{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " **Chapter 2: [Diffraction](CH2_00-Diffraction.ipynb)** \n", "\n", "\n", "
\n", "\n", "\n", "# Atomic Form Factor\n", "\n", "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM//main/Diffraction/CH2_02-Atomic_Form_Factor.ipynb)\n", "\n", "\n", "[![OpenInColab](https://colab.research.google.com/assets/colab-badge.svg)](\n", " https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Diffraction/CH2_02-Atomic_Form_Factor.ipynb)\n", " \n", "part of\n", "\n", " **[MSE672: Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**\n", "\n", "**Spring 2024**\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Gerd Duscher Khalid Hattar
Microscopy Facilities Tennessee Ion Beam Materials Laboratory
Materials Science & Engineering Nuclear Engineering
Institute of Advanced Materials & Manufacturing
The University of Tennessee, Knoxville
\n", "\n", "Background and methods to analysis and quantification of data acquired with transmission electron microscopes." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Import numerical and plotting python packages\n", "### Check Installed Packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "installing pyTEMlib\n", "done\n" ] } ], "source": [ "import sys\n", "import importlib.metadata\n", "def test_package(package_name):\n", " \"\"\"Test if package exists and returns version or -1\"\"\"\n", " try:\n", " version = importlib.metadata.version(package_name)\n", " except importlib.metadata.PackageNotFoundError:\n", " version = '-1'\n", " return version\n", "\n", "if test_package('pyTEMlib') < '0.2024.1.0':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install --upgrade pyTEMlib -q\n", "if 'google.colab' in sys.modules:\n", " !{sys.executable} -m pip install numpy==1.24.4\n", "print('done')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load the plotting and figure packages" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You don't have igor2 installed. If you wish to open igor files, you will need to install it (pip install igor2) before attempting.\n", "You don't have gwyfile installed. If you wish to open .gwy files, you will need to install it (pip install gwyfile) before attempting.\n", "Symmetry functions of spglib enabled\n", "Using kinematic_scattering library version {_version_ } by G.Duscher\n" ] } ], "source": [ "%matplotlib widget\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# additional package \n", "import scipy # we use the constants part again.\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " from google.colab import output\n", " output.enable_custom_widget_manager()\n", " \n", "# Import libraries from the pyTEMlib\n", "import pyTEMlib.kinematic_scattering as ks # Kinematic scattering Library\n", " # with Atomic form factors from Kirklands book" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coulomb Force\n", "\n", "The electron scatters at the Coulomb force of the screened nucleus of an atom. This force is:\n", "\n", "$\\mathbf{F} = \\frac{1}{4\\pi\\varepsilon_0}\\frac{Qq}{r^2}\\mathbf{\\hat{e}}_r \n", "= k_\\text{e}\\frac{Qq}{r^2}\\mathbf{\\hat{e}}_r $\n", "\n", "$k_\\text{e} = \\frac{1}{4\\pi\\varepsilon_0}= 8.987\\,551\\,787\\,368\\,1764\\times 10^9~\\mathrm{N\\ m^2\\ C^{-2}}$\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " k_e = 8.9876e+09 N m²C⁻²\n", " F_r_m = 20007.8 N m² kg⁻¹ = 20007.8 m³s⁻²\n" ] } ], "source": [ "Z = 79 # gold\n", "\n", "k_e = 1/(4* scipy.constants.pi * scipy.constants.epsilon_0)\n", "F_r_m = k_e * Z* scipy.constants.elementary_charge**2 /scipy.constants.electron_mass\n", "print(f\" k_e = {k_e:.5} N m\\u00b2C\\u207B\\u00b2\")\n", "print(f\" F_r_m = {F_r_m:.1f} N m\\u00b2 kg\\u207B\\u00B9 = {F_r_m:.1f} m\\u00b3s\\u207B\\u00B2\")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e1b7f6a51f754a2ca2ecb5bdab56e145", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def coulomb_plot(impact_param = 1.0, Z = 79, v_c = 0.5):\n", " # all length are in m\n", " #time interval for each iteration. Should be chosen small enough so that\n", " #the velocity change and position change in this interval is relatively\n", " #small. If too small this calculation will take a while\n", " dt = 1e-20 # s\n", " \n", " x = -50.0*1e-9 # starting x in m\n", " y = impact_param*1e-9 #in m\n", " #starting y\n", " x_coords=[x] #array for the x coordinates of the plot\n", " y_coords=[y] #array for the y coordinates of the plot\n", " vx = v_c * scipy.constants.c #initial x velocity in m/s\n", " vy = 0.0 #initial y velocity\n", " \n", " r = np.sqrt(x*x + y*y)\n", " rold = r*2 # an arbitrary value more than r\n", "\n", " k_e = 1/(4* scipy.constants.pi * scipy.constants.epsilon_0) #[N m^2 C^-2]\n", " F_r_m = -k_e * Z* scipy.constants.elementary_charge**2 /scipy.constants.electron_mass # [ N m^2 / kg]\n", " \n", " # The plot coordinates are generated as long as the incident particle\n", " # is going towards the origin( which means that r < rold )\n", " # or\n", " # if it is coming out, as long as r < 50.0 nm. You can choose this to be\n", " # something else.