volume 27.24-27.31 cm 3 mol -1 depends on T f Density conversion

Thermal diffusivity D 0.795 -0.870 mm 2 s -1 at 298 K [START_REF] Hofmeister | Effects of hydration, annealing, and melting on heat transport properties of fused quartz and fused silica from laser-flash analysis[END_REF] Refractive Index n 1.4583-1.4589 depends on T f [START_REF] Brückner | Properties and structure of vitreous silica. I[END_REF] Calorimetric T g 1480 °C - [START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF] Configurational entropy 5.1 ±2 J mol -1 K -1 from calorimetric data [START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF] Table 2: Examples of properties of the silica glass.

In addition to T f , the densification of the silica glass also modifies the ring statistics, and, hence, its elastic properties. Indeed, upon densification, the frequency of the R band significantly increases, pointing to a puckering of the rings in the network without significant changes in the Si coordination or Si-O bond distance, at least up to pressure of ~ 8GPa [START_REF] Hemley | Raman Spectroscopy of Si${\mathrm{O}}_{2}$ Glass at High Pressure[END_REF][START_REF] Weigel | Polarized Raman spectroscopy of $v-{\mathrm{SiO}}_{2}$ under rare-gas compression[END_REF]. Such changes are reversible up to 8 GPa. After this pressure, irreversible changes are observed and reflect a change in ring statistics [START_REF] Hemley | Raman Spectroscopy of Si${\mathrm{O}}_{2}$ Glass at High Pressure[END_REF]. Compared to the ambient pressure SiO 2 glass, permanently densified glasses typically exhibit higher concentrations of four and particularly three membered rings [START_REF] Burgin | Vibrational modes and local order in permanently densified silica glasses: Femtosecond and Raman spectroscopy study[END_REF]. The inter-tetrahedral angles in those rings is unaffected by the densification, contrary to the Si-O-Si angles of large rings that significantly decreases of ~ 6° with a 20% densitification [START_REF] Hehlen | Inter-tetrahedra bond angle of permanently densified silicas extracted from their Raman spectra[END_REF]. Molecular dynamic simulations from Huang et al. [START_REF] Huang | Tailoring structure and properties of silica glass aided by computer simulation[END_REF] further suggest that an increase of dense, a-cristobalite-like 6-membered rings in SiO 2 upon densification may explain the densification mechanism of amourphous SiO 2 . The authors of this study indicate that the anomalous elastic property of amorphous SiO 2 , i.e. its decreasing elastic modulus upon compression, actually is explained by the conversion of b-cristobalite-like 6-membered rings in a-cristobalite-like 6-membered rings upon compression. Their simulation further shows that the introductions of elements such as rare gas or alkali oxides in the SiO 2 3D tetrahedral structure further prevent this convertion process, and help reducing the elastic anomaly of the SiO2 glass.

Aluminium-free Silicate Glasses

In silicate glasses, other elements are frequently present and play a role different to that of Si 4+ . Amongst the major cations present in industrial and geologic silicate glasses, we can cite Al 3+ , Fe 3+ , Ti 4+ , Li + , Na + , K + , Fe 2+ , Ca 2+ and Mg 2+ (Fig. 1). At the present time, we will focus on a brief description of the Al-free silicate glasses.

As visible in Fig. 13, the properties of the silica glass, such as, for instance, its T g , can be greatly affected by addition of small fractions of impurities, such as for instance of Na + metal cations. The latter actually are considered as network modifier cations, which break Si-O-Si bonds, and form ionic bonds with the newly transformed non-bridging apical oxygens. Such process leads to the dramatic depletion in the glass T g observed in Fig. 13. The following section will describe in more detail such processes at the molecular scale, and their effect on the glass properties.

Network modifier elements and Q n units

Alkali (Li, Na, K) and alkaline-earth (Ca, Mg) metal cations can be present together with SiO 2 in glasses, forming sensu stricto silicate glasses (aluminum free). However, such cations present ionic field strengths (IFS = Z/r 2 , with Z the cation electronic charge and r its ionic radius) too low to be able to enter the glass structure in tetrahedral units as Si 4+ does. Indeed, according to Dietzel [START_REF] Dietzel | Die Kationfeldstërken und ihre Beziehungen zu entlasungs-vorgängen, zur verbindunsbildung und zu den Scmelzpunkten von Silikaten[END_REF], cations presenting large IFS tend to enter in tetrahedral coordination and act as network former cations. For instance, the IFS of Si 4+ As a result of the process previously described, SiO 4 tetrahedral units in alkali and alkaline-earth silicate glasses carry different numbers of NBOs and BOs, and, hence, the local environment of Si 4+ atoms vary.

For instance, the Si-BO distances are shorter than the Si-NBO distances, as revealed by molecular dynamic simulations from Ispas et al. [START_REF] Ispas | Structural properties of lithium and sodium tetrasilicate glasses: Molecular dynamics simulations versus NMR experimental and firstprinciples data[END_REF]]. This study provides values of 1.63-1.64 Å for Si-BO distances and 1.58-1.60 Å for Si-NBO distances in the Li 2 Si 4 O 9 glasses, depending on the potential used for the calculations (empirical or Car-Parrinello ab initio). Such difference in the local environment of Si 4+ results in variations of the frequency of Si-O stretching in different tetrahedral units [START_REF] Virgo | Anionic Constitution of 1-Atmosphere Silicate Melts: Implications for the Structure of Igneous Melts[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF]] as well as of the 29 Si NMR frequency [START_REF] Engelhardt | Structural studies of calcium aluminosilicate glasses by high resolution solid state 29 Si and 27 Al magic angle spinning nuclear magnetic resonance[END_REF][START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF]. Those variations can be detected with using Raman and 29 Si NMR spectroscopy, respectively. The study of the Raman and 29 Si NMR spectra thus allows observing how the glass polymerization changes with its composition [START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Virgo | Anionic Constitution of 1-Atmosphere Silicate Melts: Implications for the Structure of Igneous Melts[END_REF][START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF][START_REF] Schramm | 29 Si Magic Angle Spinning NMR study on local silicon environments in amorphous and crystalline lithium silicates[END_REF][START_REF] Dupree | The structure of binary alkali silicate glasses[END_REF][START_REF] Emerson | High-Filed 29Si NMR studies of alkali silicate glasses[END_REF][START_REF] Sen | NMR study of Q-speciation and connectivity in K 2 O-SiO 2 glasses with high silica content[END_REF]. [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF][START_REF] Sen | NMR study of Q-speciation and connectivity in K 2 O-SiO 2 glasses with high silica content[END_REF][START_REF] Zhang | Silicon site distributions in an alkali silicate glass derived by two-dimensional 29 Si nuclear magnetic resonance[END_REF][START_REF] Davis | Q n Species Distribution in K 2 O•2SiO 2 Glass by 29 Si Magic Angle Flipping NMR[END_REF].

Figure 14 illustrates, for instance, how the fractions of tetrahedral units carrying different numbers of BO and NBOs at their summit vary along the Li 2 O-SiO 2 , Na 2 O-SiO 2 and K 2 O-SiO 2 binary joins, from 0 to 40% M 2 O (M = Li, Na, K). As illustrated in this figure, a useful way to distinguish tetrahedral units containing different numbers of BO and NBO is the Q n notation [START_REF] Schramm | 29 Si Magic Angle Spinning NMR study on local silicon environments in amorphous and crystalline lithium silicates[END_REF], where n refers to the number of BO carried by the SiO 4 tetrahedron Q. For example, the silica glass can be considered as composed of (ideally) only Q 4 units. Contrary to that, a sodium trisilicate NaSi 3 O 7 glass (75 mol% SiO 2 ) presents a distribution of Q n units with 48% Q 4 , 50% Q 3 and 2% Q 2 [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF]. Increasing the concentration in network modifier cations promotes the existence of Q n-1 units at the expense of Q n units in the glasses (Fig. 14), this effect being proportional to the fraction of added network modifiers. In addition, this effect is not ideal and depends on the ionic field strength of the network modifier cation that is present in the glass (Fig. 14). For instance, lithium silicate glasses are richer in Q 2 and Q 4 units than sodium silicate glasses.

This translates a tendency of Li + network modifier cations to cluster in the vicinity of Q 2 units in the network, leading to local enrichment in Q 4 units by compensation. This clustering may be related to the presence of network modifier percolation channels in the glass structure, as discussed in section 1.3.3. In all cases, increasing the metal cation ionic field strength in silicate glasses shifts the equilibrium:

Q n ó Q n-1 + Q n+1 , (1)
to the right-end side. One should note that, for a given composition, the equilibrium described by eq. ( 1) may also depend on the glass fictive temperature, which varies with the glass cooling rate. Indeed, higher temperature promote the shift of the reaction described by eq. ( 1) to the right, as shown by data from Raman spectroscopy and 29 Si NMR spectroscopy of alkali silicate melts [e.g., [START_REF] Brandriss | Effects of temperature on the structures of silicate liquids: 29Si NMR results[END_REF][START_REF] Mysen | Structure of silicate melts at high temperature: In-situ measurements in the system BaO-SiO 2[END_REF][START_REF] Mysen | Structure and properties of alkali silicate melts at magmatic temperatures[END_REF][START_REF] Mysen | Structure and properties of magmatic liquids: From haplobasalt to haploandesite[END_REF].

The knowledge of the Q n distribution in glasses allows evaluating their ratio of NBO to tetrahedral units, NBO/T, which is a bulk measure of the glass polymerization. The NBO/T can be calculated from knowledge of the Q n units distribution as:

NBO/T = 4 xQ 0 + 3 x(Q 1 ) + 2 x(Q 2 ) + 1 x(Q 3 ) , (2)
or from the knowledge of the molar proportions of the different network formers T, network modifier M i+ and oxygen O ions, as [START_REF] Mysen | The structure of silicate melts: Implications for chemical and physical properties of natural magma[END_REF][START_REF] Mysen | Relationships between properties and structure of aluminosilicate melts[END_REF]:

!"# $ = &#'($ $ = *+ , -. $ / /01 . ( 3
)
The glass chemical composition thus defines its NBO/T as well as the distribution of its Q n species.

Different models have been proposed to calculate the latter. The binary distribution model, suggested by Dupree et al. [START_REF] Dupree | The structure of soda-silica glasses: A mas NMR study[END_REF], predicts that only two species are present in the glass at given SiO 2 content, such that the Q n units in the glass are distributed as binary combinations of Q

4 -Q 3 , Q 3 -Q 2 , Q 2 -Q 1 and Q 1 -Q 0 as
observed in silicate minerals. Contrary to that, the random bonding model predicts that the concentration of a Q n unit can be calculated from a random distribution of the NBO and BO between the units. Figure 15 shows a representation of the two models. Neither the random bonding model nor the binary distribution model describe the measured distribution of Q n units observed in silicate glasses. Furthermore, those models do not account for the temperature dependence of the Q n unit speciation. Indeed, in glasses the Q n unit distribution is frozen-in, but as highlighted previously, it changes with T in the molten state, such that glasses with different T g s will present slight variations in their Q n unit distribution [START_REF] Brandriss | Effects of temperature on the structures of silicate liquids: 29Si NMR results[END_REF][START_REF] Mysen | Structure of silicate melts at high temperature: In-situ measurements in the system BaO-SiO 2[END_REF][START_REF] Mysen | Structure and properties of alkali silicate melts at magmatic temperatures[END_REF]. Using the thermodynamic theory of affinity, the model of associated solutions was proposed to solve such issues [START_REF] Shakhmatkin | The thermodynamic properties of oxide glasses and glass-forming liquids and their chemical structure[END_REF][START_REF] Vedishcheva | The thermodynamic modelling of glass properties: a practical proposition?[END_REF][100]. This model is based on the idea that melts are media in which chemical reactions, characterized by their standard Gibbs free energies, proceed in the direction of the equilibrium state. The latter is reached when the total Gibbs free energy of the system reaches a minimum. More recently, Gaddam et al. [101] proposed a new model based on statistical mechanics. This model assumes grand canonical ensemble of silicate units, i.e. the Q n are considered as a statistical ensemble in thermodynamic equilibrium with a reservoir from which they exchange energy and network modifiers. The first test performed with this model, which takes into account the composition and temperature in the calculation of the Q n unit fractions, are promising and may offer a new way to calculate the distribution of Q n units in silicate melts. In particular, this model allows calculating the proportions of Q n ijkl units, where the ijkl subscripts represent the n number of the adjacent tetrahedral units to the central Q unit. For instance, a Q 4 units bonded to 2 other Q 4 units and 2 Q 2 units will be described as Q 4 2244 . A Q 3 unit bonded to two other Q 3 unit and one Q 4 unit will be written Q 3 334 , the fourth subscript being omitted because of the NBO carried by the Q 3 unit. Such level of refinement has been reach by using 29 Si double quantum NMR spectroscopy, which allows discriminating the different Q n units bonded to the central Q n unit (Fig. 16). In addition to the statistical mechanic model of Gaddam et al. [101], the random connectivity model of Machacek et al. [103] also allows predicting the different fractions of Q n ijkl units in the glass network. It assumes that the tetrahedra are linked fully on a random base. The distribution of Q n ijkl units are calculated using a multinomial distribution. This model can be seen as an extension of the random bonding model presented previously. It thus faces the same limitations, particularly in regards of the effect of temperature as well as the random character of tetrahedral bonding.

Q n unit distribution: links with glass properties

In the introduction, we showed that the density of an alkali silicate glass increases upon addition of alkali oxide while its T g dramatically decreases. Such changes actually can be correlated with the changes in the glass structure. In order to calculate the density of silicate glass, Doweidar [START_REF] Doweidar | The density of alkali silicate glasses in relation to the microstructure[END_REF]104,105] assigned different partial molar volumes to the different Q n units. His calculations allow to calculate the density of silicate glass, but, maybe more importantly, give some insights about the volume properties of Q n units. Indeed, he reported that, while the volume of Q 4 units seem to be constant and equal to that in pure SiO 2 , the volumes of Q 3 , Q 2 and Q 1 units depend on the network modifier present in the glass network (Fig. 17).

First, for a given network modifier, the partial molar volume V m of the Q n units increases in the order (Q 0 ). This trend is explained by the fact that M-O distances are longer than Si-O distances (Table 3), such that Q n species surrounded by more network modifiers have higher partial V m . Turning to the linear correlation between the ionic radius of the network modifiers and the volume of the Q n units, such volume effect is explained by the difference in the M-O bond length as the ionic radius of the M cation increases. Indeed, results from experiments and molecular dynamic simulations show that the ionic radius and M-O bond length are positively correlated (Table 3). Doweidar [105,106] as a function of the ionic radius of metal network modifier cations (Li, Na, K, Rb, Cs, Ca, Sr, Ba, Cd) in silicate glasses. Ionic radius is reported for a constant CN of 6, using values from Shannon [107]. Variations in the true CN of the modifiers may explain some of the scattering in this relationship [e.g., 108-111].

V m (Q 4 ) < V m (Q 3 ) < V m (Q 2 ) < V m (Q 1 ) < V m
Table 3 show a comparison of Si-O and M-O distances obtained for alkali tetrasilicate glasses by experimental methods (X-ray and neutron diffraction experiments) and Car-Parrinello molecular dynamic simulations. We note that values from simulation and experiments are in good agreement. Both indicate that Si-NBO distances are shorter than Si-BO distances. Furthermore, in addition to being affected by the ionic radius of the M element, the M-O distance changes as a function of the O atom: M-NBO distances appear to be significantly shorter than M-BO distances.

In addition to affecting the glass density and partial molar volume, the large changes in the polymerization of the glass structure that accompanies the changes in the glass chemistry strongly affect the glass thermodynamic and rheological properties. However, those changes are different. For instance, the glass heat capacity is an additive function of the glass composition, such that it can be calculated using a set of partial molar volumes of the glass oxide components, as provided by Richet [112]. In general, the heat capacity of silicate glasses tends to the Dulong and Petit limit (=3R, with R the perfect gas constant) as T tends to T g , such that the glass heat capacity at T g can be calculated using this limit. for SiO 2 that was estimated by [START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF] using the complete thermodynamic cycle. Errors bars on the points are not reported for clarity; they vary between 0.5 to 2 J mol -1 . The red plain line (LL2017 in legend)

and its associated errors represented by dashed lines (95% confidence interval) represent the values calculated from the model of Le Losq and Neuville [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF]. Other data come from individual fits of the viscosity data by [117; R1984 in legend], [[118; T2001 in legend] and N2006: [[23; N2006 in legend].

