38
1 – Description of ionic crystals
or
| |
| |
N
N
F
and N
N
F
2
4
Ba
F
F
Ba
F
i
Ba
F
Ba
i
=
=
#
#
#
#
l
l
By using equation (1), we deduce
|F | 8
|F | 1
F
i
ε
+
= +
#
l
(6)
On the other hand, we have
| | |
|
F
V
1
F
F
•
+
=
#
(7)
and
|F | | V |
i
F
•
δ
−
=
l
(8)
By combining equations (6)–(8), we eliminate two types of site fractions
and obtain
| F |
and
7 | V | 8
8
7
i
F
•
δ
ε
δ
ε
=
+
=
+
l
b. The variation in δ as a function of fluorine pressure
We use the expression
| F | | V |
i
F
•
δ =
−
l
, which we simplify based on the
dominant species in the various ranges of fluorine pressure.
2 High pressures
F i l & V
•
F $ δ ≈ F i l $ δ ∝ P
¼
F 2
2 Low pressures
V
•
F & F i l $ δ ≈ V
•
F $ δ ∝ P F 2
−¼
2 Intermediate pressures
2 Ionic defects dominate (K AF & K e )
F i l ≈ V
•
F $ δ ≈ 0
2 Electronic defects dominate (K e & K AF )
F i l ∝ P
½
F 2 and V
•
F ∝ P F 2
−½
which gives
a P
b P
F
F
2
2
1 2
1 2
.
δ
−
−
where a and b are constants.