{ "cells": [ { "cell_type": "markdown", "id": "29680e01-8658-4085-aada-eaaa9d8705be", "metadata": {}, "source": "# Workflows\nTo demonstrate the workflows implemented in the `atomistics` package, the [LAMMPS](https://www.lammps.org/) molecular \ndynamics simulation code is used in the following demonstrations. Still the same `workflows` can also be used with other\nsimulation codes:" }, { "cell_type": "code", "execution_count": 1, "id": "76ec535d-d9cb-4d68-9208-c9b0c029c402", "metadata": { "trusted": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": "[jupyter-pyiron-2datomistics-2dloteusr2:00647] mca_base_component_repository_open: unable to open mca_btl_openib: librdmacm.so.1: cannot open shared object file: No such file or directory (ignored)\n" } ], "source": [ "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict={},\n", " potential_dataframe=potential_dataframe,\n", ")" ] }, { "metadata": {}, "cell_type": "markdown", "source": [ "The interatomic potential for Aluminium from Mishin named `1999--Mishin-Y--Al--LAMMPS--ipr1` is used in the evaluation\n", "with [LAMMPS](https://www.lammps.org/) `evaluate_with_lammpslib()`." ], "id": "452c0005b793b7fd" }, { "metadata": {}, "cell_type": "markdown", "source": [ "## Elastic Matrix \n", "The elastic constants and elastic moduli can be calculated using the `ElasticMatrixWorkflow`: " ], "id": "aca2ff262aefa8b5" }, { "metadata": {}, "cell_type": "code", "outputs": [], "execution_count": null, "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import ElasticMatrixWorkflow\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "workflow = ElasticMatrixWorkflow(\n", " structure=bulk(\"Al\", cubic=True),\n", " num_of_point=5,\n", " eps_range=0.005,\n", " sqrt_eta=True,\n", " fit_order=2,\n", ")\n", "task_dict = workflow.generate_structures()\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "fit_dict = workflow.analyse_structures(output_dict=result_dict)\n", "print(fit_dict)" ], "id": "7e0fd47b1fda8a82" }, { "cell_type": "markdown", "id": "262aefd1-9cf9-4b35-8d94-03996b21166b", "metadata": {}, "source": "The `ElasticMatrixWorkflow` takes an `ase.atoms.Atoms` object as `structure` input as well as the number of points \n`num_of_point` for each compression direction. Depending on the symmetry of the input `structure` the number of \ncalculations required to calculate the elastic matrix changes. The compression and elongation range is defined by the\n`eps_range` parameter. Furthermore, `sqrt_eta` and `fit_order` describe how the change in energy over compression and\nelongation is fitted to calculate the resulting pressure. " }, { "cell_type": "markdown", "id": "dc5356a8-0b07-4a0a-a549-9a20cf3c64cc", "metadata": {}, "source": "## Energy Volume Curve\nThe `EnergyVolumeCurveWorkflow` can be used to calculate the equilibrium properties: equilibrium volume, equilibrium \nenergy, equilibrium bulk modulus and the pressure derivative of the equilibrium bulk modulus. " }, { "cell_type": "code", "execution_count": 3, "id": "720a7662-fdee-496d-b355-ff4881f5c633", "metadata": { "trusted": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": "{'b_prime_eq': 1.279502459079921, 'bulkmodul_eq': 77.7250135953191, 'volume_eq': 66.43019853103964, 'energy_eq': -13.43996804374383, 'fit_dict': {'fit_type': 'polynomial', 'least_square_error': 3.225313797039607e-10, 'poly_fit': array([-4.17645808e-05, 1.19746500e-02, -1.03803906e+00, 1.49168639e+01]), 'fit_order': 3}, 'energy': [-13.398169481534445, -13.413389552957456, -13.425112589013958, -13.433411420804067, -13.438357630783006, -13.439999952539933, -13.438383476946305, -13.433607982916406, -13.425774537190858, -13.414961805921427, -13.401233093668836], 'volume': [63.10861874999998, 63.77291999999998, 64.43722124999998, 65.1015225, 65.76582375000004, 66.43012500000002, 67.09442624999994, 67.75872750000002, 68.42302874999999, 69.08732999999997, 69.75163125000002]}\n" } ], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import EnergyVolumeCurveWorkflow\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "workflow = EnergyVolumeCurveWorkflow(\n", " structure=bulk(\"Al\", cubic=True),\n", " num_points=11,\n", " fit_type=\"polynomial\",\n", " fit_order=3,\n", " vol_range=0.05,\n", " axes=(\"x\", \"y\", \"z\"),\n", " strains=None,\n", ")\n", "task_dict = workflow.generate_structures()\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "fit_dict = workflow.analyse_structures(output_dict=result_dict)\n", "print(fit_dict)" ] }, { "cell_type": "markdown", "id": "13c95c80-137d-49bf-8016-b3c15279fbcf", "metadata": {}, "source": "The input parameters for the `EnergyVolumeCurveWorkflow` in addition to the `ase.atoms.Atoms` object defined \nas `structure` are: \n\n* `num_points` the number of strains to calculate energies and volumes. \n* `fit_type` the type of the fit which should be used to calculate the equilibrium properties. This can either be a \n `polynomial` fit or a specific equation of state like the Birch equation (`birch`), the Birch-Murnaghan equation \n (`birchmurnaghan`) the Murnaghan equation (`murnaghan`), the Pourier Tarnatola eqaution (`pouriertarantola`) or the\n Vinet equation (`vinet`). \n* `fit_order` for the `polynomial` fit type the order of the polynomial can be set, for the other fit types this \n parameter is ignored. \n* `vol_range` specifies the amount of compression and elongation to be applied relative to the absolute volume. \n* `axes` specifies the axes which are compressed, typically a uniform compression is applied. \n* `strains` specifies the strains directly rather than deriving them from the range of volume compression `vol_range`. \n\nBeyond calculating the equilibrium properties the `EnergyVolumeCurveWorkflow` can also be used to calculate the thermal\nproperties using the [Moruzzi, V. L. et al.](https://link.aps.org/doi/10.1103/PhysRevB.37.790) model: " }, { "cell_type": "code", "execution_count": 4, "id": "8a9a8e77-a6f0-4466-8c3d-fc1ca6ebbaf0", "metadata": { "trusted": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": "{'temperatures': array([ 1, 51, 101, 151, 201, 251, 301, 351, 401, 451, 501,\n 551, 601, 651, 701, 751, 801, 851, 901, 951, 1001, 1051,\n 1101, 1151, 1201, 1251, 1301, 1351, 1401, 1451, 1501]), 'volumes': array([66.48459155, 66.48492729, 66.48841343, 66.49613572, 66.50654263,\n 66.51846055, 66.53126421, 66.5446199 , 66.55833931, 66.57230985,\n 66.58646057, 66.6007448 , 66.61513063, 66.6295956 , 66.64412341,\n 66.65870199, 66.6733222 , 66.68797701, 66.70266093, 66.71736958,\n 66.73209946, 66.74684773, 66.76161205, 66.77639048, 66.79118142,\n 66.8059835 , 66.82079558, 66.83561668, 66.85044595, 66.86528267,\n 66.88012622]), 'free_energy': array([ 0.18879418, 0.18840183, 0.18352524, 0.16909367, 0.1440755 ,\n 0.10931095, 0.06593656, 0.01498215, -0.04269081, -0.1063728 ,\n -0.1754776 , -0.24951635, -0.328077 , -0.41080851, -0.49740877,\n -0.58761537, -0.68119851, -0.77795536, -0.87770572, -0.98028844,\n -1.08555864, -1.19338539, -1.3036498 , -1.41624343, -1.53106703,\n -1.6480294 , -1.76704645, -1.88804043, -2.01093923, -2.13567578,\n -2.26218757]), 'entropy': array([ 0.75685476, 5.08219062, 18.62461552, 38.05446426,\n 57.6693229 , 75.37710506, 90.99476554, 104.78762778,\n 117.06473011, 128.09164494, 138.08127289, 147.20167195,\n 155.58579193, 163.33970927, 170.54896552, 177.28330938,\n 183.60022562, 189.54757244, 195.16556897, 200.48830826,\n 205.54492122, 210.36048158, 214.95671661, 219.35257076,\n 223.56465688, 227.60762034, 231.49443548, 235.23664867,\n 238.84457908, 242.32748555, 244.0403182 ]), 'heat_capacity': array([8.65067172e-02, 9.11255799e+00, 3.33019964e+01, 5.89575081e+01,\n 7.50185080e+01, 8.36468610e+01, 8.85256734e+01, 9.15055757e+01,\n 9.34491088e+01, 9.47846079e+01, 9.57412353e+01, 9.64498999e+01,\n 9.69896043e+01, 9.74102601e+01, 9.77446368e+01, 9.80149634e+01,\n 9.82367471e+01, 9.84210719e+01, 9.85760297e+01, 9.87076399e+01,\n 9.88204550e+01, 9.89179695e+01, 9.90029019e+01, 9.90773926e+01,\n 9.91431454e+01, 9.92015302e+01, 9.92536586e+01, 9.93004401e+01,\n 9.93426247e+01, nan, nan])}\n" } ], "source": [ "tp_dict = workflow.get_thermal_properties(\n", " t_min=1,\n", " t_max=1500,\n", " t_step=50,\n", " temperatures=None,\n", " constant_volume=False,\n", ")\n", "print(tp_dict)" ] }, { "cell_type": "markdown", "id": "ebebb63f-3897-4028-ad23-708aaaf9cc26", "metadata": {}, "source": "Or alternatively directly calculate the thermal expansion:" }, { "cell_type": "code", "execution_count": 5, "id": "6e963779-cd59-4985-9a72-9652dd1f1408", "metadata": { "trusted": true }, "outputs": [], "source": [ "thermal_properties_dict = workflow.get_thermal_properties(\n", " t_min=1,\n", " t_max=1500,\n", " t_step=50,\n", " constant_volume=False,\n", " output_keys=[\"temperatures\", \"volumes\"],\n", ")\n", "temperatures, volumes = (\n", " thermal_properties_dict[\"temperatures\"],\n", " thermal_properties_dict[\"volumes\"],\n", ")" ] }, { "cell_type": "markdown", "id": "e3f4357d-8b81-41bd-a90b-556f231b9766", "metadata": {}, "source": "The [Moruzzi, V. L. et al.](https://link.aps.org/doi/10.1103/PhysRevB.37.790) model is a quantum mechanical approximation, so the equilibrium volume at 0K is not\nthe same as the equilibrium volume calculated by fitting the equation of state. " }, { "cell_type": "markdown", "id": "ac4095fb-0e11-46bc-8c8d-54bc97ddfe18", "metadata": {}, "source": "## Molecular Dynamics \nJust like the structure optimization also the molecular dynamics calculation can either be implemented inside the\nsimulation code or in the `atomistics` package. The latter has the advantage that it is the same implementation for all\ndifferent simulation codes, while the prior has the advantage that it is usually faster and computationally more efficient." }, { "cell_type": "markdown", "id": "1cfe604e-1e02-4a64-a49b-eccd1b32c9fc", "metadata": {}, "source": "### Implemented in Simulation Code \nThe [LAMMPS](https://lammps.org/) simulation code implements a wide range of different simulation workflows, this \nincludes molecular dynamics. In the `atomistics` package these can be directly accessed via the python interface. " }, { "cell_type": "markdown", "id": "0e52ed95-1510-4944-a5a6-8ea9d49c906f", "metadata": {}, "source": "#### Langevin Thermostat\nThe Langevin thermostat is currently the only thermostat which is available as both a stand-alone python interface and\nan integrated interface inside the [LAMMPS](https://lammps.org/) simulation code. The latter is introduced here:" }, { "cell_type": "code", "execution_count": 6, "id": "2e0c22ea-562b-4669-a34b-1d60a8bd1e2c", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_langevin_with_lammpslib,\n", " get_potential_by_name,\n", ")\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = calc_molecular_dynamics_langevin_with_lammpslib(\n", " structure=bulk(\"Al\", cubic=True).repeat([10, 10, 10]),\n", " potential_dataframe=potential_dataframe,\n", " Tstart=100,\n", " Tstop=100,\n", " Tdamp=0.1,\n", " run=100,\n", " thermo=10,\n", " timestep=0.001,\n", " seed=4928459,\n", " dist=\"gaussian\",\n", " output_keys=(\n", " \"positions\",\n", " \"cell\",\n", " \"forces\",\n", " \"temperature\",\n", " \"energy_pot\",\n", " \"energy_tot\",\n", " \"pressure\",\n", " \"velocities\",\n", " ),\n", ")" ] }, { "cell_type": "markdown", "id": "e21267cb-9fb6-4c1f-8912-c281dc899323", "metadata": {}, "source": "In addition to the typical LAMMPS input parameters like the atomistic structure `structure` as `ase.atoms.Atoms` object\nand the `pandas.DataFrame` for the interatomic potential `potential_dataframe` are: \n\n* `Tstart` start temperature \n* `Tstop` end temperature\n* `Tdamp` temperature damping parameter \n* `run` number of molecular dynamics steps to be executed during one temperature step\n* `thermo` refresh rate for the thermo dynamic properties, this should typically be the same as the number of molecular\n dynamics steps. \n* `timestep` time step - typically 1fs defined as `0.001`.\n* `seed` random seed for the molecular dynamics \n* `dist` initial velocity distribution \n* `lmp` Lammps library instance as `pylammpsmpi.LammpsASELibrary` object \n* `output` the output quantities which are extracted from the molecular dynamics simulation" }, { "cell_type": "markdown", "id": "be5d582d-9952-4a5b-b704-1a9acdb8b306", "metadata": {}, "source": "#### Nose Hoover Thermostat\nCanonical ensemble (nvt) - volume and temperature constraints molecular dynamics:" }, { "cell_type": "code", "execution_count": 7, "id": "9717893e-4dea-46f7-9317-bb314bc5bbdd", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_nvt_with_lammpslib,\n", " get_potential_by_name,\n", ")\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = calc_molecular_dynamics_nvt_with_lammpslib(\n", " structure=bulk(\"Al\", cubic=True).repeat([10, 10, 10]),\n", " potential_dataframe=potential_dataframe,\n", " Tstart=100,\n", " Tstop=100,\n", " Tdamp=0.1,\n", " run=100,\n", " thermo=10,\n", " timestep=0.001,\n", " seed=4928459,\n", " dist=\"gaussian\",\n", " output_keys=(\n", " \"positions\",\n", " \"cell\",\n", " \"forces\",\n", " \"temperature\",\n", " \"energy_pot\",\n", " \"energy_tot\",\n", " \"pressure\",\n", " ),\n", ")" ] }, { "cell_type": "markdown", "id": "72797e59-72f5-4d32-b7cf-5ad806b91909", "metadata": {}, "source": "In addition to the typical LAMMPS input parameters like the atomistic structure `structure` as `ase.atoms.Atoms` object\nand the `pandas.DataFrame` for the interatomic potential `potential_dataframe` are: \n\n* `Tstart` start temperature \n* `Tstop` end temperature\n* `Tdamp` temperature damping parameter \n* `run` number of molecular dynamics steps to be executed during one temperature step\n* `thermo` refresh rate for the thermo dynamic properties, this should typically be the same as the number of molecular\n dynamics steps. \n* `timestep` time step - typically 1fs defined as `0.001`.