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 .
For an fcc lattice, the structure factor determines whether a plane (hkl) is allowed for X-ray diffraction. The condition for allowed reflections is that h, k, l are either all even or all odd. If this is not satisfied, the reflection is forbidden. Given planes: 1. (100) → h=1, k=0, l=0 → mixed (odd, even, even) → forbidden 2. (111) ____ ______ ______ ______ _______ _______ _______ ____ ___.
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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.
For a superconducting specimen, the critical fields are and
at
and
respectively. Calculate the critical temperature and critical field at
.
Calculate the resistivity of Silicon at given that its resistivity at
is
.
Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
Calculate the temperature at which the lattice contribution to the specific heat and the electronic contribution to the specific heat become equal in a metal which has a Debye temperature of and a Fermi energy
.
Show that for the superconducting transition in the absence of magnetic field, there is a discontinuity in the specific heat of a superconductor at Tc which can be written as: