The reciprocal lattice in three dimensions

As with the two-dimensional lattices, the three-dimensional (Bravais) lattices, the direct lattices, are said to occupy real space, and the reciprocal 

A direct lattice of a particular type, (triclinic, monoclinic, orthorhombic, etc.), will give a reciprocal lattice cell of the same type, (triclinic, monoclinic, orthorhombic, etc.). The reciprocal lattice of the cubic F direct lattice is a cubic / lattice and 

The reciprocal lattice of a reciprocal lattice is the direct lattice. 

The lengths of the basis vectors of the reciprocal lattice, a, b and c, are the inverse of the perpendicular distance from the lattice origin to the end faces of the direct lattice unit cell, 100 oio and dooi, that is  

For cubic, tetragonal and orthorhombic lattices, these are equivalent to  

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Imaging of the reciprocal lattice in three dimensions is easily doable in a single crystal diffraction experiment. 

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