Solutions to exercises
273
Figure 108 – Logarithm
of conductivity of TiO 2
as a function of inverse
temperature.
Table 51 – Logarithm of conductivity of TiO 2
as a function of inverse temperature for P O 2 = 10
−18
bar.
[ ]
T K
10
4
8.9
8.53
8.18
7.86
7.56
log σ [S cm
−1
]
− 0.164
0.179
0.463
0.752
0.97
b. The pre-exponential term and the activation energy E a are obtained by
linear regression. We find
° 2.56 10 S cm
7
1
σ =
−
#
and
E
162.2 kJ mol
a
1
=
−
Finally, the expression for conductivity as a function of temperature is
2.56 10 e
Scm
7
1
T
8481
σ =
−
−
#
5. Based on the properties discussed in questions 2 and 3, we conclude that
the operating principle of an oxygen sensor that uses TiO 2 is based on the
variation in electrical conductivity (resistivity) as a function of the oxygen
partial pressure in the gas being analyzed.
The main advantages are
2 the absence of reference system,
2 the very significant variation of the conductivity with oxygen partial
pressure
σ ≈ 10
−4
S cm
−1
in an oxidizing environment
σ ≈ 10 S cm
−1
in a reducing environment
2 the possibility of miniaturization,
2 small fabrication costs.
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