{ "cells": [ { "cell_type": "markdown", "metadata": { "vscode": { "languageId": "raw" } }, "source": [ "# Phonopy in Python\n", "\n", "Maintainer: Zekun Lou, Shubham Sharma\n", "\n", "This notebook provides a straightforward guide to using `phonopy` in Python scripts with graphite as example.\n", "\n", "It serves as a starting point for those who want to avoid the black box of `phonopy` shell commands, and prefer to integrate `phonopy` into their own Python scripts for customizing workflows.\n", "\n", "NOTE: To perform a phonon calculation, one needs an relaxed structure. Please relax the structure using your preferred methods (DFT or MLIPs) before computing phonons.\n", "\n", "We have done all DFT calculations in this tutorial.\n" ] }, { "cell_type": "markdown", "metadata": { "vscode": { "languageId": "ini" } }, "source": [ "Although this document is fairly detailed, **the core Python code is concise** (no more than some `import`s and simple function calls). The additional content is included to enhance clarity and provide better explanations. You can copy and modify the code snippets to fit your specific needs.\n", "\n", "The **workflow** is as follows:\n", "\n", "1. Converge the k-grid for the primitive cell and relax the primitive cell by `FHI-aims`.\n", "1. Generate supercells with displacements using `phonopy`.\n", "1. Perform force calculations for each supercell using DFT softwares or machine learning interatomic potentials (MLIPs).\n", " - Here example for `FHI-aims` and `MACE` are provided.\n", "1. Extract forces and construct force constants by `phonopy`.\n", " - This serves as a milestone for post-processing.\n", "1. Compute the phonon band structure using `phonopy`.\n", "\n", "The project’s **file structure** is as follows:\n", "\n", "```text\n", "${PROJECT_ROOT}\n", "├── fd_runs\n", "│ ├── sc_5 # for example, supercell size 5x5x5\n", "│ │ ├── aims_runs\n", "│ │ │ └── {0..${n}} # directories for each run\n", "│ │ ├── geoms_disp\n", "│ │ │ └── {0..${n}}.xyz\n", "│ │ ├── logs\n", "│ │ ├── control.force.in # for FHI-aims force calculation\n", "│ │ ├── force_constants.h5 # force_constants hdf5 file saved by phonopy\n", "│ │ ├── phono_bandstr.meV.png # phonon band structure plot\n", "│ │ └── phonopy_params.yaml # phonopy meta-settings for this calculation\n", "│ └── sc_${sc} # other supercell sizes\n", "├── relax_cell # dir for cell relaxation calculations\n", "│ └── relaxed.xyz # the relaxed cell\n", "└── phonopy_in_python.ipynb # this file\n", "```\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/home/zekunlou/Projects/pj_docs/docs_howtos/docs/source/phonopy_simple\n" ] } ], "source": [ "\"\"\" change dir to ensure the file relative paths, you shall change it for your own project \"\"\"\n", "import os\n", "\n", "PROJECT_ROOT = os.getcwd()\n", "if PROJECT_ROOT.endswith(\"docs/source\"):\n", " PROJECT_ROOT = os.path.join(PROJECT_ROOT, \"phonopy_simple\")\n", "elif PROJECT_ROOT.endswith(\"phonopy_simple\"):\n", " pass\n", "print(PROJECT_ROOT)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy\n", "from ase.atoms import Atoms as aseAtoms\n", "from ase.io import read, write\n", "from ase.build import make_supercell\n", "\n", "import h5py # for compact binary force constants storage\n", "from phonopy import Phonopy # main class\n", "from phonopy.cui.load import load as load_phonopy # load from input yaml files\n", "from phonopy.file_IO import read_force_constants_hdf5, write_force_constants_to_hdf5 # read/write FCs\n", "from phonopy.phonon.band_structure import get_band_qpoints_and_path_connections # band structure q-points\n", "from phonopy.structure.atoms import PhonopyAtoms # phonopy atoms class" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\"\"\" prepare useful functions for structure class conversion \"\"\"\n", "\n", "def atoms_ase2ph(atoms: aseAtoms):\n", " if not numpy.all(atoms.get_pbc()):\n", " print(\"WARNING: for PhonopyAtoms the pbc must be T T T. Set to T T T.