PROBLEMS -
1. A transmission Laue pattern is made of a cubic crystal having a lattice parameter of 4.00 Å. The x-ray beam is horizontal. The [OTO] axis of the crystal points along the beam towards the x-ray tube, the [100] axis points vertically upward, and the [001] axis is horizontal and parallel to the photographic film. The film is 5.00 cm from the crystal.
a) What is the wavelength of the radiation diffracted from the (310) planes?
b) Where will the 310 reflection strike the film?
2. A transmission Laue pattern is made of a cubic crystal in the orientation of Prob. 1. Show that the beams diffracted by the planes (210), (213), and (211), all of which belong to the zone [120], lie on the surface of a cone whose axis is the zone axis. What is the angle 4 between the zone axis and the transmitted beam?
3. Determine, and list in order of increasing angle, the values of 2θ and (hkl) for the first three lines (those of lowest 2θ values) on the powder patterns of substances with the following structures, the incident radiation being Cu Kα:
a) simple cubic (a = 3.00 Å),
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, α = 80o).
4. Plot the reciprocal lattice for a polycrystalline sample of a material with a simple tetragonal structure and lattice parameters a = 4.0 Å and c = 5.0 Å. (Use a two-dimensional section through the three-dimensional space).
5. Sketch the Ewald sphere construction for 200 diffraction with Mo Kα radiation and a polycrystalline specimen of a simple cubic substance with a = 3.30 Å. Graphically determine the angular rotation required to orient the sample for 300 d action if a θ - 2θ diffractometer is being used.
6. Diffractometers typically can scan up to, but not beyond, 165° 2θ. For the sample in Prob. 4, what are the indices (i.e., hkl) of the highest angle reflection if (a) Ag Kα radiation is used, (b) Cu Kα radiation is used and c) Cr Kα radiation is used?