# Crystal

(Difference between revisions)
 Revision as of 11:51, 6 February 2012 (view source)m← Older edit Revision as of 10:40, 13 February 2012 (view source)Newer edit → Line 7: Line 7: - Here $\textbf{a}_{i}^{*}$ and $h_{i}$ are the reciprocal lattice vectors and integer coefficients respectively and the number ''n'' is the minimum for which the positions of the peaks can be described with integer coefficient $h_{i}$. + Here $\textbf{a}_{i}^{*}$ and $h_{i}$ 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 $h_{i}$. The conventional crystals are a special class, though very large,  for which ''n'' = 3. The conventional crystals are a special class, though very large,  for which ''n'' = 3.

## 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.