While the glass heat capacity is an additive function of the glass composition, the glass configurational entropy at T g is not. It presents complex and non-linear variations as a function of the glass composition (Fig. 18). Values reported in Fig. 18 were calculated using viscosity data, through the Adam and Gibbs theory that relates the viscous flow of silicate melts to their thermodynamic properties (see chapter XXX).

Values calculated by different authors scatter significantly, showing the sensitivity of the calculation of the glass configurational entropy S conf using melt viscosity data to 1) the quality of the viscosity data and 2) the fitting protocols performed by the different authors. Le Losq and Neuville[[20] recently proposed a simple model to calculate S conf from the distribution of the Q n species in sodium and potassium silicate melts. This model deviates from an idea originally proposed by Mysen [119], which proposed that the configurational heat capacity of silicate melts 𝐶 3 4567 (equal to the difference between the melt C p at T and the C p glass at T g ) can be calculated from partial molar heat capacity values 𝐶 3 , ( 4)

with 𝑥 8 9 the fractions of the Q n units. Figure 19 shows that such model allows reproducing fairly well the 𝐶 3 4567 values derived from calorimetric measurements on alkali silicate glasses and melts.

Figure 19: Comparison of the 𝐶 3 4567 values calculated by Mysen [START_REF] Mysen | Structure and properties of magmatic liquids: From haplobasalt to haploandesite[END_REF] using the model resumed in eq. ( 2) at 1400°C and values derived from measurements. Reprinted from Mysen [START_REF] Mysen | Structure and properties of magmatic liquids: From haplobasalt to haploandesite[END_REF], Copyright (1999), with permission from Elsevier.

Following the idea of Mysen [119], Le Losq and Neuville [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF] assigned S conf partial molar values to the different Q 2 , Q 3 and Q 4 units in the melt, allowing one to calculate the topological contribution to the configurational entropy of the glass, i.e. the entropy arising from the disorder in the tetrahedral network in term of Si-O bond distances and Si-O-Si bond length. Indeed, the configurational entropy of glasses can be divided in topological S topo and chemical S mix contributions as:

𝑆 4567 = 𝑆 =535 + 𝑆 ?*@ . ( 5) with R the perfect gaz constant, and x Si and x O the atomic fractions of Si 4+ and O 2-. In eq. ( 6), different 𝑆 8 9 4567 values are used for potassium and sodium silicate melts as the coupling between the M alkali modifier and the Q n tetrahedral species varies with the ionic radius of M. The factor 2 in eq. ( 7) arises when working using an O 2 base to express the thermodynamic values (i.e. the structural formula is expressed using an O 2 base). This simple model allows one to calculate the configurational entropy of alkali silicate glasses with a good accuracy, falling in between the individual values reported by previous studies (Fig. 18). Adopting a thermodynamic and structural point of view, this model further provides pieces of information regarding the origin of the evolution of the silicate glass T g along the binary M 2 O-SiO 2 join (Fig. 20). Values from [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF].

S
Indeed, the model predicts that the apparition of Q 3 species upon addition of a few mol% alkali oxide in SiO 2 leads to a large, dramatic increase in the chemical contribution to the glass configurational entropy because Si can mix between the existing Q 4 and the newly formed Q 3 units. In other term, this illustrates

S topo KS S topo NS S mix NS Si S mix KS
Si that the introduction of NBO in the glass network allows new configurational environments for Si, and lowers the melt viscosity and glass T g . The model further predicts that the glass topological entropy varies nearly linearly (Fig. 20), being driven by the changes in the Q n unit distribution. This model remains to be further tested by new research, but together with the works of Mysen [[94,119] and Doweidar [START_REF] Doweidar | The density of alkali silicate glasses in relation to the microstructure[END_REF]104,105], it illustrates that the Q n unit distribution can be a useful tool for modelling the properties of silicate glasses.

Structure at medium range order and the Mixed Alkali Effect

While at short range order, the structure of silicate glasses can be described as a mixture of interconnected and Mg [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF]138,139]]. In Al-free silicate glasses, mixing alkali modifier cations seems to lead to larger deviations to linearity than mixing alkaline-earth modifier cations [139]. The MME also occurs in Albearing silicate glasses [140][141][142][143], but recent data suggest that it may be more complex that the MME in Al-free silicate glasses [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF], such that it will be treated separately in the case of Al-bearing glasses in sec.

Q n units
1.4.5. In all cases, the MME affects various glass properties, such as, for instance, the glass T g , Vickers hardness, compressibility, electrical resistivity or ionic conductivity (e.g., Fig. 21).

The source of the MME has been an extensive subject of study, and no real consensus about its origin has yet been reached because of the complexity of ionic diffusion in glasses. The MRN model of the glass structure was initially accounting for this effect by assuming that the diffusions of two different modifier cations were affected by the presence of each other in the channels [128]. Greaves and Ngai [121] further refined the MRN model to explain the MAE. They proposed that the alkali modifiers diffuse in the channels through a mechanism of cooperative intrachannel hopping. According to them, the increase in electrical resistivity observed upon mixing modifier cations (Fig. 21) reflects radical changes Reprinted figure with permission from G.N. Greaves and K.L. Ngai, Physical Review B. 52, 6358-6380, 1995, doi:10.1103/PhysRevB.52.6358. Copyright (1995) lead Lee [131] to suggest that most results from NMR spectroscopy point to Q m variations in silicate glasses between 0 and 1, and that values < 0, corresponding to clustering, are unlikely.

While 23 Na and 17 O NMR from Lee and co. [120,121,[130][131][132] or Angeli et al. [153] units (called Q 4-4 units by Sen and Youngman). They proposed that Q 3 and Q 4 units were actually mixing randomly, but this naturally yields to a clustering of Q 3 units in a Q 4 rich network. According to those authors, increasing the mol% K 2 O content about a particular threshold, equal to 7. The presence of silica-rich domain in silicate glasses as well as the dependence of the MRN on the modifier nature also is supported by Raman spectroscopy data on alkali silicate glasses. For instance, Matson et al. [155] observed that the alkali ionic radius was influencing the Raman signals in the 200-700 cm -1 portion of Raman spectra of alkali silicate glasses. In particular, they observed that the 200-500 cm -1 portion of the Raman spectra of Li silicate glasses was similar to that of the SiO 2 glass, as illustrated in figure 23.

Figure 23: Raman spectra of silica and alkali tetrasilicate glasses. The Boson peak at ~60-80 cm -1 can be assignment to collective transverse acoustic vibrational modes [START_REF] Shintani | Universal link between the boson peak and transverse phonons in glass[END_REF] promoted in silicate glasses by cooperative inter-tetrahedral librations [START_REF] Bucheneau | Low-frequency modes in vitreous silica[END_REF][START_REF] Chumakov | Equivalence of the Boson Peak in glasses to the transverse acoustic van Hove singularity in crystals[END_REF][START_REF] Courtens | The vibrational modes of glasses[END_REF]. In the Raman spectra of the SiO 2 glass, the peaks between 200 and 700 cm -1 , with in particular the R, D 1 and D 2 signals, are assigned to vibrations of rings of Q 4 tetrahedral units, see section 1.3.1 and figure 11 for details. In sodium and potassium silicate, new peaks at ~ 520 and ~595 cm -1 appear; they do not result from the shift of the pre-existing peaks in SiO 2 , but are assigned to Si-O-Si vibrations involving Q 3 and Q 2 units [START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF] (those signals are annotated n s Si- 3,4 [START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Virgo | Anionic Constitution of 1-Atmosphere Silicate Melts: Implications for the Structure of Igneous Melts[END_REF]155]. In particular, the peaks near 950 and 1100 cm -1 are assigned to Si-O symmetric stretching vibrations in Q 2 and Q 3 units, respectively.

O-Si Q 2,3,4 -Q 2,
Spectra are from [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF][START_REF] Heili | The dependence of Raman defect bands in silica glasses on densification revisited[END_REF]156]. 3,4 Indeed, signals in the 200-700 cm -1 portion of the Raman spectra of silicate glasses are assigned to breathing vibrations of the Si-O-Si bonds [START_REF] Bell | The vibrational spectra of vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Bell | Normal mode assignments in vitreous silica, germania and beryllium fluoride[END_REF][START_REF] Sharma | Raman investigation of ring configurations in vitreous silica[END_REF][START_REF] Galeener | Planar rings in glasses[END_REF][START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mcmillan | Vibrational spectroscopy of silicate liquids and glasses[END_REF][START_REF] Galeener | Band limits and the vibrational spectra of tetrahedral glasses[END_REF][START_REF] Sen | Phonons in AX₂ glasses: From molecular to band-like modes[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF]. The Raman spectra of LS4 presents a maximum near 460 cm -1 and a small sharp peak at 490 cm -1 . Those signals are very similar to those found in the SiO 2 Raman spectra, where they are assigned to breathing vibrations of rings with 4

Boson D 2 D 1 R ν s Si-O in Q 3 ν s Si-O in Q 2 ν Si-O-Si Q 2,3,4 -Q 2,
or more tetrahedral units (Fig. 11 and glasses. This supports the clustering of Li in the network of silicate glasses. To conclude, it should be noted that the precedent interpretation yields to an interesting fact. In alkali silicate glasses, increasing the IFS of network modifiers seems to lead the alkalis to cluster around Q n-1 units at the expense of Q n units, and, hence, affect the distribution of the Q n units in the glass (Fig. 14). As a result, the Q n distribution actually tends toward that predicted by a random mixing of NBO and BO amongst Q n units (Fig. 15), while one may have been tempted to draw the opposite conclusion. This arises from the fact that randomness is not correlated with homogeneity, but, on the contrary, rather may led to heterogeneity as proposed by Sen and Youngman [START_REF] Sen | NMR study of Q-speciation and connectivity in K 2 O-SiO 2 glasses with high silica content[END_REF].

Aluminum in silicate glasses

Addition of aluminum in silicate glasses is known to improve their mechanical properties, such as, for instance, their chemical durability or their hardness. Aluminum is thus vastly used in technical glasses in the industry to confer interesting properties to the final products. For instance, at the present era of smartphones and tablets, one well known example of an alumino-silicate glass is the Gorilla Ò Glass from the Corning Ò company. However, the interest in alumino-silicate glasses is not limited to the industrial domain. Indeed, alumino-silicate glasses are common products of geological processes, deriving from the rapid quench of magmatic liquids. For instance, they can be entrapped in crystals in deep magma chambers, and, once retrieved at the surface, they provide fundamental information about geological processes on Earth [e.g.,[161][162][163] or the Moon [164,165]. On a fundamental note, if we assume the presence of a magmatic ocean at the surface of the Earth after its formation 4.567 Ga ago [see 166 and references cited therein], it then must be said that the properties of the alumino-silicate melt composing the magma ocean drove the segregation of Earth iron core and the formation of Earth mantle and crust.

This illustrates the importance of aluminium in silicate melts, which, hence, deserves a particular attention.

Local environment of aluminum

As previously highlighted, numerous studies have documented the effect of the addition of aluminum in silicate composition on the glass properties. For instance, adding Al in a NaSi 3 O 7 glass produces a large, non-linear increase in its glass transition temperature (Fig. 24). Such variation points to the fact that Al 3+ enters in the structure of silicate glasses as a network former element, mostly in tetrahedral coordination [START_REF] Engelhardt | Structural studies of calcium aluminosilicate glasses by high resolution solid state 29 Si and 27 Al magic angle spinning nuclear magnetic resonance[END_REF][167][168][169][170]. ratio < 0.5 (M=Na + , K + , Mg 2+ , Ca 2+ , etc.), tectosilicate glasses a ratio of 0.5 ([Al 3+ ] = [M +,2+ ]), and peraluminous glasses present an Al/(Al+M) ratio > 0.5. Data from [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF].

Results from 27 Al NMR spectroscopy show that Al also can be present in 5-and 6-fold coordination, in low concentrations that depend on the glass composition [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]124,[171][172][173][174][175]. Indeed, the ratio between Al and the alkali/alkaline-earth metal cations M +,2+ in the glasses, Al/M, is of fundamental importance in determining the role of the metal cation as well as the coordination and environment of aluminum. When Al/M < 1, the composition is peralkaline (Fig. 24). In such case, one part of the M cations compensates the electrical charge deficits around AlO 4 -units, due to the fact that Al 3+ substitutes for Si 4+ in the tetrahedral units. The remaining part of M cations acts as network modifiers. When Al/M = 1, the glass has a tectosilicate composition. The amount of aluminum and metal cations is the same, such that all metal cations should compensate for the charge deficit of AlO 4 -units and the glass should be fully polymerized, i.e. ideally constituted of only Q 4 units. In reality, as ideality and glasses are antagonistic concepts, a few percent of NBO can be present in tectosilicate glasses [176-178] (sec. 1.4.4). When Al/M > 1, the composition is peraluminous: there is an excess of aluminum in the network compared to chargebalancing metal cations.

From 27 Al NMR data [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF][171][172][173][174], a small fraction of Al is present in 5 ( [5] Al or AlO 5 ) and 6 ( [6] Al or AlO 6 ) fold coordination in tectosilicate and peraluminous glasses; the higher the Al/M, the higher the fractions of [5] Al and possibly of [6] Al. At all silica contents, increasing the Al content up to reaching the peraluminous domain leads to a very important increase of the [5] Al fraction in the glasses. In peraluminous Ca-bearing glasses, Neuville et al.

[174] also reported a small fraction (< 3%) of [6] Al at very high Al/Ca ratios.

Figure 25: fraction of [5] Al (five-fold coordinated Al) represented as a function of the ratio CaO/(CaO+Al 2 O 3 ) in silicate glasses. Data acquired through 27 Al NMR spectroscopy at different silica concentration are represented by black hexagons (60 % SiO 2 ), purple circles (50%), blue squares (33%), inverted cyan triangles (30%) and green diamonds (10%). Data at 50, 33 and 10% are from Neuville et al. [174] and data at 30 and 60 % are from Thompson and Stebbins [178].

The fractions of [4] Al, [5] Al and [6] Al not only depends on the Al/M ratio, but also on the ionic field strength of the M cation [179][180][181][182]. Indeed, Ca alumino-silicate glasses already present a few percents of [5] Al in peralkaline glasses [174,183], while Na alumino-silicate glasses don't [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]. In general, alkaline-earth alumino-silicate glasses present higher fractions of [5] Al and [6] Al than alkali aluminosilicate melts. Differences are also observed between different alkaline-earth alumino-silicate glasses:

for instance, Sr, Ca and Mg tectosilicate glasses with 50 mol% SiO 2 present [5] Al fractions of 0.02, 0.07 and 0.12, respectively [see also results from 182, 184]. In Y and Lu tectosilicate glasses with the same SiO 2 content (50 mol%), [5] Al fractions reach ~ 21 and 26 %, respectively [185]. Figure 26 illustrates the correlation between the fraction of [5] Al and the ionic field strength of metal cations: increasing the IFS of the metal cations in alumino-silicate glasses seems to promote [5] Al at the expanse of [4] Al .

Figure 26: Fraction of [5] Al detected by 27 Al NMR spectroscopy in tectosilicate glasses with 50 mol% SiO 2 as a function of the ionic field strength of the non-network former cations in the glass (i.e., Sr, Ca, Mg, Na, Y and Lu). For ensuring consistency, and because the CN of metal cation in tectosilicate glasses is not perfectly known, the cation ionic field strength has been calculated at a constant CN of 6 for all cations. Therefore, scattering in this figure may result from variations in the CN of the different cations.

Ionic radii have are from Shannon [107]; data are from [174,[184][185][186] In addition to the effect of the glass chemical composition, the conditions of the glass formation also influence the fractions of [4] Al, [5] Al and [6] Al in the glass. Increasing the parental melt temperature and pressure leads to increase the coordination of Al in the retrieved glasses, particularly for tectosilicate and peraluminous compositions [179,187,175,[188][189][190][START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]. As a result, the glass quench rate and quench pressure affects the glass fractions of [4] Al, [5] Al and [6] Al. Glasses formed at high pressure (several GPa) will contain large amounts of [5] Al and [6] Al, with several percent to tens of percent increases in their proportions depending on the pressure in the 1-10 GPa range [[179, 180, 190, 191].

