Question

Why are there (200) reflexions in the SC lattice even though there are only lattice points on the edges of the cube?

Answer 1

One way to look at it is the following: Recall Bragg's Law, \[n \lambda = 2 d \sin \theta \] in which there are two "unknowns", namely the order of refraction "n" and the interplanar spacing "d". Recall now the formula for the distance between parallel planes, \[ d = a / \sqrt{h^2 + k+^2 + l^2} \] and notice that the (200) planes would be twice as close as the (100) planes. What is meant by the (200) reflection could hence just as well be interpreted as the second order (n = 2) reflection of the (100) planes. In fact, \[ d / n \] is what is extracted from the x-ray diffraction experiments; we just reinterpret the interplanar spacing according to the above equation and set \[ n = 1 \] always.