Exercises
121
a. Calculate the conductivity of CaF 2 at 661 °C under an argon atmosphere.
b. The evolution of the conductivity under an argon atmosphere and as a
function of temperature is shown in figure 50.
Three temperature ranges are apparent: A: T > 653 °C, B: 477 °C < T < 653 °C,
and C: T < 477 °C.
2 Calculate the activation energy (expressed in eV) in ranges A and B.
2 Deduce the migration energy of fluorine vacancies in CaF 2 and the
formation energy of a pair of intrinsic defects. Justify your answer by
giving the expression for the conductivity as a function of temperature in each temperature range.
<
<
²
7>.@
ORJı>ıLQ6FP
<
@
ƒ&
ƒ&
&
%
$
Figure 50 – Conductivity of CaF 2 single crystal under argon
atmosphere plotted in Arrhenius coordinates (from Levitskii et al., 1976).
c. The study of the conductivity of CaF 2 as a function of oxygen partial
pressure in the temperature range B gives an empirical P
¼
O 2 relationship.
Propose a model that takes into account this result and explain the hypotheses used. Take the mobility of the fluorine vacancies to be independent
of their concentration.