\n* `seed` random seed for the molecular dynamics \n* `dist` initial velocity distribution \n* `lmp` Lammps library instance as `pylammpsmpi.LammpsASELibrary` object \n* `output` the output quantities which are extracted from the molecular dynamics simulation" }, { "cell_type": "markdown", "id": "8356bf7f-bf7d-40e0-8f3c-02309cd74d92", "metadata": {}, "source": "Isothermal-isobaric ensemble (npt) - pressure and temperature constraints molecular dynamics:" }, { "cell_type": "code", "execution_count": 8, "id": "1327d554-0df1-45fa-b35c-ec4955ce756f", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_npt_with_lammpslib,\n", " get_potential_by_name,\n", ")\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = calc_molecular_dynamics_npt_with_lammpslib(\n", " structure=bulk(\"Al\", cubic=True).repeat([10, 10, 10]),\n", " potential_dataframe=potential_dataframe,\n", " Tstart=100,\n", " Tstop=100,\n", " Tdamp=0.1,\n", " run=100,\n", " thermo=100,\n", " timestep=0.001,\n", " Pstart=0.0,\n", " Pstop=0.0,\n", " Pdamp=1.0,\n", " seed=4928459,\n", " dist=\"gaussian\",\n", " output_keys=(\n", " \"positions\",\n", " \"cell\",\n", " \"forces\",\n", " \"temperature\",\n", " \"energy_pot\",\n", " \"energy_tot\",\n", " \"pressure\",\n", " ),\n", ")" ] }, { "cell_type": "markdown", "id": "e6aeb0fe-ace6-4e55-a3c2-06be85aaf05e", "metadata": {}, "source": "The input parameters for the isothermal-isobaric ensemble (npt) are the same as for the canonical ensemble (nvt) plus:\n\n* `Pstart` start pressure \n* `Pstop` end pressure \n* `Pdamp` pressure damping parameter " }, { "cell_type": "markdown", "id": "04f5854b-d803-4023-af04-55efc22ee1e3", "metadata": {}, "source": "Isenthalpic ensemble (nph) - pressure and helmholtz-energy constraints molecular dynamics:" }, { "cell_type": "code", "execution_count": 9, "id": "5f64f60c-89ce-423b-a487-ea96780b1c20", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_nph_with_lammpslib,\n", " get_potential_by_name,\n", ")\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = calc_molecular_dynamics_nph_with_lammpslib(\n", " structure=bulk(\"Al\", cubic=True).repeat([10, 10, 10]),\n", " potential_dataframe=potential_dataframe,\n", " run=100,\n", " thermo=100,\n", " timestep=0.001,\n", " Tstart=100,\n", " Pstart=0.0,\n", " Pstop=0.0,\n", " Pdamp=1.0,\n", " seed=4928459,\n", " dist=\"gaussian\",\n", " output_keys=(\n", " \"positions\",\n", " \"cell\",\n", " \"forces\",\n", " \"temperature\",\n", " \"energy_pot\",\n", " \"energy_tot\",\n", " \"pressure\",\n", " ),\n", ")" ] }, { "cell_type": "markdown", "id": "3b4c6022-e1d5-467b-ac1b-d3617670fe67", "metadata": {}, "source": "#### Thermal Expansion\nOne example of a molecular dynamics calculation with the LAMMPS simulation code is the calculation of the thermal \nexpansion: " }, { "cell_type": "code", "execution_count": 10, "id": "d3e4bda7-9aa4-4a82-8c51-9606b0e77f75", "metadata": { "trusted": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": "100%|██████████| 10/10 [00:05<00:00, 1.69it/s]\n" } ], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_thermal_expansion_with_lammpslib,\n", " evaluate_with_lammpslib,\n", " get_potential_by_name,\n", ")\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "temperatures_md, volumes_md = calc_molecular_dynamics_thermal_expansion_with_lammpslib(\n", " structure=bulk(\"Al\", cubic=True).repeat([10, 10, 10]),\n", " potential_dataframe=potential_dataframe,\n", " Tstart=100,\n", " Tstop=1000,\n", " Tstep=100,\n", " Tdamp=0.1,\n", " run=100,\n", " thermo=100,\n", " timestep=0.001,\n", " Pstart=0.0,\n", " Pstop=0.0,\n", " Pdamp=1.0,\n", " seed=4928459,\n", " dist=\"gaussian\",\n", " lmp=None,\n", ")" ] }, { "cell_type": "markdown", "id": "08c20c91-9e7c-4770-b01f-1765064797dd", "metadata": {}, "source": "In addition to the typical LAMMPS input parameters like the atomistic structure `structure` as `ase.atoms.Atoms` object\nand the `pandas.DataFrame` for the interatomic potential `potential_dataframe` are: \n\n* `Tstart` start temperature \n* `Tstop` end temperature \n* `Tstep` temperature step \n* `Tdamp` temperature damping parameter \n* `run` number of molecular dynamics steps to be executed during one temperature step\n* `thermo` refresh rate for the thermo dynamic properties, this should typically be the same as the number of molecular\n dynamics steps. \n* `timestep` time step - typically 1fs defined as `0.001`.\n* `Pstart` start pressure \n* `Pstop` end pressure \n* `Pdamp` pressure damping parameter \n* `seed` random seed for the molecular dynamics \n* `dist` initial velocity distribution \n* `lmp` Lammps library instance as `pylammpsmpi.LammpsASELibrary` object \n\nThese input parameters are based on the LAMMPS fix `nvt/npt`, you can read more about the specific implementation on the\n[LAMMPS website](https://docs.lammps.org/fix_nh.html). \n" }, { "cell_type": "markdown", "id": "e57a6740-8546-4763-a9b3-140f0cae1543", "metadata": {}, "source": "#### Phonons from Molecular Dynamics\nThe softening of the phonon modes is calculated for Silicon using the [Tersoff interatomic potential](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.38.9902) \nwhich is available via the [NIST potentials repository](https://www.ctcms.nist.gov/potentials/entry/1988--Tersoff-J--Si-c/). \nSilicon is chosen based on its diamond crystal lattice which requires less calculation than the face centered cubic (fcc)\ncrystal of Aluminium. The simulation workflow consists of three distinct steps:\n\n* Starting with the optimization of the equilibrium structure. \n* Followed by the calculation of the 0K phonon spectrum. \n* Finally, the finite temperature phonon spectrum is calculated using molecular dynamics. \n\nThe finite temperature phonon spectrum is calculated using the [DynaPhoPy](https://abelcarreras.github.io/DynaPhoPy/)\npackage, which is integrated inside the `atomistics` package. As a prerequisite the dependencies, imported and the bulk \nsilicon diamond structure is created and the Tersoff interatomic potential is loaded: " }, { "cell_type": "code", "execution_count": 11, "id": "793b72ff-6b0b-46d8-a121-2c93ea6e7a32", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import (\n", " calc_molecular_dynamics_phonons_with_lammpslib,\n", " evaluate_with_lammpslib,\n", ")\n", "from atomistics.workflows import optimize_positions_and_volume, PhonopyWorkflow\n", "from dynaphopy import Quasiparticle\n", "import pandas\n", "from phonopy.units import VaspToTHz\n", "import spglib\n", "\n", "structure_bulk = bulk(\"Si\", cubic=True)\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1988--Tersoff-J--Si-c--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")" ] }, { "cell_type": "markdown", "id": "743dce70-a4f0-4063-b353-51d26def4005", "metadata": {}, "source": "The first step is optimizing the Silicon diamond structure to match the lattice specifications implemented in the Tersoff \ninteratomic potential:" }, { "cell_type": "code", "execution_count": 12, "id": "e96fb9d9-da43-49cb-8383-5eb93eea9dc1", "metadata": { "trusted": true }, "outputs": [], "source": [ "task_dict = optimize_positions_and_volume(structure=structure_bulk)\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "structure_ase = result_dict[\"structure_with_optimized_positions_and_volume\"]" ] }, { "cell_type": "markdown", "id": "c54c83b5-e710-405f-846b-e270267f8646", "metadata": {}, "source": "As a second step the 0K phonons are calculated using the `PhonopyWorkflow` which is explained in more detail below in \nthe section on [Phonons](https://atomistics.readthedocs.io/en/latest/workflows.html#phonons). " }, { "cell_type": "code", "execution_count": 13, "id": "b7532997-2cc3-4404-b108-3c599e4f92e8", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "{'mesh_dict': {'qpoints': array([[0.025, 0.025, 0.025],\n [0.075, 0.025, 0.025],\n [0.125, 0.025, 0.025],\n ...,\n [0.525, 0.525, 0.425],\n [0.475, 0.475, 0.475],\n [0.525, 0.475, 0.475]]),\n 'weights': array([ 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12,\n 12, 12, 6, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 6, 12,\n 12, 12, 12, 6, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6, 6,\n 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12,\n 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12,\n 12, 6, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 6, 12, 12, 12, 6,\n 12, 12, 6, 12, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12,\n 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 6, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6,\n 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12,\n 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12,\n 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12,\n 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12,\n 6, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6, 6, 6, 6, 6,\n 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 12,\n 12, 6, 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 6, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6,\n 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 6,\n 12, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12, 12, 6, 12, 12,\n 12, 12, 12, 6, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6, 6,\n 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 6, 12, 12, 12, 12, 12,\n 6, 12, 12, 12, 12, 6, 12, 12, 6, 12, 6, 2, 6, 6, 6, 6, 6,\n 6, 12, 12, 12, 12, 6, 12, 12, 12, 6, 12, 6, 2, 6, 6, 6, 6,\n 12, 12, 6, 2, 6]),\n 'frequencies': array([[ 0.35167322, 0.35167322, 0.71941397, 16.05999349, 16.06435417,\n 16.06435417],\n [ 0.7810313 , 1.04550359, 1.76442286, 16.01908158, 16.04238401,\n 16.0474694 ],\n [ 1.43010566, 1.69629248, 3.13109956, 15.91248433, 15.99513531,\n 16.00361669],\n ...,\n [ 4.89126604, 5.30105813, 11.18409265, 13.02666668, 15.38025565,\n 15.46187631],\n [ 4.65215064, 4.65215064, 11.21184039, 13.22967807, 15.43087981,\n 15.43087981],\n [ 4.71432047, 4.84620075, 11.26998698, 13.12729988, 15.41640899,\n 15.43613968]]),\n 'eigenvectors': None,\n 'group_velocities': None},\n 'band_structure_dict': {'qpoints': [array([[0. , 0. , 0. ],\n [0.00531915, 0. , 0.00531915],\n [0.0106383 , 0. , 0.0106383 ],\n [0.01595745, 0. , 0.01595745],\n [0.0212766 , 0. , 0.0212766 ],\n [0.02659574, 0. , 0.02659574],\n [0.03191489, 0. , 0.03191489],\n [0.03723404, 0. , 0.03723404],\n [0.04255319, 0. , 0.04255319],\n [0.04787234, 0. , 0.04787234],\n [0.05319149, 0. , 0.05319149],\n [0.05851064, 0. , 0.05851064],\n [0.06382979, 0. , 0.06382979],\n [0.06914894, 0. , 0.06914894],\n [0.07446809, 0. , 0.07446809],\n [0.07978723, 0. , 0.07978723],\n [0.08510638, 0. , 0.08510638],\n [0.09042553, 0. , 0.09042553],\n [0.09574468, 0. , 0.09574468],\n [0.10106383, 0. , 0.10106383],\n [0.10638298, 0. , 0.10638298],\n [0.11170213, 0. , 0.11170213],\n [0.11702128, 0. , 0.11702128],\n [0.12234043, 0. , 0.12234043],\n [0.12765957, 0. , 0.12765957],\n [0.13297872, 0. , 0.13297872],\n [0.13829787, 0. , 0.13829787],\n [0.14361702, 0. , 0.14361702],\n [0.14893617, 0. , 0.14893617],\n [0.15425532, 0. , 0.15425532],\n [0.15957447, 0. , 0.15957447],\n [0.16489362, 0. , 0.16489362],\n [0.17021277, 0. , 0.17021277],\n [0.17553191, 0. , 0.17553191],\n [0.18085106, 0. , 0.18085106],\n [0.18617021, 0. , 0.18617021],\n [0.19148936, 0. , 0.19148936],\n [0.19680851, 0. , 0.19680851],\n [0.20212766, 0. , 0.20212766],\n [0.20744681, 0. , 0.20744681],\n [0.21276596, 0. , 0.21276596],\n [0.21808511, 0. , 0.21808511],\n [0.22340426, 0. , 0.22340426],\n [0.2287234 , 0. , 0.2287234 ],\n [0.23404255, 0. , 0.23404255],\n [0.2393617 , 0. , 0.2393617 ],\n [0.24468085, 0. , 0.24468085],\n [0.25 , 0. , 0.25 ],\n [0.25531915, 0. , 0.25531915],\n [0.2606383 , 0. , 0.2606383 ],\n [0.26595745, 0. , 0.26595745],\n [0.2712766 , 0. , 0.2712766 ],\n [0.27659574, 0. , 0.27659574],\n [0.28191489, 0. , 0.28191489],\n [0.28723404, 0. , 0.28723404],\n [0.29255319, 0. , 0.29255319],\n [0.29787234, 0. , 0.29787234],\n [0.30319149, 0. , 0.30319149],\n [0.30851064, 0. , 0.30851064],\n [0.31382979, 0. , 0.31382979],\n [0.31914894, 0. , 0.31914894],\n [0.32446809, 0. , 0.32446809],\n [0.32978723, 0. , 0.32978723],\n [0.33510638, 0. , 0.33510638],\n [0.34042553, 0. , 0.34042553],\n [0.34574468, 0. , 0.34574468],\n [0.35106383, 0. , 0.35106383],\n [0.35638298, 0. , 0.35638298],\n [0.36170213, 0. , 0.36170213],\n [0.36702128, 0. , 0.36702128],\n [0.37234043, 0. , 0.37234043],\n [0.37765957, 0. , 0.37765957],\n [0.38297872, 0. , 0.38297872],\n [0.38829787, 0. , 0.38829787],\n [0.39361702, 0. , 0.39361702],\n [0.39893617, 0. , 0.39893617],\n [0.40425532, 0. , 0.40425532],\n [0.40957447, 0. , 0.40957447],\n [0.41489362, 0. , 0.41489362],\n [0.42021277, 0. , 0.42021277],\n [0.42553191, 0. , 0.42553191],\n [0.43085106, 0. , 0.43085106],\n [0.43617021, 0. , 0.43617021],\n [0.44148936, 0. , 0.44148936],\n [0.44680851, 0. , 0.44680851],\n [0.45212766, 0. , 0.45212766],\n [0.45744681, 0. , 0.45744681],\n [0.46276596, 0. , 0.46276596],\n [0.46808511, 0. , 0.46808511],\n [0.47340426, 0. , 0.47340426],\n [0.4787234 , 0. , 0.4787234 ],\n [0.48404255, 0. , 0.48404255],\n [0.4893617 , 0. , 0.4893617 ],\n [0.49468085, 0. , 0.49468085],\n [0.5 , 0. , 0.5 ]]),\n array([[0.5 , 0. , 0.5 ],\n [0.50378788, 0.00757576, 0.50378788],\n [0.50757576, 0.01515152, 0.50757576],\n [0.51136364, 0.02272727, 0.51136364],\n [0.51515152, 0.03030303, 0.51515152],\n [0.51893939, 0.03787879, 0.51893939],\n [0.52272727, 0.04545455, 0.52272727],\n [0.52651515, 0.0530303 , 0.52651515],\n [0.53030303, 0.06060606, 0.53030303],\n [0.53409091, 0.06818182, 0.53409091],\n [0.53787879, 0.07575758, 0.53787879],\n [0.54166667, 0.08333333, 0.54166667],\n [0.54545455, 0.09090909, 0.54545455],\n [0.54924242, 0.09848485, 0.54924242],\n [0.5530303 , 0.10606061, 0.5530303 ],\n [0.55681818, 0.11363636, 0.55681818],\n [0.56060606, 0.12121212, 0.56060606],\n [0.56439394, 0.12878788, 0.56439394],\n [0.56818182, 0.13636364, 0.56818182],\n [0.5719697 , 0.14393939, 0.5719697 ],\n [0.57575758, 0.15151515, 0.57575758],\n [0.57954545, 0.15909091, 0.57954545],\n [0.58333333, 0.16666667, 0.58333333],\n [0.58712121, 0.17424242, 0.58712121],\n [0.59090909, 0.18181818, 0.59090909],\n [0.59469697, 0.18939394, 0.59469697],\n [0.59848485, 0.1969697 , 0.59848485],\n [0.60227273, 0.20454545, 0.60227273],\n [0.60606061, 0.21212121, 0.60606061],\n [0.60984848, 0.21969697, 0.60984848],\n [0.61363636, 0.22727273, 0.61363636],\n [0.61742424, 0.23484848, 0.61742424],\n [0.62121212, 0.24242424, 0.62121212],\n [0.625 , 0.25 , 0.625 ]]),\n array([[0.375 , 0.375 , 0.75 ],\n [0.37125, 0.37125, 0.7425 ],\n [0.3675 , 0.3675 , 0.735 ],\n [0.36375, 0.36375, 0.7275 ],\n [0.36 , 0.36 , 0.72 ],\n [0.35625, 0.35625, 0.7125 ],\n [0.3525 , 0.3525 , 0.705 ],\n [0.34875, 0.34875, 0.6975 ],\n [0.345 , 0.345 , 0.69 ],\n [0.34125, 0.34125, 0.6825 ],\n [0.3375 , 0.3375 , 0.675 ],\n [0.33375, 0.33375, 0.6675 ],\n [0.33 , 0.33 , 0.66 ],\n [0.32625, 0.32625, 0.6525 ],\n [0.3225 , 0.3225 , 0.645 ],\n [0.31875, 0.31875, 0.6375 ],\n [0.315 , 0.315 , 0.63 ],\n [0.31125, 0.31125, 0.6225 ],\n [0.3075 , 0.3075 , 0.615 ],\n [0.30375, 0.30375, 0.6075 ],\n [0.3 , 0.3 , 0.6 ],\n [0.29625, 0.29625, 0.5925 ],\n [0.2925 , 0.2925 , 0.585 ],\n [0.28875, 0.28875, 0.5775 ],\n [0.285 , 0.285 , 0.57 ],\n [0.28125, 0.28125, 0.5625 ],\n [0.2775 , 0.2775 , 0.555 ],\n [0.27375, 0.27375, 0.5475 ],\n [0.27 , 0.27 , 0.54 ],\n [0.26625, 0.26625, 0.5325 ],\n [0.2625 , 0.2625 , 0.525 ],\n [0.25875, 0.25875, 0.5175 ],\n [0.255 , 0.255 , 0.51 ],\n [0.25125, 0.25125, 0.5025 ],\n [0.2475 , 0.2475 , 0.495 ],\n [0.24375, 0.24375, 0.4875 ],\n [0.24 , 0.24 , 0.48 ],\n [0.23625, 0.23625, 0.4725 ],\n [0.2325 , 0.2325 , 0.465 ],\n [0.22875, 0.22875, 0.4575 ],\n [0.225 , 0.225 , 0.45 ],\n [0.22125, 0.22125, 0.4425 ],\n [0.2175 , 0.2175 , 0.435 ],\n [0.21375, 0.21375, 0.4275 ],\n [0.21 , 0.21 , 0.42 ],\n [0.20625, 0.20625, 0.4125 ],\n [0.2025 , 0.2025 , 0.405 ],\n [0.19875, 0.19875, 0.3975 ],\n [0.195 , 0.195 , 0.39 ],\n [0.19125, 0.19125, 0.3825 ],\n [0.1875 , 0.1875 , 0.375 ],\n [0.18375, 0.18375, 0.3675 ],\n [0.18 , 0.18 , 0.36 ],\n [0.17625, 0.17625, 0.3525 ],\n [0.1725 , 0.1725 , 0.345 ],\n [0.16875, 0.16875, 0.3375 ],\n [0.165 , 0.165 , 0.33 ],\n [0.16125, 0.16125, 0.3225 ],\n [0.1575 , 0.1575 , 0.315 ],\n [0.15375, 0.15375, 0.3075 ],\n [0.15 , 0.15 , 0.3 ],\n [0.14625, 0.14625, 0.2925 ],\n [0.1425 , 0.1425 , 0.285 ],\n [0.13875, 0.13875, 0.2775 ],\n [0.135 , 0.135 , 0.27 ],\n [0.13125, 0.13125, 0.2625 ],\n [0.1275 , 0.1275 , 0.255 ],\n [0.12375, 0.12375, 0.2475 ],\n [0.12 , 0.12 , 0.24 ],\n [0.11625, 0.11625, 0.2325 ],\n [0.1125 , 0.1125 , 0.225 ],\n [0.10875, 0.10875, 0.2175 ],\n [0.105 , 0.105 , 0.21 ],\n [0.10125, 0.10125, 0.2025 ],\n [0.0975 , 0.0975 , 0.195 ],\n [0.09375, 0.09375, 0.1875 ],\n [0.09 , 0.09 , 0.18 ],\n [0.08625, 0.08625, 0.1725 ],\n [0.0825 , 0.0825 , 0.165 ],\n [0.07875, 0.07875, 0.1575 ],\n [0.075 , 0.075 , 0.15 ],\n [0.07125, 0.07125, 0.1425 ],\n [0.0675 , 0.0675 , 0.135 ],\n [0.06375, 0.06375, 0.1275 ],\n [0.06 , 0.06 , 0.12 ],\n [0.05625, 0.05625, 0.1125 ],\n [0.0525 , 0.0525 , 0.105 ],\n [0.04875, 0.04875, 0.0975 ],\n [0.045 , 0.045 , 0.09 ],\n [0.04125, 0.04125, 0.0825 ],\n [0.0375 , 0.0375 , 0.075 ],\n [0.03375, 0.03375, 0.0675 ],\n [0.03 , 0.03 , 0.06 ],\n [0.02625, 0.02625, 0.0525 ],\n [0.0225 , 0.0225 , 0.045 ],\n [0.01875, 0.01875, 0.0375 ],\n [0.015 , 0.015 , 0.03 ],\n [0.01125, 0.01125, 0.0225 ],\n [0.0075 , 0.0075 , 0.015 ],\n [0.00375, 0.00375, 0.0075 ],\n [0. , 0. , 0. ]]),\n array([[0. , 0. , 0. ],\n [0.00617284, 0.00617284, 0.00617284],\n [0.01234568, 0.01234568, 0.01234568],\n [0.01851852, 0.01851852, 0.01851852],\n [0.02469136, 0.02469136, 0.02469136],\n [0.0308642 , 0.0308642 , 0.0308642 ],\n [0.03703704, 0.03703704, 0.03703704],\n [0.04320988, 0.04320988, 0.04320988],\n [0.04938272, 0.04938272, 0.04938272],\n [0.05555556, 0.05555556, 0.05555556],\n [0.0617284 , 0.0617284 , 0.0617284 ],\n [0.06790123, 0.06790123, 0.06790123],\n [0.07407407, 0.07407407, 0.07407407],\n [0.08024691, 0.08024691, 0.08024691],\n [0.08641975, 0.08641975, 0.08641975],\n [0.09259259, 