# Crystal

Cristal (Fr). Kristall (Ge). Cristal (Sp). Кристалл (Ru). Cristallo (It). 結晶 (Ja)

## Definition

A material is a crystal if it has essentially a sharp diffraction pattern. The word essentially means that most of the intensity of the diffraction is concentrated in relatively sharp Bragg peaks, besides the always present diffuse scattering. In all cases, the positions of the diffraction peaks can be expressed by

$\textbf{H}=\sum_{i=1}^nh_{i}\textbf{a}_{i}^{*}~~(n\ge 3)$

Here $\textbf{a}_{i}^{*}$ and hi are the basis vectors of the reciprocal lattice and integer coefficients respectively and the number n is the minimum for which the positions of the peaks can be described with integer coefficient hi.

The conventional crystals are a special class, though very large, for which n = 3.