nearly finished the challenge subsection ...

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 3662b69..d797f8c 100644 (file)
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -22,7 +22,7 @@ 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}
+\subsection{Simulations at temperatures used in ion beam synthesis}
 
 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.
@@ -217,25 +217,44 @@ Short range order indeed is observed but only hardly visible is the long range o
 This indicates the formation of an amorphous SiC-like phase.
 In fact the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential \cite{gao02}.
 
-\subsection{Limitations of conventional MD and short order potentials}
-
-{\color{blue}
-Alternatively: Explain general problem of the slow propagation through phase space using conventional molecular dynamics and the accompanying difficulties for conformational search.
-Explain the methods available to overcome this limitation.
-Point out, that in this work, the sharp cut-off introduces unphysical and overestimated high forces between next neighboured atoms enhancing the problem of slow phase space propagation.
-}
-
-The formation of an amoprhous SiC-like phase although experiments show crystalline 3C-SiC precipitates at prevailing temperatures remains unexplained.
-The answer is found in the short range and sharp cut-off of the employed bond order potential.
-The cut-off funtion, which limits the interacting ions to the next neighboured atoms by gradually pushing the interaction force and energy to zero betwenn the first and second next neighbour distance, is responsible for overestimated and unphysical high forces of next neighboured atoms \cite{mattoni2007}.
-Indeed it is not only the strong C-C bond which is hard to break inhibiting carbon diffusion and further conformational changes.
-This is also true for the low concentration simulations dominated by C-Si dumbbells spread over the whole simulation volume.
+\subsection{Limitations of conventional MD and short range potentials}
+
+At first the formation of an amorphous SiC-like phase is unexpected since IBS experiments show crystalline 3C-SiC precipitates at prevailing temperatures.
+On closer inspection, however, reasons become clear, which are discussed in the following.
+
+The first reason is a general problem of MD simulations in conjunction with limitations in computer power, which results in a slow and restricted propagation in phase space.
+In molecular systems, characteristic motions take place over a wide range of time scales.
+Vibrations of the covalent bond take place on the order of $10^{-14}\,\text{s}$ of which the thermodynamic and kinetic properties are well described by MD simulations.
+To avoid dicretization errors the integration timestep needs to be chosen smaller than the fastest vibrational frequency in the system.
+On the other hand, infrequent processes, such as conformational changes, reorganization processes during film growth, defect diffusion and phase transitions are processes undergoing long-term evolution in the range of microseconds.
+This is due to the existence of several local minima in the free energy surface separated by large energy barriers compared to the kinetic energy of the particles, that is the system temperature.
+Thus, the average time of a transition from one potential basin to another corresponds to a great deal of vibrational periods, which in turn determine the integration timestep.
+Hence, time scales covering the neccessary amount of infrequent events to observe long-term evolution are not accessible by traditional MD simulations, which are limited to the order of nanoseconds.
+New methods have been developed to bypass the time scale problem like hyperdnyamics (HMD) \cite{voter97,voter97_2}, parallel replica dynamics \cite{voter98}, temperature acclerated dynamics (TAD) \cite{sorensen2000} and self-guided dynamics (SGMD) \cite{wu99} retaining proper thermodynmic sampling.
+
+In addition to the time scale limitation, problems attributed to the short range potential exist.
+The sharp cut-off funtion, which limits the interacting ions to the next neighboured atoms by gradually pushing the interaction force and energy to zero between the first and second next neighbour distance, is responsible for overestimated and unphysical high forces of next neighboured atoms \cite{tang95,mattoni2007}.
+Indeed it is not only the strong C-C bond which is hard to break inhibiting carbon diffusion and further rearrengements.
+This is also true for the low concentration simulations dominated by the occurrence of C-Si dumbbells spread over the whole simulation volume.
 The bonds of these C-Si pairs are also affected by the cut-off artifact preventing carbon diffusion and agglomeration of the dumbbells.
 This can be seen from the almost horizontal progress of the total energy graph in the continuation step, even for the low concentration simulation.
+The unphysical effects inherent to this type of model potentials are solely attributed to their short range character.
+However, since valueable insights into various physical properties can be gained using this potentials, modifications mainly affecting the cut-off were designed.
+One possibility is to simply skip the force contributions containing the derivatives of the cut-off function, which was successfully applied to reproduce the brittle propagation of fracture in SiC at zero temperature \cite{mattoni2007}.
+Another one is to use variable cut-off values scaled by the system volume, which properly describes thermomechanical properties of 3C-SiC \cite{tang95} but might be rather ineffective for the challange inherent to this study.
+
+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.
+}
 
 \subsection{Increased temperature simulations}