2000-06-24: ceria-zirconia-lanthana

GOAL

$Ce^{4+}/Ce^{3+}$ reduction energy in the $Ce_{0.5}Zr_{(0.5-y)}La_yO_{2-\frac{y}{2}},\ 0\le{}y\le0.5$ 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.

Lattice parameter

The following compares presently calculated lattice parameters with the empirical equation of Kim (1989), which, for the present case $Ce_{0.5}Zr_{(0.5-y)}La_yO_{2-\frac{y}{2}}$, reads as:

$$\begin{eqnarray*} d_{Ce}&=&0.5413\\ &&+\left(0.0220(r_{Zr^{4+}}-r_{Ce^{4+}})\ri... ...a^{3+}}-r_{Ce^{4+}})+0.00015(z_{La^{3+}}-z_{Ce^{4+}})\right)100y \end{eqnarray*}$$

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

$$\begin{eqnarray*} d_{Ce}&=&5.413\\ &&+\left(0.0220(r_{Zr^{4+}}-r_{Ce^{4+}})\rig... ...La^{3+}}-r_{Ce^{4+}})+0.0015(z_{La^{3+}}-z_{Ce^{4+}})\right)100y \end{eqnarray*}$$

with $d_{Ce}$ and the $r$'s in Å.

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

Lattice energy

Representative input file

opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 05-ce3-la20.dump
title
Ce3 impurity
end

cell
   5.329267   5.329267   5.329267  90.000000  90.000000  90.000000

fractional    7
Ce4   core 0.0000000 0.0000000 0.0000000 -3.7000000 0.5     0.00000
Zr    core 0.0000000 0.0000000 0.0000000 2.64999999 0.30    0.00000
La    core 0.0000000 0.0000000 0.0000000 3.00000000 0.20     0.00000
O     core 0.2500000 0.2500000 0.2500000 0.07700000 0.95000     0.00000
Ce4   shel 0.0000000 0.0000000 0.0000000 7.70000000 0.5     0.00000
Zr    shel 0.0000000 0.0000000 0.0000000 1.35000000 0.30     0.00000
O     shel 0.2500000 0.2500000 0.2500000 -2.0769999 0.95000     0.00000

space
225

size            9.0  20.0000
centre          0.00 0.00 0.00
impurity  Ce3   0.00 0.00 0.00

species   9
Ce3    core   -4.700000
Ce3    shel    7.700000

buck
Ce4   shel O     shel  1986.8300     0.351070  20.400      0.000 15.000
Zr    shel O     shel   985.86900    0.376000    0.0       0.000 10.000
La    core O     shel  1439.7        0.36510     0.0       0.0   15.0
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
Zr     169.61700
Ce3    291.75000
O      27.290000