\")\n", " return PhonopyAtoms(\n", " symbols=atoms.get_chemical_symbols(),\n", " cell=atoms.get_cell().array,\n", " positions=atoms.get_positions(),\n", " )\n", "\n", "def atoms_ph2ase(atoms: PhonopyAtoms):\n", " return aseAtoms(\n", " symbols=atoms.symbols,\n", " cell=atoms.cell,\n", " positions=atoms.positions,\n", " pbc=True,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate displaced structures" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loaded phonopy parameters from /home/zekunlou/Projects/pj_docs/docs_howtos/docs/source/phonopy_simple/fd_runs/sc_5/phonopy_params.yaml\n" ] } ], "source": [ "\"\"\" prepare parameters \"\"\"\n", "\n", "supercell = 5\n", "work_dpath = f\"{PROJECT_ROOT}/fd_runs/sc_{supercell}\"\n", "displacement = 1e-2\n", "xyz_eq_fpath = f\"{PROJECT_ROOT}/relax_cell/relaxed.xyz\"\n", "\n", "\"\"\" prepare directories and files \"\"\"\n", "\n", "geoms_dpath = f\"{work_dpath}/geoms_disp\"\n", "aims_dpath = f\"{work_dpath}/aims_runs\"\n", "logs_dpath = f\"{work_dpath}/logs\"\n", "phonpy_params_fpath = f\"{work_dpath}/phonopy_params.yaml\"\n", "force_constants_fpath = f\"{work_dpath}/force_constants.h5\"\n", "band_structure_fpath = f\"{work_dpath}/band_structure.h5\"\n", "[os.makedirs(dpath, exist_ok=True) for dpath in (geoms_dpath, aims_dpath, logs_dpath)]\n", "atoms_prim = read(xyz_eq_fpath)\n", "\n", "\"\"\" better load from phonopy_params.yaml for reproducibility \"\"\"\n", "\n", "if os.path.exists(phonpy_params_fpath):\n", " phonon = load_phonopy(phonpy_params_fpath)\n", " print(f\"Loaded phonopy parameters from {phonpy_params_fpath}\")\n", "else:\n", " phonon = Phonopy(\n", " unitcell=atoms_ase2ph(atoms_prim),\n", " supercell_matrix=numpy.eye(3, dtype=int) * supercell,\n", " )\n", " phonon.generate_displacements(distance=displacement)\n", " phonon.save(phonpy_params_fpath)\n", "\n", "\"\"\" write the displaced supercells for FHI-aims calculation \"\"\"\n", "\"\"\" for MLIPs: you can directly produce the force_sets with shape (n_supercells, n_atoms, 3), as the next cell \"\"\"\n", "for i, this_sc in enumerate(phonon.supercells_with_displacements):\n", " write(f\"{geoms_dpath}/{i}.xyz\", atoms_ph2ase(this_sc))\n", " os.makedirs(f\"{aims_dpath}/{i}\", exist_ok=True)\n", " write(f\"{aims_dpath}/{i}/geometry.in\", atoms_ph2ase(this_sc), format=\"aims\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we have generated the displaced structures (with symmetry considerations) to get the force constants.\n", "We need to perform single point calculations using FHI-aims or MLIPs, and then translate them to force constants using phonopy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate forces and then compute force constants" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With generated structures in `${PROJECT_ROOT}/fd_runs/sc_${supercell}/geoms_disp/`, one shall perform force calculations using FHI-aims.