# Crystal

## 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 $h_{i}$ are the reciprocal lattice vectors and integer coefficients respectively.

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