Glass or Crystal: A Matter of Time
Hervé Arribart, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris
René Vacher, Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier
Glass, an ancient and familiar material of many uses, is also the exemplar of a class of solid-state substances. Solids may exist in two different forms, crystal or glass. For example, silica, or silicon dioxide SiO2, exists in nature on the form of quartz crystals, but it can be prepared as a glass. While they have the same chemical composition the two substances have quite dissimilar properties and performances, the most remarkable difference being that it is possible to make the glass in virtually any shape, including fiber, by deforming it at an appropriate temperature, while the crystal can only be cold shaped, using mechanical tools. Glass and crystal make up two different materials with different structures. To understand the reasons for the striking polymorphism of such chemical substances, one has to include time as a major parameter in the design of materials. More precisely it’s a matter of speed in the making process.
A frozen liquid
The main difference between crystal and glass is structural.1 To understand it, we must refer to the liquid state. Liquids are obtained from solids by heating them above a certain temperature, termed melting temperature. For instance, the melting temperature of quartz is 1650 °C. In the crystal, molecules form an ordered, rigid lattice, the chemical bonds holding adjacent molecules close to each other (figure 1 left). When the melting temperature is reached, the thermal agitation breaks this perfect organization: the chemical bonds between molecules are continuously broken and rebuilt at high rate (at the picosecond scale), and molecules take distance from each other in a random way, leading to a dynamic structure which is neither fixed nor ordered as it was in the crystal phase (figure 1 middle). While molecules are constantly making and breaking their bonds, they move relatively to each other and become free-flowing, rendering the material fluid, which is the main characteristic of the liquid state. The glassy state, or vitreous2 state, has common features with both the crystalline state and the liquid state. Like a liquid, its structure is disordered (figure 1 right). In fact, for a given substance, it is impossible to make the difference between the structures of the liquid and of the corresponding glass: a snapshot of the molecular arrangement in the liquid is undistinguishable from that in the glass. But, like a crystal, glass doesn’t flow because its chemical bonds are permanent. We can say that glass is a frozen liquid – and indeed we will see in the next section that it is obtained by freezing the liquid – with the stiffness of a solid.

Figure 1 (credit : Lucy Reading-Ikkanda/Quanta Magazine)
The melting transition should be reversible: if we start at low temperature with a given substance in the solid state and heat this substance, then the solid transforms into a liquid at the melting temperature. Inversely, if we start from the high temperature side, above the melting temperature, the substance is in the liquid state; if we cool it, it should transform into a solid. But at what temperature? and which solid state can we expect, the vitreous state or the crystalline state?
Why speed matters
The transition between the liquid to glass or crystal depends on the speed of cooling. If the temperature decreases slowly, crystallization occurs at the melting temperature. Fast cooling avoids crystal formation and gives a glass at a lower temperature. This practical knowledge has been translated in scientific terms thanks to thermodynamics. The “choice” of the glassy or the crystalline state is explained by a general law of nature that any system evolves towards thermodynamic equilibrium, i.e. the state of lowest internal energy. As in all known substances the crystalline state is of lower internal energy than the vitreous state, we should always obtain the crystalline state, which, as we have seen, is not the case. How can thermodynamics be violated?
It is a matter of kinetics: if the cooling rate is fast enough, the molecules have no time enough to re-order. As the temperature becomes lower and lower, the thermal agitation is less and less efficient for them to move relatively to each other: they are frozen in the configuration they had in the liquid state. What does ‘fast enough cooling rate’ mean? It depends on the substance. In some substances, known as non-easily glass-forming substances, it must be very fast indeed, of the order or faster than one million degrees per second. This is the case of most glass-forming metal alloys. But, in easily glass-forming substances, this rate may be much slower, of the order of one degree per hour for silica (more than one trillion times slower than in the previous case!), for example. Incidentally, this need for a ‘fast enough cooling rate’ for glass formation is the reason why there are virtually no natural glasses on Earth, the only exceptions, such as obsidian, being near volcanoes or at places where meteorites have fallen. In both cases, the conditions for a fast cooling rate of rock melt are gathered. Glasses are therefore in a thermodynamically non-equilibrium state, and they are energetically trapped in this state. The latter is called ‘metastable state’ because it is in between the excited state of molecular agitation and the lower state of equilibrium. It has a longer lifetime than the former and a shorter lifetime than the ground state of equilibrium.
Fine-tuning properties through quenching
The fact that the material ‘would prefer’ to be in the crystalline state is illustrated by the observation that it is not necessary to heat it again up to the melting temperature for finding a pathway to crystallization. Heating at a temperature certainly relatively high, but below the melting temperature, can be enough, especially if some catalysts that help crystallization are introduced in the composition. It results in the formation of a composite glassy-crystalline material in which small crystals nucleate and grow in the glass matrix. The size of these crystals can be controlled by the residence time of the material at the recrystallization (also termed ‘devitrification’) temperature. Thanks to such observations glass manufacturers are able to fine-tune the properties of their products. For example, introducing crystals in a glassy structure affords mechanical reinforcement. This observation was the source of the invention of a new class of industrial materials known as glass-ceramics.3 Their unique thermal and mechanical properties make them particularly useful for the manufacture of cooktop panels.
