an amorphous solid
Pour marbles slowly into a jar, letting them settle into neat layers, and you get something like a crystal: the marbles stack in a perfect repeating grid you could photograph once and then predict forever. Now pour the same marbles in FAST, so each one jams wherever it happens to land. Every marble still touches five or six neighbours at roughly the same spacing — nobody is floating in empty space — but the neat rows are gone. There is no repeating grid, no pattern that carries across the jar. That jammed pile is the everyday picture of an amorphous solid: a rigid solid whose atoms are frozen in a disordered, liquid-like arrangement instead of a crystal lattice.
The defining feature of an amorphous solid is the ABSENCE of long-range order. Unlike a crystal it has no unit cell, no lattice, no periodicity you can extend across the sample. But here is the point beginners almost always miss: it is NOT structureless. It keeps sharp short-range order — each atom still has a well-defined set of nearest neighbours at a definite distance and roughly definite bond angles. In amorphous silicon, for example, every silicon atom still sits at the centre of a tetrahedron of four neighbours about 2.35 angstrom away, exactly as in the crystal; what is lost is the long-range registry that would let you predict where an atom sits ten or a hundred spacings away. Because there is no lattice, an amorphous solid produces no sharp diffraction spots — only broad, diffuse halos — and it must be described statistically, by the radial distribution function, rather than by a tidy list of atomic coordinates.
Amorphous solids are all around you: window glass, the silica in optical fibres, the amorphous silicon in solar cells and flat-panel displays, obsidian, hard candy, and many pharmaceuticals. They are usually made by cooling a liquid so quickly that the atoms are frozen before they can line up into a crystal, or by depositing atoms so fast that they cannot find their crystalline sites. One honest caveat about words: amorphous and glass are often used loosely as synonyms, but strictly a GLASS is the special kind of amorphous solid made by quenching a liquid through the glass transition. Amorphous solids made by other routes — vapour deposition, radiation damage, ball-milling — are amorphous but not, strictly, glasses.
Amorphous silicon and crystalline silicon are made of exactly the same atom, bonded the same way — each silicon shares four bonds in a tetrahedron. In the crystal those tetrahedra link up in perfect register, giving a diamond-cubic lattice and razor-sharp X-ray spots. In the amorphous form the tetrahedra are still there, but the bond angles and twists vary a little from site to site, so the pattern never repeats over long distances and the same X-rays give only fuzzy halos.
Same nearest-neighbour bonding, opposite long-range fate: crystal repeats, amorphous solid does not.
The single biggest misconception is that amorphous means disordered all the way down. It does not: an amorphous solid has real, sharp short-range order — definite nearest-neighbour distances — and often medium-range order too. What it lacks is only the long-range periodicity of a crystal.