0.09259259, 0.09259259],\n [0.09876543, 0.09876543, 0.09876543],\n [0.10493827, 0.10493827, 0.10493827],\n [0.11111111, 0.11111111, 0.11111111],\n [0.11728395, 0.11728395, 0.11728395],\n [0.12345679, 0.12345679, 0.12345679],\n [0.12962963, 0.12962963, 0.12962963],\n [0.13580247, 0.13580247, 0.13580247],\n [0.14197531, 0.14197531, 0.14197531],\n [0.14814815, 0.14814815, 0.14814815],\n [0.15432099, 0.15432099, 0.15432099],\n [0.16049383, 0.16049383, 0.16049383],\n [0.16666667, 0.16666667, 0.16666667],\n [0.17283951, 0.17283951, 0.17283951],\n [0.17901235, 0.17901235, 0.17901235],\n [0.18518519, 0.18518519, 0.18518519],\n [0.19135802, 0.19135802, 0.19135802],\n [0.19753086, 0.19753086, 0.19753086],\n [0.2037037 , 0.2037037 , 0.2037037 ],\n [0.20987654, 0.20987654, 0.20987654],\n [0.21604938, 0.21604938, 0.21604938],\n [0.22222222, 0.22222222, 0.22222222],\n [0.22839506, 0.22839506, 0.22839506],\n [0.2345679 , 0.2345679 , 0.2345679 ],\n [0.24074074, 0.24074074, 0.24074074],\n [0.24691358, 0.24691358, 0.24691358],\n [0.25308642, 0.25308642, 0.25308642],\n [0.25925926, 0.25925926, 0.25925926],\n [0.2654321 , 0.2654321 , 0.2654321 ],\n [0.27160494, 0.27160494, 0.27160494],\n [0.27777778, 0.27777778, 0.27777778],\n [0.28395062, 0.28395062, 0.28395062],\n [0.29012346, 0.29012346, 0.29012346],\n [0.2962963 , 0.2962963 , 0.2962963 ],\n [0.30246914, 0.30246914, 0.30246914],\n [0.30864198, 0.30864198, 0.30864198],\n [0.31481481, 0.31481481, 0.31481481],\n [0.32098765, 0.32098765, 0.32098765],\n [0.32716049, 0.32716049, 0.32716049],\n [0.33333333, 0.33333333, 0.33333333],\n [0.33950617, 0.33950617, 0.33950617],\n [0.34567901, 0.34567901, 0.34567901],\n [0.35185185, 0.35185185, 0.35185185],\n [0.35802469, 0.35802469, 0.35802469],\n [0.36419753, 0.36419753, 0.36419753],\n [0.37037037, 0.37037037, 0.37037037],\n [0.37654321, 0.37654321, 0.37654321],\n [0.38271605, 0.38271605, 0.38271605],\n [0.38888889, 0.38888889, 0.38888889],\n [0.39506173, 0.39506173, 0.39506173],\n [0.40123457, 0.40123457, 0.40123457],\n [0.40740741, 0.40740741, 0.40740741],\n [0.41358025, 0.41358025, 0.41358025],\n [0.41975309, 0.41975309, 0.41975309],\n [0.42592593, 0.42592593, 0.42592593],\n [0.43209877, 0.43209877, 0.43209877],\n [0.4382716 , 0.4382716 , 0.4382716 ],\n [0.44444444, 0.44444444, 0.44444444],\n [0.45061728, 0.45061728, 0.45061728],\n [0.45679012, 0.45679012, 0.45679012],\n [0.46296296, 0.46296296, 0.46296296],\n [0.4691358 , 0.4691358 , 0.4691358 ],\n [0.47530864, 0.47530864, 0.47530864],\n [0.48148148, 0.48148148, 0.48148148],\n [0.48765432, 0.48765432, 0.48765432],\n [0.49382716, 0.49382716, 0.49382716],\n [0.5 , 0.5 , 0.5 ]]),\n array([[0.5 , 0.5 , 0.5 ],\n [0.5 , 0.49621212, 0.50378788],\n [0.5 , 0.49242424, 0.50757576],\n [0.5 , 0.48863636, 0.51136364],\n [0.5 , 0.48484848, 0.51515152],\n [0.5 , 0.48106061, 0.51893939],\n [0.5 , 0.47727273, 0.52272727],\n [0.5 , 0.47348485, 0.52651515],\n [0.5 , 0.46969697, 0.53030303],\n [0.5 , 0.46590909, 0.53409091],\n [0.5 , 0.46212121, 0.53787879],\n [0.5 , 0.45833333, 0.54166667],\n [0.5 , 0.45454545, 0.54545455],\n [0.5 , 0.45075758, 0.54924242],\n [0.5 , 0.4469697 , 0.5530303 ],\n [0.5 , 0.44318182, 0.55681818],\n [0.5 , 0.43939394, 0.56060606],\n [0.5 , 0.43560606, 0.56439394],\n [0.5 , 0.43181818, 0.56818182],\n [0.5 , 0.4280303 , 0.5719697 ],\n [0.5 , 0.42424242, 0.57575758],\n [0.5 , 0.42045455, 0.57954545],\n [0.5 , 0.41666667, 0.58333333],\n [0.5 , 0.41287879, 0.58712121],\n [0.5 , 0.40909091, 0.59090909],\n [0.5 , 0.40530303, 0.59469697],\n [0.5 , 0.40151515, 0.59848485],\n [0.5 , 0.39772727, 0.60227273],\n [0.5 , 0.39393939, 0.60606061],\n [0.5 , 0.39015152, 0.60984848],\n [0.5 , 0.38636364, 0.61363636],\n [0.5 , 0.38257576, 0.61742424],\n [0.5 , 0.37878788, 0.62121212],\n [0.5 , 0.375 , 0.625 ],\n [0.5 , 0.37121212, 0.62878788],\n [0.5 , 0.36742424, 0.63257576],\n [0.5 , 0.36363636, 0.63636364],\n [0.5 , 0.35984848, 0.64015152],\n [0.5 , 0.35606061, 0.64393939],\n [0.5 , 0.35227273, 0.64772727],\n [0.5 , 0.34848485, 0.65151515],\n [0.5 , 0.34469697, 0.65530303],\n [0.5 , 0.34090909, 0.65909091],\n [0.5 , 0.33712121, 0.66287879],\n [0.5 , 0.33333333, 0.66666667],\n [0.5 , 0.32954545, 0.67045455],\n [0.5 , 0.32575758, 0.67424242],\n [0.5 , 0.3219697 , 0.6780303 ],\n [0.5 , 0.31818182, 0.68181818],\n [0.5 , 0.31439394, 0.68560606],\n [0.5 , 0.31060606, 0.68939394],\n [0.5 , 0.30681818, 0.69318182],\n [0.5 , 0.3030303 , 0.6969697 ],\n [0.5 , 0.29924242, 0.70075758],\n [0.5 , 0.29545455, 0.70454545],\n [0.5 , 0.29166667, 0.70833333],\n [0.5 , 0.28787879, 0.71212121],\n [0.5 , 0.28409091, 0.71590909],\n [0.5 , 0.28030303, 0.71969697],\n [0.5 , 0.27651515, 0.72348485],\n [0.5 , 0.27272727, 0.72727273],\n [0.5 , 0.26893939, 0.73106061],\n [0.5 , 0.26515152, 0.73484848],\n [0.5 , 0.26136364, 0.73863636],\n [0.5 , 0.25757576, 0.74242424],\n [0.5 , 0.25378788, 0.74621212],\n [0.5 , 0.25 , 0.75 ]]),\n array([[0.5 , 0.25 , 0.75 ],\n [0.5 , 0.24468085, 0.74468085],\n [0.5 , 0.2393617 , 0.7393617 ],\n [0.5 , 0.23404255, 0.73404255],\n [0.5 , 0.2287234 , 0.7287234 ],\n [0.5 , 0.22340426, 0.72340426],\n [0.5 , 0.21808511, 0.71808511],\n [0.5 , 0.21276596, 0.71276596],\n [0.5 , 0.20744681, 0.70744681],\n [0.5 , 0.20212766, 0.70212766],\n [0.5 , 0.19680851, 0.69680851],\n [0.5 , 0.19148936, 0.69148936],\n [0.5 , 0.18617021, 0.68617021],\n [0.5 , 0.18085106, 0.68085106],\n [0.5 , 0.17553191, 0.67553191],\n [0.5 , 0.17021277, 0.67021277],\n [0.5 , 0.16489362, 0.66489362],\n [0.5 , 0.15957447, 0.65957447],\n [0.5 , 0.15425532, 0.65425532],\n [0.5 , 0.14893617, 0.64893617],\n [0.5 , 0.14361702, 0.64361702],\n [0.5 , 0.13829787, 0.63829787],\n [0.5 , 0.13297872, 0.63297872],\n [0.5 , 0.12765957, 0.62765957],\n [0.5 , 0.12234043, 0.62234043],\n [0.5 , 0.11702128, 0.61702128],\n [0.5 , 0.11170213, 0.61170213],\n [0.5 , 0.10638298, 0.60638298],\n [0.5 , 0.10106383, 0.60106383],\n [0.5 , 0.09574468, 0.59574468],\n [0.5 , 0.09042553, 0.59042553],\n [0.5 , 0.08510638, 0.58510638],\n [0.5 , 0.07978723, 0.57978723],\n [0.5 , 0.07446809, 0.57446809],\n [0.5 , 0.06914894, 0.56914894],\n [0.5 , 0.06382979, 0.56382979],\n [0.5 , 0.05851064, 0.55851064],\n [0.5 , 0.05319149, 0.55319149],\n [0.5 , 0.04787234, 0.54787234],\n [0.5 , 0.04255319, 0.54255319],\n [0.5 , 0.03723404, 0.53723404],\n [0.5 , 0.03191489, 0.53191489],\n [0.5 , 0.02659574, 0.52659574],\n [0.5 , 0.0212766 , 0.5212766 ],\n [0.5 , 0.01595745, 0.51595745],\n [0.5 , 0.0106383 , 0.5106383 ],\n [0.5 , 0.00531915, 0.50531915],\n [0.5 , 0. , 0.5 ]])],\n 'distances': [array([0. , 0.00195846, 0.00391691, 0.00587537, 0.00783383,\n 0.00979229, 0.01175074, 0.0137092 , 0.01566766, 0.01762611,\n 0.01958457, 0.02154303, 0.02350149, 0.02545994, 0.0274184 ,\n 0.02937686, 0.03133531, 0.03329377, 0.03525223, 0.03721068,\n 0.03916914, 0.0411276 , 0.04308606, 0.04504451, 0.04700297,\n 0.04896143, 0.05091988, 0.05287834, 0.0548368 , 0.05679526,\n 0.05875371, 0.06071217, 0.06267063, 0.06462908, 0.06658754,\n 0.068546 , 0.07050446, 0.07246291, 0.07442137, 0.07637983,\n 0.07833828, 0.08029674, 0.0822552 , 0.08421366, 0.08617211,\n 0.08813057, 0.09008903, 0.09204748, 0.09400594, 0.0959644 ,\n 0.09792285, 0.09988131, 0.10183977, 0.10379823, 0.10575668,\n 0.10771514, 0.1096736 , 0.11163205, 0.11359051, 0.11554897,\n 0.11750743, 0.11946588, 0.12142434, 0.1233828 , 0.12534125,\n 0.12729971, 0.12925817, 0.13121663, 0.13317508, 0.13513354,\n 0.137092 , 0.13905045, 0.14100891, 0.14296737, 0.14492583,\n 0.14688428, 0.14884274, 0.1508012 , 0.15275965, 0.15471811,\n 0.15667657, 0.15863503, 0.16059348, 0.16255194, 0.1645104 ,\n 0.16646885, 0.16842731, 0.17038577, 0.17234422, 0.17430268,\n 0.17626114, 0.1782196 , 0.18017805, 0.18213651, 0.18409497]),\n array([0.18409497, 0.18606731, 0.18803966, 0.190012 , 0.19198435,\n 0.19395669, 0.19592904, 0.19790139, 0.19987373, 0.20184608,\n 0.20381842, 0.20579077, 0.20776311, 0.20973546, 0.2117078 ,\n 0.21368015, 0.21565249, 0.21762484, 0.21959719, 0.22156953,\n 0.22354188, 0.22551422, 0.22748657, 0.22945891, 0.23143126,\n 0.2334036 , 0.23537595, 0.23734829, 0.23932064, 0.24129299,\n 0.24326533, 0.24523768, 0.24721002, 0.24918237]),\n array([0.24918237, 0.25113499, 0.25308761, 0.25504023, 0.25699286,\n 0.25894548, 0.2608981 , 0.26285072, 0.26480334, 0.26675597,\n 0.26870859, 0.27066121, 0.27261383, 0.27456645, 0.27651908,\n 0.2784717 , 0.28042432, 0.28237694, 0.28432956, 0.28628219,\n 0.28823481, 0.29018743, 0.29214005, 0.29409267, 0.2960453 ,\n 0.29799792, 0.29995054, 0.30190316, 0.30385578, 0.30580841,\n 0.30776103, 0.30971365, 0.31166627, 0.31361889, 0.31557152,\n 0.31752414, 0.31947676, 0.32142938, 0.323382 , 0.32533463,\n 0.32728725, 0.32923987, 0.33119249, 0.33314511, 0.33509774,\n 0.33705036, 0.33900298, 0.3409556 , 0.34290822, 0.34486085,\n 0.34681347, 0.34876609, 0.35071871, 0.35267133, 0.35462396,\n 0.35657658, 0.3585292 , 0.36048182, 0.36243444, 0.36438707,\n 0.36633969, 0.36829231, 0.37024493, 0.37219755, 0.37415018,\n 0.3761028 , 0.37805542, 0.38000804, 0.38196066, 0.38391329,\n 0.38586591, 0.38781853, 0.38977115, 0.39172377, 0.3936764 ,\n 0.39562902, 0.39758164, 0.39953426, 0.40148688, 0.40343951,\n 0.40539213, 0.40734475, 0.40929737, 0.41124999, 0.41320262,\n 0.41515524, 0.41710786, 0.41906048, 0.4210131 , 0.42296573,\n 0.42491835, 0.42687097, 0.42882359, 0.43077621, 0.43272884,\n 0.43468146, 0.43663408, 0.4385867 , 0.44053932, 0.44249194,\n 0.44444457]),\n array([0.44444457, 0.44641285, 0.44838113, 0.45034942, 0.4523177 ,\n 0.45428598, 0.45625426, 0.45822255, 0.46019083, 0.46215911,\n 0.4641274 , 0.46609568, 0.46806396, 0.47003225, 0.47200053,\n 0.47396881, 0.47593709, 0.47790538, 0.47987366, 0.48184194,\n 0.48381023, 0.48577851, 0.48774679, 0.48971507, 0.49168336,\n 0.49365164, 0.49561992, 0.49758821, 0.49955649, 0.50152477,\n 0.50349306, 0.50546134, 0.50742962, 0.5093979 , 0.51136619,\n 0.51333447, 0.51530275, 0.51727104, 0.51923932, 0.5212076 ,\n 0.52317588, 0.52514417, 0.52711245, 0.52908073, 0.53104902,\n 0.5330173 , 0.53498558, 0.53695387, 0.53892215, 0.54089043,\n 0.54285871, 0.544827 , 0.54679528, 0.54876356, 0.55073185,\n 0.55270013, 0.55466841, 0.55663669, 0.55860498, 0.56057326,\n 0.56254154, 0.56450983, 0.56647811, 0.56844639, 0.57041468,\n 0.57238296, 0.57435124, 0.57631952, 0.57828781, 0.58025609,\n 0.58222437, 0.58419266, 0.58616094, 0.58812922, 0.5900975 ,\n 0.59206579, 0.59403407, 0.59600235, 0.59797064, 0.59993892,\n 0.6019072 , 0.60387549]),\n array([0.60387549, 0.60584783, 0.60782018, 0.60979252, 0.61176487,\n 0.61373721, 0.61570956, 0.6176819 , 0.61965425, 0.62162659,\n 0.62359894, 0.62557129, 0.62754363, 0.62951598, 0.63148832,\n 0.63346067, 0.63543301, 0.63740536, 0.6393777 , 0.64135005,\n 0.64332239, 0.64529474, 0.64726709, 0.64923943, 0.65121178,\n 0.65318412, 0.65515647, 0.65712881, 0.65910116, 0.6610735 ,\n 0.66304585, 0.66501819, 0.66699054, 0.66896289, 0.67093523,\n 0.67290758, 0.67487992, 0.67685227, 0.67882461, 0.68079696,\n 0.6827693 , 0.68474165, 0.68671399, 0.68868634, 0.69065869,\n 0.69263103, 0.69460338, 0.69657572, 0.69854807, 0.70052041,\n 0.70249276, 0.7044651 , 0.70643745, 0.70840979, 0.71038214,\n 0.71235449, 0.71432683, 0.71629918, 0.71827152, 0.72024387,\n 0.72221621, 0.72418856, 0.7261609 , 0.72813325, 0.73010559,\n 0.73207794, 0.73405029]),\n array([0.73405029, 0.73600874, 0.7379672 , 0.73992566, 0.74188411,\n 0.74384257, 0.74580103, 0.74775948, 0.74971794, 0.7516764 ,\n 0.75363486, 0.75559331, 0.75755177, 0.75951023, 0.76146868,\n 0.76342714, 0.7653856 , 0.76734406, 0.76930251, 0.77126097,\n 0.77321943, 0.77517788, 0.77713634, 0.7790948 , 0.78105326,\n 0.78301171, 0.78497017, 0.78692863, 0.78888708, 0.79084554,\n 0.792804 , 0.79476246, 0.79672091, 0.79867937, 0.80063783,\n 0.80259628, 0.80455474, 0.8065132 , 0.80847166, 0.81043011,\n 0.81238857, 0.81434703, 0.81630548, 0.81826394, 0.8202224 ,\n 0.82218085, 0.82413931, 0.82609777])],\n 'frequencies': [array([[2.18701057e-06, 2.19691522e-06, 2.20369934e-06, 1.60678991e+01,\n 1.60678991e+01, 1.60678991e+01],\n [1.06625590e-01, 1.06625590e-01, 1.53239098e-01, 1.60675081e+01,\n 1.60676418e+01, 1.60676418e+01],\n [2.13231909e-01, 2.13231909e-01, 3.06460038e-01, 1.60663351e+01,\n 1.60668701e+01, 1.60668701e+01],\n [3.19799678e-01, 3.19799678e-01, 4.59644667e-01, 1.60643797e+01,\n 1.60655844e+01, 1.60655844e+01],\n [4.26309607e-01, 4.26309607e-01, 6.12774843e-01, 1.60616416e+01,\n 1.60637853e+01, 1.60637853e+01],\n [5.32742383e-01, 5.32742383e-01, 7.65832440e-01, 1.60581201e+01,\n 1.60614737e+01, 1.60614737e+01],\n [6.39078667e-01, 6.39078667e-01, 9.18799354e-01, 1.60538144e+01,\n 1.60586506e+01, 1.60586506e+01],\n [7.45299086e-01, 7.45299086e-01, 1.07165751e+00, 1.60487235e+01,\n 1.60553175e+01, 1.60553175e+01],\n [8.51384225e-01, 8.51384225e-01, 1.22438885e+00, 1.60428463e+01,\n 1.60514759e+01, 1.60514759e+01],\n [9.57314622e-01, 9.57314622e-01, 1.37697538e+00, 1.60361814e+01,\n 1.60471277e+01, 1.60471277e+01],\n [1.06307076e+00, 1.06307076e+00, 1.52939913e+00, 1.60287272e+01,\n 1.60422751e+01, 1.60422751e+01],\n [1.16863306e+00, 1.16863306e+00, 1.68164218e+00, 1.60204822e+01,\n 1.60369205e+01, 1.60369205e+01],\n [1.27398186e+00, 1.27398186e+00, 1.83368666e+00, 1.60114444e+01,\n 1.60310665e+01, 1.60310665e+01],\n [1.37909745e+00, 1.37909745e+00, 1.98551477e+00, 1.60016119e+01,\n 1.60247161e+01, 1.60247161e+01],\n [1.48396001e+00, 1.48396001e+00, 2.13710877e+00, 1.59909824e+01,\n 1.60178724e+01, 1.60178724e+01],\n [1.58854964e+00, 1.58854964e+00, 2.28845098e+00, 1.59795536e+01,\n 1.60105390e+01, 1.60105390e+01],\n [1.69284632e+00, 1.69284632e+00, 2.43952381e+00, 1.59673229e+01,\n 1.60027197e+01, 1.60027197e+01],\n [1.79682995e+00, 1.79682995e+00, 2.59030972e+00, 1.59542878e+01,\n 1.59944185e+01, 1.59944185e+01],\n [1.90048030e+00, 1.90048030e+00, 2.74079128e+00, 1.59404453e+01,\n 1.59856398e+01, 1.59856398e+01],\n [2.00377700e+00, 2.00377700e+00, 2.89095116e+00, 1.59257926e+01,\n 1.59763882e+01, 1.59763882e+01],\n [2.10669956e+00, 2.10669956e+00, 3.04077208e+00, 1.59103264e+01,\n 1.59666687e+01, 1.59666687e+01],\n [2.20922736e+00, 2.20922736e+00, 3.19023691e+00, 1.58940435e+01,\n 1.59564867e+01, 1.59564867e+01],\n [2.31133960e+00, 2.31133960e+00, 3.33932858e+00, 1.58769405e+01,\n 1.59458477e+01, 1.59458477e+01],\n [2.41301534e+00, 2.41301534e+00, 3.48803016e+00, 1.58590139e+01,\n 1.59347578e+01, 1.59347578e+01],\n [2.51423346e+00, 2.51423346e+00, 3.63632482e+00, 1.58402599e+01,\n 1.59232232e+01, 1.59232232e+01],\n [2.61497266e+00, 2.61497266e+00, 3.78419585e+00, 1.58206748e+01,\n 1.59112506e+01, 1.59112506e+01],\n [2.71521144e+00, 2.71521144e+00, 3.93162667e+00, 1.58002545e+01,\n 1.58988470e+01, 1.58988470e+01],\n [2.81492813e+00, 2.81492813e+00, 4.07860083e+00, 1.57789952e+01,\n 1.58860198e+01, 1.58860198e+01],\n [2.91410081e+00, 2.91410081e+00, 4.22510199e+00, 1.57568925e+01,\n 1.58727768e+01, 1.58727768e+01],\n [3.01270737e+00, 3.01270737e+00, 4.37111398e+00, 1.57339422e+01,\n 1.58591262e+01, 1.58591262e+01],\n [3.11072544e+00, 3.11072544e+00, 4.51662075e+00, 1.57101400e+01,\n 1.58450764e+01, 1.58450764e+01],\n [3.20813243e+00, 3.20813243e+00, 4.66160641e+00, 1.56854812e+01,\n 1.58306367e+01, 1.58306367e+01],\n [3.30490548e+00, 3.30490548e+00, 4.80605520e+00, 1.56599614e+01,\n 1.58158162e+01, 1.58158162e+01],\n [3.40102147e+00, 3.40102147e+00, 4.94995155e+00, 1.56335759e+01,\n 1.58006249e+01, 1.58006249e+01],\n [3.49645700e+00, 3.49645700e+00, 5.09328001e+00, 1.56063199e+01,\n 1.57850732e+01, 1.57850732e+01],\n [3.59118839e+00, 3.59118839e+00, 5.23602533e+00, 1.55781885e+01,\n 1.57691716e+01, 1.57691716e+01],\n [3.68519163e+00, 3.68519163e+00, 5.37817241e+00, 1.55491768e+01,\n 1.57529316e+01, 1.57529316e+01],\n [3.77844244e+00, 3.77844244e+00, 5.51970631e+00, 1.55192800e+01,\n 1.57363649e+01, 1.57363649e+01],\n [3.87091618e+00, 3.87091618e+00, 5.66061230e+00, 1.54884928e+01,\n 1.57194835e+01, 1.57194835e+01],\n [3.96258789e+00, 3.96258789e+00, 5.80087581e+00, 1.54568102e+01,\n 1.57023004e+01, 1.57023004e+01],\n [4.05343226e+00, 