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2000-06-23: ceria-zirconia-gadolinia

GOAL

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

$\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}... ... -3.78657904 \\ 50 & -16.82572998 & 19.33743894 & -4.16813065 \\ \end{tabular}$

$\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100y$}} ... ...5 & 12.92404470 & 5.88579164 \\ 50 & 12.64902418 & 5.75349267 \\ \end{tabular}$

$\begin{center}\vbox{\input{2000-06-23-01.pslatex} }\end{center}$

Lattice parameter

$\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100y$}} &\multicolu... ...5.383207 \\ 40 & 5.399176 \\ 45 & 5.415248 \\ 50 & 5.431423 \\ \end{tabular}$

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

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

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

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

with $d_{Ce}$ and the 's in Å.

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

$\begin{tabular}{rD{.}{.}{-1}l} {$r_{Ce^{4+}}$}&0.97&{\it {}\AA}\\ {$r_{Zr^{4+}}... ...}&1.053&{\it {}\AA}\\ {$z_{Ce^{4+}}$}&4&\\ {$z_{Gd^{3+}}$}&3&\\ \end{tabular}$

$\begin{center}\vbox{\input{2000-06-23-02.pslatex} }\end{center}$

Lattice energy

$\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100y$}} &\multicolu... ... 40 & -85.50560172 \\ 45 & -82.98014843 \\ 50 & -80.49642517 \\ \end{tabular}$

$\begin{center}\vbox{\input{2000-06-23-03.pslatex} }\end{center}$

Representative input file


opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 09-ce4-gd40.dump
title
Ce4 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 0.10    0.00000
Gd    core 0.0000000 0.0000000 0.0000000 3.00000000 0.40     0.00000
O     core 0.2500000 0.2500000 0.2500000 0.07700000 0.90000     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 0.10     0.00000
O     shel 0.2500000 0.2500000 0.2500000 -2.0769999 0.90000     0.00000

space
225

size            9.0  20.0000
centre          0.00 0.00 0.00
impurity  Ce4   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
Gd    core O     shel  1336.8        0.35510     0.0       0.000 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