The effect of temperature on the fraction of highly coordinated Al polyhedral units in the glass is more complex. Indeed, different trends have been reported as a function of the glass composition. In pure alkali or alkaline-earth alumino-silicate glasses, increasing the quench rate and, hence, glass T f generally leads to a potential increase of a few percent the fraction of [5] Al, as supported by 27 Al NMR data from Stebbins et al. [192] and Thompson and Stebbins [193] on Ca alumino-silicate glasses. In agreement with that, Allwardt et al. [187] reported increasing [5] Al fraction in a Na 3 AlSi 7 O 17 glass (synthesized at 10 GPa)

with increasing the glass T f . However, they also reported a decreasing [5] Al fraction in a NaAlSi 3 O 8 glass

(also synthesized at 10 GPa) with increasing the glass T f . Such observation is intriguing since Le Losq et al. [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF] measured in situ higher fractions of [5] Al and [6] Al with increasing temperature in NaAlSi 3 O 8 and other Na alumino-silicate melts (peralkaline and peraluminous), using in situ laser-heated 27 Al NMR spectroscopy (Fig. 27). Therefore, an additional effect (potentially of pressure) may have affected the temperature effect in the observations of Allwardt et al. [187] on the NaAlSi 3 O 8 glass. In a Na-K aluminosilicate glass synthesized at a pressure of 3.5 GPa, Malfait et al. [190] also reported negligible changes in the Al speciation with changing the glass T f . Therefore, from this review, increasing T f in alkali and alkaline-earth alumino-silicate glasses tend to increase the fraction of highly coordinated Al species. This effect is small compared to that of pressure:

it is only of a few % for quench rate variations of several orders of magnitude [e.g., 193]. Furthermore, it also probably depends on the melt composition. The latter dependence is illustrated in Fig. 27, which

shows 27 Al NMR spectra acquired on Na alumino-silicate glasses at room temperature and acquired on their corresponding melts at high temperature [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]. While 27 Al NMR spectra from peralkaline glasses and melts (Na/(Na+Al) < 0.5) show a peak at a comparable chemical shift that can be assigned to [4] Al, the tectosilicate and peraluminous glasses and melts 27Al NMR spectra present significant differences: they are broader and, for the peraluminous composition, shifted to lower 27 Al chemical shifts. Those differences are assigned to the presence of [5] Al and even [6] Al in those tectosilicate and peraluminous composition. From observations shown in Fig. 27, effects of melt composition, discussed previously in the case of glasses, seem to be enhanced in the molten state. As a result, depending on the glass composition, changing the quench rate leads to different outcomes in term of the Al coordination number. Data from boro-alumino-silicate composition further corroborate this idea. Indeed, while both Morin et al. [182] and Wu and Stebbins [194] reported decreasing coordination of Al with increasing the T f of Na, Ba, Ca, La and Y aluminoborosilicate, Kiczenski et al. [195] 75 mol% SiO 2 [4] Al [5] Al [6] Al their observations by a coupling between B and Al species in the melt, and suggested that the reverse trend reported by Kiczenski et al. [195] may arise from an increase in association of F with Al at higher temperatures. Therefore, it appears that coupling of Al with other network former elements such as boron or with volatile elements may have an influence on the final coordination of Al in the glass, and its dependence on the glass T f .

Aluminum coordination and glass properties: examples

The changes in the aluminum coordination number are affecting various properties of the glass. In particular, increasing the aluminum coordination is an important component in the densification mechanism of alumino-silicate glasses [179]. Indeed, there is a clear trend between the change in the glass molar volume with pressure and the average Al coordination (Fig. 28). The scatter visible in Fig. 28 indicates that other mechanisms occur, such as changes in the mean inter-tetrahedral angle and compression of the sites of modifier and charge-compensator cations [179,180,191,196]]. The melt composition may be an important control in determining which mechanism prevails [180,191]. (KAS) glasses reported as a function of their relative molar volume, calculated as the ratio between their molar volume at high pressure [START_REF] Rasmussen | Origins of Glass: Myth and Known History[END_REF][START_REF] Rasmussen | How Glass Changed the World[END_REF][START_REF] Gandy | The Romance of Glass-making[END_REF](6)(7)[START_REF] Kurkjian | Perspectives on the history of glass composition[END_REF][START_REF] Brill | L'épave Ouest-Embiez 1, Var : le commerce maritime du verre brut et manufacturé en Méditerranée occidentale dans l'Antiquité[END_REF](10) and that at room pressure. Reproduced from [START_REF] Allwardt | Aluminum coordination and the densification of high-pressure aluminosilicate glasses[END_REF] Aluminum coordination and the densification of high-pressure aluminosilicate glasses. American Mineralogist 90:1218-1222. doi: 10.2138/am.2005.1836, Copyright (2005), with permission from the Mineralogical Society of America.

In addition to the role of highly-coordinated Al species in densified glasses, their presence affect the mechanical properties of the glasses. By combining molecular dynamic simulations and MAS NMR spectroscopy, Iftekhar et al. [185] showed that, in Re 2 O 3 -Al 2 O 3 -SiO 2 (Re = Y, Lu) glasses, there is a direct correlation (R=0.9) between the Vickers hardness and the mean coordination number of Al (Fig. 29). Iftekhar et al. [185] interpreted such relationship as showing that [5] Al and [6] Al form strong [5] Al-O-T and [6] Al-O-T bonds in the network, enhancing its connectivity, and, hence, its structural strengths. The increase in connectivity following the apparition of [5] Al and [6] Al in the glass structure is further corroborated by the increase in the T g of glasses with increasing the fraction of aluminium in peraluminous glasses (Fig. 24; [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]). The variation of the viscosity of Na peraluminous silicate melts further support such idea. Indeed, close to T g , the viscosity of Na alumino-silicate melts increases with increasing the Al/(Al+Na + ) ratio in the peraluminous domain at iso-temperature [ [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]169], while at high temperature it decreases [168,197]. This effect occurs because of the decoupling between the aluminosilicate and metal cation sub-lattices relaxation at T g [198]: Na + cations diffuse rapidly in a frozen-in polyhedral alumino-silicate network at, or close to, T g . In such conditions, [5] Al and [6] Al participate in ordering the network in glasses, as shown by the large decrease in the glasses configurational entropy at T g with increasing Al/(Al+Na) from 0.5 to 0.7 in Na alumino-silicate compositions (Fig. 24). At high temperature, relaxation of all cations tends toward the same values. In such conditions, the presence of [5] Al and [6] Al in the melts seems to favor the diffusion of oxygen and, hence, to enhance viscous flow [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]199].

Aluminum, glass polymerization, and the Al avoidance rule

Sections 1.4.1 and 1.4.2 illustrated that aluminum enters preferentially in CN 4 in glasses, the proportion of CN 5 and 6 being small and dependent on the glass pressure synthesis and composition, and, in a minor extent, T f . The overall effect of adding aluminium in silicate glasses thus results in increasing their polymerization, as Al enters as a network former into the glass ionic framework. In particular, Al enters in Q 4 units in the glasses with a tendency to avoid formation of Al-O-Al bonds (the so-called Alavoidance rule or Lowenstein rule [200]) that depends on the melt chemical composition [131,201,202].

According to Mysen et al. [203], Al in Q 4 units represent at least 70% of the total aluminum in the perakaline domain in Na alumino-silicate glasses. A resulting effect of aluminum preference to reside in Q 4 units in glasses is to shift the equilibrium 2 Q 3 ó Q 2 + Q 4 to the right end side at constant NBO/T values with increasing the ratio Al/(Al+M n+ 2/n ) in peralkaline glasses [203]. The least depolymerized units in the glasses present the lowest Al/Si ratio, i.e. Al avoids entering in depolymerized units.

The "preference" of Al for polymerized environments probably results from the minimization of the energy deficit of Al polyhedral units: carrying NBO will lead to a very strong electrical charge deficit for AlO z units (z = 4, 5, 6). The Al-avoidance effect further results of such concept: Al-O-Al bonds are avoided as they are energetically not favorable. However, Al-avoidance is not perfectly respected in alumino-silicate glasses, as shown by results from 29 Si Magic Angle Spinning (MAS) and 17 O triple quantum MAS (3QMAS) spectroscopy on Ca, Li and Na alumino-silicate glasses [[132, 201, 202, 204] as well as by results from MD simulations [e.g., 205, 206]. For instance, results for 29 Si NMR spectroscopy show that the degree of Al avoidance in Na alumino-silicate melts is higher than that in Ca alumino-silicate glasses [201]. A useful parameter for quantifying such degree of Al avoidance is the Q It thus seems that the IFS of metal cations influences linearly the degree of Al avoidance in aluminosilicate glasses. However, Lee [207] warrant that increasing the cation IFS at values higher than that of Mg 2+ may lead to deviation from the linear trend observed in Fig. 30, because of the formation of highlycoordinated [5] Al and [6] Al species and possibly of Al-NBO bonds in such systems.

parameter: Q = 1
The degree of Al avoidance can further be related to the thermodynamic properties of the glass, and, in particular, to their configurational entropy. Indeed, the Si-Al ordering implies a non-random process for the integration of Al in Q 4 units. The analysis of the Raman spectra of tectosilicate glasses reveal the presence of two bands at ~ 1140-1170 and 1180-1210 cm -1 (Fig. 31), which are assigned to Si-O stretching in Q 4 units [START_REF] Seifert | Three-dimensional network structure of quenched melts (glass) in the systems SiO 2 -NaAlO 2 , SiO 2 -CaAl 2 O 4 and SiO 2 -MgAl 2 O 4[END_REF][START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF]208]. [25, 57 and references therein]. In B), the ratio of the area of the Q 4,I Raman peak other the sum of the areas of the Q 4,I and Q 4,II Raman peaks (purple squares) is represented as a function of the mol% NaAlO 2 added in SiO 2 . It presents variations very similar to those of the glass configurational entropy at T g , S conf (T g ) (Red diamonds [START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF] and hexagons [209]).

Similar to the observations made in the SiO 2 glass (Sec. 1.2.1), the splitting of the Si-O stretching signal in Q 4 units in two bands indicate a slight asymmetry of the distribution of T-O-T angles in tectosilicate glasses, in agreement with results from molecular dynamic simulations on alumino-silicate glasses and melts [205,206,210]. Neuville and Mysen [208] noticed a similarity between the variations of the entropy of configuration at T g , S conf (T g ), of the glasses between the NaAlSiO 4 and the SiO 2 composition (Fig. 31b), with the formation of a convex curvature. Such curvature in the variations of the glass S conf (T g ) is similar to the one that can be generated by mixing two cations in similar environments. The data of Neuville and Mysen [208] actually provide further information about the mechanism of Si substitution by Al in the glasses network. Indeed, the increase of the area ratio between the two peaks assigned to Si-O stretching in Q 4 units, Q 4,II /(Q 4,II +Q 4,I ), with increasing NaAlO 2 in SiO 2 below 25 mol% suggest that Al enters primarily in an environment associated with the Q 4,II signal. As the Raman shift of the Q 4,II peak is lower than that of the Q 4,I peak (Fig. 31), we expect the T-O-T bond angle of the environment associated with this signal to be lower than that of the environment associated with the Q 4,I peak[53, 54].

Therefore, Al tends to enter in Q 4 units with "small" T-O-T angles in a first time, up to an Al/Si ratio of 0.5, after which Al substitutes for Si in the second environment. This comportment may relate to the length of Al-O bonds, which are longer than Si-O bonds (Table 4). As there is an inverse correlation between T-O bond distances and T-O-T bond angles [211], this will explain the affinity of Al for the Q Other pieces of explanation may account for the variations of S conf (T g ) along the binary join, as proposed by Toplis et al. [209] or Lee and Stebbins [201]. The former indicated that the variations of the glass S conf (T g ) along the SiO 2 -NaAlO 2 join originate from variations of the topology of the glass network as well as from chemical contributions from cation mixing, the former being dominant and approximately equal to ~ 5.1 J mol-1 K -1 while the later accounts for the concave shape of the entropy variations. Lee Therefore, such model accounts for the observations made in Fig. 31.

NBO, tectosilicate glasses and triclusters

The study of tectosilicate glasses has been of particular interest in the literature as it brings information on the comportment of metal cations that act as charge compensators of the various Al polyhedral units.

While tectosilicate glasses are ideally fully polymerized, there is actually a non-negligible number of NBO oxygens in their structure, subsequently called non-stoichiometric NBO. Stebbins and Xu [176] were among the first to report a direct experimental evidence of this, as they estimated using 17 value is an estimation to consider with caution, because of the high fictive temperature of simulated glasses that may affect the modelled structure [222]. In addition to a potential effect of the metal cation ionic field strength, the existing data on the Ca tectosilicate glasses suggest that the non-stoichiometric NBO content also may vary with the Si/(Si+Al) ratio of the glass [178]. Indeed, it is comprised between 5 and 8 % for 0 < Si/(Si+Al) < 0.5, and then decreases down to the percent level at Si/(Si+Al) > 0.5 (Table 5). [START_REF] Thompson | Non-stoichiometric non-bridging oxygens and fivecoordinated aluminum in alkaline earth aluminosilicate glasses: Effect of modifier cation size[END_REF] Non-stoichiometric non-bridging oxygens and five-coordinated aluminum in alkaline earth aluminosilicate glasses: Effect of modifier cation size. Journal of Non-Crystalline Solids 358:1783-1789. doi: 10.1016/j.jnoncrysol.2012.05.022. Copyright (2012), with permission from Elsevier.

In addition of [5] Al and non-stoichiometric NBO, the study of tectosilicate glasses and melts further brought to light the possibility of the existence of tri-coordinated oxygen atoms in such compositions. Lacy [223] originally proposed the idea of the presence of triclusters in alumino-silicate melts. This idea was pursued by Toplis et al. [197], to explain why, at fixed SiO 2 concentration, the isothermal viscosity of Na alumino-silicate melts with varying Al/Na ratios form a maximum centered in the peraluminous domain at liquidus temperatures, and not, as expected, on the tectosilicate join. Following Lacy's idea, Toplis et al. [197] proposed that such oxygen triclusters was linking either 2 SiO 4 tetrahedra to one AlO 4 tetrahedron, or two AlO 4 tetrahedra with one SiO 4 tetrahedron. Such linkage will allow the presence of non-stoichiometric NBO in tectosilicate and peraluminous glasses following the reactions [197]: [START_REF] Kurkjian | Perspectives on the history of glass composition[END_REF] or [START_REF] Brill | L'épave Ouest-Embiez 1, Var : le commerce maritime du verre brut et manufacturé en Méditerranée occidentale dans l'Antiquité[END_REF] with M n+ 1/n Al 2 SiO 5.5 and AlSi 2 O 5.5 the triclusters. However, as highlighted in the previous paragraph, the presence of non-stoichiometric NBOs occur simultaneously with the presence of excess [5] Al in the structure of the melts. Stebbins et al. [192] highlighted that the formation of [5] Al and NBO could be related through some mechanism implying both species. Indeed, the fall of the non-stoichiometric NBO content in the peraluminous region seem to relate to the rise of the [5] Al content in the glasses (see figures 32 and 25, sec. 1.4.1). Stebbins et al. [192] further noted than increasing the glass fictive temperature was leading to increase both the NBO and [5] Al contents, an observation confirmed by the recent 17 O data on Ca tectosilicate glasses of Thompson and Stebbins [193]. The latter reported increases of up to 1.7% of the NBO fractions in Ca tectosilicate glasses with increasing their T f of ~ 100-140°. However, they found that such increases depend on the glass composition in a complex way. In general, the links between the formation of non-stoichiometric NBO and [5] Al in glasses are not fully clear, leading Thompson and Stebbins [[178] to propose that several mechanisms probably are playing at the same time.

2 M n+ 1/n AlO 2 + SiO 2 ó M n+ 1/n Al 2 SiO 5.5 + M n+ 1/n O 0.5 ,
M n+ 1/n AlO 2 + 2SiO 2 ó AlSi 2 O 5.5 + M n+ 1/n O 0.5 ,
The presence of oxygen triclusters in glasses thus cannot be excluded. However, while molecular dynamic simulations also suggest their presence in the network of alumino-silicate glasses [e.g., 205, 206], the only direct experimental observation of such oxygen triclusters have been made on a Ca aluminate glass by Iuga et al. [219] using heteronuclear high-resolution NMR spectroscopy. We finally should note that, while oxygen triclusters have been proposed as linking three Al-and Si-bearing tetrahedral units, it also is possible that [5] Al and potentially [6] Al polyhedra carry three-coordinated oxygen anions, [3] O, at some of their summit. Indeed, Le Losq et al. [START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF] noticed that [3] O are present at the summits of [5] Al and [6] Al species in Sillimanite or in other minerals like Low or High Albite for instance [see 224 for instance]], while [4] Al and [4] Si species are linked by two-fold coordinated oxygen anions ( [2] O) in such minerals. As a result, those authors proposed that [3] O may be present in the structure of tectosilicate and peraluminous glasses, but they connect highly coordinated Al species to other tetrahedral units rather than only tetrahedral units. This explanation will allow understanding why, for instance, both the viscosity of the NaAlSi 3 O 8 melt and its NBO content decreases with increasing pressure [225,226]. Indeed, such paradox can be explained assuming that the formation of [5] Al apportion the existing NBOs, but also favor the diffusivity of O species in the melt such that it lowers its viscosity.

