+%\r
+% should possibly be transfered to discussion section\r
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, mass C clustering is not expected.\r
+Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.\r
+The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.\r
+Thus, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.\r
+% calculate?!? ... hopefully acknowledged by 188-225 calc\r
+However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.\r
+Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.\r
+On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.\r
+In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.\r
+First of all, it constitutes the second most energetically favorable structure.\r
+Secondly, a migration path with a barrier as low as \unit[?.?]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).\r
+The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
+% 188 - 225 transition in progress\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{188-225.ps}\r
+\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[?.?]{eV} is observed.}\r
+\label{fig:188-225}\r
+\end{figure}\r
+Finally, this type of defect pair is represented four times (two times more often than the ground state configuration) within the systematically investigated configuration space.\r
+The latter is considered very important for high temperatures, which is accompanied by an increase in the entropic contribution to structure formation.\r
+Thus, C agglomeration indeed is expected but only a low probability is assumed for C clustering by thermally activated processes with regard to the considered period of time.\r
+% ?!?\r
+% look for precapture mechnism (local minimum in energy curve)\r
+% also: plot energy all confs with respect to C-C distance\r
+% maybe a pathway exists traversing low energy confs ?!?\r
+\r
+% point out that configurations along 110 were extended up to the 6th NN in that direction\r
+The binding energies of the energetically most favorable configurations with the seocnd DB located along the \hkl[1 1 0] direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{table:dc_110}.\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & 6 \\\r
+\hline\r
+ $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\\r
+C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08 \r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies $E_{\text{b}}$ and C-C distance of energetically most favorable C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs separated along bonds in the \hkl[1 1 0] direction.}\r
+\label{table:dc_110}\r
+\end{table}\r
+The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}\r
+\caption{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}\r
+\label{fig:dc_110}\r
+\end{figure}\r
+The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.\r
+Not considering the previously mentioned elevated barriers for migration an attractive interaction between the C$_{\text{i}}$ defects indeed is detected with a capture radius that clearly exceeds the \unit[1]{nm} mark.\r
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, inbetween the two lowest separation distances of the defects.\r
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clsutering.\r