\n",
" \n",
" | Gerd Duscher | \n",
" Khalid Hattar | \n",
"
\n",
" \n",
" | Microscopy Facilities | \n",
" Tennessee Ion Beam Materials Laboratory | \n",
"
\n",
" \n",
" \n",
" | Materials Science & Engineering | \n",
" Nuclear Engineering | \n",
"
\n",
" \n",
" | Institute of Advanced Materials & Manufacturing | \n",
" | \n",
"
\n",
" \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"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false
},
"source": [
"## Introduction\n",
"In this notebook, we will make a dynamic simulation of the scattering process.\n",
"\n",
"The core of this algorithm is used in many different libraries.\n",
"\n",
"I follow in my description mostly the book of Kirkland, from where we also use the scattering parameters. The code has been completely rewritten so that the mechnaism of the algorithm can be understood on a basic level. \n",
"\n",
"All commercial and open-source codes use the same base algorithm but are highly tuned for usability, variabilty, features and speed. This was not the goal here.\n",
"\n",
"Here are a few of the more common open-source programs\n",
"- [abTEM](https://github.com/jacobjma/abTEM)\n",
"- [clTEM](https://github.com/JJPPeters/clTEM)\n",
"- [MuSTEM](https://github.com/ningustc/MuSTEM)\n",
"- [Dr. Probe](https://er-c.org/barthel/drprobe/)\n",
"\n",
"\n",
"## Load relevant python packages\n",
"### Check Installed Packages"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"installing pyTEMlib\n",
"^C\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": [
"### Import numerical and plotting python packages\n",
"Import the python packages that we will use:\n",
"\n",
"Beside the basic numerical (numpy) and plotting (pylab of matplotlib) libraries, we need 3D plotting library and some scipy libraries\n",
"\n",
"and a library from pyTEMlib:\n",
"* kinematic scattering library."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"You don't have igor2 installed. If you wish to open igor files, you will need to install it (pip install igor2) before attempting.\n",
"You don't have gwyfile installed. If you wish to open .gwy files, you will need to install it (pip install gwyfile) before attempting.\n",
"Symmetry functions of spglib enabled\n",
"Using kinematic_scattering library version {_version_ } by G.Duscher\n",
"pyTEM version: 0.2023.9.1\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",
"# additional package \n",
"from mpl_toolkits.mplot3d import Axes3D \n",
"import itertools\n",
"import scipy.constants\n",
"import scipy.special \n",
"\n",
"# Import libraries from pyTEMlib\n",
"import pyTEMlib\n",
"import pyTEMlib.kinematic_scattering as ks # Kinematic sCattering Library\n",
" # Atomic form factors from Kirkland's book\n",
"\n",
"# For archiving reasons it is a good idea to print the version numbers out at this point\n",
"print('pyTEM version: ',pyTEMlib.__version__)\n",
"\n",
"__notebook__ = 'CH2_D02-Multislice'\n",
"__notebook_version__ = '2022_02_25'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Overview of Multislice Algorithm\n",
"\n",
"The multislice solution is formally equivalent to a solution of the [``Howie-Whelan equation``](https://doi-org.proxy.lib.utk.edu/10.1098/rspa.1961.0157) (which is the differential form of the Bloch wave solution), if the slice thickness $\\Delta$z is small enough. \n",
"\n",
"The idea is to slice the sample into thin slices that can be handled well in electron diffraction.\n",
"\n",
"And then we step through these slices one by one and keep track of the incoming and exiting wave.\n",
"\n",
"We seperate (serialize) the problem to conquer it iteratively.\n",
"\n",
"The algorithm can be divided in several steps.\n",
"\n",
"1. So first we need the projected atomic potentials for each element.\n",
"2. Then we need to build the slices. The slices are one layer of atoms which are all at the top. And then we have vacuum for the rest.\n",
"3. The transmission function will deal with the distortion of the wave by the atom potentials.\n",
"4. The Fresnel propagator takes care of the vacuum between the atomic layers.\n",
"5. We need to define the incident wave.\n",
"6. We let this wave travel through the different layers, iteratively.\n",
"\n",
"Step 3 is done in real space and step 4 in Fourier Space and so a lot of Fourier transfom is going on. This lends itself to speed-up through parallel fast Fourier transform algorithms, which you can see at the increasing codes with gpu usage."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step1: Projected Potential \n",
"\n",
"Providing the potentials and placing the atoms is a surprisingly computer intensive task for initialization of the simulation. This notebook gives up flexibility for speed in placing the atoms (no sub-pixel movement).\n",
"\n",
"### Projected Potential from Parametrization of Atomic Form Factor\n",
"Following Kirkland (2$^nd$ edition Appendix C page 252),\n",
"the atom potential is with $r^2 = x^2+z^2+z^2$ and $V(x,y,z) =V(\\vec{r})$ \n",
"$$\n",
"v(x, y, z) = 2 \\pi a_0 e_0 \\int f_e(q) \\exp \\left( -2 \\pi i \\vec{q} \\vec{r} \\right) d^3r \\\\\n",
"= 2 \\pi^2 a_0 e_0 \\sum_i \\frac{a_i}{r} \\exp \\left( -2 \\pi r \\sqrt{b_i} \\right) + 2\\pi^{5/2} a_0 e_0 \\sum_i c_i d_i^{-3/2} \\exp \\left(\\frac{-\\pi^2 r^2}{d_i} \\right)\n",
"$$\n",
"with $r^2 = x^2+z^2+z^2$\n",
"\n",
"The ``projected potential`` is then:\n",
"$$\n",
"v_z(x,y) = \\int_{-\\inf}^{\\inf} V(x,y,z) dz \\\\\n",
"= 4 \\pi^2 a_0 e_0 \\sum_i a_i K_0 \\left( 2 \\pi r \\sqrt{b_i} \\right)\n",
"+ 2 \\pi^2 a_0 e_0 \\sum_i \\frac{c_i}{d_i} \\exp \\left( \\frac{-\\pi^2 r^2}{d_i} \\right)\\\\\n",
"= 2 \\pi^2 a_0 e_0 \\left[2 \\sum_i a_i K_0 \\left( 2 \\pi r \\sqrt{b_i} \\right) \n",
"+\\sum_i \\frac{c_i}{d_i} \\exp \\left( \\frac{-\\pi^2 r^2}{d_i} \\right) \\right]\n",
"$$\n",
"with $ r^2 = x^2 + y^2$, we need to calculate the 1D potential only, dueto the radial symmetry of atoms.\n",
"\n",
"The ``spherical Bessel function`` $\\bf K_0$ is providedby the ``scipy`` special package.\n",
"\n",
"We will use the last of the equations in our calculation.\n",
"\n",
"The setting up of the potential can take quite some computer power, so there are a few constricts in this notebook on where to put the atoms, these constricts can easily be overcome"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"def potential_1D(element, r):\n",
" \"\"\"calculates the projected potential of an atom of element \n",
" \n",
" The projected potential will be in units of V nm^2,\n",
" however, internally we will use Angstrom instead of nm!\n",
" \"\"\"\n",
" \n",
" # get lementary constants\n",
" a0 = scipy.constants.value('Bohr radius') * 1e10 #in Angstrom\n",
" Ry_div_e = scipy.constants.value('Rydberg constant times hc in eV') # in V\n",
" e0 = 2* Ry_div_e * scipy.constants.value('Bohr radius') * 1e10\n",
"\n",
" pre_factor = 2.0 * np.pi**2 * a0 * e0\n",
"\n",
" param = ks.electronFF[element] # parametrized form factors\n",
" fL = r*0 # Lorentzian term\n",
" fG = r*0 # Gaussian term\n",
" for i in range(3):\n",
" fL += param['fa'][i] * scipy.special.k0(2 * np.pi * r * np.sqrt(param['fb'][i]))\n",