However, this proposition does not explain the positive correlation between the T f of Ca tectosilicate glasses and their non-stoichiometric NBO and [5] Al contents, reported by Stebbins et al. [192] and Thompson and Stebbins [193]. Indeed, assuming [5] Al apportion NBOs in the glass network, a decreasing fraction of non-stoichiometric NBO might be expected upon increasing the glass T f and [5] Al fraction.

Such contradiction illustrates that the links between glass composition, structure, [5] Al, nonstoichiometric NBO and possibly [3] O (either as triclusters or bonded to [5] Al) are not yet understood, and that several mechanisms that depend on melt composition and temperature probably occur simultaneously.

Medium range order structure in alumino-silicate glasses and the Mixed Alkali Effect

From the above description of the environment of aluminum at short-range order in alumino-silicate glasses, the structure at medium-range order of such glasses is complex as it needs to accommodate a few particularities. In particular, models for describing the structure at medium range order of aluminosilicate glasses need to account for the intimate relationship between AlO 4 units (and possibly AlO 5 and AlO 6 units) and the charge-compensator metal cations. Furthermore, the models should account for the fact that the distribution of Al and Si in Q n units presents a certain degree of randomness, depending on the metal cation ionic radius. As aluminum presence shift the equilibrium (6) to the right [203], its presence in silicate melts potentially promotes regions rich in inter-connected Q 4 units and regions rich in Q 2 units surrounded by network modifier cations. Therefore, it is tempting to extend the MRN model of Greaves [126,127] to the case of charge-compensating cations in alumino-silicate glasses.

Following this line of thinking, Greaves and Ngai [129] proposed the Charge-Compensated Random Network (CCRN) model. Applied to tectosilicate glasses, it depicts their structure as composed of segregated regions rich in compensating metallic and aluminum ions. Indeed, the specific coordination of charge-compensator cations may lead to a distribution of those elements that is not random in the alumino-silicate network. Such idea may explain the weak and particular mixed alkali effects (MAE) observed in alkali tectosilicate glasses (Fig. 33). Indeed, the mixture of the NaAlSi 3 O 8 andKAlSi 3 O 8 glasses leads to deviations from linearity in the glasses T g that are not explained by a random mixing of Na and K in the alumino-silicate network [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF]. T g variations suggest that Na and K have specific and different environments in alumino-silicate glasses. In particular, they probably present different coordination numbers, as observed in different alumino-silicate glasses and minerals: values between 6 and 8 have been reported for Na [109][110][111], whereas values between 9 and 12 have been reported for K + [214,224,227]. Translating such CN values in ionic radius, ionic radius values range between 102 and 118 pm for Na + and 155 and 164 pm for K + , using the Shannon [107] ionic radius dataset.

We should note that the ionic radius of K + even exceed that of O 2-, of ~135 pm [107]. Indeed, O 2-actually is one of the largest ion in usual silicate glasses, as the ionic radius of the common Ca 2+ , Mg 2+ , Na + or Li + cations are much smaller than that of O 2-. Le Losq and Neuville [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF] suggested that such large K + ionic radius and CN in alumino-silicate compositions may promote the segregation of K + ions in ionic percolation channels, with "walls" rich in AlO 4 units. Such hypothesis may explain the variations of the T g and configuration entropy of Na-K tectosilicate glasses reported in Fig. 33 because it implies a nonrandom mixing of Na and K in the glass structure. In addition, it implies that, compared to Na + , less configurations are available to accommodate K + in the aluminosilicate network, explaining the higher T g and lower configurational entropy of the potassic tectosilicate glasses. [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF]228], with using the framework of the Adam and Gibbs equation linking viscosity, heat capacity and entropy (see chapter XXX and [117]). A common high temperature viscosity limit was used during the fit. Dotted lines are guides for the eyes. The plain line illustrates the entropy variations expected between the end-member in the case of an ideal mixing of the Na and K cations in the alumino-silicate framework [see [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF]117,140]. This hypothesis of different local environments and segregation of the charge-compensator Na + and K + cations in aluminosilicate glasses is corroborated by results from Raman spectroscopy of the Na-K tectosilicate glasses. Indeed, Le Losq and Neuville [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF] reported that, upon substituting Na by K in NaAlSi 3 O 8 -KAlSi 3 O 8 glasses, the peak assigned to T-O stretching around ~ 1100 cm -1 was shifting to a higher frequency. In addition, the intensities of two peaks at ~570 cm -1 and ~590 cm -1 , assigned to breathing vibrations in three-membered rings containing different amounts of Al [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF]229], change with the glasses K/(K+Na) ratio. In particular, the intensity of the 590 cm -1 peak increases with substitution of Na by K, pointing to an increase of the fraction of three-membered rings containing only Si atoms.

Following this observation, Le Losq and Neuville [START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF] suggested that, while K cations enter in the glass network, they distort the tetrahedral cages that accommodate them, leading to a general increase of the mean T-O-T angle. Si atoms segregates in denser regions, represented by the Si-bearing three-membered rings. Overall, the variations suggest a segregation of the glass network in Si-rich and Al-K rich regions in tectosilicate glasses. This hypothesis implies that the mixing of the charge compensator Na + and K + is not ideal, as they occupy different structural positions, such that the variations of the glass T g and configurational entropy at T g upon Na-K mixing reported in Fig. 33 are closer to linear trends obtained by a mechanical mixing of two Na-Al-Si-O and K-Al-Si-O sub-lattices than to non-linear trends resulting from an ideal Na-K mixing in a single Si-Al-O sub-lattice.

From the above discussion, the CCRN model could explain the mixing of Na and K as chargecompensator in alkali silicate melts, with a non-ideal mixing of the two alkali cations in different structural environment. However, the absence of an "ideal" MAE in tectosilicate glasses is not general. Indeed, Hummer and Arndt [140] indicated that the variations of viscosity and T g in mixed Ca 2 Al 2 Si 3 O 8 -NaAlSi 3 O 8 melts can be modelled using an ideal mixing entropic model, implying a random mixing of Na and Ca in the melt structure. In peralkaline melts, a MAE also is observed when mixing Ca and Mg for instance. Indeed, the configurational entropy at T g of mixed Ca 3 Al 2 Si 3 O 12 -Mg 3 Al 2 Si 3 O 12 tectosilicate glasses follow variations that can be modelled with assuming an excess of entropy generated by a random mixing of pairs of Ca and Mg cations in the glasses [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF]]. Similarly, a MAE affects the T g , the Vickers microhardness as well as the configurational heat capacity C p conf (T g ) values (C p conf (T g ) = C p liquid (T g ) -C p glass (T g )) of Na-Ca-Mg peralkaline glasses containing 60 mol% SiO 2 and 16 mol% Al 2 O 3 has recently been reported [142]. Those data show the occurrence of a continuous MAE, as observed when mixing Ca and Mg or Na and K in silicate glasses (Fig. 34). It is interesting to note that the MAE affects properties that depends on the diffusivity of the metal cations, but not properties that relate on the structure of the alumino-silicate network in itself, such as, for instance, elastic properties or glass density (Fig. 34). For instance, Figure 34 shows that, while the Young modulus of Ca-Mg-Na aluminsoilicate glasses vary linearly upon Ca-Mg mixing, a MAE affects the Vickers hardness. Kjeldsen et al. [142] indicate that, as the Vickers hardness actually is related to the plastic flow of the glass, the occurrence of the MAE is not surprising. On the other hand, glass density and Young modulus, not affected by MAE, are related to the structural arrangements in the glass. This can be explained by the fact that structural characteristics of the glass network tend to vary linearly upon mixing metal cations between endmember compositions. For instance, data in Al-free silicate melts point to negligible or linear variations of the Q n unit distribution upon mixing metal cations in the glasses.

Indeed, Hater et al. [230] did not observe systematic change of the Q n unit distribution upon Rb-Na mixing in alkali trisilicate glasses using 29 Si and 23 Na Magic Angle Spinning (MAS) NMR spectroscopy. 23 Na, 7 Li, and 29 Si NMR data from (Na,Li) 2 Si 2 O 5 glasses also suggest an intimate, uniform mixing of the [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF] further indicate that the Q n distribution of mixed Na-K silicate glasses vary almost linearly upon Na-K mixing; when combined with the data from [152], it appears that slight deviation to linearity appear at high alkali concentration but do no excess a few percent [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF]]. Therefore, almost linear variations of the glass Q n unit distribution are suggest by NMR and Raman spectroscopy results. This may explain why, for instance, the glass density tends to vary linearly upon metal mixing in silicate and alumino-silicate melts (Fig. 34, see also [137] for instance). Indeed, as presented in section 1.3.1, it is possible to relate the volume of Q n units to the density of the glasses, such that nearly linear variations of the Q n unit fractions upon mixing metal cations in silicate and alumino-silicate glasses should result in linear variations of the glass density, as observed (Fig. 34).

The contrast between the variations of T g upon mixing Na and K in tectosilicate glasses (Fig. 33) and Ca and Mg in Na-Ca-Mg peralkaline glasses (Fig. 34) directly points to the complexity of the MAE. Charge compensators with very dissimilar ionic radius, like Na and K (Table 6), appear to mix non-randomly in the glass structure, while cations with similar ionic radius, like Ca and Mg, appear to mix more randomly.

However, even the apparent ideal mixing reported in Ca-Mg alumino-silicate melts, observed from a thermodynamic point of view [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF], may not necessarily be perfect. Indeed, recent data from 17 glasses, calculated from the viscosity of the melts [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF], are actually slightly lower than the values modelled using an ideal, random mixing of Ca and Mg in the melts structure. As a result, Kelsey et al.

[234] indicate that some ordering might take place. In addition, they discuss the fact that the simple random mixing model of the S conf (T g ) of Ca 3 Al 2 Si 3 O 12 -Mg 3 Al 2 Si 3 O 12 may be too simple, as it considers the mixing of the glasses as a binary system. Further complexity actually may arise from a change of the Al avoidance or an increasing fraction of [5] Al in the glasses when substituting Ca by Mg. Therefore, while the data from [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF] show that considering Ca and Mg as randomly mixing in the structure of alumino-silicate glasses yields a good approximation for modelling the properties of the Ca-Mg alumino-silicate melts and glasses, NMR data invite to refine such approach. In particular, future models may have to account for the influence of the metal IFS on preferences for NBO/BO bonding and for Al charge compensation, as well as on [5] Al generation and on the Al avoidance extent. Furthermore, another level of complexity appears when considering that, in the structure of peralkaline glasses, network modifiers (NM) and charge compensators (CC) mix between themselves (NM-NM or CC-CC mixing)

and potentially between each-other (NM-CC mixing). According to Greaves and Ngai [129], the structure of such peralkaline compositions should be described as a mix of the CCRN and MRN model. Charge compensator and network modifier metal cations thus will be represented as residing in different type of channels. While the local environment of charge compensator cations will be rich in Al 3+ ions, that of the network modifier cations will be rich in NBOs. Other representations of the structure of aluminosilicate melts and the repartition of metal cations in it come from the perturbed distribution model, which depicts the network modifiers and charge compensators as randomly distributed nor segregating in clusters in the network, as suggested by 17 O NMR data that show that Na + interacts with BO from Si-O-Si, Si-O-Al and Al-O-Al bonds in Na tectosilicate glasses [130]. To this date, the exact representation of the structure of alumino-silicate glasses and of the repartition of metal cations in them remains an open topic of research.

Elastic properties and density of alumino-silicate glasses

The macroscopic elastic moduli of structural glasses are generally controlled by the glass atomic density and the mean inter-atomic forces. Different metal cations will affect differently the latter properties, such that the nature of metal cations in glasses directly correlate with the glass Shear, Bulk and Young's moduli (Fig. 35).

Therefore, elastic properties of glasses are closely related to the cations present in the glass. On the other hand, the glass Poisson ratio n is differently affected by the glass chemical composition. Weigel et al.

[235]] showed that the Poisson ratios of M n+ 1/n AlSiO 4 glasses (m=Li, Na, K, Ca, Mg, Sr, Ba, Zn) showed no correlation with the glass molar volume, but were divided in 2 global mean values, depending on the charge of the metal cation present in the glass. Indeed, while the Poisson ratio of alkali-bearing glasses was ~0.234, that of alkaline-earth bearing glasses was ~0.265. Such difference arises from the different structure of alkali and alkaline-earth tectosilicate glasses, as shown by the strong difference of their Raman spectra [e.g., 30]. Such differences in glass structure implies a difference in the atomic packing density C g of the glasses, which, in turn, affects the glass Poisson ratio [236 and references therein]. In this regard, the lower Poisson ratio of alkali M n+ 1/n AlSiO 4 glasses compared to alkaline-earth M n+ 1/n AlSiO 4 glasses reported by Weigel et al. [235] highlight a difference in the 3D arrangement of the glass structure. As a result, 3D arrangements at medium-range order in alumino-silicate glasses seem influenced by the electric charge of the charge compensator metal cations. Non-Crystalline Solids 447:267-272. doi: 10.1016/j.jnoncrysol.2016.06.023. Copyright (2016), with permission from Elsevier.

Multivalent elements in silicate glasses

All natural glasses and most of manmade glasses contain several multivalent elements, such as, for instance, Fe, Cr, V, Cr, and Eu, in different concentrations. Many properties of silicate glasses and melts depend on the nature, the concentration and the oxidation state of such multivalent elements. For instance, the redox states and the coordination of multivalent elements present in glasses determine their color and optical properties [e.g., 237; see chapter XX for further details]. Several authors recently reported the influence of the bulk composition on the photoluminescence tunability of rare-earth elements [238][239][240],

showing that by adjusting the optical basicity of the host glassm it is possible to control both Eu redox and the glass optical properties. Another example is the viscosity of iron-bearing silicate melts, which is controlled by the oxidation state of Fe at given temperature [e.g., 241-243]. In addition to such effects, the oxidation state of multivalent elements further represents a probe for studying the conditions of glass formation in geologic systems. Indeed, the redox state of multivalent elements reflects the temperature and oxygen fugacity of magmatic sources [244], such that it can be used to retrieve the temperature of ancient geologic systems [e.g., 162]. Multivalent element oxidation state further affects the partitioning of elements and mass transfers processes within the Earth [245,241,246,242,243]. As a result, understanding the behavior of such multivalent elements in silicate melts is particularly important in Materials and Earth sciences.

Reduction-Oxidation (redox) reactions involve the transfer of electrons between chemical species forming the redox couple of a given element, as for instance Fe 2+ and Fe 3+ . In silicate melts, oxygen is generally the electron carrier, such that the redox state (ratio of the different species) of a given element is driven by changes in the oxygen chemical potential. In Earth and Material sciences, oxygen fugacity (f O2 ) is conventionally used to describe the oxygen chemical potential. Redox equilibria in glass-forming melts have been exhaustively discussed by the early studies of . In brief, the redox equilibrium of a multivalent element can be described as

4𝑀 ?UV= ?W + 2𝑛𝑂 ?UV= &'
↔ 4𝑀 ?UV= (?'6)W + 𝑛𝑂 & , [10] with n representing the number of electron transferred. This relationship is controlled by several factors, such as temperature, oxygen fugacity, and bulk chemical composition.

1 .5.1 Temperature,Oxygen Fugacity,and Pressure effects Increasing temperature shifts the RedOx equilibrium (10) toward reduced species, as it favors the endothermic reaction according to the Van't Hoff law [250]. The log of the redox equilibria M (m-n) /M m+ vary linearly with reciprocal temperature [e.g., 254-257], with a slope that is equal to the enthalpy of reduction, Δ𝐻, via an approximation of the Van't Hoff relation [250,254]:

log [+ `a9 ] [+ c. ] = - de &.g;gh$ + 𝑏 . ( 11
)
Δ𝐻 is always endothermique, leading to the reduction of the glass-forming silicate melt as temperature increases [250].

