{ "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 2026**
\n", "by Gerd Duscher\n", "\n", "Microscopy Facilities
\n", "Institute of Advanced Materials & Manufacturing
\n", "Materials Science & Engineering
\n", "The University of Tennessee, Knoxville\n", "\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": [ "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') < '0.2026.1.3':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install pyTEMlib -q --upgrade\n", "\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 from matplotlib\n", "* iteration_tools \n", " \n", "and some libraries from the pyTEMlib\n", "* kinematic scattering from the diffraction_tools library.\n", "* structures from the crystal_tools library\n", "> Note for Google Colab\n", ">\n", "> **Restart Session** in the **Runtime Menu**" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pyTEM version: 0.2026.1.3\n", "notebook version: 2026.01.15\n" ] } ], "source": [ "%matplotlib widget\n", "\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " from google.colab import output\n", " output.enable_custom_widget_manager()\n", "\n", "# additional package \n", "import itertools \n", "import scipy\n", "\n", "# Import libraries from the book\n", "import pyTEMlib\n", "\n", "# it is a good idea to show the version numbers at this point for archiving reasons.\n", "__notebook_version__ = '2026.01.15'\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", ">Note\n", ">\n", ">Diffraction in transmission, is more accurately named Laue condition\n", ">\n", ">and Bragg condition is originally reserved for reflection.\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": 2, "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 = pyTEMlib.crystal_tools.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\n", "\n", "Brcause if the convention of the *ase* package, all length are internally in Angstrom." ] }, { "cell_type": "code", "execution_count": 3, "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/nm\n" ] } ], "source": [ "acceleration_voltage_V = 200.0 *1000.0 #V\n", "\n", "wave_length_A = pyTEMlib.utilities.get_wavelength(acceleration_voltage_V, unit='A')\n", "\n", "print(f'The wavelength for {acceleration_voltage_V/1000:.1f}kV is : {wave_length_A*100.:.5f}pm')\n", "\n", "wave_vector_magnitude = 1/wave_length_A\n", "K0_magnitude = wave_vector_magnitude\n", "\n", "print(f'The magnitude of the incident wavevector is {K0_magnitude*10:.1f} 1/nm')" ] }, { "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. 39.8734569] 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": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9ba6cf08d1594d85a7752a9b0f0693b8", "version_major": 2, "version_minor": 0 }, "image/png": 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\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": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.float64(-9.9), np.float64(9.9), np.float64(-9.9), np.float64(9.9))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1ef1880ffaf841a2b25f010b0217f5ff", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8d2ef4d430eb40deaf776826b850b83c", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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", "Laue Zones are defined by the **Weiss Zone Law**:\n", "\n", "The recirocal lattice vectors $\\vec{g}$ with Miller indices $[\\rm{h k l}]$ are perpendicular to the zone axis $[\\rm{U V W}]$ if:\n", "$$ hU+kV+lW = 0$$\n", "This Weiss Zone Law is working in any crystal system thanks to the Miller indices and has been extended to any Laue Zone $n$ with \n", "$$ hU+kV+lW = n$$\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 higher order Laue Zones 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": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ed0e9bb976da46f595a274f9546468df", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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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": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "b5170989239545f59b7be6f41944d0a9", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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 = 15. # 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": 10, "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": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1e43f96b392e4fe59cfa20fe8c0e4721", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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", "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 = pyTEMlib.utilities.get_wavelength(acceleration_voltage_V, unit='A')\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 = matplotlib.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 = matplotlib.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": 11, "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": "4da6c017b55c4f06ad0fde04472de168", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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 = pyTEMlib.utilities.get_wavelength(acceleration_voltage_V, unit='A')\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.set_aspect('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": 12, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a319dde93959448c919c14818b559854", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\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.set_aspect('equal')\n", "plt.xlabel('x [1/nm]')\n", "plt.ylabel('z [1/nm]')\n", "plt.xlim(-.1,2)\n", "plt.ylim(-.3,1.2);" ] }, { "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", "\n", "- [Fourier Transform Laboratory](CH2_06b-FFT.ipynb)\n", "- [Relrod](CH2_06c-Relrod.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": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The inner potential is 0.0kV\n", "Center of Ewald sphere [19.11813988 19.11813988 0. ]\n" ] } ], "source": [ "# INPUT\n", "zone_hkl = np.array([1,1,0])\n", "\n", "U0 = 0\n", "for atom in atoms:\n", " U0 += pyTEMlib.diffraction_tools.get_form_factor(atom.symbol, 0.)[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", "\n", "print(f'The inner potential is {U0/1000:.1f}kV')\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": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(351, 3)\n", "Of the 132651 tested reciprocal lattice points, 351 have an excitation error less than 0.10 1/nm\n" ] } ], "source": [ "# INPUT \n", "hkl_max = 25# maximum allowed Miller index\n", "Sg_max = .01 # 1/A 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 (f'Of the {len(g)} tested reciprocal lattice points, {len(g_hkl)} have an excitation error less than {Sg_max*10:.2f} 1/nm')\n" ] }, { "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.ipynb)** \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": "3.13.5" }, "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% - 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