From 272c2503f1fdbee4d9e2435c7d4d136674e75166 Mon Sep 17 00:00:00 2001 From: amkrajewski Date: Mon, 16 Oct 2023 23:40:08 -0400 Subject: [PATCH] - finished section 1 and added some assets --- Lecture1.ipynb | 905 ++++++++++++++++++++++++++++++++++++- assets/0-Cr8Fe18Ni4.POSCAR | 38 ++ assets/112-Cr12Fe10Ni8.png | Bin 0 -> 3393411 bytes 3 files changed, 940 insertions(+), 3 deletions(-) create mode 100644 assets/0-Cr8Fe18Ni4.POSCAR create mode 100644 assets/112-Cr12Fe10Ni8.png diff --git a/Lecture1.ipynb b/Lecture1.ipynb index 90ff9b5..80810a2 100644 --- a/Lecture1.ipynb +++ b/Lecture1.ipynb @@ -23,16 +23,901 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting pymatgen\n", + " Downloading pymatgen-2023.10.11.tar.gz (7.3 MB)\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m7.3/7.3 MB\u001b[0m \u001b[31m22.9 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+ "source": [ + "## Manipulating and analyzing materials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To start working with atomic structures, often referred to as atomic configurations or simply materials, we need to be able to represent and manipulate them. One of the most powerful and mature tools to do so is [pymatgen](https://github.com/materialsproject/pymatgen) which we just installed. The critical component of pymatgen is its library of representations of fundamental materials objects, such as `Structure` and `Molecule`, contained in the `pymatgen.core` module. Let's import it and create a simple cubic structure of Al, like we did in the DFTTK tutorial last week:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Basics" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "from pymatgen.core import Structure\n", + "\n", + "s = Structure(lattice=[[4.0384, 0, 0], [0, 4.0384, 0], [0, 0, 4.0384]],\n", + " species=['Al', 'Al', 'Al', 'Al'],\n", + " coords=[[0.0, 0.0, 0.0], [0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, `s` holds our initialized structure and we can apply print on it to see what it looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Full Formula (Al4)\n", + "Reduced Formula: Al\n", + "abc : 4.038400 4.038400 4.038400\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Al 0 0 0\n", + " 1 Al 0 0.5 0.5\n", + " 2 Al 0.5 0 0.5\n", + " 3 Al 0.5 0.5 0\n" + ] + } + ], + "source": [ + "print(s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Initialized** is a critical word here, because the `Structure` object is not just a collection of \"numbers\". It holds a lot of information we can access using the `Structure` object's attributes and methods. For example, density of the material is immediately available:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.721120664587368" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s.density" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also \"mutate\" the object with a few intuitive methods like `apply_strain`:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Structure Summary\n", + "Lattice\n", + " abc : 4.442240000000001 4.442240000000001 4.442240000000001\n", + " angles : 90.0 90.0 90.0\n", + " volume : 87.66092623767148\n", + " A : 4.442240000000001 0.0 0.0\n", + " B : 0.0 4.442240000000001 0.0\n", + " C : 0.0 0.0 4.442240000000001\n", + " pbc : True True True\n", + "PeriodicSite: Al (0.0, 0.0, 0.0) [0.0, 0.0, 0.0]\n", + "PeriodicSite: Al (0.0, 2.221, 2.221) [0.0, 0.5, 0.5]\n", + "PeriodicSite: Al (2.221, 0.0, 2.221) [0.5, 0.0, 0.5]\n", + "PeriodicSite: Al (2.221, 2.221, 0.0) [0.5, 0.5, 0.0]" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s.apply_strain(0.1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Importantly, as you can see `s` has been printed out when we ran the command, as if the `s.apply_strain` returned a modified `Structure` object. This is true! However, by default, pymatgen will also strain the original object, as you can see looking at the `s` density:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.0444182303436262" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s.density" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a very convenient feature, but it can be dangerous if you are not careful and, for instance, try to generate 10 structures with increasing strains" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Full Formula (Al4)\n", + "Reduced Formula: Al\n", + "abc : 297.826681 297.826681 297.826681\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Al 0 0 0\n", + " 1 Al 0 0.5 0.5\n", + " 2 Al 0.5 0 0.5\n", + " 3 Al 0.5 0.5 0\n", + "Full Formula (Al4)\n", + "Reduced Formula: Al\n", + "abc : 297.826681 297.826681 297.826681\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Al 0 0 0\n", + " 1 Al 0 0.5 0.5\n", + " 2 Al 0.5 0 0.5\n", + " 3 Al 0.5 0.5 0\n" + ] + } + ], + "source": [ + "strainedList = [s.apply_strain(0.1 * i) for i in range(1, 11)]\n", + "for strained in