The effect of oxygen fugacity is opposite to that of T: increasing f O2 favours the stabilisation of the most oxidized specie. This can be expressed for multivalent elements dilute in silicate melts by manipulating equation ( 10) to obtain:

-log 𝑓 # k = ( 6 log ( + `a9 + `. ) + 𝑘 , [START_REF] Rasmussen | Reinventing an Old Material: Venice and the New Glass[END_REF] with n the number of exchanged electrons. For a given composition, and at constant temperature, the relationship described by eq. ( 12) should yield a straight line with slope equal to 4/n. This has been experimentally corroborated for many redox couples [e.g., 244, 250, 258, 259]. Tacking the redox couple Fe 2+ /Fe 3+ as an example (fundamental for both Earth and Material science problems), studies showed that the slope of the log 𝑓 # k vs log ( mU k.

mU n. ) relationship was close to the ideal value of 4 (or 0.25 if using the log ( mU n. mU k. ) 𝑣𝑠 log 𝑓 # k relationship) [244,259,250]. However, the melt composition influences slightly this value, such that it may not be ideal in all cases. For example, Mysen et al. [259] reported a slight decrease of the slope according to the ionic potential of the alkaline-earth cation in alkaline-earth silicate glasses. This trend is corroborated by the recent result of Cicconi et al. [260], who observed that the mean ionic field strength of the alkali metal cations influence the slope of the log 𝑓 # k vs log ( mU k. mU n. ) relationship in multicomponent glasses.

While the effects of oxygen fugacity and temperature on the redox state of multivalent elements are reasonably understood and characterized, that of pressure has been the subject of only few studies and remains very elusively known. In general, existing studies indicate that higher pressures promote reduced species in many compounds. For reduction of Fe 3+ , Cu 2+ and Mn 3+ occurs at high pressure in solid compounds [261][262][263]. Experimental data confirmed that such behavior occurs for Fe in silicate melts [264,265], as the volume change accompanying the reduction of Fe 3+ in Fe 2+ favors the reduction reaction [e.g., see 257]. Such changes are small: the Fe 3+ /Fe TOT ratio only changes of a few % per GPa, at most, when P varies between 0 to 7 GPa [264,265]. At higher pressure, changes in Fe CN can be expected and may affect the pressure effect because of the influence of Fe CN on the volume change associate with the Fe 3+ -Fe 2+ redox reaction. While data on the effect of pressure on the Fe redox state are scarce, those existing for other systems are even less abundant (if simply non-existent). The data of Burnham and Berry [266] indicate that the Ce redox state may not be influenced by pressure, but those authors indicated that pressure may also favor stabilization of Ce 4+ . Data for other elements in silicate melts are virtually inexistent.

Compositional effects

The chemical composition of the initial melt heavily influences the redox equilibrium, as shown by existing experimental studies devoted to Fe [267][268][269], and to a lesser extent to Ti [247], Cr [247,270], Mo [271], V [272], Sn [273], Ce and Eu [247,266,274,275]. The optical basicity [276][277][278][279][280] of the glass generally correlates well with the redox state of multivalent elements in the melt equilibrated at given T- conditions [e.g., 252, 266]. The general glass optical basicity can be calculated from the different basicity of metal cation and network former oxides [e.g., 280]. Increasing the melt basicity results in a shift of the redox equilibrium (eq. 10) toward the reduced species (Fig. 36). In silicate glasses, metal cation present higher optical basicity than network former cations, such that increasing the fraction of metal cations promotes reduction of multivalent species. This relationship induces a general correlation of the redox equilibrium with the glass polymerization, i.e. the equilibrium constant of eq. 10 is correlated with the glass NBO/T. The common network former cations present close optical basicity in silicate glasses [e.g.,Al2O3 = 0.59,SiO2 = 0.48,TiO2 = 0.58,279]]. As a result, their influences on the Fe redox state are analogous, either in simplified quaternary system CaO-MgO-Al 2 O 3 -SiO 2 [269] as well as in natural melts [281,282]. As metal cation can present large differences in optical basicity [e.g., from 0.39 for H2O to 1.40 for K2O, 279], they influence differently the equilibrium constant of eq. 10. A consequence of this is that the glass NBO/T may not be the best parameter to truly capture the control of the melt chemical composition on the redox behavior of multivalent elements because it does not distinguish between different metal cations.

f O2
Figure 36: logarithm of the equilibrium constant of eq. ( 12) at 1673 for Eu and Ce in alumino-silicate melts as a function of the optical basicity or of the NBO/T. Note the outlier in the Eu plots: this data was acquired on a glass, contrary to other points that were acquired on melts. As a result, Eu oxidation state in the glass does not represent that in the melt. Burnham and Berry [266] assign this difference to potential interactions between Eu and Fe upon cooling. Data from [266,283].

The links between the chemical composition, the glass optical basicity and polymerization, and the redox state of multivalent elements has been studied well for iron-bearing compositions, because of the interests for iron in both Earth and Material sciences. In general, increasing the content of metal cations as well as the glass Al/(Al+Si) ratio result in reducing Fe at given T-f O2 conditions [252,267,269]. As different metal cation present different optical basicity, complex effects between the metal cation composition of the glass and itsa iron redox state further have been reported. For instance, Dickenson and Hess [268] observed that the Fe 2+ /Fe TOT ratio weakly increases with increasing the glass K 2 O/(K 2 O+Al 2 O 3 ) ratio in peralkaline melts, whereas the opposite is observed in peraluminous compositions. In Ca aluminosilicate glasses, Mysen et al. [269] reported a general decrease of the Fe 2+ /Fe TOT ratio with the glass M/(M+Al) ratio.

From the analysis of 75 peralkaline K 2 O-FeO-SiO 2 glasses, Tangeman et al. [284] reported an increase of Fe 2+ / Fe TOT ratio with increasing [K 2 O]. In peralkaline multicomponent glasses, Vetere et al. (2014) reported that both high NBO/T and high Na/(Na+K) stabilize Fe 3+ in the melt. A stabilization of Fe 3+ in CN 4 by addition of K 2 O was also suggested by several authors [268,281,282,285]. For basaltic and other complex melts, the oxidizing power of metal cations depend on their ionic field strength [e.g., 268, 282, 286]. In addition to the effect of the metal cation ionic field strength, its role in the glass network must be taken into account to explain the Fe redox state variations observed depending on the glass composition. As previously highlighted, glass optical basicity and NBO/T are parameters too simplistic to precisely depict the relationship between glass chemistry and the oxidation state of multivalent elements.

The case of multivalent elements can be further complicated by a potential change of their role in the glass structure as a function of their redox. Indeed, while Fe 2+ is commonly considered as a network modifier element, Fe 3+ acts as a network former elements as shown by increases in viscosity following oxidation of Fe (Fig. 37). Interestingly, the change of the melt viscosity at given temperature as a function of the Fe oxidation state further depends on the metal cation in the melt, illustrating the interplay between metal cations and Fe 3+ for charge compensation. Regarding the local environment of Fe in silicate glasses, data on simplified and multicomponent systems, often, are contradictory. Ferric iron is mainly regarded as 4-fold coordinated, although higher coordination numbers have been also reported [260,269,[287][288][289][290][291][292][293][294][295][296][297][298]. Regarding Fe 2+ , its structural environment is even more debated. The presence of Fe 2+ in CN 6 has been reported [241,288,299], along with trigonal bipyramidal and tetrahedral coordination [300][301][302][303][304]. Usually, it is safe to assert that Fe 2+ has an average coordination close to 5, which could be possibly translated as a coexistence of 4-, 5-and 6-or just the simultaneous presence of 4-and 6-fold Fe 2+ coordinated [260]. [241,243,246].

Volatile elements in silicate glasses

Volatile elements are present in glasses in various proportions, depending on the origin of the glass.

Industrial melts formed by batch melting (Sec. 1.1) contain gaseous inclusions of CO 2 , CO, N 2 and H 2 O.

In addition, those gaseous inclusions are usually removed by chemical fining, through introduction of sodium chloride, antimony oxide and sodium sulfate as fining agents in the melts. As a result, industrial glasses typically contain the H, C, S and Cl volatile elements at the ppm to hundreds of ppm concentration levels. For instance, we saw in sec. 1.2 that different levels of enrichments in those elements partly define the different categories of industrial silica glasses, because of their effect on the glass properties (e.g., Fig. 13).

Geologic glasses also contain the H, C, S and Cl volatile elements, and also possibly F. Water and carbone dioxide concentrations in geologic melts can reach values as high as 6-7 wt% and a few thousands ppm, respectively. The knowledge of their concentrations in volcanic products is critical in assessing the eruptive history of volcanic edifices, because of the strong effect of water on the viscosity and density of silicate melts [305][306][307][308][309][310][311][312][313][314][315]. The F, Cl and S volatile elements are present at lower levels of concentrations, but still can be present at concentrations of hundreds to thousands of ppm in geologic glasses. In this section, we will give a brief overview of the exiting knowledge on those common volatile elements in industrial and geologic silicate glasses.

Water

Large variations of water concentrations between glasses entrapped at depth in geologic systems, as glass inclusions in crystals, and glasses formed at the Earth surface testify of the extensive degassing of magmas upon their journey to the Earth surface, this degassing being associated with a dramatic evolution of their viscosity [305][306][307][308][309][310]. The effect of dissolved water on magma viscosity implies a correlation between the fraction of degassed water during volcanic eruptions and their explosive nature, as observed, for instance, for phonolitic magmas [316,317]. For example, the famous eruption of 79 CE of the Mt Vesuvius (Italy) that destroyed the cities of Pompeii and Herculaneum and killed their inhabitants [318,319] is associated with the eruption of a magma that lost ~5-6 wt% of water during its journey to surface [320,321], this dramatically increasing its viscosity [317], yielding to its explosive rupture in the volcanic conduit [322][323][324]. In contrast, the current eruption at the summit of the Mt Erebus (Antarctica) of a magma presenting a similar chemical composition but that contain only ~0.2 wt% water results in the establishment of a permanent lava lake in the volcanic crater [e.g., 317 and references cited therein]. Such dramatic contrast illustrates the importance of water in Earth science problems.

The solution mechanism of water in silicate glasses involves the presence of H 2 O molecules (H 2 O mol ), which can react with the oxygens O of the silicate network to form OH groups:

H 2 O mol (melt) + O 2- (melt) <=> 2 OH - (melt) . ( 13
)
1 H and 29 Si NMR as well as Raman and IR spectroscopic studies observed and documented the occurrence of the reaction depicted by eq. ( 13) in silicate glasses and melts [114,156,[325][326][327][328][329][330][331][332][333][334][335][336][337][338][339][340][341]. In this simple model, H 2 O mol reacts predominantly with bridging oxygens (BO), breaking T-O-T bonds (with T = Si, Al), so that equation ( 13) can be rewritten as:

H 2 O mol (melt) + T-O-T (melt) <=> 2 T-OH (melt) . (14)
Equation ( 14) implies formation of non-bridging oxygens (NBO) when the reaction shifts to the right. [e.g., 330, 346] and melt composition [156, 338, 344, 346-348].

From eq. ( 14), water addition in silicate melts and glasses results in their depolymerisation. The ratio of non-bridging oxygens over tetrahedral units, NBO/T, can be used to quantify such effect (see sec. 1.3.1., eq. 3): the higher it is, the higher the fraction of NBO in the melt, the lower the melt polymerization. For instance, solution of ~10 wt% of water in Na-bearing aluminosilicate melts can result in NBO/T increases of ~60% [339]. This, in fine, results in a great decrease of the glass T g . Figure 38 illustrates this effect:

reporting the reduced glass transition temperature T g * of hydrous glass as a function of their water content, a general trend is observed with large changes of the T g that decreases by a factor of 2 with addition of ~ 10 wt% water. Deubener et al. [349] showed that the T g of hydrous glasses can be calculated from the knowledge of the respectively represent the T g of the strictly anhydrous glass, the T g of the glass synthesized under air conditions (usually containing ~0.02 wt% water), and the virtual T g of the OH -groups and H 2 O mol species.

From the refinement of the model performed by Deubener et al. [349] that is visible in Fig. 38, 330:268-273, Copyright (2003), with permission from Elsevier.

While the modeling approach described previously is practical and coherent, the effect of the glass composition on the speciation of water actually is more complex that a simple dependence on the glass NBO/T. For instance, the IFS of alkali elements strongly affect the water speciation and bonding in Alfree silicate glasses (Fig. 39): the higher the alkali IFS, the higher the ratio [H 2 O mol ]/[OH -]. This translates a direct effect of the IFS of the alkali element on the equilibrium constant of the disproportionation reaction of H 2 O mol species in the glass network (eq. 13). 29 Si NMR and Raman spectroscopy results on alkali silicate glasses further reveal a change in the bonding of the OH -groups within the glass structure

[156]: alkali cations with high IFS favor the formation of M-OH bonds (M the alkali cation) in the glass network (Fig. 39). For instance, in hydrous

H 2 O mol + Si-O-M <=> SiOH + MOH , (15)
and

2 Si-O-M + H 2 O mol <=> SiOSi + 2 MOH . ( 16
)
The reactions depicted by eqs. ( 14), ( 15) and ( 16) result in different outcomes for the melt polymerisation.

Eq. ( 14) implies that water solution induces glass depolymerisation, but eq. ( 15) implies that water solution has no effect on the melt polymerisation (constant NBO/T). On the contrary, eq. ( 16) even implies a polymerisation of the melt as water solution subtracts the M elements from their network modifier role. Xue and Kanzaki [350] indicate that eq. ( 16) occurs only in very depolymerized melts. Eq. ( 15) should thus be the main process that account for the reaction of water with Si-O-M bonds.

Interestingly, it predicts that 1 mol of H 2 O mol should give equal amounts of SiOH and MOH entities.

Such ratio corresponds to that observed by Le Losq et al. [156] in an Li 2 Si 4 O 9 glass with ~18 mol% total H 2 O (Fig. 39), such that eq. ( 15) may be the main equilibrium accounting for the speciation of water in this glass.

In Al-bearing glasses, the mechanisms depicted by eqs. ( 14), ( 15) and ( 16) should remain valid. Reactions between H 2 O mol species and charge-compensator cations as well as Si-O-Al and Al-O-Al bonds are also possible. In Na tectosilicate glasses, a strong reaction of water with charge-compensator cations was proposed by Kohn et al. [332] on the basis of 29 Si, 27 Al, 23 Na and V m (H 2 O) = 12.0 ± 0.5 cm 3 mol -1 . Using such value, it is possible to calculate the density of hydrous silicate glasses, r(G Hyd ), from the knowledge of their anhydrous density, r(G Anh ), using the following equations:

V m (G Anh ) = M w (G Anh )/r(G Anh ) , (17) V m (G Hyd ) = x G V m (G Anh ) + x W V m (H 2 O) , (18)
M w (G Hyd ) = x G M w (G Anh ) + x W M w (H 2 O) , [START_REF] Malfait | 29Si NMR spectroscopy of silica glass: T1 relaxation and constraints on the Si-O-Si bond angle distribution[END_REF] r(G Hyd ) = M w (G Hyd )/ V m (G Hyd ) , [START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF] where V m (G Anh ) and V m (G Anh ) represent the molar volumes of the anhydrous and hydrous glasses, M w (G Anh ) and M w (G Hyd ) their molar masses, M w (H 2 O) = 18.02, and x G and x W the relative fractions of anhydrous glass and water (x G + x W = 1). species are different, and vary with the degree of polymerisation. Such remarks highlight, again, the complex effect of composition on the speciation and bonding of water in silicate glasses.

Carbon and Sulphur

Carbone is much less soluble that water in silicate glasses: usual concentrations range between a few ppm to a few thousands of ppm [e.g., see the model of 365 and references cited therein]. Increasing glass synthesis pressure largely promotes carbon solubility, whereas the effect of temperature is weaker and not well known [366]. Under redox conditions typical of geologic environments or industrial furnaces, CO 2 and CO 3 2-are the most common form of carbon molecules found in silicate glasses, as evidenced by molecular dynamic simulation [367]], Raman spectroscopy [368,369] and experiments [370,371],

for instance. Formation of CO molecules is observed only in very reducing conditions [372].

Like water, the interactions of carbon with the structure of silicate glasses depend on the carbon speciation as well as on glass composition. Raman spectroscopy data indicate that CO 2 enters in the glass structure mostly as CO 3 2-molecules, which interact mostly with NBO and network modifier cations [329]. Raman bands due to CO 2 and CO 3 2-in silicate glasses actually have been known for long [372][373][374][375][376]: a weak band at ~ 650 cm -1 corresponds to a bending mode of CO 3 2-(out of the molecule plane), a strong band at ~ 1080-1090 cm -1 is associated with the symmetric stretching mode (ν 1 ) of CO 3 2-and a doublet in the region of 1400-1500 cm -1 due to the asymmetric stretching vibrations (ν 3 ) of CO 3 2-.

