Exercises
107
2. Starting from the curve shown in figure 44 and using the Nernst-Einstein
relation, calculate the electrochemical mobility and the diffusion coefficient
of V ′ K at 440 °C and give their units. Assume that all potassium vacancies
of extrinsic origin participate in the conduction.
Figure 44 – Electrical conductivity
of solid solution (KCl) 1−x (BaCl 2 ) x
with x = 1.4 # 10
−4
in Arrhenius
coordinates.
3. From the literature, the diffusion coefficient of K
+
in KCl, which we denote
by D* K, is given by D
e
2 10
K
5
.
kT
eV
0 76
#
=
− −
*
where D* K is in cm
2
s
−1
.
a. Calculate the diffusion coefficient at 440 °C and compare it with that of
V ′
K found above in question 2.
b. Show that the relationship D * K [K
#
K ] = D V K [V ′
K ] is approximately verified.
c. Show that the activation energy of the diffusion D * K of potassium vacancies equals that of the conductivity.
d. Deduce the enthalpy of migration of the potassium vacancies V ′
K given
in kJ mol
−1
.
4. Assume in what follows that the mobility of potassium vacancies V ′
K does
not depend on the doping level x (which remains low). Given that the selfdiffusion coefficient of potassium in a pure KCl crystal takes the form
D
e
4 10
K
2
.
kT
eV
1 48
#
=
− −
*
where D * K is in cm
2
s
−1
,
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