Piezoelectricity is tricky

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
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}
 }