Exercises
227
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Figure 89 – Electrical conductivity of titanium dioxide
as a function of oxygen partial pressure at various temperatures.
a. Determine the empirical expression σ e = f (P O 2 ) at 1 000 °C
2 in the domain 10
−12
≤ P O 2 ≤ 10
−4
bar,
2 in the domain 10
−20
≤ P O 2 ≤ 10
−12
bar.
b. Deduce the nature of the dominant point defects in the domain
10
−20
≤ P O 2 ≤ 10
−12
bar.
3. a. Show that we obtain the equation for conductivity with P
−¼
O 2 if we consider
Ti i
3•
as majority defect in the oxide instead of Ti i
4•
.
b. If we consider oxygen defects as the dominant defects in the oxide, what
should its effective charge be to obtain an equation for conductivity in
terms of P
−¼
O 2 ?
4. Based on the data given in figure 89 for P O 2 = 10
−18
bar,
a. determine and tabulate the conductivity of TiO 2 as a function of 1/T and
show that the conductivity of titanium dioxide is activated according to
e
0
RT
E a
σ σ
=
−
and plot the curve
log
f T
1
σ = ` j
b. determine the pre-exponential factor σ 0 and the activation energy E a in
kJ. mol
−1
.