\n",
"\n",
"# Introduction to X-Rays \n",
"\n",
"[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM/main/Spectroscopy/CH4_12-Introduction_X_Rays.ipynb)\n",
" \n",
"\n",
"[](\n",
" https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Spectroscopy/CH4_12-Introduction_X_Rays.ipynb)\n",
"\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",
"Background and methods to analysis and quantification of data acquired with transmission electron microscopes.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load relevant python packages\n",
"### Check Installed Packages"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"done\n"
]
}
],
"source": [
"import sys\n",
"import importlib.metadata\n",
"def test_package(package_name):\n",
" \"\"\"Test if package exists and returns version or -1\"\"\"\n",
" try:\n",
" version = importlib.metadata.version(package_name)\n",
" except importlib.metadata.PackageNotFoundError:\n",
" version = '-1'\n",
" return version\n",
"\n",
"if test_package('pyTEMlib') < '0.2026.1.1':\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",
"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": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib widget\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import sys\n",
"import os\n",
"if 'google.colab' in sys.modules:\n",
" from google.colab import output\n",
" from google.colab import drive\n",
" output.enable_custom_widget_manager()\n",
" \n",
"__notebook__ = 'CH4_12-Introduction_X_Rays'\n",
"__notebook_version__ = '2026_01_19'\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inelastic Scattering:\n",
"\n",
"When a high energy electron collides with matter there are several process going on:\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In an TEM and SEM there are quite a few inelastic signals available:\n",
"- Secondary electrons\n",
"- X-Rays\n",
"- Auger electrons\n",
"- Light (photons in visible range)\n",
"\n",
"## X-Rays\n",
"Here we consider only X-Rays and Auger Electrons as those originate from competing processes:\n",
"\n",
"\n",
"The excited atom has two possibilities to return to the ground state:\n",
"\n",
"We consider the energy before and after the relaxation process.\n",
"### X-Ray branch \n",
"The emitted photon has the energy of the energy gained in the relaxtion process. In the carbon atom case above, an electron from the 2p states relaxes to the *1s* state: from the L$_3$ to the K shell.\n",
"\n",
"The energy difference of a photon is the $E_K$ - $E_L$, which is well in the X-ray range.\n",
"\n",
"*Please note that the transition from 2s to 1s is dipole forbidden and cannot occur.*\n",
"\n",
"### Auger branch \n",
"The emitted electron leaves behind an atom with a closed K shell ($-E_K$) and looses two 2p electrons ($+2 E_L$. This energy will be transfered to the Auger electron as kinetic energy $ E_{kin} = E_K-2E_L$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"X-ray photon has the energy 277 eV\n",
"Auger electron has the kinetic energy 270 eV\n"
]
}
],
"source": [
"## \n",
"E_K = 284 # in eV\n",
"E_L = 7 # in eV\n",
"\n",
"print(f'X-ray photon has the energy {E_K-E_L} eV')\n",
"print(f'Auger electron has the kinetic energy {E_K-2* E_L} eV')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fluorescent Yield\n",
"\n",
"The Auger and X-ray branches are not equally probable. In the carbon atom characteristic X-ray emission occurs at about 26% of the K-shell ionization. \n",
"\n",
"The fraction that of the ionization that *yields* photons is called **fluorescent yield** $\\omega$. \n",
"\n",
"The fluorescent yield is strongly dependent on the atomic number [E.A. Preoteasa et al. 2012 – ISBN 978-1-61470-208-5]:\n",
"\n",
"\n",
"\n",
"The fluorescent yield follows approximatively an equation of the form:\n",
"\n",
"$$ \\omega = \\frac{Z^4}{\\alpha+Z^4} $$\n",
"with \n",
"- $Z$: atomic number\n",
"- $\\alpha$: constant about 10$^6$ for K lines"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
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"model_id": "7ff266eed20a40f6b59dbf0f5ea80da6",
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",
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