Glasses: a liquid that was cooled too fast to crystallise

Cool a liquid fast enough and the atoms get stuck before they can line up

Intuition

Imagine a dance floor where everyone is slow-dancing in a swirl. If the music stops slowly, couples find partners and form neat rows (a crystal). If the lights go out and everyone freezes instantly, they stay stuck in the swirl (a glass). A glass is a liquid that was frozen in place before it could tidy up.

Lecture 24 ended with the point that very deep undercooling can stop nucleation and growth. Lecture 25 looks at what is left: glass. Glass is old (obsidian, ancient flasks) and central to science and technology (lab glassware, optical fibres, phone screens). The lecture quotes P. W. Anderson (Science, 1995): the theory of the nature of glass and the glass transition is probably the deepest and most interesting unsolved problem in solid state theory.

Does glass flow? It does, but absurdly slowly

A popular story says old window panes are thicker at the bottom because glass flows. The lecture says no. Once solidified, window glass does not flow on a scale of millions of years. Cathedral panes with the thick end up are worker mistakes. Ancient Egyptian and Roman glass bowls are not found sagging. The viscosity of glass is a billion times that of the lead holding the pieces in place.

So are glasses solids? The lecture says it is complicated. They are usually considered solids because they do not flow appreciably over very long times. But the line is not clear cut, and you can measure the viscosity of a glass. The slides give a ladder of viscosities.

• Water: 10^-4 Pa s. Ketchup: 10 Pa s.
• Pitch: about 10^8 Pa s. The Pitch Drop Experiment at the University of Queensland began in 1927 and has had 9 drops since.
• Glacier ice (a polycrystalline solid): about 10^12 Pa s.
• Fused silica glass: about 10^18 Pa s (Vannoni et al., 2011). That is a sag of less than 1 nm per year in a glass plate 15 cm across.

Whether this makes glass a liquid depends on where you draw the line.

A glass is an amorphous solid that has a glass transition

Old books define glass as any amorphous (disordered) material, one without the long-range translational order of a crystal. Examples: metallic glasses (Zr-Ti-Cu-Ni-Be), polymeric glasses (PMMA), ionic or covalent glasses (SiO$_2$). In X-ray scattering, crystalline cristobalite shows sharp peaks. Silica glass shows one broad hump near the same position and no sharp peaks.

That definition is too broad, because it also catches wood, foams, granular materials and colloids. The modern definition:

Exam detail

Glass is an amorphous solid that exhibits a glass transition. The glass transition is the gradual and reversible transition between the brittle glassy state and the liquid state as the temperature increases.

The glass transition temperature, $T_g$, is not precisely defined. It is a range that depends on whether the glass was cooled slowly (branch a) or quickly (branch b). $T_g$ is always below the melting point $T_m$ of the crystal.

The sketch is schematic and follows slide 14. Cooled slowly, the glass leaves the liquid line at a lower temperature $T_{ga}$. Cooled quickly, it leaves at a higher $T_{gb}$. Neither reaches the crystal line.

Lecture 25 lists $T_g$ for some materials (in °C): tyre rubber -70, polypropylene -10, PVC 80, polystyrene 95, polycarbonate 145, chalcogenide GeSbTe 150, cotton 230, soda-lime glass 500, fused quartz 1200.

DSC (from Lecture 23) shows two features at the glass transition: the liquid and the glass have different heat capacities, and the change between them is gradual. A trace is a flat baseline, a sigmoid step up at $T_g$, then a higher flat baseline.

The glass transition is about speed, not about equilibrium

Intuition

Think of honey in a fridge. It gets thicker and thicker and finally seems solid, but nothing about it has “switched” like ice forming. It simply got too slow to move. The glass transition is that slowing-down: nothing in the structure changes in kind, the clock just runs out.

The glass transition is not a transition between two equilibrium states.

• As a liquid cools, its viscosity rises. In a viscous liquid diffusion is slow, so atoms struggle to rearrange into the crystalline equilibrium state.
• $T_g$ depends on the cooling rate. So the glass depends on its past, and cannot be the equilibrium state.

This links back to Lecture 24, where very rapid cooling means little nucleation or growth ($T_c$ on the diagram), producing a glass. A glass can be described as a deeply supercooled liquid. Glass-forming substances are those where nucleation and growth are slow because high viscosity inhibits diffusion, such as polymers whose chains cannot move past each other easily.

Glass is metastable: stuck in a shallow dip behind a barrier

A glass is a metastable material, out of equilibrium, and can be thought of as a frozen-in liquid-like structure. Think of a book standing on its edge on a table: it stays, but a knock sends it flat. The slide shows three blocks: stable (a flat cube), metastable (a taller block that is stable until pushed), and unstable (a tilted block). In the energy picture, a metastable state sits in a shallow well. There is an energy barrier to a deeper well, the stable state, and an energy gain on the far side.

So the glass transition is a kinetic phenomenon, not a thermodynamic one. It is the temperature at which thermal energy has become so small that the barrier to crystallisation cannot be crossed on any practical timescale.

Slide 21 shows a potential energy landscape with many local basins and levels marked $T_A$, $T_g$, aged and vapour-deposited glass. A narrow deep well is the crystal and a broad deep basin is the ideal glass. Slide 22 shows a residual entropy for glass formers (B$_2$O$_3$, ethanol, propanol, glycerol, glucose, lactic acid): the curves flatten below $T_g$, with lactic acid and glycerol plateauing near 0.2 and 0.4 (values read from the plot). Slide 20 is a video page with no text.

The lecture’s other metastable materials:

• Martensite with respect to normal steel. Martensite is very hard, which is why steel is quench hardened.
• Diamond with respect to graphite at RTP (room temperature and pressure). Diamonds are not forever.
• Emulsions and colloids with respect to separated phases: milk, mayonnaise, espresso crema.
• Many native protein structures with respect to amyloid fibrils. Misfolded proteins are implicated in dozens of diseases, including Alzheimer’s, Parkinson’s and prion diseases.

Compare

Crystal

Long-range order. Sharp X-ray peaks. A sharp melting point $T_m$. The equilibrium state.

Glass

No long-range order. One broad X-ray hump. A softening range $T_g$ that depends on cooling rate. Metastable, out of equilibrium.

Pitfall

Do not call the glass transition a phase transition. The lecture’s summary says it is not. A phase transition connects two equilibrium states at a definite point. $T_g$ moves with cooling rate, and the glass keeps a memory of how it was made.

Recall

Why does a faster-cooled glass have a higher T_g?

Cooled quickly, the liquid runs out of time to rearrange sooner, so it falls out of equilibrium at a higher temperature. $T_g$ marks where the atoms can no longer keep up with the cooling, which is a kinetic matter.