From 8f5dbf6483f8496eda46f63207eca61a55d6b031 Mon Sep 17 00:00:00 2001 From: Sylvain Tricot Date: Tue, 22 Jul 2025 16:29:02 +0200 Subject: [PATCH] Finish Activity 4 --- msspecbook/Activity04/Activity04.ipynb | 104 ++++++++++++++++-- msspecbook/Activity04/Ni_2atomsSSC.png | Bin 0 -> 63017 bytes msspecbook/Activity04/Ni_SSCvsMI.jpg | Bin 0 -> 506861 bytes msspecbook/Activity04/Ni_chain.py | 78 ------------- msspecbook/Activity04/Ni_chain1.py | 19 ++++ msspecbook/Activity04/Ni_chain2.py | 24 ++++ .../Activity04/defocusing_animation.gif | Bin 0 -> 130167 bytes 7 files changed, 138 insertions(+), 87 deletions(-) create mode 100644 msspecbook/Activity04/Ni_2atomsSSC.png create mode 100644 msspecbook/Activity04/Ni_SSCvsMI.jpg delete mode 100644 msspecbook/Activity04/Ni_chain.py create mode 100644 msspecbook/Activity04/Ni_chain1.py create mode 100644 msspecbook/Activity04/Ni_chain2.py create mode 100644 msspecbook/Activity04/defocusing_animation.gif diff --git a/msspecbook/Activity04/Activity04.ipynb b/msspecbook/Activity04/Activity04.ipynb index 2d85d94..22d2654 100644 --- a/msspecbook/Activity04/Activity04.ipynb +++ b/msspecbook/Activity04/Activity04.ipynb @@ -11,7 +11,13 @@ "tags": [] }, "source": [ - "# Activity 4: From single scattering to multiple scattering" + "(ssc2ms)=\n", + "# Activity 4: From single scattering to multiple scattering\n", + "\n", + "In the [previous activity](ssc), we saw that simple single scattering calculations (SSC) can be used to simulate photodiffraction diagrams with good accuracy. The approximation works fine when the emitting atom is very close to the surface.\n", + "However, the SSC approach is no longer suitable for deeper emitter atoms, where multiple scattering effects come into play. In this activity, we will focus on a major consequence of multiple scattering: *the defocusing effect*.\n", + "\n", + "The defocusing effect is presented in the [figure below](Ni-fig1) for a chain of nickel atoms. Although purely illustrative, understanding multiple scattering in atomic chains is fundamental because they are found in many situations, such as in particular directions of a crystal or in molecules of various lengths." ] }, { @@ -26,17 +32,27 @@ }, "source": [ ":::{figure-md} Ni-fig1\n", - "\"Ni\n", + "\"defocusing\n", "\n", - "Polar scan of a Ni chain of 2-5 atoms for single and mutliple (5{sup}`th` order) scattering.\n", + "The defocusing effect dur to multiple scattering in an atomic chain of Ni atoms.\n", ":::" ] }, + { + "cell_type": "markdown", + "id": "b1b4c789-e62c-40cc-92a3-053e6a90d315", + "metadata": {}, + "source": [ + "In 1989, M.-L Xu, J.J. Barton and M.A. Van Hove studied these multiple scattering effects on atomic chains ([see their paper below](defocusing-paper)).\n", + "In the spirit of figure 3 of their paper, we will create 3 atomic chains of Ni atoms (2, 3 and 5 atoms) tilted by 45° and we will compare the intensity of the forward scattering peak for single scattering and for full multiple scattering." + ] + }, { "cell_type": "markdown", "id": "4988e7d3-2ba3-470f-9676-8116348c30a1", "metadata": {}, "source": [ + "(defocusing-paper)=\n", ":::{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", @@ -45,27 +61,97 @@ }, { "cell_type": "markdown", - "id": "b2aa92f1-3170-47f6-87c2-e7abffcbdb12", + "id": "011ef23b-5a76-410d-8d44-1c4a899e2a23", "metadata": {}, "source": [ - ":::{literalinclude} Ni_chain.py\n", - ":lineno-match:\n", + "## Polar scans of Ni atomic chains\n", + "\n", + "### Building a chain of atoms\n", + "\n", + "Start by creating a simple chain of 2 Ni atoms: an emitter and a scatterer in the [101] direction.\n", + "\n", + ":::{tip}\n", + "Nickel is *fcc* with lattice parameter $a$=3.499 Å. Use the [`Atoms`](https://wiki.fysik.dtu.dk/ase/ase/atoms.html#ase.Atoms) class of `ase` like in the [previous activity](ssc)...\n", + "\n", + ":::{admonition} if you need help to start...