Ionic Conductors: Characterisation of Defect Structure
Workshop 2
Defects, Dislocations and Defect Clusters
1. Make sketches to illustrate the main types of point defect that occur in ionic solids.
2. Using an appropriate sketch, illustrate how thermodynamics predicts that there will be
a finite number of defects present at equilibrium above 0 K.
3. Given that the enthalpy of formation for a Schottky defect in LiCl is 2.34 eV and S’/k
for this process is 9.6 and the Boltzman constant is 8.617343 617343  10-5 eV and
Avogadro’s constant is 6.022  1023, calculate the equilibrium number of Schottky
defects at 298 K in one mole of crystal.
4. Explain the difference between stoichiometric defects and non-stoichiometric defects
and give one example of each
5. Using Kroeger-Vink notation give equations for the following.
(a) Schottky defect formation in LiCl
(b) F- Fenkel defect formation in CaF2
(c) Schottky defect formation in CaF2
(d) Solid solution formation in the anion vacancy solid solution Zr1-xCaxO2-x
(e) Solid solution formation in the Li+ interstitial solid solution Li1+xTi1-xAlx(PO4)3
6. Wustite often shows non-stoichiometry (Fe1-xO). One of the proposed defect clusters
in Wustite is the Koch cluster. This has a ccp array of oxide ions on a fcc cell, with all
octahedral sites vacant and half the tetrahedral sites (all T+) filled with Fe.
(a) Using Kroeger Vink Notation give an equation describing Fe vacancy formation in
wustite.
(b) For values of x over 0, what oxidation states does Fe exist in?
(c) Sketch the structure of the Koch cluster, clearly indicating the octahedral vacancies
and the filled tetrahedral interstitials.
(d) Which oxidation state of Fe would be located in the tetrahedral site?
(e) From the charges on the vacancies and the charges on the interstitials calculate the
net charge on this cluster.
7. Mo9O26 is has a shear structure containing edge sharing groups of four molybdate
octahedra (Mo4O9) and corner sharing MO3 octahedra. Calculate the percentage of
octahedra that are corner sharing. Hint work out the overall M:O ratio, then the
average formula per Mo atom for a an Mo4O9 cluster. Finally use simultaneous
equations to derive the fraction of octahedra that are corner sharing and then convert
to percent.