{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 4 [Spectroscopy](CH4_00-Spectroscopy.ipynb)\n",
    "\n",
    "\n",
    "<hr style=\"height:1px;border-top:4px solid #FF8200\" />\n",
    "\n",
    "# Bremsstrahlung\n",
    "\n",
    "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM/main/Spectroscopy/CH4_13-Bremsstrahlung.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//Spectroscopy/CH4_13-Bremsstrahlung.ipynb)\n",
    "\n",
    "part of \n",
    "\n",
    "<font size = \"5\"> **[MSE672:  Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**</font>\n",
    "\n",
    "\n",
    "**Spring 2024**\n",
    "<table style=\"margin-right:auto;margin-left:0px\">\n",
    "  <tr>\n",
    "    <td>Gerd Duscher </td>\n",
    "    <td>Khalid Hattar</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>Microscopy Facilities</td> \n",
    "    <td> Tennessee Ion Beam Materials Laboratory </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>Materials Science & Engineering</td>\n",
    "    <td> Nuclear Engineering</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>Institute of Advanced Materials & Manufacturing</td>\n",
    "    <td> </td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td colspan=\"2\"><center> The University of Tennessee, Knoxville</center> </td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "Background and methods to analysis and quantification of data acquired with transmission electron microscopes.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load relevant python packages\n",
    "### Check Installed Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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') < '0.2024.2.3':\n",
    "    print('installing pyTEMlib')\n",
    "    !{sys.executable} -m pip install  --upgrade pyTEMlib -q\n",
    "\n",
    "print('done')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First we import the essential libraries\n",
    "All we need here should come with the annaconda or any other package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "notebook version:  2023.01.22\n"
     ]
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sys\n",
    "import os\n",
    "if 'google.colab' in sys.modules:\n",
    "    from google.colab import output\n",
    "    from google.colab import drive\n",
    "    output.enable_custom_widget_manager()\n",
    "\n",
    "__notebook_version__ = '2023.01.22'\n",
    "print('notebook version: ', __notebook_version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bremsstrahlung\n",
    "The Bremsstrahlung causes the background the characteristic X-ray peaks are sitting on.\n",
    "\n",
    "\n",
    "Because of the repulsion a fast electron by the negative electron cloud in a solid. such an electron will be de-accelerated or deflected. Any acceleration (negative or positive) is related with a photon (possibly only as an exchagne particle which is the basis of Quantum Eletrodynamics).\n",
    "\n",
    "![X-Ray_Auger](./images/Bremsstrahlung1.jpg)\n",
    "\n",
    "The energy loss in the braking of an electron will cause the emission of Bremsstrahlung (braking radiation). The energy of the photon of this electromagnetic radiation is directly the photon energy.\n",
    "\n",
    "Thus the Bremsstrahlung spans the energies from the incident electron's energy down to a practical limit of about 100eV. The Bremsstrahlung is therefore sometimes refered to as X-ray continuum.\n",
    "\n",
    "\n",
    "\n",
    "The Bremsstrahlung is anoistropic, peaked in the forwad direction of the incident electron.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kramer's formulation of Bremsstrahlung\n",
    "\n",
    "Kramers' formula for Bremsstrahlung is the most basic (and not very accurate) description of Bremsstrahlung vs energy:\n",
    "\n",
    "$$ N_E = IKZ \\frac{(E-E_0)}{E}$$\n",
    "\n",
