start of increased temperature simulations

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index d797f8c..2318a65 100644 (file)
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -23,6 +23,7 @@ Due to promising advantages over the Tersoff potential the bond order potential
 A time step of one fs is set.
 
 \subsection{Simulations at temperatures used in ion beam synthesis}
+\label{subsection:initial_sims}
 
 In initial simulations aiming to reproduce a precipitation process simulation volumes of $31\times 31\times 31$ unit cells are utilized.
 Periodic boundary conditions in each direction are applied.
@@ -245,20 +246,33 @@ Another one is to use variable cut-off values scaled by the system volume, which
 
 To conclude the obstacle needed to get passed is twofold.
 The sharp cut-off of the used bond order model potential introduces overestimated high forces between next neighboured atoms enhancing the problem of slow phase space propagation immanent to MD simulations.
-
-{\color{blue}
-Thus, applying longer time scales in order to enable the system to undergo diffusion events, which become very unlikely to happen due to the overestimated bond strengthes, and in the end observe the agglomeration and precipitation might not be sufficient.
-On the other hand longer time scales are not accessible to simulation due to limited computational ressources.
-Alternatively the approach of using higher temperatures to speed up or actually make possible the steps involved in the precipitation mechanism is applied.
-
-TAD, correcting time and undo changes for real temperature.
-Since the shot cut-off in the used potential introduces unphysical high forces use of higher temperatures in order to get the system to escape local minima and transform into the crystalline phase is the first approach followed.
-Anyways there is now conflict to experiments applying higher temepratures without the TAD corrections, since crystalline 3C-SiC is also expected for higher temperatures on the one hand and on the other hand the exact temperature inside the implantation volume is definetly higher than the temperature meassured at the surface of the sample.
-}
+Thus, pushing the time scale to the limits of computational ressources or applying one of the above mentioned accelerated dynamics methods exclusively will not be sufficient enough.
+
+Instead the first approach followed in this study, is the use of higher temperatures as exploited in TAD to find transition pathways of one local energy minimum to another one more quickly.
+Since merely increasing the temperature leads to different equilibrium kinetics than valid at low temperatures, TAD introduces basin-constrained MD allowing only those transitions that should occur at the original temperature and a properly advancing system clock \cite{sorensen2000}.
+The TAD corrections are not applied in coming up simulations.
+This is justified by two reasons.
+First of all a compensation of the overestimated bond strengthes due to the short range potential is expected.
+Secondly there is no conflict applying higher temperatures without the TAD corrections, since crystalline 3C-SiC is also observed for higher temperatures than $450\,^{\circ}\mathrm{C}$ in IBS \cite{lindner01}.
+It is therefore expected that the kinetics affecting the 3C-SiC precipitation are not much different at higher temperatures aside from the fact that it is occuring much more faster.
+Moreover, the interest of this study is focused on structural evolution of a system far from equilibrium instead of equilibrium properties which rely upon proper phase space sampling.
+On the other hand, during implantation, the actual temperature inside the implantation volume is definetly higher than the experimentally determined temperature tapped from the surface of the sample.
 
 \subsection{Increased temperature simulations}
 
-{\color{red}Todo: We go for higher temepratures first due to the potential cut-off artifact discussed above.}
+Due to the limitations of short range potentials and conventional MD as discussed above elevated temperatures are used in the following.
+The simulation sequence and other parameters aside system temperature remain unchanged as in section \ref{subsection:initial_sims}.
+Since there is no significant difference among the $V_2$ and $V_3$ simulations only the $V_1$ and $V_2$ simulations are carried on and refered to as low carbon and high carbon concentration simulations.
+Temperatures ranging from $450\,^{\circ}\mathrm{C}$ up to $2050\,^{\circ}\mathrm{C}$ are used.
+A quality value $Q$ is introduced, which is defined as
+\begin{equation}
+Q = \frac{\text{Amount of C atoms with 4 next neighboured Si atoms}}
+         {\text{Total amount of C atoms}} \text{ .}
+\label{eq:md:qdef}
+\end{equation}
+In 3C-SiC every C atom has four next neighboured Si atoms resulting in $Q=1$.
+
+Figure ... shows the radial distribution of Si-C bonds and the corresponding quality paragraphs.
 
 \subsection{Constructed 3C-SiC precipitate in crystalline silicon}