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Remove unused folders in _build

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Sylvain Tricot 2025-07-18 11:26:57 +02:00
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commit d9cc696d79
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"# Activity 1: Getting started\n",
"\n",
"MsSpec is a Fortran code with two components: Phagen (Written by R. Natoli) and Spec (written by D. Sébilleau). Phagen computes the phase shifts of the electronic wave propagating in the matter on a spherical harmonics basis. Spec uses those phase shifts to compute the multiple scattering process and simulate the intensity of different electronic spectroscopies.\n",
"\n",
"In the most recent version of MsSpec, the program is interfaced with python (https://msspec.cnrs.fr/), allowing for much more flexibility and interplay with other simulation techniques.\n",
"\n",
"## Building atomic systems\n",
"\n",
"MsSpec works in the *cluster* approach. Building such a cluster for a calculation is a fundamental step.\n",
"We use the [python Atomic Simulation Environment (ASE)](https://wiki.fysik.dtu.dk/ase/) for this.\n",
"\n",
"ASE is a set of tools and Python modules for setting up, manipulating, running, visualizing and analyzing atomistic simulations.\n",
"Building atomic systems, structures... is pretty straightforward:"
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"# To build a molecule with ASE\n",
"from ase.build import molecule\n",
"# To view\n",
"from ase.visualize import view\n",
"\n",
"# Create a water molecule\n",
"water = molecule('H2O')\n",
"# Display it\n",
"view(water)"
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"## Barebone script for MsSpec\n",
"\n",
"MsSpec can simulate different electronic spectroscopies like PED, AED, LEED, EXAFS, APECS and more will be included in the forthcoming version. However, it is really well-suited for PhotoElectron Diffraction simulation, and the python interface is only fully available for it at the moment. Since PED covers all the MsSpec features and concepts, we will focus on this technique.\n",
"\n",
"There are typically 3 steps to follow to get a result with MsSpec:\n",
"\n",
"1. Create a *cluster*\n",
"2. Create an ASE *calculator*\n",
"3. Run the simulation\n",
"\n",
"### PED polar scan for Cu(001)"
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"```{literalinclude} cu.py\n",
":end-before: The \"emitter\"\n",
":linenos:\n",
"```"
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"source": [
"from ase.io import read\n",
"from ase.visualize import view\n",
"from msspec.calculator import MSSPEC\n",
"\n",
"\n",
"cluster = read('copper.cif')\n",
"# view the cluster\n",
"view(cluster, viewer='x3d')"
]
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"source": [
"```{literalinclude} cu.py\n",
":start-at: The \"emitter\"\n",
":lineno-match:\n",
"```\n",
":::{figure-md} Cu-XPD\n",
"<img src=\"fig1.png\" width=\"600px\" align=\"center\">\n",
"\n",
"Cu(2p) polar scan for the copper cluster above\n",
":::"
]
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"source": [
"## Shaping a cluster"
]
},
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"source": [
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Based on the previous *.cif file, create a new cluster without the deepest plane and run the same calculation for the same emitter\n",
"\n",
"```{note}\n",
"As the cluster will contain fewer atoms, the emitter index will be different\n",
"```\n",
"\n",
"What do you conclude ?\n",
":::\n",
"\n",
"::::"
]
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"source": [
"```{toggle}\n",
"\n",
":::{figure-md} Cu-4planes3planes\n",
"<img src=\"fig2.png\" width=\"600px\" align=\"center\">\n",
"\n",
"Comparison between 4 and 3 planes for an emitter in the 3{sup}`rd` plane.\n",
":::\n",
"\n",
"Not all atoms contribute equally to the total signal. Some of them can be removed to save computation time and memory.\n",
"```"
]
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"The number of atoms used for the calculation greatly impact the calculation time and memory. Most of the time, a cluster is shaped as an hemisphere to minimize the number of atoms to take into account"
]
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"<Popen: returncode: None args: ['/opt/msspec/msspec_venv/bin/python', '-m', ...>"
]
},
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"source": [
"from msspec.calculator import MSSPEC\n",
"from msspec.utils import hemispherical_cluster, get_atom_index\n",
