Question

What are the reciprocal and direct lattice structures of a (100) plane of a FCC structure? What are the lattice constants of these direct and reciprocal lattices, provided that the standard lattice constant of the original FCC lattice is a?

Answer 1

Here's is the information I could gather.

In case of FCC, there is no reciprocal lattice vector cooresponding to the plane (100) as the waves diffracted by (100) planes cancel out as a result of phase difference of , because of the intervening plane (200) and the intensity of the diffracted wave is zero. [Introduction to Electron Theory of Metals by U. Mizutani, page 62-63].

Direct lattice vector is = a , = 0 and = 0 , as (100) plane in FCC intersects only the x axis at a.

Lattice constant for the direct lattice is 'a'. Since, reciprocal lattice vectors obtained from FCC planes form a BCC lattice in reciprocal space, the lattice constant for the reciprocal lattice of FCC is 4/a.

Hope this helps you in someway!

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