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Unfortunately, the absence of proper drawing technology has prevented its use so far. Further vitreous materials are the metallic glasses, containing no anions, that find numerous applications, especially in magnetism, because of the lack of grain boundaries. Finally, carbon-based polymer glasses constitute an important part of our daily life going by the name of nylon, polyvinyl chloride PVC bottles or wraps.

The stable crystal phase is, in this case, quartz. The nonequilibrium nature of glass From the point of view of physics, all glasses represent an excited state, and may, in due course, relax to the crystalline ground state. Crystallization involves two steps: i the nucleation of microscopic bubbles of crystal in the liquid phase and ii their growth, rapidly transforming the whole material into a solid whose structure is an ordered pattern. Nucleation processes tend to be extremely slow in glassy systems on experimental times. Such observation time may be very long, million-year-old silica-rich volcanic glasses not being uncommon.

It is the nature of this structural relaxation which we shall consider in this book, formally encoding it in a generalized thermodynamic framework for glassy systems. As a typical example consider window glass. Each window glass everywhere in the world is far from equilibrium, a cubic micron of such glass neither being a crystal nor an ordinary undercooled liquid.

It is, in some sense, an undercooled liquid that in the glass-forming process has fallen out of its own metastable equilibrium.

The Thermodynamics of the Glassy State | SpringerLink

As mentioned before, the glassy state is inherently a nonequilibrium state: a substance that is glassy in daily life, on a timescale of years, may behave like a liquid on a geological timescale. A thousand-year time lapse movie of a window glass would show a sequence of events akin to the popping of a soap film. Any liquid cooled down to low enough temperature sufficiently fast will become glassy, i. In principle, the larger the variety of molecules is, the easier the glass formation becomes.

Their relaxation time, then, exceeds the time needed to reach equilibrium and they progressively get out of phase with the forcing thermal field, becoming increasingly more decoupled from it. The viscosity Relaxation times in glassy systems scale with viscosity, which indicates the resistance to flow of a system and is a measure of its internal friction.

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Water of 20 degrees Celsius has viscosity 1 8 centiPoise. The viscosity of other substances of common use are reported in the following table. Viscosity has, in general, a strong temperature dependence varying, e. As a parameter, viscosity fixes the different manufacturing processes in a glass tank and industrial terms like strain point, anneal point, softening and working point are all defined for a specific viscosity.

Despite its ubiquitous operational use in industry, it is perhaps the least understood of all glass properties. In silica-based systems the viscosity is dominated by the silica concentration in the system, with high silica percentage having an enormously higher viscosity.

This manifests itself in nature in very fluid lava for low-silicacontaining fluids, or else as explosive volcanism for high-silica-containing ones, where the high viscosity prevents softer energy release. The point at which the viscosity, or relaxation time, are so large that equilibrium no longer exists between the thermal state of the glass-forming system and the surrounding heat bath, is called the glass transition temperature, commonly occurring at about two thirds of the melting temperature in silicabased glasses.

This transition temperature, with its measurable heat effect, discriminates between a glass and an undercooled liquid. There are two typical phenomenological behaviors of the viscosity as a function of the temperature, as temperature decreases towards the glass transition, that have been identified so far.

New Clue In The Mystery Of Glassy Water

In a relatively narrow temperature interval it increases from, say, some centiPoise, the value for water at room temperature, to Poise, where the liquid vitrifies. In ordinary life one may think of sugar-syrup. When heated, it flows easily, when put into the fridge, it becomes solid.

We show a pictorial representation of the viscosity behavior in logarithmic scale. Both laws indicate a very large increase in viscosity or, equivalently, in relaxation time, preventing the material from reaching thermal equilibrium, that, instead, gets stuck in the glassy state.

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During the last decennia two categories of glasses have been distinguished according to the above-mentioned temperature dependence around the glass transition: the strong glasses and the fragile glasses. The materials belonging to the Arrhenius family are designated as strong.

They display a very high viscosity above the melting point. For instance, SiO2 has a viscosity of 2. The materials whose viscosity follows the Vogel-Fulcher law are designated as fragile. The putative flow of window glass Because of the time frame over which it happens, it is difficult to envision flow of very highly viscous fluids.

However, a number of instances have been reported where the inverse was the case, the thinner side down, clearly questioning this view. By invoking old flat glass manufacturing technology, either cutting glass cylinders open or making crown glass, it has been argued that flat glass thickness would vary in antiquated technology and that artisans would systematically put the thick side down.

The jury is, of course, still out on this one. Firstly, the flow observation in ancient windows presumes that they have never been restored or cleaned and have remained in situ since the 12th century. Secondly, some fragments may flow and others may not, depending on the varying silica concentration used by different manufacturers. This concentration, as we have already mentioned, completely dominates the flow behavior of any silica-based glass.

The problem will be addressed more in detail in the next chapter but we anticipate that estimates for flow timescales at environment temperature have been computed, exceeding the age of the universe. Crizzling: the terminator of medieval glass Silica SiO2 is an acidic oxide, which means that it is only soluble in a basic solution and below a pH of about eight it is virtually insoluble. It is, therefore, not surprising that all strong acids hydrochloric, sulfuric, nitric, Resistance to acid leaching or weathering is strongly linked to the amount of silica in the glass and the type of modifier added to it.

