19981124: $Zr_{54}Ce^{4+}_{38}Ce^{3+}_{16}O_{208}$, rigid ions

Simulation of the system: $Zr_{54}Ce^{4+}_{38}Ce^{3+}_{16}O_{208}$.

Lattice parameter determination

I've run GULP with the following occupancies, corresponding to the composition of the system being simulated: ############
# Cores
############
Ce4  core  0.000000   0.000000   0.000000  -3.700000 0.35185185
Ce3  core  0.000000   0.000000   0.000000  -4.700000 0.14814815
Zr   core  0.000000   0.000000   0.000000   2.65     0.50
O    core  0.250000   0.250000   0.250000   0.07700  0.96296296
############
# Shells
############
Ce4  shel  0.000000   0.000000   0.000000   7.700000 0.35185185
Ce3  shel  0.000000   0.000000   0.000000   7.700000 0.14814815
Zr   shel  0.000000   0.000000   0.000000   1.35     0.50
O    shel  0.250000   0.250000   0.250000  -2.07700  0.96296296

From the structure optimization, I've got the value of $5.337004\;\mbox{\textit{\AA}}$ for the lattice constant.

Then, I've applied a correction for thermal expansion, based on the data in the paper [3]. From table 2 of the paper one gets a value of $5.5359\;\mbox{\textit{\AA}}$ for the lattice constant of defective $CeO_{1.860}$ at $800\;C$. From table 3 the value of $5.5425\;\mbox{\textit{\AA}}$ is taken for defective $CeO_{1.855}$ at $900\;C$. Hence, the following thermal expansion coefficient can be assumed:

$$\begin{eqnarray*} \frac{\Delta{}a}{\Delta{}T}&=&\frac{5.5425-5.5359}{100}\\ &=&6.6\times10^{-5}\;\mbox{\textit{\AA}}/K\\ \end{eqnarray*}$$

Approximations:

• The paper [3] is about defective and stoichiometric pure ceria, while my system is a solid solution with zirconia
• Even by considering $Zr^{4+}$ and $Ce^{4+}$ as being the same, the formula for my defective system turns out to be $CeO_{1.70}$, which is different from $CeO_{1.860}$ or $CeO_{1.855}$ in the paper: these latter are the compositions nearest to mine which can be found in tables 2 and 3
• I assume a constant thermal expansion coefficient

Applying the correction for thermal expansion gives:

$$\begin{eqnarray*} a&=&5.337004+6.6\times10^{-5}\times1759\\ &=&5.45309800\;\mbox{\textit{\AA}} \end{eqnarray*}$$

($1759\;K$ is the temperature of the simulation)

This was the value used in the input to the genlat program.

Nov 30 (Mon), 1998

In the light of the results obtained in 19981126, which look much better than those in this calc and which were obtained by simply reducing the lattice constant of the fluoritic structure, I was thinking that the GULP minimization had to be performed with rigid cations, like the MD calc. So I've run GULP with rigid cations to see if the optimized lattice constant was different: alas! no success. I got exactly the same value as the one with polarizable cations: $\mathbf{5.337004\;\mbox{\textit{\AA}}}$

Results

The program was killed prematurely because of a time limit overflow. Anyhow, it almost completed its task, writing successfully 4420 configurations (I set out things in the CONTROL file in order to write 5000 configurations). So we can safely consider the calculation as completed.

Sadly, the MSD plot is not good.