\n", " while (r < rold) or ( r < 50.0*1e-9) :\n", " rold = r # old r is changed to the current r\n", " x = x + vx*dt# calculate new x\n", " y = y + vy*dt# calculate new y\n", " # add x and y to the plotting coordinates for x and y\n", " x_coords.append(x)\n", " y_coords.append(y)\n", " r = np.sqrt(x*x + y*y)\n", " \n", " #vx = vx + x-acceleration*dt = vx + Fx/m*dt \n", " #Fx = x component of Coulomb force = (magnitude of F)*cos(theta) =\n", " #(magnitude of F)*x/r = \n", " #vx = vx + (F_r/m/r^2)*x/r = F_r_m * x/r^3,\n", " vx = vx + F_r_m*x/r**3*dt\n", " #as for vx\n", " vy = vy + F_r_m*y/r**3*dt\n", " \n", " return np.array(x_coords), np.array(y_coords)\n", "\n", "\n", "#plotting trajectories for 4 impact parameters\n", "plt.figure()\n", "for b in [-1e-5, -0.001, -0.1, -1.0, -2.0, -4.0, -6.0]:\n", " xc, yc = coulomb_plot(b, Z= 29, v_c = 0.7)\n", " plt.plot(xc*1e9,yc*1e9, label = str(b))\n", "\n", "plt.xlabel('distance [nm]')\n", "plt.ylabel('impact parameter [nm]')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above graph was calulated for 200keV electrons.\n", "What changes if you change the v_c = v/c parameter to higher or lower speeds?\n", "\n", "|E (keV)|$\\lambda$ (pm) | M/m$_0$ | v/c|\n", "--------|---------------|---------|----|\n", "|10 | 12.2 | 1.0796 | 0.1950 |\n", "|30 | 6.02 | 1.129 | 0.3284 |\n", "|100 | 3.70 | 1.1957 | 0.5482|\n", "|200 | 2.51 | 1.3914 | 0.6953|\n", "|400 | 1.64 | 1.7828 | 0.8275 |\n", "|1000 | 0.87 | 2.9569 | 0.9411|\n", "\n", "You can also change the atom number." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "b7c2565fed8a4050afb74695a158c9bc", "version_major": 2, "version_minor": 0 }, "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAABXs0lEQVR4nO3dd3gVZf7+8fdJD6lAICEkhN47KFIkKggou1hWAQuI+hNdUZoisIoUUYqIrLqubdeyFthdin5XUIIUQZClGIqwgJiQUGKkJIGQfub3x4Ejh1RITibJ3K/r4sJ5zjMznzNE5uaZmWdshmEYiIiIiIhleJhdgIiIiIhULgVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYvxMruA6sxut3P8+HGCgoKw2WxmlyMiIiJlYBgGZ8+eJTIyEg8Pa46FKQCWw/Hjx4mOjja7DBEREbkKycnJREVFmV2GKRQAyyEoKAhw/AAFBwebXI2IiIiURUZGBtHR0c7zuBUpAJbDxcu+wcHBCoAiIiLVjJVv37LmhW8RERERC1MAFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAvGDOnDnYbDbGjx9vdikiIiIibqUACGzbto133nmHjh07ml2KiIiIiNtZPgCeO3eO++67j3fffZfatWubXY6IiIiI21k+AI4ZM4bBgwfTv3//Uvvm5OSQkZHh8ktERESkurH0u4AXL17Mzp072bZtW5n6z5kzh5kzZ7q5KhEREQHAMMDC7+t1J8uOACYnJzNu3Dg+/vhj/Pz8yrTO1KlTSU9Pd/5KTk52c5UiIiIWlJYM/3wAtr5tdiU1ls0wDMPsIsywYsUK7rjjDjw9PZ1tBQUF2Gw2PDw8yMnJcfmsKBkZGYSEhJCenk5wcLC7SxYREanZ8rJhy+uwcSHknQf/2jBhH/jUqtDd6Pxt4UvA/fr1Y8+ePS5tDz74IK1bt2by5Mmlhj8RERGpQAe/hlWT4UyCY7lRL7h1foWHP3GwbAAMCgqiffv2Lm0BAQHUrVu3ULuIiIi4yanD8NVUOPS1YzmoAdz8AnS4S/f/uZFlA6CIiIiYKDfTcal382tQkAse3tDzceg7CXyDzK6uxlMAvMT69evNLkFERKRmMwzYtwK+fg4yjjramt0Eg+ZBvZamlmYlCoAiIiJSOVL3w8pJkLjRsRzSCAbNgdaDdbm3kikAioiIiHtlp8P6ebD1LTAKwMsPeo+HPuPB29/s6ixJAVBERETcw26H3YshbjpkpjraWv8OBr4ItRubWprVKQCKiIhIxTse77jce/S/juW6zeGWedC89FevivspAIqIiEjFOX8avpkFOz4ADPAOgNhn4LrHwcvH7OrkAgVAERERKT97gSP0rX0Bss442trfBQNegOBIU0uTwhQARUREpHyStsLKpyFlt2O5fjvHWzwa9zG3LimWAqCIiIhcnbO/wJrpsOszx7JvCNz0LHR/GDwVMaoy/emIiIjIlSnIg61vw/q5kHvW0dZlBPSbDoH1zK1NykQBUERERMru5/Ww8hk4ecCxHNkVbl0AUd1MLUuujAKgiIiIlC4tGVY/C/s+dyzXqgv9Z0Dn+8HDw9TS5MopAIqIiEjx8rJhy+vw7SuQnwU2D7jm/8GNfwL/2mZXJ1dJAVBERESKduAr+GoynEl0LDfq5Xi6N6KDqWVJ+SkAioiIiKtTh+GrqXDoa8dyUAO4+QXocBfYbObWJhVCAVBEREQccjNh4yuw+XUoyAUPb+j5OPSdBL5BZlcnFUgBUERExOoMA/atgK+fhYxjjrZmN8Et8yGshamliXsoAIqIiFhZ6n5YOQkSNzqWQxvBwDnQerAu99ZgCoAiIiJWlJ0O6+fB1rfAKAAvP+gzAXqPA29/s6sTN1MAFBERsRK7HXYvhrjpkJnqaGv9Oxj4EtSOMbc2qTQKgCIiIlZxPN5xuffofx3LdZvDLfOgeX9Ty5LKpwAoIiJS050/Dd/Mgh0fAAZ4B0DsM3Dd4+DlY3Z1YgIFQBERkZrKXuAIfWtfgKwzjrYOd8PNsyA40tTSxFwKgCIiIjVR0lZY+TSk7HYsh7d3TOvSuLe5dUmVoAAoIiJSk5z9BdZMh12fOZb9QuDG56D7Q+Cp07446CdBRESkJijIg61vw/q5kHsWsEGX+6HfdAisZ3Z1UsUoAIqIiFR3P6+Hlc/AyQOO5ciucOsCiOpmallSdSkAioiIVFdpybD6Wdj3uWO5Vl3oPwM63w8eHqaWJlWbAqCIiEh1k5cNm1+Hja9AfhbYPOCaR+DGqeBf2+zqpBpQABQREalODnwFX02GM4mO5Zjejqd7I9qbWpZULwqAIiIi1cGpw/DVFDi02rEc1AAGzIb2fwCbzdzapNpRABQREanKcjMdl3o3vw4FueDhDT0fh76TwDfI7OqkmlIAFBERqYoMA35cDqufg4xjjrZmNzku94a1MLc2qfYUAEVERKqa1P2wchIkbnQshzaCgXOg9WBd7pUKoQAoIiJSVWSnOyZy3vo2GAXg5Qd9JkDvceDtb3Z1UoMoAIqIiJjNbofdiyHuecj81dHW+ncw8CWoHWNubVIjKQCKiIiY6fgPjsu9R7c5lus2h1vmQfP+5tYlNZoCoIiIiBnOn4ZvZsGODwADvAMg9hm47nHw8jG7OqnhFABFREQqk70AdrwP37wA2WmOtg53w82zIDjS1NLEOhQARUREKkvS97DyaUjZ41gOb++Y1qVxb3PrEstRABQREXG3sykQN93xoAeAXwjc+Bx0fwg8dSqWyqefOhEREXcpyHNM6bJ+LuSeBWzQdQT0mw4BYWZXJxamACgiIuIOh9fBqslw8oBjuWE3uPVlx+8iJlMAFBERqUhpybD6Wdj3uWO5Vhj0nwGd7wMPD1NLE7lIAVBERKQi5GXD5tdh4yuQnwU2D7h2NNwwFfxDza5OxIUCoIiISHkd+Aq+mgxnEh3LMb0dT/dGtDe1LJHiKACKiIhcrVOH4aspcGi1YzmoAQyYDe3/ADabubWJlEABUERE5ErlZjou9W5+HQpywcMbeo6BvpPAN9Ds6kRKpQAoIiJSVoYBPy6H1c9BxjFHW7N+jnf3hrUwtzaRK6AAKCIiUhap+2HlJEjc6FgObQSD5kKrW3W5V6odBUAREZGSZKc7JnLe+jYYBeDlB30mQu+x4O1vdnUiV0UBUEREpCh2u+PVbXHPQ+avjrbWv4OBL0HtGHNrEyknBUAREZHLHf/Bcbn36DbHct0Wjvv8mvczty6RCqIAKCIictH50/DNLNjxAWCATyDEPgM9/ghePmZXJ1JhFABFRETsBbDjffjmBchOc7R1GAo3z4LgBqaWJuIOCoAiImJtSd/DyqchZY9jOby94y0ejXubW5eIGykAioiINZ1Ngbjpjgc9APxC4MbnoPtD4KnTo9RsHmYXYJY5c+ZwzTXXEBQURP369bn99ts5cOCA2WWJiIi7FeQ53uDxevcL4c8GXUfCkzuhx2iFP7EEywbADRs2MGbMGL7//nvi4uLIz89nwIABZGZmml2aiIi4y+F18Nfejjd55J6Fht3gkW9gyOsQEGZ2dSKVxmYYhmF2EVXBr7/+Sv369dmwYQN9+/Yt0zoZGRmEhISQnp5OcHCwmysUEZGrlpYEXz8L+79wLNcKg/4zoPN94GHZsRDL0vlb9wA6paenA1CnTh2TKxERkQqTl+243LvxFcjPApsHXDsabpgK/qFmVydiGgVAwDAMJk6cSJ8+fWjfvn2x/XJycsjJyXEuZ2RkVEZ5IiJypQwDDn4FX02BM4mOtpjejqd7I4r/e17EKhQAgSeeeILdu3ezadOmEvvNmTOHmTNnVlJVIiJyVU4ddgS/Q6sdy0ENYMBsaP8HsNnMrU2kirD8PYBPPvkkK1as4Ntvv6VJkyYl9i1qBDA6OtrS9xCIiFQZuZnw7QLY8gYU5IKHN/QcA30ngW+g2dVJFaJ7AC08AmgYBk8++STLly9n/fr1pYY/AF9fX3x9fSuhOhERKTPDgB+XweppkHHM0da8PwyaB2HNza1NpIqybAAcM2YMn376KZ9//jlBQUGkpKQAEBISgr+/v8nViYhImfyyD1Y9A4kbHcuhMTBoLrS6RZd7RUpg2UvAtmL+Ynj//fcZNWpUmbahIWQREZNkp8P6ubD1bTAKwMsP+kyE3mPBW/+Il5Lp/G3hEUCL5l4RkerNboddn8Ga6ZD5q6Otze9hwItQO8bc2kSqEcsGQBERqWaO/wArJ8HRbY7lui3glnnQvJ+5dYlUQwqAIiJStWWegrWzYMeHgAE+gRA7GXo8Bl4+ZlcnUi0pAIqISNVkL4Dtf4e1syE7zdHWYSjcPAuCG5hamkh1pwAoIiJVT9L3sPJpSNnjWA5vD7e+DDG9zK1LpIZQABQRkarjbArETYfdix3LfiFw0zTo9iB46pQlUlH0f5OIiJivIA+2vgXr50HuWcAGXUdCv+chIMzs6kRqHAVAEREx1+F1sGoynDzgWG7YzXG5t2E3c+sSqcEUAEVExBxpSfD1s7D/C8dyrTC4eSZ0uhc8PMytTaSGUwAUEZHKlZcNm1+Hja9AfhbYPOHaR+CGqeAfanZ1IpagACgiIpXDMODgV/DVFDiT6GiL6QO3zofwdqaWJmI1CoAiIuJ+pw47gt+h1Y7loAYwYDa0/wMU8252EXEfBUAREXGf3Ez4dgFseQMKcsHDG3o9Adc/Db6BZlcnYlkKgCIiUvEMA35cBqunQcYxR1vz/jBoHoQ1N7c2qfJy8+0cSDlL/NE0bmxVj6jatcwuqcZRABQRkYr1yz5Y9QwkbnQsh8bAoLnQ6hZd7pVCDMMg6fR54pPTiE9OY1dyGnuPZ5Cbbwdg7p0dGH5tI5OrrHkUAEVEpGJkpcH6ufDfd8AoAC8/6DMReo8Fb3+zq5Mq4nRmLrsuhL345DR2HU0j7XxeoX7Bfl50ig6lToCPCVXWfAqAIiJSPnY77PoU1syAzF8dbW1+DwNehNoxppYm5srOK+DH4+nEJ6c7R/eSTp8v1M/H04O2kcF0jg6lU3QInaNr07huLWwaMXYbUwLga6+9dsXrPPjggwQFBbmhGhERuWrHdsLKSXBsu2O5bgu4ZR4072duXVLp7HaDw7+e44cLQW/X0TT+d+Is+XajUN+m9QLoHBVK50ahdIoKpXWDIHy9PE2o2rpshmEU/pNxMw8PD6KiovD0LNsfdnJyMgcPHqRp06ZuruzKZGRkEBISQnp6OsHBwWaXIyJSeTJPwTczYedHgAE+gRA7GXo8Bl66ZGcFv2Rk80OSI+jFJ6Wx51g653LyC/ULC/Shc3TohdG9UDpGhRLi721Cxb/R+dvES8Dbt2+nfv36ZeqrkT8RkSrCXgDb/w5rZ0N2mqOtw1C4eRYENzC1NHGfczn57D6axq7kdOKTz7ArOZ2UjOxC/fy9PekQFeIIexdG+CJD/HQptwoyJQBOnz6dwMCyz//0pz/9iTp16rixIhERKdWRLbBqEqTscSyHd3C8xSOml7l1SYXKK7gwBcsll3IPpZ7j8uuFHjZoGR7kMrrXon4gXp56j3N1YMol4JpCQ8giYglnUyDuedi9xLHsFwI3TYNuD4KnniWszgzD4OiZLOd9e/HJaew9lk7OhSlYLtUw1P/CAxqO0b32DUMI8K2ef/46f+spYBERKU5+Lmx9CzbMg9xzgA26joR+z0NAmNnVyVU4k5nLrksv5R5N53RmbqF+QX5ezqDX6cKTufWD/EyoWNzF9AB46tQpnn/+edatW0dqaip2u+u/Ok6fPm1SZSIiFnZ4LayaDCcPOpYbdodbX4aGXc2tS8osO6+AfScyiL/woMau5DQSTxWegsXb00bbBsF0uuRSbpO6AXh46L69msz0AHj//fdz+PBhHn74YcLDw3WjqIiImdKS4OtnYf8XjuVaYXDzTOh0L3jo3q6qym43+Plkpst9e/tPZJBXUPguryZhAXS6+KBGdChtGgTj560pWKzG9AC4adMmNm3aRKdOncwuRUTEuvKyYfNrsHEh5GeBzROuHQ03TAH/ULOrk8ukZmQ736IRn5zG7uR0zhYxBUvdAB9n0OsUHUqnqBBCa2maHqkCAbB169ZkZWWZXYaIiDUZBhxYBV9PhTOJjraYPo6ne8PbmVqaOGTm5LPn2G9v0tiVnMbx9MJTsPh5e9ChYYhz+pVOUaFE1fbXlTUpkukB8M0332TKlCk8//zztG/fHm9v18khrfp0joiI25067LjP76c4x3JQJAycDe3uBIUGU+QX2Dn4yzmXS7kHfznL5S/TsNmgZf0g52vTOkWH0DI8CG9NwSJlZHoADA0NJT09nZtuusml3TAMbDYbBQUFJlUmIlJD5ZyDjQtgy1+gIBc8vKHXE3D90+Bb9jlapXwMw+BYWpYz7MUnO96mkZ1XeAqWBiF+v13KjQqlQ1QIgdV0ChapGkz/6bnvvvvw8fHh008/1UMgIiLuZBjw4zL4+jk4e9zR1rw/DJoHYc3Nrc0C0s/nOZ/GvXj/3slzRUzB4utFx+gLl3IvhL7wYE3BIhXL9AC4d+9efvjhB1q1amV2KSIiNdcv+2DVM5C40bEcGgOD5kKrW3S51w1y8gvYf+Is8UmOufZ2Jafx88nMQv28PGy0aRDsvJTbOTqEpmGBmoJF3M70ANi9e3eSk5MVAEVE3CErDdbPhf++A0YBePnB9U9BryfB29/s6moEu90g4VSm8wGN+OQ09hUzBUtM3VouEyy3i9QULGIO0wPgk08+ybhx45g0aRIdOnQo9BBIx44dTapMRKQas9th16ewZgZk/upoa/N7GPAi1I4xtbTq7tezOc4HNC7ev5eRXXgKltq1vF2mYOkcFUrtAE3BIlWD6e8C9ihiYlGbzVYtHgLRuwRFpEo6thNWToJj2x3LYS3hlnnQ7KaS15NCzufms/dYhuO1acmOqViOpRWeuszXy4P2l0zB0jkqlOg6moKlqtL5uwqMACYkJJhdgohIzZB5Cr6ZCTs/AgzwCYTYydDjMfDSyFNpCuwGh1LPOl+dFp+czsFfzlJw2RwsNhs0rxfoHN3rHB1KqwhNwSLVi+kBMCZGlyJERMrFXgDb/w5rZ0N2mqOt4zDoPxOCG5haWlVlGAbH07Od9+39kJzG3mPpnM8tfNUpPNj3t7B3YQqWID/vIrYqUn2YHgABDh48yPr160lNTcVud53/6PnnnzepKhGRauDIFlg1CVL2OJbDOzje4hHTy9y6qpj0rDz2HE0nPvkM8cnp7Dqaxq9ncwr1C/DxpGPUbyN7naNDiQjRFCxS85geAN99913++Mc/EhYWRkREhMv9EjabTQFQRKQoZ1Mg7nnYvcSx7BcCN02Dbg+Cp+l/tZsqN9/O/1IyiE/+7SGNw78WnoLF08NG64ggl7DXrF4gnpqCRSzA9L8lZs+ezYsvvsjkyZPNLkVEpOrLz4Wtb8GGeZB7DrBB15HQ73kICDO7ukpnGAaJp847p1+JT05j3/EMcgsKv00juo6/47VpUSF0jg6lXWQI/j6agkWsyfQAeObMGe6++26zyxARqfoOr3W8u/fkQcdyw+5w68vQsKu5dVWiU+dyHA9oJKURf2GC5fSsvEL9Qmt5O+fa6xIdSseoEOoG+ppQsUjVZHoAvPvuu1m9ejWPPfaY2aWIiFRNaUnw9bOw/wvHcq0wuHkmdLoXiphKq6bIyi3gx+Ppv13KPZpG8unCU7D4eHnQLjKYTlGhdGnkmGQ5pm4tTcEiUgLTA2Dz5s2ZNm0a33//fZETQY8dO9akykRETJaXBd+9BptehfwssHnCtaPhhingH2p2dRWqwG7wU+o5x6XcCyN8B4qYggWgWb0A52vTOkWH0joiGB+vmhuERdzB9ImgmzRpUuxnNpuNn3/+uRKruTKaSFJE3MIw4MAq+GoKpB1xtMX0cTzdG97O3NoqyIn0LOf0K7uS09hzNJ3MIqZgqRfk63xAo3O0YwqWYE3BIuWk83cVGAHURNAiIpc4+RN8NRl+WuNYDoqEgbOh3Z2OGYirobPZjilYLoa9XUfT+CWj8BQstXw86dAwxBn2OkWH0iDET5dyRdzA9AAoIiJAzjnYuAA2vwH2PPDwhl5PwPVPg2+g2dWVWV6Bnf+dOEv80TTnk7mHfz3H5deaPGzQKiKYztEhzrDXon6QpmARqSSmBMCJEyfywgsvEBAQUKb+U6dOZdKkSdSpU8fNlYmIVDLDgL1LYfU0OHvc0db8Zhg0F8Kam1tbKQzDIOn0+Qtz7TkmWf7xeAY5+YWnYGkY6u98R26n6FDaNwymlo/GIETMYso9gJ6enqSkpFCvXr0y9Q8ODiY+Pp6mTZu6ubIro3sIRKRcfvkRVj4DRzY5lkNj4JZ50HJQlbzcezoz1zkFy64LI3xnzheegiXYz8tlcuWOUaHUC9IULFJ16Pxt0gigYRi0bNmyzPd1ZGYWnsFdRKTaykqD9XPgv++CUQBe/nD9ROg1FryrxmvHsvMuTsGS7ryUm3T6fKF+Pp4etIkMpkt0KJ2iQ+gUFUqTsADdtydSxZkSAN9///0rXic8PNwNlYiIVCK7HXZ9CnHT4fxJR1ubITDwRQhtZGJZBod/Peecay8+OY3/nThLfhFTsDQNC3Des9cpOpQ2DYLw9dLbNESqG1MC4AMPPGDGbkVEzHNsJ6ycBMe2O5bDWjou9za7qdJL+SUj2+U9ubuPpnMuJ79Qv7BAH0fYiwqlc6NQOjYMJaSWpmARqQl0B66IiDtlnoJvZsLOjwADfAIdEzlf+yh4+bh99+dy8tlzNN0Z9uKT00jJyC7Uz9/bMQVLp+gQx/tyo0NoGOqvS7kiNZQCoIiIOxTkw473Ye1syE5ztHUcBjfPgqAIt+wyr8DOgZSzzgc04pPTOJRa9BQsLcODfruUGxVKy/BAvDz1Ng0Rq1AAFBGpaEe2OC73/rLHsRzeAW59GWJ6VtguDMPg6Jksl0u5e4+nk51XeAqWyBA/Ol94R26n6FA6NAwhwFd//YtYmf4GEBGpKBknIO552PNPx7JfKNz0HHR/CDzK96BE2vlcdh1Nd5mC5VRmbqF+QX5eF4LehUu5USHUD64aTxaLSNVhagDMz8/Hz8+P+Ph42rdvb2YpIiJXLz8Xtr4FG+ZB7jnABt0egJueh4C6V7y57LwC9p3IcLw27cIIX+KpwlOweHvaaNMg2PmgRqfoUJqGBeCht2mISClMDYBeXl7ExMRQUFD4BeAiItXC4bWwajKcPOhYbtjdcbm3YdcyrW63G/x8MtMZ9HYdTWP/iQzyCgpPwdK4bi3nfXudo0Np0yAYP29NwSIiV870S8DPPfccU6dO5eOPP9ar3kSk+khLgq//BPv/z7EcUA/6z4RO94BH8Q9TpJ7Ndr42bVdyOruOpnE2u/AULHUCXKdg6RQVQmgt9z81LCLWYHoAfO211/jpp5+IjIwkJiam0PuBd+7caVJlIiJFyMuC716DTQshPxtsnnDtaMfULv6hLl0zc/LZc8zxJo2Lr1A7nl54ChZfLw86NAxxGd2Lqq0pWETEfUwPgLfffrup+3/zzTd5+eWXOXHiBO3atWPRokVcf/31ptYkIlWQYcCBVfDVFEg74mhrfD3cMh/C25JfYOfg8QyXd+Ue/OUsl79Mw2aDFvUDXcJey/AgvDUFi4hUIpthXD5DlHUsWbKEESNG8Oabb9K7d2/efvtt3nvvPfbt20ejRqW/lkkvkxaxiJM/wVeT4ac1ABhBkZzu8zzf+8USfzSNXcnp7DmWTlZe4fuZG4T4OR/Q6BwdSoeoEAI1BYuIqXT+riIBMC0tjX//+98cPnyYSZMmUadOHXbu3El4eDgNGzZ023579OhB165d+etf/+psa9OmDbfffjtz5swpdX39AInUcDnnYOMCjM1vYLPnUWDz4qvgu5l7bjDJmYVH7AJ9vegY5XopN1xTsIhUOTp/V4FLwLt376Z///6EhISQmJjII488Qp06dVi+fDlHjhzho48+cst+c3Nz2bFjB1OmTHFpHzBgAJs3b3bLPstq75avOPO/DcV+bis1sxf/uWGAraTPKeXzMqwPUNydSxdLL24bxoX2Itc3il0orbPrzsuiHMe4TJ+Xc/u2yz42iuh/6TEuamsXj3FxpVxcv6htX9n6JX9erFKOka3Yyi75vIQONor/bhfXb5Oxidr5J7EB6wo6MSt/JAlZDQDw8rDRukHQbw9qRIfSrF6gpmARkWrB9AA4ceJERo0axfz58wkKCnK233LLLdx7771u2+/JkycpKCggPDzcpT08PJyUlJQi18nJySEnJ8e5nJGR4Zbazu7/huuT3nHLtkXkyiTZ6zEzfyQ/hfahU3Rt7r8wstcuUlOwiEj1ZXoA3LZtG2+//Xah9oYNGxYbxCrS5U/ZGYZR7JN3c+bMYebMmW6vKbBRF3ac+13JnUodZCipQ8krGzZbiT2MUnduK2U3ZRwhKbKbrbQOpWyzlO9+yTaL6mnYiv+8qONiK+1zWymfV+j6RXBu4CpHrWyF/qOYDsV8XqbdltKp1Cdlr379LN96GJ3v5eWYcOoEaAoWqXoMw8DAKPw7BnbDzsW7vOyG3dluGIX7XdzWxX4u6xTR38AAo4jtXvjdjh1HF8N1O5f87rJf7MV+l5jgGGKCY8w5wDWY6QHQz8+vyJG0AwcOUK9ePbftNywsDE9Pz0IhMzU1tdCo4EVTp05l4sSJzuWMjAyio6MrvLaYvr/j7HWxJfYpy62bJV8gc3Yq9zbK1KeC6q2I71SW7VRmvRV1G25F7Ksq/RlA5f05FLcfbwBOkZR5iqTMUndT5u90JSe/Uk+ql52gndstYwAodMIvJkg4ay3uhH/5fi8EhCsNAC61FtHfGTyKOWZlOUZXE5Iu30dZar2SP9+r/W5W8Hinx/lj5z+aXUaNY3oAvO2225g1axb//Kfj3Zk2m42kpCSmTJnCH/7wB7ft18fHh27duhEXF8cdd9zhbI+Li+O2224rch1fX198fX3dVtNFn+z7hDd3ven2/YiIiADYsOFh88CGDWzggQc2mw0bNpffPfDA0eW3/kX1u7T/xatqxfX3sDkeqLq0/6Wf16vlvsEgKzM9AC5YsIBbb72V+vXrk5WVRWxsLCkpKfTs2ZMXX3zRrfueOHEiI0aMoHv37vTs2ZN33nmHpKQkHnvsMbfutzReHl74e/lXyLZKvph7oU8pl9DKtI2yXMsrU5fy11vm7ZTSp6Im4a1K3+lCp/LvpxLrraw/hwr7TmXcTlEnP5eTMJedMC+eFC8/YV7sc/mJ9bL+FXFiL+pEXahOCu/78u061ymmf6HtXl7rxTour7WUY1TaMS3tGF1tuClxu8Uco8trLPSdiztGRfwclfhzcuF3sZ4qMQ0MwNq1a9m5cyd2u52uXbvSv3//Stnvm2++yfz58zlx4gTt27fn1VdfpW/fvmVaV4+Ri4iIVD86f1eBAPjRRx8xbNiwQpdWc3NzWbx4MSNHjjSpstLpB0hERKT60fm7CgRAT09PTpw4Qf369V3aT506Rf369SkoKDyzflWhHyAREZHqR+dvMP3lk8VNu3L06FFCQkJMqEhERESkZjPtIZAuXbo4b1jt168fXl6/lVJQUEBCQgKDBg0yqzwRERGRGsu0AHj77bcDEB8fz8CBAwkMDHR+5uPjQ+PGjd06DYyIiIiIVZkWAKdPnw5A48aNGTZsGH5+emG6iIiISGUw/R7ABx54gOzsbN577z2mTp3K6dOnAdi5cyfHjh0zuToRERGRmsf0iaB3795N//79CQkJITExkUceeYQ6deqwfPlyjhw5wkcffWR2iSIiIiI1iukjgBMmTGDUqFEcOnTI5TLwLbfcwrfffmtiZSIiIiI1k+kjgNu3b+edd94p1N6wYUNSUlJMqEhERESkZjN9BNDPz4+MjIxC7QcOHKBePb0AWkRERKSimR4Ab7vtNmbNmkVeXh7geGl1UlISU6ZM0TQwIiIiIm5gegBcsGABv/76K/Xr1ycrK4vY2FiaN29OUFAQL774otnliYiIiNQ4pt8DGBwczKZNm1i7di07d+7EbrfTtWtX+vfvb3ZpIiIiIjWSzTAMw+wiqiu9TFpERKT60fm7CowAAvz3v/9l/fr1pKamYrfbXT5buHChSVWJiIiI1EymB8CXXnqJ5557jlatWhEeHo7NZnN+dul/i4iIiEjFMD0A/vnPf+bvf/87o0aNMrsUEREREUsw/SlgDw8PevfubXYZIiIiIpZhegCcMGECf/nLX8wuQ0RERMQyTL8E/PTTTzN48GCaNWtG27Zt8fb2dvl82bJlJlUmIiIiUjOZHgCffPJJ1q1bx4033kjdunX14IeIiIiIm5keAD/66COWLl3K4MGDzS5FRERExBJMvwewTp06NGvWzOwyRERERCzD9AA4Y8YMpk+fzvnz580uRURERMQSTL8E/Nprr3H48GHCw8Np3LhxoYdAdu7caVJlIiIiIjWT6QHw9ttvN7sEEREREUuxGYZhmF1EdeWul0mn/+dLMr788upWLs8fZzl/FAxM2nd5yi7vj79px/vq1y3X//Ll/dvCrONl0rrl+n/CsYFyrFv9jld51y/f30FXv2p1PV7V5VjXGTmS0Dtuv/r9FcFd5+/qxPQRQCksNzGRc+vWmV2GiIiI6QpOnzK7hBrJ9ABYUFDAq6++yj//+U+SkpLIzc11+fz06dMmVWaewBtvwDsivHwbKfd8iuVYv7z7Lvf65d19Nf7u5f/yJu7a7J+b8qxvdu3lW708+6/ef25Qvr/ryrvr8m2geh/7YtYtYps+jRuXYz9SHNMD4MyZM3nvvfeYOHEi06ZN49lnnyUxMZEVK1bw/PPPm12eKfzbtcO/XTuzyxAREZEayvRpYD755BPeffddnn76aby8vLjnnnt47733eP755/n+++/NLk9ERESkxjE9AKakpNChQwcAAgMDSU9PB+B3v/sdX17tgxAiIiIiUizTA2BUVBQnTpwAoHnz5qxevRqAbdu24evra2ZpIiIiIjWS6QHwjjvu4JtvvgFg3LhxTJs2jRYtWjBy5Egeeughk6sTERERqXmq3DyAW7du5bvvvqN58+YMGTLE7HJKpHmEREREqh+dv01+CjgvL4/Ro0czbdo0mjZtCkCPHj3o0aOHmWWJiIiI1GimXgL29vZm+fLlZpYgIiIiYjlV4h7AFStWmF2GiIiIiGWYPhF08+bNeeGFF9i8eTPdunUjICDA5fOxY8eaVJmIiIhIzWT6QyBNmjQp9jObzcbPP/9cidVcGd1EKiIiUv3o/F0FRgATEhLMLkFERETEUky/B1BEREREKpfpI4AAR48e5YsvviApKYnc3FyXzxYuXGhSVSIiIiI1k+kB8JtvvmHIkCE0adKEAwcO0L59exITEzEMg65du5pdnoiIiEiNY/ol4KlTp/LUU0+xd+9e/Pz8WLp0KcnJycTGxnL33XebXZ6IiIhIjWN6ANy/fz8PPPAAAF5eXmRlZREYGMisWbOYN2+eydWJiIiI1DymB8CAgABycnIAiIyM5