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|=|
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.