{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "\n",
    "\n",
    "<font size = \"5\"> **Chapter 4: [Spectroscopy](CH4_00-Spectroscopy.ipynb)** </font>\n",
    "\n",
    "<hr style=\"height:1px;border-top:4px solid #FF8200\" />\n",
    "\n",
    "\n",
    "\n",
    "# Analysing Low-Loss Spectra with Drude Theory\n",
    "\n",
    "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM/main/Spectroscopy/CH4_03-Drude.ipynb)\n",
    " \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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Content\n",
    "The main feature in a low-loss EELS spectrum is the ``volume plasmon`` peak.\n",
    "\n",
    "This ``volume plasmon`` and all other features in the ``low-loss`` region of an EELS spectrum are described by Dielectric Theory of Electrodynamics.\n",
    "\n",
    "The simplest theory to interprete this energy range is the Drude theory. \n",
    "\n",
    "Another easy to observe component is the multiple scattering of this plasmon peak, which we can correct for or use for thickness determination.\n",
    "\n",
    "## Load important packages\n",
    "\n",
    "### Check Installed Packages\n"
   ]
  },
  {
   "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": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Import all relevant libraries\n",
    "\n",
    "Please note that the EELS_tools package from pyTEMlib is essential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyTEM version:  0.2024.02.2\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "%matplotlib ipympl\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",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# additional package \n",
    "import ipywidgets as ipyw\n",
    "from scipy.optimize import leastsq  ## fitting routine of scipy\n",
    "\n",
    "# Import libraries from the book\n",
    "import pyTEMlib\n",
    "import pyTEMlib.file_tools as ft          # File input/ output library\n",
    "from pyTEMlib import file_tools           # File input/ output library\n",
    "import pyTEMlib.kinematic_scattering as ks         # Kinematic sCattering Library\n",
    "                             # Atomic form factors from Kirklands book\n",
    "\n",
    "# For archiving reasons it is a good idea to print the version numbers out at this point\n",
    "print('pyTEM version: ',pyTEMlib.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dielectric Theory\n",
    "\n",
    "### Comparison to Optical Spectroscopy\n",
    "\n",
    "The interaction of a transmitted electron with a solid is here described in terms of\n",
    "a dielectric response function $\\varepsilon(q, \\omega))$. \n",
    "\n",
    "The same response function $\\varepsilon(q, \\omega))$ describes\n",
    "the interaction of any electro-magnetic wave (such as photons)  with a solid, so this formalism allows energy-loss data to be compared with the results of optical measurements.\n",
    "\n",
    "The difference is that there is no momentum transfer in an optical transition and, therefore, the relevant dielectric function is $\\varepsilon(q=0, \\omega))$.\n",
    "\n",
    "\n",
    "The optical dielectric function (permittivity) is a transverse property of the medium, in the sense that the electric field of an electromagnetic wave displaces electrons in a direction perpendicular to the direction of propagation, the electron density remaining\n",
    "unchanged. \n",
    "\n",
    "The relation between the ac conductivity $\\sigma$ (for dc conductivity the in metals $\\varepsilon$ can go to $\\inf$ and is therefore not well described) and $\\varepsilon$ is :\n",
    "$$ \\varepsilon = 1 + \\frac{4\\pi \\ i \\sigma}{\\omega} $$\n",
    "\n",
    "The relation between the complex refractive index $n+i\\kappa$ and dielectric function is:\n",
    "$$ n^2-\\kappa^2 ={\\bf Re}(\\varepsilon), \\ \\ 2n\\kappa = {\\bf Im}(\\varepsilon) $$\n",
    "\n",
    "Optical absorption spectrum is obtained through\n",
    "ABS= ${\\bf Im}( \\varepsilon(q→0,\\omega) )$\n",
    "\n",
    ">\n",
    ">So, the dielectric function describes the electrical and optical response of a material almost completely. \n",
    ">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dispersion \n",
    "From the Fourier representation of the Maxwell equations in the source free case, we get:\n",
    "$$\\frac{\\epsilon_i \\mu_i}{c^2} = k^2$$\n",
    "\n",
    "which we transform into:\n",
    "\n",
    "$$k = \\frac{\\omega}{c} \\sqrt{\\varepsilon_1 \\mu}$$\n",
    "\n",
    "which gives for non-magnetic materials:\n",
    "\n",
    "$$k = \\frac{\\omega}{c} \\sqrt{\\varepsilon_1 }$$\n",
    "\n",
    "for $\\varepsilon_1 > 0$ the wavenumber $k$ is a real function of real $\\omega$.\n",
    "\n",
    "while for $\\varepsilon_1 < 0$ the wavenumber $k$ is purely imaginary.\n",
    "\n",
    "\n",
    "for light  in vacuum the permittivity $\\varepsilon_1$ is a constant with value 1 and we get the equation for light line:\n",
    "\n",
    "$$k = \\frac{\\omega}{c}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Section\n",
    "\n",
    "$$ \\frac{d^2\\sigma}{dE d\\Omega} = \\frac{1}{\\pi a_0 m_0 v^2 n_a} \n",
    "        {\\rm Im} \\left[ \\frac{-1}{\\varepsilon(q,E)} \\right]\n",
    "         \\left( \\frac{1}{\\theta^2+\\theta_E^2}\\right)$$\n",
    "         \n",
    "The partial cross section  $\\frac{d^2\\sigma}{dE d\\Omega}$ gives us the probability that an incident electron will be scattered into angle $q$ with energy-loss $E$.\n",
    "\n",
    "There are three compenents, first a term that depends on the  ``atom density`` $n_a$ (atoms per volume).\n",
    "\n",
    "And the third term is the (Lorentzian) ``angle dependence`` with the characteristic angle $$\\theta_E = E_E/(\\gamma m_0v^2)$$\n",
    "\n",
    "The second term is the ``loss-function``.\n",
    "\n",
    "The loss function of a dielectric function $\\varepsilon = \\varepsilon_1+ i*\\varepsilon_2$ is\n",
    "$$ {\\rm Im} \\left[ \\frac{-1}{\\varepsilon(q,E)} \\right] = \\frac{\\varepsilon_1(q,E)}{\\varepsilon_1^2(q,E) + \\varepsilon_2^2(q,E)}$$\n",
    "At large energy loss and $q\\approx 0$, $\\varepsilon_2$ is small\n",
    "and $\\varepsilon_1$ close to 1, the loss function becomes proportional to\n",
    "$\\varepsilon_2$ and (apart from a factor of E$^{−3}$) the energy-loss spectrum is proportional to the X-ray absorption spectrum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Load and plot a spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ---- Input ------\n",
    "load_example = True\n",
    "# -----------------\n",
    "if not load_example:\n",
    "    if 'google.colab' in sys.modules:\n",
    "        drive.mount(\"/content/drive\")\n",
    "\n",
    "    fileWidget = file_tools.FileWidget()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
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      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4bb3f79ddc134f2f9744455de40f471b",
       "version_major": 2,
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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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' 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": [
    "# ---- Input ------\n",
    "load_example = True\n",
    "file_name = 'AL-DFoffset0.00.dm3'\n",
    "# -----------------\n",
    "if load_example:\n",
    "    if 'google.colab' in sys.modules:\n",
    "      if not os.path.exists('./'+file_name):\n",
    "        !wget  https://github.com/gduscher/MSE672-Introduction-to-TEM/raw/main/example_data/AL-DFoffset0.00.dm3\n",
    "    else:\n",
    "        datasets = file_tools.open_file('../example_data/'+file_name)\n",
    "        eels_dataset = datasets['Channel_000']\n",
    "      \n",
    "else:\n",
    "    datasets = fileWidget.datasets\n",
    "    eels_dataset = fileWidget.selected_dataset\n",
    "    \n",
    "sum_spectrum = eels_dataset.sum()\n",
    "\n",
    "eels_dataset = eels_dataset/sum_spectrum*100.\n",
    "eels_dataset.units = '%'\n",
    "eels_dataset.quantity = 'scattering probability'\n",
    "\n",
    "view = eels_dataset.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hideOutput": false,
    "hidePrompt": false
   },
   "source": [
    "### Fix energy scale and resolution function\n",
    "please see [Fitting the Zero-Loss Peak](./CH4_02-Fit_Zero_Loss.ipynb) for details\n",
