Set the default k-point to something more illuminating. Loop by defau…

…lt. Reduce arrow size and animation speed.

notebook/lattice-vibration/NGLTrajectoryClass.py

@@ -1,13 +1,15 @@
 import numpy as np
 import os
 
+
 import matplotlib.pyplot as plt
 import ipywidgets as widgets
 from IPython.display import display
 from ase import Atoms
 from ase.io.trajectory import Trajectory
 from sympy import *
 from NGLUtilsClass import NGLWidgets
+from ipywidgets import Output
 
 
 class NGLTrajectory(NGLWidgets):
@@ -68,11 +70,12 @@ def __init__(self, trajectory):
         self.output_ratio = widgets.Output()
 
         # Point is initialized at (0,0), and in acoustic mode
-        self.x = 0
-        self.y = 0
-        self.ka = 0
+        self.x = np.pi/2
+        self.y = 1
+        self.ka = np.pi/2
+        target_k=np.pi/2
         self.ka_array = np.linspace(-2 * np.pi, 2 * np.pi, 101)
-        self.idx = 50 # idx corresponding to ka=0
+        self.idx = int(101*(target_k+2*np.pi)/(4*np.pi)) # idx corresponding to ka=0
         self.optic = False
 
         self.init_delay = 20
@@ -428,6 +431,7 @@ def initialize_dispersion_plot(self, *args):
 
         # Selected frequency point
         (self.point,) = self.ax.plot([], [], ".", c="crimson", markersize=15)
+        self.point.set_data((np.pi/2, 1)) # default to non-trivial k-point
 
         self.ax.set_xlabel("k")
         self.ax.set_ylabel("$\omega$")
@@ -458,6 +462,15 @@ def band_dispersion(self, *args):
             self.lines_op.set_data(([], []))
             self.lines_ac_out.set_data(([], []))
             self.lines_op_out.set_data(([], []))
+
+            # set default k point for monatomic chain
+            self.x=np.pi/2
+            self.idx = (np.abs(self.ka_array - self.x)).argmin()
+            self.ka = self.ka_array[self.idx]
+
+            w = self.w[self.idx]
+            self.point.set_data((self.ka, w))
+
 
         elif self.button_chain.value == "diatomic":
             # Reduce figure width to "half" the size, since x axis is half as big now.
@@ -480,6 +493,13 @@ def band_dispersion(self, *args):
             # Remove monoatomic chain lines
             self.lines.set_data(([], []))
             self.lines_out.set_data(([], []))
+
+            # set default k point for diatomic chain
+            self.x=np.pi/2
+            self.idx = (np.abs(self.ka_array - self.x)).argmin()
+            self.ka = self.ka_array[self.idx]
+            w= self.w_ac[self.idx]
+            self.point.set_data((self.ka, w))
 
         # First BZ limit
         self.ax.plot([-np.pi, -np.pi], [0, 2.2], "k--", linewidth=1)
@@ -490,7 +510,7 @@ def band_dispersion(self, *args):
         # 2.2 works well for initial height
         self.ax.set_ybound(0, 2.2)
 
-        self.point.set_data((0, 0))
+        # set default point on dispersion
         self.fig.canvas.mpl_connect("button_press_event", self.onclick)
         plt.ion()
 

notebook/lattice-vibration/NGLUtilsClass.py

@@ -95,7 +95,7 @@ def __init__(self, trajectory) -> None:
             r"Arrow amplitude", layout=self.layout_description
         )
         self.slider_amp_arrow = widgets.FloatSlider(
-            value=2.0,
+            value=0.5,
             min=0.1,
             max=5.01,
             step=0.1,

notebook/lattice-vibration/Phonon_1D.ipynb

@@ -41,18 +41,18 @@
     "3. Visualize the phonon dispersion for a diatomic chain. What is the difference between the acoustic and optical branch at $k=0$ and $k=\\pm\\frac{\\pi}{2a}$ ? How do the atoms displacements relate to frequency ?\n",
     "    <details>\n",
     "    <summary style=\"color: red\">Solution</summary>\n",
-    "    At $k=0$, in the acoustic branch, as in the monoatomic chain, the atoms do not move. Instead, in the optical branch the two atoms are moving out-of-phase. The latter one has therefore a high frequency.\n",
+    "    At $k=0$, in the acoustic branch, as in the monoatomic chain, the atoms do not move. Instead, in the optical branch the two atoms are moving out-of-phase. The latter therefore has a high frequency.\n",
     "    \n",
-    "    At $k=\\pm\\frac{\\pi}{2a}$, in the acoustic branch the light atoms stand still whearas the heavier atoms move. In the optical branch, the opposite is observed. Since frequency is proportional to $\\sqrt{1/M}$, the frequency is higher when lighter atoms move. \n",
+    "    At $k=\\pm\\frac{\\pi}{2a}$, in the acoustic branch, the light atoms stand still whearas the heavier atoms move. In the optical branch, the opposite is observed. Since frequency is proportional to $\\sqrt{1/M}$, the frequency is higher when lighter atoms move. \n",
     "    </details>\n",
     "    \n",
     "    \n",
-    "4. Adjust the mass ratio of the molecules. What happens when the ratio is high ? When the ratio is close to unity ? How does the band dispersion evolve ?\n",
+    "4. Adjust the mass ratio of the molecules. What happens when the ratio is high ? How about when the ratio is close to unity ? How does the band dispersion change ?\n",
     "    <details>\n",
     "    <summary style=\"color: red\">Solution</summary>\n",
-    "    As the ratio grows, the forbidden frequencies gap grows as well. At $k=\\pm\\frac{\\pi}{2a}$, the gap is proportional to $\\sqrt{1/M_{gray}}-\\sqrt{1/M_{red}}$.\n",
+    "    As the ratio grows, the gap of forbidden frequencies grows as well. At $k=\\pm\\frac{\\pi}{2a}$, the gap is proportional to $\\sqrt{1/M_{gray}}-\\sqrt{1/M_{red}}$.\n",
     "    \n",
-    "    Furthermore, at $k=0$, we have $\\frac{u_{red}}{u_{gray}}=\\frac{-M_{gray}}{M_{red}}$, and thus the heavier atom amplitude decreases as it gets heavier.\n",
+    "    Furthermore, at $k=0$, we have $\\frac{u_{red}}{u_{gray}}=\\frac{-M_{gray}}{M_{red}}$, and thus the oscillation amplitude of the heavier atom decreases as it gets heavier.\n",
     "    </details>\n",
     "    \n",
     "    \n",
@@ -70,9 +70,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "d7013e3d8e4e48b5bd47310cd0d4742b",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "%matplotlib widget\n",
@@ -90,7 +103,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -132,7 +145,7 @@
     "    handler.widgetList.append(widget)\n",
     "\n",
     "handler.slider_atom_radius.value=0.1\n",
-    "handler.slider_arrow_radius.value=0.1\n",
+    "handler.slider_arrow_radius.value=0.05\n",
     "handler.tick_box_arrows.value=True\n",
     "handler.addArrows() # add arrows by default\n",
     "handler.set_player_parameters(delay=handler.init_delay)\n",
@@ -223,7 +236,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -254,13 +267,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "5fcc7dc436fc4fb49e968f36b35ce6ec",
+       "model_id": "60c1818f30a54bc0b04cb1a03675b7d9",
        "version_major": 2,
        "version_minor": 0
       },
@@ -274,7 +287,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "b58c0b65f41e420f953144a81ec71577",
+       "model_id": "98bc1ac74b5c4af680e96b3f5fdd1b1d",
        "version_major": 2,
        "version_minor": 0
       },