Exercises
19
1. What defects are present in a sample of SrF 2 doped simultaneously with
potassium fluoride KF and lanthanum fluoride LaF 3 ? The dopant cations
substitute for Sr
2+
in the solid.
2. What fluoride dopant should be chosen to obtain an ionic conductor via a
vacancy mechanism?
3. Consider preparing a solid solution by mixing 12.1832 g of SrF 2 , 0.0581 g
of KF, and 0.3918 g of LaF 3 .
a. Write the formula for this solid solution in the form (SrF 2 ) 1−α (KF) β (LaF 3 ) γ .
Give the expression relating α, β, and γ.
b. What is the dominant defect in this solid solution?
Data
Elements
Sr
K
La
F
Molar mass [g mol
-1
]
87.6
39.1
138.9
19.0
4. Determine the molar concentration of vacancies (expressed as mol cm
–3
)
for 5% KF doping, given that the cubic-lattice parameter is 5.799 A c .
Exercise 1.6 – Variation of the concentration of structure defects
in pure zirconium dioxide ZrO 2 as a function of oxygen partial
pressure
Zirconium oxide ZrO 2 exhibits a dominant intrinsic Schottky-type disorder.
1. Write the reaction that involves the Schottky disorder in this oxide.
2. Establish the law for the variation in concentration of cationic defects with
oxygen partial pressure for the range of very high oxygen partial pressure.
Data
No defect ionization is considered.
Denote by K S , K g , and K e the constants for the Schottky equilibrium,
the equilibrium with the gaseous phase, and the electronic equilibrium,
respectively.
Consider the case K S & K e .
3. For the same domain, give the law for the variation in concentration of
electrons as a function of oxygen partial pressure.