An amorphous material can become mechanically rigid without developing long-range crystalline order. The change from an equilibrating disordered liquid-like structure to a kinetically arrested glass occurs through a glass-transition range.

The glass transition is not ordinary crystal melting. There is no periodic lattice that disappears at one equilibrium melting temperature. Instead, the structural rearrangement time grows rapidly as temperature falls.

When rearrangements are fast compared with the observation time, the disordered structure can relax toward equilibrium. When they become much slower than the experiment or service time, the structure appears frozen. A characteristic glass-transition temperature $T_g$ is therefore operational: its measured value depends somewhat on cooling rate, heating rate and observation time.

This produces physical aging. A glass held below but near its transition can continue slowly rearranging toward lower-energy configurations, changing volume and mechanical response even without chemical reaction.

The same kinetic idea appears in inorganic glasses and in the amorphous regions of polymers. Their molecular structures and mechanical consequences differ, but the central distinction is shared:

$$\text{melting/crystallization: change of ordered phase},$$

$$\text{glass transition: loss or recovery of structural mobility in a disordered material}.$$