A metallic crystal has an fcc lattice with a lattice constant . Explain whether the following planes are allowed or forbidden for X-ray diffraction:
(100), (111), (210), (220)
Calculate the X-ray diffraction angles for the allowed planes. Assume that diffraction occurs in the first order and the X-ray wavelength is .
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In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
Calculate the energy dispersion for s-band in the bcc lattice for the tight binding approximation.
Note: For the central atom located at (0,0,0) in the bcc unit cell, the nearest neighbours are located at , where a is the lattice constant.
Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.
For Chromium () vapour at
with a number density of atoms
calculate:
i) The Larmor diamagnetic susceptibility assuming the atomic radius to be 1.2 A.
ii) The Curie paramagnetic susceptibility.
In an n-type semiconductor the Fermi level lies below the conduction band at
. Calculate the position of the Fermi level when the temperature is raised to
.
Explain the significance of the pseudogap phase in cuprates.
For the energy dispersion relation:
calculate the inverse mass tensor.