Next: 2000-02-21: with a different Up: simulation in ceria-zirconia mixed Previous: 2000-01-20: influence of region

2000-02-02: Reproduction of experimental data in Sakai et al. (1999)

GOAL

Reproduction of figure 5 in Sakai et al. (1999).

Results

$\fbox { \begin{minipage}{0.6\linewidth} \bf Mon Mar 6 18:28:52 2000\\ See the mean field correction to this analysis at 2000-03-03 \end{minipage}}%\fbox$

Evaluation of the energy change for the reaction:

$\begin{eqnarray*} H_2O_{(g)}+V_O^{\cdot\cdot}+O_O^\times&=&2OH_O^\cdot \end{eqnarray*}$

for the series of oxides: , $Ce_{0.8}M_{0.2}O_{1.9}$ , $M=\mathit{La, Nd, Gd, Y, Yb}$ .

The reaction can be decomposed in the following way (notation as in Glockner et al. (1999)):

$\begin{displaymath} \begin{array}{rcll} H_2O_{(g)}+O^{2-}_{(g)}&=&2OH^-_{(g)}&E_... ..._2O}=E_{PT}+2E_{OH_O^\cdot}-E_{V_O^{\cdot\cdot}}\\ \end{array}\end{displaymath}$

From Glockner et al. (1999), table 6, $E_{PT}=-11.77\;eV$ . The other energy terms, $E_{OH_O^\cdot }$ and $E_{V_O^{\cdot \cdot }}$ are evaluated with GULP.

Oxygen and cerium potential parameters are the usual ones Balducci et al. (1997); potential parameters for $\mathit{La, Nd, Gd, Y, Yb}$ are taken from Lewis and Catlow (1985).

$E_{OH_O^\cdot }$ determination

$\begin{threeparttable} \begin{tabular}{lD{.}{.}{6}D{.}{.}{6}D{.}{.}{0}D{.}{.}{6}... ...0.2}O_{1.9}$} &5.400688 & 9.73558558 & 694 \\ \end{tabular}\end{threeparttable}$

$\begin{threeparttable} \begin{tabular}{lD{.}{.}{10}D{.}{.}{10}D{.}{.}{3}} \multi... ..._{1.9}$} & 7.67428724 & 14.72678724 & 9.00 \\ \end{tabular}\end{threeparttable}$

Geometry of the optimized defect

In all cases, the initial orientation of the group was chosen along the direction, i.e. with the atom between two oxygen in nearest neighbor position. After relaxation, the original orientation was not changed, as can be seen from the following table, which shows the final cartesian coordinates of the oxygen, hydrogen and of the oxide ion nearest to the hydrogen along the direction and the angle in degrees between the two vectors shown in the figure below:

$\begin{xy} % xytracing <1em,0em>: (0,0)*+{O_2}; p+/u8em/*+{O}**\dir{-};p+/r8em... ...ir{>}, ''vertex''*\cir<1em>{rd_d}, ''vertex''+/va(15)1.8em/*+{\theta}, \end{xy}$

$\begin{threeparttable} \begin{tabular}{lllll} \multicolumn{1}{c}{Oxide} &\multic... ....350,1.351 & 4.079,1.350,1.350 & 0.13319158\\ \end{tabular}\end{threeparttable}$

The following table shows the $\xy* {O_1};p+/r2em/*{H}**\dir{-}\endxy$ relaxed bond length.

$\begin{threeparttable} \begin{tabular}{ll} \multicolumn{1}{c}{Oxide} &\multicolu... ... {$Ce_{0.8}Yb_{0.2}O_{1.9}$} & 0.93400428 \\ \end{tabular}\end{threeparttable}$

$E_{V_O^{\cdot \cdot }}$ determination

$\begin{threeparttable} \begin{tabular}{lD{.}{.}{6}D{.}{.}{6}D{.}{.}{0}D{.}{.}{6}... ...8 & 9.73558558 & 668 & 15.02263140 & 277.88\\ \end{tabular}\end{threeparttable}$

NOTE

The different values for the number of ions in the two series of calculations is due to a slightly different center of the defect: center was at

for the $E_{OH_O^\cdot }$ calculations and at

for the $E_{V_O^{\cdot \cdot }}$ calculations.

NOTE

The value of $E_{V_O^{\cdot\cdot}}=16.60369275\;eV$ for pure ceria reproduces well the one already obtained in Balducci et al. (1997) ( $16.62335360\;eV$ ).

$E_{H_2O}$ determination

Evaluating: $E_{H_2O}=E_{PT}+2E_{OH_O^\cdot}-E_{V_O^{\cdot\cdot}}$ for each oxide gives:

$\begin{threeparttable} \begin{tabular}{lD{.}{.}{10}D{.}{.}{10}D{.}{.}{3}} \multi... ...}Yb_{0.2}O_{1.9}$} & 5.400688 & 2.66094308 \\ \end{tabular}\end{threeparttable}$

$\begin{center}\vbox{\input{2000-02-02-01.pslatex} }\end{center}$

In accord with figure 6 of Sakai et al. (1999), pure ceria shows a much higher energy for water incorporation than any of the solid solutions. But the trend within the solid solutions is EXACTLY OPPOSITE to the experimental one!