\n", + ":class: dropdown\n", + "\n", + ":::{code} python\n", + "from msspec.calculator import MSSPEC\n", + "from ase import Atoms\n", + "\n", + "symbol = ... # The kind of atom for the chain\n", + "a = ... # The distance bewteen 2 atoms\n", + " # in [101] direction\n", + "\n", + "chain = Atoms(..., positions=[...])\n", + "chain.rotate(...)\n", + "chain.edit()\n", + ":::\n", + "\n", + ":::\n", + "\n", ":::" ] }, { "cell_type": "markdown", - "id": "bbd682d1-d142-4ac5-872d-0b57f3deecb9", + "id": "3ed73f46-c12f-452f-a584-00d142f2e133", + "metadata": {}, + "source": [ + "```{admonition} *Solution...*\n", + ":class: tip\n", + ":class: dropdown\n", + "Building the 2-atoms chain\n", + "\n", + ":::{literalinclude} Ni_chain1.py\n", + ":linenos: true\n", + ":lines: 1-10\n", + ":::\n", + "\n", + ":::{figure-md} Ni-fig2\n", + "\"Ni\n", + "\n", + "Polar scan of a Ni(3s) chain of 2 atoms for single scattering.\n", + ":::\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "5c57f951-bfa7-435e-8e74-b3de11909768", "metadata": {}, "source": [ "::::{tab-set}\n", "\n", ":::{tab-item} Quiz\n", - "Some questions to answer\n", + "Create an `MSSPEC` calculator with `expansion` algortithm and set the `scattering_order`=1 to compute a polar scan of the Ni(3s) in single scattering. How is varying the height of the peak at 45° (along the chain) if you increase the number of atoms in the chain ?\n", + "\n", + "Repeat the same experiment with `inversion` algorithm for having the full multiple scattering result. What do you observe ?\n", ":::\n", "\n", "::::" ] + }, + { + "cell_type": "markdown", + "id": "626708d9-c421-4bf0-bd70-f32113360f9c", + "metadata": {}, + "source": [ + "```{admonition} *Solution...*\n", + ":class: tip\n", + ":class: dropdown\n", + "\n", + "The peak at 45° is increasing with the number of atoms in the chain for SSC. We observe defocusing of this peak for full multiple scattering calculations (MSC). For the 2-atoms chain, both SSC and MSC give the same result owing to the fact that the emitter has only one scatterer atom and that kinetic energy is high enough to cancel out all backscattering.\n", + "\n", + ":::{figure-md} Ni-figX\n", + "\"Ni\n", + "\n", + "Polar scan of a Ni chain of 2-5 atoms for single and full mutliple scattering.\n", + ":::\n", + "\n", + "```" + ] } ], "metadata": { @@ -84,7 +170,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.13" + "version": "3.11.3" } }, "nbformat": 4, diff --git a/msspecbook/Activity04/Ni_2atomsSSC.png b/msspecbook/Activity04/Ni_2atomsSSC.png new file mode 100644 index 0000000000000000000000000000000000000000..44d62c75899f62916ef19fc6aaef39853212c844 GIT binary patch literal 63017 zcmeFZWms45*FAVZxE%Sk?s_wyGxKzN(>A@Kt!cWx*H4-C8Se2rTf1R z_u$KkH4hpDqAqHOBwXzSo=d*6)3-O}0RzJvW$o-3Dmu5z*5b9Hre z5#i;v`>#*%I5=DJ-eoI#3|GN-yrJuYAT$){Ukt0HpKz~@7dPdkH9Qj*hCDn^ckkk^ 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0 HcmV?d00001 diff --git a/msspecbook/Activity04/Ni_chain.py b/msspecbook/Activity04/Ni_chain.py deleted file mode 100644 index 8b5bfc5..0000000 --- a/msspecbook/Activity04/Ni_chain.py +++ /dev/null @@ -1,78 +0,0 @@ -# coding: utf-8 - -# import all we need and start by msspec -from msspec.calculator import MSSPEC - -# we will build a simple atomic chain -from ase import Atom, Atoms - -# we need some numpy functions -import numpy as np - - -symbol = 'Ni' # The kind of atom for the chain -orders = (1, 5) # We will run the calculation for single scattering - # and multiple scattering (5th diffusion order) -chain_lengths = (2,3,5) # We will run the calculation for differnt lengths - # of the atomic chain -a = 3.499 * np.sqrt(2)/2 # The distance bewteen 2 atoms - -# Define an empty variable to store all the results -all_data = None - -# 2 for nested loops over the chain length and the order of diffusion -for chain_length in chain_lengths: - for order in orders: - # We build the atomic chain by - # 1- stacking each atom one by one along the z axis - chain = Atoms([Atom(symbol, position = (0., 0., i*a)) for i in - range(chain_length)]) - # 2- rotating the chain by 45 degrees with respect to the y axis - #chain.rotate('y', np.radians(45.)) - chain.rotate(45., 'y') - # 3- setting a custom Muffin-tin radius of 1.5 angstroms for all - # atoms (needed if you want to enlarge the distance between - # the atoms while keeping the radius constant) - #[atom.set('mt_radius', 1.5) for atom in chain] - # 4- defining the absorber to be the first atom in the chain at - # x = y = z = 0 - chain.absorber = 0 - - # We define a new PED calculator - calc = MSSPEC(spectroscopy = 'PED') - calc.set_atoms(chain) - # Here is how to tweak the scattering order - calc.calculation_parameters.scattering_order = order - # This line below is where we actually run the calculation - all_data = calc.get_theta_scan(level='3s', #kinetic_energy=1000., - theta=np.arange(0., 80.), data=all_data) - - # OPTIONAL, to improve the display of the data we will change the dataset - # default title as well as the plot title - t = "order {:d}, n = {:d}".format(order, chain_length) # A useful title - dset = all_data[-1] # get the last dataset - dset.title = t # change its title - # get its last view (there is only one defined for each dataset) - v = dset.views()[-1] - v.set_plot_options(title=t) # change the title of the figure - - - -# OPTIONAL, set the same scale for all plots -# 1. iterate over all computed cross_sections to find the absolute minimum and -# maximum of the data -min_cs = max_cs = 0 -for dset in all_data: - min_cs = min(min_cs, np.min(dset.cross_section)) - max_cs = max(max_cs, np.max(dset.cross_section)) - -# 2. for each view in each dataset, change the scale accordingly -for dset in all_data: - v = dset.views()[-1] - v.set_plot_options(ylim=[min_cs, max_cs]) - -# Pop up the graphical window -all_data.view() -# You can end your script with the line below to remove the temporary -# folder needed for the calculation -calc.shutdown() diff --git a/msspecbook/Activity04/Ni_chain1.py b/msspecbook/Activity04/Ni_chain1.py new file mode 100644 index 0000000..491a204 --- /dev/null +++ b/msspecbook/Activity04/Ni_chain1.py @@ -0,0 +1,19 @@ +from msspec.calculator import MSSPEC +from ase import Atoms +import numpy as np + +symbol = 'Ni' # The kind of atom for the chain +a = 3.499 * np.sqrt(2)/2 # The distance bewteen 2 atoms + # in [101] direction + +chain = Atoms(symbol*2, positions=[(0,0,0), (0,0,a)]) +chain.rotate(45, 'y') + +calc = MSSPEC(spectroscopy='PED', algorithm='expansion') +calc.calculation_parameters.scattering_order = 1 + +chain.emitter = 0 +calc.set_atoms(chain) + +data = calc.get_theta_scan(level='3s', theta=np.arange(0,80,0.5)) +data.view() diff --git a/msspecbook/Activity04/Ni_chain2.py b/msspecbook/Activity04/Ni_chain2.py new file mode 100644 index 0000000..12092a2 --- /dev/null +++ b/msspecbook/Activity04/Ni_chain2.py @@ -0,0 +1,24 @@ +from msspec.calculator import MSSPEC +from ase import Atoms +import numpy as np + +symbol = 'Ni' # The kind of atom for the chain +a = 3.499 * np.sqrt(2)/2 # The distance bewteen 2 atoms + # in [101] direction + +chain = Atoms(symbol) +data = None +for i in range(1,5): + atom = Atoms(symbol, [[0,0,i*a]]) + atom.rotate('y', 45) + chain += atom + + calc = MSSPEC(spectroscopy='PED', algorithm='inversion') + calc.calculation_parameters.scattering_order = 1 + + chain.emitter = 0 + calc.set_atoms(chain) + + data = calc.get_theta_scan(level='3s', theta=np.arange(0,80,0.5), data=data) + data[-1].views[0].set_plot_options(ylim=[0,0.045]) +data.view() diff --git a/msspecbook/Activity04/defocusing_animation.gif b/msspecbook/Activity04/defocusing_animation.gif new file mode 100644 index 0000000000000000000000000000000000000000..c099327246f8861b2420dc9a1d70bd0cfb2038d9 GIT binary patch literal 130167 zcmc$F=U3Cs^Y$k_gaDz4A+!)eZ=oqo2|W}s(z^j7O;k`s^tL1rVyK2*)qr#a=|x3D 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