    "\n",
    "### Relative Thickness Determination\n",
    "\n",
    "The probabaility of an low-loss function in a solid angle is then:\n",
    "$$\\frac{\\partial^2 P}{(\\partial E \\partial \\Omega) }= t*  \\frac{e}{\\pi^2 a_0 m_0 v^2} {\\rm Im} \\left[ \\frac{-1}{\\varepsilon(q,E)} \\right]\n",
    "         \\left( \\frac{1}{\\theta^2+\\theta_E^2}\\right)$$\n",
    "         \n",
    "Please see **Kroeger Formalism** for inclusion of retardation effects, and surface plasmons.\n",
    "\n",
    "The integration over the (effective) collection angle gives:\n",
    "$$\\frac{\\partial P}{\\partial E} = \\int_0^{\\theta_c}\\frac{\\partial^2 P}{(\\partial E \\partial \\Omega) }(E,\\theta)\\sin \\theta\\ d \\theta$$\n",
    "\n",
    "So we need to get the loss-function, calculate $\\frac{\\partial^2 P}{(\\partial E \\partial \\Omega) }$ and then integrate over the angles, then we fit this to the spectrum with the sole variable of the thickness $t$.\n",
    "\n",
    "The specimen thickness $t$, it is actually the total scattering\n",
    "and mass thickness that is measured by EELS. If the physical density of a\n",
    "material were reduced by a factor $f$, the scattering per atom would remain the same\n",
    "(according to an atomic model) and the mean free path should increase by a factor $f$.\n",
    "\n",
    "The big problem hoewver, is that one has to know the **dielectric function**. \n",
    "In the case of the Drude theory, that means we need to know the electron density.\n",
    "\n",
    "Any approximation, therefore, needs to approximate this dielectric function, which cannot be generally applicable.\n",
    "\n",
    "\n",
    "The relative thickness $ t_{rel} = t/\\lambda$, in contrast, is relatively easy to determine. All the above problems are hidden in value of the inelastic mean free path (IMFP) $\\lambda$, which is the inverse of the cross section above.\n",
    "\n",
    "**When you use a tabulated value for the IMFP, be aware that this value depends on:**\n",
    "* acceleration voltage\n",
    "* effective collection angle\n",
    "* material density\n",
    " \n",
    ">**and may not be applicable for your experimental setup.**\n",
    "\n",
    "\n",
    "\n",
    "The measurement of the relative thickness $t_{rel}$ is relative easy:\n",
    "\n",
    "We already did this in the  [Fit Zero-Loss](./CH4_02-Fit_Zero_Loss.ipynb) part.\n",
    "\n",
    "The inelastic scattering can be viewed in terms of independent collisions, whose occurrences obey Poisson statistics. The probability that a transmitted electron suffers $n$ collisions is \n",
    "\\begin{equation} \\Large\n",
    "P_n = (1/n!)m^n \\exp(-m)\n",
    "\\end{equation}\n",
    "\n",
    "where $m$ is the number of average collisions for electrons travel through this sample area. The number $m$ can be set to the scattering parameter $t/\\lambda$. $P_n$ is represented in the EELS spectrum by the ration of the energy-integrated intensity $I_n$ of $n$-fold scattering divided by the {\\bf total} integrated intensity $I_t$:\n",
    "\\begin{equation} \\Large\n",
    "P_n =    I_n/I_t (1/n!) (t/\\lambda)^n \\exp(-t/\\lambda)\n",
    "\\end{equation}\n",
    "\n",
    "For a given order $n$ of scattering, the intensity  is highest when $t/\\lambda =n$\n",
    "In the case of the unscattered (n=0) component (zero--loss peak), the intensity is highest at t=0 and decreases exponentially with specimen thickness. For $n=0$, equation \\ref{equ:poisson} gives equation \n",
    "\\begin{equation} \\Large\n",
    "\\frac{t}{\\lambda}= - \\ln\\left[ \\frac{I_{\\mbox{total}}}{I_{zl}}\\right]\n",
    "\\end{equation}\n",
    "I just replaced $I_{zl}$ with $I_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zero Loss with energy resolution of -0.15 eV at position -0.000 eV\n",
      "Sum of Zero-Loss: 84 counts\n",
      "Sum of Spectrum: 100 counts\n",
      "thickness [IMFP]: 0.17734\n"
     ]
    },
    {
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      "image/png": 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",
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       "\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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       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "FWHM, energy_shift = eels_tools.get_channel_zero(np.array(eels_dataset), eels_dataset.energy_loss)\n",
    "\n",
    "print(f'Zero Loss with energy resolution of {FWHM:.2f} eV at position {energy_shift:.3f} eV')\n",
    "eels_dataset.energy_loss -= energy_shift\n",
    "\n",
    "zero_loss  = eels_tools.get_resolution_functions(eels_dataset)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(eels_dataset.energy_loss, eels_dataset, label='spectrum')\n",
    "plt.plot(eels_dataset.energy_loss, zero_loss, label = 'zero-loss')\n",
    "plt.plot(eels_dataset.energy_loss, np.array(eels_dataset)-zero_loss , label = 'difference')\n",
    "\n",
    "plt.title ('Lorentzian Product Fit of Zero-Loss Peak')\n",
    "#plt.xlim(-5,30)\n",
    "plt.legend();\n",
    "Izl = zero_loss.sum()\n",
    "Itotal = np.array(eels_dataset).sum()\n",
    "tmfp = np.log(Itotal/Izl)\n",
    "print(f'Sum of Zero-Loss: {Izl:.0f} counts')\n",
    "print(f'Sum of Spectrum: {Itotal:.0f} counts')\n",
    "print (f'thickness [IMFP]: {tmfp:.5f}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "\n",
    "## Single Scattering Deconvolution\n",
    "\n",
    "For thicker samples (relative thickness larger than half the inelastic MFP), the scattered electrons are likely to be scattered a second time by plasmon excitations. This results for thicknesses around 0.5 MFP in more intensity in the high energy tail of the plasmon peak. For thicker areas a second plasmon peak will appear at double the energy loss and for very thick areas we have a whole series of plasmon peaks.\n",
    "In spectra of very thick areas the zero-loss peak may completely vanish. Multiple scattering is easily recognized by the positions of the peaks (multiple of $E_{max}$).\n",
    "\n",
    "Multiple scattering influences the high energy side of the first plasmon peak, and makes it difficult to quantify the spectra, whether it is in the low-loss or core--loss region. Figure \\ref{fig:ssd} shows how the correction improves the determination of the width of the plasmon width. Fortunately, we can correct this multiple scattering, because mathematically, it is a kind of self-convolution. The procedure is called single scattering deconvolution (SSD).\n",
    "\n",
    "\n",
    "Electrons that lost energy can interact with the sample again. The average path between two interaction is the above introduced IMFP $\\lambda$. This multiple inelaxtic scattering is most obvious in the strongest energ-loss spectrum: the volume plasmon. This multiple scatering follows the Poisson statistic and the $n^{\\rm th}$ scattering has the intensity:\n",
    "$$I_n = I_0 P_n = (I_0/n!)(t/λ)^n \\exp(−t/λ)$$\n",
    "\n",
    "It can be shown the the single scattering spectrum in fourier space $s(v)$ can be derived by:\n",
    "\n",
    "$$s(v) = I_0 \\ln[j(v)/z(v)]$$\n",
    "\n",
    "$z(v)$ beeing the Fourier transformed zero-loss peak (resolution function) and $j(v$ the spectrum in Fourier space.\n",
    "\n",
    "The above formula would also correct for any instument broadening and a very noisy spectrum would result, so we need to convolute (multiplication in Fourier space) a new broadening function, which could be a well behaved Gaussian with slightly smaller energy width than the original zero-loss peak.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ed6ef0178cc7487385db819ce02bd207",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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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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' 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": [
    "# Single scattering deconvolution\n",
    "\n",
    "# Use resolution Function as ZL \n",
    "\n",
    "j = np.fft.fft(np.array(eels_dataset))\n",
    "z = np.fft.fft(zero_loss)\n",
    "z2 = z ## Could be a different zl i.e. extracted from Spectrum\n",
    "j1 = z2*np.log(j/z)\n",
    "ssd_low_loss =np.fft.ifft(j1).real#,'fourier-log deconvolution')\n",
    "\n",
