the glass transition
Cool a liquid slowly and, at its freezing point, it usually crystallises — atoms snap into a neat lattice and the liquid becomes an ordered solid at a sharp, fixed temperature. But cool certain liquids FAST enough and they cheat: they slip past the freezing point without crystallising, becoming a supercooled liquid, then get thicker and thicker until, over a narrow temperature range, they simply stop flowing and become a rigid glass. That gradual freezing-into-rigidity, without any crystal ever forming, is the glass transition, and the temperature where it happens is called Tg.
The key is that the glass transition is a KINETIC freezing, not a true thermodynamic phase change. As a supercooled liquid cools, its viscosity rockets upward — by Tg it reaches about 10^12 pascal-seconds, so stiff that atoms would need years to shuffle to new positions. Cool past that point and the atoms simply run out of time: they get locked into whatever disordered arrangement they happened to be in, because they can no longer rearrange on any human timescale. So nothing happens to the ARRANGEMENT of atoms at Tg — the structure of the glass just below Tg is essentially the structure of the liquid just above it, frozen. What changes abruptly is how properties like volume and heat capacity vary with temperature: their SLOPE kinks at Tg, rather than jumping discontinuously the way they would at a real melting or freezing point.
The most important and often-surprising fact is that Tg is not a fixed material constant the way a melting point is. Because it is a kinetic effect — a race between cooling rate and how fast atoms can move — cooling more slowly gives the atoms more time to keep rearranging, so they freeze at a LOWER temperature: Tg drifts down (typically by a few degrees per tenfold change in cooling rate). This is the honest heart of the matter: a glass is a non-equilibrium solid trapped by kinetics, and its transition temperature depends on how you made it. That is exactly why the glass transition is classified as a kinetic freezing rather than a genuine phase transition, and why the deep nature of the glass transition remains one of the famous unsolved problems in condensed-matter physics.
Plot the volume of a cooling glass-former against temperature. Along the liquid line the volume shrinks steadily; at the melting point it would drop sharply IF it crystallised — but a fast-cooled sample skips that and keeps following the liquid line down until, at Tg, the line bends to a gentler slope. Cool ten times slower and the bend appears a few degrees lower: same material, different Tg, proving the transition is set by kinetics, not by a fixed thermodynamic point.
At Tg the slope of volume-versus-temperature kinks; the glass is the liquid, frozen in place.
Tg is not a fixed melting-point-like constant and the glass transition is not a genuine phase change. It is a kinetic freezing whose temperature slides with cooling rate — cool slower and Tg drops. Treating Tg as a single fixed number is a common but real error.