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

Qu.Sheet 8 MATERIALS SCIENCE BQ4
Course B: Materials for Devices
Question Sheet 8
1. (a) Sketch a unit cell of CaF 2 viewed down [001].
(b) Describe the coordination of Ca by F, and of F by Ca.
(c) Comment on the packing of Ca ions and the location of the F ions. How does this
compare with the zinc blende structure
(d) In δ-Bi 2 O 3 , the Bi sub-lattice is the same as that of Ca in CaF 2 and S in ZnS, but the
stoichiometry means that there are vacant anion sites, randomly distributed. Sketch a
possible unit cell of δ-Bi 2 O 3 .
(e) Comment on why δ-Bi 2 O 3 is a fast ionic conductor whilst stoichiometric CaF 2 and ZnS
are not.
(f) Calculate the composition of YSZ (i.e. Y 2 O 3 doped ZrO 2 , Zr 1-x Y x O [2-(x/2)] ) which would
give just one quarter of the oxygen vacancy concentration as in δ-Bi 2 O 3 .
2. (Tripos Question; 2008)
How is a high-temperature cubic zirconia phase stabilised at room temperature and what
are the consequences for its oxygen mobility Describe how such a material might be
used in a hydrogen fuel cell. In your answer refer to the chemical reactions involved and
explain how a voltage is generated. [40%]
Different amounts of yttria (Y 2 O 3 ) are added to zirconia (ZrO 2 ) to produce two ceramic
materials: Y 0.1 Zr 0.9 O x and Y 0.15 Zr 0.85 O y . The molar cation compositions are readily
determined, but what are the molar oxygen compositions x and y [10%]
Both ceramic materials are cubic and give an X-ray diffraction pattern characteristic of
the fluorite structure, in which the first and largest peak is a reflection from the {111}
planes. Using CuKα radiation this peak occurs at 2θ = 30.147° for Y 0.1 Zr 0.9 O x whereas it
is shifted to 2θ = 29.732° for Y 0.15 Zr 0.85 O y . Give a reason for this change in the
diffraction pattern between the two materials. [15%]
(i) What are the oxygen vacancy concentrations, n, in Y 0.1 Zr 0.9 O x and in Y 0.15 Zr 0.85 O y
(ii) At 1000°C the ionic conductivity of Y 0.1 Zr 0.9 O x is 2.5 × 10 -4 Ω -1 m -1 . What is the
ionic conductivity of Y 0.15 Zr 0.85 O y at the same temperature
(iii) Determine the diffusivity of oxygen in Y 0.15 Zr 0.85 O y at 1000°C. [35%]
[ionic radii: Y 3+ = 1.159 Å, Zr 4+ = 0.98 Å, O 2- = 1.28 Å]
3. (a) From the Arrhenius plot in your handout (BH47), showing ionic conductivity versus
inverse temperature for a number of ionic conductors, estimate the activation energy for
ion transport in yttria-stabilised zirconia (YSZ).
(b) In Zr 0.8 Y 0.2 O 1.9 how many oxygen vacancies are there per unit cell If the lattice
parameter of (cubic) YSZ is 0.54 nm, calculate the number density of vacancies.
MT13