Page 146 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cathodes 123

space covers the space of nine unit cells, while for the SI-,,, it covers three unit
cells. The maximum oxygen excess can be determined from the maximum
number of vacancy excluding spaces available in the lattice. For x > 0.4, there is
no room for the vacancy excluding space around the metal vacancies and this
model can provide a good explanation for the disappearance of the oxygen
excess. However, even in Mizusaki's model, the inappropriate assumption of
constant [Mn;,](=[Mn4+]) was not corrected.
With decreasing oxygen partial pressure, Lal-,Sr,Mn03+d oxides become
stoichiometric as shown in the second plateau in Figure 5.2a. Even in the lower
oxygen partial pressure region (region IV in Figure 5.2a), these oxides show
deficiency from the stoichiometric composition, and oxygen vacancies are
formed. According to Mizusaki [15], the formation of oxygen vacancies can be
represented as:

1
2Mnfvz, + 0; = 2Mn&, + V; + -02 (4)
2

Here again the reduction from Mn4+ to Mn2+ appears to be improper.

5.2.2 Electrical Conductivity
LaMn03-based perovskites exhibit intrinsic p-type conductivity due to changes
in the Mn valence. The electrical conductivity of these materials is greater than
10 S cm-l at 700°C. The electrical conductivity is enhanced by replacing La3+
with lower valence cations (such as Ca2+, Sr2+) or doping with other cations
(Mg2+, Co3+, etc.) for application as a cathode material [21-23,261.
In particular, calcium and strontium doping of LaMnOs has been examined to
improve its electrical conductivity because such doped materials have high
electrical conductivity as well as thermal expansion and chemical properties
compatible with other SOFC component materials. When a La3+ ion is replaced
by a Sr2+ ion, an electric hole is formed on the Mn3+ site to maintain
electroneutrality and this leads to an increase in electrical conductivity:

LaMn03 '5' La~fxS~Mn~f,Mn~03 (5)

Figure 5.3 shows temperature dependence of the electrical conductivity [2 61.
Straight lines in this plot suggest the smalI polaron hopping conduction, which is
generally expressed as follows:
(hKvo)
( f;)
( :)
crT = (crT)"exp - - = A - c(l - c)exp --

where (oT)" and E, are the pre-exponential constant and the activation energy,
respectively. A constant, c, is the carrier occupancy on the sites and therefore
c( 1 - c) indicates the probability of hopping from the carrier occupied site to the
unoccupied sites.