# Question: 1 30 points from the accompanying xrd data taken with...

###### Question details

1. (30 points) From the accompanying XRD data (taken with Cu K-α radiation lambda = 1.5418Å), (a) determine the crystal structure (BCC, FCC or Simple cubic?) of material, (b) index each peak - assign (hkl), and (c) calculate the lattice parameter, a.

2θ: 43.16, 50.30, 73.99, 89.85, 95.03, 116.92, 136.59

(d) Can you guess what this material is?

2. (40 points) (a) Consider a monoclinic lattice in the direct space. Sketch (to scale) a portion of the direct space lattice in the plane defined by base vectors a1 and a2 (a portion of a {001} plane containing the origin; a1 = 2a2 = 4Å; gamma = 60 degrees ). Include lattice points 3,3,0 and -3,-3,0 and all other lattice points at least as close to the origin as these.

(b) Next sketch (to scale) the corresponding portion of the reciprocal lattice (plane containing hk0 type lattice points) and label the lattice points. Be sure to show the base vectors b1 and b2.

3. (30 points) On a copy of the reciprocal lattice sketched in problem 2 above, draw the Ewald sphere (circle) corresponding to an incident X-ray beam (lambda = 3Å) with So in the [110] direction. Terminate So/lambda (a radius of the Ewald sphere) on the origin. Will any diffracted beams of type hk0 be produced? Which ones?