    "plt.figure()\n",
    "#plt.plot(s.tags['ene'][start:end],  zLoss[start:end]/sumSpec*1e2)\n",
    "plt.plot(eels_dataset.energy_loss,  ssd_low_loss)\n",
    "plt.plot(eels_dataset.energy_loss, eels_dataset)\n",
    "#plt.xlim(-4,40)\n",
    "plt.ylim(-.1,.1);\n",
    "eels_dataset.metadata['resolution_function'] = zero_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Volume Plasmon Peak\n",
    "\n",
    "Most of the inelastically scattered electron arise from interaction with outer shell electrons. These interactions, therefore, have a high intensity and are easy to obtain. The quantification of this region ($<$ 100eV)  in an EELS spectrum is rather hard.\n",
    "\n",
    "The valence electrons in a solid can be considered as coupled oscillators which interact with each others and with the transmitted electrons. In a first approximation the valence electrons behave like a free electron gas (Fermi sea, jellium). The behavior of the electron gas is described in terms of the dielectric function $\\varepsilon$.\n",
    "\n",
    "\n",
    "The energy-loss function $F_{el}$ on the other hand is determined by the dielectric function $\\varepsilon$ through:\n",
    "\n",
    "$$\n",
    "F_{el} = \\Im \\left[\\frac{-1}{\\varepsilon(\\omega)} \\right]\n",
    "$$\n",
    "\n",
    "The maximum of the energy-loss function is the plasmon--peak, which is given by:\n",
    "$$\n",
    "E_{max} = \\left[(E_p)^2 - (\\Delta E_p/2)^2\\right]^{1/2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dielectric Theory\n",
    "\n",
    "We investigate the plasmon excitation in the so called jellium model. This model is enough to explain the essence of this excitation, but is not as complicated as the real solid state.\n",
    "\n",
    "\n",
    "The displacement of a {\\it quasifree} electron (with an effective mass $m$ and not the rest mass $m_0$) due to an electric field $\\vec{E}$ must fulfill the equation :\n",
    "\\begin{equation} \\Large\n",
    "m\\vec{x}'' + m\\Gamma \\vec{x}'  =  -e\\vec{E}\n",
    "\\end{equation}\n",
    "\n",
    "The usage of an effective mass approximates the interaction between the valence electrons and the ion--cores. For the same reason, we introduce $\\Gamma$ a damping constant. Instead of $\\Gamma$, we could also use its reciprocal value $\\tau = 1/\\Gamma$ as in the Drude theory. This is similar to the electronic theory of conduction.\n",
    "\n",
    "\n",
    "For an oscillatory field $\\vec{E}= \\vec{E} \\exp(-i\\omega t)$ above equation \\ref{equ:motion} has the following solution:\n",
    "\\begin{equation} \\Large\n",
    "\\vec{x} = (e\\vec{E}/m)(\\omega ^2+i\\Gamma \\omega)^{-1}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "The displacement gives raise to a polarization $\\vec{P}  = -en\\vec{x} =\\varepsilon_0\\chi\\vec{E}$, with $\\chi$ electric susceptibility and $n$ the the number of electron per unit volume. The dielectric function $\\varepsilon(\\omega)=1+\\chi$ can be expressed as:\n",
    "\\begin{equation} \\Large\n",
    "\\varepsilon(\\omega)=\\varepsilon_1+i\\varepsilon_2 = 1-\\frac{\\omega_p^2}{\\omega^2+\\Gamma^2}+\\frac{i\\Gamma\\omega^2_p}{\\omega(\\gamma^2+\\Gamma^2)}\n",
    "\\end{equation}\n",
    "Where $\\omega$ is the frequency (in rad/s) of forced oscillation and $\\omega_p$ is the Eigen or resonance frequency of the free electron gas, which is given by:\n",
    "\\begin{equation} \\Large\n",
    "\\omega_p =\\left[ \\frac{ne^2}{\\varepsilon_0 m} \\right]^{1/2}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "A sudden impulse such as a transmitted electron will contain all angular frequencies (Fourier components). It will also excite the resonance frequency of the jellium. Such an oscillation with frequency $\\omega_p$ can be viewed as a ``pseudoparticle`` with (plasmon) energy $E_p =\\hbar \\omega_p.$ We call this ``pseudoparticle``  a **plasmon**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Energy-Loss Function\n",
    "The energy-loss function (elf) is given as shown in the beginning by:\n",
    "\\begin{equation} \\Large\n",
    "E_{el}= \\left[\\frac{1}{\\varepsilon(\\omega)}\\right] = \\frac{\\varepsilon_2}{\\varepsilon_1^2+\\varepsilon_2^2}=\\frac{\\omega\\Gamma\\omega_p^2}{(\\omega^2-\\omega_p^2)^2 +(\\omega\\Gamma)^2}\n",
    "\\end{equation}\n",
    "The energy-loss is represented by $E=\\hbar \\omega$ and we can rewrite equation \n",
    "\\ref{equ:eels_function2} as:\n",
    "\\begin{equation}\n",
    " \\left[\\frac{1}{\\varepsilon(E)}\\right]  =\\frac{(E\\hbar/\\tau)E_p^2}{(E^2-E^2)^2 +(E\\hbar/\\tau)^2} %\n",
    "  =\\frac{(E \\quad \\Delta E_p)E_p^2}{(E^2-E^2)^2 +(E \\quad \\Delta E_p)^2} \n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "The relaxation time $\\tau = 1/\\Gamma$ is directly connected to the FWHM of the energy-loss function which is given by $\\Delta E_p =\\hbar\\Gamma = \\hbar/\\tau$. The effect of the effective mass on the energy-loss function is rather small.\\\\ \n",
    "The maximum of the energy-loss function is given in equation \\ref{equ:plasmon-maximum}.\n",
    "\n",
    "\n",
    "The relaxation time $\\tau$ represents the time for plasmon oscillations to decay in energy by  a factor $\\exp(-1)=0.37$. The number of oscillations which occur within this time is $\\omega_p\\tau/(2\\pi)=E_p/(2\\pi/\\Delta E_p)$. Using experimental values for $E_p$ and $\\Delta E_p$ result in 5 to 0.4 oscillations. The plasmon oscillations are, therefore, heavily  damped, which depends on the band structure of the material. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plasmon Energies\n",
    "\n",
    "The calculated plasmon energies of the Jellium model with equation \\ref{equ:plasmon_frequency} are already quite good as can be seen in table \\ref{tbl:plasmon_frequencies}.\n",
    "Only the number of valence electrons per unit area $n$ and the dielectric constant $\\varepsilon_0$ are necessary for these calculations.\n",
    "\n",
    "\n",
    "\n",
    "| Material |  $E_p$ (experimental) | $E_P$ (theoretical)|\n",
    "|----------|-----------------------|--------------------|\n",
    "|Li | 7.1 eV | 8.0 eV|\n",
    "|Diamond | 34 eV | 31 eV|\n",
    "|Si | 16.5 eV | 16.6 eV| \n",
    "|Ge | 16.0 eV | 15.6 eV|\n",
    "|InSb | 12.9 eV | 12.7 eV|\n",
    "|GaAs | 15.8 eV | 15.7 eV|\n",
    "|NaCl | 15.5 eV | 15.7 eV|\n",
    "\n",
    "A more sophisticated way of comparing the valence loss spectra to theory is to calculate the dielectric function. {\\it Ab initio} density functional theory can be used to do these calculations. To obtain the dielectric function the valence band has to be convoluted with the conduction band. A comparison between experiment and theory is shown in the figure below. \n",
    "\n",
    "<img title=\"Plasmon--Loss peak of Li\" width=\"50%\" alt=\"Plasmon--Loss peak of Li\" src=\"images/Li-plasmon.jpg\">\n",
    "\n",
    "*Plasmon--Loss peak of Li (black circles), Gibbson et al Phys.~Rev.~B {\\bf 13}:2451 (1979) and calculated energy-loss function by S.~Ramachandran et al. (unpublished)}*\n",
    "\n",
    "The plasmon--loss enables us to determine the plasmon energy, a materials parameter.\n",
    "The width plasmon peak is also a characteristic of the material and is needed to determine the plasmon energy.\n",
    "\n",
    "<img title=\"Plasmon-loss\" width=\"50%\" alt=\"Plasmon-loss\" src=\"images/Plasmon-loss.jpg\">\n",
    "\n",
    "*Plasmon--Loss peak of SrTiO$_3$ with highlighted FWHM*\n",
    "\n",
    "The spectrum here is quite complicated due to the surface plasmon--peak which shows up to the left of the volume plasmon--peak. We measure the energy of the maximum of the plasmon--peak (here $E_{\\mbox{max}} = 31$ eV) and the width of the plasmon--peak (here $\\Delta E_P = 5.3$ eV). While it is easy to determine the plasmon--peak energy , the plasmon--peak width can only be determined approximately, because we don't know how to subtract the background.\n",
    "\n",
    "Using equation above, we find that the plasmon energy is 30.5 eV for SrTiO$_3$.\n",
    "\n",
    "\n",
    "\n",
    "This spectrum shows the high dynamic range of an EELS spectrum. The valence loss part of the spectrum is noisy, but the zero-loss peak is not saturated. The surface plasmon peak is strong, which indicates a rather thin area. May be a little too thin. Without loss of information we can get spectra from thicker areas.\n",
