the amorphous state

If a crystal is neat wallpaper, an amorphous solid is a snapshot of a frozen crowd: atoms packed close together but with no repeating pattern, caught in place before they could line up. The amorphous state is the condition of a solid whose atoms have no long-range order. Window glass is the classic example, a solid, yet its atoms are arranged much like a liquid that stopped moving.

The most important and most misunderstood point: amorphous does NOT mean no order at all. Amorphous solids have sharp short-range order, each atom still has a well-defined set of nearest neighbors at definite distances and angles (in silica glass, every silicon still sits at the center of an oxygen tetrahedron, just as in crystalline quartz). What is missing is the long-range repeat: beyond about a nanometer, the arrangement drifts and never lines up into a periodic grid.

Because there is no periodicity, X-rays scattered by a glass do not add up into sharp spots, instead you get broad, diffuse halos. Amorphous materials often form when a liquid is cooled so fast the atoms cannot find their crystalline positions (rapid quenching), passing through a glass transition rather than a sharp freezing point. Glasses can be optically clear, and metallic glasses can be unusually strong; the lack of grain boundaries and slip planes changes their behavior. Caveat: many real materials are partly crystalline and partly amorphous (many polymers), so crystalline versus amorphous is often a matter of degree.