X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=58369fab1c5fee4dc78b2bd011e7b56cbddb7798;hb=f9465130d3e796c6cf3a381b62285c281704b7ab;hp=67de04d36939ec3fa44fb48e55d1ba77425e5167;hpb=95b2d1acc7fb1969b13df81cf5c3e0eeea913dff;p=lectures%2Flatex.git

diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex
index 67de04d..58369fa 100644
--- a/posic/talks/seminar_2010.tex
+++ b/posic/talks/seminar_2010.tex
@@ -182,7 +182,8 @@
          \item Density functional theory (DFT) calculations
         \end{itemize}
   \item C and Si self-interstitial point defects in silicon
-  \item Precipitation simulations
+  \item Silicon carbide precipitation simulations
+  \item Investigation of a silicon carbide precipitate in silicon
   \item Summary / Conclusion / Outlook
  \end{itemize}
 
@@ -343,7 +344,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
  \end{minipage}
  \begin{minipage}{6.3cm}
  \begin{center}
- {\color{blue}\bf\normalsize
+ {\color{blue}
   Precipitation mechanism not yet fully understood!
  }
  \renewcommand\labelitemi{$\Rightarrow$}
@@ -430,10 +431,84 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
-%\rput{-20}{\psellipse[linecolor=blue](6,6.5)(0.3,0.5)}
 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 \end{pspicture}
  
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  Basics of molecular dynamics (MD) simulations
+ }
+
+ \vspace{12pt}
+
+ \small
+
+ {\bf MD basics:}
+ \begin{itemize}
+  \item Microscopic description of N particle system
+  \item Analytical interaction potential
+  \item Numerical integration using Newtons equation of motion\\
+        as a propagation rule in 6N-dimensional phase space
+  \item Observables obtained by time and/or ensemble averages
+ \end{itemize}
+ {\bf Details of the simulation:}
+ \begin{itemize}
+  \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
+  \item Ensemble: NpT (isothermal-isobaric)
+        \begin{itemize}
+         \item Berendsen thermostat:
+               $\tau_{\text{T}}=100\text{ fs}$
+         \item Berendsen barostat:\\
+               $\tau_{\text{P}}=100\text{ fs}$,
+               $\beta^{-1}=100\text{ GPa}$
+        \end{itemize}
+  \item Potential: Tersoff-like bond order potential
+  \vspace*{12pt}
+        \[
+        E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+        \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+        \]
+ \end{itemize}
+
+ \begin{picture}(0,0)(-230,-30)
+  \includegraphics[width=5cm]{tersoff_angle.eps} 
+ \end{picture}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Basics of density functional theory (DFT) calculations
+ }
+
+ \small
+
+ Ingredients
+ \begin{itemize}
+  \item Hohenberg-Kohn (HK) theorem
+  \item \underline{Born-Oppenheimer}
+        - $N$ moving electrons in an external potential of static nuclei\\
+\[
+H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
+              +\sum_i^N V_{\text{ext}}(r_i)
+              +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
+\]
+  \item \underline{Effective potential}
+        - replace electrostatic potential by an average over e$^-$ positions\\
+\[
+V_{\text{eff}}=...
+\]
+  \item Exchange correlation (EC) LDA / GGA
+  \item Self-consistent solution
+  \item Plane wave basis set
+  \item Pseudo potential
+ \end{itemize}
+
+\end{slide}
+
+
 \end{document}