more hkls and some commas

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 6fd1629..ea16cd3 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -573,7 +573,7 @@ The C atom resides in the \hkl(-1 1 0) plane.
 This transition involves the intermediate BC configuration.
 However, results discussed in the previous section indicate that the BC configuration is a real local minimum.
 Thus, the \hkl[0 0 -1] to \hkl[0 0 1] migration can be thought of a two-step mechanism, in which the intermediate BC configuration constitutes a metastable configuration.
-Due to symmetry, it is enough to consider the transition from the BC to the \hkl<1 0 0> configuration or vice versa.
+Due to symmetry, it is enough to consider the transition from the BC to a \hkl<1 0 0> configuration or vice versa.
 In the second path, the C atom is changing its Si partner atom as in path one.
 However, the trajectory of the C atom is no longer proceeding in the \hkl(-1 1 0) plane.
 The orientation of the new DB configuration is transformed from \hkl[0 0 -1] to \hkl[0 -1 0].
@@ -592,8 +592,8 @@ The bond to the face-centered Si atom at the bottom of the unit cell breaks and
 \caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to BC transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to BC (right) transition. Bonds of the C atom are illustrated by blue lines.}
 \label{fig:defects:00-1_001_mig}
 \end{figure}
-In Fig.~\ref{fig:defects:00-1_001_mig} results of the \hkl<0 0 -1> to \hkl<0 0 1> migration fully described by the migration of the \hkl<0 0 -1> to the BC configuration is displayed.
-To reach the BC configuration, which is \unit[0.94]{eV} higher in energy than the \hkl<0 0 -1> DB configuration, an energy barrier of approximately \unit[1.2]{eV} given by the saddle point structure at a displacement of \unit[60]{\%} has to be passed.
+In Fig.~\ref{fig:defects:00-1_001_mig} results of the \hkl[0 0 -1] to \hkl[0 0 1] migration fully described by the migration of the \hkl[0 0 -1] to the BC configuration is displayed.
+To reach the BC configuration, which is \unit[0.94]{eV} higher in energy than the \hkl[0 0 -1] DB configuration, an energy barrier of approximately \unit[1.2]{eV} given by the saddle point structure at a displacement of \unit[60]{\%} has to be passed.
 This amount of energy is needed to break the bond of the C atom to the Si atom at the bottom left.
 In a second process \unit[0.25]{eV} of energy are needed for the system to revert into a \hkl<1 0 0> configuration.
 
@@ -604,7 +604,7 @@ In a second process \unit[0.25]{eV} of energy are needed for the system to rever
 \caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to the {\hkl[0 -1 0]} DB transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition. Bonds of the C atom are illustrated by blue lines.}
 \label{fig:defects:00-1_0-10_mig}
 \end{figure}
-Fig.~\ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.
+Fig.~\ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition.
 The resulting migration barrier of approximately \unit[0.9]{eV} is very close to the experimentally obtained values of \unit[0.70]{eV}~\cite{lindner06}, \unit[0.73]{eV}~\cite{song90} and \unit[0.87]{eV}~\cite{tipping87}.
 
 \begin{figure}[tp]
@@ -644,14 +644,14 @@ In addition, it is finally shown that the BC configuration, for which spin polar
 Further migration pathways, in particular those occupying other defect configurations than the \hkl<1 0 0>-type either as a transition state or a final or starting configuration, are totally conceivable.
 This is investigated in the following in order to find possible migration pathways that have an activation energy lower than the ones found up to now.
 The next energetically favorable defect configuration is the \hkl<1 1 0> C-Si DB interstitial.
-Fig.~\ref{fig:defects:110_mig_vasp} shows the migration barrier of the \hkl<1 1 0> C-Si DB to the BC, \hkl<0 0 -1> and \hkl<0 -1 0> (in place) transition.
-Indeed less than \unit[0.7]{eV} are necessary to turn a \hkl<0 -1 0>- to a \hkl<1 1 0>-type C-Si DB interstitial.
+Fig.~\ref{fig:defects:110_mig_vasp} shows the migration barrier of the \hkl[1 1 0] C-Si DB to the BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) transition.
+Indeed less than \unit[0.7]{eV} are necessary to turn the \hkl[0 -1 0] to the \hkl[1 1 0] C-Si DB interstitial.
 This transition is carried out in place, i.e.\ the Si DB pair is not changed and both, the Si and C atom share the initial lattice site.
 Thus, this transition does not contribute to long-range diffusion.
-Once the C atom resides in the \hkl<1 1 0> DB interstitial configuration it can migrate into the BC configuration requiring approximately \unit[0.95]{eV} of activation energy, which is only slightly higher than the activation energy needed for the \hkl<0 0 -1> to \hkl<0 -1 0> pathway as shown in Fig.~\ref{fig:defects:00-1_0-10_mig}.
-As already known from the migration of the \hkl<0 0 -1> to the BC configuration discussed in Fig.~\ref{fig:defects:00-1_001_mig}, another \unit[0.25]{eV} are needed to turn back from the BC to a \hkl<1 0 0>-type interstitial.
+Once the C atom resides in the \hkl[1 1 0] DB interstitial configuration, it can migrate into the BC configuration requiring approximately \unit[0.95]{eV} of activation energy, which is only slightly higher than the activation energy needed for the \hkl[0 0 -1] to \hkl[0 -1 0] pathway as shown in Fig.~\ref{fig:defects:00-1_0-10_mig}.
+As already known from the migration of the \hkl[0 0 -1] to the BC configuration discussed in Fig.~\ref{fig:defects:00-1_001_mig}, another \unit[0.25]{eV} are needed to turn back from the BC to a \hkl<1 0 0>-type interstitial.
 However, due to the fact that this migration consists of three single transitions with the second one having an activation energy slightly higher than observed for the direct transition, this sequence of paths is considered very unlikely to occur.
-The migration barrier of the \hkl<1 1 0> to \hkl<0 0 -1> transition, in which the C atom is changing its Si partner and, thus, moving to the neighbored lattice site, corresponds to approximately \unit[1.35]{eV}.
+The migration barrier of the \hkl[1 1 0] to \hkl[0 0 -1] transition, in which the C atom is changing its Si partner and, thus, moving to the neighbored lattice site, corresponds to approximately \unit[1.35]{eV}.
 During this transition the C atom is escaping the \hkl(-1 1 0) plane approaching the final configuration on a curved path.
 This barrier is much higher than the ones found previously, which again make this transition very unlikely to occur.
 For this reason, the assumption that C diffusion and reorientation is achieved by transitions of the type presented in Fig.~\ref{fig:defects:00-1_0-10_mig} is reinforced.

diff --git a/posic/thesis/simulation.tex b/posic/thesis/simulation.tex
index 8faec6f..e529986 100644 (file)
--- a/posic/thesis/simulation.tex
+++ b/posic/thesis/simulation.tex
@@ -272,7 +272,7 @@ Notation & $N^{\text{3C-SiC}}_{\text{C}}$ & $N^{\text{3C-SiC}}_{\text{Si}}$
 
 After the initial configuration is constructed, some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
 Thus, the system is equilibrated using strong coupling to the heat bath, which is set to be \unit[20]{$^{\circ}$C}.
-Once the main part of the excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another \unit[10]{ps}.
+Once the main part of the excess energy is carried out, previous settings for the Berendsen thermostat are restored and the system is relaxed for another \unit[10]{ps}.
 
 \begin{figure}[t]
 \begin{center}