Representative input files

$E_{OH_O^\cdot }$


opti conp defect regi_before
#conp defect single
dump every 1 gd-OH.dump
maxcyc  200
cutb 3.0 # what does this mean? Ronny uses it.
title
Gadolinium solid solution
N.Sakai et al. Solid State Ionics 125(1999)325-331
end
cell
   5.430000 5.430000 5.430000  90.000000  90.000000  90.000000

size        9.78784820      20.0
centre                 0.251  0.249  0.25
impurity     O2 core   0.25   0.25   0.25
interstitial H2 core   0.44   0.25   0.25
fractional   
############
# Cores
############
Ce4  core  0.000000   0.000000   0.000000  -3.700000 0.8
Gd   core  0.000000   0.000000   0.000000   3.00     0.2
O1   core  0.250000   0.250000   0.250000   0.07700  0.95
############
# Shells
############
Ce4  shel  0.000000   0.000000   0.000000   7.700000 0.8
O1   shel  0.250000   0.250000   0.250000  -2.07700  0.95
space
225

#########################
# Shell-core charges
#########################
species   
Ce3   shel    7.700000
Ce3   core   -4.700000   
O2    core   -1.4263
H2    core    0.4263         
#########################
# Short range potentials
#########################
buck 
Ce4 shel O1 shel    1986.830000 0.351070   20.40000  0.0 15.000
buck                                                    
Ce3 shel O1 shel    1731.61808  0.36372    14.43256  0.0 15.000
buck                                                    
Gd  core O1 shel    1336.8      0.35510     0.00000  0.0 15.000
buck                                                    
O1  shel O1 shel   22764.300000 0.149000   27.89000  0.0 15.000
buck                                                    
O2  core O1 shel   22764.300000 0.149000   27.89000  0.0 15.000
buck                                                    
H2  core O1 shel     311.970    0.35        0.0      0.0 15.000
morse
H2  core O2 core       7.05250  2.19860     0.9485   1.0 0.0 2.0
buck 
Ce4 shel O2 core    1986.830000 0.351070   20.40000  0.0 15.000
buck                                                    
Gd  core O2 shel    1336.8      0.35510     0.00000  0.0 15.000
#########################
# Spring parameters
#########################
spring 
Ce4    291.750000
spring 
Ce3    291.750000
spring 
O1      27.29

$E_{V_O^{\cdot \cdot }}$


opti conp defect regi_before
#conp defect single
dump every 1 la-O-vaca.dump
maxcyc  200
cutb 3.0 # what does this mean? Ronny uses it.
title
Lanthanum solid solution
N.Sakai et al. Solid State Ionics 125(1999)325-331
end
cell
   5.490000 5.490000 5.490000  90.000000  90.000000  90.000000

size        9.87352306      20.0
centre      0.25            0.25   0.25
vacancy     0.25            0.25   0.25
fractional   
############
# Cores
############
Ce4  core  0.000000   0.000000   0.000000  -3.700000 0.8
La   core  0.000000   0.000000   0.000000   3.00     0.2
O1   core  0.250000   0.250000   0.250000   0.07700  0.95
############
# Shells
############
Ce4  shel  0.000000   0.000000   0.000000   7.700000 0.8
O1   shel  0.250000   0.250000   0.250000  -2.07700  0.95
space
225

#########################
# Shell-core charges
#########################
species   
Ce3   shel    7.700000
Ce3   core   -4.700000   
O2    core   -1.4263
H2    core    0.4263         
#########################
# Short range potentials
#########################
buck 
Ce4 shel O1 shel    1986.830000 0.351070   20.40000  0.0 15.000
buck                                                    
Ce3 shel O1 shel    1731.61808  0.36372    14.43256  0.0 15.000
buck                                                    
La  core O1 shel    1439.7      0.36510     0.00000  0.0 15.000
buck                                                    
O1  shel O1 shel   22764.300000 0.149000   27.89000  0.0 15.000
buck                                                    
O2  core O1 shel   22764.300000 0.149000   27.89000  0.0 15.000
buck                                                    
H2  core O1 shel     311.970    0.35        0.0      0.0 15.000
morse
H2  core O2 core       7.05250  2.19860     0.9485   1.0 0.0 2.0
buck 
Ce4 shel O2 core    1986.830000 0.351070   20.40000  0.0 15.000
buck                                                    
La  core O2 shel    1439.7      0.36510     0.00000  0.0 15.000
#########################
# Spring parameters
#########################
spring 
Ce4    291.750000
spring 
Ce3    291.750000
spring 
O1      27.29

Next: 2000-02-21: with a different Up: simulation in ceria-zirconia mixed Previous: 2000-01-20: influence of region