Elements of Disorder in Order

Abstract

We must now confess that we have overglamorized reality by describing crystals as a mathematician’s dream frozen into space: a geometrically perfect arrangement of regular rows of atoms extending ad infinitum in severe order at equal distances and in well-defined directions. In reality, crystals are less perfect and more interesting than three-dimensional wallpapers. First of all, they are not stationary. The atoms or molecules execute various complicated movements about their equilibrium posi­tions called lattice points, and if instantaneous photographs could be taken of the particles in a crystal, they would all turn out to be different because of the thermal movement of the particles. The ideal framework of lattice points is only obtained by mental averaging of all such positions. The photographs of our crystal would also reveal that this motion has a fairly large amplitude, and that the amplitude increases with rising tempera­ture. At room temperature it amounts to 0.1–0.2 angstrom, i.e., to a few percent of the repeating period.