Problemsamling

Lattice Dynamics (LD)
1. The Debye temperature of diamond is 2000 K, its density is 3500 kgm -3
and the interatomic spacing is 0.15 nm. Calculate the velocity of sound
in diamond. Make an estimate of the dominant phonon wavelength at
300 K and the frequency of lattice vibration to which this corresponds.
The Free Electron Model (FEM)
1. Calculate the Fermi energy EF for Na, Li and Al with the help of suitable
information from a handbook. The normal valences can be assumed.
2. In a measurement of the resistance of a copper wire, the voltage was
measured to be 1.7 mV when the current was 0.5 A. The wire has a cross
sectional area of 1 mm 2 and is 20 cm long (between the voltage contacts).
Determine the average mean free path for a conduction electron if one
takes a valence of one for copper.
3. Determine the order of magnitude of the electric field strength that is
required to bring about a field induced "shift" Δk of the Fermi surface for
copper, that is equivalent to 1% of the wavevector kF.
Use the free electron model with a valence of one and the relaxation time
for copper at room temperature. What value of the current density is valid
for the field estimated?
4. Let the electrical conductivity be given by σ = ne 2 τ/m. What temperature -
coefficient should we expect to find for the resistivity of copper in the
interval 0 to 100 ˚C if the relaxation time is assumed to be independent of
temperature? Discuss the result in comparison with the experimental value
for the temperature coefficient.
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