4.05343226e+00, 5.94048245e+00, 1.54242271e+01,\n 1.56848288e+01, 1.56848288e+01],\n [4.14342363e+00, 4.14342363e+00, 6.07941802e+00, 1.53907382e+01,\n 1.56670824e+01, 1.56670824e+01],\n [4.23253595e+00, 4.23253595e+00, 6.21766853e+00, 1.53563383e+01,\n 1.56490757e+01, 1.56490757e+01],\n [4.32074280e+00, 4.32074280e+00, 6.35522016e+00, 1.53210221e+01,\n 1.56308235e+01, 1.56308235e+01],\n [4.40801738e+00, 4.40801738e+00, 6.49205931e+00, 1.52847843e+01,\n 1.56123413e+01, 1.56123413e+01],\n [4.49433246e+00, 4.49433246e+00, 6.62817257e+00, 1.52476196e+01,\n 1.55936453e+01, 1.55936453e+01],\n [4.57966044e+00, 4.57966044e+00, 6.76354674e+00, 1.52095227e+01,\n 1.55747520e+01, 1.55747520e+01],\n [4.66397327e+00, 4.66397327e+00, 6.89816884e+00, 1.51704881e+01,\n 1.55556788e+01, 1.55556788e+01],\n [4.74724248e+00, 4.74724248e+00, 7.03202608e+00, 1.51305106e+01,\n 1.55364436e+01, 1.55364436e+01],\n [4.82943918e+00, 4.82943918e+00, 7.16510590e+00, 1.50895847e+01,\n 1.55170649e+01, 1.55170649e+01],\n [4.91053403e+00, 4.91053403e+00, 7.29739597e+00, 1.50477052e+01,\n 1.54975617e+01, 1.54975617e+01],\n [4.99049726e+00, 4.99049726e+00, 7.42888415e+00, 1.50048667e+01,\n 1.54779540e+01, 1.54779540e+01],\n [5.06929865e+00, 5.06929865e+00, 7.55955856e+00, 1.49610639e+01,\n 1.54582620e+01, 1.54582620e+01],\n [5.14690753e+00, 5.14690753e+00, 7.68940753e+00, 1.49162915e+01,\n 1.54385069e+01, 1.54385069e+01],\n [5.22329282e+00, 5.22329282e+00, 7.81841962e+00, 1.48705443e+01,\n 1.54187103e+01, 1.54187103e+01],\n [5.29842297e+00, 5.29842297e+00, 7.94658362e+00, 1.48238171e+01,\n 1.53988946e+01, 1.53988946e+01],\n [5.37226600e+00, 5.37226600e+00, 8.07388856e+00, 1.47761047e+01,\n 1.53790827e+01, 1.53790827e+01],\n [5.44478953e+00, 5.44478953e+00, 8.20032372e+00, 1.47274020e+01,\n 1.53592983e+01, 1.53592983e+01],\n [5.51596076e+00, 5.51596076e+00, 8.32587860e+00, 1.46777039e+01,\n 1.53395654e+01, 1.53395654e+01],\n [5.58574651e+00, 5.58574651e+00, 8.45054294e+00, 1.46270056e+01,\n 1.53199089e+01, 1.53199089e+01],\n [5.65411319e+00, 5.65411319e+00, 8.57430676e+00, 1.45753020e+01,\n 1.53003542e+01, 1.53003542e+01],\n [5.72102691e+00, 5.72102691e+00, 8.69716027e+00, 1.45225884e+01,\n 1.52809272e+01, 1.52809272e+01],\n [5.78645342e+00, 5.78645342e+00, 8.81909398e+00, 1.44688599e+01,\n 1.52616544e+01, 1.52616544e+01],\n [5.85035821e+00, 5.85035821e+00, 8.94009862e+00, 1.44141121e+01,\n 1.52425628e+01, 1.52425628e+01],\n [5.91270648e+00, 5.91270648e+00, 9.06016518e+00, 1.43583401e+01,\n 1.52236797e+01, 1.52236797e+01],\n [5.97346325e+00, 5.97346325e+00, 9.17928491e+00, 1.43015397e+01,\n 1.52050331e+01, 1.52050331e+01],\n [6.03259336e+00, 6.03259336e+00, 9.29744928e+00, 1.42437065e+01,\n 1.51866511e+01, 1.51866511e+01],\n [6.09006155e+00, 6.09006155e+00, 9.41465007e+00, 1.41848361e+01,\n 1.51685625e+01, 1.51685625e+01],\n [6.14583250e+00, 6.14583250e+00, 9.53087927e+00, 1.41249246e+01,\n 1.51507959e+01, 1.51507959e+01],\n [6.19987090e+00, 6.19987090e+00, 9.64612916e+00, 1.40639678e+01,\n 1.51333805e+01, 1.51333805e+01],\n [6.25214152e+00, 6.25214152e+00, 9.76039224e+00, 1.40019619e+01,\n 1.51163455e+01, 1.51163455e+01],\n [6.30260929e+00, 6.30260929e+00, 9.87366131e+00, 1.39389032e+01,\n 1.50997202e+01, 1.50997202e+01],\n [6.35123937e+00, 6.35123937e+00, 9.98592942e+00, 1.38747880e+01,\n 1.50835337e+01, 1.50835337e+01],\n [6.39799726e+00, 6.39799726e+00, 1.00971898e+01, 1.38096130e+01,\n 1.50678154e+01, 1.50678154e+01],\n [6.44284885e+00, 6.44284885e+00, 1.02074362e+01, 1.37433748e+01,\n 1.50525941e+01, 1.50525941e+01],\n [6.48576059e+00, 6.48576059e+00, 1.03166622e+01, 1.36760703e+01,\n 1.50378985e+01, 1.50378985e+01],\n [6.52669951e+00, 6.52669951e+00, 1.04248621e+01, 1.36076964e+01,\n 1.50237569e+01, 1.50237569e+01],\n [6.56563338e+00, 6.56563338e+00, 1.05320301e+01, 1.35382504e+01,\n 1.50101972e+01, 1.50101972e+01],\n [6.60253081e+00, 6.60253081e+00, 1.06381608e+01, 1.34677297e+01,\n 1.49972465e+01, 1.49972465e+01],\n [6.63736135e+00, 6.63736135e+00, 1.07432492e+01, 1.33961316e+01,\n 1.49849313e+01, 1.49849313e+01],\n [6.67009563e+00, 6.67009563e+00, 1.08472903e+01, 1.33234540e+01,\n 1.49732773e+01, 1.49732773e+01],\n [6.70070547e+00, 6.70070547e+00, 1.09502796e+01, 1.32496947e+01,\n 1.49623091e+01, 1.49623091e+01],\n [6.72916397e+00, 6.72916397e+00, 1.10522127e+01, 1.31748518e+01,\n 1.49520504e+01, 1.49520504e+01],\n [6.75544567e+00, 6.75544567e+00, 1.11530855e+01, 1.30989236e+01,\n 1.49425237e+01, 1.49425237e+01],\n [6.77952663e+00, 6.77952663e+00, 1.12528941e+01, 1.30219085e+01,\n 1.49337500e+01, 1.49337500e+01],\n [6.80138457e+00, 6.80138457e+00, 1.13516350e+01, 1.29438053e+01,\n 1.49257493e+01, 1.49257493e+01],\n [6.82099896e+00, 6.82099896e+00, 1.14493049e+01, 1.28646126e+01,\n 1.49185396e+01, 1.49185396e+01],\n [6.83835113e+00, 6.83835113e+00, 1.15459006e+01, 1.27843298e+01,\n 1.49121375e+01, 1.49121375e+01],\n [6.85342435e+00, 6.85342435e+00, 1.16414194e+01, 1.27029559e+01,\n 1.49065581e+01, 1.49065581e+01],\n [6.86620396e+00, 6.86620396e+00, 1.17358587e+01, 1.26204906e+01,\n 1.49018144e+01, 1.49018144e+01],\n [6.87667737e+00, 6.87667737e+00, 1.18292162e+01, 1.25369336e+01,\n 1.48979177e+01, 1.48979177e+01],\n [6.88483424e+00, 6.88483424e+00, 1.19214899e+01, 1.24522848e+01,\n 1.48948771e+01, 1.48948771e+01],\n [6.89066641e+00, 6.89066641e+00, 1.20126778e+01, 1.23665443e+01,\n 1.48927000e+01, 1.48927000e+01],\n [6.89416806e+00, 6.89416806e+00, 1.21027784e+01, 1.22797127e+01,\n 1.48913917e+01, 1.48913917e+01],\n [6.89533567e+00, 6.89533567e+00, 1.21917904e+01, 1.21917904e+01,\n 1.48909552e+01, 1.48909552e+01]]),\n array([[ 6.89533567, 6.89533567, 12.19179039, 12.19179039, 14.89095524,\n 14.89095524],\n [ 6.89476599, 6.89721307, 12.19035931, 12.19131253, 14.89109076,\n 14.89177681],\n [ 6.8930571 , 6.90283616, 12.18607431, 12.18988157, 14.8914973 ,\n 14.89423361],\n [ 6.89020956, 6.91217764, 12.17895978, 12.18750534, 14.89217481,\n 14.89830206],\n [ 6.88622426, 6.92519216, 12.16905574, 12.18419693, 14.89312318,\n 14.90394357],\n [ 6.88110243, 6.9418166 , 12.15641674, 12.17997485, 14.89434227,\n 14.91110552],\n [ 6.8748457 , 6.96197032, 12.1411106 , 12.17486306, 14.89583189,\n 14.9197226 ],\n [ 6.86745601, 6.98555564, 12.1232168 , 12.16889124, 14.89759181,\n 14.92971834],\n [ 6.85893568, 7.0124582 , 12.10282475, 12.16209492, 14.89962177,\n 14.94100685],\n [ 6.84928737, 7.04254753, 12.08003199, 12.15451577, 14.90192145,\n 14.9534946 ],\n [ 6.83851409, 7.07567754, 12.05494232, 12.14620185, 14.90449047,\n 14.96708225],\n [ 6.8266192 , 7.11168706, 12.02766403, 12.13720797, 14.90732842,\n 14.98166641],\n [ 6.81360641, 7.1504004 , 11.99830825, 12.12759601, 14.91043482,\n 14.99714124],\n [ 6.79947975, 7.19162786, 11.96698741, 12.11743535, 14.91380915,\n 15.01339997],\n [ 6.78424361, 7.23516623, 11.93381387, 12.10680327, 14.91745083,\n 15.03033626],\n [ 6.7679027 , 7.28079926, 11.89889873, 12.0957854 , 14.9213592 ,\n 15.04784527],\n [ 6.75046209, 7.32829805, 11.86235086, 12.08447621, 14.92553355,\n 15.06582469],\n [ 6.73192714, 7.3774215 , 11.82427602, 12.07297947, 14.92997311,\n 15.0841755 ],\n [ 6.71230356, 7.42791658, 11.78477623, 12.06140874, 14.93467703,\n 15.1028026 ],\n [ 6.69159738, 7.47951874, 11.74394921, 12.0498878 , 14.93964437,\n 15.12161529],\n [ 6.66981492, 7.53195215, 11.701888 , 12.03855107, 14.94487413,\n 15.14052765],\n [ 6.64696284, 7.58493013, 11.65868065, 12.02754391, 14.95036522,\n 15.15945873],\n [ 6.62304809, 7.6381555 , 11.61441001, 12.01702285, 14.95611647,\n 15.17833279],\n [ 6.59807794, 7.69132112, 11.5691536 , 12.0071556 , 14.96212661,\n 15.19707928],\n [ 6.57205993, 7.74411056, 11.52298356, 11.99812092, 14.96839427,\n 15.21563293],\n [ 6.5450019 , 7.79619897, 11.47596658, 11.99010811, 14.974918 ,\n 15.23393372],\n [ 6.51691198, 7.8472543 , 11.42816396, 11.98331627, 14.98169623,\n 15.25192677],\n [ 6.48779857, 7.89693879, 11.3796316 , 11.9779531 , 14.98872728,\n 15.26956229],\n [ 6.45767036, 7.94491097, 11.33042012, 11.97423316, 14.99600936,\n 15.28679543],\n [ 6.42653627, 7.99082805, 11.28057486, 11.97237575, 15.00354058,\n 15.30358621],\n [ 6.39440553, 8.03434895, 11.23013602, 11.97260212, 15.01131889,\n 15.31989932],\n [ 6.36128757, 8.07513774, 11.17913872, 11.97513212, 15.01934216,\n 15.33570402],\n [ 6.3271921 , 8.11286763, 11.12761311, 11.98018037, 15.02760809,\n 15.35097401],\n [ 6.29212906, 8.1472254 , 11.07558447, 11.98795191, 15.03611427,\n 15.36568722]]),\n array([[6.29212906e+00, 8.14722540e+00, 1.10755845e+01, 1.19879519e+01,\n 1.50361143e+01, 1.53656872e+01],\n [6.25647352e+00, 8.17762824e+00, 1.10236007e+01, 1.19985158e+01,\n 1.50447695e+01, 1.53796873e+01],\n [6.21988972e+00, 8.20417287e+00, 1.09711594e+01, 1.20121030e+01,\n 1.50536551e+01, 1.53931105e+01],\n [6.18238794e+00, 8.22662180e+00, 1.09182714e+01, 1.20288578e+01,\n 1.50627683e+01, 1.54059471e+01],\n [6.14397867e+00, 8.24476801e+00, 1.08649436e+01, 1.20488984e+01,\n 1.50721062e+01, 1.54181907e+01],\n [6.10467261e+00, 8.25843843e+00, 1.08111782e+01, 1.20723127e+01,\n 1.50816657e+01, 1.54298385e+01],\n [6.06448062e+00, 8.26749638e+00, 1.07569737e+01, 1.20991563e+01,\n 1.50914436e+01, 1.54408909e+01],\n [6.02341375e+00, 8.27184310e+00, 1.07023245e+01, 1.21294507e+01,\n 1.51014366e+01, 1.54513515e+01],\n [5.98148322e+00, 8.27141809e+00, 1.06472210e+01, 1.21631830e+01,\n 1.51116412e+01, 1.54612269e+01],\n [5.93870041e+00, 8.26619826e+00, 1.05916501e+01, 1.22003070e+01,\n 1.51220536e+01, 1.54705266e+01],\n [5.89507685e+00, 8.25619607e+00, 1.05355947e+01, 1.22407444e+01,\n 1.51326701e+01, 1.54792629e+01],\n [5.85062423e+00, 8.24145671e+00, 1.04790345e+01, 1.22843880e+01,\n 1.51434866e+01, 1.54874505e+01],\n [5.80535435e+00, 8.22205454e+00, 1.04219458e+01, 1.23311050e+01,\n 1.51544990e+01, 1.54951070e+01],\n [5.75927918e+00, 8.19808909e+00, 1.03643013e+01, 1.23807412e+01,\n 1.51657030e+01, 1.55022519e+01],\n [5.71241078e+00, 8.16968082e+00, 1.03060712e+01, 1.24331247e+01,\n 1.51770940e+01, 1.55089071e+01],\n [5.66476132e+00, 8.13696682e+00, 1.02472222e+01, 1.24880707e+01,\n 1.51886673e+01, 1.55150965e+01],\n [5.61634311e+00, 8.10009673e+00, 1.01877186e+01, 1.25453849e+01,\n 1.52004182e+01, 1.55208458e+01],\n [5.56716850e+00, 8.05922898e+00, 1.01275221e+01, 1.26048678e+01,\n 1.52123416e+01, 1.55261825e+01],\n [5.51724999e+00, 8.01452741e+00, 1.00665919e+01, 1.26663173e+01,\n 1.52244322e+01, 1.55311356e+01],\n [5.46660010e+00, 7.96615838e+00, 1.00048851e+01, 1.27295323e+01,\n 1.52366848e+01, 1.55357354e+01],\n [5.41523147e+00, 7.91428833e+00, 9.94235680e+00, 1.27943144e+01,\n 1.52490938e+01, 1.55400135e+01],\n [5.36315676e+00, 7.85908189e+00, 9.87896026e+00, 1.28604702e+01,\n 1.52616534e+01, 1.55440024e+01],\n [5.31038872e+00, 7.80070024e+00, 9.81464731e+00, 1.29278126e+01,\n 1.52743579e+01, 1.55477354e+01],\n [5.25694012e+00, 7.73930008e+00, 9.74936842e+00, 1.29961616e+01,\n 1.52872010e+01, 1.55512465e+01],\n [5.20282376e+00, 7.67503275e+00, 9.68307301e+00, 1.30653456e+01,\n 1.53001767e+01, 1.55545700e+01],\n [5.14805250e+00, 7.60804370e+00, 9.61570966e+00, 1.31352015e+01,\n 1.53132784e+01, 1.55577406e+01],\n [5.09263918e+00, 7.53847222e+00, 9.54722637e+00, 1.32055749e+01,\n 1.53264997e+01, 1.55607929e+01],\n [5.03659669e+00, 7.46645125e+00, 9.47757079e+00, 1.32763204e+01,\n 1.53398339e+01, 1.55637613e+01],\n [4.97993788e+00, 7.39210746e+00, 9.40669052e+00, 1.33473013e+01,\n 1.53532739e+01, 1.55666801e+01],\n [4.92267563e+00, 7.31556132e+00, 9.33453328e+00, 1.34183894e+01,\n 1.53668129e+01, 1.55695827e+01],\n [4.86482279e+00, 7.23692730e+00, 9.26104725e+00, 1.34894651e+01,\n 1.53804435e+01, 1.55725021e+01],\n [4.80639218e+00, 7.15631413e+00, 9.18618123e+00, 1.35604165e+01,\n 1.53941585e+01, 1.55754701e+01],\n [4.74739660e+00, 7.07382508e+00, 9.10988493e+00, 1.36311397e+01,\n 1.54079504e+01, 1.55785176e+01],\n [4.68784882e+00, 6.98955824e+00, 9.03210916e+00, 1.37015378e+01,\n 1.54218114e+01, 1.55816741e+01],\n [4.62776153e+00, 6.90360685e+00, 8.95280611e+00, 1.37715211e+01,\n 1.54357340e+01, 1.55849678e+01],\n [4.56714742e+00, 6.81605958e+00, 8.87192951e+00, 1.38410062e+01,\n 1.54497101e+01, 1.55884254e+01],\n [4.50601906e+00, 6.72700084e+00, 8.78943483e+00, 1.39099162e+01,\n 1.54637317e+01, 1.55920716e+01],\n [4.44438898e+00, 6.63651108e+00, 8.70527953e+00, 1.39781798e+01,\n 1.54777906e+01, 1.55959297e+01],\n [4.38226965e+00, 6.54466702e+00, 8.61942314e+00, 1.40457313e+01,\n 1.54918787e+01, 1.56000208e+01],\n [4.31967342e+00, 6.45154194e+00, 8.53182751e+00, 1.41125102e+01,\n 1.55059874e+01, 1.56043639e+01],\n [4.25661258e+00, 6.35720591e+00, 8.44245688e+00, 1.41784608e+01,\n 1.55201084e+01, 1.56089764e+01],\n [4.19309930e+00, 6.26172600e+00, 8.35127806e+00, 1.42435321e+01,\n 1.55342331e+01, 1.56138729e+01],\n [4.12914566e+00, 6.16516649e+00, 8.25826052e+00, 1.43076773e+01,\n 1.55483527e+01, 1.56190663e+01],\n [4.06476362e+00, 6.06758902e+00, 8.16337647e+00, 1.43708539e+01,\n 1.55624585e+01, 1.56245671e+01],\n [3.99996504e+00, 5.96905281e+00, 8.06660096e+00, 1.44330230e+01,\n 1.55765418e+01, 1.56303834e+01],\n [3.93476163e+00, 5.86961477e+00, 7.96791195e+00, 1.44941494e+01,\n 1.55905936e+01, 1.56365214e+01],\n [3.86916501e+00, 5.76932964e+00, 7.86729031e+00, 1.45542014e+01,\n 1.56046049e+01, 1.56429847e+01],\n [3.80318663e+00, 5.66825013e+00, 7.76471990e+00, 1.46131503e+01,\n 1.56185667e+01, 1.56497750e+01],\n [3.73683782e+00, 5.56642700e+00, 7.66018754e+00, 1.46709706e+01,\n 1.56324701e+01, 1.56568916e+01],\n [3.67012976e+00, 5.46390917e+00, 7.55368306e+00, 1.47276397e+01,\n 1.56463058e+01, 1.56643318e+01],\n [3.60307349e+00, 5.36074380e+00, 7.44519925e+00, 1.47831375e+01,\n 1.56600648e+01, 1.56720909e+01],\n [3.53567988e+00, 5.25697637e+00, 7.33473184e+00, 1.48374466e+01,\n 1.56737379e+01, 1.56801621e+01],\n [3.46795965e+00, 5.15265073e+00, 7.22227948e+00, 1.48905521e+01,\n 1.56873160e+01, 1.56885369e+01],\n [3.39992337e+00, 5.04780917e+00, 7.10784369e+00, 1.49424412e+01,\n 1.56972047e+01, 1.57007899e+01],\n [3.33158144e+00, 4.94249245e+00, 6.99142877e+00, 1.49931033e+01,\n 1.57061535e+01, 1.57141505e+01],\n [3.26294407e+00, 4.83673984e+00, 6.87304180e+00, 1.50425299e+01,\n 1.57153696e+01, 1.57273887e+01],\n [3.19402132e+00, 4.73058919e+00, 6.75269253e+00, 1.50907144e+01,\n 1.57248376e+01, 1.57404953e+01],\n [3.12482308e+00, 4.62407689e+00, 6.63039332e+00, 1.51376519e+01,\n 1.57345411e+01, 1.57534612e+01],\n [3.05535904e+00, 4.51723796e+00, 6.50615903e+00, 1.51833393e+01,\n 1.57444621e+01, 1.57662775e+01],\n [2.98563873e+00, 4.41010602e+00, 6.38000697e+00, 1.52277750e+01,\n 1.57545816e+01, 1.57789351e+01],\n [2.91567149e+00, 4.30271333e+00, 6.25195683e+00, 1.52709592e+01,\n 1.57648794e+01, 1.57914252e+01],\n [2.84546649e+00, 4.19509079e+00, 6.12203053e+00, 1.53128930e+01,\n 1.57753347e+01, 1.58037389e+01],\n [2.77503270e+00, 4.08726795e+00, 5.99025217e+00, 1.53535793e+01,\n 1.57859255e+01, 1.58158673e+01],\n [2.70437890e+00, 3.97927300e+00, 5.85664796e+00, 1.53930220e+01,\n 1.57966294e+01, 1.58278019e+01],\n [2.63351372e+00, 3.87113280e+00, 5.72124608e+00, 1.54312262e+01,\n 1.58074231e+01, 1.58395340e+01],\n [2.56244556e+00, 3.76287285e+00, 5.58407662e+00, 1.54681979e+01,\n 1.58182831e+01, 1.58510552e+01],\n [2.49118267e+00, 3.65451734e+00, 5.44517149e+00, 1.55039443e+01,\n 1.58291854e+01, 1.58623571e+01],\n [2.41973308e+00, 3.54608907e+00, 5.30456433e+00, 1.55384733e+01,\n 1.58401057e+01, 1.58734313e+01],\n [2.34810468e+00, 3.43760952e+00, 5.16229042e+00, 1.55717939e+01,\n 1.58510196e+01, 1.58842699e+01],\n [2.27630514e+00, 3.32909882e+00, 5.01838660e+00, 1.56039154e+01,\n 1.58619024e+01, 1.58948649e+01],\n [2.20434195e+00, 3.22057576e+00, 4.87289117e+00, 1.56348481e+01,\n 1.58727296e+01, 1.59052083e+01],\n [2.13222245e+00, 3.11205777e+00, 4.72584387e+00, 1.56646028e+01,\n 1.58834767e+01, 1.59152926e+01],\n [2.05995377e+00, 3.00356093e+00, 4.57728573e+00, 1.56931907e+01,\n 1.58941193e+01, 1.59251103e+01],\n [1.98754288e+00, 2.89509999e+00, 4.42725903e+00, 1.57206235e+01,\n 1.59046335e+01, 1.59346539e+01],\n [1.91499656e+00, 