19990824: $Ce^{4+}_{250}Ce^{3+}_{250}O_{875}(V_O^{\cdot \cdot })_{125}$

GOAL

This is a calculation on pure ceria, to be compared with another one (still to be done) on the mixed system: $Zr_{100}Ce^{4+}_{200}Ce^{3+}_{200}O_{900}(V_O^{\cdot \cdot })_{100}$, which has the same reduction degree.
To evidence any effect of zirconia addition on the oxygen diffusion coefficient.

Results

Based on Vegard's law, I set a lattice constant of $5.62339162\;\mbox{\textit{\AA}}$, derived from:

$$\begin{eqnarray*} a&=&\frac{4}{\sqrt{3}}(r_C+r_{O^{2-}}) \end{eqnarray*}$$

with:

$$\begin{eqnarray*} r_C&=&0.5r_{Ce^{IV}}+0.5r_{Ce^{III}} \end{eqnarray*}$$

and

$$\begin{array}{ll} r_{Ce^{IV}} & 0.97\;\mbox{\textit{\AA}}\\ ... ...{\AA}}\\ r_{O^{2-}} & 1.38\;\mbox{\textit{\AA}}\\ \end{array}$$

GULP optimization gives: $5.636366\;\mbox{\textit{\AA}}$.