1-An x-ray diffractometer recorder chart for an element that has either the BCC or the FCC crystal structure shows diffraction peaks at the following 2θ angles: 400, 580, 730, 86.80, 100.40, and 114.70. The wavelength of the incoming x-ray used was 0.154 nm.

a) Determine the Bravais lattice of the element.
b) Determine the lattice constant, a of the element.

 2-A copper-target x-ray tube is operated at 40,000 volts and 25mA. The efficiency of an x-ray tube is so low that, for all practical purposes, one may assume that all the input energy goes into heating the target. If there were no dissipation of heat by water-cooling, conduction, radiation, etc., how long would it take a 100-gm copper target to melt? 

(Melting point of copper = 1083^OC, mean specific heat = 6.65 cal/mole/^OC, latent heat of fusion = 3,220 cal/mole.) 

3-Filters for Co K radiation are usually made of iron oxide (Fe₂O₃) powder rather than iron foil. If a filter contains 5 mg Fe₂O₃/cm², what is the transmission factor for the Co K? line? What is the intensity ratio of Co K? to Co K? in the filtered beam? 

Density of Fe₂O₃ = 5.24 gm/cm³,

?/? of iron for Co K? radiation = 59.5 cm²/gm,

?/? of oxygen for Co K? radiation = 20.2 cm²/gm,

?/? of iron for Co K? radiation = 371 cm²/gm,

?/? of oxygen for Co K? radiation = 15.0 cm²/gm. 

4- Determine the values of 2? and (hkl) for the first three lines (those of lowest

2? values) on the powder patterns of substances with the following structures, the incident radiation being Cu K?: (4 points)

(a) Simple cubic (a = 3.00Å)

(b) Simple tetragonal (a = 2.00 Å, c = 3.00 Å)

(c) Simple tetragonal (a == 3.00 Å, c = 2.00 Å)

(d) Simple rhombohedral (a = 3.00 Å, ? = 80^O) 

4- Plot the reciprocal lattice for a polycrystalline sample of a material with a simple tetragonal structure and lattice parameters a=4.0Å and c=5.0 Å.

 5-What strain is required to produce the same broadening as a crystallite size of 5nm? 

6-Using Bragg ‘s law, calculate the diffraction angles (2?) for the first three peaks in the aluminum thin film.

7-Show that the structure factor, I is independent of the shape and size of the unit cell.

8-Calculate the velocity and kinetic energy with which the electrons strike the target of an x-ray tube operated at 50K volts. What is the short-wavelength limit of the continuous spectrum emitted and the maximum energy per quantum of radiation?

  9-Plane A is represented on a stereographic projection by a great circle passing through the N and S poles and the point 00 N, 700W. The pole of plane B is located at 300N, 500W.

(a)Find the angle between the two planes.

(b)Draw the great circle of plane B and demonstrate that the stereographic projection is angle-true by measuring With a protractor the angle between the great circles of A and B.

Find out the magnitude of the maximum non-uniform yield stress required to produce the same broadening as a crystallite size of 5nm if the elastic modulus is equal to ?. Ignore instrumental effect and make necessary assumptions.