    "- K -- A constant,\n",
    "- Z -- The average atomic number of the specimen,\n",
    "- E0 -- The incident beam energy, \n",
    "- I -- The electron beam current,\n",
    "- E -- The continuum photon energy.\n",
    "\n",
    "The factor K in Kramers’ law actually takes\n",
    "account of numerous parameters. These include\n",
    "- Kramers’ original constant.\n",
    "- The collection efficiency of the detector.\n",
    "- The processing efficiency of the detector.\n",
    "- The absorption of X-rays within the specimen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "model_id": "3d645e7bc3504b8dac488083f35dbee9",
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       "version_minor": 0
      },
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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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8HdQADA5iorKzVkyBDNmTPnqPs89thjmj17tubMmaPPPvtMGRkZuvDCC1VeXh6UOk2ZMkXV1dV64403Wr32xhtvqKqqStdee21QyrYyAqCF+O4FXNmReQAlpoIBAJsbP368HnnkEV1xxRVtvm4Yhp588knde++9uuKKKzRo0CA9//zzqqqq0ksvvdTuctasWaO0tDT99re/lSSVlpbqpptuUlpamhISEjRu3Dh98cUXkqTU1FRNmDBB8+bNa3WcefPm6bLLLlNqamoHPq29EQAtxNcFXN2RO4FITAUDAMFiGOb11eF4GEbAPkZ+fr6KioqUm5vbvM3j8WjMmDFauXJlu46xbNkynX/++XrooYd07733yjAMXXLJJSoqKtLixYu1Zs0aDRs2TOeff74OHDggSZo2bZqWL1+u/Pz85uNs375dH3zwgaZNmxawz2cn7nBXAIET09wC2IEuYIkWQAAIlvoq6XdZ4Sn7N3ukyNiAHKqoqEiSlJ6e3mJ7enq6duzY8b3vf+utt3Tttdfq6aef1tVXXy1J+uCDD7R+/XoVFxfL4zGvRX/88cf15ptv6vXXX9dNN92kiy66SFlZWZo/f74eeughSdJzzz2nrKysFmEU7UcLoIX4AmBtg1eN3g78j48WQABAOzgcjhbPDcNote27Pv30U02aNEnPP/98c/iTzO7giooKJScnKy4urvmRn5+vrVu3SpJcLpeuu+46zZ8/X16vV4Zh6Pnnn9fUqVPlcrkC/wFtgBZAC4n1HP7jrKprUHxUxHEeoGkuQCaDBoDAiogxW+LCVXaAZGRkSDJbAjMzM5u3FxcXt2oV/K6+ffsqOTlZ8+bN0yWXXKLIyEhJktfrVWZmppYtW9bqPUlJSc3rN9xwg2bNmqWlS5dKkgoKCnT99df7+YnsiwBoIR63Uw6HeblHdV3j8QdAWgABIDgcjoB1w4ZTTk6OMjIylJeXp6FDh0qS6urqtHz5cj366KPHfG9KSooWLlyosWPHavLkyXr11VcVERGhYcOGqaioSG63W3369Dnq+/v27asxY8boueeek2EYGjt2rPr27RvIj2crdAFbiMPhUFzTQJCKjlwHyDWAAGBrFRUVWrdundatWyfJHPSxbt06FRQUSDJ/Z2bMmKHf/e53WrRokb766itNnTpVMTExuuaaa773+GlpaVq6dKm+/vprXX311WpoaNAFF1ygkSNHauLEiXr//fe1fft2rVy5Uvfdd59Wr17d4v3Tpk3TwoULtWjRIgZ/+IkAaDG+buAOTQVDCyAA2Nrq1as1dOjQ5ta9mTNnaujQobr//vub9/nlL3+pGTNm6JZbbtGIESO0e/duLVmyRPHx8e0qIyMjQ0uXLtX69ev14x//WF6vV4sXL9a5556rG264Qf3799dVV12l7du3t+pWnjRpkjwejzwez1GnqkH7OAwjgOPDbaasrEyJiYkqLS1VQkJCuKsjSbpg9nJ9W1yhl396lkb2TT6+N+/fKv15mBQRK90bpmtVAKCLq6mpUX5+vnJychQVFRXu6tjWsf4cOuPvd6jRAmgxvhbADnUBxzQFxvpKqb46gLUCAACdCQHQYuKbu4A7EACjEiVn08ARuoEBALAsAqDFxHrM+ZDKOxIAHY7DrYAMBAEAwLIIgBYT5zFb8CpqOng3kLg0c1mxL0A1AgAAnQ0B0GLiPH7eDi6uacRVxd4A1QgAAHQ2BECLiYvyYxCIRAAEgABhko3w4vs/NgKgxTR3AXc4AKaay4riANUIAOwlIsL8d7iqqirMNbE33/fv+/NAS9wKzmJ8XcAdvwaQFkAA8IfL5VJSUpKKi83/SMfExMjhcIS5VvZhGIaqqqpUXFyspKQkuVyucFepUyIAWoyvC7iyzt9BILQAAkBHZWRkSFJzCEToJSUlNf85oDUCoMXENt0LuNzfFsBK/tECgI5yOBzKzMxUWlqa6uvrw10d24mIiKDl73sQAC2muQXQ70EgBEAA8JfL5SKIoFNiEIjFxPlzKzjpcBdwbZlUxwXMAABYEQHQYvwOgJ4Eyd1002y6gQEAsCQCoMXEHXEv4A7NgeRwMBAEAACLIwBajO8aQK8hVdc3duwgsb4AyFQwAABYEQHQYqIjXHI2TTfFXIAAAKAtBECLcTgcig3UQJCKfQGqFQAA6EwsFQDnzp2rnJwcRUVFafjw4frwww+Puf+LL76oIUOGKCYmRpmZmbr++uu1f//+ENU2eOL9DoC0AAIAYGWWCYALFizQjBkzdO+992rt2rUaPXq0xo8fr4KCgjb3/+ijjzRlyhRNmzZNGzZs0GuvvabPPvtMN954Y4hrHniBawFkEAgAAFZkmQA4e/ZsTZs2TTfeeKMGDhyoJ598UtnZ2Xrqqafa3P+TTz5Rnz59dMcddygnJ0fnnHOObr75Zq1evTrENQ8830AQrgEEAABtsUQArKur05o1a5Sbm9tie25urlauXNnme0aNGqVdu3Zp8eLFMgxDe/fu1euvv65LLrkkFFUOKv8ng+ZuIAAAWJklAmBJSYkaGxuVnp7eYnt6erqKiorafM+oUaP04osvavLkyYqMjFRGRoaSkpL05z//+ajl1NbWqqysrMWjMzpyLsCOHeCIaWA6MpcgAADo1CwRAH0cDkeL54ZhtNrms3HjRt1xxx26//77tWbNGr333nvKz8/X9OnTj3r8WbNmKTExsfmRnZ0d0PoHii8AlnW4C7gpADbWmreEAwAAlmKJAJiSkiKXy9Wqta+4uLhVq6DPrFmzdPbZZ+sXv/iFTj31VF100UWaO3eu5s2bp8LCwjbfc88996i0tLT5sXPnzoB/lkBIiI6QJJV3NABGRJu3hJOkcq4DBADAaiwRACMjIzV8+HDl5eW12J6Xl6dRo0a1+Z6qqio5nS0/vsvlkqSj3kLN4/EoISGhxaMzSogyA2BZTX3HD+K7DrC87TAMAAC6LksEQEmaOXOmnnnmGc2bN0+bNm3SnXfeqYKCguYu3XvuuUdTpkxp3n/ChAlauHChnnrqKW3btk0ff/yx7rjjDp1xxhnKysoK18cIiITopi7gaj8CYEKmuSxv+xpKAADQdbnDXYFAmTx5svbv36+HH35YhYWFGjRokBYvXqzevXtLkgoLC1vMCTh16lSVl5drzpw5uuuuu5SUlKRx48bp0UcfDddHCJjDLYAd7AKWpPimEFy+JwA1AgAAnYllAqAk3XLLLbrlllvafG3+/Pmttt1+++26/fbbg1yr0PNdAxiQFsAyuoABALAay3QB47CEKN8oYD8CIC2AAABYFgHQgg63APrTBZxhLmkBBADAcgiAFtQcAP1pAUzwtQAyCAQAAKshAFqQrwu4rsGrmvrGjh0kvukawIoiyesNUM0AAEBnQAC0oNhIt5xNN0DpcCtgXLrkcEreBqlyX+AqBwAAwo4AaEFOp0PxUX5eB+hyS7FNt4RjIAgAAJZCALSo+ICMBGYgCAAAVkQAtKjmyaD9mgvQNxCEAAgAgJUQAC2q+XZwft0NxHc7OAIgAABWQgC0qMC0AHI3EAAArIgAaFEBmQuQu4EAAGBJBECLSvB3FLBECyAAABZFALSow9cA+tMCyDWAAABYEQHQogJyDaAvANYckuqr/a8UAADoFAiAFnX4GkA/uoCjEqWIGHO9jOsAAQCwCgKgRfnuB+xXC6DDISX0MNfLdgegVgAAoDMgAFpUQEYBS1JiT3NZusvPGgEAgM6CAGhRARkFLBEAAQCwIAKgRTWPAvanC1iSErPNZelOP2sEAAA6CwKgRSU2dQHXNXpVXdfox4F8LYBcAwgAgFUQAC0qzuOW2+mQJB2squv4gRKbBoHQBQwAgGUQAC3K4XAoKcZsBfQvAPq6gHdJhhGAmgEAgHAjAFpYUkykJKm0yo/rABOa7gdcXylVHwxArQAAQLgRAC2sW3MLoB8BMCJaik011+kGBgDAEgiAFuZrAfSrC1hiKhgAACyGAGhhSU0jgQ8RAAEAwBEIgBbWLdZsATzkTxewxFyAAABYDAHQwpICcQ2gRAsgAAAWQwC0sG4xvhZAuoABAMBhBEAL6xaIeQAlAiAAABZDALSwxOimFsBA3Q+4vFBq9PNYAAAg7AiAFtYt1jcK2M/QFpMiuTySDKmMewIDANDVEQAt7MhrAL1eP27j5nQe7gY+VBCAmgEAgHAiAFqYbxSw15DKaxr8O1i3Puby4A7/jgMAAMKOAGhhHrdLMZEuSQEYCNKtt7k8RAAEAKCrIwBaXPPdQPwdCJLUFAAPbvfvOAAAIOwIgBYXsPsB0wUMAIBlEAAt7vBI4AB1AdMCCABAl0cAtLjmFsBKP7uAfS2AlcVSXZV/xwIAAGFFALS45msA/W0BjO4meRLNdQaCAADQpREALS451mwBPOBvAJSkbr3MJdcBAgDQpREALS45ziNJ2l8RiADYx1zSAggAQJdGALS45DizBTAgAZCpYAAAsAQCoMUlx5otgCWVtf4fjKlgAACwBAKgxaU0tQAeqAxgFzAtgAAAdGkEQIvr3jQI5FBVveobvf4dLOmI28EZhp81AwAA4UIAtLikmEg5Heb6QX9bAZOaRgHXVUhV+/07FgAACBsCoMW5nI7mVsASfweCRERJ8ZnmOtcBAgDQZREAbcA3EGR/IAaCNI8Ezvf/WAAAICwIgDYQ0Klgup9gLg9s8/9YAAAgLAiANuCbDLqkIgAtgMl9zeX+rf4fCwAAhAUB0AZ8t4PbH4ipYHwB8AABEACArooAaAPNATAQLYDdaQEEAKCrIwDagK8LOCCTQfuuAaw+IFUd8P94AAAg5AiANuAbBOL3NDCS5Ik7PBUMA0EAAOiSCIA24LsdXECmgZHoBgYAoIsjANpA8zyAgWgBlKRk31QwBEAAALoiSwXAuXPnKicnR1FRURo+fLg+/PDDY+5fW1ure++9V71795bH41Hfvn01b968ENU2dHxdwFV1jaqqawjAAfuZy/3f+n8sAAAQcu5wVyBQFixYoBkzZmju3Lk6++yz9fTTT2v8+PHauHGjevXq1eZ7rrzySu3du1fPPvus+vXrp+LiYjU0BCAgdTJxHrc8bqdqG7wqKa9Tr2Q//9jpAgYAoEuzTACcPXu2pk2bphtvvFGS9OSTT+r999/XU089pVmzZrXa/7333tPy5cu1bds2de/eXZLUp0+fUFY5ZBwOh9ISPNp5oFrF5TXqlRzj3wGb5wLcJhmG5HD4X0kAABAylugCrqur05o1a5Sbm9tie25urlauXNnme95++22NGDFCjz32mHr06KH+/fvr7rvvVnV19VHLqa2tVVlZWYtHV5EWHyVJ2lsWgIEg3XIkOaTaMqmyxP/jAQCAkLJEC2BJSYkaGxuVnp7eYnt6erqKiorafM+2bdv00UcfKSoqSosWLVJJSYluueUWHThw4KjXAc6aNUsPPfRQwOsfCmnx5kCQ4vIa/w8WESUlZkulBeZAkLhU/48JAABCxhItgD6O73RFGobRapuP1+uVw+HQiy++qDPOOEMXX3yxZs+erfnz5x+1FfCee+5RaWlp82Pnzp0B/wzBkp5gtgAWlwdoKhjfSGAGggAA0OVYIgCmpKTI5XK1au0rLi5u1Srok5mZqR49eigxMbF528CBA2UYhnbt2tXmezwejxISElo8uopUXwtgILqApSMGghAAAQDoaiwRACMjIzV8+HDl5eW12J6Xl6dRo0a1+Z6zzz5be/bsUUVFRfO2zZs3y+l0qmfPnkGtbzgEtAtYklL6m8uSLYE5HgAACBlLBEBJmjlzpp555hnNmzdPmzZt0p133qmCggJNnz5dktl9O2XKlOb9r7nmGiUnJ+v666/Xxo0btWLFCv3iF7/QDTfcoOjo6HB9jKBJa+oC3heoLuDUpgC475vAHA8AAISMJQaBSNLkyZO1f/9+PfzwwyosLNSgQYO0ePFi9e7dW5JUWFiogoKC5v3j4uKUl5en22+/XSNGjFBycrKuvPJKPfLII+H6CEF1uAUwQAEw5SRzeWCb1FAnuSMDc1wAABB0DsMwjHBXoqsqKytTYmKiSktLO/31gAcq6zTs/5ld5JsfGa9It5+Nv4YhzcqW6sqlWz6R0gYGoJYAAARfV/r9DhbLdAHj2LrFRCjCZY6I3lcRgFZAh4NuYAAAuigCoE04HA6lxvlGAgdqIEhTN3DJ5sAcDwAAhAQB0EZSAz0XYGpTAKQFEACALoUAaCMBHwhCAAQAoEsiANpIeoIZAPcFrAu46RrA/Vskb2NgjgkAAIKOAGgjafFmF/DeQN0NpFsfyeWRGmqkQwXfuzsAAOgcCIA2kpFoBsDCQLUAOl1SyonmOt3AAAB0GQRAG8lKNO9wUnioOnAHbb4lHAEQAICuggBoI80tgKUBagGUjhgIwlQwAAB0FQRAG8lKMgNgRW2DymrqA3PQ5gC4KTDHAwAAQUcAtJGYSLcSoyMkSYWHAtQKmHaKuSzeJHm9gTkmAAAIKgKgzWQ2dQPvKQ3QdYDdT5DcUVJ9lXQwPzDHBAAAQUUAtJmsJN9AkAC1ALrch7uBizcG5pgAACCoCIA2k9k8ECSAI4HTB5nLvRsCd0wAABA0BECb8bUA7glUC6AkpZ1sLvd+FbhjAgCAoCEA2kxwWgCbBoLspQsYAICugABoM5lNk0EXBXIuQF8X8IFtUl1l4I4LAACCggBoM0eOAjYMIzAHjUuVYlMlGdK+rwNzTAAAEDQEQJvx3Q2kpt6rQ1UBmgxaOqIbmIEgAAB0dgRAm4mKcCk5NlJSAOcClBgJDABAF0IAtKHMplvCBWwuQOmIkcAEQAAAOjsCoA1lNQ0E2X0oGCOBv5ICdW0hAAAICgKgDWV3j5Ek7TxQFbiDpg6QnG6p+qBUuitwxwUAAAFHALSh7G5mC+DOgwEMgBFRUupAc73wi8AdFwAABBwB0IZ6JftaAAPYBSxJWUPMJQEQAIBOjQBoQ9ndDncBB2wuQEnKPM1cFq4L3DEBAEDAEQBtqGdTACyvbVBpdQDnAsykBRAAgK6AAGhD0ZEupcR5JAW4Gzh9kORwShV7pbLCwB0XAAAEFAHQpnp1D8JAkMgYKeUkc51WQAAAOi0CoE0FZSoYiW5gAAC6AAKgTfkGghQEOgBmnWYuGQgCAECnRQC0qezmLuAATwVDCyAAAJ0eAdCmfF3AuwLdApgx2FyW7ZYq9gX22AAAICAIgDbl6wLedbBaXm8A5wL0xEvJ/cx1uoEBAOiUCIA2lZkYJbfTobpGr/aW1wT24FlDzeWetYE9LgAACAgCoE25XU71bLon8PaSAHcD9xhhLnd9FtjjAgCAgCAA2lhOSqwkKb+kMrAH7nm6udy1WgrkreYAAEBAEABtLCclTpKUX1IR2ANnDJJckVL1AenAtsAeGwAA+I0AaGM5qUFqAXR7Dk8Hs3tNYI8NAAD8RgC0sROauoC3BToASkd0A3MdIAAAnQ0B0MZ81wAW7K9SQ6M3sAfvMdxcEgABAOh0CIA2lpEQpagIpxq8hnYF+o4gvhbAovVSfYCPDQAA/EIAtDGn06E+yUG6DjCplxSbKnkbpMIvA3tsAADgFwKgzZ2QGqTrAB2Ow62Au1cH9tgAAMAvBECbOzwXYICngpGknkwIDQBAZ0QAtLmgdQFLh1sAd/6XCaEBAOhECIA219wFvC8IAbDHCMnplsp2S4cKAn98AADQIQRAm+uXGi9JKiytUXlNfWAPHhkjZZ5mrhesCuyxAQBAhxEAbS4xJkJp8R5J0rfFQbgOsNdZ5nLHysAfGwAAdAgBEOqfbrYCbtkbhADYe5S5pAUQAIBOgwAI9UuLkyRt3lse+IP3GmkuSzZLlSWBPz4AADhuBEA0twBuDkYXcEx3KXWAuU4rIAAAnQIBEOqfbrYAbglGC6B0uBVwBwEQAIDOgAAInZgexJHA0hHXATIQBACAzoAACCVGRyg9wRwJvCUoI4GbWgALv5Rqg3B8AABwXAiAkHTkSOAgdAMnZUuJ2ZLRKO38JPDHBwAAx8VSAXDu3LnKyclRVFSUhg8frg8//LBd7/v444/ldrt12mmnBbeCndjhkcBBaqHLOddc5q8IzvEBAEC7WSYALliwQDNmzNC9996rtWvXavTo0Ro/frwKCo59C7LS0lJNmTJF559/fohq2jmd1NQC+E1RkAaC5Iwxl9uWB+f4AACg3SwTAGfPnq1p06bpxhtv1MCBA/Xkk08qOztbTz311DHfd/PNN+uaa67RyJEjQ1TTzunkrARJ0sbCMhmGEfgCfC2AhV9IVQcCf3wAANBulgiAdXV1WrNmjXJzc1tsz83N1cqVRx95+txzz2nr1q164IEH2lVObW2tysrKWjyson96vFxOhw5U1qmorCbwBSRkSiknSTKk7R8F/vgAAKDdLBEAS0pK1NjYqPT09Bbb09PTVVRU1OZ7tmzZol//+td68cUX5Xa721XOrFmzlJiY2PzIzs72u+6dRVSES/1SzesAN+4JUrA9oakbOJ9uYAAAwskSAdDH4XC0eG4YRqttktTY2KhrrrlGDz30kPr379/u499zzz0qLS1tfuzcudPvOncmzd3AwQqAXAcIAECn0L6mr04uJSVFLperVWtfcXFxq1ZBSSovL9fq1au1du1a3XbbbZIkr9crwzDkdru1ZMkSjRs3rtX7PB6PPB5PcD5EJ3BKVoIWrd2tDcEKgH3OkRxOaf8WqWyPlJAVnHIAAMAxWaIFMDIyUsOHD1deXl6L7Xl5eRo1alSr/RMSErR+/XqtW7eu+TF9+nSddNJJWrdunc4888xQVb1TOTnz8ECQoIhOkjJPM9dpBQQAIGws0QIoSTNnztS1116rESNGaOTIkfrb3/6mgoICTZ8+XZLZfbt792698MILcjqdGjRoUIv3p6WlKSoqqtV2O/F1ARccqFJZTb0SoiICX8gJY6Q9n5vXAZ52deCPDwAAvpdlAuDkyZO1f/9+PfzwwyosLNSgQYO0ePFi9e7dW5JUWFj4vXMC2l1STKR6JEVr96FqbdpTpjNPSA58ITljpI/+KG1bJhmG1MY1mgAAILgcRlAmfbOHsrIyJSYmqrS0VAkJCeGuTkDc+Pxq/XvTXj0w4WRdf3ZO4Auor5Eey5Hqq6TpH0kZgwNfBgAAx2DF3+/jZYlrABE4vm7gr3YH6TrAiKjDk0JvyTv2vgAAICgIgGjh1B6JkqQvdx0KXiEnXmguCYAAAIQFARAtDMlOkiR9u69C5TX1wSmkX1MA3PmpVH0oOGUAAICjIgCihdR4j3okRcswpPW7SoNTSLfe5m3hjEZp2wfBKQMAABwVARCtnNYrSZK0dueh4BXS3A387+CVAQAA2kQARCtDm7qBvwhFAPw2T/J6g1cOAABohQCIVnzXAa7beUhBmyWo10gpIlaq2CvtXR+cMgAAQJsIgGhlUFaiXE6HistrVVhaE5xC3B7zriCStHlJcMoAAABtIgCilehIlwZkxEsKcjdw/x+Yy2/eDV4ZAACgFQIg2nRkN3DQnDRekkPas1Yq3RW8cgAAQAsEQLRpWK9ukqTVOw4Gr5C4NKnXWeb614uDVw4AAGiBAIg2ndGnuyTzjiA19Y3BK2jAJeby63eCVwYAAGiBAIg2ZXePVnqCR/WNhtYWHApeQb4AuP1jqepA8MoBAADNCIBok8Ph0Bk5yZKkz7YHMZh1P0FKO8W8K8gWRgMDABAKBEAc1Rl9zOsA/5sf5JY5XyvgJrqBAQAIBQIgjur0HPM6wM8LDqqhMYh36xh4qbn89j9SXVXwygEAAJIIgDiG/mnxSoyOUFVdozbsKQteQRmnSom9pIZq89ZwAAAgqAiAOCqn06HTQ9EN7HBIg35orn/1RvDKAQAAkgiA+B5nNHUDr9q2P7gFDZpkLje/L9WWB7csAABsjgCIYxrVN0WS9Mm2/aoP5nWAGadK3ftKDTXSN+8FrxwAAEAAxLGdnJmg5NhIVdU1Bnc+QIfjcCsg3cAAAAQVARDH5HQ6NKqf2Qr40ZZ9wS3MFwC//bdUHcRb0AEAYHMEQHyv0U0B8MNvS4JbUNoAc1Job7206Z/BLQsAABsjAOJ7nX2iGQC/2HlIZTX1wS3MNxp4w8LglgMAgI0RAPG9eiRF64SUWHkNadXWII8GPuUKc7ltuVS+N7hlAQBgUwRAtMs5J/quAwxyN3ByX6nnGea9gde/GtyyAACwKQIg2uWcpusAl2/eJ8MwglvYadeYy3UvScEuCwAAGyIAol3O7peiSJdTBQeqtHVfRXALO+WHkjtKKt4oFa4LblkAANgQARDtEutx66y+yZKkf28qDm5h0UnSgEvN9XUvBbcsAABsiACIdrtgYJok6T+bQjA4w9cNvP41qaE2+OUBAGAjBEC027gBZgBcs+OgDlTWBbewE8ZK8VnmhNCbuTUcAACBRABEu/XsFqMBGfHyGtIHXwe5G9jpkoZMNtfXvhjcsgAAsBkCII7LBQPTJUn/+ToU3cA/Npff5kmlu4JfHgAANkEAxHE5v+k6wBWbS1Tb0BjcwlJOlPqMlgyv9PkLwS0LAAAbIQDiuAzpmaT0BI8qahv04eYgTwotSSOuN5drnpcag3wbOgAAbIIAiOPidDp08eBMSdK76wuDX+CACVJsqlRRJH3zr+CXBwCADRAAcdwuPdUMgHkb96qmPsjdwO5Iaei15vrqecEtCwAAmyAA4rgNze6mjIQosxs42PcGlqThUyU5pG0fSPu3Br88AAAsjgCI49aiG/jLPcEvsFtv6cQLzXVaAQEA8BsBEB1ySSi7gSVpxDRzufb/pNog34sYAACLIwCiQ4ZmJykrMUqVdY36T7DvDSxJJ+ZK3U+QakqlL14OfnkAAFgYARAd4nQ6NHFoD0nSG5+HYJJmp1M66xZz/ZO5ktcb/DIBALAoAiA6bNLwnpKk5Zv3qbi8JvgFDrlaikqUDmzj/sAAAPiBAIgO65sap6G9ktToNfTW2hAMBvHEScObJoZe9ZfglwcAgEURAOGX/2lqBXx9zS4ZhhH8As+4SXK6pR0fSXvWBb88AAAsiAAIv1x6apYi3U59s7dcG/aUBb/AxB7SKT8012kFBACgQwiA8EtidIRyT06XJL22emdoCh15q7n86g3p4PbQlAkAgIUQAOG3K0dkS5IWfr5blbUNwS8wa6jUd5xkNEof/2/wywMAwGIIgPDbOf1S1Cc5RuW1DXprXQgGg0jS6LvN5dp/SGUhKhMAAIsgAMJvTqdDPzmrtyTphVXbQzMYpM/ZUq+RUmOdtHJO8MsDAMBCCIAIiB8Nz1ZUhFNfF5Xr84KDoSn03KZWwNXzpMqS0JQJAIAFEAAREIkxEbpsSJYk6YVVO0JTaN/zpczTpIZq8+4gAACgXQiACJhrz+ojSVq8vlDFZSG4M4jDIZ37C3P9079JlfuDXyYAABZAAETADO6ZqOG9u6m+0dBzK7eHptCTLpYyBkt15dLHfwxNmQAAdHEEQATUTeeeIEn6xyc7VBGKKWGcTmnc/eb6f/8ulRUGv0wAALo4AiAC6sKB6TohJVblNQ165b8FoSn0xAul7LOkhhppxR9CUyYAAF2YpQLg3LlzlZOTo6ioKA0fPlwffvjhUfdduHChLrzwQqWmpiohIUEjR47U+++/H8LaWpPT6dBPm1oBn/0oX/WN3uAX6nBI5ze1An7+vHQgP/hlAgDQhVkmAC5YsEAzZszQvffeq7Vr12r06NEaP368CgraboVasWKFLrzwQi1evFhr1qzReeedpwkTJmjt2rUhrrn1/HBoD6XEeVRYWhO6iaH7nG2OCvY2SMt+H5oyAQDoohxGSGbtDb4zzzxTw4YN01NPPdW8beDAgZo4caJmzZrVrmOccsopmjx5su6///527V9WVqbExESVlpYqISGhQ/W2qrnLvtVj732jPskx+vfMMXK7QvB/jT1rpb+NleSQbl4hZZ4a/DIBAF0Ov98WaQGsq6vTmjVrlJub22J7bm6uVq5c2a5jeL1elZeXq3v37kfdp7a2VmVlZS0eaNuUkX3UPTZS2/dXadHa3aEpNGuoNGiSJEN6/zeSNf5vAwBAwFkiAJaUlKixsVHp6ekttqenp6uoqKhdx3jiiSdUWVmpK6+88qj7zJo1S4mJic2P7Oxsv+ptZXEet25uuhbwz0u/Dc21gJJ0wYOSO0ra/qH0zeLQlAkAQBdjiQDo43A4Wjw3DKPVtra8/PLLevDBB7VgwQKlpaUddb977rlHpaWlzY+dO3f6XWcru3Zkb6XERargQJUWfr4rNIUm9ZJG3mquL7lPaqgLTbkAAHQhlgiAKSkpcrlcrVr7iouLW7UKfteCBQs0bdo0vfrqq7rggguOua/H41FCQkKLB44uJtKt6WP6SpL+9J9vVdcQolbAc+6UYtOkA9ukz/4emjIBAOhCLBEAIyMjNXz4cOXl5bXYnpeXp1GjRh31fS+//LKmTp2ql156SZdcckmwq2lLPzmrt9LiPdp9qFovrNoemkI98dK4+8z15Y9yizgAAL7DEgFQkmbOnKlnnnlG8+bN06ZNm3TnnXeqoKBA06dPl2R2306ZMqV5/5dffllTpkzRE088obPOOktFRUUqKipSaWlpuD6CJUVFuHR37kmSpD/9Z4sOVoaoS3boT6T0wVJNqfTvB0JTJgAAXYRlAuDkyZP15JNP6uGHH9Zpp52mFStWaPHixerdu7ckqbCwsMWcgE8//bQaGhp06623KjMzs/nx85//PFwfwbImDe+pARnxKqtp0P/+Z0toCnW6pIub7gqy9v+kgk9DUy4AAF2AZeYBDAfmEWq/j7aU6CfPfiq306Eld56rE1LjQlPwm7dK6/4hpQ+SblouudyhKRcA0Gnx+22hFkB0buecmKJxA9LU4DX023c3ha7gCx+WortJe7+SPv1r6MoFAKATIwAiZH5z8UC5nQ795+tiLdnQvvkZ/RabLF3wkLm+bJZUGqJJqQEA6MQIgAiZfmlxuqlpcugH396gytqG0BQ89Fqp5xlSXYW0+G7uEAIAsD0CIELq9nEnqme3aO0prQnhgBCnNOFJyRlh3h1k/euhKRcAgE6KAIiQio506f9dPkiS9OxH+dq4J0T3U04/RRrzS3P9X7+QKopDUy4AAJ0QARAhd96ANI0flKFGr6G7X/sitHcIyRgsVR+U3p1JVzAAwLYIgAiLhy4/Rd1iIrSxsExzloaoK9gVIV0+V3K6pU3vSBsWhaZcAAA6GQIgwiItPkr/b6LZFfyXZVv15a5DoSk481Rp9F3m+uK7pfK9oSkXAIBOhACIsLn01CxdcmqmGr2G7nr1C9XUN4am4NF3m7eJq9ovvXWL5A1RFzQAAJ0EARBh9f8uH6SUuEhtKa4I3QTR7khp0jOSO0r69t9MEA0AsB0CIMKqe2ykHv/REEnS/32yQ4vXF4am4LQB0kW/Ndf//YBU+GVoygUAoBMgACLsxp6Upulj+kqSfvX6lyrYXxWagkdMk066WGqsk964UaoLUbkAAIQZARCdwl25/TW8dzeV1zbotpc/D831gA6HdNkcKS5DKvlGeu9XwS8TAIBOgACITiHC5dSfrh6qpJgIfbmrVPe9+ZWMUMzTF5ss/fCvkhzS5y9Ia/8R/DIBAAgzAiA6jR5J0frTVUPldEivr9mleR9vD03Bfc+TzvuNuf7uXVwPCACwPAIgOpVz+6fqNxcPlCT99t2N+nDLvtAUPPpu6cRcqaFGevVa824hAABYFAEQnc60c3I0aVhPeQ3ptpfW6tviiuAX6nRKP3xaSuolHdwuLfoZ8wMCACyLAIhOx+Fw6Lc/HKRhvZJUWl2v6+b9V3vLaoJfcEx36cr/k1weafO/pOW/D36ZAACEAQEQnVJUhEvPXHe6TkiJ1e5D1bpu3n9VVlMf/IKzTpMunW2uL39UWv968MsEACDECIDotLrHRur5G85QarxHXxeV66YXVqu2IQTTwwz9iTTyNnP9rVulXWuCXyYAACFEAESnlt09RvOvP11xHrc+2XZAt720VnUNIbg278KHpRMvMgeFvHK1VLo7+GUCABAiBEB0eqdkJepvU4bL43Yqb+Ne3fHyWtU3BjkEOl3m/YLTTpYq9kovXyXVlge3TAAAQoQAiC5hVN8U/W3KCEW6nXpvQ5FmvLJODcEOgVEJ0tWvSDEpUtGX0oJrpYa64JYJAEAIEADRZYzpn6qnfzJckS6n3l1fqJ+/si743cHdekvXvCpFxEjbPpDeuoXpYQAAXR4BEF3KeQPS9NRPhinC5dC76ws17fnPVFXXENxCew43p4dxuqX1r0l5/19wywMAIMgIgOhyzh+YrmevO13RES59uKVEP37mUx2qCnLX7IkXSJf/xVxfNUf6+H+DWx4AAEFEAESXdG7/VL340zOVGB2htQWHdOXTq7TnUHVwCx1ylXTh/zPX8+6XPns2uOUBABAkBEB0WcN6ddNr00cqPcGjzXsrdPlfPta6nYeCW+jZd0hnzzDX350pff5/wS0PAIAgIACiS+ufHq+Ft5ytARnx2ldeq8lPr9I/v9wT3EIveFA66xZz/e3bpS8WBLc8AAACjACILq9HUrRe/9kojRuQptoGr257aa3+999b5PUawSnQ4ZAu+p10+o2SDOnN6dJXbwSnLAAAgoAACEuI87j19ykjdOM5OZKkP/57s258YXXwBoc4HNL4P0jDrpMMr/