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Next: 2000-12-15: ceria-scandia Up: Aliovalent cation doped ceria Previous: 2000-09-26. Activation energy for


2000-12-12: ceria-calcia

GOAL

Calculations on the $Ce_{(1-x)}Ca_xO_{2-x},\ 0.1\le{}x\le0.9$ system, to test a $+2$ dopant. $Ca$ potential parameters from Lewis and Catlow (1985), consistent with all other ones.

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. Notation as in section 2000-08-10.

\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{8}R{1}{8}R{1}{8}}... ...9.55264749 \\ 90 & -45.48562569 & -13.36633753 & -13.36633753 \\ \end{tabular}

\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{2}{8}R{1}{8}} \multi... ...0 & 6.15918120 & -0.08416477 \\ 90 & 5.22294500 & -1.85733058 \\ \end{tabular}

\begin{center}\vbox{\input{2000-12-12-01.pslatex} }\end{center}

In the following figure we compare the $Ce^{4+}/Ce^{3+}$ reduction energy as a function of the fraction of oxygen vacancies in the structure (and NOT as a function of dopant composition) for the different dopants. Subscripts are the effective ionic radii of the dopants for 8-coordination, according to Shannon (1976):

\begin{center}\vbox{\input{2000-12-12-04.pslatex} }\end{center}

Lattice parameter

\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{6}} \multicolumn{... ...5.439654 \\ 70 & 5.442366 \\ 80 & 5.445478 \\ 90 & 5.449088 \\ \end{tabular}

No comparison with Kim's empirical equation (Kim, 1989), as we have already seen that the accord does not seem to be bery good in the other cases.

\begin{center}\vbox{\input{2000-12-12-02.pslatex} }\end{center}

Lattice energy

\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{6}} \multicolumn{... ... 70 & -44.54354638 \\ 80 & -37.96367342 \\ 90 & -31.90945152 \\ \end{tabular}

\begin{center}\vbox{\input{2000-12-12-03.pslatex} }\end{center}

Representative input file 

opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 oimp-20.dump
title
O 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  0.8000  0.0000 
    Ca  core  0.0000  0.0000  0.0000   2.0000  0.2000  0.0000 
     O  core  0.2500  0.2500  0.2500   0.0770  0.9000  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  0.9000  0.0000  
                                                     
space
225

size 10.38912042    21.81715289
centre          0.25 0.25 0.25
impurity O      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
Ca    core O     shel  1227.7        0.33720     0.000     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: 2000-12-15: ceria-scandia Up: Aliovalent cation doped ceria Previous: 2000-09-26. Activation energy for