The method without updating the constraints but still applying them to all atoms shows a delayed crossing of the saddle point.
This is understandable since the update results in a more aggressive advance towards the final configuration.
In any case the barrier obtained is slightly higher, which means that it does not constitute an energetically more favorable pathway.
-The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}in progress} ...
+The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}Todo: does not work!} ...
\subsection{Migration barriers obtained by classical potential calculations}
\label{subsection:defects:mig_classical}
As expected by the initialization conditions the two carbon atoms form a bond.
This bond has a length of 1.38 \AA{} close to the nex neighbour distance in diamond or graphite, which is approximately 1.54 \AA.
The minimum of binding energy observed for this configuration suggests prefered C clustering as a competing mechnism to the C-Si dumbbell interstitial agglomeration inevitable for the SiC precipitation.
-{\color{red}Todo: Activation energies to obtain separated C confs currently in progress - could be added in the combined defect migration chapter and mentioned here, too!}
+{\color{red}Todo: Activation energies to obtain separated C confs FAILED (again?) - could be added in the combined defect migration chapter and mentioned here, too!}
However, for the second most favorable configuration, presented in figure \ref{fig:defects:comb_db_01} a), the amount of possibilities for this configuration is twice as high.
In this configuration the initial Si (I) and C (I) dumbbell atoms are displaced along \hkl<1 0 0> and \hkl<-1 0 0> in such a way that the Si atom is forming tetrahedral bonds with two silicon and two carbon atoms.
The carbon and silicon atom constituting the second defect are as well displaced in such a way, that the carbon atom forms tetrahedral bonds with four silicon neighbours, a configuration expected in silicon carbide.
The substitutional C is located next to the lattice site shared by the \hkl<1 1 0> Si self-interstitial along the \hkl<1 -1 0> direction.
Thus, the compressive stress along \hkl<1 1 0> of the Si \hkl<1 1 0> interstitial is not compensated but intensified by the tensile stress of the substitutional C atom, which is no longer loacted along the direction of stress.
-{\color{red}Todo: Mig of C-Si DB conf to or from C sub + Si 110 int conf.}
+{\color{red}Todo: Erhart/Albe calc for most and less favorable configuration!}
+
+{\color{red}Todo: Mig of C-Si DB conf to or from C sub + Si 110 in progress.}
+
+{\color{red}Todo: Mig of Si DB located next to a C sub (also by MD!).}
\section{Migration in systems of combined defects}
Due to this and due to the formation of new bonds, that is the bond of silicon atom number 1 to silicon atom number 5 and the bond of the carbon atom to its siliocn neighbour in the bottom left, a less steep increase of free energy is observed.
At a displacement of approximately 30 \% the bond of silicon atom number 1 to the just recently created siliocn atom is broken up again, which explains the repeated boost in energy.
Finally the system gains energy relaxing into the configuration of zero displacement.
+{\color{red}Todo: Direct migration of C in progress.}
Due to the low binding energy observed, the configuration of the vacancy created at position 3 is assumed to be stable against transition.
However, a relatively simple migration path exists, which intuitively seems to be a low energy process.
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