-A measure for the mobility of the interstitial carbon is the activation energy for the migration path from one stable \r
-position to another. The stable defect geometries have been discussed in the previous subsection. We now investigate \r
-the migration from the most stable structure (...should be named somehow...) on one site of the silicon host lattice to \r
-a neighbored site. \r
-On the lowest energy path (first principles), the carbon atom starts to move along (110)..(check that!)... The center of the line connecting \r
-initial and final structure has been found to be a local minimum and not a saddle point as could be expected. The two \r
-saddle points shortly before and behind this local minimum are slightly displaced out of the (110) plane by ... {\AA}. ..(check that!)..\r
-This path is not surprising -- a similar behavior was e.g. found earlier for the carbon split interstitial \cite{rauls03a} and the phosphorus \r
-interstitial \cite{rauls03b,gerstmann03} in SiC. However, an interesting effect is the change of the spin state from zero at the (110) dumb bell \r
-configuration to one at the local minimum. By this, the energy of the local minimum is lowered by 0.3 eV (... check it!!..). \r
-%\begin{figure}\r
-%\includegraphics[width=1.0\columnwidth]{path-DFT.eps}\r
-%\caption{\label{fig:path-DFT} Energy of the carbon interstitial during migration from ... to ... calculated from first principles. The \r
-% activation energy of 0.9 eV (?) agrees well with experimental findings (0.7-0.9 eV?). }\r
-%\end{figure} \r
-Fig.\ref{fig:path-DFT} shows the energy along this lowest energy migration path. The activation energy of 0.9 eV (?) agrees well \r
-with experimental findings (0.7-0.9 eV?).\r
+\r
+A measure for the mobility of the interstitial carbon is the activation energy for the migration path from one stable position to another.\r
+The stable defect geometries have been discussed in the previous subsection.\r
+In the following the migration of the most stable configuration, i.e. C$_{\text{I}}$, from one site of the Si host lattice to a neighbored site is investigated by both, EA and VASP calculations utilizing the constrained conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.\r
+Three migration pathways are investigated.\r
+The starting configuration for all pathways is the \hkl<0 0 -1> dumbbell interstitial configuration.\r
+In path 1 and 2 the final configuration is a \hkl<0 0 1> and \hkl<0 -1 0> dumbbell interstitial respectively, located at the next neighboured Si lattice site displaced by $\frac{a_{\text{Si}}}{4}$\hkl<1 1 -1>, whereat $a_{\text{Si}}$ is the Si lattice constant.\r
+Path 3 ends in a \hkl<0 -1 0> configuration at the initial lattice site and, for this reason, corrsponds to a reorientation of the dumbbell, a process not contributing to long range diffusion.\r
+\r
+\begin{figure}\r
+\begin{center}\r
+\includegraphics[width=\columnwidth]{00-1_0-10_nosym_sp_fullct.ps}\\[1.0cm]\r
+\begin{picture}(0,0)(90,0)\r
+\includegraphics[width=0.2\columnwidth]{00-1_a.eps}\r
+\end{picture}\r
+\begin{picture}(0,0)(10,0)\r
+\includegraphics[width=0.2\columnwidth]{00-1_0-10_sp.eps}\r
+\end{picture}\r
+\begin{picture}(0,0)(-70,0)\r
+\includegraphics[width=0.2\columnwidth]{0-10.eps}\r
+\end{picture}\r
+\begin{picture}(0,0)(15,15)\r
+\includegraphics[width=0.2\columnwidth]{100_arrow.eps}\r
+\end{picture}\r
+\begin{picture}(0,0)(130,0)\r
+\includegraphics[height=0.2\columnwidth]{001_arrow.eps}\r
+\end{picture}\r
+\end{center}\r
+\caption{Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to the \hkl<0 -1 0> dumbbell (right) transition as obtained by first principles methods. The activation energy of \unit[0.9]{eV} agrees well with experimental findings (\unit[0.73]{eV}\cite{song90} and \unit[0.87]{eV}\cite{tipping87}).}\r
+\label{fig:vasp_mig}\r
+\end{figure} \r
+The lowest energy path (path 2) as detected by the first principles approach is illustrated in Fig. \ref{fig:vasp_mig}.\r
+The activation energy of \unit[0.9]{eV} agrees well with experimental findings (\unit[0.73]{eV}\cite{song90} and \unit[0.87]{eV}\cite{tipping87}).\r
+% not the path you expected!\r
+%This path is not surprising -- a similar behavior was e.g. found earlier for the carbon split interstitial \cite{rauls03a} and the phosphorus interstitial \cite{rauls03b,gerstmann03} in SiC.\r