Molecular CO 2 , when present, gives rise to two bands in the 1270-1400 cm -1 range (see [[[377]; for comparison, the molecular CO 2 doublet in gas hydrates is at 1274-1382 cm -1 [[378]). Combining Raman spectroscopy with IR and NMR spectroscopy, Brooker et al. [[372] showed that increasing the glass Al/(Al+Si) ratio along the SiO 2 -NaAlO 2 binary join promotes solution of carbon as CO 3 2-, at the expense of molecular CO 2 . IR spectroscopy results further indicate that the availability of NBO promote solution of CO 3 2-in the glass [[379]. From the Molecular Dynamic simulation data of Guillot and Sator [[367],

this results from a preferential association of CO 3 2-carbonate groups with NBO in the melts, such that the availability of NBO controls the dissolution of carbonate ions. In addition, the MD simulation results

show that network modifier cations are not randomly distributed in close vicinity of the carbonate groups, explaining why the solubility of carbon also varies as a function of the metal cation present in the glass [370,379].

In addition to melt composition, the synthesis temperature also affect the ratio of CO 3 2-/CO 2 in the glasses. In agreement with molecular simulation data [367], results from synchrotron infrared experiments in diamond anvil cells [380] reveal that, in Al-bearing silicate melts, CO 3 2-carbonate groups convert in CO 2 molecules with increasing the melt temperature. Therefore, CO 2 -bearing glasses quenched at different rates may present differences in their CO 3 2-/CO 2 ratios.

The important structural changes resulting from the solution of CO 2 in glasses result in variations of the glass properties. For instance, Bourgue and Richet [381] showed that both the relative density and T g of a potassium silicate glass decrease upon CO 2 solution (Fig. 41).

Figure 41: T g and relative density of a potassium silicate glass, as a function of the fraction of CO 2 dissolved as CO 3 2-. Data from [381].

From the density measurement presented in Fig. 41, Bourgue and Richet [381] derived a constant partial molar volume of CO 2 , V m (CO 2 ), for silicate glasses of 25.6 ±0.8 cm 3 mol -1 . They further indicate that CO 2 seems to have no effect on the glass thermal expansion coefficient, at least up to 2.2 wt% dissolved CO 2 . The V m (CO 2 ) indicated by Bourgue and Richet [381] agrees with other estimates for V m (CO 2 ) in melts at high temperature, which range between 20 and 30 cm 3 mol -1 [367, 382, 383].

In parallel to Carbon, Sulfur is the other element that is commonly found in concentrations of hundreds to thousands of ppm in both geologic and industrial glasses. In the latter, S is introduced during the addition of fining agents in the glass-making chain process. Those fining agents are introduced to aid refining the glass as well as the dissolution of silica. But S is not only present in glasses aimed at commercial application. Indeed, it is an important element of interest in the glass matrix used to confine nuclear wastes. As a result, the understanding of the reaction between S and the molecular structure of such glass confining matrix is an important goal for the long-term storage of nuclear waste [384]. In Earth sciences, sulphur is of wide interest because of its role in geological and biogeochemical processes [385].

A difficulty in understanding the solution mechanisms of sulphur in silicate glasses is its multivalent character. Indeed, sulfur present four different oxidation states: S 2-, S 0 , S 4+ and S 6+ . However, mostly S 2- and S 6+ have been detected in silicate glasses, as a function of their synthesis redox. For instance, S Kedge XANES data suggest that S is dissolved as S 2-and S 6+ in natural and industrial glasses [386][387][388][389][390].

S 4+ was reported in early studies [[e.g., 387] but actually this results from an artifact due to a change of S oxidation state under the irradiation of a synchrotron X-ray beam [390]. Presence of S 6+ as SO 4 2-in silicate glasses is corroborated by Raman data: S-O stretching in SO 4 2-yields a characteristic signal at ~ 990-1000 cm -1 [391-394]. Raman signals at ~ 2574 cm -1 and ~ 400 cm -1 have been detected in S 2-bearing glasses and have been assigned to H-S and Fe-S vibrations, respectively [394]. Therefore, S 2-bonds with H + in Fe-free hydrous glasses and with Fe 2+ in Fe-bearing glasses [395]. Sulphur thus reacts differently in the melt as a function of its oxidation state and of the melt composition.

The S solubility in glasses will vary depending on S oxidation state as well as on temperature, pressure at glass formation, and glass chemical composition [396]. The solubility of sulfide, S 2-, is strongly affected by the iron concentration of the melt because of the importance of sulfide saturation on the sulfur solution process following the equation [[397] FeO melt + ½ S 2 melt ó FeS sulfide melt + ½ O 2 sulfide melt . [START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF] Presence of dissolved water and the melt composition affect the equilibrium constant of eq. ( 22), and, hence, the solubility of S the latest one [396,398] allowing one to calculate the sulfur solubility in glass-forming silicate melts with an accuracy of typically ±10% (relative).

Halogens

F and Cl are halogen elements that are commonly found in silicate glasses in low concentrations (≤ 1 wt%). In geosciences, F and Cl are of interest because they both can affect, for instance, the viscosity and liquidus of magmas. They further are used as geochemical tracers, allowing to reconstruct the eruptive dynamics of volcanic edifices [402]. In industrial glasses, F and Cl can be added to silica to modify its photonic properties [403,404]. For instance, F reduces the silica glass refractive index (Fig. 42), and, hence, can be introduced for loss reduction in optical fibers. The Cl 2 gas is used for dehydration during the fabrication process of silica glass, leading to Cl impurities that affect the glass refractive index.

In -Crystalline Solids 353:568-572, doi:10.1016/j.jnoncrysol.2006.10.025, Copyright (2007), with permission from Elsevier.

Dissolution of Cl leads to a different pattern: according to Dalou et al. [410], it slightly depolymerizes the structure in Al-free melts, while it tends to polymerize that of Al-bearing melts. Such variations in the effect of Cl on melt polymerization may explain Cl effect on melt viscosity. Indeed, Baasner et al.

[411] report an increase of melt viscosity for peralkaline Na 2 O-CaO-Al 2 O 3 -SiO 2 melts; a decrease of melt viscosity is observed in peraluminous melts, and may be assigned to Al-Cl bonding favored by the absence of Ca and Na network modifiers available for bonding with Cl. Indeed, formation of M-Cl complexes seems to be the main mechanisms of Cl solution in the glasses [410,[412][413][414][415][416]

Conclusion

-The backbone of the molecular disordered structure of silicate glasses is the tri-dimentionnal network of interconnected Q 4 tetrahedral units containing Si at the center and O at the summits.

At medium range order, tetrahedral units can form tri-dimentional molecular arrangements (e.g., rings and cages) that influence the glass elastic properties.

-Metal cations play a role of network modifiers, breaking Si-O-Si inter-tetrahedral bonds, decreasing the network polymerization as they produce the transformation of bridging oxygens to non-bridging oxygens. Q 0 , Q 1 , Q 2 , and Q 3 units are formed upon addition of network modifiers, in proportion that depends on the fraction of added modifiers and of its Ionic Field Strength.

Indeed, as described by the Modified Random Network model, modifiers tend to cluster in the network, potentially forming percolation channels that percolates through the disrupted tetrahedral network. The fractions of Q n units as well as the medium range order organization of the network controls the glass properties, such as its entropy, density and T g .

-Aluminum enters mostly in four-fold coordination in Q 4 units. Metal cations in vicinity do not modify the network but charge-compensate the electric charge deficit of AlO 4 -units. AlO 5 and AlO 6 units are present in low fractions in the glasses, depending on the Al/(Al+M) ratio as well as on the charge compensator IFS; similar conclusions are drawn for the presence of non-stoichiometric non-bridging oxygens. Presence of non-stoichiometric NBO and AlO 5 units influence the glass properties related to its plastic flow, such as its T g and Vickers hardness.

-Multivalent elements in silicate glasses present oxidation states that mostly depend on temperature, oxygen fugacity and melt composition applied during the glass formation process.

Coordination state of multivalent elements can be a complex function of melt composition, as

shown by the various findings for Fe.

-Volatile elements are commonly present in small concentrations in geologic and industrial silicate glasses. Despite such low concentrations, they play determining roles on the glass structure and on its rheological properties. It is found that most volatile elements actually react with metal cations M as well as Al and Si cations, in proportions that depends on the M cation IFS and the glass Al/(Al+Si) and Al/(Al+M) ratios. In addition, glass composition also affect the speciation of the volatile elements in different species, as does the oxygen fugacity and temperature during the glass synthesis.

Figure 1 :

 1 Figure 1: Ring and earring reproduction. Image reproduced from Henrivaux, 1897, "Le Verre et le cristal" Vicq-Dunaud Editors, Paris [1].

Figure 2 :

 2 Figure 2: Representation of Egyptian glassworkers blowing glasses on brazier at Beni-Hassan.

Figure 3 :

 3 Figure 3: Examples of chemical composition of various geologic (lunar glass, dunite, peridotite, tephrite,

Figure 4 :

 4 Figure 4: a) millefiori glasses, b) pearls, c) fragment of Roman glass and d) bottle from the Roman empire. Pictures Daniel R. Neuville.

Figure 5 :

 5 Figure 5: Chemical composition of ashes generated by burning different plant and trees. Data from Vernioles [13].

Figure 6 :

 6 Figure 6: Formation of flat glass using the cylindrical sleeve technique: a) b) and c) a cylinder of glass is formed by blowing, d) each end is removed and one of the cylinder side is cut, e) the cylinder is then softened under fire to obtain a flat window, and f) final product can be colored or uncolored. Pictures Daniel R. Neuville, from the Saint-Just Factory -Saint-Gobain Compagny.

Figure 7 :

 7 Figure 7: Representation of the three different furnaces needed to made glass and proposed by Agricola. This representation is extracted from "Dans l'art de la verrerie" from Neri, Merret and Kunckel (1752) [6].

(

   invented the crystal glass through the addition of an important quantity of lead oxide in the composition. From this invention, patented in 1673 by Ravenscroft, lead-based glass spread among Europe, representing an important turnover as it allowed improving the appearance of glass as well as lowering the melting and working temperatures. In parallel, the naturalist and physicist René-Antoine Ferchault de Réaumur (1683-1757) observed the partial crystallization of a glass and created the first glass-ceramic in 1727. While such aspect was considered to be a defect at this time, it is a particular focus in glass and materials sciences nowadays because glass-ceramic materials open new doors to the manufactures of new strategic materials [e.g.,see 14].

Figure 8 :

 8 Figure 8: Picture of two glass drops observed under polarized and analyzed light. The sample at the left is unrelaxed, while that at the right was annealed, removing any intern stress. Picture courtesy of Prof. D. de Ligny.

Figure 9 :

 9 Figure 9: A) Glass transition temperature T g and B) relative density of binary silicate glasses along the M n+ 2/n O-SiO 2 join. T g of Na 2 O-SiO 2 and K 2 O-SiO 2 glasses compiled by[START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF]; T g of Li 2 O-SiO 2 glasses:[START_REF] Losq | Rôle des éléments alcalins et de l'eau sur les propriétés et la structure des aluminosilicates fondus et vitreux : implications volcanologiques[END_REF]; T g of MgO-SiO 2 and of CaO-SiO 2 glasses:[START_REF] Neuville | Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets[END_REF][START_REF] Neuville | Viscosity, structure and mixing in (Ca, Na) silicate melts[END_REF]. Density data are from[START_REF] Losq | Rôle des éléments alcalins et de l'eau sur les propriétés et la structure des aluminosilicates fondus et vitreux : implications volcanologiques[END_REF][START_REF] Neuville | Viscosity, structure and mixing in (Ca, Na) silicate melts[END_REF][START_REF] Doweidar | The density of alkali silicate glasses in relation to the microstructure[END_REF][START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF].

Figure 12 :

 12 Figure 12: Distribution of the mean Si-O-Si bond angle in silica derived from 29 Si NMR spectroscopy, using either a linear relationship between the 29 Si chemical shifts and Si-O-Si bond angles measured in SiO 2 polymorphs and zeolites (plain curve), or a correlation determined by density functional theory by

Figure 13 :

 13 Figure 13: Glass transition temperature T g of the silica glass as a function of the molar concentrations in Na 2 O (blue circles), OH (red diamonds), Al 2 O 3 (pink hexagons) or Ga 2 O 3 impurities (purple inverted triangles), predicted from the viscosity data ofLeko et al. [70] assuming that log(h) = 12 Pa s at T = T g .

Figure 14 :

 14 Figure 14: Changes in the fractions of Q n units measured by29 Si NMR spectroscopy as a function of the alkali metal content of binary M 2 O-SiO 2 glasses (M=Li, Na, K). Alkali content is restricted to the 0-40 mol% range, but can reach higher values for Na 2 O-SiO 2 glasses, such that Q 1 and Q 0 units also has been detected in Na 2 O-rich silicate glasses. On the right is shown a schematic view of the structure of an alkali silicate glasses, in which the Q 2 , Q3 and Q 4 units are distinguished; NBO and BO refer to non-bridging and bridging oxygen atoms, respectively, and M + refers to alkali network modifier cations. Si 4+ network former cations are in purple at the center of the tetrahedra. Curves are calculated from the equilibrium constant of the 2Q 3 = Q 2 +Q4 relationship, with values of 0.008, 0.02 and 0.08 for the K, Na and Li silicate compositions. Data are from[START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF][START_REF] Sen | NMR study of Q-speciation and connectivity in K 2 O-SiO 2 glasses with high silica content[END_REF][START_REF] Zhang | Silicon site distributions in an alkali silicate glass derived by two-dimensional 29 Si nuclear magnetic resonance[END_REF][START_REF] Davis | Q n Species Distribution in K 2 O•2SiO 2 Glass by 29 Si Magic Angle Flipping NMR[END_REF].

Figure 15 :

 15 Figure 15: the binary (A) and random bonding (B) models predicting the fractions of the different Q n units as a function of the mol% of M n+ 2/n O in SiO 2 (M a network modifier element, such as Li, Na, K, Ca or Mg).

Figure 16 :

 16 Figure 16: Top: Enlarged 29 Si double quantum (DQ) NMR spectrum of a Na 2 Si 3 O 7 glass. The marked peaks with chemical shifts of 89, 92 and 94 ppm on the horizontal axis belong to Q 3 333 , Q 3 334 , Q 3 344 units. These values can be used to fit the 1D 29 Si NMR spectrum of the glass with Gaussian peaks, as shown at the bottom. Hatched lines are used for the Q 3 jkl lines whereas long hatched lines with dots are used for

Figure 17 :

 17 Figure17: Partial molar volume of Q n units V u estimated byDoweidar [105, 106] as a function of the

Figure 20 :

 20 Figure 20: Variation of the topological and mixing contributions to the entropy of potassium and sodium silicate melts as predicted by equation 3 and 4, respectively, as a function of the concentration in alkali oxide in the melt. Values from[START_REF] Losq | Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow[END_REF].

  Figure22shows the results of such calculation: the diffusivity of Na and K are calculated at25, 200 and 350°C in mixed Na-K trisilicate glasses; this allows the calculation of the electrical conductivity. The agreement between the model and experimental data is also shown, and the model reproduces fairly well the predicted deviations. However, looking in details, it predicts too strong depletion of the electrical conductivity at K/(K+Na) ~ 0.5.

Figure 22 :

 22 Figure 22: A) Isothermal diffusion coefficients and B) electrical conductivities for the mixed alkali glasses 0.25 [KgKNa1-gK] 2 O -0.75 SiO 2 . Points are experimental data, dashed lines are interpolations of those data, and the plain lines are the prediction by the model proposed by Greaves and Ngai [129].