\n", "\n", "Pre-calculation is done with results in `${PROJECT_ROOT}/fd_runs/sc_${supercell}/aims_runs/{0..n}/`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loaded force constants from /home/zekunlou/Projects/pj_docs/docs_howtos/docs/source/phonopy_simple/fd_runs/sc_5/force_constants.h5\n", "phonon.force_constants.shape=(4, 500, 3, 3)\n" ] } ], "source": [ "\"\"\" FHI-aims: load force constants and save it h5, because it could be slow, especially for large supercells and repeated calculations \"\"\"\n", "\n", "if os.path.exists(force_constants_fpath):\n", " phonon.force_constants = read_force_constants_hdf5(force_constants_fpath)\n", " print(f\"Loaded force constants from {force_constants_fpath}\")\n", "else:\n", " \"\"\"Load from aims output. Please rewrite this part for your own code.\"\"\"\n", " force_sets = numpy.array([\n", " read(os.path.join(f\"{aims_dpath}/{task_idx}/aims.out\"), format=\"aims-output\").get_forces()\n", " for task_idx in sorted(os.listdir(aims_dpath), key=lambda x: int(x))\n", " ])\n", " phonon.produce_force_constants(\n", " forces=force_sets,\n", " calculate_full_force_constants=False,\n", " ) # we are generating compact force constants here\n", " write_force_constants_to_hdf5(\n", " phonon.get_force_constants(),\n", " filename=force_constants_fpath,\n", " )\n", "print(f\"{phonon.force_constants.shape=}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MLIPs can also serve as a calculator here, and ASE calculator interface makes it handy.\n", "\n", "Please check [this python script](./phonopy_committee_MACE_mlip.py) for running phonopy with MACE calculator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot and save phonon band structure\n", "\n", "With computed force constants, we can calculate, plot, and save the phonon bands and modes.\n", "\n", "Website https://henriquemiranda.github.io/phononwebsite/phonon.html is very useful for interactive visualization of phonon bands with the data we have generated so far.\n", "It is highly recommended to give it a try." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\" calculate phonon band structure \"\"\"\n", "\n", "special_points = { # for hexagon cell with gamma = 60.0 deg\n", " \"G\": [0.0, 0.0, 0.0],\n", " \"M\": [1 / 2, 1 / 2, 0.0],\n", " \"K\": [1 / 3, 2 / 3, 0.0],\n", " \"A\": [0.0, 0.0, 1 / 2],\n", "}\n", "\n", "bz_labels = [\"A\", \"G\", \"M\", \"K\", \"G\"]\n", "kpath = [[special_points[label] for label in bz_labels]] # must be 2-level list\n", "kpts, connections = get_band_qpoints_and_path_connections(kpath, npoints=101)\n", "\n", "phonon.run_band_structure(kpts, path_connections=connections, labels=bz_labels)\n", "# phonon.write_hdf5_band_structure(filename=band_structure_fpath) # if you want to save detailed band structure data\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n", "phonon._band_structure.plot([ax]) # a hack here, should be List[Axes]\n", "xscale_factor = (\n", " max([numpy.max(fq) for fq in phonon._band_structure.frequencies])\n", " / phonon._band_structure.distances[-1][-1]\n", " * 1.5\n", ") # this can be found in phonopy src code\n", "for d in phonon._band_structure.distances:\n", " ax.axvline(d[-1] * xscale_factor, color=\"b\", linestyle=\":\", linewidth=0.5)\n", "\n", "ax_unit = [\"meV\", \"cm-1\", \"THz\"][2] # choose your preferred unit\n", "if ax_unit == \"meV\":\n", " ax.set_ylabel(\"Energy (meV)\")\n", " ax.set_ylim(ax.get_ylim())\n", " ax_yticks_in_meV = numpy.arange(0, 220, 20)\n", " ax.set_yticks(ax_yticks_in_meV / 4.1357, ax_yticks_in_meV)\n", "elif ax_unit == \"cm-1\":\n", " ax_yticks_in_cm = numpy.arange(0, 1800, 200)\n", " ax.set_yticks(ax_yticks_in_cm / 4.1357 / 8.1, ax_yticks_in_cm)\n", " ax.set_ylabel(\"Frequency (cm$^{-1}$)\")\n", "elif ax_unit == \"THz\":\n", " ax.set_ylabel(\"Frequency (THz)\")\n", "else:\n", " raise ValueError(f\"Unknown ax_unit: {ax_unit}\")\n", "\n", "fig.suptitle(\n", " f\"graphite phonon band structure in primitive cell\\nFC based on supercell={supercell}x{supercell}x{supercell}\"\n", ")\n", "fig.tight_layout()\n", "fig = plt.gcf()\n", "fig.savefig(f\"{work_dpath}/phonon_bandstr.