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| -rw-r--r-- | vorlesungen/punktgruppen/slides.pdf | bin | 883884 -> 901246 bytes | |||
| -rw-r--r-- | vorlesungen/punktgruppen/slides.tex | 156 |
2 files changed, 84 insertions, 72 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf Binary files differindex ea4164d..d34f6a3 100644 --- a/vorlesungen/punktgruppen/slides.pdf +++ b/vorlesungen/punktgruppen/slides.pdf 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}; \\ }; |