Question

a) A monochromatic x-ray beam gives diffraction of a 18 °C
degree cubic crystal at an angle of 2θ = 150.8 °. When the same
experiment is repeated at a temperature of 318 degrees, the
diffraction angle is 141.6 °. What is the linear expansion
coefficient of this crystal? Calculate.

b) Find the lattice vectors and the angles between the lattice
vectors of conventional and primitive unit cells for surface
centered cubic (FCC) lattice. Find the volume of the unit cells and
obtain the ratio of the volume of the conventional cell to the
volume of the primitive cell. Find out if your result is
correct.

Answer #1

a) Generally, the crystals are expected to expand by
temperature. What are the reasons for this? In which cases, it can
be expected to decrease the size of the objects whose temperature
increases.
b) Explain the reasons for the formation of the forbidden
band.
c) Explain the source of diamagnetism (Paul Langevin 1905).
d) Find the mesh vectors and the angles between the mesh vectors of
conventional and primitive brim cells for volume centered cubic
(BCC) mesh. Find the volume...

1. A powder diffraction pattern is recorded on a sample of an
unknown elemental substance
known to have cubic symmetry. Cu K-alpha x-rays (wavelength of
0.154 nm) are used and the θ
values of the first 7 peaks are 14.22°, 23.64°, 28.05°, 34.55°,
38.17°, 43.99° and 47.45°.
(a) What are the lengths of the reciprocal lattice vectors (or
change in x-ray wave-vector)
corresponding to these Bragg angles?
(b) For a cubic structure, these lengths should be equal to
(2*Pi/a)(h 2...

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