Posted by Saad on March 2, 2015, 2:22 pm, in reply to "Re: Fourier Transform of Any Periodic Function"
Thanks for the reply. Option 1 is easy to understand, but I'm not sure I fully understand Option 2. We need to do a fourier transform over all of space. In option 2, we split the lattice into conventional unit cells. The fourier transform then consists of the sum over appropriate lattice points (NOT all, to avoid multiple counting) multiplied by the fourier transform in the conventional unit cell. Now, in this case, the latter fourier transform itself can be split up into a lattice structure factor and a basis structure factor. Considering this lattice structure factor, and the original sum, we get the same restriction on G as in option 1. The restriction is that G has to be an integer linear combination of primitive reciprocal lattice vectors (Obvious when option 1 considered). In option 2, since we are not using primitive lattice vectors, reciprocal lattice vectors are not primitive, meaning we require additional restrictions on h,k and l, given by the lattice structure factor. Is that right? 
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