"from ase.build import bulk\n",
"from ase.visualize import view\n",
"\n",
"copper = bulk('Cu', cubic=True)\n",
"cluster = hemispherical_cluster(copper, planes=3, emitter_plane=2)\n",
"cluster.emitter = get_atom_index(cluster, 0,0,0)\n",
"\n",
"view(cluster)"
]
},
{
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{
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"\n",
" </X3D>\n",
" </body>\n",
"</html>\n",
"\n"
],
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"<IPython.core.display.HTML object>"
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},
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"view(cluster, viewer='x3d')"
]
},
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"id": "4a71c734-8c73-49a2-9f27-12157841405c",
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"source": [
":::{figure-md} Cu-hemi\n",
"<img src=\"fig3.png\" width=\"600px\" align=\"center\">\n",
"\n",
"Cu(2p) polar scan for the hemispherical cluster.\n",
":::"
]
},
{
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}
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msspecbook/_build/jupyter_execute/Activity02/Activity02.ipynb
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{
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{
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"source": [
"# Activity 3: Adsorbates and the single scattering approach\n",
"\n",
"Photoelectron diffraction is widely used to study the adsorption of atoms or molecules on a crystalline surface. Photoelectrons from adsorbates are scattered by the underlying surface, carrying information about the adsorption site, bond length and/or molecule orientation…. Thanks to a simulation, such information becomes quantitative with a high degree of accuracy.\n",
"\n",
"Calculations of the multiple scattering using matrix inversion have the great advantage of being exact, including all scattering paths. On the other hand, memory consumption soon becomes a problem as the kinetic energy and number of atoms to be considered increase. As an approximation, it is possible to only consider a single scattering from the emitter to any atom in the cluster. This approximation is extremely computationally fast and can give satisfactory results for adsorbates. We’ll see later that this approach is rather too simplistic for most cases.\n",
"\n",
"## Oxygen on Rh(001)\n",
"In a paper published in 1998, T. Gerber *et al.* used the quite high backscattering factor of Rhodium atoms to probe the distance of Oxygen atoms adsorbed on a Rhodium surface. Some electrons coming from Oxygen atoms are ejected toward the Rhodium surface. They are then backscattered and interfere with the direct signal comming from Oxygen atoms (see the figure below). They demonstrated both experimentally and numerically with a sinle scattering computation that this lead to a very accurate probe of adsorbed species that can be sensitive to bond length changes of the order of {math}`\\pm 0.02 \\mathring{A}`.\n",
"\n",
":::{seealso}\n",
"based on this paper from T. Greber *et al.* [Phys. Rev. Lett. **81**(8) p1654 (1998)](https://doi.org/10.1103/PhysRevLett.81.1654)\n",
":::"
]
},
{
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"source": [
":::{figure-md} RhO-fig\n",
"<img src=\"RhO_fig0.jpg\" alt=\"RhO\" width=\"300px\" align=\"center\">\n",
"\n",
"Interferences produced by the backscattering effect\n",
":::"
]
},
{
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"source": [
"### Computing the scattering factor\n",
"\n",
"To illustrate that photoelectrons emitted by Oxygen adsorbates towards the Rhodium surface can be backscattered, we will start by computing the scattering factor for both O and Rh atoms.\n",
"\n",
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"By using the `Atoms` class of the `ase` package, try to build a O-Rh chain where atoms are 4 Å apart. Here is the begining of the script. Try to complete the line of code and view your two-atoms chain.\n",
"\n",
"```python\n",
"from ase import Atoms\n",
"from ase.visualize import view\n",
"\n",
"# Create an atomic chain O-Rh\n",
"cluster = Atoms(... # Fill this line\n",
"```\n",
":::\n",
"\n",
"::::"
]
},
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"hide-cell"
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},
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"source": [
"from ase import Atoms\n",
"from ase.visualize import view\n",
"\n",
"# Create an atomic chain O-Rh\n",
"cluster = Atoms(['O', 'Rh'], positions = [(0,0,0), (0,0,4.)])"