For instance, medieval glass is under a continuous threat not due to flow but due to a phenomenon called crizzling or crisseling, causing every large museum to have a conservator for medieval glass and making transport of ancient glass artifacts for an exhibition in other museums a delicate matter. This instability of the glass, including the archetypal sodalime window glass, lowers its defenses against attacks by atmospheric moisture the glasses absorbing moisture from the air are said hygroscopic. Among the most hygroscopic glasses, one has potassium, rubidium or cesium silicates, and, to a minor extent, sodium silicate.

The mixture of sodium with calcium, or lithium, can decrease this absorption. It has been observed that ancient glass is often wet and, when dried, turns wet again. Alkalis usually present in the aqueous film covering the glass, generate a local basic environment in which silica is very soluble, 9 The latter combination is a manifestation of the mixed alkali effect. In due time, these cracks grow and may suddenly destroy the glass. This picture is confirmed by the fact that in archaeology relatively little glass is recovered. Crizzling can be slowed or even halted by treating the glass with soluble lithium silicates, but the dissolved silica cannot be replaced: the degeneration of the material cannot be reversed. The failure of equilibrium thermodynamics for glasses The term thermodynamics was originally coined to describe processes dealing with the flow of heat.

Flow processes are notoriously nonequilibrium processes and it is, therefore, surprising that the word thermodynamics implicitly and tacitly got the predicated equilibrium attached to it. A different, somehow complementary, widespread opinion concerns the inapplicability of many thermodynamic approaches to glasses, depending on the identification of thermodynamics with a theory exclusively concerning equilibrium processes see, e.

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  5. Though similar opinions are diffused in the scientific community, especially among senior scientists, this is clearly a faulty notion because thermodynamics, the dynamics of heat flow, is intrinsically not constrained to equilibrium, which is but an extremely limited case in the total set of thermal flow processes. During a visit to the Newton Institute in one of us, Th. A more recent variant of the same mistake concerns Hawking radiation by black holes.


    Though not always stated in theoretical considerations, it is a two temperature problem, involving the Hawking temperature of the black hole and the 3 K temperature of the cosmic microwave background. Clearly, this is a nonequilibrium situation, akin to glasses [Nieuwenhuizen, b].

    Crystalline and Amorphous or Glassy Solids

    For glasses, a smeared discontinuity in thermodynamic variables such as heat capacity, thermal expansion and compressibility is observed in the vicinity of the glass transition temperature. These discontinuities tend to be damped and smeared out, looking somewhat similar to continuous phase transitions of the mean-field type. The analogy to mean-field type phase transition is not perfect, however, not only because of the smeared out nature of the transition, but also because of the smaller specific heat value recorded below the glass transition temperature.

    In first order phase transitions, there holds the well known Clausius-Clapeyron relation between discontinuities of thermodynamic quantities and the slope of the transition line. For continuous phase transitions, there is a pair of similar relations, called Keesom-Ehrenfest relations [Keesom, ; Ehrenfest, ]. Let us just sketch the confusing situation regarding their application to glasses, as it has existed for decades in literature, postponing a formal discussion to the next chapter. It was investigated experimentally whether the jumps in properties of glass versus liquid still satisfied the two Keesom-Ehrenfest relations for crystalline materials.

    In a very well-known review, Angell [] discusses that one Keesom-Ehrenfest relation, involving a discontinuity in the compressibility is always violated, whereas the other, involving a discontinuity in the specific heat, is commonly but not always satisfied. It has become fashionable to combine these two relations by introducing the so-called Prigogine-Defay ratio.

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    For equilibrium transitions this quantity should be equal to unity. Values below 1 were expected not to be possible, and for glasses typical values are supposed to range between 2 and 5 even though very careful experiments on glassy polystyrene led to a value around 1.

    The Keesom-Ehrenfest relations are characteristic for equilibrium thermodynamics and their failure in applications to glasses has prevented the construction of an equilibrium thermodynamics for glassy systems. This consensus, as we will see, is not well founded as the search for a thermodynamic theory of nonequilibrium systems is a lively field. We shall present in this book a number of instances where a quasi equilibrium fails to describe the physics, such as in its assertion that the original Keesom-Ehrenfest relations are always satisfied for glassy systems, violating experimental observation.

    The challenge, then, lies in developing a thermodynamic description valid for systems not close to equilibrium, with very large orders of magnitude variation in the time dependence of their flow properties, ranging from the picosecond regime to, for silic-rich glasses, the age of the solar system, covering a range of twenty five orders of magnitude. We may expect naively that each time window of a couple of orders of magnitude has its own characteristic dynamics, which is approximately independent of the ones above and below it, and that the existing huge nonlinearity could be segmented in quasi-linear fragments.

    We will see whether this expectation is met, and under which conditions, in the following chapters. Our book is structured as follows. In the first chapter we will review most of the known basic properties of glasses and glass-forming liquids and we will set a unique notation for quantities and phenomena that will hold in the rest of the book. In Chapters 3, 4 and 5 we present and study some simplified models, holding all the characteristic of glass formers, yet being analytically approachable, with the aim of exemplifying and discussing the properties, possibilities and limits of the proposed thermodynamics for the glassy state.

    Chapter 6 is dedicated to the potential energy landscape approach, widely used in numerical simulations of computer glass models, where the concept of effective temperature has been thoroughly investigated. In the last chapter we dedicate some space both to well established theories that we often recall in the book, such as the mode-coupling theory for undercooled liquids, or the replica theory for mean-field glasses, both when quenched disordered interactions are explicitly introduced and when disorder is self-induced, and to recent theories, such as the avoided critical point theory and the random first order transition theory.

    This was the first artificier in glass employed, though without his knowledge or expectation.