PDhw87PTp48aVZZIiIiIjWW6fcAXnfddXz33Xe0bduWwYMH89RTT7Fnzx6WLVvGddddZ3Z5IiIiIjWO6QFw4cKFnDt3DoAZM2Zw7tw5lixZQvPmzXn11VdNrk5ERESk5jH9TSDVmWYSFxERqX50/q4CI4AXbd++nf3792Oz2WjTpg3dunUzuyQRERGRGsn0AHj06FHuuecevvvuO0JDQwFIS0ujV69efPbZZ0RHR5tboIiIiEgNY/pTwA899BB5eXns37+f06dPc/r0afbv349hGDz88MNmlyciIiJS45h+D6C/vz+bN2+mS5cuLu07d+6kd+/eZGVlmVRZ6XQPgYiISPWj83cVuATcqFEj8vLyCrXn5+fTsGFDEyoSERGpeAUFBUWe76TieXt74+npaXYZVZrpAXD+/Pk8+eST/OUvf6Fbt27YbDa2b9/OuHHjWLBggdnliYiIlIthGKSkpJCWlmZ2KZYSGhpKREQENpvN7FKqJNMvAdeuXZvz58+Tn5+Pl5cjj17874CAAJe+p0+fNqPEYmkIWURESnPixAnS0tKoX78+tWrVUiBxM8MwOH/+PKmpqYSGhtKgQYNCfXT+rgIjgIsWLar0fSYmJvLCCy+wdu1aUlJSiIyM5P777+fZZ5/Fx8en0usREZGaqaCgwBn+6tata3Y5luHv7w9Aamoq9evX1+XgIpgeAB944IFK3+f//vc/7HY7b7/9Ns2bN2fv3r088sgjZGZm6rKziIhUmIv3/NWqVcvkSqzn4jHPy8tTACyC6QHQDIMGDWLQoEHO5aZNm3LgwAH++te/KgCKiEiF02XfyqdjXjJLBsCipKenU6dOnRL75OTkkJOT41zOyMhwSy3xa5LY9U2yW7ZdEtPuBjXxNlTT9mzSjs37vtZ746R5/z+ZtVur/VCXjW+wjVY3B3LaLxNvr2r+BLBJxzo4zA/fWt7m7LwGUwAEDh8+zOuvv84rr7xSYr85c+Ywc+ZMt9eTm13AuTM5pXcUEZEqzebtAQYYdgPDXsXTqliK6U8BV6QZM2aUGtC2bdtG9+7dncvHjx8nNjaW2NhY3nvvvRLXLWoEMDo6usKfIspMyyEz3ZwAaMkhc5O+snmH2pwdW/FHy7SfLfN2bM5uq/DPVm5eDifTTxAT0xg/Pz+zyymX5cuX8+5777Bz505OnTrFtv9up3PnzhWy7WXLljFjxnQO/3yYZk2bMWvWC9x+++0AeHh6MGvWzELn9/DwcFJSUordZnZ2NgkJCTRp0qTQsddTwFVgBPChhx7iz3/+M0FBQS7tmZmZPPnkk/z9738v87aeeOIJhg8fXmKfxo0bO//7+PHj3HjjjfTs2ZN33nmn1O37+vri6+tb5nquVkCoLwGh7t+PiIi4V3a2J6fPeeDl7YmXd/V+ECE7J4s+ffowdOhQHnnkkQr7Tlu2bOHe++7hhRde4I477mD58uXcc+9wNm3aRI8ePZz92rVrx5o1a5zLerCjfEwfAfT09OTEiRPUr1/fpf3kyZNERESQn5/vlv0eO3aMG2+8kW7duvHxxx9f1Q+S/gUhIiIlKWkUqrpKTEykSZMm/PDDD4VGANPT05k0aRIrVqwgOzub7t278+qrr9KpU6ditzds2DAyMjJYtWqVs23QoEHUrl2bzz77DHBc4VuxYgXx8fFlrlMjgCUzbQQwIyMDwzAwDIOzZ8+6/OEUFBSwcuXKQqGwohw/fpwbbriBRo0asWDBAn799VfnZxEREW7Zp4iICDgmKs7KKzBl3/7enm671ccwDAYPHkydOnVYuXIlISEhvP322/Tr14+DBw8W+6Dlli1bmDBhgkvbwIEDC80TfOjQISIjI/H19aVHjx689NJLNG3a1C3fxQpMC4ChoaHYbDZsNhstW7Ys9LnNZnPbAxerV6/mp59+4qeffiIqKsrlsxp0S6SIiFRBWXkFtH3+a1P2vW/WQGr5uOfUv27dOvbs2UNqaqrzdqkFCxawYsUK/v3vfzN69Ogi10tJSSE8PNyl7fL7+3r06MFHH31Ey5Yt+eWXX5g9eza9evXixx9/1ATbV8m0ALhu3ToMw+Cmm25i6dKlLv8y8PHxISYmhsjISLfse9SoUYwaNcot2xYREanuPvnkEx599FHn8qpVq7j++utLXGfHjh2cO3euUCDLysri8OHDJCUl0bZtW2f7n/70J/70pz8BhR9ANAzDpe2WW25x/neHDh3o2bMnzZo148MPP2TixIlX/gXFvAAYGxsLQEJCAo0aNbLm06ciImI5/t6e7Js10LR9l8WQIUNcHsBo2LBhqevY7XYaNGjA+vXrC30WGhpKaGioyz18Fwd+IiIiCj3Nm5qaWmhU8FIBAQF06NCBQ4cOlVqXFM30p4DXrl1LYGAgd999t0v7v/71L86fP2/Kq+JERETcxWazue0ybEUJCgoqNDtHabp27UpKSgpeXl4uM25cqnnz5oXaevbsSVxcnMt9gKtXr6ZXr17F7isnJ4f9+/eXOiopxfMwu4C5c+cSFhZWqL1+/fq89NJLJlQkIiIilzt9+jTx8fHs27cPgAMHDhAfH+8cvevfvz89e/bk9ttv5+uvvyYxMZHNmzfz3HPPsX379mK3O27cOFavXs28efP43//+x7x581izZg3jx4939nn66afZsGEDCQkJbN26lbvuuouMjAwNEpWD6QHwyJEjNGnSpFB7TEwMSUlJJlQkIiIil/viiy/o0qULgwcPBmD48OF06dKFt956C3CMbK5cuZK+ffvy0EMP0bJlS4YPH05iYmKJl3N79erF4sWLef/99+nYsSMffPABS5YscbkEffToUe655x5atWrFnXfeiY+PD99//z0xMTHu/dI1mOnzADZq1Ig33niDIUOGuLR//vnnjBkzhqNHj5pUWek0j5CIiJSkJs4DWF1oHsCSmT4COHz4cMaOHcu6desoKCigoKCAtWvXMm7cuFLf6iEiIiIiV870u1Bnz57NkSNH6NevH15ejnLsdjsjR47UPYAiIiIibmB6APTx8WHJkiW88MIL7Nq1C39/fzp06KDr+iIiIiJuYnoAvKhly5ZFvhFERERERCpWlQiAR48e5YsvviApKYnc3FyXzxYuXGhSVSIiIiI1k+kB8JtvvmHIkCE0adKEAwcO0L59exITEzEMg65du5pdnoiIiEiNY/pTwFOnTuWpp55i7969+Pn5sXTpUpKTk4mNjS30dhARERERKT/TA+D+/fudM3l7eXmRlZVFYGAgs2bNYt68eSZXJyIiIlLzmB4AAwICyMnJASAyMpLDhw87Pzt58qRZZYmIiIjUWKbfA3jdddfx3Xff0bZtWwYPHsxTTz3Fnj17WLZsGdddd53Z5YmIiIjUOKaPAC5cuND5vr8ZM2Zw8803s2TJEmJiYvjb3/5mcnUiIiICYBgGM2bMIDIyEn9/f2644QZ+/PHHUtdbunQpbdu2xdfXl7Zt27J8+fJCfd58803nK9u6devGxo0bXT5ftmwZAwcOJCwsDJvNRnx8fEV9LcsyPQA2bdqUjh07AlCrVi3efPNNdu/ezbJlyzQZtIiISBUxf/58Fi5cyBtvvMG2bduIiIjg5ptv5uzZs8Wus2XLFoYNG8aIESPYtWsXI0aMYOjQoWzdutXZZ8mSJYwfP55nn32WH374geuvv55bbrmFpKQkZ5/MzEx69+7N3Llz3fodrcRmGIZhdhEA27dvZ//+/dhsNtq0aUO3bt3MLqlUepm0iIiUJDs7m4SEBOfoVnVlGAaRkZGMHz+eyZMnA5CTk0N4eDjz5s3j0UcfLXK9YcOGkZGRwapVq5xtgwYNonbt2nz22WcA9OjRg65du/LXv/7V2adNmzbcfvvtzJkzx2V7iYmJNGnShB9++IHOnTuXWHNJx17n7ypwD+DRo0e55557+O677wgNDQUgLS2NXr168dlnnxEdHW1ugSIiIhXJMCDvvDn79q4FNtsVr5aQkEBKSgoDBgxwtvn6+hIbG8vmzZuLDYBbtmxhwoQJLm0DBw5k0aJFAOTm5rJjxw6mTJni0mfAgAFs3rz5iuuUsjM9AD700EPk5eWxf/9+WrVqBcCBAwd46KGHePjhh1m9erXJFYqIiFSgvPPwUqQ5+/7TcfAJuOLVUlJSAAgPD3dpDw8P58iRIyWuV9Q6F7d38uRJCgoKSuwj7mH6PYAbN27kr3/9qzP8AbRq1YrXX3+90E2gIiIi4n6ffPIJgYGBzl95eXkA2C4bPTQMo1Db5cqyztVsV8rH9BHARo0aOX+wLpWfn0/Dhg1NqEhERMSNvGs5RuLM2ncZDBkyxDlDB+CcrzclJYUGDRo421NTUwuN3l0qIiKi0EjepeuEhYXh6elZYh9xD9NHAOfPn8+TTz7J9u3bufg8yvbt2xk3bhwLFiwwuToREZEKZrM5LsOa8auMo2pBQUE0b97c+att27ZEREQQFxfn7JObm8uGDRvo1atXsdvp2bOnyzoAq1evdq7j4+NDt27dCvWJi4srcbtSfqaPAI4aNYrz58/To0cPvLwc5eTn5+Pl5cVDDz3EQw895Ox7+vRps8oUERGxLJvNxvjx43nppZdo0aIFLVq04KWXXqJWrVrce++9zn4jR46kYcOGzqd3x40bR9++fZk3bx633XYbn3/+OWvWrGHTpk3OdSZOnMiIESPo3r07PXv25J133iEpKYnHHnvM2ef06dMkJSVx/Lhj5PTAgQOAY4QxIiKiMg5BjWN6ALz4JJCIiIhUXc888wxZWVk8/vjjnDlzhh49erB69WqCgoKcfZKSkvDw+O3iYq9evVi8eDHPPfcc06ZNo1mzZixZssTl8vKwYcM4deoUs2bN4sSJE7Rv356VK1e6zAX8xRdf8OCDDzqXhw8fDsD06dOZMWOGG791zVVl5gGsjjSPkIiIlKSmzANYHWkewJKZPgJ4UWpqKqmpqdjtdpf2i28JEREREZGKYXoA3LFjBw888AD79+/n8sFIm81GQUGBSZWJiIiI1EymB8AHH3yQli1b8re//Y3w8HDN+yMiIiLiZqYHwISEBJYtW0bz5s3NLkVERETEEkyfB7Bfv37s2rXL7DJERERELMP0EcD33nuPBx54gL1799K+fXu8vb1dPh8yZIhJlYmIiIjUTKYHwM2bN7Np0yZWrVpV6DM9BCIiIiJS8Uy/BDx27FhGjBjBiRMnsNvtLr8U/kREREQqnukB8NSpU0yYMEEvfRYRERGpJKYHwDvvvJN169aZXYaIiIiIZZh+D2DLli2ZOnUqmzZtokOHDoUeAhk7dqxJlYmIiMhFhmEwc+ZM3nnnHee7gP/yl7/Qrl27Ytf58ccfef7559mxYwdHjhzh1VdfZfz48ZVXtBTL9AD43nvvERgYyIYNG9iwYYPLZzabTQFQRESkCpg/fz4LFy7kgw8+oGXLlsyePZubb76ZAwcOEBQUVOQ658+fp2nTptx9991MmDChkiuWkpgeABMSEswuQUREREpgGAaLFi3i2Wef5c477wTgww8/JDw8nE8//ZRHH320yPWuueYarrnmGgCmTJlSafVK6UwPgCIiIlZiGAZZ+Vmm7Nvfy/+qXrmakJBASkoKAwYMcLb5+voSGxvL5s2biw2AUnWZEgAnTpzICy+8QEBAABMnTiyx78KFCyupKhEREffLys+ix6c9TNn31nu3Usu71hWvl5KSAlBoxo7w8HCOHDlSIbVJ5TIlAP7www/k5eU5/7s4V/OvFBERESmfTz75xGVU78svvwQKn5cNw9C5upoyJQBeOu2LpoAREREr8ffyZ+u9W03bd1kMGTKEHj1+G6XMyckBHCOBDRo0cLanpqZqHt9qSvcAioiIVCKbzXZVl2ErU1BQkMuTvYZhEBERQVxcHF26dAEgNzeXDRs2MG/ePLPKlHJQABQREZES2Ww2xo8fz0svvUSLFi1o0aIFL730ErVq1eLee+919hs5ciQNGzZkzpw5gCMk7tu3z/nfx44dIz4+nsDAQJo3b27KdxEHBUAREREp1TPPPENWVhaPP/64cyLo1atXu4wUJiUl4eHx20vGjh8/7hwxBFiwYAELFiwgNjaW9evXV2b5chmbYRiG2UVUVxkZGYSEhJCenk5wcLDZ5YiISBWTnZ1NQkICTZo0wc/Pz+xyLKWkY6/zdxV4F7CIiIiIVC4FQBERERGLUQAUERERsRgFQBERERGLUQAUERERsRgFQBERERGLUQAUERERsRgFQBERERGLUQAUERERsRjLB8CcnBw6d+6MzWYjPj7e7HJERERE3M7yAfCZZ54hMjLS7DJERESqtGXLljFw4EDCwsKuaNBk6dKltG3bFl9fX9q2bcvy5cvdW6iUiaUD4KpVq1i9ejULFiwwuxQREZEqLTMzk969ezN37twyr7NlyxaGDRvGiBEj2LVrFyNGjGDo0KFs3brVjZVKWXiZXYBZfvnlFx555BFWrFhBrVq1zC7HRdovKaT/kmJ2GaYyMMwuwVyGxb8/WP4YWPvbX1ADfgYKDMj39CI36zw2e4HZ5ZTL0D/cCUDikSMA5GZlkXM+s8R1Fr6ygH433cTEcWMBmDhuLOvWruWVBQv4x4cflLpPm4cHPn7+5StcimTJAGgYBqNGjeKxxx6je/fuJCYmlmm9nJwccnJynMsZGRluqW/ft2vZ8u9P3bJtERGpPLXqhNH1ngdJ/zUVb09PwHEO4pJzSaXy9cVms5VrExmpvzh+P5nKmRPHS+y7efMWRj84yqVf72uv4d0PPix1XQBvPz/qNowuV71StBoVAGfMmMHMmTNL7LNt2zY2b95MRkYGU6dOvaLtz5kzp9TtV4SA0FDqNWrs9v1UeeX8S6ras/r3B2xY/BhY/OsD5Q4rZvMJCsbDywsvHx+8vRynXCMrm1//MNSUeur93+fY/PzKtQ0vH1/n796+JW/r15MniYho4NIvIqIBv548Weq6AF7ePuWqVYpXowLgE088wfDhw0vs07hxY2bPns3333+Pr6+vy2fdu3fnvvvu48MPPyxy3alTpzJx4kTnckZGBtHRFf8vk04330qnm2+t8O2KiEjlys7OJiEhgdoRkfhdCF728+f51aR66jSMwqMMtz198sknPProo87lVatWcf311wNwNt9xKTs0PIK6UaWfA4PDwlz6Bdapg81mK9O64j41KgCGhYURFhZWar/XXnuN2bNnO5ePHz/OwIEDWbJkCT169Ch2PV9f30KhUURE5ErY/P1ptXOHafsuiyFDhricDxs2bHhV+4uIiCAlxfWe9tTUVMLDw69qe1JxalQALKtGjRq5LAcGBgLQrFkzoqKizChJREQswmazYatiDx9eLigoiKCgoHJvp2fPnsTFxTFhwgRn2+rVq+nVq1e5ty3lY8kAKCIiIlfm9OnTJCUlcfy44+GNAwcOAI5RvoiICABGjhxJw4YNmTNnDgDjxo2jb9++zJs3j9tuu43PP/+cNWvWsGnTJnO+hDhZeh7Aixo3boxhGHTu3NnsUkRERKqkL774gi5dujB48GAAhg8fTpcuXXjrrbecfZKSkjhx4oRzuVevXixevJj333+fjh078sEHH5R6u5VUDpth1ICJlkySkZFBSEgI6enpBAcHm12OiIhUMRcfAmnSpInzIRCpHCUde52/NQIoIiIiYjkKgCIiIiIWowAoIiIiYjEKgCIiIiIWowAoIiIiYjEKgCIiIiIWowAoIiIiYjEKgCIiIiIWowAoIiIiYjEKgCIiIiIWowAoIiIiJcrLy2Py5Ml06NCBgIAAIiMjGTlyJMePHy913aVLl9K2bVt8fX1p27Yty5cvr4SKpTQKgCIiIlKi8+fPs3PnTqZNm8bOnTtZtmwZBw8eZMiQISWut2XLFoYNG8aIESPYtWsXI0aMYOjQoWzdurWSKpfi2AzDMMwuorrSy6RFRKQk2dnZJCQk0KRJE/z8/Mwup0Jt27aNa6+9liNHjtCoUaMi+wwbNoyMjAxWrVrlbBs0aBC1a9fms88+c2t9JR17nb/By+wCRERErMQwDPJz7abs28vHA5vNViHbSk9Px2azERoaWmyfLVu2MGHCBJe2gQMHsmjRogqpQa6eAqCIiEglys+18864Dabse/SfY/H29Sz3drKzs5kyZQr33ntviSNoKSkphIeHu7SFh4eTkpJS7hqkfHQPoIiIiLj45JNPCAwMdP7auHGj87O8vDyGDx+O3W7nzTffLHVbl484GoZRYaOQcvU0AigiIlKJvHw8GP3nWNP2XRZDhgyhR48ezuWGDRsCjvA3dOhQEhISWLt2ban3z0VERBQa7UtNTS00KiiVTwFQRESkEtlstgq5DOtOQUFBBAUFubRdDH+HDh1i3bp11K1bt9Tt9OzZk7i4OJf7AFevXk2vXr0qvGa5MgqAIiIiUqL8/Hzuuusudu7cyX/+8x8KCgqcI3t16tTBx8cHgJEjR9KwYUPmzJkDwLhx4+jbty/z5s3jtttu4/PPP2fNmjVs2rTJtO8iDgqAIiIiUqKjR4/yxRdfANC5c2eXz9atW8cNN9wAQFJSEh4ev11m7tWrF4sXL+a5555j2rRpNGvWjCVLlrhcXhZzKACKiIhIiRo3bkxZpg1ev359oba77rqLu+66yw1VSXnoKWARERERi1EAFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAFBEREbEYBUARERG5Io8++ig2m41FixaV2nfp0qW0bdsWX19f2rZty/Lly91foJRKAVBERETKbMWKFWzdupXIyMhS+27ZsoVhw4YxYsQIdu3axYgRIxg6dChbt26thEqlJAqAIiIiUibHjh3jiSee4JNPPsHb27vU/osWLeLmm29m6tSptG7dmqlTp9KvX78yjRyKe3mZXYCIiIiVGIZBfk6OKfv28vXFZrNd1bp2u50RI0YwadIk2rVrV6Z1tmzZwoQJE1zaBg4cqABYBSgAioiIVKL8nBxee+AuU/Y99sN/4+3nd1Xrzps3Dy8vL8aOHVvmdVJSUggPD3dpCw8PJyUl5apqkIqjS8AiIiLi4pNPPiEwMND5a8OGDfz5z3/mgw8+uOIRxMv7G4Zx1aOQUnE0AigiIlKJvHx9Gfvhv03bd1kMGTKEHj16OJf/9a9/kZqaSqNGjZxtBQUFPPXUUyxatIjExMQitxMREVFotC81NbXQqKBUPgVAERGRSmSz2a76MmxlCQoKIigoyLk8evRofv/737v0GThwICNGjODBBx8sdjs9e/YkLi7O5T7A1atX06tXr4ovWq6IAqCIiIiUqG7dutStW9elzdvbm4iICFq1auVsGzlyJA0bNmTOnDkAjBs3jr59+zJv3jxuu+02Pv/8c9asWcOmTZsqtX4pTPcAioiISIVISkrixIkTzuVevXqxePFi3n//fTp27MgHH3zAkiVLXC4vizk0AigiIiJXrKj7/tavX1+o7a677uKuu8x56lmKpxFAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAEREREYtRABQRERGxGAVAERERKZP9+/czZMgQQkJCCAoK4rrrriMpKanEdZYuXUrbtm3x9fWlbdu2LF++vJKqlZIoAIqIiEipDh8+TJ8+fWjdujXr169n165dTJs2DT8/v2LX2bJlC8OGDWPEiBHs2rWLESNGMHToULZu3VqJlUtRbIZhGGYXUV1lZGQQEhJCeno6wcHBZpcjIiJVTHZ2NgkJCTRp0qTEoFQdDB8+HG9vb/7xj3+UeZ1hw4aRkZHBqlWrnG2DBg2idu3afPbZZ+4o06mkY6/zt0YARUREKpVhGNhzC0z5dbVjPna7nS+//JKWLVsycOBA6tevT48ePVixYkWJ623ZsoUBAwa4tA0cOJDNmzdfVR1ScbzMLsBMX375JbNmzWL37t0EBATQt29fli1bZnZZIiJSgxl5do4/b04AipzVC5uP5xWvl5qayrlz55g7dy6zZ89m3rx5fPXVV9x5552sW7eO2NjYItdLSUkhPDzcpS08PJyUlJSrql8qjmUD4NKlS3nkkUd46aWXuOmmmzAMgz179phdloiIiOk++eQTHn30Uefyl19+CcBtt93GhAkTAOjcuTObN2/mrbfeKjYAAthsNpdlwzAKtUnls2QAzM/PZ9y4cbz88ss8/PDDzvZWrVqZWJWIiFiBzduDyFm9TNt3WQwZMoQePXo4l+vVq4eXlxdt27Z16demTRs2bdpU7HYiIiIKjfalpqYWGhWUymfJALhz506OHTuGh4cHXbp0ISUlhc6dO7NgwQLatWtX7Ho5OTnk5OQ4lzMyMtxSX9bek5zfe9It25ZL6PEnqWn0TF+Vk+tjp6BxAflnssn3qT5/Pv540bh2w98a8qF7l27s372P/FNZzuYDe/fTKCLKpe1S13W9ltUrv+LJkY85277+chU9u/Uodh0nTxteodX7wZmqzJIB8OeffwZgxowZLFy4kMaNG/PKK68QGxvLwYMHqVOnTpHrzZkzh5kzZ7q9vryUTLLif3X7fkRExL3yg2wYkQHYcwqwF+SbXU65THxkLPeNGUWf7j2J7Xk9qzes4T9fryTunyuxZzm+20PjRxMZEcnsKTMAGDPqMfrdNYj5r7zM7wYM5j+rv+SbDetYt+xr5zrF8tJzqu5UowLgjBkzSg1o27Ztw263A/Dss8/yhz/8AYD333+fqKgo/vWvf7nc93CpqVOnMnHiROdyRkYG0dHRFVT9b3xb1ibEr0b90YiAbvmpFDrMlaSM97Dl2PLJ9M/AM8gbT19fNxflXnfecxdv5p1j3sL5TJz+DK1atORfHy+m74AbnH2SfzmOp683nqGO79qnf18+/eBjnp81nRkLZtOsSVM+++ATet7Yp/Qd6j5Bt6pR8wCePHmSkydLvnTauHFjtmzZwk033cTGjRvp0+e3H8IePXrQv39/XnzxxTLtT/MIiYhISWrSPIDVjeYBLFmNGmYKCwsjLCys1H7dunXD19eXAwcOOANgXl4eiYmJxMTEuLtMEREREVPVqABYVsHBwTz22GNMnz6d6OhoYmJiePnllwG4++67Ta5ORERExL0sGQABXn75Zby8vBgxYgRZWVn06NGDtWvXUrt2bbNLExEREXErywZAb29vFixYwIIFC8wuRURERKRS6RlrERERN6tBz1tWGzrmJVMAFBERcRNvb28Azp8/b3Il1nPxmF/8MxBXlr0ELCIi4m6enp6EhoaSmpoKQK1atfQeXDczDIPz58+TmppKaGgonp6eZpdUJSkAioiIuFFERASAMwRK5QgNDXUeeylMAVBERMSNbDYbDRo0oH79+uTl5ZldjiV4e3tr5K8UCoAiIiKVwNPTU6FEqgw9BCIiIiJiMQqAIiIiIhajACgiIiJiMboHsBwuTjKZkZFhciUiIiJSVhfP21aeLFoBsBzOnj0LQHR0tMmViIiIyJU6e/YsISEhZpdhCpth5fhbTna7nePHjxMUFKSJPXH8iyo6Oprk5GSCg4PNLqfG0nGuHDrOlUPHuXLoOLsyDIOzZ88SGRmJh4c174bTCGA5eHh4EBUVZXYZVU5wcLD+gqkEOs6VQ8e5cug4Vw4d599YdeTvImvGXhERERELUwAUERERsRgFQKkwvr6+TJ8+HV9fX7NLqdF0nCuHjnPl0HGuHDrOcjk9BCIiIiJiMRoBFBEREbEYBUARERERi1EAFBEREbEYBUARERERi1EAlAqTk5ND586dsdlsxMfHu3yWlJTE73//ewICAggLC2Ps2LHk5uaaU2g1lZiYyMMPP0yTJk3w9/enWbNmTJ8+vdBx1LEuvzfffJMmTZrg5+dHt27d2Lhxo9klVWtz5szhmmuuISgoiPr163P77bdz4MABlz6GYTBjxgwiIyPx9/fnhhtu4McffzSp4pphzpw52Gw2xo8f72zTcZaLFAClwjzzzDNERkYWai8oKGDw4MFkZmayadMmFi9ezNKlS3nqqadMqLL6+t///ofdbuftt9/mxx9/5NVXX+Wtt97iT3/6k7OPjnX5LVmyhPHjx/Pss8/yww8/cP3113PLLbeQlJRkdmnV1oYNGxgzZgzff/89cXFx5OfnM2DAADIzM5195s+fz8KFC3njjTfYtm0bERER3Hzzzc53rsuV2bZtG++88w4dO3Z0addxFidDpAKsXLnSaN26tfHjjz8agPHDDz+4fObh4WEcO3bM2fbZZ58Zvr6+Rnp6ugnV1hzz5883mjRp4lzWsS6/a6+91njsscdc2lq3bm1MmTLFpIpqntTUVAMwNmzYYBiGYdjtdiMiIsKYO3eus092drYREhJivPXWW2aVWW2dPXvWaNGihREXF2fExsYa48aNMwxDx1lcaQRQyu2XX37hkUce4R//+Ae1atUq9PmWLVto3769y+jgwIEDycnJYceOHZVZao2Tnp5OnTp1nMs61uWTm5vLjh07GDBggEv7gAED2Lx5s0lV1Tzp6ekAzp/dhIQEUlJSXI67r68vsbGxOu5XYcyYMQwePJj+/fu7tOs4y6W8zC5AqjfDMBg1ahSPPfYY3bt3JzExsVCflJQUwsPDXdpq166Nj48PKSkplVRpzXP48GFef/11XnnlFWebjnX5nDx5koKCgkLHMDw8XMevghiGwcSJE+nTpw/t27cHcB7boo77kSNHKr3G6mzx4sXs3LmTbdu2FfpMx1kupRFAKdKMGTOw2Wwl/tq+fTuvv/46GRkZTJ06tcTt2Wy2Qm2GYRTZbjVlPdaXOn78OIMGDeLuu+/m//2//+fymY51+V1+rHT8Ks4TTzzB7t27+eyzzwp9puNePsnJyYwbN46PP/4YPz+/YvvpOAtoBFCK8cQTTzB8+PAS+zRu3JjZs2fz/fffF3q/ZPfu3bnvvvv48MMPiYiIYOvWrS6fnzlzhry8vEL/ErWish7ri44fP86NN95Iz549eeedd1z66ViXT1hYGJ6enoVG+1JTU3X8KsCTTz7JF198wbfffktUVJSzPSIiAnCMUDVo0MDZruN+ZXbs2EFqairdunVzthUUFPDtt9/yxhtvOJ+81nEWQA+BSPkcOXLE2LNnj/PX119/bQDGv//9byM5OdkwjN8eTDh+/LhzvcWLF+vBhKtw9OhRo0WLFsbw4cON/Pz8Qp/rWJfftddea/zxj390aWvTpo0eAikHu91ujBkzxoiMjDQOHjxY5OcRERHGvHnznG05OTl6OOEKZWRkuPx9vGfPHqN79+7G/fffb+zZs0fHWVwoAEqFSkhIKPQUcH5+vtG+fXujX79+xs6dO401a9YYUVFRxhNPPGFeodXQsWPHjObNmxs33XSTcfToUePEiRPOXxfpWJff4sWLDW9vb+Nvf/ubsW/fPmP8+PFGQECAkZiYaHZp1dYf//hHIyQkxFi/fr3Lz+358+edfebOnWuEhIQYy5YtM/bs2WPcc889RoMGDYyMjAwTK6/+Ln0K2DB0nOU3CoBSoYoKgIbhGCkcPHiw4e/vb9SpU8d44oknjOzsbHOKrKbef/99Ayjy16V0rMvvL3/5ixETE2P4+PgYXbt2dU5XIlenuJ/b999/39nHbrcb06dPNyIiIgxfX1+jb9++xp49e8wruoa4PADqOMtFNsMwDBOuPIuIiIiISfQUsIiIiIjFKACKiIiIWIwCoIiIiIjFKACKiIiIWIwCoIiIiIjFKACKiIiIWIwCoIiIiIjFKACKiIiIWIwCoIhUuhtuuIHx48c7lxs3bsyiRYtMq8ddZsyYgc1mw2azVcr3GzVqlHN/K1ascPv+RKT6UgAUEdNt27aN0aNHl6lvdQuL7dq148SJE2X+fuXx5z//mRMnTrh9PyJS/XmZXYCISL169cwuwW28vLyIiIiolH2FhIQQEhJSKfsSkepNI4Ai4laZmZmMHDmSwMBAGjRowCuvvFKoz+WjejNmzKBRo0b4+voSGRnJ2LFjAcel4yNHjjBhwgTnpU6AU6dOcc899xAVFUWtWrXo0KEDn332mcs+brjhBsaOHcszzzxDnTp1iIiIYMaMGS590tLSGD16NOHh4fj5+dG+fXv+85//OD/fvHkzffv2xd/fn+joaMaOHUtmZuYVHxObzcZ7773HHXfcQa1atWjRogVffPGF8/P169djs9n4+uuv6dKlC/7+/tx0002kpqayatUq2rRpQ3BwMPfccw/nz5+/4v2LiCgAiohbTZo0iXXr1rF8+XJWr17N+vXr2bFjR7H9//3vf/Pqq6/y9ttvc+jQIVasWEGHDh0AWLZsGVFRUcyaNYsTJ044L3dmZ2fTrVs3/vOf/7B3715Gjx7NiBEj2Lp1q8u2P/zwQwICAti6dSvz589n1qxZxMXFAWC327nlllvYvHkzH3/8Mfv27WPu3Ll4enoCsGfPHgYOHMidd97J7t27WbJkCZs2beKJJ564quMyc+ZMhg4dyu7du7n11lu57777OH36tEufGTNm8MYbb7B582aSk5MZOnQoixYt4tNPP+XLL78kLi6O119//ar2LyIWZ4iIuMnZs2cNHx8fY/Hixc62U6dOGf7+/sa4ceOcbTExMcarr75qGIZhvPLKK0bLli2N3NzcIrd5ad+S3HrrrcZTTz3lXI6NjTX69Onj0ueaa64xJk+ebBiGYXz99deGh4eHceDAgSK3N2LECGP06NEubRs3bjQ8PDyMrKysIteZPn260alTp0LtgPHcc885l8+dO2fYbDZj1apVhmEYxrp16wzAWLNmjbPPnDlzDMA4fPiws+3RRx81Bg4cWOT2ly9fXmRNIiKGYRgaARQRtzl8+DC5ubn07NnT2VanTh1atWpV7Dp33303WVlZNG3alEceeYTly5eTn59f4n4KCgp48cUX6dixI3Xr1iUwMJDVq1eTlJTk0q9jx44uyw0aNCA1NRWA+Ph4oqKiaNmyZZH72LFjBx988AGBgYHOXwMHDsRut5OQkFBifUW5tJaAgACCgoKctRTVJzw8nFq1atG0aVOXtsvXEREpCz0EIiJuYxjGFa8THR3NgQMHiIuLY82aNTz++OO8/PLLbNiwAW9v7yLXeeWVV3j11VdZtGgRHTp0ICAggPHjx5Obm+vS7/L1bTYbdrsdAH9//xLrstvtPProo877ES/VqFGjK/mKpdZSVB+bzVamdUREykIBUETcpnnz5nh7e/P99987Q9KZM2c4ePAgsbGxxa7n7+/PkCFDGDJkCGPGjKF169bs2bOHrl274uPjQ0FBgUv/jRs3ctttt3H//fcDjrB26NAh2rRpU+ZaO3bsyNGjRzl48GCRo4Bdu3blxx9/pHnz5mXepohIVaVLwCLiNoGBgTz88MNMmjSJb775hr179zJq1Cg8PIr/q+eDDz7gb3/7G3v37uXnn3/mH//4B/7+/sTExACOJ4a//fZbjh07xsmTJwFH0IyLi2Pz5s3s37+fRx99lJSUlCuqNTY2lr59+/KHP/yBuLg4EhISWLVqFV999RUAkydPZsuWLYwZM4b4+HgOHTrEF198wZNPPnmVR0dExDwKgCLiVi+//DJ9+/ZlyJAh9O/fnz59+tCtW7di+4eGhvLuu+/Su3dvOnbsyDfffMP//d//UbduXQBmzZpFYmIizZo1c84fOG3aNLp27crAgQO54YYbiIiI4Pbbb7/iWpcuXco111zDPffcQ9u2bXnmmWeco40dO3Zkw4YNHDp0iOuvv54uXbowbdo0GjRocOUHRUTEZDbjam7SERGRUs2YMYMVK1YQHx9fqfu12WwsX778qkKwiFiDRgBFRNxoz549BAYG8uabb7p9X4899hiBgYFu34+IVH8aARQRcZPTp087J3euV6+e21/TlpqaSkZGBuCY4iYgIMCt+xOR6ksBUERERMRidAlYRERExGIUAEVEREQsRgFQRERExGIUAEVEREQsRgFQRERExGIUAEVEREQsRgFQRERExGIUAEVEREQs5v8DW0LXxSscUmQAAAAASUVORK5CYII=", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#plotting trajectories for 7 impact parameters\n", "plt.figure()\n", "for b in [-1e-5, -0.001, -0.1, -1.0, -2.0, -4.0, -6.0]:\n", " xc, yc = coulomb_plot(b, Z= 6, v_c = 0.7)\n", " plt.plot(xc*1e9,yc*1e9, label = str(b))\n", "\n", "plt.xlabel('distance [nm]')\n", "plt.ylabel('impact parameter [nm]')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we look at the scattering power of a single atom that deflects an electron:\n", " \n", "![Single Electron Scattering](images/scattering_single_atom.jpg)\n", "\n", "The scattering power is dependent on the so-called atomic form factor $f_e$ ( the subscript $_e$ means this is for electrons).\n", "\n", "All form factors (X-ray, electrons, ions, neutrons, ...) are based on a Fourier transform of a density distribution of the scattering object from real space to momentum (or reciprocal) space.\n", "\n", "Since an electron scatters through the coulomb force of the (screend) nucleus, the form factor is the inner potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Atomic Form Factor\n", "\n", "$$ |f(\\theta)|^2 = \\frac{d\\sigma(\\theta)}{d\\Omega} $$\n", "\n", "What does that mean for us:\n", "\n", "- The atomic structure factor gives the amplitude of an electron wave\n", "\tscattered from an isolated atom.\n", "- $|f(\\theta)|^2$ is proportional to the scattered intensity.\n", "- The atomic scattering factor depends on atomic number $Z$, wavelength $\\lambda$ and scattering angle $\\theta$. \n", "- The atomic structure factors for each element are tabulated.\n", "\n", "The atomic form factor gives us the probability of an electron scattering in a certain angle." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tabulated Atomic Form Factors\n", "The calculated form factors are tabulated and can be plotted according to the momentum transfer.\n", "\n", "Here we use the values from Appendix C of Kirkland, \"Advanced Computing in Electron Microscopy\", 3rd ed.\n", "\n", "The calculation of electron form factor for specific $q$ perfommed by the function *feq* in the kinematic_scattering of pyTEMlib using equation Kirkland C.17" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a239b1073c364c1187f263f4ef336029", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# recreating figure 5.8 (p.110) of Kirkland, \"Advanced Computing in Electron Microscopy\" 3rd ed. \n", "x = []\n", "ySi = []\n", "yC = []\n", "yCu =[]\n", "yAu =[]\n", "yU = []\n", "for i in range(100):\n", " x.append(i/5)\n", " ySi.append(ks.feq('Si', i/5))\n", " yC.append(ks.feq('C', i/5))\n", " yCu.append(ks.feq('Cu', i/5))\n", " yAu.append(ks.feq('Au', i/5))\n", " yU.append(ks.feq('U', i/5))\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(x,ySi,label='Si')\n", "plt.plot(x,yC,label='C')\n", "plt.plot(x,yCu,label='Cu')\n", "plt.plot(x,yAu,label='Au')\n", "plt.plot(x,yU,label='U')\n", "plt.legend()\n", "plt.ylabel('scattering factor (Å)')\n", "plt.xlabel('scattering angle q (1/Å)')\n", "plt.xlim(0,2)\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adding atoms in a row makes the atom just look heavier:\n", "\n", "![Structure Factor](images/form_factor.jpg)\n", "\n", "Similar effects appear if atoms are periodically arranged. That is discussed in more detail in the \n", "[Structure Factors](CH2_04-Structure_Factors.ipynb) notebook." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "The scattering power of an atom is given by the tabulated scattering factors. As long as there are no dynamic effects the scattering factors can be combined linearly.\n", "\n", "Next we need to transfer our knowledge into a diffraction pattern." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Navigation\n", "- **Back [The Electron](CH2_01-Electron.ipynb)** \n", "- **Next: [Basic Crystallography](CH2_03-Basic_Crystallography.ipynb)** \n", "- **Chapter 2: [Diffraction](CH2_00-Diffraction.ipynb)** \n", "- **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" }, "livereveal": { "height": 768, "theme": "sky", "transition": "zoom", "width": 1024 }, "toc": { "base_numbering": "2", "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "240px" }, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }