{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " **Chapter 2: [Diffraction](CH2_00-Diffraction.ipynb)** \n", "\n", "\n", "
\n", "\n", "\n", "# Atomic Form Factor\n", "\n", "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM//main/Diffraction/CH2_02-Atomic_Form_Factor.ipynb)\n", "\n", "\n", "[![OpenInColab](https://colab.research.google.com/assets/colab-badge.svg)](\n", " https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Diffraction/CH2_02-Atomic_Form_Factor.ipynb)\n", " \n", "part of\n", "\n", " **[MSE672: Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**\n", "\n", "**Spring 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", "Background and methods to analysis and quantification of data acquired with transmission electron microscopes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In this notebook we explore how an electron interacts with a single atom.\n", "\n", "The key parameter for the interaction of an electron interacting with an atom is the **atomic form-factor**.\n", "\n", "In the following of this *diffraction* section, we will look at the interaction of electrons with assemblies of atoms." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Import numerical and plotting python packages\n", "### Check Installed Packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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') < '0.2026.1.2':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install --upgrade pyTEMlib -q\n", "\n", "print('done')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load the plotting and figure packages\n", "> Note for Google Colab\n", ">\n", "> **Restart Session** in the **Runtime Menu**\n", "\n", "The kinematic scattering package is in diffraction_tools of pyTEMlib.\n", "That library also includes the atomic form factors from Kirkland's book." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# additional package \n", "import scipy # we use the constants part again.\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " from google.colab import output\n", " output.enable_custom_widget_manager()\n", " \n", "# Import libraries from the pyTEMlib\n", "import pyTEMlib # Kinematic scattering Library is in pyTEMlib.diffraction_tools\n", " # with Atomic form factors from Kirklands book" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coulomb Force\n", "\n", "The electron scatters at the Coulomb force of the screened nucleus of an atom. This force is:\n", "\n", "$\\mathbf{F} = \\frac{1}{4\\pi\\varepsilon_0}\\frac{Qq}{r^2}\\mathbf{\\hat{e}}_r \n", "= k_\\text{e}\\frac{Qq}{r^2}\\mathbf{\\hat{e}}_r $\n", "\n", "$k_\\text{e} = \\frac{1}{4\\pi\\varepsilon_0}= 8.987\\,551\\,787\\,368\\,1764\\times 10^9~\\mathrm{N\\ m^2\\ C^{-2}}$\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " k_e = 8.9876e+09 N m²C⁻²\n", " F_r_m = 20007.8 N m² kg⁻¹ = 20007.8 m³s⁻²\n" ] } ], "source": [ "Z = 79 # gold\n", "\n", "k_e = 1/(4* scipy.constants.pi * scipy.constants.epsilon_0)\n", "F_r_m = k_e * Z* scipy.constants.elementary_charge**2 /scipy.constants.electron_mass\n", "print(f\" k_e = {k_e:.5} N m\\u00b2C\\u207B\\u00b2\")\n", "print(f\" F_r_m = {F_r_m:.1f} N m\\u00b2 kg\\u207B\\u00B9 = {F_r_m:.1f} m\\u00b3s\\u207B\\u00B2\")" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { 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", 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If too small this calculation will take a while\n", " dt = 1e-20 # s\n", " \n", " x = -50.0*1e-9 # starting x in m\n", " y = impact_param*1e-9 #in m\n", " #starting y\n", " x_coords=[x] #array for the x coordinates of the plot\n", " y_coords=[y] #array for the y coordinates of the plot\n", " vx = v_c * scipy.constants.c #initial x velocity in m/s\n", " vy = 0.0 #initial y velocity\n", " \n", " r = np.sqrt(x*x + y*y)\n", " rold = r*2 # an arbitrary value more than r\n", "\n", " k_e = 1/(4* scipy.constants.pi * scipy.constants.epsilon_0) #[N m^2 C^-2]\n", " F_r_m = -k_e * Z* scipy.constants.elementary_charge**2 /scipy.constants.electron_mass # [ N m^2 / kg]\n", " \n", " # The plot coordinates are generated as long as the incident particle\n", " # is going towards the origin( which means that r < rold )\n", " # or\n", " # if it is coming out, as long as r < 50.0 nm. You can choose this to be\n", " # something else.\n", " while (r < rold) or ( r < 50.0*1e-9) :\n", " rold = r # old r is changed to the current r\n", " x = x + vx*dt# calculate new x\n", " y = y + vy*dt# calculate new y\n", " # add x and y to the plotting coordinates for x and y\n", " x_coords.append(x)\n", " y_coords.append(y)\n", " r = np.sqrt(x*x + y*y)\n", " \n", " #vx = vx + x-acceleration*dt = vx + Fx/m*dt \n", " #Fx = x component of Coulomb force = (magnitude of F)*cos(theta) =\n", " #(magnitude of F)*x/r = \n", " #vx = vx + (F_r/m/r^2)*x/r = F_r_m * x/r^3,\n", " vx = vx + F_r_m*x/r**3*dt\n", " #as for vx\n", " vy = vy + F_r_m*y/r**3*dt\n", " \n", " return np.array(x_coords), np.array(y_coords)\n", "\n", "\n", "#plotting trajectories for 4 impact parameters\n", "plt.figure()\n", "for b in [-1e-5, -0.001, -0.1, -1.0, -2.0, -4.0, -6.0]:\n", " xc, yc = coulomb_plot(b, Z= 29, v_c = 0.7)\n", " plt.plot(xc*1e9,yc*1e9, label = str(b))\n", "\n", "plt.xlabel('distance [nm]')\n", "plt.ylabel('impact parameter [nm]')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above graph was calulated for 200keV electrons.\n", "What changes if you change the v_c = v/c parameter to higher or lower speeds?\n", "\n", "|E (keV)|$\\lambda$ (pm) | M/m$_0$ | v/c|\n", "--------|---------------|---------|----|\n", "|10 | 12.2 | 1.0796 | 0.1950 |\n", "|30 | 6.02 | 1.129 | 0.3284 |\n", "|100 | 3.70 | 1.1957 | 0.5482|\n", "|200 | 2.51 | 1.3914 | 0.6953|\n", "|400 | 1.64 | 1.7828 | 0.8275 |\n", "|1000 | 0.87 | 2.9569 | 0.9411|\n", "\n", "You can also change the atom number." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c7cc59864ac64684a5ce6a1b14a92da9", "version_major": 2, "version_minor": 0 }, "image/png": 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"text/html": [ "\n", "
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transform of a density distribution of the scattering object from real space to momentum (or reciprocal) space.\n", "\n", "Since an electron scatters through the coulomb force of the (screend) nucleus, the form factor is the inner potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Atomic Form Factor\n", "\n", "$$ |f(\\theta)|^2 = \\frac{d\\sigma(\\theta)}{d\\Omega} $$\n", "\n", "What does that mean for us:\n", "\n", "- The atomic structure factor gives the amplitude of an electron wave\n", "\tscattered from an isolated atom.\n", "- $|f(\\theta)|^2$ is proportional to the scattered intensity.\n", "- The atomic scattering factor depends on atomic number $Z$, wavelength $\\lambda$ and scattering angle $\\theta$. \n", "- The atomic structure factors for each element are tabulated.\n", "\n", "The atomic form factor gives us the probability of an electron scattering in a certain angle." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tabulated Atomic Form Factors\n", "The calculated form factors are tabulated and can be plotted according to the momentum transfer.\n", "\n", "Here we use the values from Appendix C of Kirkland, \"Advanced Computing in Electron Microscopy\", 3rd ed.\n", "\n", "The calculation of electron form factor for specific $q$ perfommed by the function *feq* in the kinematic_scattering of pyTEMlib using equation Kirkland C.17" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "b267a14c758241d1bd7f74d1870c3b57", "version_major": 2, "version_minor": 0 }, "image/png": 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