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-rw-r--r--vorlesungen/punktgruppen/slides.pdfbin883884 -> 901246 bytes
-rw-r--r--vorlesungen/punktgruppen/slides.tex156
2 files changed, 84 insertions, 72 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf
index ea4164d..d34f6a3 100644
--- a/vorlesungen/punktgruppen/slides.pdf
+++ b/vorlesungen/punktgruppen/slides.pdf
Binary files differ
diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index dbcf40f..01d59f4 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -259,73 +259,59 @@
}
\section{Kristalle}
-\begin{frame}[fragile]{M\"ogliche Kristallstrukturen}
- \begin{center}
- \begin{tikzpicture}[]
- \node[circle, dashed, draw = gray,
- thick, fill = background,
- minimum size = 4cm] {};
- \node[gray] at (.9,-1.2) {674};
-
- \node[circle, draw = white, thick,
- fill = orange!40!background,
- xshift = -3mm, yshift = 2mm,
- minimum size = 2.75cm] (A) {};
- \node[white, yshift = 2mm] at (A) {230};
-
- \node[circle, draw = white, thick,
- fill = red!20!background,
- xshift = -5mm, yshift = -5mm,
- minimum size = 1cm] {32};
- \end{tikzpicture}
- \end{center}
-\end{frame}
-
\begin{frame}[fragile]{}
\begin{columns}
- \begin{column}{.5\textwidth}
- \begin{center}
- \begin{tikzpicture}[
- dot/.style = {
- draw, circle, thick, white, fill = gray!40!background,
- minimum size = 2mm,
- inner sep = 0pt,
- outer sep = 1mm,
- },
- ]
-
- \begin{scope}
- \clip (-2,-2) rectangle (3,4);
- \foreach \y in {-7,-6,...,7} {
- \foreach \x in {-7,-6,...,7} {
- \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
+ \onslide<1->{
+ \begin{column}{.5\textwidth}
+ \begin{center}
+ \begin{tikzpicture}[
+ dot/.style = {
+ draw, circle, thick, white, fill = gray!40!background,
+ minimum size = 2mm,
+ inner sep = 0pt,
+ outer sep = 1mm,
+ },
+ ]
+
+ \begin{scope}
+ \clip (-2,-2) rectangle (3,4);
+ \foreach \y in {-7,-6,...,7} {
+ \foreach \x in {-7,-6,...,7} {
+ \node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
+ }
}
- }
- \end{scope}
- \draw[white, thick] (-2, -2) rectangle (3,4);
-
- \draw[red!80!background, thick, ->]
- (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
- \draw[cyan!80!background, thick, ->]
- (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
- \end{tikzpicture}
- \end{center}
- \end{column}
- \pause
+ \end{scope}
+ \draw[white, thick] (-2, -2) rectangle (3,4);
+
+ \draw[red!80!background, thick, ->]
+ (N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
+ \draw[cyan!80!background, thick, ->]
+ (N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
+ \end{tikzpicture}
+ \end{center}
+ \end{column}
+ }
\begin{column}{.5\textwidth}
- Kristallgitter:
- \(n_i \in \mathbb{Z}\),
- \(\vec{a}_i \in \mathbb{R}^3\)
- \[
- \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 + n_3 \vec{a}_3
- \]
+ \onslide<2->{
+ Kristallgitter:
+ \(n_i \in \mathbb{Z}\),
+ }
+ \onslide<3->{
+ \(\vec{a}_i \in \mathbb{R}^3\)
+ }
+ \onslide<2->{
+ \[
+ \vec{r} = n_1 \vec{a}_1 + n_2 \vec{a}_2 \onslide<3->{+ n_3 \vec{a}_3}
+ \]
+ }
\vspace{1cm}
- \pause
-
- Invariant unter Translation
- \[
- Q_i(\vec{r}) = \vec{r} + \vec{a}_i
- \]
+
+ \onslide<4->{
+ Invariant unter Translation
+ \[
+ Q_i(\vec{r}) = \vec{r} + \vec{a}_i
+ \]
+ }
\end{column}
\end{columns}
\end{frame}
@@ -383,23 +369,21 @@
(B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
}
- \onslide<7->{
- \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (X) {};
- \draw[gray, dashed, thick] (A2) to (A2 |- B2);
- }
-
- \onslide<8->{
- \node[above left, xshift=-2mm] at (X) {\(x\)};
+ \onslide<10->{
+ \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (Xl) {};
+ \draw[gray, dashed, thick] (A2) to (A2 |- B2) node (Xr) {};
+ \node[above left, xshift=-2mm] at (Xl) {\(x\)};
+ \node[above right, xshift= 2mm] at (Xr) {\(x\)};
}
\end{tikzpicture}
\end{center}
\end{column}
\begin{column}{.5\textwidth}
- \onslide<9->{
+ \onslide<7->{
Sei \(q = |\vec{Q}|\), \(\alpha = 2\pi/n\) und \(n \in \mathbb{N}\)
}
\begin{align*}
- \onslide<10->{q' = n q &= q + 2x \\}
+ \onslide<9->{q' = n q \onslide<10->{&= q + 2x \\}}
\onslide<11->{nq &= q + 2q\sin(\alpha - \pi/2) \\}
\onslide<12->{n &= 1 - 2\cos\alpha}
\end{align*}
@@ -415,6 +399,34 @@
\end{columns}
\end{frame}
+\begin{frame}[fragile]{M\"ogliche Kristallstrukturen}
+ \begin{center}
+ \begin{tikzpicture}[]
+ \node[circle, dashed, draw = gray,
+ thick, fill = background,
+ minimum size = 4cm] {};
+ \node[gray] at (.9,-1.2) {674};
+
+ \node[circle, draw = white, thick,
+ fill = orange!40!background,
+ xshift = -3mm, yshift = 2mm,
+ minimum size = 2.75cm,
+ outer sep = 1mm] (A) {};
+ \node[white, yshift = 2mm] at (A) {230};
+ \node[white, font=\large, above right = of A] (Al) {Raumgruppe};
+ \draw[white, thick, ->] (Al.west) to[out=180, in=60] (A);
+
+ \node[circle, draw = white, thick,
+ fill = red!20!background,
+ xshift = -5mm, yshift = -5mm,
+ minimum size = 1cm,
+ outer sep = 1mm] (B) {32};
+ \node[white, font=\large, below left = of B, xshift=-4mm] (Bl) {Kristallklassen};
+ \draw[white, thick, ->] (Bl.east) to[out = 0, in = 180] (B);
+ \end{tikzpicture}
+ \end{center}
+\end{frame}
+
{
\usebackgroundtemplate[fragile]{
\begin{tikzpicture}[
@@ -678,7 +690,7 @@
]
\matrix [nodes = {box, align = center}, column sep = 1cm, row sep = 1.5cm] {
- & \node (A) {32 Punktgruppen}; \\
+ & \node (A) {32 Kristallklassen}; \\
\node (B) {11 Mit\\ Inversionszentrum}; & \node (C) {21 Ohne\\ Inversionszentrum}; \\
& \node[fill=red!20!background] (D) {20 Piezoelektrisch}; & \node (E) {1 Nicht\\ piezoelektrisch}; \\
};