26
1 – Description of ionic crystals
B – NiO doped with Li 2 O
The equilibrium corresponding to the intrinsic disorder is
Ni
#
Ni m V ′′
Ni + Ni
••
i
The reaction for doping NiO with Li 2 O is
Li 2 O + 2
1
O 2 $ 2Li ′
Ni + 2O
#
O + 2h
•
The appearance of electron holes h
•
gives rise to p-type semiconductivity.
The electroneutrality relation is
2[Ni
••
i ] + p = [Li ′
Ni ] + 2[V ′′
Ni ] + n
Note – Some of the holes created are trapped by the nickel. Under these conditions, we can write
Li 2 O + 2
1
O 2 + 2Ni
#
Ni $ 2Li ′
Ni + 2O
#
O + 2Ni
•
Ni
Using x to denote the doping level gives
2
1
xLi 2 O +
1
4 xO 2 + (1 − x)NiO $ xLi ′
Ni + O
#
O + (1 − 2x)Ni
#
Ni + xNi
•
Ni
C – La 2 O 3 doped with SrO
1. Consider the reaction for doping La 2 O 3 with SrO.
The equilibrium describing the dominant disorder in La 2 O 3 is
O
#
O m V
••
O + O ′′
i
The reaction to introduce SrO is
SrO $ Sr ′
La + O
#
O + 2
1
V
••
O
or
xSrO + 2
1
(1 −x)La 2 O 3 $ xSr ′
La + (1 −x)La
#
La + 2
1
(3 − x)O
#
O + 2
1
xV
••
O
The electroneutrality relation is
2[V
••
O ] + p = [Sr ′
La ] + 2[O ′′
i ] + n
2. Consider the reaction to dope LaMnO 3 with SrO
a. The Schottky equilibrium in LaMnO 3 and the corresponding equilibrium
constant are written as
0 m V
3
′
La + V
3
′
Mn + 3V
••
O ; K S = [V
3
′
La ] [V
3
′
Mn ] [V
••
O ]
3