]
},
{
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{
"data": {
"text/html": [
"<html>\n",
" <head>\n",
" <title>ASE atomic visualization</title>\n",
" <link rel=\"stylesheet\" type=\"text/css\" href=\"https://www.x3dom.org/release/x3dom.css\"></link>\n",
" <script type=\"text/javascript\" src=\"https://www.x3dom.org/release/x3dom.js\"></script>\n",
" </head>\n",
" <body>\n",
" <X3D width=\"400px\"; height=\"300px\";>\n",
"\n",
"<!--Inserting Generated X3D Scene-->\n",
"<scene>\n",
" <viewpoint position=\"0 0 8.0\">\n",
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"\n",
" </X3D>\n",
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"</html>\n",
"\n"
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},
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"source": [
"As previously, we create a calculator, we attach our 2 atoms cluster to this calculator and we define the first atom in the chain as the emitter\n",
"\n",
":::{literalinclude} RhO_sf.py\n",
":start-at: calc =\n",
":end-at: emitter =\n",
":::"
]
},
{
"cell_type": "markdown",
"id": "21763c63-9bd1-4e80-944a-9cf313894b89",
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"source": [
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"We use the `get_scattering_factors` method [(see its documentation)](https://msspec.cnrs.fr/modules/calculator.html#calculator._PED.get_scattering_factors) to compute the scattering factors at 723 eV.\n",
"\n",
"How large is the backscattering factor of Rhodium with respect to that of Oxygen ?\n",
":::\n",
"\n",
"::::"
]
},
{
"cell_type": "markdown",
"id": "14d39e21-eee0-411b-8347-25e932075c83",
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"source": [
"```{toggle}\n",
"\n",
":::{literalinclude} RhO_sf.py\n",
":start-at: Compute\n",
":::\n",
"\n",
":::{figure-md} SF-fig\n",
"<img src=\"RhO_fig1.jpg\" alt=\"Scattering factors\" width=\"600px\" align=\"center\">\n",
"\n",
"Polar representation of the scattering factor\n",
":::\n",
"\n",
"```"
]
},
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"source": [
"### Interferences due to backscattering\n",
"\n",
"Let an Oxygen atom (in red) being adsorbed at a distance $z_0$ of an *fcc* site of the Rh(111) surface."
]
},
{
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"source": [
":::{figure-md} Rho-fig2a\n",
"<img src=\"RhO_fig2a.jpg\" width=\"600px\" align=\"center\">\n",
"\n",
"Small cluster used for the calculation.\n",
":::"
]
},
{
"cell_type": "markdown",
"id": "d6145250-5548-49a6-8b50-0bb7c5b454da",
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"source": [
"We will compute for different values of the adsorption height $z_0$.\n",
"\n",
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Complete the script below to compute the ($\\theta,\\phi$) scan of the photodiffraction of O(1s) adsorbed on a *fcc* site on Rh(111) surface.\n",
"\n",
"```{literalinclude} RhO_tofill.py\n",
":lineno-match:\n",
":emphasize-lines: 6,8,12,13\n",
"```\n",
"\n",
"As proposed in the comments, add a loop to vary the adsorption height of Oxygen between 1.10 and 1.65 Å.\n",
"What is the bond length difference between to intensity maxima ?\n",
":::\n",
"\n",
"::::"
]
},
{
"cell_type": "markdown",
"id": "4ff0c14f-b2f6-47c6-91f4-9edc7ee7260d",
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"source": [
"```{toggle}\n",
"\n",
":::{literalinclude} RhO_completed.py\n",
":lineno-match:\n",
":emphasize-lines: 6,8,12,13\n",
":::\n",
"\n",
":::{figure-md} stereo-fig\n",
"<img src=\"RhO_fig2b.gif\" alt=\"Scattering factors\" width=\"600px\" align=\"center\">\n",
"\n",
"Stereographic projections of O(1s) emission at {math}`E_0` = 723 eV for an oxygen atom \n",
"on top of a fcc site of 3 Rh atoms at various altitudes {math}`z_0`\n",
":::\n",
"\n",
"\n",
"You can see on the stereographic projection 3 bright circles representing fringes of constructive interference between the direct O(1s) photoelectron wave and that backscattered by the Rhodium atoms. The center of these annular shapes changes from bright to dark due to the variation of the Oxygen atom height above the surface which changes the path difference.\n",
"\n",
"```"
]
},
