Reciprocal Lattice 2D

b/a

1.58114

γ

ab

71.5651

centered

h

1

k

0

This Demonstration indexes the 2D lattice in the left graphic according to the pair of basis vectors

a≡[1,0]

and

b≡[0,1]

defined by the figure. This gives insight into the indexing of 2D electron diffraction patterns, as well as into the reciprocal-lattice indexing of 3D crystals.

On the right, note that the reciprocal-lattice basis vectors

*

b

≡(1,0)⊥b

and

*

b

≡(0,1)⊥a

have lengths inversely proportional to the corresponding inter-row spacing in direct space. Also, the choice of a nonprimitive (centered) unit cell adds lattice points in direct space on the left but subtracts them in frequency space on the right.