  Distribution (PCD) model, which neither implies a random distribution of the modifiers nor their segregation in specific regions of the network. The PCD model particularly predicts that if different network modifier cations are present in the glass network, they present various degree of ordering between them. The model thus introduces a parameter Q m that describes the degree of intermixing between different network modifier cation: Q m = 1 for a chemical order favoring dissimilar pairs, Q m = 0 for a random mixing and Q m = -1 for clustering of similar cations[120, 131]. For instance, as indicated earlier, 2D Dynamic Angle Spinning NMR data support a random mixing of Na and K in silicate glasses[152], resulting in an excess of entropy that explains the observed minima in the glass transition temperature during the Na-K mixing (e.g., Fig.21). Contrary to that,17 O MAS and 3QMAS NMR data on Ca and Na silicate glasses indicate that those two cations mix in dissimilar pairs[120], this explaining why the random mixing model does no explain the viscosity variations upon mixing Na and Ca in silicate melts[START_REF] Neuville | Viscosity, structure and mixing in (Ca, Na) silicate melts[END_REF]. Similarly, Ba shows a stronger affinity for NBO than Na in Ba-Na silicate melts, while in Ba-Mg silicate melts, a Ba and Mg are not randomly ordered around the NBOs[121]. Overall, those results

  5 mol% K 2 O, yields to a three-dimensional percolation of those clusters. This ultimately forms the ionic percolation channels depicted by the MRN model. Sen and Youngman further indicate that such interpretation would explain why results from molecular dynamic simulation from [154] indicated that the MAE was not occurring a very low alkali concentration.

Figure 24 :

 24 Figure 24: Glass transition temperature T g and configurational entropy at T g of alumino-silicate glasses containing 75 mol% SiO 2 and different Al/(Al+Na) ratios. Peralkaline glasses present an Al/(Al+M)

Figure 25

 25 illustrates this dependence in the CaO-Al 2 O 3 -SiO 2 diagram. In this ternary diagram, a significant fraction of Al already is in CN 5 in the peralkaline domain.

Figure 27 :

 27 Figure27:27 Al NMR spectra acquired at room temperature and at 1200°C on sodium alumino-silicate glasses and melts presenting different Na/Al ratios. The peralkaline glasses and melts show no significant difference, as Al is at ~ 99% in CN4. In tectosilicate and peraluminous compositions, the broadening of the27 Al NMR signal indicate the existence of Al in 5-and even 6-fold coordination at high temperature.

Figure 28 :

 28 Figure 28: Average Al coordination in Ca 3 Al 2 Si 2 O 18 (CAS & CAS5R), Na 3 AlSi 3 O 9 (NAS) and K 3 AlSi 3 O 9

Figure 29 :

 29 Figure 29: Vickers hardness versus average Al coordination in Re 2 O 3 -Al 2 O 3 -SiO 2 (Re = Y, Lu) glasses with various compositions (0.99 ≤ Al/Lu ≤ 2.4 and ~49 ≤ mol% SiO 2 ≤ ~65 for Lu 2 O 3 -Al 2 O 3 -SiO 2 glasses; 0.72 ≤ Al/Y ≤ 1.77 and ~41 ≤ mol% SiO 2 ≤ ~68 for Y 2 O 3 -Al 2 O 3 -SiO 2 glasses). Data from [185].

  in case of perfect Al avoidance (no Al-O-Al bonds), and 0 in case of a purely random Al-Si distribution [131, 201]. In alkaline-earth and alkali tectosilicate melts, Q values range from 0.65 to 0.99; Figure 30 show how Q values decrease with increasing the ionic field strength of the charge compensating metal cation in the glass framework [201, 204].

Figure 30 :

 30 Figure 30: Relationship between the degree of Al avoidance in alumino-silicate melts and the ionic field strength of the metal cation. Reprinted with permission from Lee SK, Kim H-I, Kim EJ, Mun KY, Ryu S (2016) Extent of Disorder in Magnesium Aluminosilicate Glasses: Insights from 27 Al and 17 O NMR. J Phys Chem C 120:737-749. doi: 10.1021/acs.jpcc.5b10799 Copyright (2016) American Chemical Society.

Figure 31 :

 31 Figure31: A) 850-1300 cm -1 portion of the Raman spectrum of thee NaAlSi 3 O 8 glass, presenting an Al/Si ratio of 0.5. The dotted blue peak is assigned to T-BO asymmetric stretching in TO 4 units, while the peaks in purple (Q 4,I ) and orange (Q4,II ) are assigned to T-O symmetric stretching in TO 4 units[25, 57 and

and

  Stebbins [201]] further modelled the chemical variation using a mixing of the different Si-O-Si, Si-O-Al and Al-O-Al bonds in the network. From this model, in case of a perfect Si-Al ordering (perfect Al avoidance, Q = 1), S conf (T g ) between the SiO 2 and NaAlSiO 4 compositions is expected to show a maximum at the NaAlSi 3 O 8 composition with an Al/Si = 0.5 (25 mol% NaAlO 2 )[201, 209]. The Q values in Na tectosilicate melts are between 0.93-0.99, implying strong to nearly perfect Al avoidance[201].

Figure 32 :

 32 Figure 32: Proportion of non-stoichiometric non-bridging oxygens NBO relatively to the total proportion of oxygens in the network of tectosilicate glasses as a function of the ratio R of the concentrations of metal cation and aluminum M n+ 2/n O/( M n+ 2/n O+Al 2 O 3). BaASx.y.30: barium tectosilicate glasses with 30 mol% SiO 2 ; CASx.y.30 and CASx.y.60: calcium tectosilicate glasses with 30 and 60 mol% SiO 2 ,

Figure 33 :

 33 Figure 33: Viscous glass transition temperature T g and configurational entropy at the glass transition temperature S conf (T g ) of NaAlSi 3 O 8 -KAlSi 3 O 8 glasses as a function of the glass K/(K+Na) ratio. S conf (T g ) values have been determined performing a global fit of the viscosity data in the binary NaAlSi 3 O 8 -KAlSi 3 O 8 system from[START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF] 228], with using the framework of the Adam and Gibbs equation linking

Figure 34 :

 34 Figure 34: A) Glass transition temperature T g and Vickers hardness H v as well as B) Young modulus and density of glasses as a function of the Ca/(Ca+Mg) ratio of glasses composed of 60 mol% SiO 2 , 16 mol% Al 2 O 3 , 15.8 mol% Na 2 O and the remaining proportion as CaO+MgO. While glass T g and H v values show significant deviations to linearity, marking the occurrence of a Mixed Alkaline-earth Effect, the glass Young modulus and density vary linearly as a function of Ca/(Ca+Mg). Data from [142].

Figure 35 :

 35 Figure 35: Elastic moduli of M n+ 1/n AlSiO 4 glasses (m=Li, Na, K, Ca, Mg, Sr, Ba, Zn) as a function of the glasses' molar volume. Reprinted from Weigel C, Le Losq C, Vialla R, Dupas C, Clément S, Neuville DR, Rufflé B (2016) Elastic moduli of XAlSiO 4 aluminosilicate glasses: effects of charge-balancing cations. Journal ofNon-Crystalline Solids 447:267-272. doi: 10.1016/j.jnoncrysol.2016.06.023.

Figure 37 :

 37 Figure 37: Viscosity (log Pa s) of alkali ferrosilicate melts at constant temperature as a function of the Fe 3+ /Fe TOT ratio. Data from[241, 243, 246].

22 .

 22 The A and B parameters depend on the melt NBO/T as A =35- 7.58*NBO/T and B = 7-3.03*NBO/T. The hydrous glass T g can thus be obtained from the knowledge of 𝑇 r ~!. This model allows simple estimations of the T g of hydrous glasses, as shown in the study ofBehrens and Yamashita [344] of the speciation of water in Na silicate glasses and melts. It further corroborates the observation that the glass composition has an effect on the influence of water on the hydrous glass T g , because the parameters A and B depend on the glass NBO/T. Besides, the dependence of water speciation on glass composition yieldedDeubener et al. [349] to introduce a calculation of the glass OH - and H 2 O mol concentrations that depends on the glass anhydrous NBO/T.

Figure 38 :

 38 Figure 38: Reduced glass transition temperature T g * as a function of the total content of water in the glasses in wt%. T g * = T g hydrous /T g GN , with T g GN the T g of the glass with 0.02 wt% water, a content typical of glass synthesized at ambient conditions. See Fig. 1 for examples of compositions of the basanite, tephrite, trachyte, phonolite, andesite, granite and obsidian geologic glasses. The curve represents the model of Deubener et al. [349]. Reproduced with minor alterations from Deubener J, Müller R, Behrens H, Heide G (2003) Water and the glass transition temperature of silicate melts, Journal of Non-Crystalline Solids

  silica glass, termination of Si-O-Si bonds by F and Cl seem to be the preferred interpretation for the solution mechanism of F and C[404]. The solution of F in Al-free and Al-bearing glasses is a more complex process. Raman and NMR spectroscopy data indicate the occurrence of Si-F, Al-F and M-F complexes [405-410], in proportions that depend on the glass Al/(Al+Si) and metal cation IFS. From 19 F NMR data on Mg, Na and La Al-free and Al-bearing silicate glasses, increasing the metal cation IFS promotes the formation of M-F bonds [407]. Such trend explains the findings of Bassner et al. [409],who noticed that F was preferentially associated with Ca in Ca-Na aluminosilicate glasses, despite the much lower concentration of Ca in the investigated glass. The latter authors further indicate that glass water content affect the F-Al and F-M fractions: it seems that F -and OH -groups occupy similar Al environments, and that F cannot compete with OH groups for populating those environments. Small fractions of Si-F and high fractions of Al-F bonding are further evident from Raman spectroscopy and NMR results[405][406][407][408] 410]. The proportions of the different M-F, Al-F and, in a smaller extent, Si-F complexes depend on the Al/(Al+Si) ratio of the glasses[406, 410], resulting in a control of the solubility of F by the glass Al/(Al+Si) ratio[410]. In addition, the formation of Al-F and possibly Si-F bonds in the network of alumino-silicate glasses result in their depolymerisation, as observed by Raman spectroscopy[406, 410].

Figure 42 :

 42 Figure 42: Refractive indices of halogen-doped silica glasses at 633 nm as a function of fictive temperature: (a) F-and (b) Cl-doped silica glasses. Solid lines are approximate linear fittings. Reprinted from Kakiuchida H, Sekiya EH, Shimodaira N, Saito K, Ikushima AJ (2007) Refractive index and density changes in silica glass by halogen doping. Journal ofNon-Crystalline Solids 353:568-572, doi:10.1016/j.jnoncrysol.2006.10.025, Copyright (2007), with permission from Elsevier.

  The 19 th and 20 th century saw a rapid evolution of the glass market, as glass was needed as a technological material for various applications. For instance, in 1893, the Duran boro-silicate glass, was developed by Otto Schott, a German glass maker. This glass presented a low thermal expansion, such that the Corning Glass Works company used it to form the first light bulb for Thomas Edison. At the turn of the 20 th century, other technical problems appeared with the development of railroad, automobiles and other mechanical transportation means. For instance, the glass globes of signal lanterns on United States of America railroads were sensible to extreme temperature changes (e.g., heavy rain on hot glass), leading them to shatter. This problem was solved by the development of the Nonex and the famous Pyrex ® glasses, respectively in 1908 and 1915 by the Corning Glass Works company. Those boro-silicate glasses present a very low thermal expansion, making them particularly suitable for uses in environments with

extreme temperature changes. The E glass, a calcium boro-silicate, was subsequently developed for electrical insulators has thus been found to have excellent mechanical properties. From the middle of the 20th century, it was this glass that was produced in the form of fibres to reinforce composite materials.

Table 2

 2

	]. Because of such sensitivity, four different types of silica glasses are usually
	distinguished depending on the level of impurities they contain [74]:

  However, this relationship should not be extended to other type of glasses, because, for instance, the glass heat capacity of B 2 O 3 at T g only reach values ~0.6 3R [see 112 and references therein].

	Glass	Si-O	Si-NBO Si-BO M-O	M-NBO M-BO	Method References
	Li 2 Si 4 O 9	1.60(-)	-	-	1.96(-)	-	-	Exp.	[113]
	Li 2 Si 4 O 9	1.63(-)	1.58(-) 1.64(-) 1.92(-)	1.87(-)	-	MD.	[81]
	Na 2 Si 4 O 9 1.625(11) 1.589(8) 1.65(8) 2.45(40) 2.29(24) 2.52(25) Exp.	[114]
	Na 2 Si 4 O9	1.63(-)	1.58(-) 1.65(-) 2.28(-)	-	-	MD.	[115]
	K 2 Si 4 O 9	-	-	-	2.77	-	-	MD.	[116]

Table 3 :

 3

Examples M-O bond distances in tetrasilicate glasses reported from molecular dynamic simulations (MD.) and experimental (Exp.) studies.

Figure

18

: Glass configurational entropy, equal to the melt configurational entropy at T g , as a function of the mol% of Na 2 O added in SiO 2 . Those values were estimated from the fit of the melt viscosity data using the Adam and Gibbs theory of viscous flow (see chapter XXX), except the value of 5.1 ±2 J mol

-1

  topo originates from the disorder in the glass network, in term of Si-O bond distances and Si-O-Si bond length for instance. S mix represents the excess of entropy generated by the mixing of different elements

	and S mix as:
	𝑆 E* ?*@ = -𝑥 E* 𝑥 # * 2𝑅 *	( 60&	𝑥 8 9	𝑙𝑛 𝑥 8 9 ,	(7)
	𝑆	=535 =	( 60&	𝑥 8 9	𝑆 8 9 4567 ,		(6)

in similar structural positions. Le

Losq and Neuville [[20]

thus calculated S topo as:

  The MME refers to the strong and non-linear changes in silicate glass properties that can occur upon mixing two metal cations [e.g., see 136, 137 and references cited therein]. Figure21illustrates this effect on the T g and the electric resistivity of glasses that are mixtures of K 2 Si 2 O 5 and Na 2 Si 2 O 5 . Upon mixing Na + and K + in the glasses, a large depression in the glass T g is observed while the electric resistivity increases of several orders of magnitude. The MME usually results in maxima or minima of the glass

	However, the interpretations of 23 Na and 17 O NMR data on sodium silicate and alumino-silicate glasses
	lead Lee and co. [130-132] to propose an alternative model: the Perturbed Cation Distribution (PCD)
	model. The PCD model assumes a relatively homogeneous distribution of metal cations in the glass
	network, neither random nor forming clusters. It describes network modifiers as surrounded by both

with interstitial network modifier elements forming ionic bonds with NBOs as discussed in the previous section, such vision is difficult to extrapolate at the medium range order. Indeed, the network modifier cations have high coordination numbers, and are surrounded by both BO and NBOs from several Q n units

[e.g., 120, 121]

. For instance, in aluminum-free silicate glasses, Ca 2+ and Mg 2+ coordinence numbers are of

~4-5 [109, 122-124]

, whereas that of Na + is ~6

[110, 111, 125]

. The network modifier cations thus have defined local environment, such that the RN model (see section 1.1) cannot account for their distribution in silicate glasses because it assumes their random repartition in the free volume in the silicate network [126]. An alternative model is thus needed to describe the arrangement of the different network former and modifiers cations in the glass structure. Two models were proposed to account for the environment of network modifiers in silicate glasses. From the interpretation of X-ray absorption results [126-129], Greaves and co. proposed the Modified Random Network (MRN) model. It depicts the glass structure as a tri-dimensional arrangement of dynamic channels of network modifier metal cations percolating through a disrupted silicate tetrahedral network. Such channels are dynamic features in the molten state, and become frozen-in in the glasses below T g . NBO and BO anions, as indicated by NMR data [e.g., 132]. Whether one adopts the MRN or the PCD model to describe the glass structure, the adopted model needs to explain an effect that greatly affect the glass properties: the Mixed Modifier Effect. This effect is also called the Mixed Alkali Effect (MAE) or the Mixed Alkaline-earth Effect (MME) in the literature. To avoid confusion, we chose to use the MME denomination in the present handbook.

Figure 21: Glass transition temperature T g and logarithm of the electrical resistivity at 373K of K 2 Si 2 O 5 -Na 2 Si 2 O 5 mixed glasses, as a function of the fraction of K in the glasses. The Mixed Modifier Effect (MME) refers to the non-linear and large deviations of many glasses properties when mixing two network modifier elements in the glasses. Data from [133-135].

properties when the ratio A/(A+B) between the mixed A and B cations reach 0.5. This effect has been extensively documented for Na and K in silicate glasses [e.g., see 136, 137 and references therein], but it also occurs in silicate glasses when mixing different alkaline-earth cations such as, for instance, Ca

  In the framework of theAdam and Gibbs [151] theory of viscous flow, which describes liquid relaxation, and hence, viscous flow as a cooperative re-arrangement mechanism of sub-systems in the liquid, the minima in T g(and, hence, viscosity) observed upon mixing Na and K in silicate melts is explained by an excess of configurational entropy at T g that originates from a random mixing of pairs of alkali metals[117], as shown by17 O Dynamic Angle Spinning NMR experiments [152]. This interpretation supports the cooperative inter-diffusion and mixing of metal cations in ionic channels percolating through a disrupted silicate tetrahedral network. It is interesting to note that the MAE affects properties that are related to the diffusivity of the network modifiers, but it affects much less properties related to the silicate tetrahedral network. Indeed, mixing alkali elements in silicate glasses yields to nearly-linear variations in the fraction of the Q n species [see 20 and references cited therein] as well as in that of NBO in the network[152].

by the American Physical Society

In all cases, the existence of ionic diffusive pathway for modifier cations, as depicted by the MRN model, has been supported by results from atomic force microscopy [e.g., 144], molecular dynamic simulation

[e.g., 145, 146]

,

NMR [e.g., 102

] and inelastic neutron scattering [e.g., 147-150] experiments.