TGT7lvMACgyyAAwjJcTofuu/RkPTbpVHncTi39uliX/OkjfRGs6wKdTunSJ6XTfiwZjdIbN0prng9OWQAABBABEJZz5enZWnjLKPVOjtHuQ9X60V9X6YVV22UYQegSdjqly+ZII6ZJMqR37pBW/SXw5QAAEEAEQFjSKVmJeuf2c3TRKemqa/Tq/rc26Ib5n6m4vCbwhTmd0iVPSGf/3Hz+/m+kZY9KwQicAAAEAAEQlpUQFaG//mS47r/0ZEW6nfrgm3266I8r9N5XhYEvzOGQLnhIOu8+8/my30nv/VryNga+LAAA/EQAhKU5HA7dcE6O/nn7OTo5M0EHq+o1/R+f665Xv1BpVX2gC5PG/EL6we/N55/+VXp1ilQf5AmqAQA4TgRA2EL/9Hi9eevZ+tnYvnI4pDc+36XzZy/XO1/sCfy1gWf9TPqfeZIrUvr6n9Lzl0mV+wNbBgAAfiAAwjYi3U796gcD9NrNI9U3NVYlFbW6/eW1un7+Z9p5oCqwhQ2aJF37phSVKO36r/TshdKBbYEtAwCADiIAwnZG9OmuxT8frRkXnKhIl1PLvtmn3D+u0Nxl36qmPoDX7PU5W5qWJyX2kg5slf5+vpS/InDHBwCggxxGUObGsIeysjIlJiaqtLRUCQkJ4a4OOuDb4gr9ZtF6/Tf/gCQpu3u07r14oC46JUMOhyMwhZQXSS9fJe1ZKzlc0vhHzbuIBOr4AIDjwu83AdAvnEDW4PUaenPdbj363tfaW1YrSTrrhO66/9JTdHJWgP5c66vN+wavf818Puw66eLHJXdkYI4PAGg3fr8JgH7hBLKWytoG/XX5Vv1txTbVNnjlcEgTT+uhGRecqN7Jsf4XYBjSyj9JeQ9IMqTss6QrX5Di0/0/NgCg3fj9JgD6hRPImnYdrNKsf32td7805wt0Ox268vRs3T6unzITo/0vYEue9Po0qbZUikuXJj0j5Zzr/3EBAO3C7zcB0C+cQNa2flepHl/yjZZv3ifJHEX8kzN766ZzT1BGYpR/By/5Vnr1Wql4o+RwSmPvkUbfbd5VBAAQVPx+EwD9wglkD//NP6DH3/9G/91uDhSJcDl0xdCeunnMCTohNa7jB66rkhb/Qlr3D/P5CedJV/xdiksNQK0BAEfD7zcB0C+cQPZhGIY+3FKiOR982zxi2OGQxg/K0C1j+2lQj8SOH3zdS9I/Z0oN1VJ8pvTDv0onjA1MxQEArfD7TQD0CyeQPa3ZcUBzP9iq/3xd3LztjJzuun5UH114crrcrg504+7dKL12nVSy2Xx+1i3S+fdLEQG45hAA0AK/3wRAv3AC2dvXRWV6atlW/fPLQjV6zb9GWYlR+snI3rrq9F7qHnucU7zUVUpL7pNWzzOfpw4wu4QzTw1wzQHA3vj9JgD6hRMIklRYWq0XPynQy/8t0P7KOknmgJEJp2Zp8unZOr1Pt+ObVHrz+9Jbt0mVxZIzQhp3rzTqDsnpCtInAAB74febAOgXTiAcqaa+Uf/8slDPr9yu9btLm7efkBKrH43I1qThPZQW387Rw5Ul0tt3SN+8az7vMUK67M9S+slBqDkA2Au/3wRAv3ACoS2GYWjtzkNa8N+deufLPaqqM+8v7HI6dN5Jafqf4T019qRURUV8T4ueYUhr/yG9/xuptsxsDRw9Uxp9l+T2hOCTAIA18ftNAPQLJxC+T2Vtg979slALVu/Umh0Hm7fHe9y6aFCGLhuSpVF9k489cKRsj/TuXdI3i83nKSdJl8+Rss8Icu0BwJr4/SYA+oUTCMfj2+IKvbZmp95Zt0d7Smuat6fEReriwZm6bEiWhvXqJqezjesFDUPa+KY5b2DlPkkO6fRp0rj7pOhuIfsMAGAF/H4TAP3CCYSO8HoNrd5xUG9/sVuL1xfpQNPAEUlKifPowpPTddEp6RrZN1ke93e6iasOmCOF171oPo9Jli54UDrtJ9xFBADaid9vAqBfOIHgr/pGrz7+tkRvr9ujvI17VV7b0PxanMetsSelKveUDJ13UqrioyIOvzF/hdkauO9r83mP4dLFj0s9hoX4EwBA18PvNwHQL5xACKS6Bq8+2bZfSzYWacmGvSour21+ze10aHjvbhpzUqrG9E/VyZkJcngbpE+flpb9Xqorl+SQhl8nnXevFJcWvg8CAJ0cv98WC4Bz587VH/7wBxUWFuqUU07Rk08+qdGjRx91/+XLl2vmzJnasGGDsrKy9Mtf/lLTp09vd3mcQAgWr9fQF7sO6f0Ne7VkQ5G2lVS2eD013qMx/c0weG5mgxI/ekT6coH5YmScdPYMaeStUmRM6CsPAJ0cv98WCoALFizQtddeq7lz5+rss8/W008/rWeeeUYbN25Ur169Wu2fn5+vQYMG6ac//aluvvlmffzxx7rlllv08ssva9KkSe0qkxMIobJjf6WWb96n5d/s08qt+1Vd39j8mtMhnZKVqCvTduryvX9RwoH15gvxmeYgkSFXM4k0AByB328LBcAzzzxTw4YN01NPPdW8beDAgZo4caJmzZrVav9f/epXevvtt7Vp06bmbdOnT9cXX3yhVatWtatMTiCEQ21Do1ZvP9gcCL/ZW978mkNeTXB9ons9ryndu1eS1Jh6sly5D0v9LpCO544kAGBR/H5L7nBXIBDq6uq0Zs0a/frXv26xPTc3VytXrmzzPatWrVJubm6LbRdddJGeffZZ1dfXKyIios33AeHmcbt0dr8Und0vRb+5eKD2ltXok237tWrrfq3atl9v7x+l96pO1xTXEt3uXqTEfRulF/9HO2MHaedpd6r3iIuVlRR9fLenAwBYiiUCYElJiRobG5Went5ie3p6uoqKitp8T1FRUZv7NzQ0qKSkRJmZma3eU1tbq9rawxfml5WVBaD2gH/SE6J0+Wk9dPlpPSRJew5VNwXCHF219SL9sGKBpriWKLvyK2V/PE2ffjhAj0T+WM6cczS0V5KG9+6mU7ISFelmGhkAsAtLBECf77ZoGIZxzFaOtvZva7vPrFmz9NBDD7Xa/tprrykmhovt0bkMkzSst1RTf7H+VjFG7tJ8JdYWyuk0dG7Dah3Y/I02fZOpVYqT0+FQnMethCi3EqIjFB8VoTiPi1ZCAJZUVVUV7iqEnSUCYEpKilwuV6vWvuLi4latfD4ZGRlt7u92u5WcnNzme+655x7NnDmz+XlZWZmys7P1ox/9yLbXEKCLKd2t+uWPy7Xu/+T01ksOaY0G6s91E7SodohUdjjwRbqdOjkzQYN7JGpwz0QN7pGofmlxijjWbesAoAsoKyvTjTfeGO5qhJUlAmBkZKSGDx+uvLw8/fCHP2zenpeXp8svv7zN94wcOVLvvPNOi21LlizRiBEjjnr9n8fjkcfjCVzFgVBL7KGIy/4onXuntOJxad1LGu7dpPmRm1SWeJI+SPmxXqseoS/2VKi8pkHrdh7Sup2Hmt8e4XKoX1q8BmQ0PTITNDAjXqnxHloLAaALscwoYN80MH/96181cuRI/e1vf9Pf//53bdiwQb1799Y999yj3bt364UXXpB0eBqYm2++WT/96U+1atUqTZ8+nWlgYC9le6RVf5FWPyfVN8012K2PvCPvUEGvy/Xl3jqt33VI63eX6qvdZao44k4lR+oWE6EBGQkakBmvgRkJOjE9Tn3T4pQQxWAqAJ0Pv98WCoCSORH0Y489psLCQg0aNEh//OMfde6550qSpk6dqu3bt2vZsmXN+y9fvlx33nln80TQv/rVr5gIGvZUdUD67Bnpk6ek6gPmtuhu0vCp0uk3Sok9ZRiGdh2s1tdF5fqmqEybisr1dWGZ8ksq5T3KvyJp8R71S4tT39Q49UuLa15PT6DFEED48PttsQAYapxAsJy6SmntP6RVc6RDBeY2h0s6+TLpzOlS9pmt5hKsqW/Ulr0V+rqoTF8XlevrojJt2VvR4lZ23xXncatvaqz6NgXC3skx6pMcq97JMS3veQwAQcDvNwHQL5xAsCxvo/TNv6RP/ypt//Dw9szTzCB4yg+liKhjHqKspl5biyu0dV+lvi2u0NZ9FdpaXKEdB6rUeLQmQ0nJsZHqnRyj3k2BsM8Ry6SYCFoOAfiN328CoF84gWALRevNIPjla1JjU6teVJJ02jXSsOuktAHHdbi6Bq927K/U1n0V+ra4QttKKlWwv0rb91eppOLorYaSFB/lVu/kGGV3i1GPpGj17BatHt1impbRXHMIoF34/SYA+oUTCLZSWSKteU5aPV8q23V4e6+R5rWCJ18uRUT7VURFbYN27K/Ujv1VTY9KbW96Xlha873vT4hyq8cR4dD36JEUo6ykKHWPjaQFEQC/3yIA+oUTCLbkbZS+/Y+0Zr60+T3JaDS3RyVKQ642WwYzTg34fYdr6hu184DZUrj7YJV2H6rWroPmY/ehah2orPveY0S6nEpP9CgzIVrpiVHKTIxSeoK5zEiMUkZClNLiPXIz1yFgafx+EwD9wgkE2ysrNAeNfP6CVFpweHvaydKQq6TBP5ISskJSlaq6Bu1uCoS7DlVr18Gqw88PVn9v97KP0yGlxHlahsKEKKXGe8xHnEdp8R51j40kKAJdFL/fBEC/cAIBTbyN0tYPpHX/kL5efPhaQTmkE8aaLYMDL5UiY8NWxboGr4rLa1RUWqOiMnNZeMR6UWmN9pbVqOEYA1SO5HCYA1ZS4jyHw2FTQPStp8V7lBoXpYRoN13PQCfC7zcB0C+cQEAbqg9JG9+UvnhFKlh1eHtErBkCT/mh1Hec5O58d9Xxeg3tr6w7IiRWq7C0RvvKa7WvotZclteqpKL2qHMftiXS5VS32Ah1j/UoOTZS3ZseybGR6ta07B4bqeS4SHWP9SgpOkJOJ4ERCBZ+vwmAfuEEAr7HgW3Sl69KX7wsHdx+eLsnURpwiTToCilnjOSODFsVO6LRa+hAZV2rYHj4eU3z87Katu+ecixOh9QtxgyH3Y8MiLGRSoqJVFJMhJJiIpQY3bQeHaHE6Ai6pIF24vebAOgXTiCgnQxD2vmptGGRtOFNqaLo8GtRSU0tg1dIOedKLmtN5VJT36iSilodqKzT/so6Haio08Gqw+v7K+t0oLJWB6vqtb+iY4HRJ97jVmJTOEyKjjTXo9t6fjg4JkRHKCrCFcBPDHR+/H4TAP3CCQR0gNcr7fxE+mqhtPEtqbL48GtRidKJF0kDLpb6XSB54sNXzzCpb/TqoC8sHvHwBcVDVfUqra7Xoap6Haqu06GqepX7ERolKdLtVEKUWwlREYqPcishumkZ1XIZHxXR+rXoCMV73HRZo0vh95sA6BdOIMBP3kZpx0qzZXDjW1JVyeHXXJFm9/CAi6WTLpbiM8JXz06uodGrspoGHaqq06HqepUeEQ4PB0bztSOfl1bXH9e1jMcS73G3Co9xUW7FetyKa3qY6y7FNq3Hew6/bm5zyeOmNRLBx+83AdAvnEBAAHkbpZ3/lb551xxJfGBry9d7DDeD4Im5UsbggM8zaEder6Hy2gaV15itiGXVTcum5+U19SrzLavN7Uc+L6+pV22DN6B1inQ5FdsUEuM83w2QrjYCpVsxkS7FRLoVHelSrMelmAhzPSbSpegIF62TaIXfbwKgXziBgCAxDKlks/T1u+Zj9+qWr8elm13E/c6XTjhPiukennpCtQ2NbYZH3/OK2gZV1jaosq5BFbWNqqw1t1XUmNt8z2vqAxskjxQd0RQGfaEw0q3YI9ZjIlyK8bgOB8mm/WM8Ta81vTfW425xrCg34bKr4vebAOgXTiAgRMqLpG/+JW1+X8pfIdVXHn7N4ZR6jJBOvNAMhJlDJSejYbuahkavKmsbVXFEKKxsCoqHQ2Rj6+11DaqsbVR1XaOq6htUXddoPq9vDEm9I91ORUe4FBXhW7rkiXApOsKpqAhX87ao7+zjW/ccsY/vOG3v75KLsBkw/H4TAP3CCQSEQUOtOb/gljzzlnT7NrV8PSbZHE2cc655DWH3E+gutiGv11BNQ6Oq6hpVVWuGw6q6pqBY16iquoamZaOqj1j3bW9zv3rzeTBbK48l0uVsDojRkS553E553E3LiCPWfdsjnIp0tfFaxOH3Rjbvf+T2luuRbvM4VprMnN9vAqBfOIGATuDQTmnrf8xAuG25VFfe8vWEnkcEwnOlxB7hqScso9FrqKa+UTX1Ziisqfc2P6+p9zZtM1+r/c4+392/+oj3ffeY1fWNqgvwNZb+aDMotgiarubA6HE1BUe3UxGuwyEy8juhMvKI9YjvvM+3PTnWo8SYwE4Pxe83AdAvnEBAJ9NYL+36TMr/UMpfbg4q8da33Kd7X+mEMVKfc6Reo6SEzPDUFWgHX0tmywBpPmrrvapt8Kq2odFc1h+x3nDEa9/Zr873Wn3jUffz7dMZ3DGun2bmnhTQY/L7LbnDXQEACBhXhNR7lPkY+yuprsqcczB/hdk6WLjOHF18YKu0ep75nm59pF4jDz9STqTLGJ2G0+lQTKRbMWG4WY5hGKpr9LYOl/Vec/tRAmRdQ6PqGs2gWdfgVe0R6/W+9cbDQfTI5771+qZlbYNXMR6iSjDQAugH/gcBdDHVh8x5B/OXm8u9X0nGd1o5YpJbBsLMUy13dxLA7vj9JgD6hRMI6OJqSs0u4x2rpIJPzOlmGmpa7hMRI2WeJvUcbo427jlCSuhBKyHQhfH7TQD0CycQYDENtVLhF+Yo4x2rzGXNodb7xWWYQbDHcHOZNdSWt60Duip+vwmAfuEEAizO65X2b5F2rTZbB3etlvZukIzvzDHncEqpA8xAmDXUbDFMP1mKiA5LtQEcG7/fBEC/cAIBNlRXZbYS+gLh7jVS6c7W+zlcZijMHHL4kTGIlkKgE+D3mwDoF04gAJLMO5XsXmM+Cr+Q9qyTqkra2NEhJfc7IhSeKqUPkmJTQl1jwNb4/SYA+oUTCECbDEMqLzTD4JGPst1t7x+bJqWfYj7STjaXqSfRhQwECb/fBEC/cAIBOC4V+6SiI0Phl9LB7ZLa+GfY4TQnrf5uMEzqzb2OAT/x+00A9EtpaamSkpK0c+dO255AAPxUWyGVbJaKv5ZKvpaKN5nrNQfb3t8dLSX3lZJPlFL6NS1PNCe0Zr5CoF3KysqUnZ2tQ4cOKTExMdzVCQum1/ZDebl5z9Hs7Oww1wSAfZRLKpa0KtwVAbq88vJy2wZAWgD94PV6tWfPHsXHx8sRoElhff8roVXx+/FdHR++r/bjuzo+fF/tx3fVfsH8rgzDUHl5ubKysuS06SUVtAD6wel0qmfPnkE5dkJCAv84tBPf1fHh+2o/vqvjw/fVfnxX7Res78quLX8+9oy9AAAANkYABAAAsBkCYCfj8Xj0wAMPyOPxhLsqnR7f1fHh+2o/vqvjw/fVfnxX7cd3FVwMAgEAALAZWgABAABshgAIAABgMwRAAAAAmyEAAgAA2AwBsBOZO3eucnJyFBUVpeHDh+vDDz8Md5U6pQcffFAOh6PFIyMjI9zV6jRWrFihCRMmKCsrSw6HQ2+++WaL1w3D0IMPPqisrCxFR0dr7Nix2rBhQ3gqG2bf911NnTq11bl21llnhaeyYTZr1iydfvrpio+PV1pamiZOnKhvvvmmxT6cW6b2fFecW4c99dRTOvXUU5snfB45cqT+9a9/Nb/OeRUcBMBOYsGCBZoxY4buvfderV27VqNHj9b48eNVUFAQ7qp1SqeccooKCwubH+vXrw93lTqNyspKDRkyRHPmzGnz9ccee0yzZ8/WnDlz9NlnnykjI0MXXnhh872t7