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"# Activity 4: From single scattering to multiple scattering"
]
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":::{figure-md} Ni-fig1\n",
"<img src=\"Ni_fig1.png\" alt=\"Ni chain\" width=\"600px\" align=\"center\">\n",
"\n",
"Polar scan of a Ni chain of 2-5 atoms for single and mutliple (5{sup}`th` order) scattering.\n",
":::"
]
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"source": [
":::{seealso}\n",
"based on this paper from M.-L. Xu *et al.*\n",
"[Phys. Rev. B **39** p8275 (1989)](https://doi.org/10.1103/PhysRevB.39.8275) \n",
":::"
]
},
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"cell_type": "markdown",
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"source": [
":::{literalinclude} Ni_chain.py\n",
":lineno-match:\n",
":::"
]
},
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"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Some questions to answer\n",
":::\n",
"\n",
"::::"
]
}
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"source": [
"(forward-scattering)=\n",
"# Activity 5: Multiple scattering in the forward scattering regime"
]
},
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"In photoelectron diffraction, it is well known that for high photoelectron kinetic energy (typically > 900 eV), the scattering factor is strongly peaked in the forward direction. It means that photoelectrons are almost not deviated after a scattering event.\n",
"\n",
"Peaks of intentisity are then usually observed for dense atomic directions of the sample. This is the **forward scattering approximation**.\n",
"\n",
"For such high kinetic energy, multiple scattering is needed to accurately describe the measured intensity, but the matrix inversion algorithm cannot be used since the memory needed for storing the matrix itself would be generally too large. The matrix will contain\n",
"$(N \\times (L_{max}+1)^2)^2$ elements of complex type with double precision (64 bits) where $N$ is the number of atoms and $L_{max}$ is the number of spherical harmonics used to expand the electron wave around each atomic center. As the kinetic energy increases, the mean free path (MFP) of the photoelectron is larger and the number of atoms in the cluster has to be greater. Lmax also increases with the kinetic energy."
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"source": [
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Try to evaluate how much memory you would need for this matrix for a hemispherical cluster of copper 15 angströms thick (1 MFP) for $L_{max} = 25$ ?\n",
":::\n",
"\n",
"::::"
]
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"text": [
"606 atoms, 2.685 TB\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"# lattice constant of fcc copper\n",
"a = 3.6\n",
"# radius of the cluster\n",
"r = 15\n",
"# volume of the cluster\n",
"V = .5 * (4/3) * np.pi * r**3\n",
"# volume of the cell\n",
"v = a**3\n",
"# number of atoms in the unit cell\n",
"n = 4\n",
"# number of atoms in the cluster\n",
"N = int(V/v * n)\n",
"\n",
"Lmax = 25\n",
"M = (N * (Lmax+1)**2 )**2 * 2 * 64 / 8\n",
"print(f\"{N:d} atoms, {M/1e12:.3f} TB\")"
]
},
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"This is too much memory. We will use another algorithm available in MsSpec: The *Rehr-Albers series expansion*. We already used that algorithm in activity 3 for the single scattering approach. But this time, we will explore a bit more the effect of the scattering order > 1"
]
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"source": [
"## PED of the 1T-TiSe<sub>2</sub> surface"
]
},
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"source": [
"Let us try to model the Ti2p XPD pattern of the transition metal dichalcogenide 1T-TiSe<sub>2</sub>.\n",
"\n",
":::{seealso}\n",
"based on this paper from M.V. Kuznetsov *et al.*\n",
"[Surf. Sci. **606** p1760–70 (2012)](https://doi.org/10.1016/j.susc.2012.06.008)\n",
":::\n",
"\n",
"### Creating the TiSe{sub}`2` cluster\n",
"\n",
"Start by creating a small cluster of 1T-TiSe<sub>2</sub> using the `mx2` function of `ase.build` and the `hemispherical_cluster` function of `msspec.utils`."
]
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"source": [
":::{figure-md} TiSe2-fig\n",
"<img src=\"TiSe2_cell.jpg\" alt=\"TiSe2\" width=\"300px\" align=\"center\">\n",
"\n",
"Structure of 1T-TiSe<sub>2</sub> ($a_0=b_0=3.535$ Å, $c_0=6.004$ Å, $d=3.450$ Å, $D=2.554$ Å)\n",
":::"
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"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Complete the code snipet provided below to create a small TiSe{sub}`2` cluster with Ti emitter in the 2{sup}`nd` plane:\n",
"\n",
"```{literalinclude} TiSe2_1_tofill.py\n",
":start-at: from\n",
":end-before: Create a calculator\n",
":lineno-match:\n",
"```\n",
"\n",
":::\n",
"\n",
"::::"
]
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"from ase.build import mx2\n",
"from ase.visualize import view\n",
"from msspec.calculator import MSSPEC\n",
"from msspec.utils import hemispherical_cluster, get_atom_index\n",
"\n",
"# Some usefull constants (a, c, d, D) for defining the structure\n",
"a=3.535;c=6.004;d=3.450;D=2.554\n",
"\n",
"# Create the TiSe2 trilayer\n",
"# use ase help for this function\n",
"TiSe2 = mx2(formula='TiSe2', kind='1T', a=a, thickness=d, size=(1, 1, 1), vacuum=None)\n",
"\n",
"# The preious cell is 2D, let's define the c-axis to take into account \n",
"# the Van der Waals gap between trilayers\n",
"TiSe2.cell[2] = [0, 0, c]\n",
"\n",
"# To be aligned like in the paper\n",
"TiSe2.rotate(60, 'z', rotate_cell=True)\n",
"\n",
"# Since the material is multi-elements, \"tag\" each inequivalent atom \n",
"# of the unit cell with a number. The \"Ti\" atom is tagged 0 and \"Se\" \n",
"# atoms are 1 and 2.\n",
"for i in range(3): \n",
" TiSe2[i].tag = i\n",
"\n",
"cluster = hemispherical_cluster(TiSe2, emitter_tag=0, emitter_plane=1, planes=5)\n",
"cluster.emitter = get_atom_index(cluster, 0, 0, 0)"
]
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"view(cluster, viewer='x3d')"
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"### Effect of the scattering order\n",
"\n",
"Use the line belows to create a calculator and compute a $\\theta$-$\\phi$ scan of the Ti(2p)\n",
"\n",
"```{literalinclude} TiSe2_1_tofill.py\n",
" :start-at: Create a\n",
"```"
]
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"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Compute a scan for an emitter in the first trilayer and in the second trilayer for scattering orders from 1 (single scattering) to 3 in order to complete the figure below.\n",
"What do you conclude about the value of the `calc.calculation_parameters.scattering_order` ?\n",
"\n",
"```{figure-md} results-fig\n",
"<img src=\"results.jpg\" width=\"400px\" align=\"center\">\n",
"\n",
"$\\theta$-$\\phi$ scan of Ti(2p) at 1030 eV kinetic energy for an emitter in the first trilayer (left column) and in the second trilayer (right column). Each row correspond to a growing value for the `calc.calculation_parameters.scattering_order` parameter (from 1 to 5).\n",
"```\n",
"\n",
":::\n",
"\n",
"::::"
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"```{toggle}\n",
"\n",
":::{figure-md} results-completed-fig\n",
"<img src=\"results_completed.jpg\" width=\"400px\" align=\"center\">\n",
"\n",
"$\\theta$-$\\phi$ scan of Ti(2p) at 1030 eV kinetic energy for an emitter in the first trilayer (left column) and in the second trilayer (right column). Each row correspond to a growing value for the `calc.calculation_parameters.scattering_order` parameter (from 1 to 5).\n",
":::\n",
"\n",
"The deeper the emitter, the greater the scattering order should be for the intensity to converge.\n",
"Typically, in the forward scattering regime, the scattering order corresponds to the number of planes above the emitter.\n",
"\n",
"```"
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"# Activity 6: Effect of the temperature\n",
"\n",
"\n",
"## Surface and bulk effects of the temperature\n",
"\n",
