Introduction into defect studies in ceramic materials(III) - Positron ...
Introduction into defect studies in ceramic materials(III) - Positron ...
Introduction into defect studies in ceramic materials(III) - Positron ...
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Simultaneous Defect Equilibria:<br />
Equilibria<br />
The Brouwer Diagram<br />
For MgO, there are four <strong>defect</strong>s of <strong>in</strong>terst • •<br />
•,<br />
for<br />
which the relevant <strong>defect</strong>-form<strong>in</strong>g reactions V ′ are: ′<br />
Mg , VO<br />
, e and h<br />
null Mg O V V → ′′ + ′′<br />
•<br />
null = e′<br />
+ h<br />
x 1 ••<br />
OO = O2(<br />
g)<br />
+ VO<br />
+ 2e′<br />
With the respective equilibrium 2 constants:<br />
K<br />
s<br />
Ki = np<br />
( 2.<br />
39)<br />
[ ] 2 ••<br />
1/<br />
2<br />
K R = n VO<br />
PO<br />
( 2.<br />
30)<br />
2<br />
one additional equation is always necessary. This is provided by the<br />
requirement of bulk electrical neutrality.<br />
21<br />
( 2.<br />
11)<br />
( 2.<br />
24)<br />
( 2.<br />
29)<br />
[ ][ ] ••<br />
V ′<br />
V<br />
( 2.<br />
13)<br />
= Mg O<br />
[ ] [ ] ••<br />
′<br />
+ n = 2 V +<br />
( 2.<br />
40)<br />
2 P<br />
VMg O
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