{ax_unit}.png\", dpi=300, transparent=True)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\"save for visualization\"\"\"\n", "bz_labels = [\"G\", \"K\",]\n", "kpath = [[special_points[label] for label in bz_labels]] # must be 2-level list\n", "kpts, connections = get_band_qpoints_and_path_connections(kpath, npoints=101)\n", "\n", "phonon.run_band_structure(kpts, path_connections=connections, labels=bz_labels, with_eigenvectors=True,)\n", "phonon.write_hdf5_band_structure(filename=f\"{work_dpath}/band_structure.GK.h5\")\n", "phonon._band_structure.plot([plt.gca()])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Phonopy using command line for FHI-aims\n", "\n", "Phonopy calculation parameter:\n", "```bash\n", "phonopy -d --dim=\"5 5 5\" --tolerance=1e-4 --aims\n", "```\n", "Then one creates FHI-aims calculation folders for each structure:\n", "```bash\n", "for i in {001..008}; do cd disp-${i}; cp ../control.in ./; cp ../geometry.in.$i ./; cd ../; done\n", "```\n", "and then perform DFT calculations.\n", "Once finished, use the following line to create force constants:\n", "```bash\n", "phonopy -f disp-???/aims.out # Create FORCESET file\n", "```\n", "Then create a `mesh.conf` file copy below parameters, k-path A-$\\Gamma$-M-K-$\\Gamma$:\n", "```text\n", "DIM = 5 5 5\n", "BAND = 0.0 0.0 0.5 0.0 0.0 0.0 0.5 0.5 0.0 0.333 0.667 0.0 0.0 0.0 0.0\n", "BAND_POINTS = 101\n", "EIGENVECTORS = .TRUE.\n", "HDF5 = .TRUE.\n", "BAND_CONNECTION = .TRUE.\n", "```\n", "Finally, compute phonon band structure and save plot:\n", "```bash\n", "phonopy -s mesh.conf --tolerance=1e-4 >> phonopy.out\n", "```\n", "For saving plot also use `-p` flag before `-s`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Phonon mode visualization" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", "in phonopy.harmonics.dynamical_matrix.DynamicalMatrix._run_py_dynamical_matrix,\n", "the phase factor is phase.append(np.vdot(vec, q) * 2j * np.pi) # positive sign\n", "\"\"\"\n", "\n", "def generate_phonon_visuals(\n", " atoms: aseAtoms,\n", " ph_eigvec: numpy.ndarray,\n", " k: numpy.ndarray,\n", " supercell: numpy.ndarray,\n", " num_frames: int = 16,\n", " amp_factor: float = 1.0, # mass-scaling factor\n", " comment: str = \"\",\n", ") -> list:\n", " \"\"\"\n", " Generate phonon frames for visualization.\n", " For postprocessing phonopy output for visualization.\n", "\n", " Note:\n", " The phonon eigenvectors should be like phonopy, i.e. bloch phase applied to each atom but not unit cell.\n", "\n", " Args:\n", " atoms (ase.atoms.Atoms): The atomic structure.\n", " ph_eigvec (numpy.ndarray): Phonon eigenvector, better from phonopy.\n", " k (numpy.ndarray): Wave vector contains the 2*pi factor.\n", " supercell (numpy.ndarray): Supercell transformation matrix.\n", " num_frames (int, optional): Number of frames to generate. Defaults to 16.\n", " amp_factor (float, optional): Amplitude scaling factor. Defaults to 1.0.\n", " comment (str, optional): Comment to add to each frame. Defaults to \"\".\n", "\n", " Returns:\n", " list: List of Atoms objects representing the frames.\n", "\n", " Reference:\n", " Eq.27 in A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py,\n", " J. Phys.: Condens. Matter 35, 353001 (2023).