2000-07-04: ceria-yttria

GOAL

From 2000-06-27 it appears that in the system $Ce_{0.5}D_{0.5}O_{1.75},\ D=Y,Gd,La$, the $Ce^{4+}/Ce^{3+}$ reduction energy is more favorable than in the corresponding $Ce_{0.5}Zr_{0.5}O_2$ system. So let's do some calcs without zirconia.

This refers to the $Ce_{(1-x)}Y_xO_{2-\frac{x}{2}},\ 0.1\le{}x\le0.9$ system.

Results

$Ce^{4+}/Ce^{3+}$ reduction energy

The $Ce^{4+}/Ce^{3+}$ reduction energy was evaluated according to the procedure outlined in section 2000-06-21: even if the system does not contain zirconia, the mean field analysis remains identical.

Lattice parameter

The following compares presently calculated lattice parameters with the empirical equation of Kim (1989), which, for the present case $Ce_{(1-x)}Y_xO_{2-\frac{x}{2}}$, reads as:

$$\begin{eqnarray*} d_{Ce}&=&0.5413\\ &&+\left(0.0220(r_{Y^{3+}}-r_{Ce^{4+}})+0.00015(z_{Y^{3+}}-z_{Ce^{4+}})\right)100x \end{eqnarray*}$$

with $d_{Ce}$ and the $r$'s in $nm$, or:

$$\begin{eqnarray*} d_{Ce}&=&5.413\\ &&+\left(0.0220(r_{Y^{3+}}-r_{Ce^{4+}})+0.0015(z_{Y^{3+}}-z_{Ce^{4+}})\right)100x \end{eqnarray*}$$

with $d_{Ce}$ and the $r$'s in Å.

The values of the various parameters are (Shannon, 1976):

The accord does not seem to be very good, at least not as good as previously found.

Note that $d_{Ce}$ decreases as the fraction of $Y_2O_3$ increases, notwithstanding that $r_{Y^{3+}}>r_{Ce^{4+}}$. This should be due to the creation of oxygen vacancies. This is handled by the $0.00015(z_{Y^{3+}}-z_{Ce^{4+}})$ term in Kim's model: this is negative for trivalent dopants so that it prevails if the difference in radii is not large enough.

Lattice energy

Representative input file

opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 ce4-30.dump
title
Ce4+ impurity
end

cell
   5.329267   5.329267   5.329267  90.000000  90.000000  90.000000

fractional    5
   Ce4  core  0.0000  0.0000  0.0000  -3.7000  0.7000  0.0000 
     Y  core  0.0000  0.0000  0.0000   3.0000  0.3000  0.0000 
     O  core  0.2500  0.2500  0.2500   0.0770  0.9250  0.0000 
   Ce4  shel  0.0000  0.0000  0.0000   7.7000  0.7000  0.0000 
     O  shel  0.2500  0.2500  0.2500  -2.0770  0.9250  0.0000  
                                                     
space
225

size            9.0  20.0000
centre          0.00 0.00 0.00
impurity  Ce4   0.00 0.00 0.00

species   2
Ce3    core   -4.700000
Ce3    shel    7.700000

buck
Ce4   shel O     shel  1986.8300     0.351070  20.400      0.000 15.000
Y     core O     shel  1345.1000     0.349100    0.0       0.000 15.000
Ce3   shel O     shel  1731.6181     0.363720   14.433     0.000 15.000
O     shel O     shel 22764.300      0.149000   27.890     0.000 15.000
spring
Ce4    291.75000
Ce3    291.75000
O      27.290000