finished mig

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index d7f3052..4e31dfb 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -769,13 +769,14 @@ However, in some cases  a time constant of 100 fs resuls in lower barriers and,
 % red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20 -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.75 -1.25 -0.25 -L -0.25 -0.25 -0.25 -r 0.6 -B 0.1
 % blue: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20_tr100/ -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.0 -0.25 1.0 -L 0.0 -0.25 -0.25 -r 0.6 -B 0.1
 \end{figure}
-Figure \ref{fig:defects:cp_bc_00-1_mig} shows the migration barrier iand corresponding structures of the bond-centered to \hkl<0 0 -1> dumbbell transition.
+Figure \ref{fig:defects:cp_bc_00-1_mig} shows the migration barrier and corresponding structures of the bond-centered to \hkl<0 0 -1> dumbbell transition.
 Since the bond-centered configuration is unstable relaxing into the \hkl<1 1 0> C-Si dumbbell interstitial configuration within this potential the low kinetic energy state is used as a starting configuration.
 Depending on the time constant activation energies of 2.4 eV and 2.2 eV respectively are obtained.
 The migration path obtained by simulations with a time constant of 1 fs remains in the \hkl(1 1 0) plane.
 Using 100 fs as a time constant the C atom breaks out of the \hkl(1 0 0) plane already at the beginning of the migration accompanied by a reduction in energy.
 The energy barrier of this path is 0.2 eV lower in energy than the direct migration within the \hkl(1 1 0) plane.
 However, the investigated pathways cover an activation energy approximately twice as high as the one obtained by quantum-mechanical calculations.
+For the entire transition of the \hkl<0 0 -1> into the \hkl<0 0 1> configuration by passing the bond-centered configuration an additional activation energy of 0.5 eV is necessary to escape from the bond-centered and reach the \hkl<0 0 1> configuration.
 
 \begin{figure}[th!]
 \begin{center}
@@ -818,21 +819,38 @@ Indeed, this configuration is obtained by relaxation simulations without constra
 Activation energies of roughly 2.8 eV and 2.7 eV respectively are needed for migration.
 
 The \hkl<1 1 0> configuration seems to play a decisive role in all migration pathways.
-In the first migration path it is the configuration resulting from a further relaxation of the rather unstable bond-centered configuration, which is fixed to be a transition point.
+In the first migration path it is the configuration resulting from further relaxation of the rather unstable bond-centered configuration, which is fixed to be a transition point in the migration calculations.
 The last two  pathways show configurations almost identical to the \hkl<1 1 0> configuration, which constitute a local minimum within the pathway.
 Thus, migration pathways with the \hkl<1 1 0> C-Si dumbbell interstitial configuration as a starting or final configuration are further investigated.
-Figure ... shows ...
-
-
-The
-... diffusion ...
-... indicate a problem that is formulated and discussed in more detail in section ...
-
+\begin{figure}[ht!]
+\begin{center}
+\includegraphics[width=13cm]{110_mig.ps}
+\end{center}
+\caption[Migration barriers of the \hkl<1 1 0> dumbbell to bond-centered (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) C-Si dumbbell transition.]{Migration barriers of the \hkl<1 1 0> dumbbell to bond-centered (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) C-Si dumbbell transition. Solid lines show results for a time constant of 1 fs and dashed lines correspond to simulations employing a time constant of 100 fs.}
+\label{fig:defects:110_mig}
+\end{figure}
+Figure \ref{fig:defects:110_mig} shows migration barriers of the C-Si \hkl<1 1 0> dumbbell to  \hkl<0 0 -1>, \hkl<0 -1 0> (in place) and bond-centered configuration.
+As expected there is no maximum for the transition into the bond-centered configuration.
+As mentioned earlier the bond-centered configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl<1 1 0> configuration.
+An activation energy of 2.2 eV is necessary to reorientate the \hkl<0 0 -1> dumbbell configuration into the \hkl<1 1 0> configuration, which is 1.3 eV higher in energy.
+Residing in this state another 0.9 eV is enough to make the C atom form a \hkl<0 0 -1> dumbbell configuration with the Si atom of the neighboured lattice site.
+In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermmediate migration steps is very unlikely to occur the just presented pathway is much more supposable in classical potential simulations, since the energetically most favorable transition found so far is also composed of two migration steps with activation energies of 2.2 eV and 0.5 eV.
+{\color{red}TODO: 00-1 to 001 transition, does it pass the bc conf?}
+
+Although classical potential simulations reproduce the order in energy of the \hkl<1 0 0> and \hkl<1 1 0> C-Si dumbbell interstitial configurations as obtained by more accurate quantum-mechanical calculations the obtained migration pathways and resulting activation energies differ to a great extent.
+On the one hand the most favorable pathways differ.
+On the other hand the activation energies obtained by classical potential simulations are tremendously overestimated by a factor of almost 2.4.
+Thus, atomic diffusion is wrongly described in the classical potential approach.
+The probability of already rare diffusion events is further decreased for this reason.
+Since agglomeration of C and diffusion of Si self-interstitials are an important part of the proposed SiC precipitation mechanism a problem arises, which is formulated and discussed in more detail in section \ref{subsection:md:limit}.
 
 \section{Combination of point defects}
 
 The structural and energetic properties of combinations of point defects are examined in the following.
-Investigations are restricted to quantum-mechanical calculations.
+Investigations are restricted to quantum-mechanical calculations for two reasons.
+First of all, as mentioned in the last section, they are far more accurate.
+Secondly, the restrictions in size and simulation time for this type of calculation due to limited computational resources, necessitate to map the complex precipitation mechanism to a more compact and simplified modelling.
+The investigations of defect combinations approached in the following are still feasible within the available computational power and allow to draw conclusions on some important ongoing mechanisms during SiC precipitation.
 
 \subsection[Combinations with a C-Si \hkl<1 0 0>-type interstitial]{\boldmath Combinations with a C-Si \hkl<1 0 0>-type interstitial}