Similarly, molar volume or density of silicate glasses are only slightly affected by the MAE

[136, 137]

.

As highlighted previously, not all data support the clustering of modifiers in percolation channels.

observed that modifier cations are interacting with both BO and NBOs, such that they should be homogeneously distributed in the glass network. Recently,

Angeli et al. [153]

also interpreted

17

O MQMAS data as showing a uniform distribution of Na in sodium silicate glasses, because the twodimensional projection of the

17

O NMR chemical shift and quadrupolar coupling constant distributions for BO oxygens in the Na 2 Si 2 O 5 and the SiO 2 glasses are not overlapping. Therefore,

23

Na and

17

O NMR results on silicate and alumino-silicate glasses seem to support the alternative Perturbed Cation

  support the PCD model for accounting of the metal cation distribution in silicate glasses, it must be said that other29 Si NMR data point in favour of the MRN model. Results ofOlivier et al. [102] from29 Si Double Qantum NMR experiments and MD simulations indicate that Q 4 units are connected to both Q 4 and Q 3 units, supporting the existence of silica-rich domains as depicted in the MRN model. Performing29 Si and17 O experiments on potassium silicate glasses with SiO 2 contents higher than 75 mol%, Sen and Youngman[START_REF] Sen | NMR study of Q-speciation and connectivity in K 2 O-SiO 2 glasses with high silica content[END_REF] identified two different type of Q 4 units in silica-rich potassium silicate glasses: some Q 4 are connected to Q 3 units (called Q4-3 units by Sen and Youngman) while others are only connected to Q4

  in the figure). The change in the 200-700 cm -1 Raman signal occurring upon addition of Na or K in SiO 2 thus indicate a breaking of the three-dimensional tetrahedral network in those glasses. However, we observe that the 200-500 cm -1 signals from the Li 2 Si 4 O 9 glass are very similar to those in SiO 2 . As this glass contain more Q 2 and Q 4 units than the Na 2 Si 4 O 9 or K 2 Si 4 O 9 glasses (Fig 14), this suggests that it exists silica-like molecular complexes containing Q 4 units in this glass, and, hence, support the modified random network of the structure of silicate glasses. The peaks between 900 and 1300 cm -1 are assigned to Si-O vibrations in Q n units

  sec.1.2.1). Contrary to that, the Raman spectra of the sodium and potassium tetrasilicate glasses do not present such signals, but two new peaks centred at 518 and 595 cm - 1 , assigned to Si-O-Si vibrations involving Q 3 and Q 2 units[START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF] 155,[157][158][159]. According toMatson et al[155], the similarity between the Raman spectra of the SiO 2 and Li 2 Si 4 O 9 glasses indicate the presence of silica-rich regions in the Li silicate glass. Therefore, a dissociation of Q 3 species into Q 2 and Q 4 species higher in the Li silicate than in the Na and K silicate glasses (Figure14) may actually suggest a segregation of Li around Q 2 units, and of Q 4 units in silica-like regions as depicted by the MRN model.For lithium silicate glasses, such interpretation is supported by the 29 Si{ 7 Li} rotational echo double resonance spectroscopy results from Voig et al[160]]. Indeed, almost independently of the silica content, the Li 7 dipolar filed measured at the Q 3 sites is stronger than that measured at the Q 4 sites in Li silicate

Table 4 :

 4 Examples of ranges of bond lengths for common metal cations in alumino-silicate melts, reported in the literature by experimental (Exp.) and modeling (Mod.) studies of alkali and alkalineearth alumino-silicate glasses. *values derived from figures.

	4,II

  O MASNMR spectroscopy that ~5% of non-stoichiometric NBO are present in a calcium tectosilicate glass with ~50 mol% SiO 2 . Other experimental studies further reported fractions of a few percents of nonstoichiometric NBO in tectosilicate glasses, as listed in Table5.

	Compensating	Si/(Si+Al) % non-stoichiometric NBO Remark	Ref.
	cation
	Ca	0	5(-)	-	[219]
	Ca	0.3	5.9(4)	-	[178]
	Ca	0.33	5(1)	-	[220]
	Ca	0.43	8(-)
	Ca	0.5	5(1.0)	-	[176]
	Ca	0.5	7.6(1.9)-9.4(2.4)	for 2 different T f [192]
	Ca	0.6	2.7(4)	-	[178]
	Ca	0.75	1(-)	-	[221]
	Ba	0.3	5.0(7)	-	[181]
	K	0.6	0.9(4)-1.6(4)	-	[178]
	K	0.8	n.d.	-	[178]

Table 5 :

 5 Proportion of NBO in percent in tectosilicate glasses, measured by various NMR spectroscopy technics (principally 17 O NMR).

	At fixed SiO 2 content, the variations of the fraction of non-stoichiometric NBO with the M n+	2/n O/(
	M n+	2/n O+Al 2 O 3 ) ratio describe linear trends (Fig. 32). The disappearance of non-stoichiometric NBOs
	occur in the peraluminous domain, for M n+	2/n O/(M n+	2/n O+Al 2 O 3 ) < 0.5 (reciprocally M n+	2/n O/(
	M n+	2/n O+Al 2 O 3 ) > 0.5).
	While up to 9 percent of non-stoichiometric NBO are reported in Ca tectosilicate glasses, the fractions
	reported in K tectosilicate glasses are lower (Fig. 32). An effect of the ionic field strength of the modifier
	cation thus appears possible: reducing the cation ionic field strength apparently results in a reduced
	content of non-stoichiometric NBO in the glass[178]. However, very few direct data are available in
	other systems (e.g., Na-bearing glasses) to test this statement, such that it should be considered with
	caution. Indirect evidences from Raman spectroscopy and viscosity measurements suggested the

presence of non-stoichiometric NBOs in Na and Mg tectosilicate glasses

[177, 197]

, but do not provide any quantification. The molecular dynamic simulation results from

Xiang et al. [205]

on Na aluminosilicate glasses with 60 mol% SiO 2 indicate that, at such silica concentration, the tectosilicate glass may contain 4-5 % non-stoichiometric NBO, depending on the potential used during the calculations. Such

  CASx.y.30 and CASx.y.60: calcium tectosilicate glasses with 30 and 60 mol% SiO 2 , respectively; KASx.y.60: potassium tectosilicate glasses with 60 mol% SiO 2 . Lines fits are shown as guides to the eye. Reprinted from

). BaASx.y.30: barium tectosilicate glasses with 30 mol% SiO 2 ;

  Li and Na alkali metal cations without significant changes in the silicate tetrahedral network[231]. On the other hand, using6 Li,7 Li and29 Si static NMR spectroscopy,Bray et al. [232] observed a linear change of the fraction of Q 3 units upon mixing Li and K in disilicate glasses. The 29 Si static NMR data from Emerson and Bray [233] further suggest a slight departure from linearity of the Q 3 unit fraction when mixing Na 2 Si 2 O 5 and Cs 2 Si 2 O 5 glasses. Such interpretation may be coherent with 17 O Dynamic Angle Spinning NMR data from mixed Na 2 Si 2 O 5 -K 2 Si 2 O 5 glasses [152], showing slightly non-linear changes of the fractions of Bridging (BO) and Non-Bridging (NBO) oxygen anions with changes in the glasses K/(K+Na) ratios. Recent analysis of Raman spectra of mixed (K,Na)Si 3 O 7 and (K,Na) 2 Si 2 O 9 glasses by Le Losq and Neuville

  O MAS and 3QMAS NMR spectroscopy indicate that, in mixed Ca 3 Al 2 Si 3 O 12 -Mg 3 Al 2 Si 3 O 12 glasses, the mixing of Ca and Mg around NBO is not perfectly random [234]. A slight excess of Mg-NBO pairing is observed, implying that extra Ca must be associated with BO from Al-O-Si bonds according to Kelsey et al. .[234]. The latter authors indicate that the S conf (T g ) values of mixed Ca 3 Al 2 Si 3 O 12 -Mg 3 Al 2 Si 3 O 12

Table 6 :

 6

	Cation	Coordination	Corresponding	Method	Reference
		number	Ionic	radius
			from Shannon
			[107], Å
	Na	6-8	1.02-1.18		Exp., Mod.	[110, 111, 125]
	K	9-11	1.55-1.64*	Exp.	[214]
	Ca	5-7	1.00*-1.06	Exp., Mod.	[206, 215-217]
	Mg	~ 5	0.66		[218]	[213]

Examples of ionic radius reported in experimental (Exp.) and/or modeling (Mod.) studies of the structure of Na, K, Ca and Mg alumino-silicate glasses. *: no value for this CN is provided by

Shannon [107]

, such that the value for the closest CN is reported hereby.

  This reaction usually does not proceed to completion. Indeed, both H 2 O mol and OH groups coexist in silicate melts, and hence glasses, in proportions defined by temperature[342][343][344][345], water concentration

  glasses concentrations in H 2 O mol and OH -and anhydrous T g GN values (i.e. the T g of glasses synthesized at ambient conditions, which typically contain ~0.02 wt% water according toDeubener et al. [349]). Indeed, ) where C w is the total glass water content, 𝐶 #e a the concentration of hydroxyl groups OH -and 𝐶 e k # `|} the concentration of H 2 O mol species in the glass.

	the reduced T g	* is equal to:
	𝑇 r * =	s t ×	v w t v w tx Wy×s z{ a× s t Wy×s z{ aW"×s { k z v w z{ a v w tx W"×s { k z `|} ×	{ k z `|} v w tx v w	,	(14g)
	with C G = (1-C 𝑇 r ~, 𝑇 r ~!, 𝑇 r #e a and 𝑇 r e k # `|}

w

  Li 2 Si 4 O 9 glasses, up to ~50% of the OH -groups can be bonded to Li + , the remaining fraction forming Si-O-H bonds [[156] Spectroscopic data thus indicate the occurrence of other mechanisms for the solution of water in silicate glasses. The formation of M-OH groups, documented by 1 H and 29 Si NMR spectroscopy as well as Raman spectroscopy and molecular dynamic simulations studies in silicate and aluminosilicate glasses [156, 338, 350-354], should occur through the reaction of H 2 O mol species with Si-O-M bonds (M a network modifier element), following the mechanisms [350]:

	Filled symbols: OH -
	Empty symbols: H 2 O mol
	Figure 39: A) Concentration in mol% of OH -(filled symbols) or H 2 O mol (empty symbols) species in M 2 Si 4 O 9 glasses; B) Concentrations of OH -groups bonded to Si (SiOH) or the alkalis M (MOH) in M 2 Si 4 O 9 glasses represented as a function of the ionic field strength of the alkali element. The total content of OH K Na Li

-groups in the M 2 Si 4 O 9 glasses is also reported and is equal to the sum of the SiOH and MOH contents. Data from

[[156, 344]

  1 H NMR spectroscopy results from a hydrous NaAlSi 3 O 8 glass. Indeed, those authors observed that the23 Na NMR signals from NaAlSi 3 O 8 glasses change significantly with water addition while their29 Si and27 Al NMR signals seemed barely affected. As a result, they proposed that water was mostly reacting with Na + charge-compensator cations.Following this study, further data were acquired on NaAlSi 3 O 8 , NaAlSiO 4 and CaAl 2 Si 6.6 O 17.3 glasses, They explained the strong decrease in T g and viscosity of such glasses and melts [e.g., 357] as resulting from a weakening of T-O-T bonds due to their protonation.Such hypothesis is questioned by recent 1 H-29 Si and 1 H-27 Al heteronuclear correlation NMR experiments[340, 351, 358, 359], which indicate formation of SiOH and AlOH bonds in tectosilicate glasses, with a repartition of proton between them that is a function of the Al/(Al+Si) ratio as well as of the degree of Al avoidance.While the relationships between glass chemical composition and water solution mechanisms are complex, as highlighted by the previous discussion, some other properties intriguingly depend on the glass water content in a simple fashion. For instance, the partial molar volume of water, V m (H 2 O), seems to tend toward a unique value in silicate glasses[311][312][313]. Using density measurements on various water-bearing geologic and simple silicate glasses (mostly Al-bearing),Richet et al. [[313] showed that

leading

Kohn and co. [355, 356]

to propose that water reacts with charge-compensator elements rather than with T-O-T bonds in tectosilicate glasses.

... O bond distance, Å Relative fraction in

  Despite slight differences between different studies in the provided estimations of V m (H 2 O), ex and in situ experiments on silicate melts tend to corroborate the assumption that V m (H 2 O) is independent of O distances around protons in alkali silicate glasses (Fig.40), such that V m (H 2 O) in such glasses must depend on their composition[[341] in particular, the alkali IFS seems to exert a significant influence on Ca and Mg, corroborate the independence of C p (H 2 O) on melt composition. However, those data suggest that the C p values of the OH -and H 2 O mol

	V m (H 2 O).
	glass composition. [312, 314, 315, 360]. However, from water solubility measurements, Mysen [339] indicated that, if V m (H 2 O) was constant at a value of ~ 12.5 cm 3 mol -1 , the H 2 O activity coefficient must increase with the glass Al/(Al+Si) to explain water solubility values observed in Na silicate and Therefore, while V m (H 2 O) appears to be constant in most aluminosilicate glasses, as suggested by the comparable O-H stretching Raman signals from various Al-bearing geologic glasses for instance [361, 362], compositions rich in metal cations may depart from such trend, and, hence, present different V m (H 2 O) as a function of the IFS of the metal cations. The partial molar volume of water in glasses is not the only property that does not depend on water speciation or glass composition. Indeed, analysing different Al-bearing silicate glasses, Bouhifd et al. [363] showed that the partial molar heat capacity of water in glasses, C p (H 2 O), do not depend on glass composition and can be calculated as: 𝐶 3 𝐻 & 𝑂 = -122.319 + 341.631×10 'g 𝑇 + 63.4426×10 'ƒ /𝑇 & . (21) Calculating C M 2 Si 4 O 9 + 17.6 mol% H 2 O O-H

aluminosilicate glasses. On the other hand, keeping the H 2 O activity coefficient constant would imply changing V m (H 2 O) of a few cm 3 mol -1 . Small variations in V m (H 2 O) in glasses actually may be coherent with spectroscopic observations. Indeed, 1 H NMR spectroscopy data reveal strong differences in the O-Figure 40: Relative fraction of protons in alkali tetrasilicate glasses as a function of the O-H … O bond distance. Glasses contain 17.6 mol% nominal water; data are from [341]. p (H 2 O) with eq. (21) and using partial C p values for the other glass oxide components [e.g., 112] allows one to calculate the heat capacity of hydrous silicate glasses. Further recent calorimetric data on water-bearing tephrite and foidite glasses [364], Al-bearing silicate glasses (~40-50 mol% SiO 2 ) rich

  2-[398]. The solubility of sulfate, S 6+ , is further driven by the concentration of Ca in the melt as its solution mechanism can be described by the equation [396]:Various empirical models have been proposed to calculate the sulfur solubility at sulfide and sulfate saturation, either based on empirical approaches[396][397][398][399] or thermodynamic modeling[396, 400, 401],

	S 6+	melt + 4O 2-	melt + Ca 2+	melt ó CaSO 4 anhydrite .	(23)

  . Such solution mechanism is corroborated by the fact that the metal cation IFS influence the solubility of Cl: at given Al/(Al+Si), cations with higher IFS promote solution of Cl[410]. Cl thus may have the tendency to bond with metal cations that present high IFS, as shown by the Cl XANES data ofEvans et al. [415]. Indeed, the latter suggest that, in CaO-MgO-Al 2 O 3 -SiO 2 glasses with variables amounts of Na 2 O, K 2 O and MnO, Cl preferentially associates with Ca and Mg.