Page 149 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

126 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

hysteresis in thermal expansion curves caused by thermal cycling. It should be
noted that their experiments were made on dense bars, while electrodes used in
SOFCs are porous in which no geometrical change has been observed on thermal
cycling. This is apparently due to a difference in the relaxation time for oxygen
stoichiometry to reach a new equilibrium value on changing temperature
between dense and porous samples. Particularly in the oxygen-excess region,
longer time is required for equilibration.
LaCo03-based cathodes show TEC values of about 20 x IC1 which are
too high compared to that of YSZ. Attempts have been made to reduce TEC by
doping with Sr and other alkaline earth ions.

5.2.4 Surface Reaction Rate and Oxide ion Conductivity
Oxygen incorporation is a very important process for perovskite cathode
materials because the oxygen stoichiometry can change during cell operation
and also on thermal cycling. The oxygen incorporation rate and the oxygen
flux through the materials can be characterised in terms of two parameters:
the oxygen diffusion coefficient and the oxygen surface exchange coefficient. The
l60/l8O isotope exchange technique provides very meaningful data on these
parameters [30-3 71. During l80 isotope annealing, the net isotope flux crossing
a 02/solid surface is directly proportional to the difference in isotope fractions
between the gas and the solid. This flux is equal to the l80 flux diffusing away
from the surface into the solid. This leads to the following boundary condition:

where D" and k" are the lSO diffusion coefficient and surface exchange
coefficient, respectively. C, and C, are the l80 fractions in the gas and at the
surface, respectively. The solution for a semi-infinite medium with the above
boundary condition has been given by Crank in the following equation [38]:

X

where C'(x,t) is the l80 fraction after being corrected for the natural isotope
background level of l80 (Cb = 0.2%) and for the isotope enrichment of the gas
(C, = 9598%); t is the corrected time of the isotope exchange, and h is a
parameter, h=k*/D*. The labelled stable l80 isotope is analysed by secondary ion
mass spectrometry (SIMS) in the diffusion profiles or in the secondary ion images.
Kilner and co-workers have collected many k* and D* data for perovskites, and
derived a correlation between these two parameters [30]. Figure 5.5 shows
the relation between D" and k", a so-called h-plane plot. A linear regression of the
(logarithmic) data gives a slope near 0.5. This correlation is valid over a wide