aboutsummaryrefslogtreecommitdiffstats
diff options
context:
space:
mode:
authorNao Pross <np@0hm.ch>2021-05-08 14:58:28 +0200
committerNao Pross <np@0hm.ch>2021-05-08 14:58:28 +0200
commit5ea80792f7fea3d05b62239cb5d6220fb43b3d41 (patch)
treef33eba7dc6e6fd885f6dbe1ac359c1924b2c1b84
parentLittle fix (diff)
downloadSeminarMatrizen-5ea80792f7fea3d05b62239cb5d6220fb43b3d41.tar.gz
SeminarMatrizen-5ea80792f7fea3d05b62239cb5d6220fb43b3d41.zip
Piezoelectricity is tricky
-rw-r--r--vorlesungen/punktgruppen/slides.pdfbin901496 -> 905022 bytes
-rw-r--r--vorlesungen/punktgruppen/slides.tex81
2 files changed, 43 insertions, 38 deletions
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf
index 67c9f4a..2b2e0d8 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 ddc7ed1..e15dd9a 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -738,20 +738,28 @@
\end{scope}
\pause
+ %%
\node[below = of title] {Polarisation Feld \(\vec{E}_p\)};
+
+ %% hex with vertical pressure
\begin{scope}[xshift=11cm, yshift=-4.5cm]
- \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
- \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
- \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
- \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
- \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
- \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
+ \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
+ \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
+ \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
+ \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
+ \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
+ \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
\draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
% \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
- \draw[orange, very thick, <-] (C6) to ++(.7,0);
- \draw[orange, very thick, <-] (C3) to ++(-.7,0);
+ \foreach \d in {C1, C2} {
+ \draw[orange, very thick, <-] (\d) to ++(0,.7);
+ }
+
+ \foreach \d in {C4, C5} {
+ \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+ }
\node[white] (E) {\(\vec{E}_p\)};
\begin{scope}[node distance = .5mm]
@@ -761,8 +769,9 @@
% \draw[gray, thick, dotted] (E) to ++(0,2);
% \draw[gray, thick, dotted] (E) to ++(0,-2);
\end{scope}
- \pause
+ \pause
+ %% square with vertical pressure
\begin{scope}[yshift=-4.5cm]
\matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
\node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
@@ -782,33 +791,32 @@
\end{scope}
\pause
+ %% hex with horizontal pressure
\begin{scope}[xshift=5.5cm, yshift=-4.5cm]
- \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
- \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
- \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
- \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
- \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
- \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
+ \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
+ \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
+ \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
+ \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
+ \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
+ \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
\draw[white] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
% \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
- \foreach \d in {C1, C2} {
- \draw[orange, very thick, <-] (\d) to ++(0,.7);
- }
-
- \foreach \d in {C4, C5} {
- \draw[orange, very thick, <-] (\d) to ++(0,-.7);
- }
+ \draw[orange, very thick, <-] (C6) to ++(.7,0);
+ \draw[orange, very thick, <-] (C3) to ++(-.7,0);
\node[white] (E) {\(\vec{E}_p\)};
\begin{scope}[node distance = .5mm]
- \node[red!50, right = of E] {\(+\)};
- \node[blue!50, left = of E] {\(-\)};
+ \node[blue!50, right = of E] {\(-\)};
+ \node[red!50, left = of E] {\(+\)};
\end{scope}
% \draw[gray, thick, dotted] (E) to ++(0,2);
% \draw[gray, thick, dotted] (E) to ++(0,-2);
\end{scope}
+ \pause
+
+
\end{tikzpicture}
\end{frame}
@@ -816,22 +824,11 @@
\frametitle{Licht in Kristallen}
\begin{columns}[T]
\begin{column}{.5\textwidth}
- Symmetriegruppe und Darstellung
- \begin{align*}
- G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
- &\Phi : G \to O(n)
- \end{align*}
- \begin{align*}
- U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
- &= \mathrm{null}\left(\Phi - \lambda I\right)
- \end{align*}
Helmholtz Wellengleichung
\[
\nabla^2 \vec{E} = \ten{\varepsilon}\mu
\frac{\partial^2}{\partial t^2} \vec{E}
\]
- \end{column}
- \begin{column}{.5\textwidth}
Ebene Welle
\[
\vec{E} = \vec{E}_0 \exp\left[i
@@ -841,9 +838,17 @@
\[
(\ten{K}\ten{\varepsilon})\vec{E} = \frac{k^2}{\mu \omega^2} \vec{E}
\]
- \[
- \vec{E} \in U_\lambda \implies (\ten{K}\ten{\varepsilon}) \vec{E} = \lambda \vec{E}
- \]
+ \end{column}
+ \begin{column}{.5\textwidth}
+ Symmetriegruppe und Darstellung
+ \begin{align*}
+ G &= \left\{\mathbb{1}, r, \sigma, \dots \right\} \\
+ &\Phi : G \to O(n)
+ \end{align*}
+ \begin{align*}
+ U_\lambda &= \left\{ v : \Phi v = \lambda v \right\} \\
+ &= \mathrm{null}\left(\Phi - \lambda I\right)
+ \end{align*}
\end{column}
\end{columns}
}