\n", " \"\"\"\n", " assert ph_eigvec.ndim == 1, f\"ph_eigvec should be a 1D array, but got {ph_eigvec.ndim}D\"\n", " assert ph_eigvec.size == len(atoms) * 3, \\\n", " f\"ph_eigvec size should be (natoms * 3)=({len(atoms) * 3}), but got {ph_eigvec.size}\"\n", " assert supercell.ndim == 2 and supercell.shape[0] == supercell.shape[1] == 3, \\\n", " f\"supercell should be a 3x3 matrix, but got shape {supercell.shape}\"\n", "\n", " # Generate the supercell\n", " supercell_atoms = make_supercell(atoms, supercell)\n", " sc_positions = supercell_atoms.get_positions()\n", "\n", " # Repeat phonon eigenvector for the supercell\n", " natoms = len(atoms)\n", " sc_eigvec = numpy.tile(ph_eigvec.reshape(natoms, 3), (len(supercell_atoms) // natoms, 1)) # shape (n_sc_atoms, xyz)\n", "\n", " # Apply Bloch phase correction for each atom in the supercell\n", " bloch_phase_factor = numpy.exp(1j * (sc_positions @ k))[:, None] # shape (n_sc_atoms, 1)\n", "\n", " # Apply Bloch phase to eigenvector\n", " sc_eigvec = (sc_eigvec * bloch_phase_factor)\n", "\n", " # Compute phonon displacements\n", " ph_phase = numpy.angle(sc_eigvec) # shape (n_sc_atoms, xyz)\n", " ph_amp = amp_factor * numpy.abs(sc_eigvec) * (supercell_atoms.get_masses()**(-0.5))[:, None] # shape (n_sc_atoms, xyz)\n", " ph_disp_time = numpy.linspace(0, 2 * numpy.pi, num_frames) # omega*t for one period\n", "\n", " # Calculate displacements for each frame\n", " ph_disp = ph_amp[None, :] * numpy.sin(\n", " ph_phase[None, :] + ph_disp_time[:, None, None]\n", " ) # shape (n_frames, n_sc_atoms, xyz)\n", "\n", " # Generate frames\n", " ph_frames = []\n", " for i in range(num_frames):\n", " this_atoms = supercell_atoms.copy()\n", " this_atoms.positions = sc_positions + ph_disp[i]\n", " this_atoms.info[\"comment\"] = comment\n", " ph_frames.append(this_atoms)\n", "\n", " return ph_frames\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "k='distance', shape=(1, 101)\n", "k='eigenvector', shape=(1, 101, 12, 12)\n", "k='frequency', shape=(1, 101, 12)\n", "k='label', shape=(1, 2), content=[[b'G' b'K']]\n", "k='nqpoint', shape=(1,), content=[101]\n", "k='path', shape=(1, 101, 3)\n", "k='segment_nqpoint', shape=(1,), content=[101]\n", "ph_eigvals.shape=(101, 12), ph_eigvecs.shape=(101, 12, 12), ph_kpath.shape=(101, 3)\n" ] } ], "source": [ "work_dpath = f\"{PROJECT_ROOT}/fd_runs/sc_5\"\n", "atoms = read(f\"{PROJECT_ROOT}/relax_cell/relaxed.xyz\")\n", "\n", "with h5py.File(f\"{work_dpath}/band_structure.GK.h5\", \"r\") as h5:\n", " # show the keys and arrays in the h5 file\n", " print(h5.keys())\n", " for k in h5.keys():\n", " if h5[k].size < 10:\n", " print(f\"{k=}, shape={h5[k].shape}, content={h5[k][()]}\")\n", " else:\n", " print(f\"{k=}, shape={h5[k].shape}\")\n", " if k == \"frequency\":\n", " data = h5[k][()]\n", " ph_kpath_frac = h5[\"path\"][0,:]\n", " ph_freqs = h5[\"frequency\"][0,:]\n", " ph_eigvecs = h5[\"eigenvector\"][0,:] # shape (n_kpoints, n_atoms*3, n_bands/n_modes)\n", "ph_kpath = ph_kpath_frac @ atoms.cell.reciprocal() # without the 2pi factor\n", "print(f\"{ph_freqs.shape=}, {ph_eigvecs.shape=}, {ph_kpath.shape=}\")\n", "\n", "# Example usage\n", "os.makedirs(ph_viz_dpath:=f\"{PROJECT_ROOT}/fd_runs/sc_5/ph_GK_viz_sc\", exist_ok=True)\n", "supercell_matrix = numpy.array([[10, 0, 0], [0, 10, 0], [0, 0, 1]]) # Example 10x10x1 supercell\n", "\n", "kpt_idx, band_idx = 10, 2\n", "for band_idx in (2, 3): # TA and TA(antisymm) mode\n", " ph_eigvec = ph_eigvecs[kpt_idx][:, band_idx]\n", " ph_frames = generate_phonon_visuals(\n", " atoms,\n", " ph_eigvec,\n", " k=2 * numpy.pi * ph_kpath[kpt_idx], # Convert k-point to reciprocal space\n", " supercell=supercell_matrix,\n", " comment=f\"seg=GK,kpt_idx={kpt_idx},band_idx={band_idx}\"\n", " )\n", " write(f\"{ph_viz_dpath}/GK_kpt_{kpt_idx}_band_{band_idx}.xyz\", ph_frames)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rendering phonon modes with OVITO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then you can put the frames into OVITO ([docs on rendering](https://www.ovito.org/manual/usage/rendering.html)) or VMD for visualization.