Use of G in X-ray lecture
In the X-ray diffraction lecture the letter G is used for two different purposes: G can be a reciprocal lattice vector, or G can be the set of all reciprocal lattice vectors. This is confusing.
I propose the following solution: let G be the set of all reciprocal lattice vectors (R is used in the same way in real space), and use g for any specific reciprocal lattice vector. Also rewrite the Laue condition to k - k' \in G.