strainedList[:2]:\n", + " print(strained)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we will now end up with a single object with 67 times the original volume (1.1 * 1.2 * ... * 2.0) repeated 10 times. To avoid this, we can get regenerate original `s` and use the `copy` method to create a new object each time:" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [], + "source": [ + "from copy import copy\n", + "\n", + "s = Structure(lattice=[[4.0384, 0, 0], [0, 4.0384, 0], [0, 0, 4.0384]],\n", + " species=['Al', 'Al', 'Al', 'Al'],\n", + " coords=[[0.0, 0.0, 0.0], [0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0]])" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Full Formula (Ni3 Au1)\n", + "Reduced Formula: Ni3Au\n", + "abc : 4.038400 4.038400 4.038400\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Au 0 0 0\n", + " 1 Ni 0 0.5 0.5\n", + " 2 Ni 0.5 0 0.5\n", + " 3 Ni 0.5 0.5 0\n", + "Full Formula (Ni3 Au1)\n", + "Reduced Formula: Ni3Au\n", + "abc : 4.442240 4.442240 4.442240\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Au 0 0 0\n", + " 1 Ni 0 0.5 0.5\n", + " 2 Ni 0.5 0 0.5\n", + " 3 Ni 0.5 0.5 0\n" + ] + } + ], + "source": [ + "strainedList = [copy(s).apply_strain(0.1 * i) for i in range(0, 11)]\n", + "for strained in strainedList[:2]:\n", + " print(strained)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now everything works as expected! We can also easily do some modifications to the structure, like replacing one of the atoms with another" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Full Formula (Ni3 Au1)\n", + "Reduced Formula: Ni3Au\n", + "abc : 4.038400 4.038400 4.038400\n", + "angles: 90.000000 90.000000 90.000000\n", + "pbc : True True True\n", + "Sites (4)\n", + " # SP a b c\n", + "--- ---- --- --- ---\n", + " 0 Au 0 0 0\n", + " 1 Ni 0 0.5 0.5\n", + " 2 Ni 0.5 0 0.5\n", + " 3 Ni 0.5 0.5 0\n" + ] + } + ], + "source": [ + "s.replace(0, \"Au\")\n", + "print(s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or all of the atoms of a given element at once" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Structure Summary\n", + "Lattice\n", + " abc : 4.0384 4.0384 4.0384\n", + " angles : 90.0 90.0 90.0\n", + " volume : 65.860951343104\n", + " A : 4.0384 0.0 0.0\n", + " B : 0.0 4.0384 0.0\n", + " C : 0.0 0.0 4.0384\n", + " pbc : True True True\n", + "PeriodicSite: Au (0.0, 0.0, 0.0) [0.0, 0.0, 0.0]\n", + "PeriodicSite: Ni (0.0, 4.038, 4.038) [0.0, 0.5, 0.5]\n", + "PeriodicSite: Ni (4.038, 0.0, 4.038) [0.5, 0.0, 0.5]\n", + "PeriodicSite: Ni (4.038, 4.038, 0.0) [0.5, 0.5, 0.0]" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s.replace_species({\"Al\": \"Ni\"})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lastly, with `Structure` objects, we also have access to lower-order primitives, such as `Composition`" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Composition('Au1 Ni3')" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = s.composition\n", + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which may look like a simple string but is actually a powerful object that can be used to do things like calculate the fraction of each element in the structure:" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Composition('Au0.25 Ni0.75')" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c.fractional_composition" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "including the weight fractions (I wrote this part of pymatgen 🙂):" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Au': 0.5279943035775228, 'Ni': 0.47200569642247725}" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c.to_weight_dict" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Symmetry Analysis\n", + "\n", + "With some basics of the way, let's look at some more advanced features of pymatgen that come from integration with 3rd party libraries like [spglib](https://spglib.readthedocs.io/en/latest/index.html) which is a high performance library for symmetry analysis (1) written in C, (2) wrapped in Python by the authors, and finally (3) wrapped in pymatgen for convenience.\n", + "\n", + "Such approach introduces a lot of perfromance bottlenecks (4-20x slower and 50x RAM needs compared to my interface written in [Nim](https://nim-lang.org)), but allowing us to get started with things like symmetry analysis in with just one line of code, where `SpacegroupAnalyzer` puts `s` in a new context:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, "metadata": {}, "outputs": [], + "source": [ + "from pymatgen.symmetry.analyzer import SpacegroupAnalyzer\n", + "spgA = SpacegroupAnalyzer(s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now many useful methods are available to us, allowing quickly getting `crystal_system`, `space_group_symbol`, and `point_group_symbol`:" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'cubic'" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spgA.get_crystal_system()" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'Pm-3m'" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spgA.get_space_group_symbol()" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'m-3m'" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spgA.get_point_group_symbol()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also do some more advanced operations involving symmetry. For example, as some may have noticed, the `s` structure we created is primitive, but if we fix its symmetry, we can describe it with just 1 face centered atom instead of 3 as they are symmetrically equivalent. We can do this with the `get_symmetrized_structure` " + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SymmetrizedStructure\n", + "Full Formula (Ni3 Au1)\n", + "Reduced Formula: Ni3Au\n", + "Spacegroup: Pm-3m (221)\n", + "abc : 4.038400 4.038400 4.038400\n", + "angles: 90.000000 90.000000 90.000000\n", + "Sites (4)\n", + " # SP a b c Wyckoff\n", + "--- ---- --- --- --- ---------\n", + " 0 Au 0 0 0 1a\n", + " 1 Ni 0 0.5 0.5 3c" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "symmetrized = spgA.get_symmetrized_structure()\n", + "symmetrized" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which we can then use to get the primitive or conventional structure back (here they are the same):" + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Structure Summary\n", + "Lattice\n", + " abc : 4.0384 4.0384 4.0384\n", + " angles : 90.0 90.0 90.0\n", + " volume : 65.860951343104\n", + " A : 4.0384 0.0 2.472806816838336e-16\n", + " B : -2.472806816838336e-16 4.0384 2.472806816838336e-16\n", + " C : 0.0 0.0 4.0384\n", + " pbc : True True True\n", + "PeriodicSite: Ni (-1.236e-16, 2.019, 2.019) [0.0, 0.5, 0.5]\n", + "PeriodicSite: Ni (2.019, 0.0, 2.019) [0.5, 0.0, 0.5]\n", + "PeriodicSite: Ni (2.019, 2.019, 2.473e-16) [0.5, 0.5, 0.0]\n", + "PeriodicSite: Au (0.0, 0.0, 0.0) [0.0, 0.0, 0.0]" + ] + }, + "execution_count": 104, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "symmetrized.to_primitive()" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Structure Summary\n", + "Lattice\n", + " abc : 4.0384 4.0384 4.0384\n", + " angles : 90.0 90.0 90.0\n", + " volume : 65.860951343104\n", + " A : 4.0384 0.0 2.472806816838336e-16\n", + " B : -2.472806816838336e-16 4.0384 2.472806816838336e-16\n", + " C : 0.0 0.0 4.0384\n", + " pbc : True True True\n", + "PeriodicSite: Ni (-1.236e-16, 2.019, 2.019) [0.0, 0.5, 0.5]\n", + "PeriodicSite: Ni (2.019, 0.0, 2.019) [0.5, 0.0, 0.5]\n", + "PeriodicSite: Ni (2.019, 2.019, 2.473e-16) [0.5, 0.5, 0.0]\n", + "PeriodicSite: Au (0.0, 0.0, 0.0) [0.0, 0.0, 0.0]" + ] + }, + "execution_count": 105, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "symmetrized.to_conventional()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### More Complex Structures\n", + "\n", + "Armed with all the basics, let's look at some more complex structures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Manipulating and analyzing materials" + "

\n", + " \n", + "

" ] }, { @@ -78,8 +963,22 @@ } ], "metadata": { + "kernelspec": { + "display_name": "580demo", + "language": "python", + "name": "python3" + }, "language_info": { - "name": "python" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" }, "orig_nbformat": 4 }, diff --git a/assets/0-Cr8Fe18Ni4.POSCAR b/assets/0-Cr8Fe18Ni4.POSCAR new file mode 100644 index 0000000..0f9a39e --- /dev/null +++ b/assets/0-Cr8Fe18Ni4.POSCAR @@ -0,0 +1,38 @@ +Cr8 Fe18 Ni4 +1.0 +8.547048 0.000000 0.000000 +0.000000 8.547048 0.000000 +0.000000 0.000000 4.477714 +Cr Fe Ni +8 18 4 +direct +0.737702 0.063709 0.000000 Cr +0.262298 0.936291 0.000000 Cr +0.436291 0.237702 0.500000 Cr +0.762298 0.563709 0.500000 Cr +0.563709 0.762298 0.500000 Cr +0.237702 0.436291 0.500000 Cr +0.063709 0.737702 0.000000 Cr +0.936291 0.262298 0.000000 Cr +0.000000 0.000000 0.000000 Fe +0.500000 0.500000 0.500000 Fe +0.463029 0.129472 0.000000 Fe +0.536971 0.870528 0.000000 Fe +0.370528 0.963029 0.500000 Fe +0.036971 0.629472 0.500000 Fe +0.629472 0.036971 0.500000 Fe +0.963029 0.370528 0.500000 Fe +0.129472 0.463029 0.000000 Fe +0.870528 0.536971 0.000000 Fe +0.182718 0.182718 0.251726 Fe +0.817282 0.817282 0.748274 Fe +0.817282 0.817282 0.251726 Fe +0.317282 0.682718 0.751726 Fe +0.317282 0.682718 0.248274 Fe +0.182718 0.182718 0.748274 Fe +0.682718 0.317282 0.248274 Fe +0.682718 0.317282 0.751726 Fe +0.399910 0.399910 0.000000 Ni +0.600090 0.600090 0.000000 Ni +0.100090 0.899910 0.500000 Ni +0.899910 0.100090 0.500000 Ni diff --git a/assets/112-Cr12Fe10Ni8.png b/assets/112-Cr12Fe10Ni8.png new file mode 100644 index 0000000000000000000000000000000000000000..1a7e79cdafb2082fdef9238cacf475df8c07ad6f GIT binary patch literal 3393411 zcmeEuhgXy7*1a=cMHEqyDow=^rHV+CW&`wE&_QY_l1LE(2nZOejtEL9qEe)eG6Nz6 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