\n", "After rendering by OVITO and concatenating by ffmpeg, we get\n", "\n", "For TA (transverse acoustic) mode:\n", "\n", "![phonon_mode_TA.gif](./fd_runs/sc_5/ph_GK_viz_sc/GK_kpt_10_band_2.gif)\n", "\n", "For T $\\!\\!\\tilde{A}$ (transverse acoustic anti-symmetric) mode:\n", "\n", "![phonon_mode_TAantisymm.gif](./fd_runs/sc_5/ph_GK_viz_sc/GK_kpt_10_band_3.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or OVITO python script for rendering.\n", "\n", "OVITO provides different renderers, and git output timing benchmark:\n", "```text\n", "OpenGLRenderer: 0.78 s\n", "TachyonRenderer: 16.09 s\n", "OSPRayRenderer: 53.30 s\n", "```\n", "Also OpenGL is the fastest, the output quality is ill.\n", "Maybe Tachyon is the best choice for rendering." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "from ovito.io import import_file\n", "# from ovito.data import *\n", "from ovito.vis import Viewport\n", "from ovito.vis import OpenGLRenderer, TachyonRenderer, OSPRayRenderer\n", "\n", "kpt_idx, band_idx = 10, 2\n", "pipeline = import_file(\n", " f\"{ph_viz_dpath}/GK_kpt_{kpt_idx}_band_{band_idx}.xyz\",\n", " columns = [\"Particle Type\", \"Position.X\", \"Position.Y\", \"Position.Z\"],\n", ")\n", "pipeline.add_to_scene()\n", "atoms_frame_0 = read(f\"{ph_viz_dpath}/GK_kpt_{kpt_idx}_band_{band_idx}.xyz\", index=0)\n", "center = atoms_frame_0.positions.mean(axis=0)\n", "camera_pos_from_center = numpy.array((1, -1, 1))\n", "vp = Viewport(\n", " type=Viewport.Type.Ortho,\n", " camera_pos = tuple(center + camera_pos_from_center),\n", " camera_dir=tuple(-camera_pos_from_center), # look backwards to the center\n", ")\n", "vp.zoom_all()\n", "vp.render_anim(\n", " size=(800,600),\n", " filename=f\"{ph_viz_dpath}/GK_kpt_{kpt_idx}_band_{band_idx}.tachyon.gif\",\n", " background=(1,1,1),\n", " fps=16,\n", " renderer=TachyonRenderer(),\n", ")\n", "pipeline.remove_from_scene() # must remove, or the next import will be added to the scene and there will be multiple geometries" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For TA (transverse acoustic) mode rendered by OpenGL:\n", "\n", "![phonon_mode_TA.opengl.gif](./fd_runs/sc_5/ph_GK_viz_sc/GK_kpt_10_band_2.opengl.gif)\n", "\n", "For TA (transverse acoustic) mode rendered by Tachyon:\n", "\n", "![phonon_mode_TA.tachyon.gif](./fd_runs/sc_5/ph_GK_viz_sc/GK_kpt_10_band_2.tachyon.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize phonons locally in ovito, we need to generate an xyz file with phonon displacements.\n", "We provide the following two implementations:\n", "- In this tutorial, you can find xyz files containing phonon displacements in `${PROJECT_ROOT}/fd_runs/sc_5/ph_GK_viz_sc`.\n", " - The output is more or less like the results by OVITO python script above.\n", "- Please check [this python script](./create_jmol_from_hdf5.py) for creating xyz files from phonopy hdf5 output for ovito visualization and jmol visualization.\n", " - It visualizes phonon modes with arrows indicating displacement directions as below. Image from [arXiV 2504.11224](https://arxiv.org/abs/2504.11224).\n", "![](results_for_create_jmol_from_hdf5.png)\n" ] } ], "metadata": { "kernelspec": { "display_name": "research", "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 2 }