X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fsimulation.tex;h=cb04ce7082cb9ff1ddbfa0178c0cc3bd070a09cf;hb=74eed718613ff04a1e09a6a5663ac4d38f733e61;hp=094c482f972a083dd4887f5b7000ffdbbd5c00e8;hpb=9d12247bb6a9386ad3c0d8cc5a7ff61e9d2b7350;p=lectures%2Flatex.git

diff --git a/posic/thesis/simulation.tex b/posic/thesis/simulation.tex
index 094c482..cb04ce7 100644
--- a/posic/thesis/simulation.tex
+++ b/posic/thesis/simulation.tex
@@ -74,7 +74,7 @@ Thus, investigating supercells containing more than 56 primitive cells or $112\p
 Throughout this work sampling of the BZ is restricted to the $\Gamma$ point.
 The calculation is usually two times faster and half of the storage needed for the wave functions can be saved since $c_{i,q}=c_{i,-q}^*$, where the $c_{i,q}$ are the Fourier coefficients of the wave function.
 As discussed in section~\ref{subsection:basics:bzs} this does not pose a severe limitation if the supercell is large enough.
-Indeed, it was shown~\cite{dal_pino93} that already for calculations involving only 32 atoms energy values obtained by sampling the $\Gamma$ point differ by less than \unit[0.02]{eV} from calculations using the Baldereschi point~\cite{baldereschi73}, which constitutes a mean-value point in the BZ.
+Indeed, it was shown~\cite{dal_pino93} that already for calculations involving only 32 atoms, energy values obtained by sampling the $\Gamma$ point differ by less than \unit[0.02]{eV} from calculations using the Baldereschi point~\cite{baldereschi73}, which constitutes a mean-value point in the BZ.
 Thus, the calculations of the present study on supercells containing $108$ primitive cells can be considered sufficiently converged with respect to the $k$-point mesh.
 
 \subsection{Energy cut-off}
@@ -188,7 +188,7 @@ Nevertheless, a further and rather uncommon test is carried out to roughly estim
 \subsection{Time step}
 
 The quality of the integration algorithm and the occupied time step is determined by the ability to conserve the total energy.
-Therefore, simulations of a $9\times9\times9$ 3C-SiC unit cell containing 5832 atoms in total are carried out in the $NVE$ ensemble.
+Therefor, simulations of a $9\times9\times9$ 3C-SiC unit cell containing 5832 atoms in total are carried out in the $NVE$ ensemble.
 The calculations are performed for \unit[100]{ps} corresponding to $10^5$ integration steps and two different initial temperatures are considered, i.e.\ \unit[0]{$^{\circ}$C} and \unit[1000]{$^{\circ}$C}.
 \begin{figure}[t]
 \begin{center}