eT7vitJ+sEPftDiXFu8eHEIa9h5LF++XLfeeqs++eQT5eXlqaGhQbm5uaqsrGzeh3PL1J7vSuLc8unZs6d+//vfa/Xq1Vq9erXGjRunyy+/vDnkcV4FiYFO4YwzzjCmT5/eYtuAAQOMX//612GqUef1wAMPGEOGDAl3NboEScaiRYuan3u9XiMjI8P4/e9/37ytpqbGSExMNP7617+GoYadx3e/K8MwjOuuu864/PLLw1Kfzq64uNiQZCxfvtwwDM6tY/nud2UYnFvfp1u3bsYzzzzDeRVEtAB2AnV1dVqzZo1yc3NbbM/NzdXKlSvDVKvObcuWLcrKylJOTo6uuuoqbdu2LdxV6hLy8/NVVFTU4lzzeDwaM2YM59pRLFu2TGlpaerfv79++tOfqri4ONxV6hRKS0slSd27d5fEuXUs3/2ufDi3WmtsbNQrr7yiyspKjRw5kvMqiAiAnUBJSYkaGxuVnp7eYnt6erqKiorCVKvO68wzz9QLL7yg999/X3//+99VVFSkUaNGaf/+/eGuWqfnO58419pn/PjxevHFF7V06VI98cQT+uyzzzRu3DjV1taGu2phZRiGZs6cqXPOOUeDBg2SxLl1NG19VxLn1netX79ecXFx8ng8mj59uhYtWqSTTz6Z8yqI3OGuAA5zOBwtnhuG0WobzH84fQYPHqyRI0eqb9++ev755zVz5sww1qzr4Fxrn8mTJzevDxo0SCNGjFDv3r317rvv6oorrghjzcLrtttu05dffqmPPvqo1WucWy0d7bvi3GrppJNO0rp163To0CG98cYbuu6667R8+fLm1zmvAo8WwE4gJSVFLper1f9miouLW/2vB63FxsZq8ODB2rJlS7ir0un5RktzrnVMZmamevfubetz7fbbb9fbb7+tDz74QD179mzezrnV2tG+q7bY/dyKjIxUv379NGLECM2aNUtDhgzR//7v/3JeBREBsBOIjIzU8OHDlZeX12J7Xl6eRo0aFaZadR21tbXatGmTMjMzw12VTi8nJ0cZGRktzrW6ujotX76cc60d9u/fr507d9ryXDMMQ7fddpsWLlyopUuXKicnp8XrnFuHfd931RY7n1ttMQxDtbW1nFfBFLbhJ2jhlVdeMSIiIoxnn33W2LhxozFjxgwjNjbW2L59e7ir1uncddddxrJly4xt27YZn3zyiXHppZca8fHxfFdNysvLjbVr1xpr1641JBmzZ8821q5da+zYscMwDMP4/e9/byQmJhoLFy401q9fb1x99dVGZmamUVZWFuaah96xvqvy8nLjrrvuMlauXGnk5+cbH3zwgTFy5EijR48etvyufvaznxmJiYnGsmXLjMLCwuZHVVVV8z6cW6bv+644t1q65557jBUrVhj5+fnGl19+afzmN78xnE6nsWTJEsMwOK+ChQDYifzlL38xevfubURGRhrDhg1rMWUADps8ebKRmZlpREREGFlZWcYVV1xhbNiwIdzV6jQ++OADQ1Krx3XXXWcYhjldxwMPPGBkZGQYHo/HOPfcc43169eHt9JhcqzvqqqqysjNzTVSU1ONiIgIo1evXsZ1111nFBQUhLvaYdHW9yTJeO6555r34dwyfd93xbnV0g033ND825eammqcf/75zeHPMDivgsVhGIYRuvZGAAAAhBvXAAIAANgMARAAAMBmCIAAAAA2QwAEAACwGQIgAACAzRAAAQAAbIYACAAAYDMEQAAAAJshAAIAANgMARAAAMBmCIAAAAA2QwAEAACwGQIgAACAzRAAAQAAbIYACAAAYDMEQAAAAJshAAIAANgMARAAAMBmCIAAAAA2QwAEAACwGQIgAACAzRAAAQAAbIYACAAAYDMEQAAAAJshAAIAANgMARAAAMBmCIAAAAA2QwAEAACwGQIgAACAzRAAAQAAbIYACAAAYDP/P4AkWrGfMJJKAAAAAElFTkSuQmCC' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = 26\n",
    "E_0 = 10 # keV\n",
    "\n",
    "K = -4000\n",
    "I = 1\n",
    "\n",
    "E = energy_scale = np.linspace(.1,30,2048) #in keV\n",
    "N_E = I*K*Z*(E-E_0)/E\n",
    "\n",
    "Z2 = 58\n",
    "E_02 = 10 # keV\n",
    "N_E2 = I*K*Z2*(E-E_02)/E\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(energy_scale, N_E, label= f'{E_0} keV');\n",
    "plt.plot(energy_scale, N_E2, label= f'{E_02} keV');\n",
    "plt.axhline(y=0., color='gray', linestyle='-', linewidth = 0.5)\n",
    "plt.ylim( -1e5, 1e6)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please change the atomic number *Z* and the acceleration voltage *E_0* in the code cell \n",
    "above to see the influence of these values on the Bremsstrahlung."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bremsstrahlung and EDS Background\n",
    "\n",
    "At low energies,  this background above does not look anything like the background we obtain in the EDS spectrum.\n",
    "\n",
    "This is due to the  response of the EDS detector system\n",
    "\n",
    "![X-Ray_Auger](./images/DetectorEfficiency.png).\n",
    "\n",
    "The effect of the detector system will be discussed in the [Detector Efficiency notebook](CH4_15-Detector.ipynb). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Navigation\n",
    "- <font size = \"3\">  **Back: [Introduction to X-Ray](CH4_12-Introduction_X_Rays.ipynb)** </font>\n",
    "- <font size = \"3\">  **Next: [Characteristic X-Rays](CH4_14-Characteristic_X_Rays.ipynb)** </font>\n",
    "- <font size = \"3\">  **Chapter 4: [Spectroscopy](CH4_00-Spectroscopy.ipynb)** </font>\n",
    "- <font size = \"3\">  **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "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": "3.11.7"
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 },
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}