    "\n",
    "\n",
    "Not only the plasmon energy (or the plasmon maximum) can be used for an identification of materials,\n",
    "but also the shape, especially the width of the plasmon peak.\n",
    "\n",
    "As seen above, it is rather difficult to determine the FWHM of a plasmon peak. However, it is much easier after subtraction of the zero-loss peak, as can be seen in figure below.\n",
    "\n",
    "<img title=\"Ni plasmon-loss\" width=\"50%\" alt=\"Ni plasmon-loss\" src=\"images/plasmon2.jpg\">\n",
    "\n",
    "*Plasmon--Loss peak of  Ni (black) after subtraction of the zero-loss peak and with highlighted FWHM. The original spectrum and the zero-loss peak are displayed in the background.*\n",
    "\n",
    "A comparison of the plasmon peak width of Ni (above) and Si (figure  below)\n",
    " makes it apparent  how different the shape of plasmon peaks can be. The Si plasmon peak is sharp (FWHM: 7.3 eV) and has a well defined maximum, while the Ni plasmon peak is very broad (FWHM: 40 eV).\n",
    "\n",
    "<img title=\"Si plasmon-loss\" width=\"50%\" alt=\"Si plasmon-loss\" src=\"images/plasmon3.jpg\">\n",
    "*Plasmon--Loss peak of  Si (black) after subtraction of the zero-loss peak and with highlighted FWHM. The original spectrum and the zero-loss peak are displayed in the background.*\n",
    "\n",
    "The Si plasmon peak is obtained from a rather thin area, which also makes it easier to determine the width, because the right hand tail is not broadened by the thicker sample (please see section above about single scattering deconvolution). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Drude Function\n",
    "\n",
    "The dielectric function in the Drude theory is given by two input parameters the position of the plasmon energy $E_p$\n",
    "and the width of the plasmon $\\Gamma$\n",
    "\n",
    "$$ ε(ω) = ε1 + iε2 = 1 + χ = 1 − \\frac{\\omega_p^2}{\\omega^2+\\Gamma^2} + \\frac{i\\Gamma \\omega_p^2}{\\omega(\\omega^2+\\Gamma^2)}$$\n",
    "Here $\\omega$ is the angular frequency (rad/s) of forced oscillation and $\\omega_p$ is the natural or resonance frequency for plasma oscillation, given by\n",
    "$$ ω_p = \\sqrt{\\frac{ne^2}{(ε_0m_0)}} $$\n",
    "A transmitted electron represents a sudden impulse of applied electric field, containing\n",
    "all angular frequencies (Fourier components). Setting up a plasma oscillation of the loosely bound outer-shell electrons in a solid is equivalent to creating a pseudoparticle of energy $E_p = \\hbar \\omega_p$, known as a plasmon (David Pines, Elementary Excitations in Solids, 1963)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'energy loss (eV)')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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",
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       "\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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' 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": [
    "# ----------- Input -------------\n",
    "E_p = plasmon_energy = 17. # in eV\n",
    "E_w = plasmon_gamma = .7 # in eV\n",
    "# -------------------------------\n",
    "energy_scale = eels_dataset.energy_loss+1e-18 #= np.linspace(0,50,1024)+1e-18\n",
    "\n",
    "def Drude(E,E_p,E_w):\n",
    "    eps = 1 - E_p**2/(E**2+E_w**2) +1j* E_w* E_p**2/E/(E**2+E_w**2)\n",
    "    elf = (-1/eps).imag\n",
    "    return eps,elf\n",
    "\n",
    "eps,elf = Drude(energy_scale, plasmon_energy, plasmon_gamma)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(energy_scale, eps.real, label='Re($\\epsilon_{Drude}$)')\n",
    "plt.plot(energy_scale, eps.imag, label='Im($\\epsilon_{Drude}$)')\n",
    "plt.plot(energy_scale, elf, label='loss function$_{Drude}$')\n",
    "plt.plot([0,energy_scale[-1]],[0,0],c='black')\n",
    "\n",
    "plt.legend()\n",
    "plt.gca().set_ylim(-2,max(elf)*1.05);\n",
    "plt.xlim(-1,40);\n",
    "plt.xlabel('energy loss (eV)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Fitting a Drude Function to Plasmon\n",
    "\n",
    "The position and the width are important materials parameters and we can derive them by fitting the Drude function to the volume plasmon region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drude Theory with Plamson Energy: 15.049794 eV and plasmon Width 0.72 eV\n",
      "Max of Plasmon at 15.04 eV\n",
      "Amplitude of  0.01 was deteremined by fit \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2bc8ea34e561478299debfcd79234707",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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lyxY8Hg8TJ04E4Ic//CHTp0/njDPOwO/389BDD7FlyxYefvjhEz7uyUouAqMhYEkzN694E4A7f/8un5syLMW9ERERK6Q8AM6ZM4eGhgbuueceampqmDx5MmvWrKGsrAyILfx89Np85557bvLPmzZt4re//S1lZWXs2rULgMbGRr7+9a9TW1tLQUEB5557Li+//DIXXHDBCR/3ZGkSiKS7htZgqrsgIiIWMUyVrHrN7/dTUFBAU1MTq97/O79473/jCg9n800vpLprIpY5545V/KvrBX4Tvpg3fnJ9qrsjItJnR35+d3s5VwZIeQUwXRgDY0K1iKUiUZM7XCu51vUSlznepC14Ldke/bMhImJ3Si0i0qNDbUG+7FwHwARHNf72cIp7JCIiVlAAtIgjeQmgRtQlfRxqDdLC4Xtot7QHUtgbERGxigKgRQyt/yJp6GBrkAjO5Pcd/roU9kZERKyiAGg5VQAlfbQGguTTmvw+0NKYus6IiIhlFAAtomVgJB2FWxtxGof/U6MAKCKSHhQALab6n6STaOvBTt+H25pS1BMREbGSAqBFdA2gpCOzvaHT95H2xtR0RERELKUAaDnVACWNtPs7fRvt8PfQUERE7EQB0CKHrwFUAJT0EQ22dvreVAAUEUkLCoAWcWgSiKQh86gA6AgoAIqIpAMFQBHpWbCt07fucEuKOiIiIlZSALSIloGRtBTqHACd4fYUdURERKykAGgxU9cAShoxjgp8jkhHinoiIiJWUgC0iCqAko4c8QpgCBcALgVAEZG0oAAoIj1yRmIVwBZHfuz7aCCV3REREYsoAFrEgZaBkfTjigfANteg2PcKgCIiaUEB0CIaApZ05I4P+XZ4BsW+j2oIWEQkHSgAWk4VQEkficAX9BTGv1cFUEQkHSgAWkT3ApZ05DFjATDsLYx/rwAoIpIOFABFpEfueOCLZikAioikEwVAiySuAdQAsKQTtxkEwPANAsBLMIW9ERERqygAWuTwALAioKQPtxkCwJEdqwB6VQEUEUkLCoAW0TWAko4SAdCVEwuAWUYQTP0nR0TE7hQALWI4FAAl/SSGfD15Q5LbzLCWghERsTsFQMupOiLpwTRN3MQqgL68wcntgfbWVHVJREQsogBoEQ0BS7oJRqJ44wEwKyePiBn7HQ8G2lPZLRERsYACoOVUAZT0EAxH8RAGICsrhyDu2HYFQBER21MAtIgjcSs4FQIlTYRCIdxGBACPNzsZAEMdCoAiInanAGgRDQFLugkdUelzeHwEjVgADIc0CURExO4UAC2nIWBJD6HAEUHP6SWUqAAGFABFROxOAdAiySFgkTQRCrYBEMYBThfhRAUwqAAoImJ3CoCWSdwKThVASQ+JSl+y8md4AIgEdQ2giIjdDYgAuHTpUsrLy/H5fFRUVPDKK6/02LampoavfOUrnHnmmTgcDubPn9+lzWOPPcasWbMoLCyksLCQSy65hNdff71Tm7vvvhvDMDo9SktLe30OTkfiR6kAKOkhEr/WLzH5I1kBDOl2cCIidpfyALh69Wrmz5/PokWL2Lx5M7NmzWL27NlUV1d32z4QCFBcXMyiRYs4++yzu23z0ksvcd111/Hiiy+yceNGRo8eTWVlJXv37u3UbtKkSdTU1CQf77zzTq/P4/AQsAKgpIdIogKYqPw5EhVADQGLiNhdygPgAw88wE033cTNN9/MhAkTWLJkCaNGjWLZsmXdth8zZgwPPvggN9xwAwUFBd22+c1vfsMtt9zCOeecw/jx43nssceIRqP89a9/7dTO5XJRWlqafBQXF/f6PAxdAyhpJlEBDMUrf5H4V1OzgEVEbC+lATAYDLJp0yYqKys7ba+srGTDhg2WHaetrY1QKMTgwYM7bd++fTvDhw+nvLyca6+9lh07dvT6GA5UAZT0krjWL1EBDDu8AETDGgIWEbE7VyoPXl9fTyQSoaSkpNP2kpISamtrLTvOHXfcwYgRI7jkkkuS26ZNm8aKFSsYN24c+/fv595772XmzJls3bqVIUOGdLufQCBAIHD4w8/v9yf/bGgIWNJMNH6tX+Lav6gjUQFUABQRsbuUDwFD1+FT0zQtG1K97777WLlyJc888ww+ny+5ffbs2Vx99dVMmTKFSy65hOeffx6Ap556qsd9LV68mIKCguRj1KhRyecOTwIRSQ/R+FBv2IhX/uLXAJphDQGLiNhdSlNLUVERTqezS7Wvrq6uS1WwN+6//35+/OMfs3btWs4666xjts3JyWHKlCls3769xzYLFy6kqakp+dizZ0/yOUNDwJJmEgEwMfkj6owFQVUARUTsL6UB0OPxUFFRQVVVVaftVVVVzJw5s0/7/tnPfsaPfvQj/vznPzN16tTjtg8EAmzbto1hw4b12Mbr9ZKfn9/pkaBZwJJuzPi1focDYOwrkWCquiQiIhZJ6TWAAAsWLGDu3LlMnTqVGTNm8Oijj1JdXc28efOAWNVt7969rFixIvmaLVu2ANDS0sKBAwfYsmULHo+HiRMnArFh3zvvvJPf/va3jBkzJllhzM3NJTc3F4Dbb7+dK664gtGjR1NXV8e9996L3+/nxhtv7NV5JCuAmgwsacIMxSaBJAKgmfgaUQVQRMTuUh4A58yZQ0NDA/fccw81NTVMnjyZNWvWUFZWBsQWfj56TcBzzz03+edNmzbx29/+lrKyMnbt2gXEFpYOBoNcc801nV531113cffddwPw8ccfc91111FfX09xcTHTp0/n1VdfTR73ZDkduhOIpJlwrNKXvPbPFbuG1tAsYBER20t5AAS45ZZbuOWWW7p97sknn+yyzTSPHbISQfBYVq1adSJdO2EOQ3cCkTQTr/Qlrv0jPgRsqAIoImJ7mrpqEQMFQEkvidm+yckf8a+GrgEUEbE9BUCLOBy6+E/SzFFDwLhiAdChCqCIiO0pAFrkcPxTBVDSgyMSqwCa8eBnJL5GVQEUEbE7BUCLOB3OVHdBxFLJod74tX8OdywAOjUELCJiewqAFkneucRQBVDSQ3KoNzH7N14BdKoCKCJiewqAFjl8CaACoKSHwwEwPvTrjgVBp6kAKCJidwqAFnHoRylpxpGo9MVn/zrilUBHNJSqLomIiEWUWixi6FZwkmYSATBZ+fPEgqBLFUAREdtTALSIU8vASJpxHhUAHfGvLl0DKCJiewqAFkksBG1oEoikCVcyAMYrf554ADQ1BCwiYncKgBZxGIcrgNFoNIU9EbFGYrKHIzH7Nz4E7EYBUETE7hQALdIpAB7nXsUidpCoADoTFUB3FgAeXQMoImJ7CoAWcRqHf5QKgJIOEkO9zsS1f97YV1UARUTsTwHQIkfeCzhsRlLYExFrHB0A3fFrAN1mOGV9EhERaygAWsQ44kdp6hJASQPuRABMLP+SqAAaEYjqPzkiInamAGgR48hrAFECFPtLDPUmrgF0e7KSz0VDHSnpk4iIWEMB0CJHLgOoawAlHSQCoMsbC35eX3byuWBAAVBExM4UAC3idDiTfzYVACUNeOJDwInKn8ftIWrG/qcTDLSnrF8iItJ3CoAWcXC4BBjRRYBid9Fo7Fo/Di8A7XY5COICIKQAKCJiawqAFjlyFnA0qgqg2Fs0HEj+OTH71zAMAngACAc1BCwiYmcKgBY5sgIYRQFQ7O3Ia/zc8dm/AKFEBVABUETE1hQALXLkLGBTQ8Bic6Hg4SFez5EB0HADEA5qCFhExM4UAC3idOhOIJI+QvEKYMB04XEdnuB0OAAGun2diIjYgwKgRRxH/CgjugZQbC4xxBvC3am6HSYWACOqAIqI2JoCoEWOuBUwphaCFpsLxyuAiVm/ye2O2CSQqCqAIiK2pgBokU6TQFQBFJuLhGIVvsSQb0LIiM8CDmsSiIiInSkAWsR1xELQmgUsdnfkEPCRIvFAGA2pAigiYmcKgBZxHHGdVCSqIWCxt0j8Xr/hoyqAkcQQsAKgiIitKQBaxKFZwJJGIvFr/I4eAlYAFBFJDwqA/UCTQMTuoskKoKfzdkc8EOoaQBERW1MAtJBpGvGvKe6ISB8lKnxdAqDTC4CpACgiYmsKgJaKBUANAYvdJQJgxNF5CNiMDwGb4eAp75OIiFhHAbAfRMxIqrsg0ifRcCIAHl0BjH8f1jWAIiJ2NiAC4NKlSykvL8fn81FRUcErr7zSY9uamhq+8pWvcOaZZ+JwOJg/f3637Z5++mkmTpyI1+tl4sSJPPvss3067olJVAD7uBuRFDPjAS96dAUwHgCNiCqAIiJ2lvIAuHr1aubPn8+iRYvYvHkzs2bNYvbs2VRXV3fbPhAIUFxczKJFizj77LO7bbNx40bmzJnD3Llzeeutt5g7dy5f/vKXee2113p93BMSD36mhoDF5sweKoDErwHUJBAREXtLeQB84IEHuOmmm7j55puZMGECS5YsYdSoUSxbtqzb9mPGjOHBBx/khhtuoKCgoNs2S5Ys4dJLL2XhwoWMHz+ehQsXcvHFF7NkyZJeH/fEJCqAmgUs9na4Atg5AKoCKCKSHlIaAIPBIJs2baKysrLT9srKSjZs2NDr/W7cuLHLPi+77LLkPvvruIkAqAqg2F48ACYCX5LLB4ARVQAUEbEz1/Gb9J/6+noikQglJSWdtpeUlFBbW9vr/dbW1h5zn709biAQIBA4fPG73+/vtl1EFwGK3cVn+R4dAA1XbAhYFUAREXtL+RAwgHHEbdQgVkE7elt/7PNkj7t48WIKCgqSj1GjRh191Nh+tBC02JwRiVcAHd7OT8QDoEMVQBERW0tpACwqKsLpdHaputXV1XWpzp2M0tLSY+6zt8dduHAhTU1NyceePXuOaqF1ACU9JANgDxVApwKgiIitpTQAejweKioqqKqq6rS9qqqKmTNn9nq/M2bM6LLPtWvXJvfZ2+N6vV7y8/M7PY5kJCuACoBib8khXlfnCqBDAVBEJC2k9BpAgAULFjB37lymTp3KjBkzePTRR6murmbevHlArOq2d+9eVqxYkXzNli1bAGhpaeHAgQNs2bIFj8fDxIkTAbj11lu58MIL+elPf8qVV17Jc889x1/+8hfWr19/wsftlXjui0Q1BCz2lgyAR1UAHe7YJBAFQBERe0t5AJwzZw4NDQ3cc8891NTUMHnyZNasWUNZWRkQW/j56LX5zj333OSfN23axG9/+1vKysrYtWsXADNnzmTVqlV8//vf584772Ts2LGsXr2aadOmnfBxe0dDwJIekrN8j64AuhMVwNCp7pKIiFgo5QEQ4JZbbuGWW27p9rknn3yyy7YTWWblmmuu4Zprrun1cftCQ8Bid4kKn3FUAHR64gHQVAVQRMTOBsQs4PShdQAlPSRm+RruowJgfAjYZaoCKCJiZwqAltIQsKSHHiuA8UDoVgVQRMTWFAAtFQuAEd0KTmzOEb/GzxG/80eC05MFgFsVQBERW1MA7AcaAha7c5ndDwG7PLFA6EYBUETEzhQALaUhYEkPiVm+zqMCoNurACgikg4UAC2lhaAlPSQmeSTW/Utud8eGgD1mGPQfHRER21IAtFDiTiBRLQQtNpe4xs91VAXQ44sFQodhQkRVQBERu1IA7AcaAha7S1QAnZ7OFUD3Ed9HQh2ntE8iImIdBUBLaQhY0oOH2CQQ51FDwB5vVvLPwYACoIiIXSkAWime+1QBFLtLTPJwHVUB9HjchEwnACEFQBER21IAtFTsx6kKoNiaaeIhDBye9ZvgchgE43eQDAbbTnnXRETEGgqA/SCiSSBiZ5HDd/k4ugJoGAZB3IAqgCIidqYAaCFD9wKWdBAOJP/oPioAAoSMWAAMBxUARUTsSgGwH2gIWOwsEjocAI+c9JGQqAAqAIqI2JcCoKVUART7CwbaY19NJx63q8vz4XgFMKIAKCJiWwqAloovBK0KoNhYOH5tXxA3HlfXfyLChgfQOoAiInamAGgh3QlE0kEwFK8A4sLlMLo8n6wAHjFULCIi9qIA2A+0DqDYWSQYC3Yh3BhGzwEwqiFgERHbUgC0lK4BFPtLTO4IxSd7HC3i0BCwiIjdKQBayNCt4CQNJAOg0X0ATFwDGNUQsIiIbSkAWip+DaCpawDFviLJAOjp9vmoM7bdDCsAiojYlQKgpRIBMMXdEOmDSPwWb8GeAqBDAVBExO4UAPuBiSqAYl/R41UAHbGhYQVAERH7UgC0lCaBiP1F48vAhAxv98/Hh4AJaxKIiIhdKQBaKLkOYIr7IdIXZnx2b2K2b5fnnfFgGA6eqi6JiIjFFACtZCQWgo6kuCMivWfGK4BhR/cVQDOxPaIhYBERu1IAtFBiyVwNAIuthRMVwB4CoCu23RHRELCIiF0pAFoqcQ2gBoHFxuJDwGFn9wEQlw8AQ5NARERsSwHQUokAmOJuiPSBGY4NAUd7rABmAeDQELCIiG0pAFro8CQQJUCxr0RlLxqv9HXhjm13aghYRMS2FAAtlZgEoiFgsS8jcQ2gs4cAGK8AOqOqAIqI2JUCYD/QvYDFzoz40K7ZwzWAhju23RVVBVBExK4UAC2UHALWRYBiY8nZvT0MARvuWAXQpQqgiIhtDYgAuHTpUsrLy/H5fFRUVPDKK68cs/26deuoqKjA5/Nx2mmn8cgjj3R6/lOf+hSGYXR5XH755ck2d999d5fnS0tL+3QehhaCkTTgSMzudXdfAXR4YgHQrQAoImJbKQ+Aq1evZv78+SxatIjNmzcza9YsZs+eTXV1dbftd+7cyec+9zlmzZrF5s2b+d73vse3v/1tnn766WSbZ555hpqamuTj3Xffxel08qUvfanTviZNmtSp3TvvvNPHs4kFwIiWgREbc8SHdo34tX5HcyYCoKk7gYiI2JUr1R144IEHuOmmm7j55psBWLJkCS+88ALLli1j8eLFXdo/8sgjjB49miVLlgAwYcIE3nzzTe6//36uvvpqAAYPHtzpNatWrSI7O7tLAHS5XH2u+nWmZWDE/hyRWLBLVPq6PK8KoIiI7aW0AhgMBtm0aROVlZWdtldWVrJhw4ZuX7Nx48Yu7S+77DLefPNNQqFQt69Zvnw51157LTk5OZ22b9++neHDh1NeXs61117Ljh07+nA2yTvBYepuwGJjickdhrv7awCdntjfIzeqAIqI2FVKA2B9fT2RSISSkpJO20tKSqitre32NbW1td22D4fD1NfXd2n/+uuv8+677yYrjAnTpk1jxYoVvPDCCzz22GPU1tYyc+ZMGhoaeuxvIBDA7/d3enSWqACqBCj25YzGgp2zhwpgYrtXQ8AiIraV8msAAYxE6SzONM0u247XvrvtEKv+TZ48mQsuuKDT9tmzZ3P11VczZcoULrnkEp5//nkAnnrqqR6Pu3jxYgoKCpKPUaNGde5XIgD2uAeRgS8xtOvqKQB6swHwEAKteSkiYkspDYBFRUU4nc4u1b66urouVb6E0tLSbtu7XC6GDBnSaXtbWxurVq3qUv3rTk5ODlOmTGH79u09tlm4cCFNTU3Jx549e45qkVgGRh+KYl9uMxYAe6oAuuIBEICw1gIUEbGjlAZAj8dDRUUFVVVVnbZXVVUxc+bMbl8zY8aMLu3Xrl3L1KlTcbvdnbb/7ne/IxAIcP311x+3L4FAgG3btjFs2LAe23i9XvLz8zs9jmRoCFjSQGJ2b6egd+Tz3iOCoQKgiIgtpXwIeMGCBTz++OM88cQTbNu2jdtuu43q6mrmzZsHxKpuN9xwQ7L9vHnz2L17NwsWLGDbtm088cQTLF++nNtvv73LvpcvX85VV13VpTIIcPvtt7Nu3Tp27tzJa6+9xjXXXIPf7+fGG2/s8znpTiBiZ554AHT7ug+AXo+HkOmMfRNqP1XdEhERC6V8GZg5c+bQ0NDAPffcQ01NDZMnT2bNmjWUlZUBUFNT02lNwPLyctasWcNtt93Gww8/zPDhw3nooYeSS8AkfPDBB6xfv561a9d2e9yPP/6Y6667jvr6eoqLi5k+fTqvvvpq8ri9oQqg2F4kjIsI0PM1gF6Xgw48uGlXBVBExKZSHgABbrnlFm655ZZun3vyySe7bLvooov4xz/+ccx9jhs37phBbNWqVSfVxxNixAqqWghabOuIQOfJyum2icfloAM3ebQTDrQOjH9ERETkpKR8CDidJG8Epwqg2FX48OLOXl/3FUCPy0EAT7x52ynploiIWEsB0FKJZWAUAMWmwrFr+gKmC+9Rk6oSvC4nHWYsAAYDugZQRMSOFAAtlFyFUPlPbMoMxYaAA7jxurv/58HpMAgY8QDYoQqgiIgdKQBayEDXAIq9heJDugE8+NzOHtsFDW+svQKgiIgtKQBaKX4nkqjuBSw2lajoBXDjc/UcAMPxAKhrAEVE7EkB0EKORAVQt8cSm0pU9AKmG7ez59sxhh2aBCIiYmcKgBZyxJeBUQVQ7CocaAWgw/Ad837cYUesAhhRABQRsSUFQAslrwGMRlLcE5HeCXe0ABCID/H2JOL0xdoHNQtYRMSOFAAtZBgKgGJv4Y5YBTBg+I7ZLuqMBURTt4ITEbElBUALOYhdNK8hYLGraDAWAIOOYwfARAXQVAVQRMSWFAAt5DA0CUTsLRq/pi/k6P4uIAmmKx4AVQEUEbElBUALJSeBmBoCFntKVADDzuMMAbviATGkSSAiInakAGihZAVQAVDsKh4AQ85jVwBx5wDgUAAUEbElBUALGVoHUOwuHugixwmApiceACMaAhYRsSMFQAs5jcQkEFUAxabi1/RFXMcOgEa8AugMqwIoImJHCoAWMpLXAKoCKPZkxCuAUVf2sdt5Y8+7w6oAiojYkQKghZIVQAVAsalERc88TgXQ4c0FwBVVABQRsSMFQAs5VAEUm3PEK3pR97ErgA5vbAjYrWsARURsSQHQQgqAYnfOeKBzxCd59MTti1UAPWZHv/dJRESspwBoIQdaBkbszRlOBMBjVwBdWbGA6NMQsIiILSkAWsjhiP04TVUAxabc0VhFz+k9XgUwDwAfAdCyRyIitqMAaKHEvYBVARS7SlzT5/IdOwB6svIOf6OZwCIitqMAaCFnogKIKiJiTx4zAIDzyIDXDW/2EQExfvcQERGxDwVAC2kZGLG1aBRvfFKH5zgVwGyPh1bTG/tGAVBExHYUAC3kUAAUOztiKNeTlXvMpj6PgzZiAdBUABQRsR0FQAs5NQlE7Cx4+LZu3uMEwCy3k/Z4BTDY0dKv3RIREespAFoosQxMVNcAih2FYpW8dtNDttdzzKZZbiet+AAItDb3e9dERMRaCoAWcjo0BCw2FooNAbfjIcvjPGZTl9NBwIgHwDYFQBERu1EAtFAiAJpoGRixofgQcBs+so8TAAECjlgADLYrAIqI2I0CoIWcuhWc2Fg4ELuWr930nlAADDmyAF0DKCJiRwqAFkouA6NrAMWGAq1NALSQddwhYICQMxYAw+0KgCIidqMAaCGHYQCaBSz2FGrzA7EA6HEe/5+GiDN2v+BIQAFQRMRuFAAtlKgA6k4gYkfhtkYA2o1sjPh/Zo4l6o5VAKMdWgdQRMRuBkQAXLp0KeXl5fh8PioqKnjllVeO2X7dunVUVFTg8/k47bTTeOSRRzo9/+STT2IYRpdHR0dHn457PK7EJBBVAMWGwu2xCmCH49h3AUmIumNrBZpBVQBFROwm5QFw9erVzJ8/n0WLFrF582ZmzZrF7Nmzqa6u7rb9zp07+dznPsesWbPYvHkz3/ve9/j2t7/N008/3aldfn4+NTU1nR4+n6/Xxz0RyWVgMHu9D5FUiXbEZvMG40O7x23viQVAI6BZwCIidpPyAPjAAw9w0003cfPNNzNhwgSWLFnCqFGjWLZsWbftH3nkEUaPHs2SJUuYMGECN998M1/96le5//77O7UzDIPS0tJOj74c90QkZgFrGRixo2hHrAIYdB37LiBJ3nwAXCEFQBERu0lpAAwGg2zatInKyspO2ysrK9mwYUO3r9m4cWOX9pdddhlvvvkmoVAoua2lpYWysjJGjhzJ5z//eTZv3tyn456I5DqApiqAYj9mPABG3CcWAA2fAqCIiF2lNADW19cTiUQoKSnptL2kpITa2tpuX1NbW9tt+3A4TH19PQDjx4/nySef5A9/+AMrV67E5/PxiU98gu3bt/f6uACBQAC/39/pcSRNAhE7M4KxIGd68k6sva8AAHdYk0BEROwm5UPAQJcZh6ZpHnMWYnftj9w+ffp0rr/+es4++2xmzZrF7373O8aNG8cvfvGLPh138eLFFBQUJB+jRo3q9HxyEogCoNiQI7Gci/fEAqA7K1YB9EY0CURExG5SGgCLiopwOp1dqm51dXVdqnMJpaWl3bZ3uVwMGTKk29c4HA7OP//8ZAWwN8cFWLhwIU1NTcnHnj17Oj3vciSuAVQAFPtxJIZyfScWAF05g2LNI6oAiojYTUoDoMfjoaKigqqqqk7bq6qqmDlzZrevmTFjRpf2a9euZerUqbjd7m5fY5omW7ZsYdiwYb0+LoDX6yU/P7/T40hOVQDFxhJDuQ5f/nFaxnhyBwGQZbaBrnsVEbEVV6o7sGDBAubOncvUqVOZMWMGjz76KNXV1cybNw+IVd327t3LihUrAJg3bx6//OUvWbBgAV/72tfYuHEjy5cvZ+XKlcl9/vCHP2T69OmcccYZ+P1+HnroIbZs2cLDDz98wsftDa0DKHbmiVfy3NkFJ9TelxO/BpAwhDsgvjC0iIgMfCkPgHPmzKGhoYF77rmHmpoaJk+ezJo1aygrKwOgpqam09p85eXlrFmzhttuu42HH36Y4cOH89BDD3H11Vcn2zQ2NvL1r3+d2tpaCgoKOPfcc3n55Ze54IILTvi4veEyEvdPVQAU+/EmA+CJVQCzcguImgYOw4QOvwKgiIiNGKbWLOk1v99PQUEBTU1N5Ofn8+Smv/Dzd2/DGS5hy01/SXX3RE5cJAQ/KgLgf2b/nc9Pm3zcl3x8qI38JaeRb7TDtzZB0en93UsREUsc/fmdiQbELOB04XImKoDK1GIzR9zNwxef3HE8uV4XzcTuGhJub+yHTomISH9RALSQloER24oHwHbTQ272iQ3l5npdNJuxANjmP9RvXRMREespAFrIpYWgxa7iAbCFLHK9J3ZpsMvpoN2IB8BmBUARETtRALTQ4SFgBUCxmUDsrjYtpo8834nPDetw5sS+tigAiojYiQKghXwuDwCmEUlxT0ROTqStEYAmcsjzdb+eZndCrth9g4Otjf3QKxER6S8KgBbKdnvjfwqntB8iJyvQHLuPdpOZS47XeZzWh4XdsQAYamvql36JiEj/UAC0UCIAmoYCoNhLqKUBAL+Ri9d14gEw6oktn2C2KwCKiNiJAqCFcjy+2B8UAMVmEgGwzXly62GZvvhdQ9p1DaCIiJ0oAFooxxOrABqGSUcomOLeiJy4aGsswLW7Tuw2cElZgwFwBRQARUTsRAHQQskKINAaCqSwJyInJ9p2EICQ5+QCoCNnCACeoIaARUTsRAHQQjnJSSDQGuxIYU9ETlJ8CNf0DTqpl7nzYgEwK6wAKCJiJwqAFvK63JimAUBrUBVAsQ9noBEAIz6ke6J8+UMByI74re6SiIj0IwVACxmGAWZsBqUqgGIn7mAjAM6ckwuAWYOKAcg1WyCqBdBFROxCAdBihhm7i0KbrgEUG/GFYhU8T97JBcDcwlgF0EkUOhqt7paIiPQTBUDLKQCKzURC+KKtAPgKik/qpYV5ObSYsclPwfhSMiIiMvApAFpMFUCxnY7DEzhy84ec1EvzfW4aid0NpPngfku7JSIi/UcB0GIGsfuotocVAMUm4jOA/WY2g/KyT+qlDodBsxFbPLr5UJ3lXRMRkf6hAGgxR3wIuEMVQLGL+BqAjWYOg3M8J/3yxOLRbU0HLO2WiIj0HwVAizmMWABsD+tOIGIPkdZYcDtIHoOy3Sf9+kB88eigv97SfomISP9RALSYIzEErAqg2ETHwRoADpiDKMw++QpgxFsY+6pJICIitqEAaLFEBTAQUQVQ7KGjsRaAJmchbufJ/5NgZscmjhhtqgCKiNiFAqDFnEasgtKhSSBiExF/LAC2uk5uDcCk3BIA3B26BlBExC4UAC3mjgfAtpDuBCL2EG2OLd8SzDq5NQAT3AXDAMgOqAIoImIXCoAW8zlzAGgJtaS4JyInxmiNLd9i5vQuAGYNHgFAfljXAIqI2IUCoMWyXLF11FqCrSnuiciJ8XTEgpszr6RXry8sGQnAoGgjZjRiWb9ERKT/KABaLNsVqwC2hRUAxR6yQ7EA6B00rFevHzpsFABuI4JfdwMREbEFBUCL5Xpit8VqVwAUOwi04I22A5A9ZHivduHzZdFIHgAHaqot65qIiPQfBUCL5bpjAbAj0pbinoicgPj1f+2mh8GDCnu9m0ZnbAZxU93HlnRLRET6lwKgxQq8sQAYjCoAig20xAJgvVnA0PysXu+mzVMU+3pwryXdEhGR/qUAaLECX2woLGS2p7gnIscXOrQHgBoGU5Lv7f1+4kvIhJpqLemXiIj0LwVAixXGA2BYAVBswF+7C4D9RjGDc07+NnAJRl4pAI6WGiu6JSIi/UwB0GJFOQUARAwNAcvA116/G4BW3zAMw+j1fpyDRwPga1MAFBGxAwVAi40qiF0LZTpaiUajKe6NyLGZjbEh4HDeiD7tJ7/0NAAGBWswTbPP/RIRkf41IALg0qVLKS8vx+fzUVFRwSuvvHLM9uvWraOiogKfz8dpp53GI4880un5xx57jFmzZlFYWEhhYSGXXHIJr7/+eqc2d999N4ZhdHqUlpb2+VzKC2OL6RpGlL3+Q33en0h/crfEJm04B43q035KRp8BwDDzAPv9ug+2iMhAl/IAuHr1aubPn8+iRYvYvHkzs2bNYvbs2VRXd7+e2M6dO/nc5z7HrFmz2Lx5M9/73vf49re/zdNPP51s89JLL3Hdddfx4osvsnHjRkaPHk1lZSV793aeoThp0iRqamqSj3feeafP55PnzcKMxi6m33VIi+LKwJYbiE3ayC4u69N+PIPHAFBgtLHj43197ZaIiPSzlAfABx54gJtuuombb76ZCRMmsGTJEkaNGsWyZcu6bf/II48wevRolixZwoQJE7j55pv56le/yv33359s85vf/IZbbrmFc845h/Hjx/PYY48RjUb561//2mlfLpeL0tLS5KO4uHf3Qj2aMxpbCuZj/wFL9ifSLwIt5EabASgcflrf9uXNpcWRD0Bt9fa+9kxERPpZSgNgMBhk06ZNVFZWdtpeWVnJhg0bun3Nxo0bu7S/7LLLePPNNwmFQt2+pq2tjVAoxODBgztt3759O8OHD6e8vJxrr72WHTt29OFsDnMbsQ/Cfc31luxPpD+YTbFFm5vMbIaX9O4+wEdqzYrdSaR5vzV/j0REpP+kNADW19cTiUQoOerDp6SkhNra7tcTq62t7bZ9OBymvr77wHXHHXcwYsQILrnkkuS2adOmsWLFCl544QUee+wxamtrmTlzJg0NDT32NxAI4Pf7Oz26kxWvhOxv7XlfIqnWuO9DAPaaxYwa3PtFoBMi+bHrCEMNu/q8LxER6V8pHwIGuiw/YZrmMZek6K59d9sB7rvvPlauXMkzzzyDz+dLbp89ezZXX301U6ZM4ZJLLuH5558H4KmnnurxuIsXL6agoCD5GDWq+wvnc1yxpWAa2g/2uC+RVDtU/R4AdZ6ReF3OPu/PWzwGAE/zHs0EFhEZ4FIaAIuKinA6nV2qfXV1dV2qfAmlpaXdtne5XAwZMqTT9vvvv58f//jHrF27lrPOOuuYfcnJyWHKlCls397z9UsLFy6kqakp+dizZ0+37fK9gwA41KFZwDJwBes+AKA1d4wl+8sfPh6AEZF9HGjWTGARkYEspQHQ4/FQUVFBVVVVp+1VVVXMnDmz29fMmDGjS/u1a9cydepU3G53ctvPfvYzfvSjH/HnP/+ZqVOnHrcvgUCAbdu2MWzYsB7beL1e8vPzOz26M8QXu9bQH1IAlIHL3Ri7Vs8oOt2a/ZWcCcBYYx/v72+2ZJ8iItI/Uj4EvGDBAh5//HGeeOIJtm3bxm233UZ1dTXz5s0DYlW3G264Idl+3rx57N69mwULFrBt2zaeeOIJli9fzu23355sc9999/H973+fJ554gjFjxlBbW0ttbS0tLS3JNrfffjvr1q1j586dvPbaa1xzzTX4/X5uvPHGPp/TsNxY9bI5pGsAZeAa1Ba7C0jOsPHW7LBoHACjjDrerdYMeBGRgcyV6g7MmTOHhoYG7rnnHmpqapg8eTJr1qyhrCy2LllNTU2nNQHLy8tZs2YNt912Gw8//DDDhw/noYce4uqrr062Wbp0KcFgkGuuuabTse666y7uvvtuAD7++GOuu+466uvrKS4uZvr06bz66qvJ4/bFmIJYFbHDVAVQBiYz0MyQaGzS1NAxk6zZae5QAq5cvOEW9n20FS6eaM1+RUTEcikPgAC33HILt9xyS7fPPfnkk122XXTRRfzjH//ocX+7du067jFXrVp1ot07aeOKRgIQcTQSjUZxOFJeaBXppG73NkqAg2YeY0aNtGanhkF40Fi89W/RUfvP407mEhGR1FEy6Qfji2MfqIYjxF6/ZgLLwLP3/U0A1LhHk+Xp+wzgBN+wCQCUBHaz52C7ZfsVERFrKQD2g0FZORDJBmDbgY9T3BuRrjr2bAGgpXCCpft1lsT2N96xh407tBC6iMhApQDYT1zmIAA+Orj32A1FUiDn0DYAPCPPtnbHw2L7m2Ts5C/b6qzdt4iIWEYBsJ9kO2NrEu5sVACUgaW1I8So4EcADDvzfGt3Hg+A5Y79bNleTUcoYu3+RUTEEgqA/WSoL3Yd4I6mnSnuiUhnW7ZtY7DRQhgHpWPPtXbn2YMxC2K/++XhHWz4SMPAIiIDkQJgPxk7qByA2rbq47QUObX2vvt3AOq9Y8DtO3bjXjCGnQPAFIeGgUVEBioFwH4yZegZADRH9qW4JyKdOT5+DYDAsOPfIadXhp8DwDmOD/nrtv1Eo7ovsIjIQKMA2E+mj4rNhow4G2jqaEtxb0Ri9hxso7z9XQAGT5jVPwcZPQOAac732e/v4G//VBVQRGSgUQDsJ2cMGQaRbAzD5K8fvZ3q7ogA8KfNu5hsxK5LzTvjk/1zkBEV4HAzlEOMNup4fP2O/jmOiIj0mgJgP3E4HBQ4TgfgbztfS3FvRMA0Tf656UW8Rph2zxAoLO+fA7mzYMR5AEx3vs+rOw7y7t6m/jmWiIj0igJgPzpz0BQAth58K8U9EYE3dx/iNH/sPyOu0z8F/XmbtrKZAHyp8EMAlr30Uf8dS0RETpoCYD/6VNkFANSH36M1GEhxbyTT/fa1ai5yxP4z4j6zsn8PdkZs/+cG38RJhOffqeG9ff7+PaaIiJwwBcB+dM3kT0AkF5ytPPbmn1PdHclgh1qDvPrONqY4dsU2jP1M/x5w5AWQVYgr0Mg3T4/dD/v/+++3tDC0iMgAoQDYj7LcXsblXAjA77f/PrWdkYz2+PodfNp8AwBz+LmQO7R/D+h0wemXAvD10g8ozHazdZ+f/++/36Y9qBAoIpJqCoD97BsV1wJQb27izx9sTnFvJBM1tAT49d93cYVjIwDGxKtOzYHHXQZA7kdrWDLnHAwD/vjWPr765BuqBIqIpJgCYD+rPP1cio3zMQyTe/5+H6apRXHl1PrF3z4kJ1jPNOe22IZJXzg1Bz5zNnhy4dBOLvJ9yLJ/qSDH42TjjgauXraBprbQqemHiIh0oQB4Ciz+9HcxTSfNjndZ9tqfUt0dySAvf3CAJzfsYo7zJRyYMGoaFJadmoN7cmDSVbE/b/4Nn51cypNfvYAhOR627vPztf98k9ZA+NT0RUREOlEAPAWmjTqT8dmx4bDHtj5EIKTKh/S/Q61Bbv+vt3AS4WvZ62Ibp950ajtxzr/Evm59FtobOX/MYH7ztWnkeV28vvMg1zyykb2N7ae2TyIiogB4qjxQeTtEsgi79nLtf99JMKzKh/Sf+pYA//L4a9Q1B7h+0FYKQnWQPQQmXnlqOzJ6BhSPh1ArvPkEAONL83nqpgsoyvWwrcbPlb9cz6bdB09tv0REMpxh6qK0XvP7/RQUFNDU1ER+fv5x29/94lM8XX0/AO5wGd+dupA5Z3+iv7s5oPg7Qrz8QS3Pv/8GHeEAbocbt9NNrieHKyaczSfPKE51F20vHInypV9tZHN1I8U5bl4ZdBe+hvdg1nfg4h+c+g5tWQm/nwc5Q2H+27E7hQB7G9u5+ak32Vbjx2HA+WMGUzmplNOKcph22mCyPa5T31cRyQgn+/mdjhQA+6A3v0A/fPFJ/nvXQ+AIYZoOTvfO5s5Z36BiZD/dlmuAaGoLcd/fXuL3u36Nkf0BhrPrwtjRQBFjHF/il1fdSHlRTgp6aX+NbUG+vWoLL39wgDyfi79cdpCSF+aBJy8WvrIHn/pORULw0LnQtAcu+SF8cn7yqdZAmO8+/Tb/83ZNp5dke5x8ZvxQPnF6EWeW5jFmSA6DczynuOMikq4UABUA+6S3v0Dv7N/Jd/7yY2rCrwJgRrL42pl3cusnruivrqZMMBzlubc/YvGrPyWUc/ieyG4jhyxHHu1RP27DR0e0mSixayMjLRP4wuhbuOPST5Dnc6eq67azrcbPN/5zE9UH2/C6HPzyS+O59MUroXE3XHQHfHph6jq3+Tfw3C2xIPrtf3RZh3DPwTZe2FrLho8a2F7XzJ6Dna8L9DgdTDttMGePHETZkGymjCzgtKJcnA6DxrYgUROKcj0Y/Xl7OxFJGwqACoB90tdfoF+++izL33uYsHM/AMMcn+a70+dx8RkTre5qv4tETV7+8GNWv/MyYBCMBPEHmtnu30IkewuGIwjAhPwZ3PnJ/2BS0SQcxuFLUFtDrfz01V/w7EerwIhgRt1E/Rdw8Ygvcv15FZw7uhCPS5esdudga5BfrfuIx9fvJBI1GTU4i19dP5WJW38Of18C+SPgm6+BNy91nYxG4fHPwL7NMPEq+NKTPd6L2DRN3th1iL/+cz+vfFDPezUndgu5ITkeJo0oYMyQbCYOy6ck30dBtptcr4sstxOnw8DlMIiYJv72MKFIFACf28HowTnsa2ynsT1EYbYbl9PBkBwPXpeDcNRkv78Dh2HQ3BEmHI2S63XhdTnxuhwUZLlxOIzkjOYstxPDQGFUZABTAFQA7BMrfoH8HW189Y8/4P22FwAwTYNzc6/jkSu+Q453YA55RaMmhhG7huuVHbv5/T+r2Nb0BlHfPzGcHd2+psA1kp9cdBefHDn9mPve0biD7/ztLj5s3pLcFmkbjSMwjs+MuJxrzzuH6eVDcDgy+8M1GI7y0vt1PLdlHy9srSUcjf01vnRiCfddfRaFda/Biv8FZhSuXQnjP5fiHgN7/wHLL4VoGK5aBud85YRf+vbHjWzafYi39jSyr7GDd/Y20X4KFpP2uBwEw9EjtkTA2QGmM7kl35uLx+Wgob0OjAiYDlwOg3xfDnmebEYW5pPlduFyGLidDpwOgxyvk9OKchk+yMfgHC+DczwMzfeS5XbichgKjyL9TAFQAbBPrPwFWvX2iyzd8iiHzHcBMELFnFs4mxF5pVwxbhbTy8pS8qFgmibv7D3Ilpo9PL/9JbY3vU0HDWA6MNwHcXg6z9504KHANQyH4STLmcPIvJF8/dwvM7W04oT7HzWjvFT9Ek+8vZq3Dm4EDv+KhltPw91xDlNLZvDVC6Yyc2xmhcHapg4e+tt2nn+7hqb2w8sJlRfl8L3PTeDSiSXQ9DE89hlo2Q9nfwW+sCyFPT7KKz+Hv94D7mz4tzUw/Nxe7SYUidIWiGBiJkPV+7XNvPVxI5urG6lt6uBga5CapnaaA2F8LoNINEqIFpyeFlzuJrJzGjGdfjoCHsJhN+6s/TjdTURNA5Mo0agTTBeGqxmHuwGMCA5XW5e+mBEfYHZ7XWvieTMZGA0gCqabaHAwZjgfM5qFGcnCDOeA6SLXPYhpw6aR7XZT11ZPa6iF0txi8rxZjCsqYcSgLMqLcxgxKEuXSIj0kgKgAmCfWP0LZJomP3jxcX6/+3FwdP6g8YbO5PS8czhj8FgKvLmEo1FqWg7QHmpndMEIWoPtHOpowmE4cDvchKIRmoPNmKZJW7gNMOgIt9MeaWOQZzARM0q2K5fJRWdS4Msj2+0jz5PL7qZa1uz4M63hRsJmiLDZQdT7YXIItzuDnGV8csRFXD3hYs4ZehYuh3WzN2tba6na9Tf+893fUdPxUafnwi3j8AXO5/Kxl/Kl88Zy1siCtKycNLQE+PtHDWzadZCVr+8hGB+6HJrn5X+dPZyrzh3B5BEFscatDfDrz0L9B1A8Ab7219iCzANFNAK/uQY++ltsVvBNL8Dg0475kpZgCyYmPqePxkAjHxz6AMMwqGur44NDH7Bx30ZqWmvwOr3kuHNwGk5y3blEidISbKE93E5DRwNRM3rM41gh25VNKBoCDELRnv/O9JYZ8RENFRANDcEMFeAwswCDXHchpdnDOX3QGCaVlFE+pACHYeBxOXA7HYwZkk1xnjct/35YwTRNXtu9h9Xv/o09zXsoLxjDv19wOacVpWDSlJwSCoAKgH3SX79ATR0t/Gjdr/l77V9pi9YRdTRbtu9eMx3kOodxQcknOaNwFE6Hk3FDRjOpeBwl2SWn5IOlpqWGZ7c/x992r+f9prcOdy3iJdw8mTHuz/KJUVM4Z3QhE4fnUz4kZ8BXB03TZFdDG1v2HGJbTTM7DrTQHorQEYoSDEepaeqgvqVzZemskQV897PjmX7aEJxHnl/TXvjNl6Bua+y6v6++AINGneIzOgEdfvj152D/O5BbCnOfhZLYda97W/by0p6X2O3fTU1rDfta9vFR40dETOuGe/M8eRRlFTGucBzFWcU0dDTQEmxh/ODxFGUV4XK4cBpOOiIdhCIhirKLGOwbTKG3kEHeQQzOGoxB7OcejATZ0bQDn8vH8Jzh5Hpyk8cJRUO0h9vZ17IPAwOXw0UwEsRhOGgPt/Nxy8ccbD9Ic6gZf8BPbesBWoPt7PLvZn/7HgDchheH4SQQ7Vp57IkZdWJG4td7mk5M04EZGowrUkqeu5Ai31BG54+krGA4pw8ZRkl+NiX5PsoGZ+NyZtZ1ttGoyZL1L/Cb939NwP1PDOPwfxLMcA6Vpf/O/7n0X8jSkkRpRwFQAbBPTsUvkGmavFv3EY/94/d8cOifNAT3EjKbcRu5ZDsLiZoh2qN+vI5cvA4fbZFmDMDjyCbXXUDUjOB2uPE6vXhdPnLdORxoO4Db6aYxcJD64B6iZpAIQaJGG5guxuZM46ziSfhcHrLcPmaOmsLU0rNxOpzH7e+psse/h/+3bSVVu/7GgY69ye1mOJtI+2giHSNxhcoYmjWSc0rH8r/OGc4ZQ/NoCYRpag/hdhqUFmRRkuelPRShJRAmy+0kz+fuHKosZpomH+xvYcNH9fx1Wx1b9zVx6ATuiTu+NI9zRg3iM+OHcunEbgJ39Wvw3/8G/r2QWwI3/hGKz+yns+ibjnAHdQe2cuC5f2d3y8d0uLPwT7qClzpq2dqw9bivL80pJc+TR4GngHGF4xg/eDxTiqYQMSP4g34a2hsAyHJlETEjuBwuRueNJtudzRDfEByGY8BXwg52HExWNCEWNAORAAfaD/Bx88fsa9lHtX8fTR0t7G+tpzXUxoH2AzQE9hI2ux+K7o5pGpiRbMxwHoSKceDFiYtc1xCGZpcypqCM4uxCLj1jCiMLs/E4HeRnuWkLRIiaJjlely0nZx1obmPJhv9hbfVzdHjeTm7PZiRDfWXsbfsnIUfs98gIDqdi8GdZeOH1jCvWOqXpQgFQAbBP0u0XKBQJgQFuh32uKzJNkzf3v8kTb/8n62te4sjrBROi4WzC/nOJdAzDMCLgCELUTTQ0mGhwcOx//UYYM5KNzyhgXGkhnzx9CJ8YW8TQfB+Dczy4nQZOh8F+f4DdDa3k+Vy0B6N43Q4mDc8nFDbZ1dDKu/uaeOn9A3ywv5mOUAQDg0HZblxOgxyPiz0H29jX1HmijMflYMqIAs4YmsvkEQXkel343LGwXZzn5fShuRRk9fCehNph/f+Fl+8HMwJF4+D6p2HQaIt/0n3XEmzhiXefYNX7q2gOdl/VduCgorSCyUWTGeQdxKi8UZTnlzM0ZyjhaJhsVzZep4Yye2KaJjubdlLdXM0Q3xDCZphgJMhHh3axufaffNxcQ11bLS3hRtqjhzA5sWFxM5xNNJwHpgsz6o1dEmJEYn82vbjIwuPIIsc1CJ8zm2xXDoN9hQzNHsLkkrFcNv5MinK9JD5uTuX7Z5omHaEof/vwA/7ng5d5u+FNmtiK4WqOP28wIfdifnjRt5hYPBaAYDjI/LU/55W6/wIjFP8Z5FDkmMrFoz/DlybPYnyJwqCdpdvnd28oAPaBfoEGlvZwO9satrHt4Dbernubd+q3UdP6MWHzxO+9bEZdRAPDCLeeQaTlDKLhfMxQISd910QjFJ8p2vV1WW4nk0bk8ZkJeUwckc2gvHZaw35cDhdRM8rIvJEMyxl27GspoxF47/fwl7uhsTq2bcqX4fKfg2/g/S5+eOhDvrf+e2w7uC25Lc+dx5SiSWQf2k244SNmtXdwcdTLkIsWwrnXJ+8YIv0jEo1wKHCIhvYGalpqeffAh+xvOYjDcLCvZT/7Wvaxv2M3IbOdKCdeVexONDgEI1xIlBBOsnCSExuaNh2YpoGBA7fDhcfpwulw4nN5KPDmkeceRL6ngKLsQobnDaE4t4Bdh/bhcjipbWlgf2s9TcFGmoN+DAw8Tg8GBoeC9QCEogGaInuIOhpxuDsvJ+SI5nLekEv4j/Ov47xh3S+9Vdd6kP/76m94ofpZQo4Dye1m1E2hOZXPn3YFc8/9NMMLcrt9vQxc+vxWAOwT/QINfKFIiBf3vMjrta+zo3EHOe4cstxZtIfb2dm4kwPt9QQjAfK9+TQF/ETMrvdoNiMezEgeZsSH4YjidDdD1IvDcGBGsuhoGYEZySbLFyAnx0/ItYuOaOwDKcedz1DfKPLdhfiMQnxuNy3mHj5s/IDGQGOP/XYaTs4oPIOJQyZSml2Kw3AwLHcYB/0fs3P3Ogr3b2Nw60EGRaOc6R7EGZ+5B8eUa/rxJ9k7B9oO8Ku3f8Uz258hFA2R687l9qm387nTPofL4Tpcbd61Hp6/HQ7EA2LOUJj2jdhSMfnDU3cCQjAS5MPGD2nsaKQt3EFjeys5Hh/Zbh+H2ls41N5MU6CF+rZG6tsO0hpqoznYTHOoicZQLUGzEYwB8DFjGuQ7ypk8uILLz7iQz54+E4/zxJbaCoQDPPf+yzz9zz/zgf8Nwo5Dh3cb8ZAVHUeeq4hB3sFMKhrPtOGTufiMCTgdDlsOkWcCfX4rAPaJfoHSg2maGIaBaZq81/Ae2xu38/e9f+fN/W/iD/gJ9sNsziMN9g1mkHcQUTOKYRjsbd570scc7BvMhCETOL3gdMYOGssg7yCG5w5nXOG4lA2X/nX3X1n090W0hloBuGjkRdxxwR2MzBvZ/QsiIdj0JPz9wdht4wAMB5z2KZhwBZxRCQU9vFYGLH/Qzxv73mJ3437cTid1rYeIRMNEiWASxSRCJBqhIxyiPRQiFInQHGjHH2ymNdxEe6SZ9kgzQbOFqNGGy4zNeHcbOeS7ish155PnySdqRglEAoSjYXI9eRR48vG5fJQPGsF5w8YxaehYCrwFfT4f0zT5y47XeeQfK/mw5Q2iju4XKjcjWZimE1d0CLnOoRR5h5Hr6bwYe1HWEM4YXMalp1dQlJ1Lns+N22kk/z0CCEdNrQ3ZD/T5rQDYJ/oFSn/haJjq5mqaAk00djTicrgYmj0Uf3zIqaa1hldrXsVhOCjOKqY4u5jxg8czKi82+7aurY7q5moOth+kvr2etnAbZxaeyemDTqesoIw8d17nf9hNk2jTHup2vsjfd/+Fuobt1LbvJwzsdbnIMU3GuPMJFJ9Jfe4QmkKtvNfwXnypn67GFoxlxvAZXDv+Wsryy076/A92HGTxa4uZOGQi/zrpX0/oQygYCXLfG/ex+v3VAJxZeCa3n38700qnndiHWDgI7z4N/1gB1Rs6Pzd0IoyeASPPjz2GjO3xjiKSfkKREG7nwLlGOWpG2bDnLf74wXqaAy3UtNawt+1D2tkXWxT8JJimAVEvpunCMD2YhGNzzR0hiHpxmrl4jHzcDh85rkEMyxnOhaMuYPSgEiJmlHU7N7Hb/zEHAwfIduWS5crCwMCMXxed7comz5PLqIJSJhSVMa5oBCV5BbQFg1Q3HiBqmnx0cB9R06QouyA+8ShMIBzCH2jF7XQypmAYY4cMY9SgghOeMR6Nmhxq72BQlq9fJ9idLH1+D5AAuHTpUn72s59RU1PDpEmTWLJkCbNmzeqx/bp161iwYAFbt25l+PDh/O///b+ZN29epzZPP/00d955Jx999BFjx47l//yf/8MXvvCFPh33aPoFkl4LtYN/HxzaCfUfxtbtq/8ADrwPrXVd2w+dBGdcApOvgdIpnUJPKBJia8NWtjdu56PGj/jw0Id82PghTYEmwvEhbZ/TxxfO+AJfHvdlTi88/YS7ee+r9yaD3I8/+WOuGHvs+1XvbdnLd176TnI27/UTrmfB1AW9n1jU8BFsfQa2V8HHb8TubHIkTx4Uj4Pi8bFZz0POiFUJC0ZCVqHCoaRES6CVTbX/xGW42HpgJ9sbdlPd/DEd4cP3uI6YYQ4F6miN1hFxNKWkn6bp6LT0zQm/LuIB043DzMFNHg7DRcSMjVq4jCzy3UVEzDD+cC0B6jBcLZgRL4aZhcPMwokXl+FjqG80nzvtUuZNq8ThOLVD5fr8HgABcPXq1cydO5elS5fyiU98gl/96lc8/vjjvPfee4we3XUm486dO5k8eTJf+9rX+MY3vsHf//53brnlFlauXMnVV18NwMaNG5k1axY/+tGP+MIXvsCzzz7LD37wA9avX8+0adN6ddzu6BdIkiJh6GiEtoPQfgja418T37fVxwKff19sqZb2Qz3vy3BCySQYUQEjp8Jpn4aCESfdpaZAE3/a+See3v40/zz4z+T2S0Zfwo9n/Zgs17EnWbSH27lo9UW0xz+0RuSO4I9X/bHHCkx7uJ0b/nQD/zz4T7JcWdx/0f1cOPLCk+53j9oOws518PGbsTC4bwtEjjE5wZ0T+7nlj4CcYsgeAjlDILso/uci8A2K3SM58RhASx1JZjBNE3/QT1uog7qWRtpDQRo7Wsj1ZtEeClKYlUtTRxt7/QfY13yApkArda317Gr+kPrQ9tgEHcMki2GU+srJ9w6iI9xOKBrEhGQVMBgJ0BFupTlSR5BD4Oj6d8cRzQMMogQwcAJOHDhx4MUkQhh/bBUFi412VfKHa3+G8xSuQ6nP7wEQAKdNm8Z5553HsmWHb1c1YcIErrrqKhYvXtyl/Xe/+13+8Ic/sG3b4dmE8+bN46233mLjxo0AzJkzB7/fz5/+9Kdkm89+9rMUFhaycuXKXh23O/oFShHTjM2CNSOxr9Fw/M/Rw9vM+PZIGCLBzo9wIHa9WST+NRzopk38a6gdgi0QaoNg6+HH0d8fK4j0xJ0dW65lyOmx5VuKzoh9HToRPNkW/rhM1u9dz+/e/x3r964nbIY5d+i53HfhfZTmlPb4ur9V/41bX7yVQm8hToeT+vZ67px+J18+88vdHuP7f/8+f/joDxR6C/n1Z3/N2EFjLTuHboWDcPAjOPBPOPAB1L8fqxj690LrgeO/vjvu7FgQ9OQeDoUuH7i8sVnJLi+4snr+3umNhUinGxxucLpiXx2u+DbX4eccrsPPJ55LPAxHbD+GI/5QJVOs1djhxx9owetyU5Q1GBPzuHdxMk2TlmArOw7W0BLqYK+/nprmekLRCF6nG6fDycF2Pzsbd+Nz+RhbWMak4nIml5RR23KIA61N1LfFjlvf1sgbNf9gZ+AlDMPkk4U3s+x/3XqKzl6f3wApXd48GAyyadMm7rjjjk7bKysr2bBhQ7ev2bhxI5WVlZ22XXbZZSxfvpxQKITb7Wbjxo3cdtttXdosWbKk18c9ltYXH8SZ440FE8zY1+SfObwNMzaEdWS7o7fR3T6Os63Lfo84phntZh9Hb+MY+++pb0fug27ad7ftiNea0c5BLXrENo4Mdol20cPbulnrb8Dw5YOvMDb8mDUo/rUQsgZDXinkDYs98oeBr6D7D/aQCfGJE1Y5r/A8zpt+Hpv3b+Y7L32HTXs28ZVnv8KvP/trirKKun3Nn97/E9FAlEvHXEpxVjG/2PIL/vz+n7l85OVd2j6z/Rl+/97vcRgO7p11L6XuUlpbrT2HbuWMjj3GdP43ITbEXhMLg837YtXD1gZob4C2Q9DWEKvKBpoh0HI4wAdb4VT0+6QZR4VCI1YpNhzgcBwRFONLDzmc8TZHPNcpUCZCpdHN1yMCZ7dtetp+xKPHfR/9ek6gfXfHOfxj6fJzSv7R6H77sZ7r8vfxBPbX7304gdd0+f745+QGhsSf64hvDxznNQAOwyBxEck53XcytnPaoHFb7LEdBgHjj973oCIe+PgMVpn/5JWaR7nml//DsutXk+32drtnK52Sf58GuJQGwPr6eiKRCCUlJZ22l5SUUFtb2+1ramtru20fDoepr69n2LBhPbZJ7LM3xwUIBAIEAocrPX5/bPbX8Kt+cJwzlczRDOw9bquB4D3eYwxjjtvuBxz+/X6P9/g1vz5m+4u4qK9dE5EMtJX3ePo/hqS6GxljQCxQdPTMwMSyHCfT/ujtJ7LPkz3u4sWLKSgoSD5GjRqA91kVEREROY6UVgCLiopwOp1dqm51dXVdqnMJpaWl3bZ3uVwMGTLkmG0S++zNcQEWLlzIggULkt/7/X5GjRrFvn37MvYaArGvrfVb+Y+//gct4RZunnIzXz/r68nn7nv9Pv57+3/zxdO/yB3TYpdK/PT1n/L09qc5q/gsHrnkEQwMfrjxh/x5158p9hXzn5f/J4N9g1N1OiIiJ8zv9zN8eGYvMp/SAOjxeKioqKCqqqrTEi1VVVVceeWV3b5mxowZ/PGPf+y0be3atUydOhW3251sU1VV1ek6wLVr1zJz5sxeHxfA6/Xi9Xa9NiEnJ4ecnJwTOGORgeOCnAu461N38d1XvsuT25/knBHn8OnRn8Yf9PPnfX/G4XVw6bhLk7/b3zj/G7yw7wXe9b/L91//PsFokA01G3D5XPys8meMGqKKuIjYQyRycus0pqOUBkCABQsWMHfuXKZOncqMGTN49NFHqa6uTq7rt3DhQvbu3cuKFSuA2IzfX/7ylyxYsICvfe1rbNy4keXLlydn9wLceuutXHjhhfz0pz/lyiuv5LnnnuMvf/kL69evP+HjimSC2eWzWb93PX/c8UduffFWvnvBd9nftp+2cBunDzqdT474ZLLtiNwR3PvJe/nOS9/hpY9fAsDtcPPjT/6Y80vPT9EZiIhIb6Q8AM6ZM4eGhgbuueceampqmDx5MmvWrKGsLHbXgpqaGqqrq5Pty8vLWbNmDbfddhsPP/www4cP56GHHkquAQgwc+ZMVq1axfe//33uvPNOxo4dy+rVq5NrAJ7IcUUygWEY3D3zbtrCbfy1+q/85PWfJJ+bO3EuDqPzZcKXll3Kwxc/zIP/eJBB3kH82+R/4xMjPnGquy0iIn2U8nUA7UzrCEm6aAu18X83/V+e2f4MUTPKv03+N7517re6BEARkXSgz28FwD7RL5CkmwNtBwhFQwzPzeyLo0UkvenzewAMAYvIwFGcXZzqLoiIyCmg8R0RERGRDKMAKCIiIpJhFABFREREMowCoIiIiEiGUQAUERERyTAKgCIiIiIZRgFQREREJMMoAIqIiIhkGC0E3QeJm6j4/f4U90REREROVOJzO5NvhqYA2AcNDQ0AjBo1KsU9ERERkZPV0NBAQUFBqruREgqAfTB48GAAqqurM+oXyO/3M2rUKPbs2ZNR91DUeeu8M4HOW+edCZqamhg9enTyczwTKQD2gcMRu4SyoKAgo/7iJOTn5+u8M4jOO7PovDNLpp534nM8E2XumYuIiIhkKAVAERERkQyjANgHXq+Xu+66C6/Xm+qunFI6b513JtB567wzgc47s877SIaZyXOgRURERDKQKoAiIiIiGUYBUERERCTDKACKiIiIZBgFQBEREZEMowDYS0uXLqW8vByfz0dFRQWvvPJKqrvU7+6++24Mw+j0KC0tTXW3LPfyyy9zxRVXMHz4cAzD4Pe//32n503T5O6772b48OFkZWXxqU99iq1bt6amsxY63nn/67/+a5f3f/r06anprEUWL17M+eefT15eHkOHDuWqq67i/fff79QmHd/vEznvdHy/ly1bxllnnZVc9HjGjBn86U9/Sj6fju81HP+80/G97s7ixYsxDIP58+cnt6Xre34iFAB7YfXq1cyfP59FixaxefNmZs2axezZs6murk511/rdpEmTqKmpST7eeeedVHfJcq2trZx99tn88pe/7Pb5++67jwceeIBf/vKXvPHGG5SWlnLppZfS3Nx8intqreOdN8BnP/vZTu//mjVrTmEPrbdu3Tq++c1v8uqrr1JVVUU4HKayspLW1tZkm3R8v0/kvCH93u+RI0fyk5/8hDfffJM333yTz3zmM1x55ZXJD/x0fK/h+OcN6fdeH+2NN97g0Ucf5ayzzuq0PV3f8xNiykm74IILzHnz5nXaNn78ePOOO+5IUY9Ojbvuuss8++yzU92NUwown3322eT30WjULC0tNX/yk58kt3V0dJgFBQXmI488koIe9o+jz9s0TfPGG280r7zyypT051Spq6szAXPdunWmaWbO+330eZtmZrzfpmmahYWF5uOPP54x73VC4rxNM/3f6+bmZvOMM84wq6qqzIsuusi89dZbTdPMnL/fPVEF8CQFg0E2bdpEZWVlp+2VlZVs2LAhRb06dbZv387w4cMpLy/n2muvZceOHanu0im1c+dOamtrO73/Xq+Xiy66KCPe/5deeomhQ4cybtw4vva1r1FXV5fqLlmqqakJIHmD+Ex5v48+74R0fr8jkQirVq2itbWVGTNmZMx7ffR5J6Tze/3Nb36Tyy+/nEsuuaTT9kx5z3viSnUH7Ka+vp5IJEJJSUmn7SUlJdTW1qaoV6fGtGnTWLFiBePGjWP//v3ce++9zJw5k61btzJkyJBUd++USLzH3b3/u3fvTkWXTpnZs2fzpS99ibKyMnbu3Mmdd97JZz7zGTZt2pQWq+mbpsmCBQv45Cc/yeTJk4HMeL+7O29I3/f7nXfeYcaMGXR0dJCbm8uzzz7LxIkTkx/46fpe93TekL7vNcCqVav4xz/+wRtvvNHluUz4+30sCoC9ZBhGp+9N0+yyLd3Mnj07+ecpU6YwY8YMxo4dy1NPPcWCBQtS2LNTLxPf/zlz5iT/PHnyZKZOnUpZWRnPP/88X/ziF1PYM2t861vf4u2332b9+vVdnkvn97un807X9/vMM89ky5YtNDY28vTTT3PjjTeybt265PPp+l73dN4TJ05M2/d6z5493Hrrraxduxafz9dju3R9z49HQ8AnqaioCKfT2aXaV1dX1+V/EekuJyeHKVOmsH379lR35ZRJzHrW+w/Dhg2jrKwsLd7///iP/+APf/gDL774IiNHjkxuT/f3u6fz7k66vN8ej4fTTz+dqVOnsnjxYs4++2wefPDBtH+vezrv7qTLe71p0ybq6uqoqKjA5XLhcrlYt24dDz30EC6XK/m+put7fjwKgCfJ4/FQUVFBVVVVp+1VVVXMnDkzRb1KjUAgwLZt2xg2bFiqu3LKlJeXU1pa2un9DwaDrFu3LuPe/4aGBvbs2WPr9980Tb71rW/xzDPP8Le//Y3y8vJOz6fr+3288+5OOrzf3TFNk0AgkLbvdU8S592ddHmvL774Yt555x22bNmSfEydOpV/+Zd/YcuWLZx22mkZ9Z53kaLJJ7a2atUq0+12m8uXLzffe+89c/78+WZOTo65a9euVHetX33nO98xX3rpJXPHjh3mq6++an7+85838/Ly0u68m5ubzc2bN5ubN282AfOBBx4wN2/ebO7evds0TdP8yU9+YhYUFJjPPPOM+c4775jXXXedOWzYMNPv96e4531zrPNubm42v/Od75gbNmwwd+7cab744ovmjBkzzBEjRtj6vP/93//dLCgoMF966SWzpqYm+Whra0u2Scf3+3jnna7v98KFC82XX37Z3Llzp/n222+b3/ve90yHw2GuXbvWNM30fK9N89jnna7vdU+OnAVsmun7np8IBcBeevjhh82ysjLT4/GY5513XqflE9LVnDlzzGHDhplut9scPny4+cUvftHcunVrqrtluRdffNEEujxuvPFG0zRjSwfcddddZmlpqen1es0LL7zQfOedd1LbaQsc67zb2trMyspKs7i42HS73ebo0aPNG2+80ayurk51t/uku/MFzF//+tfJNun4fh/vvNP1/f7qV7+a/He7uLjYvPjii5PhzzTT8702zWOfd7q+1z05OgCm63t+IgzTNM1TV28UERERkVTTNYAiIiIiGUYBUERERCTDKACKiIiIZBgFQBEREZEMowAoIiIikmEUAEVEREQyjAKgiIiISIZRABQRERHJMAqAIiIiIhlGAVBEREQkwygAioiIiGQYBUARERGRDKMAKCIiIpJhFABFREREMowCoIiIiEiGUQAUERERyTAKgCIiIiIZRgFQREREJMMoAIqIiIhkGAVAERERkQyjACgiIiKSYRQARURERDKMAqCIiIhIhlEAFBEREckwCoAiIiIiGUYBUERERCTDKACKiIiIZBgFQBEREZEMowAoIiIikmEUAEVEREQyjAKgiIiISIb5/wEWH9l1/Rq1QQAAAABJRU5ErkJggg==",
