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2000-07-17: ceria-

GOAL

Calculations on the $Ce_{(1-x)}Mn_xO_{2-\frac{x}{2}},\ 0.1\le{}x\le0.9$ system, to test a cation much smaller than $Ce^{4+}$ for which we have a potential consistent with the other ones.

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.

$\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{8}R{1}{8}R{1}{8}}... ... -6.96469803 \\ 90 & -17.58218019 & 17.65084022 & -7.86429788 \\ \end{tabular}$

$\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{2}{8}R{1}{8}} \multi... ...0 & 11.55030012 & 6.34110073 \\ 90 & 11.11037985 & 6.05071855 \\ \end{tabular}$

$\begin{center}\vbox{\input{2000-07-17-01.pslatex} }\end{center}$

Lattice parameter

$\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{6}} \multicolumn{... ...5.094056 \\ 70 & 5.016554 \\ 80 & 4.930027 \\ 90 & 4.832925 \\ \end{tabular}$

NOTE

In Shannon (1976) there is no quotation for the ionic radius of 8-coordinated $Mn^{3+}$ . The only value is for 6-coordination (i.e. octahedral, I guess): $0.58\;$ Å for low spin and $0.645\;$ Å for high spin. We could do something like in (Minervini et al., 1999, table 4,note (a)), if we could understand what they have done (referring to the radii of $Al^{3+},Cr^{3+},Ga^{3+}$ , note (a) of table 4 literally says: ``(a) extrapolated using octahedral ionic radii''. Huh??). Anyway, the ionic radius of $Mn^{3+}$ is much smaller than that of $Ce^{4+}$ , which is what we want here.

$\begin{center}\vbox{\input{2000-07-17-02.pslatex} }\end{center}$

Lattice energy

$\rcRoundingfalse \fpDecimalSign{.} \begin{tabular}{R{2}{0}R{1}{6}} \multicolumn{... ... 70 & -77.03058676 \\ 80 & -73.62873305 \\ 90 & -70.42530124 \\ \end{tabular}$

$\begin{center}\vbox{\input{2000-07-17-03.pslatex} }\end{center}$

Representative input file


opti conp defect

maxcyc opt      200
maxcyc fit      200
dump every   1 ce4-80.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  0.2000  0.0000 
    Mn  core  0.0000  0.0000  0.0000   3.0000  0.8000  0.0000 
     O  core  0.2500  0.2500  0.2500   0.0770  0.8000  0.0000 
   Ce4  shel  0.0000  0.0000  0.0000   7.7000  0.2000  0.0000 
     O  shel  0.2500  0.2500  0.2500  -2.0770  0.8000  0.0000  
                                                     
space
225

size  9.15583990  19.22726379
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
Mn    core O     shel  1257.9        0.32140     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