36
1 – Description of ionic crystals
c. Case of intermediate fluorine partial pressure with
2 ionic defects dominate (K AF & K e ).
Under these conditions, we have
[V
•
F ] = [F′ i ]
2 electronic defects dominate (K e & K AF ).
Here we have the approximation
p = n
The solution of the system of equations (1)–(4) gives the variation in concentration of each defect as a function of P F 2 . The results are gathered in table 6.
Table 6 – Variation of defect concentration as a function of fluorine pressure.
Defect Low pressure
Intermediate pressure
High pressure
K AF & K e
ionic defects
dominate
K AF % K e
electronic defects
dominate
[F′ i ]
∝ P
¼
F 2
= [V
•
F ] = K
½
AF = const.
∝ P
½
F 2
∝ P
¼
F 2
p
∝ P
¼
F 2
∝ P
½
F 2
= n = K
½
e = const.
∝ P
¼
F 2
[V
•
F ]
∝ P F 2
–¼
= [F′ i ] = K
½
AF = const.
∝ P F 2
–½
∝ P F 2
–¼
n
∝ P F 2
–¼
∝ P F 2
–½
= p = K
½
e = const.
∝ P F 2
–¼
Figure 6 shows the Brouwer diagram corresponding to defects in BaF 2 .