free volume
Picture a crowded room where people can only move if there happens to be a gap next to them to step into. If the room is packed to the walls, nobody can budge; leave a little slack — some empty space scattered about — and people can shuffle, swap places, and flow past each other. In a liquid or glass, that scattered slack is the free volume: the extra empty space, beyond the bare minimum the atoms need just to touch, that lets atoms actually move and rearrange. It is the 'elbow room' distributed through a disordered material.
More precisely, free volume is the difference between the actual volume an atom occupies on average and the minimum volume it would take up if packed as tightly as possible. In a liquid there is plenty of it, so atoms constantly trade places and the liquid flows. As the liquid cools, it contracts and the free volume shrinks; atoms find fewer gaps to jump into, so they move more sluggishly and the viscosity climbs. In the free-volume model of the glass transition, when cooling squeezes the free volume below some critical amount, there is no longer enough room for cooperative rearrangement, motion effectively stops, and the liquid freezes into a glass at Tg. Once frozen, a glass carries an EXCESS free volume locked in from the liquid — which is why a glass is slightly less dense than the same material would be as a crystal, and why annealing a glass just below Tg lets it slowly densify as trapped free volume leaks out.
The free-volume idea is powerful because it links, in one intuitive picture, why liquids thicken on cooling, why the glass transition happens, and why atoms move faster in a loosely packed glass than a dense one — it underlies the well-known WLF description of how viscosity varies near Tg, and it explains why metallic glasses soften and flow when deformation creates extra free volume. But be honest about its status: free volume is a simplified, semi-quantitative model, not a directly measured quantity with one rigorous definition. It captures the essential intuition beautifully, yet the full story of the glass transition needs more than free volume alone, and researchers rightly treat it as a useful picture rather than the complete truth.
Deform a metallic glass hard and it does not slip on planes like a crystal — instead, atoms shoved past each other locally create extra free volume, and deformation concentrates into thin shear bands where that loosened, higher-free-volume material flows. Heat the same glass just below Tg and the reverse happens: trapped free volume slowly anneals out and the glass densifies by a fraction of a percent.
Free volume is the scattered 'elbow room' that lets atoms move; squeeze it out and motion freezes.
Free volume is an intuitive, semi-quantitative model, not a directly measurable quantity with a single rigorous definition. It captures the key physics of the glass transition beautifully but does not fully explain it — treat it as a useful picture, not the whole story.