Lecture handout including QS - Department of Materials Science ...

Qu.Sheet 8 MATERIALS SCIENCE BQ4
Course B: Materials for Devices
(c) The Nernst-Einstein equation indicates that the ratio σ /D for a given material varies
only with temperature. Calculate σ/D for Zr 0.8 Y 0.2 O 1.9 at 800°C.
(d) It is often found that the experimental values differ from those predicted by the Nernst-
Einstein equation. Suggest why this might be the case.
4. The α phase of silver iodide (AgI) has a cubic I lattice with a = 5.0855 Å. It is a Ag +
ionic conductor at 150ºC with a diffusivity of 4.5 × 10 -11 m 2 s -1 . A potential difference is
applied across a sample of AgI, using Ag for both electrodes, and current is allowed to
flow:
e - ↑
Ag + is reduced to Ag at the cathode: Ag + + e → Ag
Ag is oxidised to Ag + at the anode: Ag → Ag + + e
What is the number density of charge carriers in AgI
What is the conductivity of the AgI at 150°C
AgI
anode cathode
What is the mass of silver deposited at the cathode if a current of 5 mA flows through
the circuit for 5 minutes
5. (Tripos Question; 2009)
Describe the phenomenon of pyroelectricity, giving an example of a widespread
application. [15%]
ZnO can have the wurtzite crystal structure. Draw a plan of a 2 × 2 array of unit cells of
this structure, projected down the z-axis and with an oxygen atom at the origin. Describe
this structure in terms of coordination polyhedra. What fraction of tetrahedral interstices
in the anion lattice are occupied by Zn cations [30%]
Assuming that the magnitude of the charge on each ion is 2e, and taking into account the
sharing of oxygen ions between filled interstices, determine the charge due to oxygen
which acts at the centre of charge of one of these anion tetrahedra. Give the fractional
coordinates of this centre of charge. [Hint: the geometric centre of a tetrahedron is 1 / 4 of
the distance from its base to its apex.] [20%]
With the zinc ion positioned at ( 2 / 3 , 1 / 3 , u), show that the net dipole moment of one
tetrahedron is 2ec ( 1 / 8 – u), where c is the lattice parameter (along z). Hence, calculate
the electric polarisation, P, of a single crystal of ZnO at room temperature. What further
information would be required to determine the magnitude of the pyroelectric coefficient
of ZnO [35%]
[For ZnO: a = 0.325 nm; c = 0.521 nm; u = 0.118]
MT13