= Solution
Assume one temperature-independent <activation energy> over this interval and an unchanged dopant-controlled carrier population. Write the <Arrhenius equation> as $D=D_0\exp[-Q/(k_BT)]$. The two measurements give
$$
\frac Q{k_B}=\frac{\ln 10}{1/1000-1/1180}=1.5095\times10^4\,\mathrm K,
\qquad Q=1.301\,\mathrm{eV}=125.5\,\mathrm{kJ\,mol^{-1}}.
$$
Using $D(T)=10^{-13}\exp[(Q/k_B)(1/1000-1/T)]$ yields
$$
\boxed{D(1250)=2.047\times10^{-12},\qquad
D(1110)=4.463\times10^{-13}\quad\mathrm{m^2\,s^{-1}}.}
$$
The <Nernst-Einstein relation> includes the factor $1/T$: $\sigma=nq^2D/(k_BT)$. For fixed $n$ and a fixed correlation correction,
$$
\sigma(1110)=0.08\frac{D(1110)}{D(1250)}\frac{1250}{1110}
=\boxed{1.964\times10^{-2}\,\mathrm{S\,m^{-1}}}.
$$
Using conductivity proportional to $D$ alone would miss the <temperature> factor. Carrier association, a changing vacancy population or a changing <diffusion> correlation factor would invalidate this simple extrapolation.
Back to article page
