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 ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Defect Chemical Reaction<br />
5. Intr<strong>in</strong>sic Ionic and Electronic Defect<br />
Concentrations <strong>in</strong> MgO and NaCl. NaCl<br />
The lowest energy <strong>in</strong>tr<strong>in</strong>sic <strong>defect</strong> <strong>in</strong> MgO is the Schottky pair, with an<br />
enthalpy estimated to be 7.7 eV.<br />
The bandgap is rather close <strong>in</strong> value, be<strong>in</strong>g 7.65 eV at room<br />
temperature. At 1673 K the bandgap energy is Eg ~6.28 eV.<br />
For absolutely pure and stoichiometric MgO, the Schottky <strong>defect</strong><br />
concentration is given at a high temperature of 1400 ºC by:<br />
−12<br />
= 2.<br />
5×<br />
10 mole<br />
11 −3<br />
fraction = 1.<br />
4×<br />
10 cm<br />
The electron and hole concentrations at 1673 K are given by:<br />
n=<br />
p=<br />
K<br />
1/<br />
2<br />
i<br />
[ ] [ ] ••<br />
V ′<br />
= V<br />
=<br />
Mg<br />
⎛ E ⎞<br />
⎜−<br />
2 ⎟<br />
⎝ kT⎠<br />
⎛ kT ⎞<br />
⎜ ⎟<br />
⎝2πh<br />
⎠<br />
1/<br />
2<br />
g<br />
( ) ( ∗ ∗<br />
exp 2<br />
)<br />
3/<br />
4<br />
g<br />
N N ⎜ ⎟=<br />
m m exp⎜<br />
⎟ ( 2.<br />
36)<br />
c<br />
v<br />
O<br />
=<br />
K<br />
1/<br />
2<br />
s<br />
⎛ ∆hs<br />
≈ exp⎜−<br />
⎝ 2kT<br />
13<br />
⎞<br />
⎟<br />
⎠<br />
3/<br />
2<br />
e<br />
h<br />
( 2.<br />
35)<br />
⎛ E ⎞<br />
⎜−<br />
2 ⎟<br />
⎝ kT⎠<br />
( 20 −3<br />
) 10 −3<br />
1.<br />
3×<br />
10 cm exp( −6.<br />
28eV<br />
/ 2kT)<br />
= 4.<br />
6×<br />
10<br />
n<br />
= p =<br />
cm
Change language