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.
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The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
A metallic element has a density of , a lattice constant of
and an atomic weight
. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.
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 the energy dispersion relation:
calculate the inverse mass tensor.
Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
The critical temperature of lead (Pb) of average atomic mass is
. Calculate the critical temperature of a specimen of lead isotope with mass
using the normal isotope effect.