"In this example, we will look at the effects of the temperature on the X-Ray photoelectron diffraction from a copper substrate. We will base our python script on a paper published in 1986 by R. Trehan and S. Fadley. In their work, they performed azimutal scans of a copper(001) surface at 2 different polar angles: one at grazing incidence and one at 45° for incresing temperatures from 298K to roughly 1000K.\n",
"\n",
"For each azimutal scan, they looked at the anisotropy of the signal, that is:\n",
"\n",
"```{math}\n",
":label: eq-anisotropy\n",
"\\frac{I_{max} - I_{min}}{I_{max}}=\\frac{\\Delta I}{I_{max}}\n",
"```\n",
"\n",
"This value is representative of how clear are the *modulations* of the signal. They also proposed single scattering calculations that reproduced well these results.\n",
"\n",
"We will reproduce this kind of calculations to introduce the parameters that control the vibrational damping.\n",
"\n",
"(msd-paper)=\n",
":::{seealso}\n",
"based on this paper from R. Trehan and C.S. Fadley\n",
"[Phys. Rev. B **34** p6784–98 (2012)](https://doi.org/10.1103/PhysRevB.34.6784)\n",
":::\n",
"\n",
"### The script\n",
"\n",
"Since we want to distinguish between bulk (low polar angles, $\\theta = 45°$ in the paper) and surface effects (large polar angles, $\\theta = 83°$ in the paper), we need to compute scans for different emitters and different depths in the cluster.\n",
"\n",
"The script contains 3 functions:\n",
"1. The `create_clusters` function will build clusters with increasing number of planes, with the emitter being in the deepest plane for each cluster.\n",
"2. The function `compute` will compute the azimuthal scan for a given cluster.\n",
"3. The `analysis` function will sum the intensity from each plane for a given temperature. This will be the *substrate total signal* (more on this in the {ref}`path-filtering` section). The function will also compute the anisotropy (equation {eq}`eq-anisotropy`).\n",
"\n",
"MsSpec can introduce temperature effects in two ways: either by using the Debye Waller model or by doing an average over the phase shifts. We will explore the latter in this example.\n",
"\n",
"Regardless of the option chosen to model temperature effects, we need to define mean square displacement (MSD) values of the atoms in our cluster. We will use the Debye model for this. The MSD is defined as follows:\n",
"\n",
":::{math}\n",
":label: eq-debye\n",
"<U_j^2(T)> = \\frac{3\\hbar^2 T}{M K_B \\Theta_D^2}\n",
":::\n",
"\n",
"where $\\hbar$ is the reduce Planck's constant, $T$ is the temperature, $M$ is the mass of the atom, $k_B$ is the Boltzmann's constant and $\\Theta_D$ is the Debye temperature of the sample.\n",
"\n",
"To get an idea of the typical order of magnitude for MSD, the figure below plots the values of MSD for copper for temperatures ranging from 300 K to 1000 K.\n",
"\n",
":::{figure-md} msd-fig\n",
"<img src=\"msd.jpg\" alt=\"Cu MSD\" width=\"600px\" align=\"center\">\n",
"\n",
"Variation of MSD for copper versus temperature using equation {eq}`eq-debye`\n",
":::"
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"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"With the help of the [MsSpec documentation](https://msspec.cnrs.fr/parameters.html) and the second paragraph p6791 of the [article cited above](#msd-paper),\n",
"complete the hilighted lines in the following script to compute the anisotropy of Cu(2p) $\\phi$-scans for polar angle $\\theta$=45° and 83°.\n",
"\n",
"How is varying the anisotropy versus the temperature. How can you qualitatively explain this variation ?\n",
"\n",
"```{literalinclude} Cu_temperature.py\n",
":lineno-match:\n",
":emphasize-lines: 40-41,44-48\n",
"```\n",
"\n",
":::\n",
"\n",
"::::"
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"```{toggle}\n",
"\n",
":::{literalinclude} Cu_temperature_completed.py\n",
":lineno-match:\n",
":emphasize-lines: 40-41,44-48\n",
":::\n",
"\n",
":::{figure-md} anisotropy-fig\n",
"<img src=\"anisotropies.png\" alt=\"anisotropies\" width=\"600px\" align=\"center\">\n",
"\n",
"Variation of anisotropy as a function of temperature and polar angle for Cu(2p).\n",
":::\n",
"\n",
