started explanation of si-c pc

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index a35037b..8f762a3 100644 (file)
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -9,10 +9,19 @@ Simulations targeting the formation of silicon carbide precipitates are, thus, a
 
 \section{Ab initio MD simulations}
 
+No pressure control, since VASP does not support this feature in MD mode.
+The time step is set to one fs.
+Explain some more parameters that differ from the latter calculations ...
+
 Molecular dynamics simulations of a single, two and ten carbon atoms in $3\times 3\times 3$ unit cells of crytsalline silicon are performed.
 
 \section{Classical potential MD simulations}
 
+In contrast to the quantum-mechanical MD simulations the developed classical potential MD code is able to do constant pressure simulations using the Berendsen barostat.
+The system pressure is set to zero pressure.
+Due to promising advantages over the Tersoff potential the bond order potential of Erhard and Albe is used.
+A time step of one fs is set.
+
 \subsection{Initial simulations}
 
 In initial simulations aiming to reproduce a precipitation process simulation volumes of $31\times 31\times 31$ unit cells are utilized.
@@ -165,11 +174,13 @@ The number of C-C bonds is much smaller for $V_1$ than for $V_2$ and $V_3$ since
 These carbon atoms are assumed to form strong bonds.
 This is supported by figure \ref{fig:md:energy_450} displaying the total energy of all three simulations during the whole simulation sequence.
 A huge decrease of the total energy during carbon insertion is observed for the simulations with high carbon concentration in contrast to the $V_1$ simulation, which shows a slight increase.
-The difference in energy $\Delta$ growing within the carbon insertion process persists unchanged until the end of the simulation.
+The difference in energy $\Delta$ growing within the carbon insertion process up to a value of roughly 0.06 eV per atom persists unchanged until the end of the simulation.
 Here is the problem.
 The excess amount of next neighboured strongly bounded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
 However, in the same way a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
 Thus, this transformation is very unlikely to happen.
+This is in accordance with the constant total energy observed in the continuation step of 100 ps inbetween the end of carbon insertion and the cooling process.
+Obviously no energetically favorable relaxation is taking place at a system temperature of $450\,^{\circ}\mathrm{C}$.
 
 The C-C peak at about 0.31 nm perfectly matches the nearest neighbour distance of two carbon atoms in the 3C-SiC lattice.
 As can be seen from the inset this peak is also observed for the $V_1$ simulation.
@@ -183,12 +194,24 @@ Without the abrubt increase a maximum around 0.31 nm gets even more conceivable.
 For low concentrations of carbon, that is the $V_1$ simulation and early stages of the $V_2$ and $V_3$ simulations, analyses of configurations in which Si-Si distances around 0.3 nm appear and which are identifiable in regions of high disorder, which especially applies for the high concentration simulations, identify the \hkl<1 0 0> C-Si dumbbell to be responsible for stretching the Si-Si next neighbour distance.
 This excellently agrees with the calculated value $r(13)$ in table \ref{tab:defects:100db_cmp} for a resulting Si-Si distance in the \hkl<1 0 0> C-Si dumbbell configuration.
 
+\begin{figure}[!ht]
+\begin{center}
+ \includegraphics[width=12cm]{sic_prec_450_si-c.ps}
+\end{center}
+\caption{Radial distribution function of the Si-C distances for 6000 carbon atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of $450\,^{\circ}\mathrm{C}$ and cooled down to room temperature together with Si-C bonds resulting in a C-Si \hkl<1 0 0> dumbbell configuration.}
+\label{fig:md:pc_si-c}
+\end{figure}
+Figure \ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a C-Si \hkl<1 0 0> dumbbell configuration.
+The first peak observed for all insertion volumes is at approximately 0.185 nm.
+This corresponds quite well to the expected next neighbour distance of 0.189 nm for Si and C atoms in 3C-SiC.
+
+
 \subsection{Increased temperature simulations}
 
 It is not only the C-C bonds which seem to be unbreakable.
 Also the C-Si pairs, as observed in the low concentration simulations, are stuck.
 This can be seen from the horizontal progress of the total energy graph in the continue-step.
-Higher time periods or alternatively higher temperatures to spped up the simulation are needed.
+Higher time periods or alternatively higher temperatures to speed up the simulation are needed.
 {\color{red}Todo: Read again about the accelerated dynamics methods and maybe explain a bit more here.}
 
 \subsection{Simulations at temperatures exceeding the silicon melting point}