Assume that we have a crystal with SC structure with no basis atoms (each atom sits at the Bravais lattice point). The lattice constant is ‘a’. Assume that the crystal is aligned so that each side of the cube is parallel to each of Cartesian Coordinate x, y, and z. Assume an incoming X-ray in a direction of (1,0, -1) with wavelength of (a/sqrt (2)). (a) Construct Ewald sphere. (b) For the reciprocal vectors which fall on the Ewald sphere, represent them in the Cartesian Coordinates. (c) For each of the reciprocal vector on the Ewald sphere, there exist a family of lattice planes. Calculate the spacing of the family of lattice planes for each corresponding reciprocal lattice vector. (d) For each reciprocal vector in (b), represent the direction of the outcoming wave. Calculate the angle between incoming and outcoming waves for each constructive interference.