The temperature at which the liquid becomes a glass is called the ‘glass transition temperature’. For a given composition the glass transition temperature depends on the quenching rate: the faster the cooling (case b versus case a in figure 2), the more the glass transition occurs at high temperature. The explanation is simple: as thermal agitation decreases with temperature it prevents crystallization in rapid cooling. And the sudden temperature decrease forces the molecules to stay still in the glassy state. The slower the cooling, the lower the temperature where the supercooled liquid can exist before freezing into a glass. The value of the glass transition temperature can vary over a wide range: for certain material’s compositions, this transformation range can extend over more than 100 °C.

Figure 1 (from P.G. Debenedetti and F.H. Stillinger. “Supercooled liquids and the glass transition”. Nature, Vol 410, 8 March 2001)
The direct consequence of the above is as follows: at any temperature below the glass transition, the specific volume of glasses of the same composition varies with the speed at which they have been tempered. This is also true for many properties such as refractive index, elastic moduli, etc. In addition, if a glass sample is brought to a temperature within the transformation interval, maintained for a sufficient time at this temperature, then cooled rapidly, its properties become those of a glass whose transition temperature is that temperature. We can conclude that, as the microscopic organization of the supercooled liquid varies with temperature, this organization is fixed at the glass transition and determines the properties of the resulting glass.
This is also true for the surface of the glass. In the liquid state, the liquid-air interface is traversed by thermal stirring waves. These waves freeze at the glass transition and are the cause of the roughness of the glass surface. In vitreous silica as well as in conventional glasses, this roughness is of the order of one nanometer. The study of glass fibers makes it possible to highlight the important consequences of rapid cooling. In particular, optical fibers are obtained from a ‘preform’, a glass cylinder a few centimeters in diameter, the composition of which is very close to pure silica. These preforms are heated until they become a viscous liquid, then stretched to obtain fibers whose diameter is a few hundred micrometers. This treatment leads to very rapid cooling. Also, in this case, glass is formed in the presence of strong unidirectional stretching. A recent study by atomic force microscopy shows that the glass surface is strongly affected by these drastic preparation conditions4 . The surface of the fiber is very much flatter than that of the preform: the roughness reaches only 0.15 nanometers, which is approximately the distance between the silicon atom and its oxygen neighbor in silica. This is explained by the fact that the high cooling rate does not allow thermal motion waves to settle down. In addition, while the surface roughness of the preform is isotropic, i.e. the same in all directions, the image of that of the fiber surface is anisotropic: it shows streaks in the direction of stretching. The diagram of figure 1 makes it possible to propose an explanation for this result. The glass lattice presented in this figure comprises rings of several atoms. If we deform this lattice by stretching, it is much easier to change the angle of the bonds in the rings than to change the distance between neighboring atoms. During fiberizing, the glass becomes more and more viscous, the stressed rings elongate in the direction of this stress, then freeze in this position: the surface of the fiber remembers the direction in which it has been stretched.
Still a scientific mystery
The intimate structure of a potentially glass-forming substance is therefore dependent on its thermal history; it is governed by the temperature evolution as a function of time during the cooling from the liquid state or during re-heating at the devitrification temperature. Two important consequences are i) that glass only exists if there is not enough time for thermodynamics to do its work, and ii) that the physical properties of the obtained glass depend on the cooling rate.
These facts have been known for centuries and they have given rise to a large variety of industrial processes in the glass industry. Yet, they rely on a mystery in physics: we are far to understand the structural evolution which occurs in the liquid at the vicinity of the glass transition temperature. Philip W. Anderson, a Nobel Prize-winning physicist at Princeton, wrote in 1995: “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition.” The situation has not changed much since.
- For an introduction to glass science, including the structure of glass and the liquid-to-glass transformation, see: Zarzycki, J, “Glasses and the vitreous state”, Cambridge University Press (1991) [↩]
- From the latin vitrum, glass. [↩]
- For an history of the glass-ceramics discovery by its inventor, see: Stookey D., “Journey to the center of the crystal ball: An Autobiography”, American Ceramic Society. ISBN 978-0916094690. [↩]
- B. Bresson, C. Brun, X. Buet, Y. Chen, M. Ciccotti, J. Gâteau, G. Gasion, M.N. Petrovich, F. Poletti, D.J. Richardson, S.R. Sandoghchi, G. Tessier, B. Tyudoki, and D. Vandembroucq, Phys. Rev. Lett. 119, 235501 (2017). [↩]

