A1 HANDWRITTEN THEN BOX THE FINAL ANSWERS (DO NOT USE AI)

1. BRAGG REFLECTION [40 pts] Consider a monatomic crystal structure on an fcc lat- tice with lattice constant a (length). 10 pts Make a sketch of a family of parallel planes that pass through three adjacent, but noncollinear facial centers. For example, passing through the atoms at (0, a/2, a/2), (a/2, 0, a/2), and (a/2, a/2, 0). 10 pts Provide the Miller indices for the set of such planes. 20 pts Calculate the interplanar spacing and the Bragg diffraction angle corresponding to these planes