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Next: 2000-07-07: summary for ceria-{Y/Gd/La} Up: Aliovalent cation doped ceria Previous: 2000-07-05: ceria-gadolinia


2000-07-06: ceria-lanthana

GOAL

Calculations on the $Ce_{(1-x)}La_xO_{2-\frac{x}{2}},\ 0.1\le{}x\le0.9$ 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.

\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}... ...& -6.14924820 \\ 90 & -30.50619511 & 4.18556205 & -6.76456388 \\ \end{tabular}

\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100x$}} ... ...80 & 10.23555639 & 3.12811033 \\ 90 & 9.58860593 & 2.34668413 \\ \end{tabular}

\begin{center}\vbox{\input{2000-07-06-01.pslatex} }\end{center}

Lattice parameter

\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100x$}} &\multicolu... ...5.586480 \\ 70 & 5.616721 \\ 80 & 5.648287 \\ 90 & 5.681272 \\ \end{tabular}

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

\begin{eqnarray*} d_{Ce}&=&0.5413\\ &&+\left(0.0220(r_{La^{3+}}-r_{Ce^{4+}})+0.00015(z_{La^{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_{La^{3+}}-r_{Ce^{4+}})+0.0015(z_{La^{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):

\begin{tabular}{rD{.}{.}{-1}l} {$r_{Ce^{4+}}$}&0.97&{\it {}\AA}\\ {$r_{La^{3+}}$}&1.160&{\it {}\AA}\\ {$z_{Ce^{4+}}$}&4&\\ {$z_{La^{3+}}$}&3&\\ \end{tabular}

\begin{center}\vbox{\input{2000-07-06-02.pslatex} }\end{center}

Like with the Yttria and Gadolinia containing systems, the accord does not seem to be very good.

Lattice energy

\begin{tabular}{D{.}{.}{-1}D{.}{.}{-1}} \multicolumn{1}{c}{{$100x$}} &\multicolu... ... 70 & -69.31164275 \\ 80 & -64.81871877 \\ 90 & -60.48691774 \\ \end{tabular}

\begin{center}\vbox{\input{2000-07-06-03.pslatex} }\end{center}

Representative input file 


opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 ovaca-20.dump
title
O vacancy
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  0.8000  0.0000 
    La  core  0.0000  0.0000  0.0000   3.0000  0.2000  0.0000 
     O  core  0.2500  0.2500  0.2500   0.0770  0.9500  0.0000 
   Ce4  shel  0.0000  0.0000  0.0000   7.7000  0.8000  0.0000 
     O  shel  0.2500  0.2500  0.2500  -2.0770  0.9500  0.0000  
                                                     
space
225

size            9.0  20.0000
centre          0.25 0.25 0.25
vacancy         0.25 0.25 0.25

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
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
Ce3    291.75000
O      27.290000

next up previous contents
Next: 2000-07-07: summary for ceria-{Y/Gd/La} Up: Aliovalent cation doped ceria Previous: 2000-07-05: ceria-gadolinia