" fG += param['fc'][i] / param['fd'][i] * np.exp(-np.pi**2 * r**2 / param['fd'][i])\n",
" fL[0,0] = fL[0,1]\n",
" \n",
" return pre_factor * (2 * fL + fG) /100 # V Angstrom^2\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To retrieve the atomic projected potential, the function above uses a rather unconventional unit for the elementary charge $e$.\n",
"\n",
"Starting from the relationship for the Rydberg energy: \n",
"$$Ry = 0.5 e^2/ a_0 $$\n",
"\n",
"and using the value for $Ry$ as 13.6 eV so that $Ry/e = 13.6$ V; we get:\n",
"\n",
"$$e_0 = 2* a_0 Ry/e$$\n",
"\n",
">\n",
">The elementary charge $e_0$ is then 1.44 V nm \n",
">\n",
"\n",
"for $a_0 = 0.0529$ nm"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ry = 13.6057 eV and Ry/e = 13.6057 V\n",
"elemntary charge e = 1.4400 V nm\n"
]
}
],
"source": [
"Ry = scipy.constants.value('Rydberg constant times hc in eV') # in V\n",
"print(f'Ry = {Ry:.4f} eV and Ry/e = {Ry:.4f} V')\n",
"e = 2* Ry *scipy.constants.value('Bohr radius') * 1e9 # conversion to nm\n",
"print(f'elemntary charge e = {e:.4f} V nm')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot quarter of projected atom potential\n",
"\n",
"We now use this function to plot a projected atom potential up in a 1nm by 1nm image. "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"def potential_1D(element, r):\n",
" \"\"\"calculates the projected potential of an atom of element \n",
" \n",
" The projected potential will be in units of V nm^2,\n",
" however, internally we will use Angstrom instead of nm!\n",
" \"\"\"\n",
" \n",
" # get lementary constants\n",
" a0 = scipy.constants.value('Bohr radius') * 1e10 #in Angstrom\n",
" Ry_div_e = scipy.constants.value('Rydberg constant times hc in eV') # in V\n",
" e0 = 2* Ry_div_e * scipy.constants.value('Bohr radius') * 1e10\n",
" \n",
" pre_factor = 2 * np.pi ** 2 * a0 * e0\n",
"\n",
" param = ks.electronFF[element] # parametrized form factors\n",
" fL = r*0 # Lorentzian term\n",
" fG = r*0 # Gaussian term\n",
" for i in range(3):\n",
" fL += param['fa'][i] * scipy.special.k0(2 * np.pi * r * np.sqrt(param['fb'][i]))\n",
" fG += param['fc'][i] / param['fd'][i] * np.exp(-np.pi**2 * r**2 / param['fd'][i])\n",
" fL[0,0] = fL[0,1]\n",
" \n",
" return pre_factor * (2 * fL + fG) # V Angstrom^2\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'distance ($\\\\AA$)')"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
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",
"text/html": [
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],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"atom_potential_round = np.zeros([2*a_nx, 2*a_ny])\n",
"atom_potential_round[a_nx:,a_ny:] = atom_potential\n",
"atom_potential_round[a_nx:,:a_ny] = np.flip(atom_potential, axis=1)\n",
"atom_potential_round[:a_nx,a_ny:] = np.flip(atom_potential, axis=0)\n",
"atom_potential_round[:a_nx,:a_ny] = np.flip(np.flip(atom_potential, axis=0), axis=1)\n",
"plt.figure()\n",
"plt.title(f'Log plot of atomic potential of {element_name}')\n",
"\n",
"plt.imshow(np.log(atom_potential_round), extent=[0,2*a_nx*pixel_size,2*a_ny*pixel_size,0])\n",
"plt.xlabel('distance ($\\AA$)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Embedd atoms in projected crystals\n",
"\n",
"We place the atom in the corner of a matrix with the same size as the image to be simulated.\n",
"\n",
"With the numpy roll function we now can move this atom wherever we want, but only with pixel precision.\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
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