      "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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' 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": [
    "from scipy.optimize import leastsq\n",
    "\n",
    "def Drude(E,Ep,Ew):\n",
    "    eps = 1 - Ep**2/(E**2+Ew**2) +1j* Ew* Ep**2/E/(E**2+Ew**2)\n",
    "    elf = (-1/eps).imag\n",
    "    return eps,elf\n",
    "\n",
    "def errfDrude(p, y, x):\n",
    "    eps,elf = Drude(x,p[0],p[1])\n",
    "    err = y - p[2]*elf\n",
    "    #print (p,sum(np.abs(err)))\n",
    "    return np.abs(err)#/np.sqrt(y)\n",
    "\n",
    "\n",
    "pin2 = np.array([15,1,.7])\n",
    "E = energy_scale\n",
    "startFit =np.argmin(abs(energy_scale-13))\n",
    "endFit = np.argmin(abs(energy_scale-18))\n",
    "    \n",
    "p2, lsq = leastsq(errfDrude, pin2, args=(ssd_low_loss[startFit:endFit], energy_scale[startFit:endFit]), maxfev=2000)\n",
    "\n",
    "eps, elf =Drude(energy_scale,p2[0],p2[1])\n",
    "drudePSD = p2[2]* elf\n",
    "plt.figure()\n",
    "\n",
    "plt.plot(energy_scale,eels_dataset)\n",
    "plt.plot(energy_scale,drudePSD)\n",
    "plt.plot(energy_scale,eels_dataset-drudePSD)\n",
    "plt.axhline(0, color='black')\n",
    "\n",
    "plt.gca().set_xlim(0,40)\n",
    "plt.gca().set_ylim(-0.01,0.2)\n",
    "print(f\"Drude Theory with Plamson Energy: {p2[0]:2f} eV and plasmon Width {p2[1]:.2f} eV\") \n",
    "print(f\"Max of Plasmon at {energy_scale[drudePSD.argmax(0)]:.2f} eV\")\n",
    "print(f\"Amplitude of  {p2[2]:.2f} was deteremined by fit \")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hideCode": false,
    "hideOutput": true,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\gduscher\\AppData\\Local\\Temp\\ipykernel_28844\\467939617.py:1: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`). Consider using `matplotlib.pyplot.close()`.\n",
      "  plt.figure()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74356cbbff56454bb8450431c1767ce8",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
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       "\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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' 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": [
    "plt.figure()\n",
    "plt.title ('Drude Fit: Dielectric Function - Permittivity')\n",
    "plt.plot(energy_scale,eps.real,label = 'Re($\\epsilon)$')\n",
    "plt.plot(energy_scale,eps.imag,label = 'Im($\\epsilon)$')\n",
    "plt.plot(energy_scale,drudePSD,label = 'loss-function$_{Drude}$')\n",
    "plt.plot(energy_scale,eels_dataset,label = 'loss-function$_{exp}$')\n",
    "plt.axhline(0, color='black')\n",
    "\n",
    "plt.gca().set_xlim(0,40)\n",
    "plt.gca().set_ylim(-2.5,5.3)\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plasmon Frequency and Phase Identification\n",
    "\n",
    "\n",
    "Plasmon peaks occurring in EELS is directly related to valence electron density and can thereby be used as a means for materials characterization and phase identification.  Free-electron metals have very sharp plasmon peaks as compared to semiconductors and insulators with broader peaks, where the valence electrons are no longer free (covalent or ionic bonding).  While many materials properties are a function of valence electron density, knowing the plasmon energy can prove to be a useful tool in identifying micro structures.\n",
    "\n",
    "\n",
    "Microstructural phases are observed by shifts in the plasmon energy. Examples of phase identification are observed easily in alloys and also precipitate structures.  A common textbook example is EELS low loss comparison of diamond and graphite.  The example given in Figure is a line scan showing the variation of plasmon energies with position.  The plasmon energies range from 21 to 23 eV, corresponding to SiC (20.8 eV) and SiN3 (22.5 eV) respectively.   Figure \\ref{plasmon-ls2}  is a reconstructed map of the plasmon energies.  Blue regions correspond to SiC, while the red regions correspond to SiN3.  \n",
    "    \n",
    "    \n",
    "Appendix C in Egerton's Electron Energy Loss Spectroscopy in the Electron Microscope lists plasmon energies of some elements and compounds [Egerton-1999]."
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    "## Surface Plasmon\n",
    "\n",
    "Spectra from thin specimen show the excitations of the surface plasmons on each side of the specimen. For any normal specimen these surface plasmons do interact, but this is not true for extremely thick specimen ($>> 10$nm).\n",
    "The surface plasmon frequency $\\omega_S$ for thin specimen  is related to the bulk plasmon frequency $\\omega_P$ by Ritchie [Ritchie-PR1957]:  \n",
    "$$\n",
    "\\omega_S=\\omega_P\\left[  \\frac{1\\pm \\exp(-q_st) }{1+\\varepsilon} \\right]^{1/2}\n",
    "$$\n",
    "\n",
    "\n",
    "The symmetric mode, where like charges face one another, corresponds to the higher angular frequency $q_s$. Please note, that this relationship does only apply for large $q_s$\n",
    "\n",
    "The differential probability for surface excitation at both surfaces of a sample with thickness $t$ can be expressed (normal incident, no retardation effects) by:\n",
    "$$\n",
    "\\frac{d^2 P_s}{d\\Omega d E}=\\frac{2\\hbar}{\\pi^2 \\gamma a_0 m_0^2 \\mu^3}\\frac{\\theta}{(\\theta^2+\\theta^2_E)^2} \\Im\\left[  \\frac{(\\varepsilon_a - \\varepsilon_b)^2 } {\\varepsilon_a^2 \\varepsilon_b}\\right]\n",
    "$$\n",
    "with \n",
    "$$\n",
    "R_c = \\frac{\\varepsilon_a \\sin^2(tE/2\\hbar\\mu)}{\\varepsilon_b + \\varepsilon_z }\\tanh (q_s t/2) \n",
    "+ \\frac{\\varepsilon_a \\cos^2(tE/2\\hbar\\mu)}{\\varepsilon_b + \\varepsilon_a} \\coth (q_s t/2) \n",
    "$$\n",
    "and $\\varepsilon_a$ and $\\varepsilon_b$ are the permitivities of the two surfaces.\n",
    "\n",
    "\n",
    "A secondary effect of the surface excitation is the reduced intensity of the bulk plasmon peak. The effect is usually smaller than 1\\%, but can be larger for spectra with small collection angle, because the preferred scattering of surfuce losses into small angles.\n",
    "The correction for surface plasmon will be discussed in the Kramers--Kronig Analysis.\n",
    "\n"
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    "## Summary\n",
    "\n",
    "The beauty of ``Low--Loss spectroscopy`` is its derivation of the dielectric function to high energies without prior knowledge of the composition. The signal is strong and the acquisition time is mostly restricted by the dynamic range of the spectrum.\n",
    "\n",
    "\n",
    "**Think of low-loss spectroscopy as Electrodynamics**\n",
    "\n",
    "The advantages of EELS is the derivation of these values spatially resolved.\n",
    "And from a linescan across an Si/SiO$_2$ interface the dielectric function per pixel can be obtained. From that we can calculate the dielectric polarizability $\\alpha_e (E)$, which may be  a measure of the dielectric strength.\n",
    "\n",
    "\n",
    "We obtain more or less easily:\n",
    "- relative thickness\n",
    "- absolute thickness \n",
    "- inelastic mean free path\n",
    "- plasmon frequency\n",
    "- plasmon width\n",
    "- band gap\n",
    "- dielectric function\n",
    "- reflectivity \n",
    "- absorption\n",
    "- effective number of electrons per atoms \n",
    " \n",
    "\n",
    "\n",
    "The analysis of the optical data requires the exact knowledge of the zero-loss peak. Because of the weighting in the Fourier Analysis, the low energy part contributes heavily to the dielectric function. Therefore, energy resolution is critical for an exact determination of all the optical values from EELS. The new monochromated TEMs are now able to achieve an energy resolution of 10 meV (one is at the oak Ridge National Laboratory), which allows for a sharper zero-loss peak. Such a sharp zero-loss peak will enable us to extract this low energy data more accurately. The dielectric function and the parameters derived from it, can be more precisely determined from such EELS spectra.\n"
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    "## Navigation\n",
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