The area, A, of the real space unit cell is given by the cross product of the basis vectors. That is:

A=|asurf x bsurf|=| asurf| | bsurf|sin a

The area, A*, of the reciprocal space unit cell is again given by the cross product of the basis vectors. That is:

A*=|asurf* x bsurf*| = | asurf*| | bsurf*|sin a

= 4p 2/A

Remembering that the unit vector length for the reciprocal lattice is 2p ,

(e.g. |asurf*|= 2p /|asurf|), this means that the reciprocal lattice unit cell area is the inverse of the area of the real space unit cell.


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