chapters · 00 the material
Every color here is computed from absorption spectra through the CIE 1931 observer, under the lamp at the foot of the screen. The same lesson sits on the walk between its neighbors.
Glass is a liquid that stopped
Cool most liquids and at one temperature their atoms drop into a repeating crystal. Cool a silicate melt and it only gets stiffer, smoothly, until it is too stiff to rearrange at all. What is left keeps the liquid's disorder and gains a solid's rigidity. Glass has no melting point, and everything a glassblower does depends on that slow stiffening.
A network with no pattern
Silica is the network former. Each silicon sits inside four oxygens, a tetrahedron, and each oxygen is shared by two tetrahedra: a bridge. In quartz the tetrahedra join in a repeating pattern. In silica glass they join just as firmly, corner to corner, but the rings they close have five, six or seven members in no order. W. H. Zachariasen proposed this picture in 1932 from the rules an oxide must obey to form a glass, eighty years before a sheet of silica glass two atoms thick was imaged atom by atom and looked like his drawing (Huang et al., 2012).
Pure silica glass is too stiff for any studio furnace. Soda is the flux. Each Na₂O brings one more oxygen, which cuts a bridge into two non-bridging oxygens with a sodium ion beside each. Fewer bridges make a looser network that flows at lower temperature. A soda–silica glass also dissolves in water; it is sold as water glass. Lime is the stabilizer. A Ca²⁺ ion holds two non-bridging oxygens at once and moves far less readily than sodium, so the glass stops leaching.
Model. Drawn in two dimensions, as Zachariasen drew it: triangles stand in for tetrahedra, with three corners instead of four. The glass is made from the crystal by Stone–Wales bond switches and spring relaxation, after Wooten, Winer and Weaire's method for amorphous silicon (1985); it is a sketch of that method, not its energy-minimised result. The drawing cuts the same fraction of corners that the composition does in three dimensions, NBO/T = 2x / (1 − x) for a mole fraction x of modifier oxide, with potash counted alongside soda and alumina ignored. Sodium and calcium ions are placed in the gap they open, not at modeled sites. The standard glass is NBS glass No. 710: 70.5 SiO₂, 8.7 Na₂O, 7.7 K₂O, 11.6 CaO by weight.
Falling out of equilibrium
The atoms of a liquid are always rearranging, and the time that takes, the relaxation time, grows with viscosity. Cooling gives them less time at each temperature. At some point the melt can no longer keep up and its structure freezes in as it was. That point is the glass transition, Tg, and it belongs to the cooling as much as to the glass: cool faster and the structure freezes in hotter, looser and larger. A quenched glass and a slowly cooled one of the same batch differ in density and refractive index.
Model. Relaxation time τ = η / G∞ (Maxwell), with G∞ ≈ 30 GPa as in Zanotto (1998) and η from the curve below. The melt falls out of equilibrium where q · τ · |d ln τ / dT| = 1: where the time to cool through one e-fold change in τ has grown as long as τ itself. At 10 K/min that gives Tg near 552 °C, close to the measured annealing point of 546 °C, as the usual rule of thumb (Tg near η ≈ 10¹² Pa·s) expects. Below 560 °C the viscosity fit is extrapolated, so the slow end of the slider is the least certain. Volumes are schematic: the liquid is drawn expanding three times as fast as the glass, and the transition is smoothed over a few kelvin. Crystallization, which a very slow cool through the liquidus range invites, is not modeled here; the Structure Lab runs it with atoms.
One curve runs the studio
Viscosity is the number the studio works by. Between the melting point and the strain point it rises by more than twelve orders of magnitude, and every step in making a piece sits somewhere on this one curve. Glassmakers name its points: melting, where the melt is runny enough for bubbles to rise out; working, stiff enough to hold a shape on the pipe; softening, where a hanging fiber stretches under its own weight; annealing, where stress relaxes in minutes; and strain, where it takes hours and below which nothing moves at all on a human timescale. For scale, water is 10⁻³ Pa·s.
Measured, then fitted. The curve is the Fulcher fit to NBS standard glass No. 710, log₁₀ η [poise] = -1.626 + 4239 / (T − 265.7) with T in °C, fitted to measurements from 560 to 1400 °C by Napolitano and Hawkins (1964); it is drawn solid where it was fitted and dashed where it is extrapolated. Rings are the average of the laboratories' measured softening (724 °C), annealing (546 °C) and strain (504 °C) points. The fit runs 25 °C hot at the strain point, the usual sign that a Fulcher curve rises too steeply below its range. The furnace and glory-hole marks are typical studio temperatures, not measurements, and studio color glasses each have their own curve. The sag time, η / (ρgR) for a 10 cm gather of density 2.5 g/cm³, is an order of magnitude, not a prediction. The gather is drawn in its cold color, clear glass with its trace of iron; how it glows is stage 04's subject.
Do old windows flow?
A popular story says medieval windows are thicker at the bottom because glass is a very slow liquid that has run downhill. The curve above cannot answer the question: its fitted form goes to infinity at 266 °C, far above room temperature. Zanotto (1998) instead extrapolated the gentler curve of germania glass, which stiffens more slowly on cooling than window glass and so gives a lower bound, and found a room-temperature relaxation time near 10³² years, against a universe about 10¹⁰ years old. By his estimate a medieval glass would have to be held near 414 °C to flow noticeably in 800 years. Gulbiten, Mauro and colleagues (2018), working from the composition of 13th-century glass at Westminster Abbey, found it could flow about a nanometer in a billion years.
The thick bottoms come from how the glass was made. Window glass was blown into cylinders, split and flattened by hand, so panes came out uneven, and glaziers often set the heavy edge down.
Zanotto, Do cathedral glasses flow? ↗ Gulbiten, Mauro, Guo and Boratav, Viscous flow of medieval cathedral glass (2018) ↗ Zachariasen, The atomic arrangement in glass (1932) ↗ Wooten, Winer and Weaire, Computer generation of structural models of amorphous Si and Ge (1985) ↗
explain it back5 questions. Answer each in your head, then open it.
Why does adding soda make a silica melt flow at a lower temperature?
Each Na₂O brings an extra oxygen that cuts a bridge between two tetrahedra into two non-bridging oxygens. With fewer bridges the network is looser, so it flows at lower temperature.
Lime and soda both break bridges. Why does lime make the glass last instead of dissolve?
A Ca²⁺ ion holds two non-bridging oxygens at once and moves far less readily than Na⁺, so the glass stops leaching in water. Soda–silica glass alone dissolves; it is sold as water glass.
Two pieces of the same batch were cooled at different rates. Which has the higher glass transition temperature, and why?
The one cooled faster. Tg is where the melt's relaxation time outgrows the time cooling allows, so faster cooling makes the structure freeze in sooner, at a higher temperature, looser and less dense.
Name the viscosity points from runniest to stiffest and what each is for.
Melting (bubbles rise out), working (holds a shape on the pipe), softening (a hanging fiber stretches under its own weight), annealing (stress relaxes in minutes), strain (stress takes hours; below it nothing moves on a human timescale).
Do medieval windows flow? What is the evidence?
No. Extrapolated viscosity gives room-temperature relaxation times near 10³² years (Zanotto 1998), and Westminster Abbey glass would flow about a nanometer in a billion years (Gulbiten et al. 2018). The thick bottoms come from hand-flattened cylinder glass set heavy edge down.
go further
- Structure Lab lab
- Network lab lab