Summary
Description 
Demonstration of the reciprocal lattice. A real space 2D lattice with primitive vectors and , shown blue and green arrows respectively. is a general lattice vector, shown red. is a vector from the origin to any point. Plotting plane waves of the form , we see that for any integer combination of reciprocal lattice vector basis and , the resulting plane waves have the same periodicity of the lattice  that is that any translation from point to a point , the value of the plane wave is the same. These plane waves can be added together and the above relation will still apply. 
Date  
Source  Own work 
Author  Hugh Ramsden 
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