Solutions to exercises
37
<
<
<
<
<
< ORJ3 6
<
<
<
Q
9
)
S
6
6
D
ORJ.
ò
$)
ORJ.
ò
H
ORJ>L@
E
ORJ3 ) >3 ) LQEDU@
<
<
<
<
<
< ORJ3 6
<
<
<
ORJ.
ò
$)
ORJ.
ò
H
ORJ>L@
ORJ3 ) >3 ) LQEDU@
) L l
Figure 6 – Brouwer diagram for BaF 2 with (a) K AF & K e , and
(b) K AF % K e . P S is the pressure at the stoichiometric point S.
3. a. To derive the expression relating δ to ε, we must express ε as a function
of the site fractions F i l and V
•
F . The formula BaF 2(1+ε) dictates
total number of Ba
total number of F
2(1 )
ε
=
+
or
N
N
N
2(1 )
Ba
F
F
Ba
F
i
ε
+
=
+
#
#
l
(5)
Moreover, we have
N
N
N
4 int
Ba
fluorine sites
erstitial sites
2
1
Ba
=
=
#
37
<
<
<
<
<
< ORJ3 6
<
<
<
Q
9
)
S
6
6
D
ORJ.
ò
$)
ORJ.
ò
H
ORJ>L@
E
ORJ3 ) >3 ) LQEDU@
<
<
<
<
<
< ORJ3 6
<
<
<
ORJ.
ò
$)
ORJ.
ò
H
ORJ>L@
ORJ3 ) >3 ) LQEDU@
) L l
Figure 6 – Brouwer diagram for BaF 2 with (a) K AF & K e , and
(b) K AF % K e . P S is the pressure at the stoichiometric point S.
3. a. To derive the expression relating δ to ε, we must express ε as a function
of the site fractions F i l and V
•
F . The formula BaF 2(1+ε) dictates
total number of Ba
total number of F
2(1 )
ε
=
+
or
N
N
N
2(1 )
Ba
F
F
Ba
F
i
ε
+
=
+
#
#
l
(5)
Moreover, we have
N
N
N
4 int
Ba
fluorine sites
erstitial sites
2
1
Ba
=
=
#