{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", " **Chapter 2: [Diffraction](CH2_00-Diffraction.ipynb)** \n", "\n", "
\n", "\n", "# Kinematic Scattering Geometry\n", "\n", "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM//main/Diffraction/CH2_06-Kinematic_Scattering_Geometry.ipynb)\n", "\n", "[![OpenInColab](https://colab.research.google.com/assets/colab-badge.svg)](\n", " https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Diffraction/CH2_06-Kinematic_Scattering_Geometry.ipynb)\n", " \n", "part of\n", "\n", " **[MSE672: Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**\n", "\n", "**Spring 2024**\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Gerd Duscher Khalid Hattar
Microscopy Facilities Tennessee Ion Beam Materials Laboratory
Materials Science & Engineering Nuclear Engineering
Institute of Advanced Materials & Manufacturing
The University of Tennessee, Knoxville
\n", "\n", "\n", "Background and methods to analysis and quantification of data acquired with transmission electron microscopes.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Load relevant python packages\n", "### Check Installed Packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "installing pyTEMlib\n", "done\n" ] } ], "source": [ "import sys\n", "import importlib.metadata\n", "def test_package(package_name):\n", " \"\"\"Test if package exists and returns version or -1\"\"\"\n", " try:\n", " version = importlib.metadata.version(package_name)\n", " except importlib.metadata.PackageNotFoundError:\n", " version = '-1'\n", " return version\n", "\n", "if test_package('pyTEMlib') < '0.2024.1.0':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install git+https://github.com/pycroscopy/pyTEMlib.git@main -q --upgrade\n", "\n", "if 'google.colab' in sys.modules:\n", " !{sys.executable} -m pip install numpy==1.24.4\n", "print('done')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load the plotting and figure packages\n", "Import the python packages that we will use:\n", "\n", "Beside the basic numerical (numpy) and plotting (pylab of matplotlib) libraries,\n", "* three dimensional plotting\n", "and some libraries from the book\n", "* kinematic scattering library." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pyTEM version: 0.2024.01.1\n", "notebook version: 2022.01.21\n" ] } ], "source": [ "%matplotlib widget\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " from google.colab import output\n", " output.enable_custom_widget_manager()\n", "\n", "# 3D plotting package \n", "from mpl_toolkits.mplot3d import Axes3D # 3D plotting\n", "from matplotlib import patches\n", "\n", "# additional package \n", "import itertools \n", "import scipy\n", "\n", "# Import libraries from the book\n", "import pyTEMlib\n", "import pyTEMlib.kinematic_scattering as ks # Kinematic sCattering Library\n", " # with Atomic form factors from Kirklands book\n", " \n", "# it is a good idea to show the version numbers at this point for archiving reasons.\n", "__notebook_version__ = '2022.01.21'\n", "print('pyTEM version: ', pyTEMlib.__version__)\n", "print('notebook version: ', __notebook_version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bragg's Law\n", "\n", "$$ \\Large\n", "2d \\sin{\\theta} = n \\lambda\n", "$$\n", "\n", "with:\n", "- d: interplanar spacing\n", "- $\\theta$: Bragg angle\n", "- $\\lambda$: wavelength\n", "\n", "The origin of Bragg's law is most conveniently explained in real space, but we want to understand the Ewald sphere construction, one of the most omportant concepts in diffraction.\n", "\n", "real space | reciprocal space | wave vectors | shifted wave vectors | Ewald sphere\n", "- | - | - | - | -\n", "\"Bragg's|\"Bragg's|\"Bragg's|\"Bragg's|\"Bragg's" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reciprocal Space" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "### Define silicon crystal" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true, "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lattice(symbols='Si8', pbc=True, cell=[5.43088, 5.43088, 5.43088])\n", "[[0. 0. 0. ]\n", " [0.25 0.25 0.25]\n", " [0.5 0.5 0. ]\n", " [0.75 0.75 0.25]\n", " [0.5 0. 0.5 ]\n", " [0.75 0.25 0.75]\n", " [0. 0.5 0.5 ]\n", " [0.25 0.75 0.75]]\n" ] } ], "source": [ "#Initialize the dictionary with all the input\n", "atoms = ks.structure_by_name('Silicon')\n", "\n", "print(atoms)\n", "print(atoms.get_scaled_positions())" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Wavelength and Magnitude of Incident Wavevector" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The wavelength for 200.0kV is : 2.50793pm\n", "The magnitude of the incident wavevector is 398.7 1/Ang\n" ] } ], "source": [ "acceleration_voltage_V = 200.0 *1000.0 #V\n", "\n", "wave_length_A = ks.get_wavelength(acceleration_voltage_V)\n", "\n", "print('The wavelength for {0:.1f}kV is : {1:.5f}pm'.format(acceleration_voltage_V/1000.,wave_length_A*100.))\n", "\n", "wave_vector_magnitude = 1/wave_length_A\n", "K0_magnitude = wave_vector_magnitude\n", "\n", "print('The magnitude of the incident wavevector is {0:.1f} 1/Ang'.format(K0_magnitude*10) )" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Reciprocal Lattice and Incident Wavevector\n", "\n", "We use ase to invert the unit_cell \"matrix\" to get the reciprocal cell\n", "\n", "And we calculate the incident wave vector from \n", "- this reciprocal cell, \n", "- Miller indices of the zone axis and \n", "- wavelength" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reciprocal lattice\n", " Cell([0.18413222166573373, 0.18413222166573373, 0.18413222166573373])\n", "Incident wavevector: [ 0. 0. 39.87345688] in units of [1/Ang]\n" ] } ], "source": [ "zone = [0, 0, 1] #Parallel to z-axis for simplicity\n", "\n", "# Reciprocal Lattice \n", "# We use ase to invert the unit_cell \"matrix\"\n", "reciprocal_lattice = atoms.cell.reciprocal() # transposed of inverted unit_cell: np.linalg.inv(atoms.cell]).T\n", "\n", "print('reciprocal lattice\\n', reciprocal_lattice)\n", "\n", "# Incident wavevector in vacuum \n", "# zone axis in global coordinate system\n", "zone_vector = np.dot(zone, reciprocal_lattice)\n", "K0_unit_vector = zone_vector / np.linalg.norm(zone_vector) # incident unit wave vector \n", "K0_vector = K0_unit_vector * K0_magnitude\n", "\n", "print('Incident wavevector: ',K0_vector,' in units of [1/Ang]')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "### 2D Plot of Unit Cell in Reciprocal Space" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e94d25cf9a2e40fead50d2aa16203dee", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(reciprocal_lattice[:,0], reciprocal_lattice[:,2], c='red', s=100)\n", "plt.xlabel('h')\n", "plt.ylabel('l')\n", "ax.axis('equal');" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "### 2D plot of Reciprocal Lattice\n", "\n", "Now we get all possible Miller (negative and positive) indices up to a maximum value \n", "\n", "We do get those combination with the itertool package." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-9.9, 9.9, -9.9, 9.9)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d1c5be8538814a10bc4df60c41ddf582", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hkl_max = 9\n", "indices = np.linspace(-hkl_max,hkl_max, 2*hkl_max+1) # all evaluated single Miller Indices\n", "hkl = np.array(list(itertools.product(indices, indices, indices))) # all evaluated Miller indices\n", "\n", "# Plot 2D\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(hkl[:,0], hkl[:,2], c='red', s=100)\n", "plt.xlabel('h')\n", "plt.ylabel('l')\n", "ax.axis('equal')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Origin and Laue Zones\n", "We really do not need that many reflections in the z-direction, so we reduce those.