At high temperatures, matter exists as either liquids or gases. These are characterised by random arrangements of the atoms which are also highly mobile (moving from place to place).

At low temperatures, on the other hand, matter forms crystals. The structure of these is characterised by highly regular arrangements of atoms, which are strongly fixed in location. The atoms in the crystal may still move, but their motion is restricted to vibration about a fixed point. The regularity of a crystal structure can be seen in the formation of "crystal planes" of atoms. These planes can extend over large distances, and can be detected by x-ray diffraction experiments. Crystals are said to show "long-range order".

Generally speaking, crystals form when the attraction between the atoms is strong enough to overcome their kinetic energy and pack them so closely together that they form regular structures. The change of state from a liquid to a solid is known as a "phase transition".