28 December 2018 1 5K Report

Most books on solid state physics and/or crystallography state that the reciprocal lattice is the Fourier transform of the crystalline lattice in real space. I have not, however, come across a demonstration of this.

I attempted the following:

(1) Represent the lattice with a collection of delta functions (Dirac masses), one at each lattice point.

(2) Express the lattice as f(x,y,z), where x,y,z are spatial coordinates in real space.

(3) Find the Fourier transform of f.

My confusion is related to the complex terms in the transform- what do they mean? How do we plot them to generate the reciprocal lattice?

Do we ignore imaginary terms, take absolute values etc?

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