"The anisotropy decreases when the temperature is increased due to the increased disorder in the structure coming from thermal agitation. This variation in anisotropy is more pronounced for grazing incidence angles since surface atoms are expected to vibrate more than bulk ones and the expected mean depth of no-loss emission is $\\sim 1$ atomic layer at $\\theta = 83°$ and 3-4 layers at $\\theta = 45°$ as estimated by $\\Lambda_e\\sin\\theta$ (where $\\Lambda_e$ is the photoelectron mean free path at 560 eV).\n",
"\n",
"```"
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"(path-filtering)=\n",
"# Activity 7: Large clusters and path filtering"
]
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"So far you have seen that multiple scattering calculations with MsSpec can use two different algorithms: *matrix inversion* or *Rehr Albers series expansion*. When matrix inversion becomes impossible because the kinetic energy is too high and the number of atoms is too large, serial expansion is the alternative. This algorithm requires very little memory but it processes the scattering paths sequentially, which can lead to very long calculation times.\n",
"\n",
"In this activity, we will explore how to configure MsSpec to reduce this calculation time to compute the signal from a deep emitter in Si(001).\n",
"\n",
"\n",
"\n",
":::"
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"## The number of scattering paths\n",
"\n",
"To fix the idea, we will first evaluate how many scattering paths we need to compute for an emitter in the subsurface (2{sup}`nd` plane) or in the bulk (7{sup}`th` plane) of a Si(001) cluster."
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"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"Create a cluster of Si(001) with the emitter in the subsurface, 40 Å diameter with 2 planes (since atoms below the emitter can be ignored at high kinetic energies).\n",
"\n",
"1. For an emitter in the subsurface, we can use single scattering (see {ref}`forward-scattering`). How many paths would be generated for this calculation ?\n",
"\n",
"2. Same question for an emitter in the 7{sup}`th` plane. If we were able to treat each scattering path within only 1 µs. How long would be such calculation ?\n",
"\n",
"```{note}\n",
"Remember that \n",
"1. for an emitter in plane $p$, the scattering order has to be at least the number of planes `above` the emitter\n",
"2. The number of scattering paths of order $n$ corresponds to the number of possibilities of arranging up to $n$ atoms (taking order into account).\n",
"```\n",
"\n",
"\n",
"::::"
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":::{toggle}\n",
"\n",
"To get the total number of paths generated by a cluster of $N$ atoms up to order $M$, use the following formula:\n",
"\n",
"```{math}\n",
":label: eq-nbpaths\n",
"\\sum_{i=0}^{i=M} (N-1)^i\n",
"```\n",
"\n",
":::{figure-md} nbpaths-fig\n",
"<img src=\"fig1.jpg\" alt=\"path filtering\" width=\"600px\" align=\"center\">\n",
"\n",
"The time for computing all scattering path for increasing cluster size and scattering order (up to 6{sup}`th` order with 739 atoms. (One path is assumed to be calculated within 1 µs)\n",
":::\n",
"\n",
":::"
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"## Paths filtering in MsSpec\n",
"\n",
"As you may expect, not all paths contribute significantly to the total intensity. This is why we can filter out some scattering paths and drastically reduce the computation time. MsSpec offers several filters for this. The 3 most common filters are:\n",
"1. the `forward_scattering` filter which allows all paths where each scattering angle is within a cone of defined aperture\n",
"2. the `backward_scattering` filter which is similar to the previous one but for backscattering direction\n",
"3. the `distance` filter which rejects all paths longer than a threshold distance\n",
"\n",
"The following figure illustrate the effect of theses filters on scattering paths\n",
"\n",
":::{figure-md} filters-fig\n",
"<img src=\"filters.jpg\" alt=\"path filtering\" width=\"600px\" align=\"center\">\n",
"\n",