\n", "\n", "We chose a spot in a reciprocal lattice (3 dimensional, but we usually draw only a two dimensional projection), where we let `end` the incident wavevector $\\vec{k}_I$. \n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "63363b97048c4eec9edc6913c8b0bc11", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hkl_max = 11\n", "indices_u_v = np.linspace(-hkl_max, hkl_max, 2*hkl_max+1) # all evaluated single Miller Indices\n", "indices_w = np.linspace(-1, 2,4) # all evaluated single Miller Indices \n", "hkl = np.array(list(itertools.product(indices_u_v, indices_u_v, indices_w))) # all evaluated Miller indices\n", "\n", "g = np.dot(hkl, reciprocal_lattice) # all evaluated reciprocal lattice points\n", "\n", "# Plot 2D\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(g[:,0], g[:,2], c='red', s=100)\n", "ax.axis('equal')\n", "secax_y = ax.secondary_yaxis('right')\n", "secax_y.set_ylabel('w (1/Å)')\n", "ax.set_yticks(g[1:4,2])\n", "ax.set_yticklabels(['ZOLZ', 'FOLZ', 'SOLZ'])\n", "plt.xlabel('u (1/Å)')\n", "plt.ylabel('Laue zones') \n", "ax.scatter(0, 0, c='black', s=100, marker='x');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we defined the `Laue zones` (look at the right for the lables of the w-axis).\n", "You are most familiar with the ``Zero Order Laue Zone (ZOLZ)``, the only Laue zone reachable with X-rays.\n", "\n", "However the reciprocal lattice points do not lay only in one plane and so other orders exist as well.\n", "These other planes are called ``Higher Order Laue Zones or HOLZ``.\n", "\n", "the first few higher order Laue zones have extra names:\n", "- FOLZ: first order Laue zone\n", "- SOLZ: second order Laue zone\n", "\n", "In electron diffraction these planes can diffract and so we need to consider them, moreover, they allow for very precise measurements." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Ewald Sphere\n", "\n", "\n", "The origin of the reciprocal lattice is defined as above as the end point of the wave-vector $\\vec{k}_I$.\n", "The length of $\\vec{k}_I$ is given by the energy of the beam or the reciprocal of the wave_length (we are n reciprocal space). \n", "\n", "Because all diffracted wave vectors $\\vec{k}_D$ have to have the same length in elastic scattering, they have to end at the sphere, whose center is the beginning of the incident wave vector. \n", "\n", "This sphere is called Ewald sphere and gives us all possible diffracted wave vectors.\n", "\n", "For a short explanation of Braggs Law and Ewald sphere construction please see the *top of this notebook*\n", "\n", "Below we show the difference the wavelength makes on size of the Ewald sphere for electron and X-ray diffraction.\n", "Please ``zoom in`` to the reciprocal lattice to see clearly the difference between X-ray and electron diffraction." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "37b36b241aba432c9bccde098456fd0c", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ewald_Sphere = plt.Circle((0, K0_magnitude), K0_magnitude, color='b', fill=False, label='TEM')\n", "Ewald_Sphere_CuKa = plt.Circle((0, 1./1.5418), 1./1.5418, color='g', fill=False, label='Cu-Kα')\n", "\n", "# Plot 2D\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(g[:,0], g[:,2], c='red',s=100)\n", "ax.scatter(0, K0_magnitude, c='blue',s=100)\n", "\n", "ax.add_artist(Ewald_Sphere)\n", "ax.add_artist(Ewald_Sphere_CuKa)\n", "ax.scatter(0, 0, c='black', s=100, marker='x');\n", "ax.axis('equal')\n", "plt.xlabel('u (1/Å)')\n", "plt.ylabel('w (1/Å)');\n", "line1 = plt.plot([-300], [0], color=\"white\", marker='o', markerfacecolor=\"white\", markeredgecolor=\"blue\", label='TEM')\n", "line2 = plt.plot([-300], [0], color=\"white\", marker='o', markerfacecolor=\"white\", markeredgecolor=\"green\", label='X-Ray')\n", "line3 = plt.plot([-300], [0], color=\"white\", marker='o', markerfacecolor=\"white\", markeredgecolor=\"white\", linewidth = 3)\n", "plt.legend()\n", "plt.xlim(-15,15);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Only if a wave vector hits a reciprocal lattice point is the Bragg condition fulfilled and we will get an intensity. Therefore, we look where the Ewald sphere cuts one of the reciprocal lattice points.\n", "- Higher order Laue zone (HOLZ) excitations are due to diffraction from reciprocal lattice planes that are not the one the incident scattering vector end. These excitations are possible as soon as we have an Ewald sphere much larger than the inter{atom reciprocal lattice vector. The most prominent HOLZ features in a diffraction pattern are the so called HOLZ rings. We will learn later how to use the HOLZ rings to extract information." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tilting\n", "\n", "Mathematically it is equivalent to tilt the reciprocal lattice or the Ewald Sphere.\n", "\n", "Tilting is the way to achieve exact Bragg conditions." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0240e273ff6749fead159c7f6a820cb7", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ----Input ----\n", "tilt_angle = 9. # in degree\n", "# --------------\n", "\n", "tilt_angle_r = np.radians(tilt_angle) # now in radians\n", "rotation_matrix = np.array([[np.cos(tilt_angle_r), -np.sin(tilt_angle_r)],\n", " [np.sin(tilt_angle_r), np.cos(tilt_angle_r)]])\n", "K0_tilt = np.dot([0, K0_magnitude], rotation_matrix)\n", "K_xray_tilt = np.dot([0, 1./1.5418], rotation_matrix)\n", "\n", "g_tilt = g[:, [0, 2]].copy()\n", "g_tilt = np.dot(g_tilt, rotation_matrix)\n", "\n", "Ewald_Sphere = plt.Circle((0, K0_magnitude), K0_magnitude, color='b', fill=False, label='TEM')\n", "Ewald_Sphere_CuKa = plt.Circle((0, 1/1.5418), 1/1.5418, color='g', fill=False, label='Cu-K$\\alpha$')\n", "Ewald_Sphere_tilt = plt.Circle((-K0_tilt[0], K0_tilt[1]), K0_magnitude, color='b', fill=False, label='TEM')\n", "Ewald_Sphere_CuKa_tilt = plt.Circle((-K_xray_tilt[0], K_xray_tilt[1]), 1./1.5418, color='green', fill=False, label='TEM')\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(8, 4))\n", "ax1.scatter(0, K0_magnitude, c='blue',s=100)\n", "ax1.scatter(g_tilt [:,0], g_tilt [:,1], c='red',s=100)\n", "ax1.add_artist(Ewald_Sphere)\n", "ax1.add_artist(Ewald_Sphere_CuKa)\n", "ax1.set_aspect('equal')\n", "ax1.set_xlabel('u (1/Å)')\n", "ax1.set_ylabel('w (1/Å)');\n", "ax1.set_title('Tilt sample')\n", "\n", "ax2.scatter(g[:,0], g[:,2], c='red',s=100)\n", "ax2.scatter(-K0_tilt[0], K0_tilt[1], c='blue',s=100)\n", "ax2.add_artist(Ewald_Sphere_tilt)\n", "ax2.add_artist(Ewald_Sphere_CuKa_tilt)\n", "ax2.set_xlabel('u (1/Å)')\n", "ax2.set_aspect('equal')\n", "\n", "ax2.set_title('Tilt Ewald sphere')\n", "ax1.set_xlim(-2, 2.1)\n", "ax1.set_ylim(-1, 3);\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Precise Bragg Condition\n", "\n", "The precise Bragg condition is important in X-ray Diffraction and is the reason for the $\\theta - 2\\theta$ scans in X-ray diffraction experiments. \n", "\n", "The precise Bragg condition will become important in section of conventional TEM (two beam condition).\n", "\n", "Obviously, angles are too small for acceleration voltages used in a TEM to show nicely in a graph.\n", "Reduce the acceleration voltage to about 1000 to see a decent graphic with larger angles (why?)." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C:\\Users\\gduscher\\.matplotlib\n" ] } ], "source": [ "import matplotlib\n", "print(matplotlib.get_cachedir()) " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The wavelength for 1.0kV is : 38.76403pm\n", "Reflection [8, 0, 0] with magnitude of reciprocal vector 1.47 1/A has the Bragg angle 16.6°\n" ] }, { "data": { "text/plain": [ "(-1.0, 3.0)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "27de10dd8c0d466885fe9ed0d142d93f", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib import patches\n", "# -----Input -------\n", "Miller_index_h = 8\n", "acceleration_voltage_V = 1.0*1000.0 #V\n", "# ---------------------\n", "\n", "hkl_g=[Miller_index_h, 0, 0]\n", "wave_length_A = ks.get_wavelength(acceleration_voltage_V)\n", "\n", "print(f'The wavelength for {acceleration_voltage_V/1000:.1f}kV is : {wave_length_A*100.:.5f}pm')\n", "\n", "K0_magnitude = 1/wave_length_A\n", "\n", "\n", "reciprocal_unit_cell = atoms.cell.reciprocal() # transposed of inverted unit_cell\n", "g_hkl = np.dot(reciprocal_unit_cell, hkl_g) # calculate g vector for reflection\n", "g_norm = np.linalg.norm(g_hkl) # calculate length or norm of g vector \n", "theta_B = np.arcsin(g_norm/2./K0_magnitude) #calculate Bragg angle in degree\n", "#theta_B =g_norm/2./K0\n", "d_theta_B = np.arctan(g_hkl[2]/g_hkl[0])\n", "tilt_angle_rad=(theta_B-d_theta_B)\n", "\n", "theta_B =theta_B/np.pi*180\n", "\n", "print(f'Reflection {hkl_g} with magnitude of reciprocal vector {np.linalg.norm(g_hkl):.2f} 1/A',\n", " f' has the Bragg angle {theta_B:.1f}\\u00b0')\n", "\n", "\n", "# Tilted coordinates\n", "x = 0\n", "y = K0_magnitude\n", "start = 0\n", "# Tilt reciprocal lattice\n", "c, s = np.cos(tilt_angle_rad), np.sin(tilt_angle_rad)\n", "rot_matrix = np.array([[c, 0 ,s],[0, 1, 0],[-s, 0, c]])\n", "g_tilt = g.copy()\n", "g_tilt = np.dot(g_tilt , rot_matrix)\n", "Ewald_Sphere = plt.Circle((x,y), K0_magnitude, color='b', fill=False, label='TEM')\n", "theta_Arc = patches.Arc((x,y), K0_magnitude, -K0_magnitude, angle=-90-start, theta1=theta_B, theta2=0, color='black', fill=False,linewidth = 2)\n", "g_hkl_tilt = np.dot(g_hkl , rot_matrix)\n", "\n", "# Plot 2D\n", "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(8, 4))\n", "ax1.scatter(g_tilt[:,0], g_tilt[:,2], c='red',s=100)\n", "ax1.scatter(x,y, c='blue',s=100)\n", "\n", "ax1.add_artist(Ewald_Sphere)\n", "#Plot K0\n", "ax1.quiver([x],[y],[-x],[-y], units='xy', scale =1, width = .025)\n", "ax1.text(x/2-.1,y/2,r'$\\vec{K}_0$', horizontalalignment='right')# , size=20)\n", "#Plot Kg\n", "ax1.quiver([x],[y],[g_hkl_tilt[0]-x],[g_hkl_tilt[2]-y], units='xy', scale =1, width = .025)\n", "ax1.text(g_hkl_tilt[0]-.4,y/2,r'$\\vec{K}_g=\\vec{K}_0+\\vec{g}$', horizontalalignment='left')#, size=12)\n", "#Plot middle line \n", "ax1.plot([x,g_hkl_tilt[0]/2],[y,g_hkl_tilt[2]/2],'black', )\n", "# Plot g\n", "ax1.quiver([0],[0],[g_hkl_tilt[0]],[g_hkl_tilt[2]], units='xy', scale =1, width = .025)\n", "ax1.text(g_hkl_tilt[0]/2+.07,g_hkl_tilt[2]/2-.13 ,r'$\\vec{g}$')#, size=12)\n", "# Plot Brag angle\n", "ax1.add_patch(theta_Arc)\n", "ax1.text(x/2+.05,y/2-.2,r'$\\theta_{B}$', horizontalalignment='left')#, size=12)\n", "\n", "ax1.set_aspect('equal')\n", "ax1.set_ylim(-2,K0_magnitude)\n", "ax1.set_xlim(-5,15)\n", "ax1.set_title('Tilted sample')\n", "#plt.title('Wavevectors for exact Bragg Condition for {0} in Silicon'.format(hkl_g)) \n", "ax1.set_xlabel('u (1/Å)')\n", "ax1.set_ylabel('w (1/Å)')\n", "\n", "## titled Ewald sphere in untilted coordinates\n", "\n", "x = g_hkl[0]/2\n", "y = np.sqrt(K0_magnitude**2-g_norm**2/4)\n", "start = np.arctan(x/y)/np.pi*180. # start of Arc in degree\n", "\n", "Ewald_Sphere = plt.Circle((x,y), K0_magnitude, color='b', fill=False, label='TEM')\n", "theta_Arc = patches.Arc((x,y), K0_magnitude, -K0_magnitude, angle=-90-start, theta1=theta_B, theta2=0, color='black', fill=False,linewidth = 2)\n", "\n", "ax2.scatter(g[:,0], g[:,2], c='red',s=100)\n", "ax2.scatter(x,y, c='blue',s=100)\n", "\n", "ax2.add_artist(Ewald_Sphere)\n", "#Plot K0\n", "ax2.quiver([x],[y],[-x],[-y], units='xy', scale =1, width = .025)\n", "ax2.text(x/2-.1,y/2,r'$\\vec{K}_0$', horizontalalignment='right')# , size=20)\n", "#Plot Kg\n", "ax2.quiver([x],[y],[g_hkl[0]-x],[g_hkl[2]-y], units='xy', scale =1, width = .025)\n", "ax2.text(g_hkl[0]-.3,y/2,r'$\\vec{K}_g=\\vec{K}_0+\\vec{g}$', horizontalalignment='left')#, size=12)\n", "#Plot middle line \n", "ax2.plot([x,g_hkl[0]/2],[y,g_hkl[2]/2],'black', )\n", "# Plot g\n", "ax2.quiver([0],[0],[g_hkl[0]],[g_hkl[2]], units='xy', scale =1, width = .025)\n", "ax2.text(g_hkl[0]/2+.07,g_hkl[2]/2-.13 ,r'$\\vec{g}$')#, size=12)\n", "# Plot Brag angle\n", "ax2.add_patch(theta_Arc)\n", "ax2.text(x/2+.05,y/2-.2,r'$\\theta_{B}$', horizontalalignment='left')#, size=12)\n", "\n", "ax2.set_aspect('equal')\n", "ax2.set_title('Tilted Ewald sphere')\n", "#plt.title('Wavevectors for exact Bragg Condition for {0} in Silicon'.format(hkl_g)) \n", "ax2.set_xlabel('u (1/Å)')\n", "\n", "fig.suptitle('Exact Bragg condition')\n", "plt.tight_layout()\n", "ax1.set_xlim(-1, 2.1)\n", "ax1.set_ylim(-1, 3)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "source": [ "## Excitation Error\n", "\n", "### 2D Plot of Reciprocal Lattice with Excitation Error\n", "\n", "Here we define the excitation error.\n", "With the wave vector coming in parallel to a zone axis, the Ewald sphere should not cut any point in reciprocal space. \n", "\n", "However the dimensions of a TEM specimen are rather small, for a minimum the thickness paralllel to the beam has to be in the nanometer range (<200nm). This leads to the effect that the reciprocal lattice spots now are 3 dimensional objects reflecting the specimen geometry in reciprocal space. The spots are theFourier transfrom of the specimen geometry. A normal specimen is a thin disk perpendicular to the beam and in reciprocal space it is a thin rod parallel to the wave vector.\n", "\n", "Therefore we can excite Bragg reflections even though we not exactly cut the reflection spot with the Ewald sphere. This deviation is called excitation error and is expressed as a vector.\n", "\n", "If this vector is inside the Ewald sphere (here pointing down) the excitation error $|\\vec{s}_g|$ < 0 if the vector is outside $|\\vec{s}_g|$ > 0 " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The wavelength for 100.0kV is : 3.70144pm\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "93fec876c9614161b0500d2d9fe78e07", "version_major": 2, "version_minor": 0 }, "image/png": "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", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "acceleration_voltage_V = 100.0 *1000.0 #V\n", "\n", "wave_length_A = ks.get_wavelength(acceleration_voltage_V)\n", "\n", "print('The wavelength for {0:.1f}kV is : {1:.5f}pm'.format(acceleration_voltage_V/1000.,wave_length_A*100.))\n", "\n", "K0_magnitude = 1/wave_length_A\n", "\n", "Ewald_Sphere = plt.Circle((0, K0_magnitude), K0_magnitude, color='b', fill=False)\n", "\n", "# Plot 2D\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(g[:,0], g[:,2], c='red',s=100)\n", "ax.scatter(0, K0_magnitude, c='green',s=100)\n", "\n", "ax.add_artist(Ewald_Sphere)\n", "\n", "ax.quiver([0,0,0,g[2001,0]],[K0_magnitude,K0_magnitude,0,0],[0,g[2001,0],g[2001,0],0],[-K0_magnitude, -K0_magnitude+0.063,0,0.063], units='xy', scale =1, width = .005)\n", "\n", "plt.text(1.86, .01,r'$\\vec{S_g}$', size=20)\n", "plt.text(1.56, -.06,r'$\\vec{g}_{ZOLZ}$', size=20)\n", "plt.text(1.77, .21,r'$\\vec{K_g}$', size=20)\n", "plt.text(.1,10,r'$\\vec{K_0}$', size=20)\n", "plt.title('Parallel Illumination')\n", "\n", "ax.axis('equal')\n", "plt.xlabel('u [1/Å]')\n", "plt.ylabel('w [1/Å]')\n", "ax.set_xlim(1.6,2.0)\n", "ax.set_ylim(-.2,.3);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "source": [ "### 2D Plot of Reciprocal Lattice with Excitation Error\n", "The same plot as above but a little zoomed out will show also the incident wave vector." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c284894b6e7b429dbae6e94eab9b5eaf", "version_major": 2, "version_minor": 0 }, "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABgHUlEQVR4nO3deVhUdfsG8HvY900QMBfQCNxFXEBzS4Xc0szUFtIyy1aXNrG31Ba1skJzKdPitVzfULTSX2hulahpgJXmUpiGoKIw4ML+/f0xzsTIADPDzJwzM/fnus7FzDnfOXPPcRwenrOMQgghQERERER2w0HqAERERERkWSwAiYiIiOwMC0AiIiIiO8MCkIiIiMjOsAAkIiIisjMsAImIiIjsDAtAIiIiIjvDApCIiIjIzrAAJCIiIrIzLACJiIiI7AwLQCIiIiI7wwKQiIiIyM6wACQiIiKyMywAiYiIiOwMC0AiIiIiO8MCkIiIiMjOsAAkIiIisjMsAImIiIjsDAtAIiIiIjvDApCIiIjIzrAAJCIiIrIzLACJiIiI7AwLQCIiIiI7wwKQiIiIyM6wACQiIiKyMywAiYiIiOwMC0AiIiIiO8MCkIiIiMjOsAAkIiIisjMsAImIiIjsDAtAIiIiIjvDApCIiIjIzrAAJCIiIrIzLACJiIiI7AwLQCIiIiI7wwKQiIiIyM6wACSyQSkpKVAoFJrJyckJzZs3x6OPPorc3FxJMk2cOBFhYWFa88LCwjBx4kSj1qfvY8PCwjB8+HCteQqFAnPmzNHc37NnDxQKBfbs2WNUlsbq378/+vfvb9bnOHbsGObMmYMzZ87UWqbr34aIbJuT1AGIyHw+//xzREVF4caNG9i3bx/mz5+PvXv34tdff4Wnp6fU8eimZcuWmf05jh07hrlz56J///61ir3XXnsNU6dONXsGIpIPFoBENqxDhw7o1q0bAGDAgAGoqqrCm2++ibS0NDz00EONWveNGzfg7u5uiph2r127dpI+f5s2bSR9fiKyPO4CJrIjsbGxAIC///4bADB37lz07NkTAQEB8PHxQdeuXbFq1SoIIbQep96NumnTJkRHR8PNzQ1z584FACxduhR9+/ZF06ZN4enpiY4dO+Ldd99FRUWFURmLi4vx4osvIjw8HC4uLrjtttswbdo0XLt2rRGv3HB17Za9dXfpmTNnoFAo8N577+Gdd95BWFgY3N3d0b9/f5w8eRIVFRWYOXMmmjVrBl9fX9x77724ePFivc+lXufChQvxwQcfIDw8HF5eXoiLi8OBAwe0Hnv48GGMHz9e87xhYWF44IEHNP/GgOqQgPvvvx+A6g8B9aEBKSkpOl8TAJSWliIpKUnr3+GZZ55BUVGR1jj1e+P//u//0LVrV7i7uyMqKgqfffaZfhuaiCTBDiCRHTl9+jQAICgoCICq0HjyySfRsmVLAMCBAwfw3HPPITc3F6+//rrWY3/55RccP34c//nPfxAeHq7Zhfznn3/iwQcf1BQK2dnZePvtt/HHH38YXARcv34d/fr1wz///INZs2ahU6dO+P333/H666/j119/xc6dO6FQKBq7Gcxi6dKl6NSpE5YuXYqioiK88MILGDFiBHr27AlnZ2d89tln+Pvvv/Hiiy/i8ccfx9atW/VaZ1RUFJKTkwGodtUOHToUOTk58PX1BaD6N4yMjMT48eMREBCAvLw8LF++HN27d8exY8cQGBiIYcOGYd68eZg1axaWLl2Krl27Aqi78yeEwKhRo/D9998jKSkJffr0wdGjRzF79mxkZGQgIyMDrq6umvHZ2dl44YUXMHPmTAQHB2PlypWYNGkSbr/9dvTt27eRW5aIzIEFIJENq6qqQmVlJUpLS7F371689dZb8Pb2xj333ANAdYygWnV1Nfr37w8hBBYtWoTXXntNq9i6ePEijh07hjvuuEPrOT744AOtdfTp0wdNmjTBo48+ivfffx/+/v565128eDGOHj2KgwcPanZdDxw4ELfddhvGjBmD//u//8OQIUOM2hbm5ufnh7S0NDg4qHasFBQUYNq0aYiKisKWLVs04/744w8kJyejuLgYPj4+9a7T29sb33zzDRwdHQEAzZo1Q48ePbB9+3aMHz8eADBmzBiMGTNG85iqqioMHz4cwcHBWLt2LZ5//nkEBQUhIiICgGp3s7oTXJf09HR89913ePfdd/HSSy8BAAYPHowWLVpg3LhxWL16NSZPnqwZX1BQgJ9++knzh0Tfvn3x/fffY+3atSwAiWSKu4CJbFhsbCycnZ3h7e2N4cOHIyQkBNu3b0dwcDAAYNeuXRg0aBB8fX3h6OgIZ2dnvP7667h8+XKt3ZSdOnWqVfwBQGZmJu655x40adJEs45HHnkEVVVVOHnypEF5v/nmG3To0AFdunRBZWWlZkpISJD0LF19DB06VFP8AUDbtm0BAMOGDdMap55/9uzZBtc5bNgwTfEHqP4NAGjt3r169SpeeeUV3H777XBycoKTkxO8vLxw7do1HD9+3KjXsmvXLgCodZb1/fffD09PT3z//fda87t06aIp/gDAzc0Nd9xxh1ZOIpIXdgCJbNjq1avRtm1bODk5ITg4GKGhoZplhw4dQnx8PPr3749PP/0UzZs3h4uLC9LS0vD222/jxo0bWuuq+Vi1s2fPok+fPoiMjMSiRYsQFhYGNzc3HDp0CM8880ytdTTkwoULOH36NJydnXUuLygoMGh9lhQQEKB138XFpd75paWlDa6zSZMmWvfVu11rbtcHH3wQ33//PV577TV0794dPj4+UCgUGDp0qMHbX+3y5ctwcnLSHCqgplAoEBISgsuXL9ebU53V2OcnIvNjAUhkw9q2bavZlXqr9evXw9nZGd988w3c3Nw089PS0nSO13XsXVpaGq5du4ZNmzahVatWmvlZWVlG5Q0MDIS7u3udxw4GBgYatV5juLm5QalU1povpyJUqVTim2++wezZszFz5kzN/LKyMly5csXo9TZp0gSVlZW4dOmSVhEohEB+fj66d+/eqNxEJD3uAiayU+oLRNfcxXjjxg188cUXBq0DgNYJAUIIfPrpp0ZlGj58OP788080adIE3bp1qzVZ8mLFYWFhOHnyJMrKyjTzLl++jP3791ssQ0MUCgWEEFrbHwBWrlyJqqoqrXm6uod1GThwIADgyy+/1JqfmpqKa9euaZYTkfViB5DITg0bNgwffPABHnzwQTzxxBO4fPkyFi5cWKuYqM/gwYPh4uKCBx54AC+//DJKS0uxfPlyFBYWGpVp2rRpSE1NRd++fTF9+nR06tQJ1dXVOHv2LNLT0/HCCy+gZ8+eRq3bUImJifjkk0/w8MMPY/Lkybh8+TLefffdBk/csCQfHx/07dsX7733HgIDAxEWFoa9e/di1apV8PPz0xrboUMHAMCKFSvg7e0NNzc3hIeH69x9O3jwYCQkJOCVV15BcXExevfurTkLODo6GomJiZZ4eURkRuwAEtmpu+66C5999hl+/fVXjBgxAq+++irGjBmjtSuxIVFRUUhNTUVhYSFGjx6N5557Dl26dMHixYuNyuTp6YkffvgBEydOxIoVKzBs2DCMHTsWixcvRvPmzS3aAezduzf++9//4vfff8fIkSPx1ltvISkpyexf2WaotWvXYsCAAXj55ZcxevRoHD58GDt27NBcJkYtPDwcycnJyM7ORv/+/dG9e3d8/fXXOtepUCiQlpaGGTNm4PPPP8fQoUOxcOFCJCYmYteuXQb9kUBE8qQQt17xlYiIiIhsGjuARERERHaGBSARERGRnWEBSERERGRnWAASERER2RkWgERERER2hgUgERERkZ1hAUhERERkZ/hNII1QXV2N8+fPw9vbW+f3pBIREZH8CCFQUlKCZs2awcHBPnthLAAb4fz582jRooXUMYiIiMgI586dQ/PmzaWOIQkWgI3g7e0NQPUGktP3g1rCvffei127duHo0aNo1aqV1HGIiCyiuroaAQEBaNWqFbKzs6WOQ0YqLi5GixYtNL/H7RELwEZQ7/b18fGxuwLQyUn11vH29ra7105E9i0gIABKpZKffTbAng/fss8d30REREby9/dHUVERqqurpY5CZDQWgERERAYICAiAEAJKpVLqKERGYwFIRERkAH9/fwDAlStXJE5CZDwWgERERAYICAgAABQWFkqchMh4LACJiIgMwA4g2QIWgERERAZgB5BsAQtAIiIiA7ADSLaABSAREZEB2AEkW8ACkIiIyADsAJItYAFIRERkAHYAyRawACQiIjIAO4BkC1gAEhERGYAdQLIFLACJiIgMwA4g2QIWgERERAZwd3eHm5sbO4Bk1VgAEhERGcjf358dQLJqLACJiIgMFBAQgOvXr6OsrEzqKERGYQFIRERkIPVxgNwNTNaKBSAREZGBeCYwWTsWgERERAbimcBk7VgAEhERGYgdQLJ2LACJiIgMxA4gWTsWgERERAZiB5CsHQtAIiIiA7EDSNaOBSAREZGB2AEka8cCkIiIyEDsAJK1YwFIRERkIHYAydqxACQiIjIQO4Bk7VgAEhERGcjPzw8AO4BkvVgAEhERGcjJyQk+Pj7sAJLVsooCcN++fRgxYgSaNWsGhUKBtLS0esfv2bMHCoWi1vTHH39ojUtNTUW7du3g6uqKdu3aYfPmzWZ8FUREZEsCAgJQWFgIIYTUUYgMZhUF4LVr19C5c2csWbLEoMedOHECeXl5mikiIkKzLCMjA+PGjUNiYiKys7ORmJiIsWPH4uDBg6aOT0RENsjf3x+VlZW4evWq1FGIDOYkdQB9DBkyBEOGDDH4cU2bNtUcp3Gr5ORkDB48GElJSQCApKQk7N27F8nJyVi3bl1j4hIRkR2oeSawt7e3xGmIDGMVHUBjRUdHIzQ0FAMHDsTu3bu1lmVkZCA+Pl5rXkJCAvbv32/JiEREZKV4JjBZM6voABoqNDQUK1asQExMDMrKyvDFF19g4MCB2LNnD/r27QsAyM/PR3BwsNbjgoODkZ+fX+d6y8rKUFZWprlfXFxsnhdARESyx2sBkjWzyQIwMjISkZGRmvtxcXE4d+4cFi5cqCkAAUChUGg9TghRa15N8+fPx9y5c00fmIiIrA47gGTNbHoXcE2xsbE4deqU5n5ISEitbt/FixdrdQVrSkpKglKp1Eznzp0zW14iIpI3dgDJmtlNAZiZmYnQ0FDN/bi4OOzYsUNrTHp6Onr16lXnOlxdXeHj46M1ERGRfWIHkKyZVewCvnr1Kk6fPq25n5OTg6ysLAQEBKBly5ZISkpCbm4uVq9eDUB1hm9YWBjat2+P8vJyfPnll0hNTUVqaqpmHVOnTkXfvn3xzjvvYOTIkdiyZQt27tyJH3/80eKvj4iIrA87gGTNrKIAPHz4MAYMGKC5P2PGDADAhAkTkJKSgry8PJw9e1azvLy8HC+++CJyc3Ph7u6O9u3b49tvv8XQoUM1Y3r16oX169fjP//5D1577TW0adMGGzZsQM+ePS33woiIyGqxA0jWTCF4CXOjFRcXw9fXF0ql0u52ByckJCA9PR05OTkICwuTOg4RkcVlZWUhOjoa999/PzZu3Ch1HDKAPf/+VrObYwCJiIhMiR1AsmYsAImIiIzAYwDJmrEAJCIiMoKXlxccHR3ZASSrxAKQiIjICAqFAgEBAewAklViAUhERGQkf39/KJVKVFVVSR2FyCAsAImIiIykPg6wqKhI2iBEBmIBSEREZCSeCUzWigUgERGRkdQFII8DJGvDApCIiMhI6l3A7ACStWEBSEREZCR2AMlasQAkIiIyEjuAZK1YABIRERmJHUCyViwAiYiIjMSvgyNrxQKQiIjISLwMDFkrFoBERERGYgeQrBULQCIiIiOxA0jWigUgERGRkXgSCFkrFoBERERGcnNzg7u7OzuAZHVYABIRETVCQEAAO4BkdVgAEhERNYK/vz9u3LiB0tJSqaMQ6Y0FIBERUSPwTGCyRiwAiYiIGoFnApM1YgFIRETUCOwAkjViAUhERNQI7ACSNWIBSERE1AjsAJI1YgFIRETUCOwAkjViAUhERNQI7ACSNWIBSERE1AjsAJI1YgFIRETUCOwAkjViAUhERNQI7ACSNWIBSERE1AjsAJI1YgFIRETUCL6+vgDYASTrwgKQiIioERwdHeHn58cOIFkVFoBERESN5O/vj8LCQgghpI5CpBcWgERERI0UEBCAqqoqlJSUSB2FSC9WUQDu27cPI0aMQLNmzaBQKJCWllbv+E2bNmHw4MEICgqCj48P4uLi8N1332mNSUlJgUKhqDWVlpaa8ZUQEZEt4pnAZG2sogC8du0aOnfujCVLlug1ft++fRg8eDC2bduGI0eOYMCAARgxYgQyMzO1xvn4+CAvL09rcnNzM8dLICIiG8YzgcnaOEkdQB9DhgzBkCFD9B6fnJysdX/evHnYsmULvv76a0RHR2vmKxQKhISEmComERHZKXYAydpYRQewsaqrq1FSUqL5C03t6tWraNWqFZo3b47hw4fX6hASERHpgx1AsjZ2UQC+//77uHbtGsaOHauZFxUVhZSUFGzduhXr1q2Dm5sbevfujVOnTtW5nrKyMhQXF2tNRERE7ACStbGKXcCNsW7dOsyZMwdbtmxB06ZNNfNjY2MRGxurud+7d2907doVH330ERYvXqxzXfPnz8fcuXPNnpmIiKwLO4BkbWy6A7hhwwZMmjQJGzduxKBBg+od6+DggO7du9fbAUxKSoJSqdRM586dM3VkIiKyQuwAkrWx2Q7gunXr8Nhjj2HdunUYNmxYg+OFEMjKykLHjh3rHOPq6gpXV1dTxiQiIhvADiBZG6soAK9evYrTp09r7ufk5CArKwsBAQFo2bIlkpKSkJubi9WrVwNQFX+PPPIIFi1ahNjYWOTn5wMA3N3dNd/ZOHfuXMTGxiIiIgLFxcVYvHgxsrKysHTpUsu/QCIismrsAJK1sYpdwIcPH0Z0dLTmEi4zZsxAdHQ0Xn/9dQBAXl4ezp49qxn/ySefoLKyEs888wxCQ0M109SpUzVjioqK8MQTT6Bt27aIj49Hbm4u9u3bhx49elj2xRERkdVjB5CsjULwiwuNVlxcDF9fXyiVSvj4+Egdx6ISEhKQnp6OnJwchIWFSR2HiEhSV69ehbe3N7p06cJLilkBe/79rWYVHUAiIiI58/T0hLOzMzuAZDVYABIRETWSQqGAv78/jwEkq8ECkIiIyAQCAgJQUlKCiooKqaMQNYgFIBERkQmozwQuKiqSNgiRHlgAEhERmQDPBCZrwgKQiIjIBHgtQLImLACJiIhMgB1AsiYsAImIiEyAHUCyJiwAiYiITIAdQLImLABJti5duoTz589LHYOISC9SdQD5WUnGYAFIsnXo0CG0aNECS5YskToKEVGD1AWgpTuA/KwkY7AAJNkaNmwY3n//fUybNg3bt2+XOg4RUb3Uu4At3QHkZyUZw0nqAGSfioqKNH8t62P8+PE4efIkgoODzZiKiMh45ugA8rOSzIUFIEnC09MTX3zxRYPjsrOzsXDhQjz88MP8QCMiWTNHB5CflWQuCiGEkDqEtSouLoavry+USiV8fHykjmNRCQkJSE9PR05ODsLCwszyHHl5eejZsyc6duyIrVu3wtHR0SzPQ0RkCuXl5XB1dUW7du3w+++/W+x5+VlpOHv+/a3GYwBJtn799VdMmzYN69ev5wcaEcmei4sLPD09LX4MID8ryRjcBUyyFR8fj/j4eKljEBHpzd/fH5cuXYIQAgqFwiLPyc9KMgY7gERERCYSEBCAsrIy3LhxQ+ooRPViAUhERGQiUl0LkMhQLADJLJYvXw6FQgGFQoE1a9bUO/b7779HQEAAFAoFHB0dsWDBAgulJCIyLUO/Do6flSQVHgNIZpGVlaW53aVLlzrHLVu2DFOnTkVlZSW8vLzw5ZdfYuTIkeYPSERkBoZ+HRw/K0kqLADJLNQfau7u7oiKiqq1vLKyEtOmTcPSpUsBAC1btsTXX3+NTp06WTImEZFJGdoB5GclSYUFIJlcdXU1fvvtNwBAhw4dal2WoLCwEGPHjsXOnTsBAHFxcdi8eTMvXkpEVs+QDiA/K0lKPAaQTO7EiRO4fv06gNq7NE6ePInY2FjNB1piYiJ2797NDzQisgmGdAD5WUlSYgFIJlfzmJbo6GjN7Z07dyI2NhYnT56EQqHAvHnzsHr1ari6ukqQkojI9AzpAPKzkqTEXcBkcroOaq55ALOnpyfWrFnDA5iJyOYY0gHkZyVJiQUgmZz6Q83BwQHt2rXDM888g2XLlgFQHcC8detWdO7cWcKERETmYUwHkJ+VJAUWgGRy2dnZAIDg4GDcd999+P777wHwAGYisn2GdAD5WUlSYgFIJpWfn48LFy4AAPLy8pCXlwcAePjhh7Fy5Uoew0JENk3fDiA/K0lqPAmETCozM1Nz28XFRXO7d+/e/EAjIpvn6+sLhULRYAeQn5UkNRaAZFI1D2r++OOP0bRpUwDA1KlT8dNPPxm0rp9//hlDhw6Fv78/PD090aNHD6xdu9aUcYmITMrBwQF+fn4NdgBN+VlJZAwWgGRSNT/Uhg8fjg0bNsDJyQnl5eUYM2YMzp8/r9d69uzZgzvvvBM//PADxowZg6eeegoFBQV46KGHMG/ePDOlJyJqvICAABQVFaG6urrOMab6rCQyFgtAMin1h1poaCiCgoLQv39/vPvuuwBUx7yMHj0aZWVl9a6jsrISjz/+OBQKBfbt24dPP/0UCxcuRHZ2Ntq3b4/Zs2fj1KlT5n4pRERG8ff3R3V1NYqLi+scY4rPSqLGYAFIJnP9+nWcPn0agPZV7adPn44HHngAAHDw4EE888wz9a5n165d+PPPP/Hggw9qXRzV29sbr732GiorK/H555+b/gUQEZlAQ2cCm+qzUq2kpASvvvoq2rRpAzc3N3Tq1AmbNm3CDz/8AIVCgblz5zbi1ZCtYgFIJpOdna3Z5XHr1xqtXLlS8+Xlq1at0lzrSpc9e/YAAOLj42stU8/bu3evCRITEZleQ2cCm+qzEgAuX76M2NhYzJs3D2FhYZg2bRrCw8MxZswYzWNr/iFNpGYVBeC+ffswYsQINGvWDAqFAmlpaQ0+Zu/evYiJiYGbmxtat26Njz/+uNaY1NRUtGvXDq6urmjXrh02b95shvT2Q9dV7dU8PDywefNmzQfjtGnT8OOPP+pcj3r3bkRERK1l/v7+CAwM5C5gIpKthjqApvqsBIAJEybg+PHj+Pzzz/H9999jwYIF2LJlC2bPno3169cDYAFIullFAXjt2jV07twZS5Ys0Wt8Tk4Ohg4dij59+iAzMxOzZs3C888/j9TUVM2YjIwMjBs3DomJicjOzkZiYiLGjh2LgwcPmutl2LyaH2q6rl7funVrrF27Fg4ODqioqMCYMWPwzz//1BqnVCoBqC6noIuPj49mDBGR3DTUATTVZ2V6ejq+/fZbTJkyBRMnTtRaNmHCBACqYrRFixZGvhKyZVZRAA4ZMgRvvfUWRo8erdf4jz/+GC1btkRycjLatm2Lxx9/HI899hgWLlyoGZOcnIzBgwcjKSkJUVFRSEpKwsCBA5GcnGymV2H71B9qnp6eOrt3AHD33XfjjTfeAABcuHCBBzoTkc3RtwPY2M9K9Z6tV155pc4M7P5RXayiADRURkZGrePHEhIScPjwYVRUVNQ7Zv/+/RbLaUuqq6vx22+/AQA6duwIB4e631qzZs3CqFGjAKiu9TdlyhSt5erOX11dvuLi4jq7g0REUquvA2jKz8qdO3ciMjISrVq1qvXY/Px8ACwAqW42WQDm5+fX+g7F4OBgVFZWoqCgoN4x6v80upSVlaG4uFhrIpWTJ0/i+vXrAGof03IrhUKB1atXIyoqCgCQkpKCjz76SLNc/RexruP8CgsLUVBQUOdfzUREUquvA2iqz8rCwkKUlJTUuXtXfTJdQ89B9stmvwtYoVBo3RdC1Jqva8yt82qaP38+T6evQ1RUlGYb68Pb2xvHjx/Xuaxfv36YP38+0tPTMX78eK1l6enpmjFERHJUXwfQVJ+V6q+L01VkVlZWYtGiRQDYAaS62WQHMCQkpFYn7+LFi3ByckKTJk3qHXNrV7CmpKQkKJVKzXTu3DnThycMHDhQcxB0zYOlS0pK8Oabb8LJyanWAc9ERHLR0DGApuDh4YGwsDBkZWUhOztbM7+yshJTpkzBsWPH4O7ujsjISLNlIOtmkwVgXFwcduzYoTUvPT0d3bp1g7Ozc71jevXqVed6XV1d4ePjozWR6Tk5OWHlypWorq5Gnz598MQTT+DFF19E586d8fvvv2POnDm44447pI5JRKRTQ2cBm8pLL72Eqqoq9O3bF08++SReeOEFdOzYEb/88gs8PT3RuXNnODo6mjUDWS+r2AV89epVzVXTAdVlXrKyshAQEICWLVsiKSkJubm5WL16NQBgypQpWLJkCWbMmIHJkycjIyMDq1atwrp16zTrmDp1Kvr27Yt33nkHI0eOxJYtW7Bz5856r7dEljNgwAD8+OOPmD17NjZu3Ijy8nK0b98eb775Jh566CGp4xER1ckSHUAAeOqpp6BUKrFs2TKkpKQgLCwM48ePx/Dhw9GjRw/07dvXrM9PVk5Ygd27dwsAtaYJEyYIIYSYMGGC6Nevn9Zj9uzZI6Kjo4WLi4sICwsTy5cvr7Xe//3vfyIyMlI4OzuLqKgokZqaalAupVIpAAilUmnsS7Na8fHxAoDIycmROgoRkaxUV1cLFxcX0aJFC0me/9lnnxUAxJEjRyR5fmtgz7+/1RRCGHA0KmlRX45EqVTa3e7ghIQEpKenIycnB2FhYVLHISKSldDQUFy9ehUlJSVmWX9FRQWKi4s1x7UDqhMZV6xYgSlTpmDkyJF6fWuWvbLn399qVrELmIiIyJr4+/sjPz8fFRUVmmPPTeno0aPo06cPhgwZgtatW6OkpAQZGRk4evQoOnXqhFWrVpn8Ocm2sAAkIiIysZrHATZt2tTk6/fw8MDgwYOxf/9+fPPNN3BxcUFkZCTeeecdPPfcc3B3dzf5c5JtYQFIRERkYjXPBDZHAdi2bVts2bLF5Osl+2GTl4EhIiKSkqXOBCYyFgtAIiIiE7PUtQCJjMUCkIiIyMTYASS5YwFIRERkYuwAktyxACQiIjIxdgBJ7lgAEhERmRg7gCR3LACJiIhMjB1AkjsWgERERCbGDiDJHQtAIiIiE2MHkOSOBSAREZGJ+fn5AWAHkOSLBSAREZGJOTs7w9vbmx1Aki0WgERERGbg7++PK1euQAghdRSiWlgAEhERmYG/vz8qKipw/fp1qaMQ1cICkIiIyAzUJ4LwOECSIxaAREREZqC+FAyPAyQ5YgFIRERkBuwAkpyxACQiIjIDdgBJzlgAEhERmQE7gCRnLACJiIjMgB1AkjOn+hZu3brV4BUOHjwY7u7uRgciIiKyBewAkpzVWwCOGjXKoJUpFAqcOnUKrVu3bkwmIiIiq8cOIMlZg7uA8/PzUV1drdfk4eFhicxERESyxw4gyVm9BeCECRMM2p378MMPw8fHp9GhiIiIrB07gCRn9e4C/vzzzw1a2fLlyxsVhoiIyFaoO4AsAEmOeBYwERGRGXh7e8PBwYG7gEmW6u0A1lRaWoqPPvoIu3fvxsWLF1FdXa21/JdffjF5OCIiImvl4OAAf39/dgBJlvQuAB977DHs2LEDY8aMQY8ePaBQKMyZi4iIyOr5+/vjzz//RHV1NRwcuNON5EPvAvDbb7/Ftm3b0Lt3b3PmISIishkBAQE4ffo0lEql5qQQIjnQ+8+R2267Dd7e3ubMQkREZFPURR+PAyS50bsAfP/99/HKK6/g77//NmceIiIim8EzgUmu9N4F3K1bN5SWlqJ169bw8PCAs7Oz1nL+dUNERKSNHUCSK70LwAceeAC5ubmYN28egoODeRIIERFRA9gBJLnSuwDcv38/MjIy0LlzZ3PmISIishnsAJJc6X0MYFRUFG7cuGHOLPVatmwZwsPD4ebmhpiYGPzwww91jp04cSIUCkWtqX379poxKSkpOseUlpZa4uUQEZEdYAeQ5ErvAnDBggV44YUXsGfPHly+fBnFxcVakzlt2LAB06ZNw6uvvorMzEz06dMHQ4YMwdmzZ3WOX7RoEfLy8jTTuXPnEBAQgPvvv19rnI+Pj9a4vLw8uLm5mfW1EBGR/WAHkORK713Ad999NwBg4MCBWvOFEFAoFKiqqjJtsho++OADTJo0CY8//jgAIDk5Gd999x2WL1+O+fPn1xrv6+sLX19fzf20tDQUFhbi0Ucf1RqnUCgQEhJittxERGTf2AEkudK7ANy9e7c5c9SpvLwcR44cwcyZM7Xmx8fHY//+/XqtY9WqVRg0aBBatWqlNf/q1ato1aoVqqqq0KVLF7z55puIjo6ucz1lZWUoKyvT3Dd355OIiKwbO4AkV3oXgP369TNnjjoVFBSgqqoKwcHBWvODg4ORn5/f4OPz8vKwfft2rF27Vmt+VFQUUlJS0LFjRxQXF2PRokXo3bs3srOzERERoXNd8+fPx9y5c41/MUREZFfYASS50rsABICioiIcOnQIFy9eRHV1tdayRx55xKTBbnXrZWfUu54bkpKSAj8/P4waNUprfmxsLGJjYzX3e/fuja5du+Kjjz7C4sWLda4rKSkJM2bM0NwvLi5GixYtDHgVRERkT9gBJLnSuwD8+uuv8dBDD+HatWvw9vbWKr4UCoXZCsDAwEA4OjrW6vZdvHixVlfwVkIIfPbZZ0hMTISLi0u9Yx0cHNC9e3ecOnWqzjGurq5wdXXVPzwREdk1d3d3uLm5sQNIsqP3WcAvvPACHnvsMZSUlKCoqAiFhYWayZx/2bi4uCAmJgY7duzQmr9jxw706tWr3sfu3bsXp0+fxqRJkxp8HiEEsrKyEBoa2qi8RERENfn7+7MDSLKjdwcwNzcXzz//PDw8PMyZR6cZM2YgMTER3bp1Q1xcHFasWIGzZ89iypQpAFS7ZnNzc7F69Wqtx61atQo9e/ZEhw4daq1z7ty5iI2NRUREBIqLi7F48WJkZWVh6dKlFnlNRERkHwICApCXl4eysjLuRSLZ0LsATEhIwOHDh9G6dWtz5tFp3LhxuHz5Mt544w3k5eWhQ4cO2LZtm+as3ry8vFrXBFQqlUhNTcWiRYt0rrOoqAhPPPEE8vPz4evri+joaOzbtw89evQw++shIiL7oT4OsLCwkJceI9nQuwAcNmwYXnrpJRw7dgwdO3aEs7Oz1vJ77rnH5OFqevrpp/H000/rXJaSklJrnq+vL65fv17n+j788EN8+OGHpopHRESkU80zgVkAklzoXQBOnjwZAPDGG2/UWmbuC0ETERFZK54JTHKkdwF462VfiIiIqGG8FiDJUYNnAT/44IPYuHEjSkpKLJGHiIjIprADSHLUYAEYGRmJd955B0FBQYiPj8fSpUtx7tw5S2QjIiKyeuwAkhw1WADOnj0bR44cwenTpzFq1Chs3boVERER6Nq1K+bMmYPMzExL5CQiIrJK7ACSHOl9IejmzZvj6aefxnfffYdLly5h5syZOHXqFAYOHIhWrVrh2Wefxe+//27OrERERFaHHUCSI70LwJq8vb0xduxYrFmzBpcuXcJnn30GR0dHZGRkmDofERGRVWMHkORI77OA6+Lo6IiBAwdi4MCBpshDRERkU9gBJDkyqgNY0/HjxyX5dhAiIiJrwA4gyVGjC8Dy8nL8/fffpshCRERkc/z8/ACwA0jy0uAu4BkzZtS7/NKlSyYLQ0REZGucnJzg4+PDDiDJSoMF4KJFi9ClSxf4+PjoXH716lWThyIiIrIlAQEB+OeffyCEgEKhkDoOUcMFYEREBKZPn46HH35Y5/KsrCzExMSYPBgREZGt8Pf3x5kzZ3D16lV4e3tLHYeo4WMAY2JicOTIkTqXKxQKCCFMGoqIiMiW8ExgkpsGO4Dvv/8+ysrK6lzeuXNnVFdXmzQUERGRLal5JnDLli0lTkOkRwEYEhJiiRxEREQ2ix1AkptGXwaGiIiI6sdrAZLc1FsABgQEoKCgQO+VtWzZktcEJCIiuoW6AGQHkOSi3l3ARUVF2L59O3x9ffVa2eXLl1FVVWWSYERERLZCvQuYHUCSiwaPAZwwYYIlchAREdksdgBJbuotAHl2LxERUeOxA0hyw5NAiIiIzIwdQJIbFoBERERmxg4gyQ0LQCIiIjNjB5DkhgUgERGRmXl7e8PR0ZEdQJINFoBERERmplAo4O/vzw4gyYbeBeBdd92FuXPn1ppfWFiIu+66y6ShiIiIbE1AQACUSiWvl0uyoHcBuGfPHixZsgSjRo3CtWvXNPPLy8uxd+9es4QjIiKyFerjAIuKiqQNQgQDdwHv3LkT+fn5iI2NxZkzZ8wUiYiIyPbwTGCSE4MKwNDQUOzduxedOnVC9+7dsWfPHjPFIiIisi08E5jkRO8CUKFQAABcXV2xZs0aTJ06FXfffTeWLVtmtnBERES2gh1AkpMGvwtYTQihdf8///kP2rZty+8KJiIi0gM7gCQneheAOTk5CAoK0pp33333ISoqCocPHzZ5MCIiIlui7gCyACQ50LsAbNWqlc757du3R/v27U0WiIiIyBapO4DcBUxywAtBExERWQA7gCQnVlMALlu2DOHh4XBzc0NMTAx++OGHOsfu2bMHCoWi1vTHH39ojUtNTUW7du3g6uqKdu3aYfPmzeZ+GUREZKfYASQ5sYoCcMOGDZg2bRpeffVVZGZmok+fPhgyZAjOnj1b7+NOnDiBvLw8zRQREaFZlpGRgXHjxiExMRHZ2dlITEzE2LFjcfDgQXO/HCIiskPsAJKcWEUB+MEHH2DSpEl4/PHH0bZtWyQnJ6NFixZYvnx5vY9r2rQpQkJCNJOjo6NmWXJyMgYPHoykpCRERUUhKSkJAwcORHJysplfDRER2SN2AElOZF8AlpeX48iRI4iPj9eaHx8fj/3799f72OjoaISGhmLgwIHYvXu31rKMjIxa60xISKh3nWVlZSguLtaaiIiI9MHLwJCcyL4ALCgoQFVVFYKDg7XmBwcHIz8/X+djQkNDsWLFCqSmpmLTpk2IjIzEwIEDsW/fPs2Y/Px8g9YJAPPnz4evr69matGiRSNeGRER2RM3Nze4u7uzA0iyoPdlYKSm/iYSNSFErXlqkZGRiIyM1NyPi4vDuXPnsHDhQvTt29eodQJAUlISZsyYoblfXFzMIpCIiPQWEBDAApBkQfYdwMDAQDg6OtbqzF28eLFWB68+sbGxOHXqlOZ+SEiIwet0dXWFj4+P1kRERKQvf39/3LhxA6WlpVJHITsn+wLQxcUFMTEx2LFjh9b8HTt2oFevXnqvJzMzE6GhoZr7cXFxtdaZnp5u0DqJiIgMwTOBSS6sYhfwjBkzkJiYiG7duiEuLg4rVqzA2bNnMWXKFACqXbO5ublYvXo1ANUZvmFhYWjfvj3Ky8vx5ZdfIjU1FampqZp1Tp06FX379sU777yDkSNHYsuWLdi5cyd+/PFHSV4jERHZvppnAtdsShBZmlUUgOPGjcPly5fxxhtvIC8vDx06dMC2bds0X0+Xl5endU3A8vJyvPjii8jNzYW7uzvat2+Pb7/9FkOHDtWM6dWrF9avX4///Oc/eO2119CmTRts2LABPXv2tPjrIyIi+8AOIMmFQgghpA5hrYqLi+Hr6wulUml3xwMmJCQgPT0dOTk5CAsLkzoOEZFVeOGFF/DBBx9gy5YtuOeee6SOY7fs+fe3muyPASQiIrIV7ACSXLAAJCIishB+GwjJBQtAIiIiC2EHkOSCBSAREZGFsANIcsECkIiIyELYASS5YAFIRERkIewAklywACQiIrIQdgBJLlgAEhERWYivry8AdgBJeiwAiYiILMTR0RF+fn7sAJLkWAASERFZkL+/PwoLC8Ev4iIpsQC0JhcuAK1bA25uqp8XLkiX44cfVLf79JE2h1y2B3MwB3Mwh54CAgJQVVWFkpIS+WwPQF5ZyPwEGU2pVAoAQqlUmveJYmKEAOqeYmLM+/w6csQDAoDIkTiHXLYHczAHczCHvgYNGlT781Oq7SGELLaJpVns97eMKYRgD9pYFvkyaYVC/7Hm/Ke8JUcCgHQAOQDCJMxRL+ZgDuZgDhnmGKdQYCOAXwBES5gDgGy2iaVZ5Pe3zHEXsCncPKvL5Az5j2nMeOZgDuZgDuaweA7/mzf1Og/YXDmMWbc5s5DFsQA0lW7d5LE+5mAO5mAO5pB1joCbd/U+D9jUORqzTnNkIUlwF3AjaFrIAHwA07bHG/OXlgVy1LsL2II59MIczMEczCGjHO8BeBnAJwCekCJHjSxGsYGygbuA2QE0LVOdMdXY9TAHczAHczCHbHMY3AE0ZQ5TrItnB9sEFoCm1KePadYTF8cczMEczMEcNprDoGMATZ3jlixGMWUWkgwLQFM6e9Y06zl/njmYgzmYgzlsNIdRHUBT5bgli1FMmYUkwwLQlFq2NM16mjVjDuZgDuZgDhvNYVQH0FQ5bsliFFNmIcmwADQl9bdjNFZGBnMwB3MwB3PYaA6jOoCmynFLFqOYMgtJhmcBNwLPAuZZwMzBHMzBHIbmuArAG0AXAJlS5KiRxSg2UDbwLGB2AE0nJkYe62MO5mAO5mAOWefwBOAEAzqAps7RmHWaIwtJgh3ARtDqAJpjMxrzF5qFcjTYAbSz7cEczMEczGFIjmAANwAUS5WjRhaD2EjJwA4gO4CmoVSaZ72G/kcz139M5mAO5mAO5jBpDn8AJQAqpMphzLptpPgjFRaAcidEwy33uDjz/8dkDuZgDuZgDpPlCPD0BAAUSZnjZhZZbBOyPEFGUyqVAoBQKpWWecL8fCEiIoRwdVX9zM+3zPPqyBHv4SEAiJywMElzyGV7MAdzMAdzGGLo0KECgDjx00/y2B5CSL5NLMniv79liMcANoI9H0OQkJCA9PR05OTkICwsTOo4RERWJTExEV9++SUyMjIQGxsrdRy7Y8+/v9W4C5iIiMjC/P1Vl4MuLDToaoBEJsMCkIiIyMICAlSXg75yxaDvAyEyGRaAREREFsYOIEmNBSAREZGFsQNIUmMBSEREZGHsAJLUWAASERFZGDuAJDUWgERERBbGDiBJzWoKwGXLliE8PBxubm6IiYnBDz/8UOfYTZs2YfDgwQgKCoKPjw/i4uLw3XffaY1JSUmBQqGoNZWWlpr7pRARkZ1jB5CkZhUF4IYNGzBt2jS8+uqryMzMRJ8+fTBkyBCcPXtW5/h9+/Zh8ODB2LZtG44cOYIBAwZgxIgRyMzM1Brn4+ODvLw8rcnNzc0SL4mIiOwYO4AkNSepA+jjgw8+wKRJk/D4448DAJKTk/Hdd99h+fLlmD9/fq3xycnJWvfnzZuHLVu24Ouvv0Z0dLRmvkKhQEhIiFmzExER3crFxQWenp7sAJJkZN8BLC8vx5EjRxAfH681Pz4+Hvv379drHdXV1SgpKdG03NWuXr2KVq1aoXnz5hg+fHitDiEREZG5+Pv7swNIkpF9AVhQUICqqioEBwdrzQ8ODkZ+fr5e63j//fdx7do1jB07VjMvKioKKSkp2Lp1K9atWwc3Nzf07t0bp06dqnM9ZWVlKC4u1pqIiIiMERAQgLKyMty4cUPqKGSHZF8AqikUCq37Qoha83RZt24d5syZgw0bNqBp06aa+bGxsXj44YfRuXNn9OnTBxs3bsQdd9yBjz76qM51zZ8/H76+vpqpRYsWxr8gIiKya+rjALkbmKQg+wIwMDAQjo6Otbp9Fy9erNUVvNWGDRswadIkbNy4EYMGDap3rIODA7p3715vBzApKQlKpVIznTt3Tv8XQkREVIP6sCTuBiYpyL4AdHFxQUxMDHbs2KE1f8eOHejVq1edj1u3bh0mTpyItWvXYtiwYQ0+jxACWVlZCA0NrXOMq6srfHx8tCYiIiJjsANIUrKKs4BnzJiBxMREdOvWDXFxcVixYgXOnj2LKVOmAFB15nJzc7F69WoAquLvkUcewaJFixAbG6vpHrq7u8PX1xcAMHfuXMTGxiIiIgLFxcVYvHgxsrKysHTpUmleJBER2RV2AElKsu8AAsC4ceOQnJyMN954A126dMG+ffuwbds2tGrVCgCQl5endU3ATz75BJWVlXjmmWcQGhqqmaZOnaoZU1RUhCeeeAJt27ZFfHw8cnNzsW/fPvTo0cPir09vFy4ArVsDbm6qnxcuSJdDfSHuPn2kzSGX7cEczMEczGEgTQfw8cel3x6ALLYJWZAgoymVSgFAKJVK8z5RTIwQQN1TTIx5n19HjnhAABA5EueQy/ZgDuZgDuYwNMfym5+j70uZ42YWWWwTC7LY728ZUwghhLQlqPUqLi6Gr68vlEql+Y4H1ONMZw1z/lPekiMBQDqAHABhEuaoF3MwB3Mwh4xzbAAwHsCrAN6SIkeNLHqxoXLBIr+/Zc4qdgHL3s3jCk3OkP+YxoxnDuZgDuZgDslyqL+aoN4jAM2Vw5h1mzMLWRwLQFPp1k0e62MO5mAO5mAOq8jhf/Nng+cAmzpHY9ZpjiwkCe4CbgRNCxmAD2Da9nhj/tKyQI56dwFbMIdemIM5mIM5ZJjjLwBtoPo8/T9L5tCRxSA2UDZwFzA7gKZlqjOmGrse5mAO5mAO5pB9Dr07gKbMYYp18exgm8AC0JT69DHNeuLimIM5mIM5mMPGc/gCUKCBYwBNnaOOLAYxZRaSDHcBN0KtXcCurkBpaeNX7OYGlJUZ/3gL5NBrF7AdbQ/mYA7mYA5jcgRAVQRetlSOerLozZRZJMJdwOwAmlbLlqZZT7NmzMEczMEczGEHOQIAFAGotkCOS5cu4fz58/LZJiQpFoCmpP52jMbKyGAO5mAO5mAOO8jhD1XxV2yBHIcOHUKLFi2w5PHHG7ciU20TkhR3ATcCzwLmWcDMwRzMwRyNyaH+LP0LQLgFciQnJ+PFF1/E11VVGGLsSmygbOAuYHYATScmRh7rYw7mYA7mYA6ryaHXmcB65CgqKoJCoWhwmj59OqqqqjDewQFGnctr6m1CkmEHsBG0OoDm2IzG/NVqoRwNdgDtbHswB3MwB3MYk+NpAMsB7AAwqBE5KioqsGHDhgbHZWdnY+HChXj66aexdNmyBscbk8UasAMIOEkdwCYoleZZrxDy+J5G5mAO5mAO5jBLjgY7gHrmcHZ2xsMPP1zvmLy8PMyaNQtDhw7F4sWLgaVL5bFNSBLcBSx3QjTcco+LM/9/TOZgDuZgDuYweY46vw/YDDl+/fVXTJs2DevXr4ejo2OtLHWyxDYhyxNkNKVSKQAIpVJpmSfMzxciIkIIV1fVz/x8yzyvjhzxHh4CgMgJC5M0h1y2B3MwB3MwhzFWffCBACDmOTpKuz2EkM02sQSL//6WIR4D2Aj2fAxBQkIC0tPTkZOTg7CwMKnjEBFZpbS0NNx777146aWX8O6770odx27Y8+9vNe4CJiIikoi/v+oowCtX9PpGYCKT4UkgREREEgkIUB0FWFio1zcCa8b+97//xY4dO5CdnY0rV66gsrISvr6+CA8PR8+ePTFw4EAMGDAAvr6+5opOVo4FIBERkURu7QAWFRXBz89P51ghBJYuXYqZM2fi2rVrtZYXFBSgoKAAP//8M5YsWYIHHngAa9euNVt2sm4sAImIiCTw+uuvIyIiAgBw9uxZJCYmonv37nj++ed1jn/uueewdOlSAEBoaCgeffRR9O7dGyEhISgvL8fZs2exf/9+bNq0CefOnUMML9pM9WABSEREJIGWLVvikUceAQD89ddf+Ouvv+os/lJSUjTF36hRo/DFF1/Ay8tLa0xsbCzGjh2LDz/8EGlpaZri0t4IAVy9Cly8+O904YL2/fPnpU4pPZ4F3Aj2fBYRzwImImqc4uJihISE4MaNGwAAd3d3KJVKODs7a40TQqBVq1Y4d+4cbrvtNpw8eRIeHh5SRJZMZSVQUKC7mLv1/sWLwM1NqqFQAEFBQNOmqsnfvxipqfb5+1uNHUAiIiIJ+Pj44L777sOXX34JAOjRo0et4g8AsrKycO7cOQDA0KFDbaL4EwIoKQEuXWq4oLtwAbhypfa1qD08gODgf4u6zp3/vd20qfayJk0A9bWvAaC4GEhNtexrlhsWgERERBKZOHGipgDs1auXzjFnzpzR3HasWcXIRGWlqkC7fFl7KiioPU89XbkCVFRor8fBAQgM/LdoCwmpv6jz9JTm9doKFoBEREQSGTBgAFq0aIFz587VWQDWLPq++uorvPDCC7j99ttNnkUI4Nq1uou2uialUvf6fHxUnbfAQNXPli2B6GjVbfVUs7i7tUtH5sUCkIiISCIODg6YMGEC3nrrLcTGxuocExcXB1dXV5SVlaGgoABt27bF8OHDMWrUKAwaNAi33XZbrcdUVQGFhYYXc2VltZ/fyUm7aGvSBOjUqfa8mlNAAKBjbzbJCAtAIiIiCU2cOBFfffUVAgMDdS738grCG298hFmznkJVVRUqKyuRlpaGtLQ0AICPTySaNBkOL69HcONGJ1y+DBQV1T5mTrUu7UItJARo3167U3fr5O2tOomCbAsLQCIiIjOrrFTtKi0q0p5U89ogImImnnpKd1dOdUbrZACxAN4DsAnAvxeCLi4+geLiEwDeR2TkWDz//Arcdpuvzq6cq6ulXznJFQtAIiKiBpSX1y7gdBV0ugs81XXp6uLtDbi5heO22/7txEVG6urGdURg4Gp4eq5AZuZe7N79PXbu3InMzEzNuk6c2IiMjCJ89913ZtoSZCtYABIRkc0rK6u7OGuoeCsqAq5fr3vdvr6An9+/P/38gDZt/r2tnmouV0+qS9BVIibmOfzySxYUeu1rdcOQIQkYMiQBAPDnn39i1qxZ2LhxIwAgPT0dWVlZ6NKli76bh+wQC0AyyPHjx9GqVSuteUeOHOFXDhGR2QgBlJYaX7wVFaker4tCobtAi4zUr4Dz9m78mav79u3H0aNHkZWVhejoaIMf36ZNG6xduxbZ2dk4ceIEALAApAaxACSD/P333+jfv7/msgSjR49GWFgYNm3aJHEyIpKbigrVxX6vXlX9vPV2Xct0FXfl5bqfw9FRd4F22236FXBeXqrrz0np66+/1vw0pgAEVJeK6dGjh6YA1NVJLCkpwYIFC7B+/Xrk5ubijjvuwJw5cxAUFIS+fftizpw5mD17tvEvhKwKC0BrcuECEBen+hLDZs2AjAzVVTEtqH///rh29Squ3dwfkpmZiedufpelxclgezAHc9hSjrIy/Qo0fQs5XZcUqckZ5fD2d4KXtwO8vVXdNC8vVWHWsmXDxZufn+piwEadoXrhAtBFHv8uXy9aBAD4+u238fqTTxqd48qVK5rb4eHhWssuX76Mvn374tixY7jrrrtw//334/jx4xgzZgzGjRsHAIgODwdat5Z+m5BF8LuAG8Fi3wXcrRtw5Ejdy2NigMOHzff8t+QYDWDzzVkKAPkAmkqQo07MwRx2kEMIVYHVYLH2zjKUnC/GVXihBN4ogbfW7RKXJrjqFYqSktrfzHArV1dVgaYu1tQFm67btZY9/xi8T/wMb5TAC1fhjRK4okZbz0b+XQzNcQrAHTVmnwcQejOH+PlnPY8JVO2diYqKQmlpKYKCgnD+/Hk4Of3b4xk+fDi2bduGzz77DBMnTtTMnzt3LubMmQMAOAugha6VW2qbWJDFfn/LGAvARrDIG8iQP23N+U9ZI8dnACbdvB0LIEOiHA1iDuaQMIcAUAZXXIcHbsAd1+GhdVvz87//w/Xrqkt93PpTXcTV1Xmrqqo/hjuua4qtmoWXrvteS95psLAz+sK+Mvp3kVuODwHMqLHoUwCP37y9CsDexETMnj0bbdq0qXN1f/31F0aOHInffvsNAPDJJ5/giSee0CxPT09HQkICnnrqKSxbtkzrsWcUCoQDCABwuaHcNlQusAC0ogJw2bJleO+995CXl4f27dsjOTkZffr0qXP83r17MWPGDPz+++9o1qwZXn75ZUyZMkVrTGpqKl577TX8+eefaNOmDd5++23ce++9emfSvIEA+JhjMxqzX8MCOS5A9ReqAPA2gFkS5dALczBHzaeFqijTFF+ncussvoz+ea4AN+COG3CHgH4Hlzk4qL7Y3sMDcHf/96enp57dNR3LvPyd4IQGKsRaG8i+3x9S5LgLwO4a9+8BsOXm7ScBrIDqeL4BAwYgISEB0dHRCAwMREVFBf766y+kp6dj3bp1KL15lsszzzyDJUuWaD3H6NGjsXnzZpw5c0b7JD6FAsUAfAEMBLBTn/zWUTI0iAWglRwDuGHDBkybNg3Lli1D79698cknn2DIkCE4duwYWrZsWWt8Tk4Ohg4dismTJ+PLL7/ETz/9hKeffhpBQUG47777AAAZGRkYN24c3nzzTdx7773YvHkzxo4dix9//BE9e/Y0PGS3bqZtkXfrZvzjzJwjGEAPAAcBjJAwh96PYw5Z5RAAKmN6onzfQZSVqQ7uV/+s63ZpaQNF14atuIF1ujtst3TftIqyiLpzKhS1C7JbfwYG/nvfwwNwX/MpPPAn3HEDHriu90/nLp2gOGLqfxcDiz/14/g+NXkOIYRqV+4tOYoA/AGgN4CfAPQDcATADQDuAC7WePyuXbuwa9euOp/D19cX7777rlbnT23nzp2IjIzULv5uZsm/eVfvU09M/W9DkrGKDmDPnj3RtWtXLF++XDOvbdu2GDVqFObPn19r/CuvvIKtW7fi+PHjmnlTpkxBdnY2MjJUOyzHjRuH4uJibN++XTPm7rvvhr+/P9atW6dXLq0OIGDav4wa8707FsjxNlR/mZ6B6jhAqXLoxc5yVEOBCjijHC4og6vWz3K4oOznX+sttvS5rZm37ivtdet1261RL/3WQszDA3DP2m9QwaX188BunQWei4sR/9xW8P6wtRyXLl1CRUUFmjVrJmmO+ixatAiHDx/GiC+/RAJUHTcAKATgDOATAC/e/DkOqs9UdU8qC0A6gP0jR+LEiRM4f/48rl27Bg8PDwQFBSE6Ohrx8fF48MEH4eXlVeu5CwsLERAQgEGDBmHHjh3/Lri5TVZA1Wn8EsBD+r4g+ZcNDWIH0Ao6gOXl5Thy5AhmzpypNT8+Ph779+/X+ZiMjAzEx8drzUtISMCqVatQUVEBZ2dnZGRkYPr06bXGJCcnG5zxCzwELzjCcakSjgG+cHJSXZrg1knv+YUFcEQrOKESjqiqNdWc74Dq2gXYhQumOXPrwoU6Fw2H6i/X43WOALBvn6pF0lgFBbVmVQOogiOq4aC1ddT3a86vXvsTqnz8UV2tOmaqulr1tUw171dV/Tvpml9dDVQVlaAKo26u2+nm1nfU+llfjqoxR1Dt4q573Q3kUOetrAQqSitQgTRUwAUVcL5Z7Dlr7leigQO1uh9rcJM7O6sKIGfnem6jAi64fDNBBTxRAT+tJNrpVPPL//35+iw4+3s3/Dw3b7u5qU5CqPW7vKAA6NdP//fTrcr2Ad6BmiK3qMjI9eh4nxrEjP9fbDnH3r178eyzz2LmzJl46CEdJYwMtkdMTAxeeuklfAnVL91+UO09GQ7g1iP7fG+53+XmhE8+Mepz3fXmd78VFhb+O/PmZ3slgEU3Zxl08RlT/Y4haQmZy83NFQDETz/9pDX/7bffFnfccYfOx0RERIi3335ba95PP/0kAIjz588LIYRwdnYWa9as0RqzZs0a4eLiUmeW0tJSoVQqNdO5c+cEAAEohepPIuknBaqEAlXCwUEIBwchHB1Vk5OTanJ2FsLFRTW5uqomNzfV5O6umjw8VJOn4qrwQrHwQrHwhlJ4Qyl8UHRzuiIccMfN18+JEydOnIyZ2gJiJCBiAbEF9Xy4R0QY8ytUCCFEWFiYcHR0FFlZWaoZ4eGiAhCTbmZwB0Rlfc9twixyoVQqBQChVCqljiIZ2XcA1W49FV6oj6kwYPyt8w1d5/z58zF37txa86/AD55wQpWLB6ouF6GqStWpqdnNUU96zR98N6oqqlAFR1TCSUcP8N/51TePZxI3+4ACCggnF2DJEk2X3uifL8wGqiq11l3z51Z440qtv19vblv1jY4da2xv3du1ob0ziqPZgKi+Zf3i5qS+XV1jnnr+zXkKBRR39oZCgcZN33wDhaise5d3QxwcgHvuMfbR/9q6VdUOZA7msPEc5XffjW3btun9ECcnJwwaNAhubjUOM5DJ9vg2LQ01r7LjC2AIVJ3Au6E6C7deZ88a/dwvvfQSnnnmGfTt2xfjx4+H19mz2AbVcYaeADoCMOjLTBqRheRD9gVgYGAgHB0dkZ+frzX/4sWLCK6jBR0SEqJzvJOTE5o0aVLvmLrWCQBJSUmYMePfE/aLi4vRokULOELABRVAq6ZA7UMwDNf8JJCTY/zjwyNUB3U01qJN9eZ4oaHHR0QARzc3Pkfr1kDO38Y//vYIYJ+pcjTi36VNG2AzczAHc+iboyItDRs2bGhwaHZ2NhYuXIgnnngCS5cuNXmOxm6PPXv2IC0tDRH4d9fvnUBDB2to03HCo76eeuopKJVKLFu2DCkpKQhzcMD4qioMh+qEvr6GrrARWUhGJO5A6qVHjx7iqaee0prXtm1bMXPmTJ3jX375ZdG2bVuteVOmTBGxsbGa+2PHjhVDhgzRGnP33XeL8ePH651L00JWt8Xz8/V+bL3y8xu3H5g5mIM5mMNOcpw/f160aNFCDB06VFRWVspye+zevVv88eOPkufQuLlNnoVqF/ARKbNIhLuAhYDUAfSxfv164ezsLFatWiWOHTsmpk2bJjw9PcWZM2eEEELMnDlTJCYmasb/9ddfwsPDQ0yfPl0cO3ZMrFq1Sjg7O4uvvvpKM+ann34Sjo6OYsGCBeL48eNiwYIFwsnJSRw4cEDvXLUKQFNqzAcFczAHczCHneT47rvvxPvvvy+Ki4slzaEXCXKUl5eLgoICrXnV1dXiY6iKv5FSbxOJsAAU1lEACiHE0qVLRatWrYSLi4vo2rWr2Lt3r2bZhAkTRL9+/bTG79mzR0RHRwsXFxcRFhYmli9fXmud//vf/0RkZKRwdnYWUVFRIjU11aBMWgVgTIxRr6tOMTHGfUgwB3MwB3MwB3PcdPjwYeHu7i5Gjx4tXnzxRfHkk0+KTp06CQCiEyAKpN4mEmEBKIRVXAdQruz1m0CYgzmYgzmYwzpyHD9+HDNnzsShQ4dw5coVuLi4IDIyEmPHjsVzr7wCdwtmkRNeB9BKLgQtV/b6XcDMwRzMwRzMYQM5AHllsSAWgNDziypJOkIAMTH1j4mLM/9/TOZgDuZgDolyCCGwdu1aJCQkICgoCJ6enujcuTOSk5NRWVmJGzduwMHBAQqFAu+8847ZcpiMXHLILQtZlqQ7oK2cxY8hyM9XXYDT1VX1U6ozsZiDOZiDOSyU48KFCyIuLk4Aui+kPGTIEPHLL79o7m/fvt0sOcxGLjnklsXMeAwgjwFsFLaQiYjM5+rVq+jRoweOHz8OhUKBBx54AOPHj8dtt92GnJwczJs3D7/88gsGDBiA3bt3AwDy8vIQEhIicXKSO/7+toILQRMRkX2aMmUKjh8/DicnJ2zatAkjRozQLOvatSvuvvtuREVFaYq/pk2bsvgj0hOPASQiItn54YcfsGbNGgDAnDlztIo/NU9PT0ydOlVzv0uXLpaKR2T1WAASEZHsvPHGGwCAli1b4pVXXqlzXPv27TW3O3fubPZcRLaCBSAREclKXl4edu7cCQB4+umn4eRU99FKvr6+mtu3dgCnT58OhUKh1/T888/rXH9mZiaeffZZREVFwcvLC15eXujcuTNmz56NoqIinY9p164dFAoFLl68WO/rNEU+ImPxGEAiIpKV7du3a24PHTq03rFXrlzR3L61A9itWzfMnj27zsceOnQI27dvh6OjI4YPH661rKKiAtOnT8fy5cvh7OyMhIQEDB8+HFVVVdi5cyfeeOMNrF69Grt27UJ4eLjmcdevX8fJkydx2223oWnTpvVmb0w+osZiAUhERLKSlZUFAHB1dUXHjh3rHfvbb78BANzc3BAVFaW17KGHHqrzcQcOHMCHH34IBwcHpKSkID4+XrOsvLwco0ePxrfffosRI0Zg1apVCAoK0iwXQmD69OlYtGgRxo0bh0OHDmllr6qqQteuXRt8ncbmIzIF7gImIiJZyc/PBwCtoqsuO3bsAKA6FtDR0VGv9R88eBAJCQm4evUqUlJS8PDDD2stnzVrFr799lvce++92LJlS60cCoUCCxYsQIsWLfDzzz/jp59+0iz75ZdfAECvAtDYfESmwAKQiIhkpaysDIDqWm31+eOPPzSXgNH3DOBDhw5piqvPP/8ciYmJWsuPHTuGDz/8EMHBwfjss8+gqOOr0tzc3HDnnXcCUBVsakeOHAFgfAHYUD4iU2EBSEREsqI+dq64uBjnzp3TOaa6uhrPPfcc1N9loM8ZwD///DPi4+NRUlKCVatW4ZFHHqk1ZuHChaiursb06dPh5+dX7/qaN28OAFAqlZp5jekA6pOPyFRYABIRkazExsZqbs+fP7/W8qqqKjz33HOaM4WBhjuAhw8fRnx8PIqLi7Fy5UpMnDix1pjq6mp8/fXXAIBx48Y1mPPy5csAgCZNmgAASktLcezYMQQFBWmKQ33pk4/IlHgSCBERycr999+Pl156CYWFhVi+fDkqKirw4IMPwsvLC8eOHcOSJUtw+PBhtGzZEmfPngUAdOrUqc71HTlyBIMHD4ZSqcTKlSvx6KOP6hx37tw5FBQUIDAwEGFhYQ3mPHDgAAAgOjoaAHD06FFUVlYa3P3TNx+RKbEAJCIiWfHx8cHKlSsxbtw4VFZWYuXKlVi5cqVmuaOjI2bNmoXr168jOTkZbdu21boeYE01i6tPP/0Ujz32WJ3Pq+7oBQQENJjx119/xbFjx9C0aVPExcUBMG73ryH5iEyJu4CJiEh2Ro8ejX379mHo0KHw8/ODm5sb2rRpgyeeeAJHjhzB22+/jX379gEA+vbtq3Mdv/zyCwYPHoyioiJ88sknmDRpUr3PqS4iz58/32C+119/HYDqYs7qC1UbWgAamo/IlNgBJCIiWYqLi8O3336rc9lvv/2mKbjuv//+WsszMzM1xdXHH3+MyZMnN/h8rVu3RtOmTXHx4kUcPHgQPXv21Dnu008/RVpaGjp16oRp06Zp5htSABqTj8iU2AEkIiKroj5LFwDuuOMO3HXXXVrLs7KyMGjQIM0xhE888YRe61UoFHj22WcBAM8++6zW2b2A6gLRCxYswJQpU9CiRQukpqbCzc0NgOqbQ3799Vf4+fmhdevW9T6PsfmITEkh1OfQk8GKi4vh6+sLpVIJHx8fqeMQEdmEP//8E23atNG5rLS0FE8//TQ+//xzAMDWrVsxYsQIzfLz58+jU6dOuHz5Mjp06ID77ruv3ucaMWIEYmJiNPcrKytx3333YevWrQgKCsLIkSMRFBSE3NxcfPfdd7hw4QLi4uKwdu1arRNFMjMz0bVrVzRp0gSjRo3S+Vx9+vTB4MGDG5WPTIO/vwEIMppSqRQAhFKptMwT5ucLER4uhKur6md+vmWelzmYgzmYw4I5oqOjRWxsrEhOThZ79uwRmZmZYteuXWLevHkiPDxcABAAxIwZM2o9duPGjZrl+kx7nZ1r5aiqqhIpKSmiX79+ws/PT7i4uIjmzZuLe+65R6xfv15UV1fXet6VK1c2+Fzvvfee4fn27jXt9q+PXN4jFmDx398yxAKwESz2BoqJEQKoe4qJMe/zMwdzMAdzWChHRUWFcHV1rbcocnJyEm+99ZbOQsxUOcxOLjnklsVCWAAKwV3AjWCRFnIdX0Okkzn/KZmDOZiDOSyQo7KiAl999RW2bt2KzMxMXLp0SfMZe/vtt2PgwIGYMmUKWrZsadYcctkeZs0ByCuLBXEXMI8BbBTNGwiAjzk2oyH/MdWYgzmYgzmYgzn0IacsFsYCkGcBm063bvJYH3MwB3MwB3Mwh7nWaY4sJAl2ABtBqwMImPYvI2P+MlNjDuZgDuZgDuaoj5yySIAdQHYATevCBXmshzmYgzmYgzmYw1zrMmUWkgwLQFPq08c067n5vZLMwRzMwRzMwRwmzQHIKwtJhruAG6HWLmBXV6C0tPErdnMDysqMfzxzMAdzMAdzMIc1ZJEIdwGzA2haxlyWQJdmzZiDOZiDOZiDOUyfA5BXFpIMO4CNUKsDmJ8PBAc3fsUXLgAhIcY/njmYgzmYgzmYwxqySIQdQBaAjcKzgJmDOZiDOZjD6nIA8soiARaA3AVsOqb+sm5j18cczMEczMEczGGudZojC0mCHcBG4DeBMAdzMAdzMIdV5gDklcXC2AFkB9A0lErzrNfQ/2jm+o/JHMzBHMzBHLaVw5h120jxRyqyLwALCwuRmJgIX19f+Pr6IjExEUVFRXWOr6iowCuvvIKOHTvC09MTzZo1wyOPPILz589rjevfvz8UCoXWNH78eDO/GiMI0XDLPS7O/P8xmYM5mIM5mMO2csgtC1mWkLm7775bdOjQQezfv1/s379fdOjQQQwfPrzO8UVFRWLQoEFiw4YN4o8//hAZGRmiZ8+eIiYmRmtcv379xOTJk0VeXp5mKioqMiibUqkUAIRSqTTqtRksP1+IiAghXF1VP/PzLfO8zMEczMEczGHbOeSWxcws/vtbhmR9DODx48fRrl07HDhwAD179gQAHDhwAHFxcfjjjz8QGRmp13p+/vln9OjRA3///Tda3rx+Uf/+/dGlSxckJycbnY/HEBAREVkf/v6W+S7gjIwM+Pr6aoo/AIiNjYWvry/279+v93qUSiUUCgX8/Py05q9ZswaBgYFo3749XnzxRZSUlJgqOhEREZFsOUkdoD75+flo2rRprflNmzZFfn6+XusoLS3FzJkz8eCDD2pV+Q899BDCw8MREhKC3377DUlJScjOzsaOHTvqXFdZWRnKanx9TnFxsQGvhoiIiEgeJOkAzpkzp9YJGLdOhw8fBgAodJymLoTQOf9WFRUVGD9+PKqrq7Fs2TKtZZMnT8agQYPQoUMHjB8/Hl999RV27tyJX375pc71zZ8/X3Myiq+vL1q0aGHgKyciIiKSniQdwGeffbbBM27DwsJw9OhRXLhwodayS5cuIbiBr6GpqKjA2LFjkZOTg127djW4j79r165wdnbGqVOn0LVrV51jkpKSMGPGDM394uJiFoFERERkdSQpAAMDAxEYGNjguLi4OCiVShw6dAg9evQAABw8eBBKpRK9evWq83Hq4u/UqVPYvXs3mjRp0uBz/f7776ioqEBoaGidY1xdXeHq6trguoiIiIjkTNYngbRt2xZ33303Jk+ejAMHDuDAgQOYPHkyhg8frnUGcFRUFDZv3gwAqKysxJgxY3D48GGsWbMGVVVVyM/PR35+PsrLywEAf/75J9544w0cPnwYZ86cwbZt23D//fcjOjoavXv3luS1EhEREVmKrAtAQHWmbseOHREfH4/4+Hh06tQJX3zxhdaYEydOQHnz2zj++ecfbN26Ff/88w+6dOmC0NBQzaQ+c9jFxQXff/89EhISEBkZieeffx7x8fHYuXMnHB0dLf4aiYiIiCxJ1tcBlDteR4iIiMj68Pe3FXQAiYiIiMi0WAASERER2RlZXwha7tR7z3lBaCIiIuuh/r1tz0fBsQBsBPVXx/FagERERNanpKQEvr6+UseQBE8CaYTq6mqcP38e3t7een0ziS1RXwT73LlzdnsAraVxm1sWt7dlcXtbnj1vcyEESkpK0KxZMzg42OfRcOwANoKDgwOaN28udQxJ+fj42N0Hh9S4zS2L29uyuL0tz163ub12/tTss+wlIiIismMsAImIiIjsDAtAMoqrqytmz57N70a2IG5zy+L2tixub8vjNrdvPAmEiIiIyM6wA0hERERkZ1gAEhEREdkZFoBEREREdoYFIBEREZGdYQFIdVq2bBnCw8Ph5uaGmJgY/PDDD/WO37t3L2JiYuDm5obWrVvj448/tlBS22DI9t6zZw8UCkWt6Y8//rBgYuu1b98+jBgxAs2aNYNCoUBaWlqDj+H7u3EM3eZ8jzfO/Pnz0b17d3h7e6Np06YYNWoUTpw40eDj+D63HywASacNGzZg2rRpePXVV5GZmYk+ffpgyJAhOHv2rM7xOTk5GDp0KPr06YPMzEzMmjULzz//PFJTUy2c3DoZur3VTpw4gby8PM0UERFhocTW7dq1a+jcuTOWLFmi13i+vxvP0G2uxve4cfbu3YtnnnkGBw4cwI4dO1BZWYn4+Hhcu3atzsfwfW5nBJEOPXr0EFOmTNGaFxUVJWbOnKlz/MsvvyyioqK05j355JMiNjbWbBltiaHbe/fu3QKAKCwstEA62wZAbN68ud4xfH+blj7bnO9x07p48aIAIPbu3VvnGL7P7Qs7gFRLeXk5jhw5gvj4eK358fHx2L9/v87HZGRk1BqfkJCAw4cPo6KiwmxZbYEx21stOjoaoaGhGDhwIHbv3m3OmHaN72/p8D1uGkqlEgAQEBBQ5xi+z+0LC0CqpaCgAFVVVQgODtaaHxwcjPz8fJ2Pyc/P1zm+srISBQUFZstqC4zZ3qGhoVixYgVSU1OxadMmREZGYuDAgdi3b58lItsdvr8tj+9x0xFCYMaMGbjzzjvRoUOHOsfxfW5fnKQOQPKlUCi07gshas1raLyu+aSbIds7MjISkZGRmvtxcXE4d+4cFi5ciL59+5o1p73i+9uy+B43nWeffRZHjx7Fjz/+2OBYvs/tBzuAVEtgYCAcHR1rdZ8uXrxY669DtZCQEJ3jnZyc0KRJE7NltQXGbG9dYmNjcerUKVPHI/D9LRd8jxvuueeew9atW7F79240b9683rF8n9sXFoBUi4uLC2JiYrBjxw6t+Tt27ECvXr10PiYuLq7W+PT0dHTr1g3Ozs5my2oLjNneumRmZiI0NNTU8Qh8f8sF3+P6E0Lg2WefxaZNm7Br1y6Eh4c3+Bi+z+2MhCegkIytX79eODs7i1WrVoljx46JadOmCU9PT3HmzBkhhBAzZ84UiYmJmvF//fWX8PDwENOnTxfHjh0Tq1atEs7OzuKrr76S6iVYFUO394cffig2b94sTp48KX777Tcxc+ZMAUCkpqZK9RKsSklJicjMzBSZmZkCgPjggw9EZmam+Pvvv4UQfH+bg6HbnO/xxnnqqaeEr6+v2LNnj8jLy9NM169f14zh+9y+sQCkOi1dulS0atVKuLi4iK5du2pdPmDChAmiX79+WuP37NkjoqOjhYuLiwgLCxPLly+3cGLrZsj2fuedd0SbNm2Em5ub8Pf3F3feeaf49ttvJUhtndSXGLl1mjBhghCC729zMHSb8z3eOLq2NQDx+eefa8bwfW7fFELcPMKTiIiIiOwCjwEkIiIisjMsAImIiIjsDAtAIiIiIjvDApCIiIjIzrAAJCIiIrIzLACJiIiI7AwLQCIiIiI7wwKQiIiIyM6wACQim3TmzBkoFAooFAp06dJF6jh16t+/vyZnVlaW1HGIyE6wACQim7Zz5058//33mvu///477rvvPoSFhUGhUCA5ObnOx06cOBEzZ840a75Nmzbh0KFDZn0OIqJbsQAkIpvWpEkTNGnSRHP/+vXraN26NRYsWICQkJA6H1ddXY1vv/0WI0eONGu+gIAABAUFmfU5iIhuxQKQiGTv0qVLCAkJwbx58zTzDh48CBcXF6Snpxu0ru7du+O9997D+PHj4erqWue4n376CQ4ODujZs6dmd/KmTZswYMAAeHh4oHPnzsjIyNCMT0lJgZ+fH7755htERkbCw8MDY8aMwbVr1/Df//4XYWFh8Pf3x3PPPYeqqirDNwIRkQk5SR2AiKghQUFB+OyzzzBq1CjEx8cjKioKDz/8MJ5++mnEx8eb5Tm3bt2KESNGwMHh37+TX331VSxcuBARERF49dVX8cADD+D06dNwclJ9lF6/fh2LFy/G+vXrUVJSgtGjR2P06NHw8/PDtm3b8Ndff+G+++7DnXfeiXHjxpklNxGRPlgAEpFVGDp0KCZPnoyHHnoI3bt3h5ubGxYsWGC259u6dSsWLlyoNe/FF1/EsGHDAABz585F+/btcfr0aURFRQEAKioqsHz5crRp0wYAMGbMGHzxxRe4cOECvLy80K5dOwwYMAC7d+9mAUhEkuIuYCKyGgsXLkRlZSU2btyINWvWwM3NzSzPc/z4cfzzzz8YNGiQ1vxOnTppboeGhgIALl68qJnn4eGhKf4AIDg4GGFhYfDy8tKaV/MxRERSYAFIRFbjr7/+wvnz51FdXY2///7bbM+zdetWDB48GO7u7lrznZ2dNbcVCgUA1ckiuparx+iaV/MxRERS4C5gIrIK5eXleOihhzBu3DhERUVh0qRJ+PXXXxEcHGzy59qyZQsef/xxk6+XiEguWAASkVV49dVXoVQqsXjxYnh5eWH79u2YNGkSvvnmG4PWU15ejmPHjmlu5+bmIisrC15eXrj99ttx8eJF/Pzzz0hLSzPDqyAikgfuAiYi2duzZw+Sk5PxxRdfwMfHBw4ODvjiiy/w448/Yvny5Qat6/z584iOjkZ0dDTy8vKwcOFCREdHazp+X3/9NXr27ImmTZua46UQEcmCQgghpA5BRGRqZ86cQXh4ODIzMw36Krh77rkHd955J15++WXzhbuFsVmJiIzFDiAR2bRevXqhV69eeo+/88478cADD5gxkbYhQ4agffv2Fns+IiKAHUAislGVlZU4c+YMAMDV1RUtWrSQNlAdcnNzcePGDQBAy5Yt4eLiInEiIrIHLACJiIiI7Ax3ARMRERHZGRaARERERHaGBSARERGRnWEBSERERGRnWAASERER2RkWgERERER2hgUgERERkZ1hAUhERERkZ/4fawjk3ViNS0EAAAAASUVORK5CYII=", "text/html": [ "\n", "
\n", "
\n", " Figure\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ewald_Sphere = plt.Circle((0, K0_magnitude), K0_magnitude, color='b', fill=False)\n", "\n", "# Plot 2D\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.scatter(g[:,0], g[:,2], c='red',s=100)\n", "ax.scatter(0, K0_magnitude, c='green',s=100)\n", "\n", "ax.add_artist(Ewald_Sphere)\n", "\n", "ax.quiver([0,0,0,g[2001,0]],[K0_magnitude,K0_magnitude,0,0],[0,g[2001,0],g[2001,0],0],[-K0_magnitude, -K0_magnitude+0.063,0,0.063], units='xy', scale =1, width = .01)\n", "\n", "plt.text(1.86, .01,r'$\\vec{S_g}$', size=20)\n", "plt.text(1.5, -.13,r'$\\vec{g}_{ZOLZ}$', size=20)\n", "plt.text(1.8, 1,r'$\\vec{K_g}$', size=20)\n", "plt.text(.01,1,r'$\\vec{K_0}$', size=20)\n", "plt.title('Parallel Illumination')\n", "\n", "ax.axis('equal')\n", "plt.xlabel('x [1/nm]')\n", "plt.ylabel('z [1/nm]')\n", "plt.xlim(0,2)\n", "plt.ylim(-.3,1.7);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Origin of Excitation Error\n", "Part of the reason why we have an excitation error lays in the sample dimensions required for TEM investigations.\n", "\n", "This influence of the sample geometry is further explored in these notebooks:\n", "- [Relrod](CH2_06b-Relrod.ipynb)\n", "- [Fourier Transform Laboratroy](CH2_06b-3D_FFT.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Center of Ewald Shere\n", "So far we have considered the incident wave vector to be parallel to the Z-axis. \n", "However, we need to know the center of the Ewald sphere for any zone axis.\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The inner potential is 8.5kV\n", "Center of Ewald sphere [68.07196543 68.07196543 0. ]\n" ] } ], "source": [ "# INPUT\n", "zone_hkl = np.array([1,1,0])\n", "\n", "U0 = 0\n", "for atom in atoms:\n", " U0 += ks.feq(atom.symbol,0)*0.023933754\n", "\n", "volume = atoms.cell.volume # Needs to be in Angstrom for form factors\n", "AngstromConversion = 1.0e10 # So [1A (in m)] * AngstromConversion = 1\n", "NanometerConversion = 1.0e9 \n", "\n", "ScattFacToVolts=(scipy.constants.h**2)*(AngstromConversion**2)/(2*np.pi*scipy.constants.m_e*scipy.constants.e)*volume\n", "U0=U0*ScattFacToVolts\n", "print('The inner potential is {0:.1f}kV'.format(U0/1000))\n", "\n", "incident_wave_vector_vacuum = 1/wave_length_A\n", "K0_magnitude = incident_wave_vector = np.sqrt(1/wave_length_A**2 + U0 )#1/Ang\n", "\n", "center_ewald = np.dot(zone_hkl,reciprocal_lattice)\n", "center_ewald = center_ewald /np.linalg.norm(center_ewald)* incident_wave_vector\n", " \n", "normal = zone_hkl/ np.linalg.norm(zone_hkl)\n", "print('Center of Ewald sphere ',center_ewald)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Possible Reflections\n", "must be within the excitation error to the Ewald sphere.\n", "\n", "Find all Miller indices whose reciprocal point lays near the Ewald sphere with radius $K_0$ within a maximum excitation error $S_g$\n", "\n", "with $S_g \\approx (K_0^2 -|\\vec{K_0}+\\vec{g}|^2)/ 2K_0$\n", "\n", "First we produce all Miller indices up to a maximum value of \"hkl_max\" and then we check whether they fullfil above condition.\n", "\n", "Please change \"hkl_max\" and the maximum excitation error \"Sg_max\" and see what happens." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(3869, 3)\n", "Of the 132651 tested reciprocal lattice points, 3869 have an excitation error less than 0.10 1/nm\n" ] } ], "source": [ "# INPUT \n", "hkl_max = 25# maximum allowed Miller index\n", "Sg_max = .1 # 1/nm maximum allowed excitation error\n", "\n", "h = np.linspace(-hkl_max,hkl_max,2*hkl_max+1) # all evaluated single Miller Indices\n", "hkl = np.array(list(itertools.product(h,h,h) )) # all evaluated Miller indices\n", "g = np.dot(hkl,reciprocal_lattice) # all evaluated reciprocal lattice points\n", "\n", "# Calculate exitation errors for all reciprocal lattice points\n", "S = []\n", "for i in range(len(g)):\n", " ## Zuo and Spence, 'Adv TEM', 2017 -- Eq 3:14\n", " S.append(float((K0_magnitude**2-np.linalg.norm(g[i] - center_ewald)**2)/(2*K0_magnitude)))\n", "S = np.array(S)\n", "\n", "# Determine reciprocal lattice points with excitation error less than the maximum allowed one: Sg_max\n", "reflections = abs(S)< Sg_max\n", "\n", "Sg = S[reflections]\n", "g_hkl =g[reflections]\n", "print(g_hkl.shape)\n", "hkl = hkl[reflections]\n", " \n", "print ('Of the {0} tested reciprocal lattice points, {1} have an excitation error less than {2:.2f} 1/nm'.format( len(g) , len(g_hkl), Sg_max))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "The scattering geometry provides all the tools to determine which reciprocal lattice points are possible and which of them are allowed and which are forbidden.\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Navigation\n", "\n", "- **Back: [Analyzing Ring Diffraction Pattern](CH2_05-Diffraction_Rings)** \n", "- **Next: [Plotting of Diffraction Pattern](CH2_07-Plotting_Diffraction_Pattern.ipynb)** \n", "- **Chapter 2: [Diffraction](CH2_00-Diffraction.ipynb)** \n", "- **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" }, "livereveal": { "height": 768, "theme": "sky", "transition": "zoom", "width": 1024 }, "toc": { "base_numbering": "6", "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "191.2px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }