# Reciprocal space

The animation below shows the relationship between the real lattice and the reciprocal lattice. Note that this 2D representation omits the **c*** vector, but that it follows the same rules as **a*** and **b***.

The key things to note are that:

- The reciprocal lattice has reciprocal vectors
**a***and**b***, separated by the angle γ*. -
**a***is perpendicular to the (100) planes, and equal in magnitude to the inverse of d_{100}. - Similarly,
**b***is perpendicular to the (010) planes and equal in magnitude to the inverse of d_{010}. - γ and γ* will sum to 180º.

Due to the linear relationship between planes (for example, d_{200} = ½ d_{100} ), a periodic lattice is generated. In general, the periodicity in the reciprocal lattice is given by

\({\rho _{hkl}}^ *\) = \(\frac{1}{{{d_{hkl}}}}\)

In vector form, the general reciprocal lattice vector for the (h k l) plane is given by

\({s_{hkl}}\) = \(\frac{{{{\rm{n}}_{hkl}}}}{{{d_{hkl}}}}\)

where **n**_{hkl} is the unit vector normal to the (h k l) planes.

This concept can be applied to crystals, to generate a reciprocal lattice of the crystal lattice. The units in reciprocal space are Å^{-1} or nm^{-1}