lots of punctuation stuff

[lectures/latex.git] / posic / thesis / simulation.tex

diff --git a/posic/thesis/simulation.tex b/posic/thesis/simulation.tex
index 511019e..a32d343 100644 (file)
--- a/posic/thesis/simulation.tex
+++ b/posic/thesis/simulation.tex
@@ -73,7 +73,7 @@ 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.
+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.
 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.
 
@@ -315,7 +315,7 @@ Using $a_{\text{3C-SiC prec}}=4.34\,\text{\AA}$ as observed from the radial dist
 However, each side length and the total volume of the simulation box is increased by \unit[0.20]{\%} and \unit[0.61]{\%} respectively compared to plain c-Si at \unit[20]{$^{\circ}$C}.
 Since the c-Si surrounding resides in an uncompressed state, the excess increase must be attributed to relaxation of strain with the strain resulting from either the compressed precipitate or the 3C-SiC/c-Si interface region.
 This also explains the possibly identified slight increase of the c-Si lattice constant in the surrounding as mentioned earlier.
-As the pressure is set to zero the free energy is minimized with respect to the volume enabled by the Berendsen barostat algorithm.
+As the pressure is set to zero, the free energy is minimized with respect to the volume enabled by the Berendsen barostat algorithm.
 Apparently the minimized structure with respect to the volume is a configuration of a small compressively stressed precipitate and a large amount of slightly stretched c-Si in the surrounding.
 
 To finally draw some conclusions concerning the capabilities of the potential, the 3C-SiC/c-Si interface is now addressed.