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How does rapid cooling from a melt make a material amorphous?

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A rough, translucent yellow crystal of elemental sulfur displayed against a solid black background. — crystal A crystal form of elemental sulfur. Sulfur has an atomic weight of about 32.06 atomic mass units (amu), which means that its molar mass is 32.06 grams.

Rapid cooling from a melt makes a material amorphous by bypassing the process of crystallization.12

Crystallization requires two distinct processes: nucleation, where atoms adopt a patterned arrangement, and growth, where that pattern extends to surrounding atoms. These processes occur over a specific temperature range as a liquid cools. By cooling the melt rapidly—a process often called quenching—the material is forced to cross the temperature interval between the freezing point ( $T_{f}$ ) and the glass transition temperature ( $T_{g}$ ) so quickly that these crystallization kinetics cannot take place.312

As the temperature drops below $T_{g}$ , the viscosity of the liquid rises enormously, and the molecular response time becomes significantly longer than experimental timescales. Consequently, the liquid-like mobility disappears, and the atomic configuration becomes frozen into a disordered, non-periodic state. This results in an amorphous solid that possesses short-range order due to chemical bonding but lacks the long-range order characteristic of crystals.324