tarted w first two combos

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 48e9351..6299739 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -710,24 +710,27 @@ Relative silicon neighbour positions:
 \end{table}
 Figure \ref{fig:defects:pos_of_comb} shows the initial \hkl<0 0 -1> dumbbell interstitial defect and the positions of next neighboured silicon atoms used for the second defect.
 Table \ref{tab:defects:e_of_comb} summarizes energetic results obtained after relaxation of the defect combinations.
-The energy of interest $E$ is defined to be
+The energy of interest $E_{\text{b}}$ is defined to be
 \begin{equation}
-E=
+E_{\text{b}}=
 E_{\text{f}}^{\text{defect combination}}-
 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
 E_{\text{f}}^{\text{2nd defect}}
 \label{eq:defects:e_of_comb}
 \end{equation}
 with $E_{\text{f}}^{\text{defect combination}}$ being the formation energy of the defect combination, $E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}$ being the formation energy of the C \hkl<0 0 -1> dumbbell interstitial defect and $E_{\text{f}}^{\text{2nd defect}}$ being the formation energy of the second defect.
-For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects with zero interaction resulting in $E=0$.
-In fact, for another \hkl<0 0 -1> dumbbell interstitial created at position $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx 10.2$ \AA) and $\frac{a_{\text{Si}}}{2}\hkl<2 3 2>$ ($\approx 12.8$ \AA, maximum distance due to periodic boundary conditions) relative to the initial one an energy of -0.19 eV and ... is obtained.
+For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects without an interaction resulting in $E_{\text{b}}=0$.
+Thus, $E_{\text{b}}$ can be best thought of a binding energy, which is required to bring the defects to infinite separation.
+In fact, further \hkl<0 0 -1> dumbbell interstitials created at position $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx 10.2$ \AA) and $\frac{a_{\text{Si}}}{2}\hkl<2 3 2>$ ($\approx 12.8$ \AA) relative to the initial one result in energies as low as -0.19 eV and -0.12 eV.
+There is still a low interaction which is due to the equal orientation of the defects.
+By changing the orientation of the second dumbbell interstitial to the \hkl<0 -1 0>-type the interaction is even mor reduced, which results in an energy of $E_{\text{b}}=...\text{ eV}$ for a distance of $\frac{a_{\text{Si}}}{2}\hkl<2 3 2>$, which is the maximum that can be reached due to periodic boundary conditions.
 Configurations wih energies greater than zero are energetically unfavorable and expose a repulsive interaction.
 These configurations are unlikely to arise or to persist for non-zero temperatures.
 Energies below zero indicate configurations favored compared to configurations in which these point defects are separated far away from each other.
 
 Investigating the first part of table \ref{tab:defects:e_of_comb}, namely the combinations with another \hkl<1 0 0>-type interstitial, most of the combinations result in energies below zero.
 Surprisingly the most favorable configurations are the ones with the second defect created at the very next silicon neighbour and a change in orientation compared to the initial one.
-This leads to the conclusion that an agglomeration of C-Si dumbbell interstitials as proposed by the precipitation model introduced in section\ref{section:assumed_prec} is indeed an energetically favored configuration of the system.
+This leads to the conclusion that an agglomeration of C-Si dumbbell interstitials as proposed by the precipitation model introduced in section \ref{section:assumed_prec} is indeed an energetically favored configuration of the system.
 The reason for nearby interstitials being favored compared to isolated ones is most probably the reduction of strain energy enabled by combination in contrast to the strain energy created by two individual defects.
 \begin{figure}[h]
 \begin{center}
@@ -748,12 +751,13 @@ b) \underline{$E=-2.39\text{ eV}$}
 \label{fig:defects:comb_db_01}
 \end{figure}
 Figure \ref{fig:defects:comb_db_01} shows the structure of these two configurations.
-
 Structure b) is the energetically most favorable configuration.
-The two carbon atoms form a bond to each other.
-This suggests an unwanted C clustering in SiC production.
-However, for the second most favorable configuration, presented in figure a), the amount of possibilitie for this configuration is twice as high.
-Investigating C-Si and C-C bond lengths ...
+The two carbon atoms form a bond with a length of 1.38 \AA close to the nex neighbour distance in diamond or graphite, which is approximately 1.54 \AA.
+This suggests prefered C clustering as a competing mechnism to the C-Si dumbbell agglomeration inevitable for the SiC precipitation.
+Todo: Activation energy to obtain a configuration of separated C atoms again?
+However, for the second most favorable configuration, presented in figure a), the amount of possibilities for this configuration is twice as high.
+C-Si and C-C PC ...
+
 
 001 at pos 2 looks as if there is no interaction.
 There is an interaction but in the same time strain is reduced due to the opposing orientations of the defects, which leads to this low energy value.