"Some examples of scattering paths with `forward_scattering`, `backward_scattering` and `distance` filters selected. The accepted forward angle is 45°, the accepted backscattering angle is 20° and the threshold distance is $6a_0$ where $a_0$ is the lattice parameter. Note that the yellow path is rejected but if the `off_cone_events` option is set to a value > 1, then it could have been accepted.\n",
":::"
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"## Application to a deep plane in a Si(001) sample\n",
"\n",
"The following script will compute the contribution of a Si(2p) atom in the 4{sup}`th` plane of a Si(001) cluster at scattering order 3.\n",
"\n",
"Taking into account all scattering paths took 15 minutes to compute.\n",
"\n",
"(msd-paper)=\n",
":::{seealso}\n",
"based on this paper from S. Tricot *et al.*\n",
"[J. Electron. Spectrosc. Relat. Phenom. **256** 147176 (2022)](https://doi.org/10.1016/j.elspec.2022.147176)\n",
":::\n",
"\n",
"\n",
"::::{tab-set}\n",
"\n",
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
"\n",
"The following script is almost completed, try to define path filtering options (no backscattering, accept all paths with forward angles < 40° and reject paths longer than the diameter of the cluster).\n",
"\n",
"```{literalinclude} Si001.py\n",
":lineno-match:\n",
":emphasize-lines: 37-41\n",
"```\n",
"\n",
"1. How long was your calculation ?\n",
"2. How does it compare to the calculation with **all** scattering paths up to order 3 ?\n",
"3. What is the proportion of scattering paths of order 3 that were actually taken into account ?\n",
"\n",
":::\n",
"\n",
"::::"
]
},
{
"cell_type": "markdown",
"id": "19fbd486-b0c1-450c-a00d-79984945aefd",
"metadata": {},
"source": [
"```{toggle}\n",
"The calculation took few seconds and the result is very close to the calculation with all scattering paths.\n",
"\n",
"Only 0.01% of 3{sup}`rd` order paths were actually taken into account\n",
"\n",
":::{figure-md} si-fig\n",
"<img src=\"results.png\" alt=\"Si polar scan\" width=\"600px\" align=\"center\">\n",
"\n",
"Si(2p) polar scan (contribution of an emitter in the 4{sup}`th` plane with all 7 114 945 scattering paths taken into account (orange curve), and for only 1525 filtered paths (blue curve).\n",
"\n",
":::\n",
"\n",
":::{literalinclude} Si001_completed.py\n",
":lineno-match:\n",
":emphasize-lines: 37-41\n",
":::\n",
"\n",
"``` "
]
}
],
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
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@ -1,41 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"id": "2ff5929f-c066-496f-b078-0bbc2ab49428",
"metadata": {},
"source": [
"# Activity 8: Inequivalent emitters and the XPD of a substrate"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1df76138-c957-4da2-bcc8-ec977c209b81",
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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@ -1,41 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"id": "aa43e0e7-0c18-4750-9e2b-3a48f106d2ca",
"metadata": {},
"source": [
"# Activity 9: Comparing simulation and experiment with R-factors"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b9b32bbf-7635-4e14-b246-468f2e74bb17",
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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@ -1,41 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"id": "38d3e621-e866-43e1-9c92-f473d1e755c0",
"metadata": {},
"source": [
"# Activity 10: Auger Electron Diffraction"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "526d98f6-5a18-4ed9-9870-29b08b54e073",
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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@ -1,41 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"id": "140adc62-2a15-4806-b6e1-1a0a0b7054e2",
"metadata": {},
"source": [
"# Activity 11: Spectral radius and convergence"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8adb2f68-32bc-4e45-95b6-bd9fb7f96439",
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
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