2.78668835e+00, 4.27580725e+00, 1.57469133e+01,\n 1.59149954e+01, 1.59439165e+01],\n [1.84232146e+00, 2.67833808e+00, 4.12297496e+00, 1.57720725e+01,\n 1.59251816e+01, 1.59528909e+01],\n [1.76952401e+00, 2.57005993e+00, 3.96880779e+00, 1.57961136e+01,\n 1.59351692e+01, 1.59615704e+01],\n [1.69661051e+00, 2.46186333e+00, 3.81335233e+00, 1.58190493e+01,\n 1.59449357e+01, 1.59699486e+01],\n [1.62358710e+00, 2.35375641e+00, 3.65665612e+00, 1.58408924e+01,\n 1.59544591e+01, 1.59780189e+01],\n [1.55045976e+00, 2.24574602e+00, 3.49876755e+00, 1.58616557e+01,\n 1.59637183e+01, 1.59857754e+01],\n [1.47723431e+00, 2.13783775e+00, 3.33973581e+00, 1.58813519e+01,\n 1.59726925e+01, 1.59932120e+01],\n [1.40391643e+00, 2.03003593e+00, 3.17961087e+00, 1.58999937e+01,\n 1.59813619e+01, 1.60003231e+01],\n [1.33051166e+00, 1.92234372e+00, 3.01844339e+00, 1.59175935e+01,\n 1.59897072e+01, 1.60071033e+01],\n [1.25702542e+00, 1.81476304e+00, 2.85628468e+00, 1.59341635e+01,\n 1.59977100e+01, 1.60135473e+01],\n [1.18346297e+00, 1.70729471e+00, 2.69318669e+00, 1.59497156e+01,\n 1.60053528e+01, 1.60196502e+01],\n [1.10982948e+00, 1.59993840e+00, 2.52920191e+00, 1.59642614e+01,\n 1.60126188e+01, 1.60254073e+01],\n [1.03612996e+00, 1.49269275e+00, 2.36438337e+00, 1.59778120e+01,\n 1.60194921e+01, 1.60308142e+01],\n [9.62369353e-01, 1.38555533e+00, 2.19878458e+00, 1.59903781e+01,\n 1.60259578e+01, 1.60358666e+01],\n [8.88552464e-01, 1.27852278e+00, 2.03245949e+00, 1.60019699e+01,\n 1.60320020e+01, 1.60405607e+01],\n [8.14684015e-01, 1.17159077e+00, 1.86546247e+00, 1.60125969e+01,\n 1.60376114e+01, 1.60448929e+01],\n [7.40768631e-01, 1.06475413e+00, 1.69784826e+00, 1.60222682e+01,\n 1.60427741e+01, 1.60488597e+01],\n [6.66810854e-01, 9.58006865e-01, 1.52967192e+00, 1.60309922e+01,\n 1.60474790e+01, 1.60524581e+01],\n [5.92815147e-01, 8.51342252e-01, 1.36098882e+00, 1.60387766e+01,\n 1.60517159e+01, 1.60556853e+01],\n [5.18785904e-01, 7.44752868e-01, 1.19185462e+00, 1.60456283e+01,\n 1.60554758e+01, 1.60585387e+01],\n [4.44727457e-01, 6.38230684e-01, 1.02232518e+00, 1.60515536e+01,\n 1.60587508e+01, 1.60610163e+01],\n [3.70644079e-01, 5.31767125e-01, 8.52456593e-01, 1.60565579e+01,\n 1.60615337e+01, 1.60631159e+01],\n [2.96540000e-01, 4.25353148e-01, 6.82305119e-01, 1.60606459e+01,\n 1.60638187e+01, 1.60648360e+01],\n [2.22419407e-01, 3.18979315e-01, 5.11927163e-01, 1.60638214e+01,\n 1.60656010e+01, 1.60661753e+01],\n [1.48286457e-01, 2.12635869e-01, 3.41379243e-01, 1.60660875e+01,\n 1.60668768e+01, 1.60671327e+01],\n [7.41452829e-02, 1.06312817e-01, 1.70717968e-01, 1.60674463e+01,\n 1.60676434e+01, 1.60677074e+01],\n [2.18701057e-06, 2.19691522e-06, 2.20369934e-06, 1.60678991e+01,\n 1.60678991e+01, 1.60678991e+01]]),\n array([[2.18701057e-06, 2.19691522e-06, 2.20369934e-06, 1.60678991e+01,\n 1.60678991e+01, 1.60678991e+01],\n [8.68987455e-02, 8.68987455e-02, 1.77711678e-01, 1.60674173e+01,\n 1.60676826e+01, 1.60676826e+01],\n [1.73771843e-01, 1.73771843e-01, 3.55392732e-01, 1.60659718e+01,\n 1.60670336e+01, 1.60670336e+01],\n [2.60593637e-01, 2.60593637e-01, 5.33012548e-01, 1.60635622e+01,\n 1.60659527e+01, 1.60659527e+01],\n [3.47338458e-01, 3.47338458e-01, 7.10540526e-01, 1.60601876e+01,\n 1.60644410e+01, 1.60644410e+01],\n [4.33980615e-01, 4.33980615e-01, 8.87946095e-01, 1.60558468e+01,\n 1.60625002e+01, 1.60625002e+01],\n [5.20494388e-01, 5.20494388e-01, 1.06519872e+00, 1.60505385e+01,\n 1.60601324e+01, 1.60601324e+01],\n [6.06854021e-01, 6.06854021e-01, 1.24226790e+00, 1.60442608e+01,\n 1.60573401e+01, 1.60573401e+01],\n [6.93033715e-01, 6.93033715e-01, 1.41912319e+00, 1.60370117e+01,\n 1.60541264e+01, 1.60541264e+01],\n [7.79007624e-01, 7.79007624e-01, 1.59573422e+00, 1.60287888e+01,\n 1.60504947e+01, 1.60504947e+01],\n [8.64749842e-01, 8.64749842e-01, 1.77207066e+00, 1.60195894e+01,\n 1.60464489e+01, 1.60464489e+01],\n [9.50234402e-01, 9.50234402e-01, 1.94810227e+00, 1.60094105e+01,\n 1.60419936e+01, 1.60419936e+01],\n [1.03543527e+00, 1.03543527e+00, 2.12379889e+00, 1.59982489e+01,\n 1.60371336e+01, 1.60371336e+01],\n [1.12032632e+00, 1.12032632e+00, 2.29913045e+00, 1.59861010e+01,\n 1.60318742e+01, 1.60318742e+01],\n [1.20488137e+00, 1.20488137e+00, 2.47406698e+00, 1.59729630e+01,\n 1.60262213e+01, 1.60262213e+01],\n [1.28907413e+00, 1.28907413e+00, 2.64857859e+00, 1.59588309e+01,\n 1.60201811e+01, 1.60201811e+01],\n [1.37287823e+00, 1.37287823e+00, 2.82263554e+00, 1.59437003e+01,\n 1.60137605e+01, 1.60137605e+01],\n [1.45626718e+00, 1.45626718e+00, 2.99620815e+00, 1.59275668e+01,\n 1.60069667e+01, 1.60069667e+01],\n [1.53921441e+00, 1.53921441e+00, 3.16926692e+00, 1.59104255e+01,\n 1.59998074e+01, 1.59998074e+01],\n [1.62169322e+00, 1.62169322e+00, 3.34178242e+00, 1.58922716e+01,\n 1.59922907e+01, 1.59922907e+01],\n [1.70367680e+00, 1.70367680e+00, 3.51372537e+00, 1.58730998e+01,\n 1.59844254e+01, 1.59844254e+01],\n [1.78513824e+00, 1.78513824e+00, 3.68506663e+00, 1.58529049e+01,\n 1.59762205e+01, 1.59762205e+01],\n [1.86605049e+00, 1.86605049e+00, 3.85577716e+00, 1.58316813e+01,\n 1.59676856e+01, 1.59676856e+01],\n [1.94638637e+00, 1.94638637e+00, 4.02582809e+00, 1.58094236e+01,\n 1.59588308e+01, 1.59588308e+01],\n [2.02611858e+00, 2.02611858e+00, 4.19519065e+00, 1.57861259e+01,\n 1.59496667e+01, 1.59496667e+01],\n [2.10521970e+00, 2.10521970e+00, 4.36383622e+00, 1.57617825e+01,\n 1.59402042e+01, 1.59402042e+01],\n [2.18366216e+00, 2.18366216e+00, 4.53173632e+00, 1.57363875e+01,\n 1.59304548e+01, 1.59304548e+01],\n [2.26141827e+00, 2.26141827e+00, 4.69886256e+00, 1.57099349e+01,\n 1.59204304e+01, 1.59204304e+01],\n [2.33846020e+00, 2.33846020e+00, 4.86518671e+00, 1.56824189e+01,\n 1.59101434e+01, 1.59101434e+01],\n [2.41475999e+00, 2.41475999e+00, 5.03068062e+00, 1.56538334e+01,\n 1.58996067e+01, 1.58996067e+01],\n [2.49028953e+00, 2.49028953e+00, 5.19531627e+00, 1.56241727e+01,\n 1.58888336e+01, 1.58888336e+01],\n [2.56502062e+00, 2.56502062e+00, 5.35906572e+00, 1.55934309e+01,\n 1.58778377e+01, 1.58778377e+01],\n [2.63892491e+00, 2.63892491e+00, 5.52190112e+00, 1.55616024e+01,\n 1.58666334e+01, 1.58666334e+01],\n [2.71197391e+00, 2.71197391e+00, 5.68379466e+00, 1.55286816e+01,\n 1.58552351e+01, 1.58552351e+01],\n [2.78413905e+00, 2.78413905e+00, 5.84471859e+00, 1.54946631e+01,\n 1.58436580e+01, 1.58436580e+01],\n [2.85539161e+00, 2.85539161e+00, 6.00464518e+00, 1.54595418e+01,\n 1.58319175e+01, 1.58319175e+01],\n [2.92570282e+00, 2.92570282e+00, 6.16354668e+00, 1.54233130e+01,\n 1.58200294e+01, 1.58200294e+01],\n [2.99504375e+00, 2.99504375e+00, 6.32139531e+00, 1.53859722e+01,\n 1.58080101e+01, 1.58080101e+01],\n [3.06338544e+00, 3.06338544e+00, 6.47816320e+00, 1.53475153e+01,\n 1.57958762e+01, 1.57958762e+01],\n [3.13069883e+00, 3.13069883e+00, 6.63382235e+00, 1.53079386e+01,\n 1.57836448e+01, 1.57836448e+01],\n [3.19695480e+00, 3.19695480e+00, 6.78834460e+00, 1.52672393e+01,\n 1.57713331e+01, 1.57713331e+01],\n [3.26212420e+00, 3.26212420e+00, 6.94170153e+00, 1.52254148e+01,\n 1.57589589e+01, 1.57589589e+01],\n [3.32617785e+00, 3.32617785e+00, 7.09386444e+00, 1.51824635e+01,\n 1.57465403e+01, 1.57465403e+01],\n [3.38908653e+00, 3.38908653e+00, 7.24480421e+00, 1.51383844e+01,\n 1.57340955e+01, 1.57340955e+01],\n [3.45082108e+00, 3.45082108e+00, 7.39449126e+00, 1.50931777e+01,\n 1.57216433e+01, 1.57216433e+01],\n [3.51135231e+00, 3.51135231e+00, 7.54289542e+00, 1.50468445e+01,\n 1.57092025e+01, 1.57092025e+01],\n [3.57065115e+00, 3.57065115e+00, 7.68998576e+00, 1.49993872e+01,\n 1.56967922e+01, 1.56967922e+01],\n [3.62868855e+00, 3.62868855e+00, 7.83573054e+00, 1.49508094e+01,\n 1.56844317e+01, 1.56844317e+01],\n [3.68543561e+00, 3.68543561e+00, 7.98009691e+00, 1.49011166e+01,\n 1.56721405e+01, 1.56721405e+01],\n [3.74086353e+00, 3.74086353e+00, 8.12305082e+00, 1.48503158e+01,\n 1.56599383e+01, 1.56599383e+01],\n [3.79494372e+00, 3.79494372e+00, 8.26455669e+00, 1.47984162e+01,\n 1.56478448e+01, 1.56478448e+01],\n [3.84764774e+00, 3.84764774e+00, 8.40457720e+00, 1.47454295e+01,\n 1.56358798e+01, 1.56358798e+01],\n [3.89894744e+00, 3.89894744e+00, 8.54307290e+00, 1.46913700e+01,\n 1.56240633e+01, 1.56240633e+01],\n [3.94881489e+00, 3.94881489e+00, 8.68000183e+00, 1.46362550e+01,\n 1.56124152e+01, 1.56124152e+01],\n [3.99722251e+00, 3.99722251e+00, 8.81531907e+00, 1.45801056e+01,\n 1.56009552e+01, 1.56009552e+01],\n [4.04414305e+00, 4.04414305e+00, 8.94897617e+00, 1.45229472e+01,\n 1.55897031e+01, 1.55897031e+01],\n [4.08954967e+00, 4.08954967e+00, 9.08092045e+00, 1.44648099e+01,\n 1.55786787e+01, 1.55786787e+01],\n [4.13341596e+00, 4.13341596e+00, 9.21109424e+00, 1.44057295e+01,\n 1.55679014e+01, 1.55679014e+01],\n [4.17571599e+00, 4.17571599e+00, 9.33943387e+00, 1.43457486e+01,\n 1.55573906e+01, 1.55573906e+01],\n [4.21642438e+00, 4.21642438e+00, 9.46586854e+00, 1.42849178e+01,\n 1.55471651e+01, 1.55471651e+01],\n [4.25551631e+00, 4.25551631e+00, 9.59031884e+00, 1.42232967e+01,\n 1.55372439e+01, 1.55372439e+01],\n [4.29296759e+00, 4.29296759e+00, 9.71269507e+00, 1.41609564e+01,\n 1.55276452e+01, 1.55276452e+01],\n [4.32875473e+00, 4.32875473e+00, 9.83289509e+00, 1.40979808e+01,\n 1.55183871e+01, 1.55183871e+01],\n [4.36285493e+00, 4.36285493e+00, 9.95080172e+00, 1.40344699e+01,\n 1.55094870e+01, 1.55094870e+01],\n [4.39524622e+00, 4.39524622e+00, 1.00662796e+01, 1.39705427e+01,\n 1.55009619e+01, 1.55009619e+01],\n [4.42590741e+00, 4.42590741e+00, 1.01791712e+01, 1.39063409e+01,\n 1.54928283e+01, 1.54928283e+01],\n [4.45481822e+00, 4.45481822e+00, 1.02892922e+01, 1.38420341e+01,\n 1.54851020e+01, 1.54851020e+01],\n [4.48195930e+00, 4.48195930e+00, 1.03964254e+01, 1.37778256e+01,\n 1.54777983e+01, 1.54777983e+01],\n [4.50731227e+00, 4.50731227e+00, 1.05003136e+01, 1.37139594e+01,\n 1.54709315e+01, 1.54709315e+01],\n [4.53085979e+00, 4.53085979e+00, 1.06006514e+01, 1.36507288e+01,\n 1.54645154e+01, 1.54645154e+01],\n [4.55258558e+00, 4.55258558e+00, 1.06970744e+01, 1.35884865e+01,\n 1.54585629e+01, 1.54585629e+01],\n [4.57247450e+00, 4.57247450e+00, 1.07891482e+01, 1.35276567e+01,\n 1.54530860e+01, 1.54530860e+01],\n [4.59051254e+00, 4.59051254e+00, 1.08763552e+01, 1.34687473e+01,\n 1.54480960e+01, 1.54480960e+01],\n [4.60668693e+00, 4.60668693e+00, 1.09580822e+01, 1.34123627e+01,\n 1.54436029e+01, 1.54436029e+01],\n [4.62098611e+00, 4.62098611e+00, 1.10336096e+01, 1.33592147e+01,\n 1.54396162e+01, 1.54396162e+01],\n [4.63339981e+00, 4.63339981e+00, 1.11021066e+01, 1.33101273e+01,\n 1.54361441e+01, 1.54361441e+01],\n [4.64391906e+00, 4.64391906e+00, 1.11626377e+01, 1.32660299e+01,\n 1.54331937e+01, 1.54331937e+01],\n [4.65253622e+00, 4.65253622e+00, 1.12141885e+01, 1.32279317e+01,\n 1.54307713e+01, 1.54307713e+01],\n [4.65924501e+00, 4.65924501e+00, 1.12557173e+01, 1.31968704e+01,\n 1.54288819e+01, 1.54288819e+01],\n [4.66404052e+00, 4.66404052e+00, 1.12862369e+01, 1.31738300e+01,\n 1.54275295e+01, 1.54275295e+01],\n [4.66691923e+00, 4.66691923e+00, 1.13049205e+01, 1.31596347e+01,\n 1.54267169e+01, 1.54267169e+01],\n [4.66787904e+00, 4.66787904e+00, 1.13112137e+01, 1.31548379e+01,\n 1.54264459e+01, 1.54264459e+01]]),\n array([[ 4.66787904, 4.66787904, 11.31121369, 13.15483786, 15.42644585,\n 15.42644585],\n [ 4.66883944, 4.67093501, 11.31069683, 13.15420714, 15.42624753,\n 15.42662672],\n [ 4.6717197 , 4.68008535, 11.30914699, 13.15231706, 15.42565317,\n 15.42716712],\n [ 4.67651706, 4.69527771, 11.30656644, 13.14917383, 15.42466453,\n 15.42806041],\n [ 4.68322686, 4.71642595, 11.30295898, 13.14478769, 15.42328455,\n 15.42929564],\n [ 4.69184265, 4.74341172, 11.29832994, 13.13917277, 15.42151735,\n 15.43085774],\n [ 4.70235612, 4.77608661, 11.2926863 , 13.13234687, 15.41936818,\n 15.43272765],\n [ 4.71475714, 4.8142747 , 11.28603666, 13.12433117, 15.41684348,\n 15.43488268],\n [ 4.72903381, 4.85777545, 11.2783914 , 13.11514998, 15.4139508 ,\n 15.43729674],\n [ 4.74517241, 4.90636678, 11.26976269, 13.10483036, 15.41069884,\n 15.43994075],\n [ 4.7631575 , 4.95980823, 11.26016464, 13.09340178, 15.40709737,\n 15.44278297],\n [ 4.78297187, 5.01784414, 11.2496134 , 13.08089571, 15.40315728,\n 15.44578941],\n [ 4.80459662, 5.08020666, 11.2381273 , 13.06734527, 15.39889052,\n 15.4489242 ],\n [ 4.82801117, 5.14661861, 11.22572702, 13.0527848 , 15.39431009,\n 15.45215004],\n [ 4.85319328, 5.21679606, 11.21243575, 13.0372495 , 15.38943 ,\n 15.45542857],\n [ 4.88011907, 5.29045068, 11.1982794 , 13.02077504, 15.38426525,\n 15.45872076],\n [ 4.90876308, 5.36729169, 11.18328681, 13.00339721, 15.37883182,\n 15.46198731],\n [ 4.93909829, 5.44702758, 11.16749005, 12.98515157, 15.3731466 ,\n 15.46518895],\n [ 4.97109613, 5.5293674 , 11.15092462, 12.96607314, 15.3672274 ,\n 15.46828687],\n [ 5.00472652, 5.61402185, 11.13362983, 12.94619611, 15.36109287,\n 15.47124292],\n [ 5.03995793, 5.700704 , 11.11564913, 12.92555359, 15.35476249,\n 15.47401998],\n [ 5.07675735, 5.78912978, 11.09703046, 12.90417733, 15.34825653,\n 15.47658222],\n [ 5.11509038, 5.87901817, 11.07782674, 12.88209755, 15.34159598,\n 15.47889527],\n [ 5.15492119, 5.97009122, 11.05809624, 12.85934274, 15.33480255,\n 15.48092653],\n [ 5.19621261, 6.06207386, 11.03790317, 12.83593951, 15.32789857,\n 15.48264529],\n [ 5.23892611, 6.15469351, 11.01731817, 12.81191244, 15.32090699,\n 15.48402293],\n [ 5.28302184, 6.24767954, 10.99641896, 12.78728396, 15.3138513 ,\n 15.48503308],\n [ 5.32845864, 6.34076267, 10.9752909 , 12.76207432, 15.30675548,\n 15.48565171],\n [ 5.37519406, 6.43367414, 10.9540277 , 12.73630143, 15.29964395,\n 15.48585731],\n [ 5.42318436, 6.52614493, 10.93273212, 12.7099809 , 15.2925415 ,\n 15.48563092],\n [ 5.47238454, 6.61790486, 10.91151663, 12.68312596, 15.28547325,\n 15.48495625],\n [ 5.52274835, 6.7086817 , 10.89050415, 12.65574747, 15.27846454,\n 15.48381973],\n [ 5.57422825, 6.79820026, 10.86982865, 12.62785393, 15.27154095,\n 15.48221057],\n [ 5.62677547, 6.88618163, 10.84963575, 12.5994515 , 15.26472812,\n 15.48012081],\n [ 5.68033995, 6.97234249, 10.83008312, 12.57054404, 15.25805176,\n 15.47754532],\n [ 5.73487036, 7.05639464, 10.81134075, 12.5411332 , 15.25153756,\n 15.47448184],\n [ 5.79031407, 7.13804489, 10.7935908 , 12.51121847, 15.24521107,\n 15.47093096],\n [ 5.84661715, 7.21699523, 10.77702722, 12.4807973 , 15.23909766,\n 15.46689616],\n [ 5.90372431, 7.2929437 , 10.76185465, 12.44986521, 15.23322244,\n 15.46238371],\n [ 5.96157886, 7.36558575, 10.74828691, 12.41841593, 15.22761012,\n 15.45740272],\n [ 6.0201227 , 7.43461652, 10.73654446, 12.38644156, 15.22228498,\n 15.45196503],\n [ 6.07929625, 7.49973393, 10.72685125, 12.35393277, 15.21727073,\n 15.44608518],\n [ 6.13903837, 7.56064276, 10.71943035, 12.32087899, 15.21259043,\n 15.43978036],\n [ 6.19928628, 7.61705972, 10.71449888, 12.28726865, 15.20826641,\n 15.43307027],\n [ 6.25997552, 7.66871935, 10.71226189, 12.25308943, 15.2043201 ,\n 15.42597708],\n [ 6.32103977, 7.71538058, 10.71290574, 12.21832858, 15.20077199,\n 15.41852527],\n [ 6.3824108 , 7.75683366, 10.71659108, 12.1829732 , 15.19764149,\n 15.41074154],\n [ 6.44401828, 7.79290678, 10.72344609, 12.14701063, 15.1949468 ,\n 15.40265463],\n [ 6.50578968, 7.82347218, 10.73356042, 12.11042881, 15.19270483,\n 15.39429522],\n [ 6.56765 , 7.84845077, 10.74698037, 12.07321672, 15.19093108,\n 15.3856957 ],\n [ 6.62952167, 7.86781512, 10.76370597, 12.03536482, 15.18963947,\n 15.37689002],\n [ 6.69132422, 7.88159025, 10.78369008, 11.99686561, 15.18884231,\n 15.36791351],\n [ 6.75297411, 7.88985221, 10.80683981, 11.95771409, 15.18855011,\n 15.35880262],\n [ 6.81438433, 7.89272444, 10.83302013, 11.91790844, 15.18877153,\n 15.34959476],\n [ 6.87546417, 7.8903724 , 10.86205919, 11.87745058, 15.18951322,\n 15.34032804],\n [ 6.93611876, 7.88299691, 10.89375497, 11.83634691, 15.19077974,\n 15.33104105],\n [ 6.99624871, 7.87082671, 10.92788271, 11.79460901, 15.19257349,\n 15.32177261],\n [ 7.05574959, 7.85411092, 10.9642024 , 11.75225444, 15.19489459,\n 15.31256153],\n [ 7.11451149, 7.83311182, 11.00246595, 11.70930758, 15.1977408 ,\n 15.30344637],\n [ 7.17241836, 7.80809838, 11.04242367, 11.66580048, 15.2011075 ,\n 15.29446521],\n [ 7.22934748, 7.77934065, 11.08382976, 11.62177384, 15.2049876 ,\n 15.2856554 ],\n [ 7.28516874, 7.7471053 , 11.12644676, 11.57727795, 15.20937152,\n 15.27705331],\n [ 7.33974397, 7.7116521 , 11.17004895, 11.53237371, 15.21424716,\n 15.26869413],\n [ 7.39292613, 7.67323138, 11.21442482, 11.48713365, 15.21959992,\n 15.26061169],\n [ 7.44455862, 7.6320824 , 11.25937862, 11.44164301, 15.22541272,\n 15.25283819],\n [ 7.49447447, 7.58843228, 11.30473122, 11.39600072, 15.23166602,\n 15.24540409],\n [ 7.54249562, 7.54249562, 11.3503204 , 11.3503204 , 15.23833788,\n 15.23833788]]),\n array([[ 7.54249562, 7.54249562, 11.3503204 , 11.3503204 , 15.23833788,\n 15.23833788],\n [ 7.54166641, 7.54166641, 11.35130975, 11.35130975, 15.23801134,\n 15.23801134],\n [ 7.53918446, 7.53918446, 11.35427194, 11.35427194, 15.23703255,\n 15.23703255],\n [ 7.53506676, 7.53506676, 11.35918952, 11.35918952, 15.23540407,\n 15.23540407],\n [ 7.52934132, 7.52934132, 11.36603365, 11.36603365, 15.23313011,\n 15.23313011],\n [ 7.52204673, 7.52204673, 11.37476455, 11.37476455, 15.23021665,\n 15.23021665],\n [ 7.51323165, 7.51323165, 11.38533198, 11.38533198, 15.22667136,\n 15.22667136],\n [ 7.50295407, 7.50295407, 11.39767597, 11.39767597, 15.22250365,\n 15.22250365],\n [ 7.49128048, 7.49128048, 11.41172752, 11.41172752, 15.21772475,\n 15.21772475],\n [ 7.47828508, 7.47828508, 11.42740943, 11.42740943, 15.21234764,\n 15.21234764],\n [ 7.46404878, 7.46404878, 11.44463718, 11.44463718, 15.20638716,\n 15.20638716],\n [ 7.44865827, 7.44865827, 11.46331976, 11.46331976, 15.19986003,\n 15.19986003],\n [ 7.43220511, 7.43220511, 11.48336059, 11.48336059, 15.19278485,\n 15.19278485],\n [ 7.41478473, 7.41478473, 11.50465834, 11.50465834, 15.18518221,\n 15.18518221],\n [ 7.39649562, 7.39649562, 11.5271077 , 11.5271077 , 15.17707467,\n 15.17707467],\n [ 7.3774384 , 7.3774384 , 11.55060018, 11.55060018, 15.16848683,\n 15.16848683],\n [ 7.35771513, 7.35771513, 11.57502474, 11.57502474, 15.15944541,\n 15.15944541],\n [ 7.33742851, 7.33742851, 11.60026839, 11.60026839, 15.14997924,\n 15.14997924],\n [ 7.3166813 , 7.3166813 , 11.62621676, 11.62621676, 15.14011934,\n 15.14011934],\n [ 7.29557569, 7.29557569, 11.65275454, 11.65275454, 15.12989893,\n 15.12989893],\n [ 7.27421283, 7.27421283, 11.6797659 , 11.6797659 , 15.11935352,\n 15.11935352],\n [ 7.25269237, 7.25269237, 11.7071348 , 11.7071348 , 15.10852087,\n 15.10852087],\n [ 7.23111204, 7.23111204, 11.73474528, 11.73474528, 15.09744106,\n 15.09744106],\n [ 7.20956738, 7.20956738, 11.76248171, 11.76248171, 15.08615647,\n 15.08615647],\n [ 7.1881514 , 7.1881514 , 11.79022897, 11.79022897, 15.07471177,\n 15.07471177],\n [ 7.16695438, 7.16695438, 11.81787268, 11.81787268, 15.06315389,\n 15.06315389],\n [ 7.14606363, 7.14606363, 11.84529928, 11.84529928, 15.05153196,\n 15.05153196],\n [ 7.12556335, 7.12556335, 11.87239625, 11.87239625, 15.03989724,\n 15.03989724],\n [ 7.10553446, 7.10553446, 11.89905224, 11.89905224, 15.02830298,\n 15.02830298],\n [ 7.08605448, 7.08605448, 11.92515725, 11.92515725, 15.01680429,\n 15.01680429],\n [ 7.06719745, 7.06719745, 11.95060282, 11.95060282, 15.00545792,\n 15.00545792],\n [ 7.0490338 , 7.0490338 , 11.97528226, 11.97528226, 14.994322 ,\n 14.994322 ],\n [ 7.0316303 , 7.0316303 , 11.99909093, 11.99909093, 14.98345578,\n 14.98345578],\n [ 7.01504997, 7.01504997, 12.02192655, 12.02192655, 14.97291925,\n 14.97291925],\n [ 6.99935206, 6.99935206, 12.04368954, 12.04368954, 14.96277273,\n 14.96277273],\n [ 6.98459195, 6.98459195, 12.0642835 , 12.0642835 , 14.9530764 ,\n 14.9530764 ],\n [ 6.97082113, 6.97082113, 12.08361559, 12.08361559, 14.94388978,\n 14.94388978],\n [ 6.95808712, 6.95808712, 12.10159715, 12.10159715, 14.93527117,\n 14.93527117],\n [ 6.94643348, 6.94643348, 12.1181442 , 12.1181442 , 14.92727697,\n 14.92727697],\n [ 6.93589974, 6.93589974, 12.13317811, 12.13317811, 14.91996108,\n 14.91996108],\n [ 6.92652136, 6.92652136, 12.14662617, 12.14662617, 14.91337418,\n 14.91337418],\n [ 6.9183297 , 6.9183297 , 12.15842227, 12.15842227, 14.90756307,\n 14.90756307],\n [ 6.91135203, 6.91135203, 12.16850756, 12.16850756, 14.90256997,\n 14.90256997],\n [ 6.90561144, 6.90561144, 12.17683102, 12.17683102, 14.89843186,\n 14.89843186],\n [ 6.90112687, 6.90112687, 12.18335004, 12.18335004, 14.89517991,\n 14.89517991],\n [ 6.89791305, 6.89791305, 12.18803092, 12.18803092, 14.89283897,\n 14.89283897],\n [ 6.89598055, 6.89598055, 12.19084928, 12.19084928, 14.89142709,\n 14.89142709],\n [ 6.89533567, 6.89533567, 12.19179039, 12.19179039, 14.89095524,\n 14.89095524]])],\n 'eigenvectors': None,\n 'group_velocities': None},\n 'total_dos_dict': {'frequency_points': array([-1.21959488e+00, -1.12531879e+00, -1.03104271e+00, -9.36766620e-01,\n -8.42490534e-01, -7.48214449e-01, -6.53938363e-01, -5.59662277e-01,\n -4.65386192e-01, -3.71110106e-01, -2.76834020e-01, -1.82557935e-01,\n -8.82818488e-02, 5.99423689e-03, 1.00270323e-01, 1.94546408e-01,\n 2.88822494e-01, 3.83098580e-01, 4.77374665e-01, 5.71650751e-01,\n 6.65926837e-01, 7.60202922e-01, 8.54479008e-01, 9.48755094e-01,\n 1.04303118e+00, 1.13730727e+00, 1.23158335e+00, 1.32585944e+00,\n 1.42013552e+00, 1.51441161e+00, 1.60868769e+00, 1.70296378e+00,\n 1.79723987e+00, 1.89151595e+00, 1.98579204e+00, 2.08006812e+00,\n 2.17434421e+00, 2.26862029e+00, 2.36289638e+00, 2.45717246e+00,\n 2.55144855e+00, 2.64572464e+00, 2.74000072e+00, 2.83427681e+00,\n 2.92855289e+00, 3.02282898e+00, 3.11710506e+00, 3.21138115e+00,\n 3.30565724e+00, 3.39993332e+00, 3.49420941e+00, 3.58848549e+00,\n 3.68276158e+00, 3.77703766e+00, 3.87131375e+00, 3.96558984e+00,\n 4.05986592e+00, 4.15414201e+00, 4.24841809e+00, 4.34269418e+00,\n 4.43697026e+00, 4.53124635e+00, 4.62552244e+00, 4.71979852e+00,\n 4.81407461e+00, 4.90835069e+00, 5.00262678e+00, 5.09690286e+00,\n 5.19117895e+00, 5.28545504e+00, 5.37973112e+00, 5.47400721e+00,\n 5.56828329e+00, 5.66255938e+00, 5.75683546e+00, 5.85111155e+00,\n 5.94538764e+00, 6.03966372e+00, 6.13393981e+00, 6.22821589e+00,\n 6.32249198e+00, 6.41676806e+00, 6.51104415e+00, 6.60532024e+00,\n 6.69959632e+00, 6.79387241e+00, 6.88814849e+00, 6.98242458e+00,\n 7.07670066e+00, 7.17097675e+00, 7.26525284e+00, 7.35952892e+00,\n 7.45380501e+00, 7.54808109e+00, 7.64235718e+00, 7.73663326e+00,\n 7.83090935e+00, 7.92518544e+00, 8.01946152e+00, 8.11373761e+00,\n 8.20801369e+00, 8.30228978e+00, 8.39656586e+00, 8.49084195e+00,\n 8.58511804e+00, 8.67939412e+00, 8.77367021e+00, 8.86794629e+00,\n 8.96222238e+00, 9.05649846e+00, 9.15077455e+00, 9.24505064e+00,\n 9.33932672e+00, 9.43360281e+00, 9.52787889e+00, 9.62215498e+00,\n 9.71643106e+00, 9.81070715e+00, 9.90498323e+00, 9.99925932e+00,\n 1.00935354e+01, 1.01878115e+01, 1.02820876e+01, 1.03763637e+01,\n 1.04706397e+01, 1.05649158e+01, 1.06591919e+01, 1.07534680e+01,\n 1.08477441e+01, 1.09420202e+01, 1.10362963e+01, 1.11305723e+01,\n 1.12248484e+01, 1.13191245e+01, 1.14134006e+01, 1.15076767e+01,\n 1.16019528e+01, 1.16962289e+01, 1.17905049e+01, 1.18847810e+01,\n 1.19790571e+01, 1.20733332e+01, 1.21676093e+01, 1.22618854e+01,\n 1.23561615e+01, 1.24504375e+01, 1.25447136e+01, 1.26389897e+01,\n 1.27332658e+01, 1.28275419e+01, 1.29218180e+01, 1.30160941e+01,\n 1.31103701e+01, 1.32046462e+01, 1.32989223e+01, 1.33931984e+01,\n 1.34874745e+01, 1.35817506e+01, 1.36760267e+01, 1.37703027e+01,\n 1.38645788e+01, 1.39588549e+01, 1.40531310e+01, 1.41474071e+01,\n 1.42416832e+01, 1.43359593e+01, 1.44302353e+01, 1.45245114e+01,\n 1.46187875e+01, 1.47130636e+01, 1.48073397e+01, 1.49016158e+01,\n 1.49958919e+01, 1.50901679e+01, 1.51844440e+01, 1.52787201e+01,\n 1.53729962e+01, 1.54672723e+01, 1.55615484e+01, 1.56558245e+01,\n 1.57501005e+01, 1.58443766e+01, 1.59386527e+01, 1.60329288e+01,\n 1.61272049e+01, 1.62214810e+01, 1.63157571e+01, 1.64100331e+01,\n 1.65043092e+01, 1.65985853e+01, 1.66928614e+01, 1.67871375e+01,\n 1.68814136e+01, 1.69756897e+01, 1.70699657e+01, 1.71642418e+01,\n 1.72585179e+01, 1.73527940e+01, 1.74470701e+01, 1.75413462e+01,\n 1.76356223e+01]),\n 'total_dos': array([0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 3.17526949e-04, 1.35171618e-03, 2.50831797e-03,\n 3.78733233e-03, 5.26373813e-03, 6.90328284e-03, 8.78451412e-03,\n 1.08845716e-02, 1.31202482e-02, 1.58239881e-02, 1.84817583e-02,\n 2.14099537e-02, 2.44295300e-02, 2.78000795e-02, 3.14939706e-02,\n 3.52413320e-02, 3.92909859e-02, 4.36423577e-02, 4.83495504e-02,\n 5.31903107e-02, 5.81462801e-02, 6.35669356e-02, 6.94844360e-02,\n 7.55171874e-02, 8.19720137e-02, 8.86760193e-02, 9.58023138e-02,\n 1.03099606e-01, 1.11366958e-01, 1.19969573e-01, 1.28656383e-01,\n 1.38210214e-01, 1.48087177e-01, 1.58993039e-01, 1.70577194e-01,\n 1.82773665e-01, 1.96102840e-01, 2.10318186e-01, 2.25609695e-01,\n 2.42775583e-01, 2.61718244e-01, 2.82966510e-01, 3.07071183e-01,\n 3.35572804e-01, 3.71503640e-01, 4.23538191e-01, 5.01245367e-01,\n 5.06757340e-01, 5.10673514e-01, 5.13884731e-01, 5.18635687e-01,\n 5.22215630e-01, 5.26790868e-01, 5.30317993e-01, 5.33703746e-01,\n 5.38149099e-01, 5.41609848e-01, 5.45017573e-01, 5.48177732e-01,\n 5.52308667e-01, 5.54935999e-01, 5.58609041e-01, 5.61624143e-01,\n 5.64469403e-01, 5.68022742e-01, 5.70890330e-01, 5.72980739e-01,\n 5.77439994e-01, 5.83268678e-01, 5.49870464e-01, 4.81961887e-01,\n 4.49243839e-01, 4.26254220e-01, 4.10187378e-01, 3.95199652e-01,\n 3.98624284e-01, 4.05995249e-01, 4.25103229e-01, 4.54252120e-01,\n 4.65563502e-01, 3.65773926e-01, 2.85541037e-01, 2.23526600e-01,\n 1.44473263e-01, 1.04439534e-01, 1.08917911e-01, 1.13417776e-01,\n 1.18953226e-01, 1.24441198e-01, 1.29621905e-01, 1.36164980e-01,\n 1.42605861e-01, 1.49045426e-01, 1.56851391e-01, 1.64582559e-01,\n 1.72682584e-01, 1.82141611e-01, 1.91321788e-01, 2.02261449e-01,\n 2.13762731e-01, 2.26135950e-01, 2.40393404e-01, 2.55442497e-01,\n 2.74046636e-01, 2.93902607e-01, 3.19085171e-01, 3.48960866e-01,\n 3.91473391e-01, 4.54354038e-01, 5.99226889e-01, 6.56603266e-01,\n 4.43486451e-01, 3.58148235e-01, 2.92612110e-01, 2.34458733e-01,\n 1.57664249e-01, 9.44996839e-02, 7.64989495e-02, 6.21782198e-02,\n 7.46273535e-02, 8.86461614e-02, 1.06333999e-01, 1.36147948e-01,\n 1.87831258e-01, 2.67221370e-01, 2.89615750e-01, 3.09688343e-01,\n 3.30425521e-01, 3.30668402e-01, 3.40062237e-01, 3.45284499e-01,\n 3.55917538e-01, 3.60077500e-01, 3.69186627e-01, 3.71502854e-01,\n 3.72120651e-01, 3.48181936e-01, 3.16317708e-01, 2.98435672e-01,\n 2.84862196e-01, 2.74096441e-01, 2.64721157e-01, 2.56360104e-01,\n 2.48761334e-01, 2.41852996e-01, 2.35018844e-01, 2.28859604e-01,\n 2.22571780e-01, 2.16655364e-01, 2.10807826e-01, 2.04860365e-01,\n 1.99221497e-01, 1.93100666e-01, 1.87355107e-01, 2.53244401e-01,\n 8.43177422e-01, 1.43196664e+00, 3.18170027e+00, 2.79552678e+00,\n 3.13543115e+00, 4.55809708e+00, 2.72396129e+00, 1.52338820e+00,\n 1.06733102e+00, 7.67955185e-01, 5.18138351e-01, 2.28096624e-01,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00])},\n 'dynamical_matrix': array([[ 5.50912534e-01-0.00000000e+00j, 1.87768043e-17-4.38872430e-34j,\n 1.92709307e-17+5.81987920e-18j, -3.23420540e-17+4.98906381e-17j,\n -1.68412801e-30+5.84523400e-17j, -3.95652763e-17-3.56372327e-01j],\n [ 1.87768043e-17+4.38872430e-34j, 6.08181944e-01-0.00000000e+00j,\n -1.56143951e-16-1.15555797e-33j, -7.84788746e-30+5.84523400e-17j,\n -3.23420540e-17+2.45450096e-18j, 4.20932852e-30+1.58872850e-17j],\n [ 1.92709307e-17-5.81987920e-18j, -1.56143951e-16+1.15555797e-33j,\n 5.50912534e-01-0.00000000e+00j, -3.95652763e-17-3.56372327e-01j,\n 8.83023845e-30+1.58872850e-17j, -3.23420540e-17-3.36800318e-19j],\n [-3.23420540e-17-4.98906381e-17j, -7.84788746e-30-5.84523400e-17j,\n -3.95652763e-17+3.56372327e-01j, 5.50912534e-01-0.00000000e+00j,\n -9.24016421e-17-9.32340591e-30j, -8.30132400e-17-1.39858661e-29j],\n [-1.68412801e-30-5.84523400e-17j, -3.23420540e-17-2.45450096e-18j,\n 8.83023845e-30-1.58872850e-17j, -9.24016421e-17+9.32340591e-30j,\n 6.08181944e-01-0.00000000e+00j, -1.49226181e-16+4.66355445e-30j],\n [-3.95652763e-17+3.56372327e-01j, 4.20932852e-30-1.58872850e-17j,\n -3.23420540e-17+3.36800318e-19j, -8.30132400e-17+1.39858661e-29j,\n -1.49226181e-16-4.66355445e-30j, 5.50912534e-01-0.00000000e+00j]]),\n 'force_constants': array([[[[ 1.57151912e+01, 9.62277932e-16, 9.62277932e-16],\n [ 2.01508898e-31, 1.57151912e+01, -3.56057418e-15],\n [-6.31781728e-30, -4.83151945e-15, 1.57151912e+01]],\n \n [[-8.88178420e-13, -2.31481372e-29, -6.32321319e-29],\n [ 8.33886532e-31, 1.11022302e-12, -2.01086934e-28],\n [ 3.91666326e-46, -3.53409686e-28, 1.11022302e-12]],\n \n [[ 1.11022302e-12, 7.59032102e-29, 1.18329136e-28],\n [-1.78078948e-29, -8.88178420e-13, -4.17598292e-28],\n [ 5.04870979e-29, 2.72945873e-28, 1.11022302e-12]],\n \n ...,\n \n [[-6.32890635e-13, 5.20587829e-13, -5.20587829e-13],\n [-1.25573862e-13, -5.61838490e-13, -2.31561886e-13],\n [ 1.25573862e-13, -2.31561886e-13, -5.61838490e-13]],\n \n [[-5.61838490e-13, -1.25573862e-13, -2.31561886e-13],\n [ 5.20587829e-13, -6.32890635e-13, -5.20587829e-13],\n [-2.31561886e-13, 1.25573862e-13, -5.61838490e-13]],\n \n [[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]]],\n \n \n [[[-8.88178420e-13, -2.31481372e-29, -6.32321319e-29],\n [ 8.33886532e-31, 1.11022302e-12, -2.01086934e-28],\n [ 1.63734993e-45, -3.53409686e-28, 1.11022302e-12]],\n \n [[ 1.57151912e+01, 9.62277932e-16, 9.62277932e-16],\n [ 2.19141532e-31, 1.57151912e+01, -3.56057418e-15],\n [-6.30018465e-30, -4.83151945e-15, 1.57151912e+01]],\n \n [[ 1.59872116e-12, 7.17863424e-29, 1.13595970e-28],\n [ 2.73057674e-29, 1.59872116e-12, -1.11175775e-27],\n [ 5.04870979e-29, -4.03896783e-28, 4.08562073e-12]],\n \n ...,\n \n [[-3.70859075e+00, -2.50222375e+00, 2.50222375e+00],\n [-2.50222375e+00, -3.70859075e+00, 2.50222375e+00],\n [ 2.50222375e+00, 2.50222375e+00, -3.70859075e+00]],\n \n [[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]],\n \n [[-5.61838490e-13, -1.25573862e-13, -2.31561886e-13],\n [ 5.20587829e-13, -6.32890635e-13, -5.20587829e-13],\n [-2.31561886e-13, 1.25573862e-13, -5.61838490e-13]]],\n \n \n [[[ 1.11022302e-12, 7.59032102e-29, 1.18329136e-28],\n [-1.78078948e-29, -8.88178420e-13, -4.17598292e-28],\n [ 5.04870979e-29, 2.72945873e-28, 1.11022302e-12]],\n \n [[ 1.59872116e-12, 7.17863424e-29, 1.13595970e-28],\n [ 2.73057674e-29, 1.59872116e-12, -1.11175775e-27],\n [ 5.04870979e-29, -4.03896783e-28, 4.08562073e-12]],\n \n [[ 1.57151912e+01, 9.62277932e-16, 9.62277932e-16],\n [ 2.19141532e-31, 1.57151912e+01, -3.56057418e-15],\n [-6.30018465e-30, -4.83151945e-15, 1.57151912e+01]],\n \n ...,\n \n [[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]],\n \n [[-3.70859075e+00, -2.50222375e+00, 2.50222375e+00],\n [-2.50222375e+00, -3.70859075e+00, 2.50222375e+00],\n [ 2.50222375e+00, 2.50222375e+00, -3.70859075e+00]],\n \n [[-6.32890635e-13, 5.20587829e-13, -5.20587829e-13],\n [-1.25573862e-13, -5.61838490e-13, -2.31561886e-13],\n [ 1.25573862e-13, -2.31561886e-13, -5.61838490e-13]]],\n \n \n ...,\n \n \n [[[-6.32890635e-13, 5.20587829e-13, -5.20587829e-13],\n [-1.25573862e-13, -5.61838490e-13, -2.31561886e-13],\n [ 1.25573862e-13, -2.31561886e-13, -5.61838490e-13]],\n \n [[-3.70859075e+00, -2.50222375e+00, 2.50222375e+00],\n [-2.50222375e+00, -3.70859075e+00, 2.50222375e+00],\n [ 2.50222375e+00, 2.50222375e+00, -3.70859075e+00]],\n \n [[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]],\n \n ...,\n \n [[ 1.57151912e+01, -2.88683380e-15, -2.88683380e-15],\n [-1.92455586e-15, 1.57151912e+01, -4.83151945e-15],\n [-1.92455586e-15, -3.56057418e-15, 1.57151912e+01]],\n \n [[ 1.59872116e-12, -2.84139296e-28, -6.91248574e-28],\n [-1.83165100e-28, 1.59872116e-12, -1.36396903e-27],\n [-4.81749809e-28, -2.63475263e-28, 4.08562073e-12]],\n \n [[ 1.11022302e-12, 4.85458861e-29, -1.58051213e-28],\n [ 9.61487114e-29, -8.88178420e-13, -4.50532933e-28],\n [-1.17892900e-28, 2.33671810e-28, 1.11022302e-12]]],\n \n \n [[[-5.61838490e-13, -1.25573862e-13, -2.31561886e-13],\n [ 5.20587829e-13, -6.32890635e-13, -5.20587829e-13],\n [-2.31561886e-13, 1.25573862e-13, -5.61838490e-13]],\n \n [[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]],\n \n [[-3.70859075e+00, -2.50222375e+00, 2.50222375e+00],\n [-2.50222375e+00, -3.70859075e+00, 2.50222375e+00],\n [ 2.50222375e+00, 2.50222375e+00, -3.70859075e+00]],\n \n ...,\n \n [[ 1.59872116e-12, -2.84139296e-28, -6.91248574e-28],\n [-1.83165100e-28, 1.59872116e-12, -1.36396903e-27],\n [-4.81749809e-28, -2.63475263e-28, 4.08562073e-12]],\n \n [[ 1.57151912e+01, -2.88683380e-15, -2.88683380e-15],\n [-1.92455586e-15, 1.57151912e+01, -4.83151945e-15],\n [-1.92455586e-15, -3.56057418e-15, 1.57151912e+01]],\n \n [[-8.88178420e-13, -7.27309754e-29, -1.12814970e-28],\n [-1.35963107e-28, 1.11022302e-12, -3.53409686e-28],\n [-1.36796994e-28, -2.01086934e-28, 1.11022302e-12]]],\n \n \n [[[-1.15412764e-12, -4.39732284e-13, 3.10095250e-14],\n [-4.39732284e-13, -1.15412764e-12, 3.10095250e-14],\n [ 1.56993370e-13, 1.56993370e-13, -7.37047351e-13]],\n \n [[-5.61838490e-13, -1.25573862e-13, -2.31561886e-13],\n [ 5.20587829e-13, -6.32890635e-13, -5.20587829e-13],\n [-2.31561886e-13, 1.25573862e-13, -5.61838490e-13]],\n \n [[-6.32890635e-13, 5.20587829e-13, -5.20587829e-13],\n [-1.25573862e-13, -5.61838490e-13, -2.31561886e-13],\n [ 1.25573862e-13, -2.31561886e-13, -5.61838490e-13]],\n \n ...,\n \n [[ 1.11022302e-12, 4.85458861e-29, -1.58051213e-28],\n [ 9.61487114e-29, -8.88178420e-13, -4.50532933e-28],\n [-1.17892900e-28, 2.33671810e-28, 1.11022302e-12]],\n \n [[-8.88178420e-13, -7.27309754e-29, -1.12814970e-28],\n [-1.35963107e-28, 1.11022302e-12, -3.53409686e-28],\n [-1.36796994e-28, -2.01086934e-28, 1.11022302e-12]],\n \n [[ 1.57151912e+01, -2.88683380e-15, -2.88683380e-15],\n [-1.92455586e-15, 1.57151912e+01, -4.83151945e-15],\n [-1.92455586e-15, -3.56057418e-15, 1.57151912e+01]]]])}" }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cell = (\n", " structure_ase.cell.array,\n", " structure_ase.get_scaled_positions(),\n", " structure_ase.numbers,\n", ")\n", "primitive_matrix = spglib.standardize_cell(cell=cell, to_primitive=True)[\n", " 0\n", "] / structure_ase.get_volume() ** (1 / 3)\n", "workflow = PhonopyWorkflow(\n", " structure=structure_ase,\n", " interaction_range=10,\n", " factor=VaspToTHz,\n", " displacement=0.01,\n", " dos_mesh=20,\n", " primitive_matrix=primitive_matrix,\n", " number_of_snapshots=None,\n", ")\n", "task_dict = workflow.generate_structures()\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "workflow.analyse_structures(output_dict=result_dict)" ] }, { "metadata": {}, "cell_type": "markdown", "source": [ "The calcualtion of the finite temperature phonons starts by computing the molecular dynamics trajectory using the \n", "`calc_molecular_dynamics_phonons_with_lammpslib()` function. This function is internally linked to [DynaPhoPy](https://abelcarreras.github.io/DynaPhoPy/)\n", "to return an `dynaphopy.dynamics.Dynamics` object: " ], "id": "6f442d932c6a769b" }, { "metadata": {}, "cell_type": "code", "outputs": [], "execution_count": null, "source": [ "trajectory = calc_molecular_dynamics_phonons_with_lammpslib(\n", " structure_ase=structure_ase,\n", " potential_dataframe=potential_dataframe,\n", " force_constants=workflow.phonopy.get_force_constants(),\n", " phonopy_unitcell=workflow.phonopy.get_unitcell(),\n", " phonopy_primitive_matrix=workflow.phonopy.get_primitive_matrix(),\n", " phonopy_supercell_matrix=workflow.phonopy.get_supercell_matrix(),\n", " total_time=2, # ps\n", " time_step=0.001, # ps\n", " relaxation_time=5, # ps\n", " silent=True,\n", " supercell=[2, 2, 2],\n", " memmap=False,\n", " velocity_only=True,\n", " temperature=600,\n", ")" ], "id": "2d31cb8d827833a0" }, { "cell_type": "markdown", "id": "5b533910-8e65-4c57-91bc-ccfa1e49d4ce", "metadata": {}, "source": "When a total of 2 picoseconds is selected to compute the finite temperature phonons with a timestep of 1 femto second\nthen this results in a total of 2000 molecular dynamics steps. While more molecular dynamics steps result in more precise\npredictions they also require more computational resources. " }, { "cell_type": "markdown", "id": "58cbd845-ad6e-41e1-b37c-dcc426e110c1", "metadata": {}, "source": "The postprocessing is executed using the [DynaPhoPy](https://abelcarreras.github.io/DynaPhoPy/) package: " }, { "cell_type": "code", "execution_count": 15, "id": "54169376-3978-4c25-b1d6-509030a4cea7", "metadata": { "trusted": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": "Using 2000 steps\nUsing Fast Fourier transform (Numpy) function\nset frequency range: 0.0 - 21.200000000000003\n\nQ-point: 1 / 32 [ 0.00000 0.00000 0.00000 ]\nHarmonic frequencies (THz):\n[2.18910938e-06 2.19854601e-06 2.20383682e-06 1.60678991e+01\n 1.60678991e+01 1.60678991e+01]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nMD cell size relation: [2 2 2]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\n\nPeak # 1\n----------------------------------------------\nWidth 0.472941 THz\nPosition 0.032545 THz\nArea () (Lorentzian) 0.000000 eV\nArea () (Total) 0.000000 eV\n<|dQ/dt|^2> 0.000000 eV\nOccupation number -0.500000\nFit temperature nan K\nBase line -0.000000 eV * ps\nMaximum height 0.000000 eV * ps\nFitting global error 534601240663.551514\nFrequency shift 0.032543 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.472941 THz\nPosition 0.032545 THz\nArea () (Lorentzian) 0.000000 eV\nArea () (Total) 0.000000 eV\n<|dQ/dt|^2> 0.000000 eV\nOccupation number -0.500000\nFit temperature nan K\nBase line -0.000000 eV * ps\nMaximum height 0.000000 eV * ps\nFitting global error 534601240663.551514\nFrequency shift 0.032543 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.472941 THz\nPosition 0.032545 THz\nArea () (Lorentzian) 0.000000 eV\nArea () (Total) 0.000000 eV\n<|dQ/dt|^2> 0.000000 eV\nOccupation number -0.500000\nFit temperature nan K\nBase line -0.000000 eV * ps\nMaximum height 0.000000 eV * ps\nFitting global error 534601240663.551514\nFrequency shift 0.032543 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.786715 THz\nPosition 15.561772 THz\nArea () (Lorentzian) 0.014497 eV\nArea () (Total) 0.013722 eV\n<|dQ/dt|^2> 0.028993 eV\nOccupation number 2.330539\nFit temperature 332.921392 K\nBase line -0.000016 eV * ps\nMaximum height 0.011731 eV * ps\nFitting global error 0.033291\nFrequency shift -0.506127 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.786715 THz\nPosition 15.561772 THz\nArea () (Lorentzian) 0.014497 eV\nArea () (Total) 0.013722 eV\n<|dQ/dt|^2> 0.028993 eV\nOccupation number 2.330539\nFit temperature 332.921392 K\nBase line -0.000016 eV * ps\nMaximum height 0.011731 eV * ps\nFitting global error 0.033291\nFrequency shift -0.506127 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.786715 THz\nPosition 15.561772 THz\nArea () (Lorentzian) 0.014497 eV\nArea () (Total) 0.013722 eV\n<|dQ/dt|^2> 0.028993 eV\nOccupation number 2.330539\nFit temperature 332.921392 K\nBase line -0.000016 eV * ps\nMaximum height 0.011731 eV * ps\nFitting global error 0.033291\nFrequency shift -0.506127 THz\nFixing gamma point 0 frequencies\n\nQ-point: 2 / 32 [ 0.00000 0.25000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\n\nPeak # 1\n----------------------------------------------\nWidth 0.520799 THz\nPosition 4.512511 THz\nArea () (Lorentzian) 0.018113 eV\nArea () (Total) 0.016786 eV\n<|dQ/dt|^2> 0.036226 eV\nOccupation number 11.696398\nFit temperature 420.145058 K\nBase line -0.000042 eV * ps\nMaximum height 0.022141 eV * ps\nFitting global error 0.016919\nFrequency shift -0.151463 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.520799 THz\nPosition 4.512511 THz\nArea () (Lorentzian) 0.018113 eV\nArea () (Total) 0.016786 eV\n<|dQ/dt|^2> 0.036226 eV\nOccupation number 11.696398\nFit temperature 420.145058 K\nBase line -0.000042 eV * ps\nMaximum height 0.022141 eV * ps\nFitting global error 0.016919\nFrequency shift -0.151463 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.884643 THz\nPosition 6.802090 THz\nArea () (Lorentzian) 0.034381 eV\nArea () (Total) 0.042075 eV\n<|dQ/dt|^2> 0.068762 eV\nOccupation number 14.858240\nFit temperature 797.669964 K\nBase line 0.000413 eV * ps\nMaximum height 0.024742 eV * ps\nFitting global error 0.034947\nFrequency shift -0.096079 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.816224 THz\nPosition 14.710909 THz\nArea () (Lorentzian) 0.050561 eV\nArea () (Total) 0.056117 eV\n<|dQ/dt|^2> 0.101122 eV\nOccupation number 9.943370\nFit temperature 1172.575784 K\nBase line 0.000331 eV * ps\nMaximum height 0.039435 eV * ps\nFitting global error 0.029537\nFrequency shift -0.459579 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.906396 THz\nPosition 15.069443 THz\nArea () (Lorentzian) 0.021839 eV\nArea () (Total) 0.023547 eV\n<|dQ/dt|^2> 0.043678 eV\nOccupation number 3.903565\nFit temperature 504.681860 K\nBase line 0.000115 eV * ps\nMaximum height 0.015339 eV * ps\nFitting global error 0.023072\nFrequency shift -0.486236 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.906396 THz\nPosition 15.069443 THz\nArea () (Lorentzian) 0.021839 eV\nArea () (Total) 0.023547 eV\n<|dQ/dt|^2> 0.043678 eV\nOccupation number 3.903565\nFit temperature 504.681860 K\nBase line 0.000115 eV * ps\nMaximum height 0.015339 eV * ps\nFitting global error 0.023072\nFrequency shift -0.486236 THz\n\nQ-point: 3 / 32 [ 0.00000 0.50000 0.50000 ]\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\n\nPeak # 1\n----------------------------------------------\nWidth 0.579259 THz\nPosition 6.561490 THz\nArea () (Lorentzian) 0.025327 eV\nArea () (Total) 0.027369 eV\n<|dQ/dt|^2> 0.050654 eV\nOccupation number 11.228659\nFit temperature 587.462942 K\nBase line 0.000121 eV * ps\nMaximum height 0.027835 eV * ps\nFitting global error 0.025639\nFrequency shift -0.333845 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.579259 THz\nPosition 6.561490 THz\nArea () (Lorentzian) 0.025327 eV\nArea () (Total) 0.027369 eV\n<|dQ/dt|^2> 0.050654 eV\nOccupation number 11.228659\nFit temperature 587.462942 K\nBase line 0.000121 eV * ps\nMaximum height 0.027835 eV * ps\nFitting global error 0.025639\nFrequency shift -0.333845 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.605260 THz\nPosition 11.933579 THz\nArea () (Lorentzian) 0.030516 eV\nArea () (Total) 0.034730 eV\n<|dQ/dt|^2> 0.061032 eV\nOccupation number 7.270035\nFit temperature 707.271378 K\nBase line 0.000225 eV * ps\nMaximum height 0.032097 eV * ps\nFitting global error 0.023688\nFrequency shift -0.258211 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.605260 THz\nPosition 11.933579 THz\nArea () (Lorentzian) 0.030516 eV\nArea () (Total) 0.034730 eV\n<|dQ/dt|^2> 0.061032 eV\nOccupation number 7.270035\nFit temperature 707.271378 K\nBase line 0.000225 eV * ps\nMaximum height 0.032097 eV * ps\nFitting global error 0.023688\nFrequency shift -0.258211 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.634083 THz\nPosition 14.446261 THz\nArea () (Lorentzian) 0.042334 eV\nArea () (Total) 0.048339 eV\n<|dQ/dt|^2> 0.084669 eV\nOccupation number 8.404323\nFit temperature 981.504236 K\nBase line 0.000327 eV * ps\nMaximum height 0.042504 eV * ps\nFitting global error 0.015367\nFrequency shift -0.444694 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.634083 THz\nPosition 14.446261 THz\nArea () (Lorentzian) 0.042334 eV\nArea () (Total) 0.048339 eV\n<|dQ/dt|^2> 0.084669 eV\nOccupation number 8.404323\nFit temperature 981.504236 K\nBase line 0.000327 eV * ps\nMaximum height 0.042504 eV * ps\nFitting global error 0.015367\nFrequency shift -0.444694 THz\n\nQ-point: 4 / 32 [ 0.00000 0.75000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\n\nPeak # 1\n----------------------------------------------\nWidth 0.513715 THz\nPosition 4.501773 THz\nArea () (Lorentzian) 0.024073 eV\nArea () (Total) 0.021107 eV\n<|dQ/dt|^2> 0.048147 eV\nOccupation number 15.748632\nFit temperature 558.542395 K\nBase line -0.000113 eV * ps\nMaximum height 0.029833 eV * ps\nFitting global error 0.014530\nFrequency shift -0.162201 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.513715 THz\nPosition 4.501773 THz\nArea () (Lorentzian) 0.024073 eV\nArea () (Total) 0.021107 eV\n<|dQ/dt|^2> 0.048147 eV\nOccupation number 15.748632\nFit temperature 558.542395 K\nBase line -0.000113 eV * ps\nMaximum height 0.029833 eV * ps\nFitting global error 0.014530\nFrequency shift -0.162201 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.840450 THz\nPosition 6.833587 THz\nArea () (Lorentzian) 0.047750 eV\nArea () (Total) 0.056965 eV\n<|dQ/dt|^2> 0.095499 eV\nOccupation number 20.731750\nFit temperature 1108.018836 K\nBase line 0.000500 eV * ps\nMaximum height 0.036169 eV * ps\nFitting global error 0.027488\nFrequency shift -0.064582 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.864892 THz\nPosition 14.761576 THz\nArea () (Lorentzian) 0.036911 eV\nArea () (Total) 0.042399 eV\n<|dQ/dt|^2> 0.073823 eV\nOccupation number 7.097870\nFit temperature 855.439740 K\nBase line 0.000312 eV * ps\nMaximum height 0.027169 eV * ps\nFitting global error 0.033172\nFrequency shift -0.408912 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.690963 THz\nPosition 15.047965 THz\nArea () (Lorentzian) 0.029989 eV\nArea () (Total) 0.029744 eV\n<|dQ/dt|^2> 0.059977 eV\nOccupation number 5.555378\nFit temperature 694.419722 K\nBase line 0.000024 eV * ps\nMaximum height 0.027630 eV * ps\nFitting global error 0.016899\nFrequency shift -0.507714 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.690963 THz\nPosition 15.047965 THz\nArea () (Lorentzian) 0.029989 eV\nArea () (Total) 0.029744 eV\n<|dQ/dt|^2> 0.059977 eV\nOccupation number 5.555378\nFit temperature 694.419722 K\nBase line 0.000024 eV * ps\nMaximum height 0.027630 eV * ps\nFitting global error 0.016899\nFrequency shift -0.507714 THz\n\nQ-point: 5 / 32 [ 0.25000 0.00000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nSkipped, equivalent to [0. 0.25 0.25]\n\nQ-point: 6 / 32 [ 0.25000 0.25000 0.50000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\n\nPeak # 1\n----------------------------------------------\nWidth 0.528069 THz\nPosition 4.477183 THz\nArea () (Lorentzian) 0.042227 eV\nArea () (Total) 0.040708 eV\n<|dQ/dt|^2> 0.084453 eV\nOccupation number 28.158070\nFit temperature 979.942696 K\nBase line -0.000024 eV * ps\nMaximum height 0.050907 eV * ps\nFitting global error 0.012211\nFrequency shift -0.190696 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.890764 THz\nPosition 6.695151 THz\nArea () (Lorentzian) 0.080890 eV\nArea () (Total) 0.093342 eV\n<|dQ/dt|^2> 0.161780 eV\nOccupation number 36.211198\nFit temperature 1877.262480 K\nBase line 0.000706 eV * ps\nMaximum height 0.057811 eV * ps\nFitting global error 0.020823\nFrequency shift -0.265939 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.879866 THz\nPosition 8.803246 THz\nArea () (Lorentzian) 0.043886 eV\nArea () (Total) 0.052217 eV\n<|dQ/dt|^2> 0.087772 eV\nOccupation number 14.647678\nFit temperature 1018.178741 K\nBase line 0.000449 eV * ps\nMaximum height 0.031753 eV * ps\nFitting global error 0.028094\nFrequency shift -0.202601 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.757650 THz\nPosition 13.371395 THz\nArea () (Lorentzian) 0.021906 eV\nArea () (Total) 0.026391 eV\n<|dQ/dt|^2> 0.043812 eV\nOccupation number 4.477924\nFit temperature 506.700041 K\nBase line 0.000237 eV * ps\nMaximum height 0.018407 eV * ps\nFitting global error 0.037761\nFrequency shift -0.353521 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.668122 THz\nPosition 14.983805 THz\nArea () (Lorentzian) 0.023784 eV\nArea () (Total) 0.024310 eV\n<|dQ/dt|^2> 0.047568 eV\nOccupation number 4.323155\nFit temperature 550.026025 K\nBase line 0.000052 eV * ps\nMaximum height 0.022663 eV * ps\nFitting global error 0.013903\nFrequency shift -0.442641 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.793991 THz\nPosition 15.147433 THz\nArea () (Lorentzian) 0.067893 eV\nArea () (Total) 0.078771 eV\n<|dQ/dt|^2> 0.135785 eV\nOccupation number 13.119087\nFit temperature 1575.015042 K\nBase line 0.000607 eV * ps\nMaximum height 0.054436 eV * ps\nFitting global error 0.022076\nFrequency shift -0.435323 THz\n\nQ-point: 7 / 32 [ 0.25000 0.50000 0.75000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\n\nPeak # 1\n----------------------------------------------\nWidth 0.907126 THz\nPosition 7.246330 THz\nArea () (Lorentzian) 0.086024 eV\nArea () (Total) 0.104037 eV\n<|dQ/dt|^2> 0.172047 eV\nOccupation number 35.571453\nFit temperature 1996.396673 K\nBase line 0.000973 eV * ps\nMaximum height 0.060371 eV * ps\nFitting global error 0.020717\nFrequency shift -0.296166 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.907126 THz\nPosition 7.246330 THz\nArea () (Lorentzian) 0.086024 eV\nArea () (Total) 0.104037 eV\n<|dQ/dt|^2> 0.172047 eV\nOccupation number 35.571453\nFit temperature 1996.396673 K\nBase line 0.000973 eV * ps\nMaximum height 0.060371 eV * ps\nFitting global error 0.020717\nFrequency shift -0.296166 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.639111 THz\nPosition 11.064519 THz\nArea () (Lorentzian) 0.021923 eV\nArea () (Total) 0.025269 eV\n<|dQ/dt|^2> 0.043847 eV\nOccupation number 5.520612\nFit temperature 507.650279 K\nBase line 0.000178 eV * ps\nMaximum height 0.021838 eV * ps\nFitting global error 0.024793\nFrequency shift -0.285801 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.639111 THz\nPosition 11.064519 THz\nArea () (Lorentzian) 0.021923 eV\nArea () (Total) 0.025269 eV\n<|dQ/dt|^2> 0.043847 eV\nOccupation number 5.520612\nFit temperature 507.650279 K\nBase line 0.000178 eV * ps\nMaximum height 0.021838 eV * ps\nFitting global error 0.024793\nFrequency shift -0.285801 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.828868 THz\nPosition 14.801411 THz\nArea () (Lorentzian) 0.039716 eV\nArea () (Total) 0.043893 eV\n<|dQ/dt|^2> 0.079432 eV\nOccupation number 7.653201\nFit temperature 920.616703 K\nBase line 0.000252 eV * ps\nMaximum height 0.030504 eV * ps\nFitting global error 0.031513\nFrequency shift -0.436927 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.828868 THz\nPosition 14.801411 THz\nArea () (Lorentzian) 0.039716 eV\nArea () (Total) 0.043893 eV\n<|dQ/dt|^2> 0.079432 eV\nOccupation number 7.653201\nFit temperature 920.616703 K\nBase line 0.000252 eV * ps\nMaximum height 0.030504 eV * ps\nFitting global error 0.031513\nFrequency shift -0.436927 THz\n\nQ-point: 8 / 32 [ 0.25000 0.75000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\n\nPeak # 1\n----------------------------------------------\nWidth 0.522556 THz\nPosition 4.483775 THz\nArea () (Lorentzian) 0.037188 eV\nArea () (Total) 0.034635 eV\n<|dQ/dt|^2> 0.074376 eV\nOccupation number 24.701308\nFit temperature 862.984199 K\nBase line -0.000079 eV * ps\nMaximum height 0.045305 eV * ps\nFitting global error 0.012393\nFrequency shift -0.184104 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.898262 THz\nPosition 6.707279 THz\nArea () (Lorentzian) 0.067887 eV\nArea () (Total) 0.079212 eV\n<|dQ/dt|^2> 0.135775 eV\nOccupation number 30.254428\nFit temperature 1575.464581 K\nBase line 0.000635 eV * ps\nMaximum height 0.048114 eV * ps\nFitting global error 0.023773\nFrequency shift -0.253812 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.835420 THz\nPosition 8.803037 THz\nArea () (Lorentzian) 0.013150 eV\nArea () (Total) 0.016324 eV\n<|dQ/dt|^2> 0.026301 eV\nOccupation number 4.039095\nFit temperature 303.968669 K\nBase line 0.000166 eV * ps\nMaximum height 0.010021 eV * ps\nFitting global error 0.059276\nFrequency shift -0.202810 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.730369 THz\nPosition 13.368389 THz\nArea () (Lorentzian) 0.016678 eV\nArea () (Total) 0.021238 eV\n<|dQ/dt|^2> 0.033357 eV\nOccupation number 3.290872\nFit temperature 384.834117 K\nBase line 0.000234 eV * ps\nMaximum height 0.014538 eV * ps\nFitting global error 0.045590\nFrequency shift -0.356527 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.674322 THz\nPosition 14.951363 THz\nArea () (Lorentzian) 0.036155 eV\nArea () (Total) 0.038613 eV\n<|dQ/dt|^2> 0.072311 eV\nOccupation number 6.847775\nFit temperature 837.833762 K\nBase line 0.000157 eV * ps\nMaximum height 0.034134 eV * ps\nFitting global error 0.014619\nFrequency shift -0.475083 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.902049 THz\nPosition 15.073779 THz\nArea () (Lorentzian) 0.021209 eV\nArea () (Total) 0.022490 eV\n<|dQ/dt|^2> 0.042418 eV\nOccupation number 3.775244\nFit temperature 489.986369 K\nBase line 0.000094 eV * ps\nMaximum height 0.014968 eV * ps\nFitting global error 0.022499\nFrequency shift -0.508977 THz\n\nQ-point: 9 / 32 [ 0.50000 0.00000 0.50000 ]\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nSkipped, equivalent to [0. 0.5 0.5]\n\nQ-point: 10 / 32 [ 0.50000 0.25000 0.75000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nSkipped, equivalent to [0.25 0.5 0.75]\n\nQ-point: 11 / 32 [ 0.50000 0.50000 0.00000 ]\nHarmonic frequencies (THz):\n[ 6.89533567 6.89533567 12.19179039 12.19179039 14.89095524 14.89095524]\nSkipped, equivalent to [0. 0.5 0.5]\n\nQ-point: 12 / 32 [ 0.50000 0.75000 0.25000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nSkipped, equivalent to [0.25 0.5 0.75]\n\nQ-point: 13 / 32 [ 0.75000 0.00000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nSkipped, equivalent to [0. 0.75 0.75]\n\nQ-point: 14 / 32 [ 0.75000 0.25000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\n\nPeak # 1\n----------------------------------------------\nWidth 0.521991 THz\nPosition 4.484158 THz\nArea () (Lorentzian) 0.036566 eV\nArea () (Total) 0.033926 eV\n<|dQ/dt|^2> 0.073131 eV\nOccupation number 24.277431\nFit temperature 848.537722 K\nBase line -0.000083 eV * ps\nMaximum height 0.044595 eV * ps\nFitting global error 0.012530\nFrequency shift -0.183721 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.899617 THz\nPosition 6.704187 THz\nArea () (Lorentzian) 0.061915 eV\nArea () (Total) 0.071943 eV\n<|dQ/dt|^2> 0.123830 eV\nOccupation number 27.561609\nFit temperature 1436.830957 K\nBase line 0.000565 eV * ps\nMaximum height 0.043814 eV * ps\nFitting global error 0.025259\nFrequency shift -0.256903 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.840794 THz\nPosition 8.777709 THz\nArea () (Lorentzian) 0.009473 eV\nArea () (Total) 0.011919 eV\n<|dQ/dt|^2> 0.018945 eV\nOccupation number 2.779076\nFit temperature 218.134959 K\nBase line 0.000127 eV * ps\nMaximum height 0.007172 eV * ps\nFitting global error 0.078651\nFrequency shift -0.228137 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.814357 THz\nPosition 13.294667 THz\nArea () (Lorentzian) 0.012215 eV\nArea () (Total) 0.016240 eV\n<|dQ/dt|^2> 0.024429 eV\nOccupation number 2.291679\nFit temperature 280.431129 K\nBase line 0.000205 eV * ps\nMaximum height 0.009549 eV * ps\nFitting global error 0.061800\nFrequency shift -0.430249 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.706639 THz\nPosition 14.920962 THz\nArea () (Lorentzian) 0.033379 eV\nArea () (Total) 0.034927 eV\n<|dQ/dt|^2> 0.066758 eV\nOccupation number 6.297384\nFit temperature 773.297146 K\nBase line 0.000113 eV * ps\nMaximum height 0.030072 eV * ps\nFitting global error 0.021423\nFrequency shift -0.505484 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.901748 THz\nPosition 15.110122 THz\nArea () (Lorentzian) 0.021178 eV\nArea () (Total) 0.023049 eV\n<|dQ/dt|^2> 0.042356 eV\nOccupation number 3.758704\nFit temperature 489.249960 K\nBase line 0.000121 eV * ps\nMaximum height 0.014951 eV * ps\nFitting global error 0.028888\nFrequency shift -0.472634 THz\n\nQ-point: 15 / 32 [ 0.75000 0.50000 0.25000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nSkipped, equivalent to [0.25 0.5 0.75]\n\nQ-point: 16 / 32 [ 0.75000 0.75000 0.50000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\n\nPeak # 1\n----------------------------------------------\nWidth 0.521626 THz\nPosition 4.484270 THz\nArea () (Lorentzian) 0.040369 eV\nArea () (Total) 0.037483 eV\n<|dQ/dt|^2> 0.080738 eV\nOccupation number 26.853838\nFit temperature 936.816651 K\nBase line -0.000091 eV * ps\nMaximum height 0.049268 eV * ps\nFitting global error 0.011912\nFrequency shift -0.183609 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.898998 THz\nPosition 6.706088 THz\nArea () (Lorentzian) 0.060155 eV\nArea () (Total) 0.069989 eV\n<|dQ/dt|^2> 0.120310 eV\nOccupation number 26.756362\nFit temperature 1395.986799 K\nBase line 0.000553 eV * ps\nMaximum height 0.042598 eV * ps\nFitting global error 0.025425\nFrequency shift -0.255003 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.847729 THz\nPosition 8.762397 THz\nArea () (Lorentzian) 0.009423 eV\nArea () (Total) 0.011871 eV\n<|dQ/dt|^2> 0.018846 eV\nOccupation number 2.767683\nFit temperature 216.985862 K\nBase line 0.000127 eV * ps\nMaximum height 0.007077 eV * ps\nFitting global error 0.078128\nFrequency shift -0.243450 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.822505 THz\nPosition 13.296042 THz\nArea () (Lorentzian) 0.012441 eV\nArea () (Total) 0.016789 eV\n<|dQ/dt|^2> 0.024882 eV\nOccupation number 2.343156\nFit temperature 285.744350 K\nBase line 0.000221 eV * ps\nMaximum height 0.009629 eV * ps\nFitting global error 0.060141\nFrequency shift -0.428874 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.692941 THz\nPosition 14.927237 THz\nArea () (Lorentzian) 0.037140 eV\nArea () (Total) 0.038953 eV\n<|dQ/dt|^2> 0.074280 eV\nOccupation number 7.060040\nFit temperature 860.720270 K\nBase line 0.000129 eV * ps\nMaximum height 0.034121 eV * ps\nFitting global error 0.019502\nFrequency shift -0.499209 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.873800 THz\nPosition 15.089642 THz\nArea () (Lorentzian) 0.020289 eV\nArea () (Total) 0.022192 eV\n<|dQ/dt|^2> 0.040578 eV\nOccupation number 3.585462\nFit temperature 468.522604 K\nBase line 0.000120 eV * ps\nMaximum height 0.014782 eV * ps\nFitting global error 0.026540\nFrequency shift -0.493114 THz\n\nQ-point: 17 / 32 [ 0.25000 0.25000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nSkipped, equivalent to [0.25 0. 0.25]\n\nQ-point: 18 / 32 [ 0.25000 0.50000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.25 0.25 0.5 ]\n\nQ-point: 19 / 32 [ 0.25000 0.75000 0.50000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nSkipped, equivalent to [0.25 0.5 0.75]\n\nQ-point: 20 / 32 [ 0.25000 0.00000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.75 0.75 0.5 ]\n\nQ-point: 21 / 32 [ 0.50000 0.25000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.25 0.5 0.25]\n\nQ-point: 22 / 32 [ 0.50000 0.50000 0.50000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nCalculating phonon projection power spectra\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nProjecting into phonon mode\nProjecting into wave vector\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nPower spectrum resolution requested unavailable, using maximum: 0.500000 THz\nIf you need higher resolution increase the number of data\nFFT: [##############################] 100.00% Done...\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\n\nPeak # 1\n----------------------------------------------\nWidth 0.531374 THz\nPosition 4.473540 THz\nArea () (Lorentzian) 0.029343 eV\nArea () (Total) 0.027597 eV\n<|dQ/dt|^2> 0.058686 eV\nOccupation number 19.430578\nFit temperature 680.883835 K\nBase line -0.000049 eV * ps\nMaximum height 0.035155 eV * ps\nFitting global error 0.015967\nFrequency shift -0.194339 THz\n\nPeak # 2\n----------------------------------------------\nWidth 0.531374 THz\nPosition 4.473540 THz\nArea () (Lorentzian) 0.029343 eV\nArea () (Total) 0.027597 eV\n<|dQ/dt|^2> 0.058686 eV\nOccupation number 19.430578\nFit temperature 680.883835 K\nBase line -0.000049 eV * ps\nMaximum height 0.035155 eV * ps\nFitting global error 0.015967\nFrequency shift -0.194339 THz\n\nPeak # 3\n----------------------------------------------\nWidth 0.538267 THz\nPosition 10.993312 THz\nArea () (Lorentzian) 0.062518 eV\nArea () (Total) 0.058145 eV\n<|dQ/dt|^2> 0.125036 eV\nOccupation number 16.779904\nFit temperature 1450.579488 K\nBase line -0.000158 eV * ps\nMaximum height 0.073941 eV * ps\nFitting global error 0.008088\nFrequency shift -0.317902 THz\n\nPeak # 4\n----------------------------------------------\nWidth 0.776728 THz\nPosition 12.855329 THz\nArea () (Lorentzian) 0.017087 eV\nArea () (Total) 0.019549 eV\n<|dQ/dt|^2> 0.034174 eV\nOccupation number 3.538695\nFit temperature 394.533163 K\nBase line 0.000136 eV * ps\nMaximum height 0.014005 eV * ps\nFitting global error 0.044153\nFrequency shift -0.299509 THz\n\nPeak # 5\n----------------------------------------------\nWidth 0.629022 THz\nPosition 14.951429 THz\nArea () (Lorentzian) 0.062984 eV\nArea () (Total) 0.068437 eV\n<|dQ/dt|^2> 0.125967 eV\nOccupation number 12.300000\nFit temperature 1461.048221 K\nBase line 0.000325 eV * ps\nMaximum height 0.063744 eV * ps\nFitting global error 0.012067\nFrequency shift -0.475017 THz\n\nPeak # 6\n----------------------------------------------\nWidth 0.629022 THz\nPosition 14.951429 THz\nArea () (Lorentzian) 0.062984 eV\nArea () (Total) 0.068437 eV\n<|dQ/dt|^2> 0.125967 eV\nOccupation number 12.300000\nFit temperature 1461.048221 K\nBase line 0.000325 eV * ps\nMaximum height 0.063744 eV * ps\nFitting global error 0.012067\nFrequency shift -0.475017 THz\n\nQ-point: 23 / 32 [ 0.50000 0.75000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.25 0. 0.75]\n\nQ-point: 24 / 32 [ 0.50000 0.00000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nSkipped, equivalent to [0.5 0.5 0.5]\n\nQ-point: 25 / 32 [ 0.75000 0.25000 0.50000 ]\nHarmonic frequencies (THz):\n[ 7.54249562 7.54249562 11.3503204 11.3503204 15.23833788 15.23833788]\nSkipped, equivalent to [0.25 0.5 0.75]\n\nQ-point: 26 / 32 [ 0.75000 0.50000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.25 0. 0.75]\n\nQ-point: 27 / 32 [ 0.75000 0.75000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66397327 4.66397327 6.89816884 15.17048811 15.55567884 15.55567884]\nSkipped, equivalent to [0. 0.75 0.75]\n\nQ-point: 28 / 32 [ 0.75000 0.00000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.75 0.5 0.75]\n\nQ-point: 29 / 32 [ 0.00000 0.25000 0.75000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.75 0.5 0.75]\n\nQ-point: 30 / 32 [ 0.00000 0.50000 0.00000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nSkipped, equivalent to [0.5 0.5 0.5]\n\nQ-point: 31 / 32 [ 0.00000 0.75000 0.25000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 6.96109048 9.00584683 13.72491589 15.42644585 15.58275543]\nSkipped, equivalent to [0.75 0.5 0.75]\n\nQ-point: 32 / 32 [ 0.00000 0.00000 0.50000 ]\nHarmonic frequencies (THz):\n[ 4.66787904 4.66787904 11.31121369 13.15483786 15.42644585 15.42644585]\nSkipped, equivalent to [0.5 0.5 0.5]\n" }, { "data": { "text/plain": "array([[[[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]],\n\n [[-8.53720262e-03, 7.27856464e-04, -8.95058148e-04],\n [ 7.27856464e-04, 7.22093450e-03, 8.95058148e-04],\n [-8.95058148e-04, 8.95058148e-04, 8.58955541e-03]],\n\n [[ 7.22093450e-03, 7.27856464e-04, 8.95058148e-04],\n [ 7.27856464e-04, -8.53720262e-03, -8.95058148e-04],\n [ 8.95058148e-04, -8.95058148e-04, 8.58955541e-03]],\n\n ...,\n\n [[-4.44967060e-03, 1.03899911e-04, -2.92254418e-03],\n [ 1.03899911e-04, 3.86955298e-03, 9.18164273e-03],\n [-2.92254418e-03, 9.18164273e-03, 2.64253878e-03]],\n\n [[ 3.86955298e-03, 1.03899911e-04, 9.18164273e-03],\n [ 1.03899911e-04, -4.44967060e-03, -2.92254418e-03],\n [ 9.18164273e-03, -2.92254418e-03, 2.64253878e-03]],\n\n [[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]]],\n\n\n [[[-8.53720262e-03, 7.27856464e-04, -8.95058148e-04],\n [ 7.27856464e-04, 7.22093450e-03, 8.95058148e-04],\n [-8.95058148e-04, 8.95058148e-04, 8.58955541e-03]],\n\n [[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]],\n\n [[ 5.72248779e-03, -7.27856464e-04, -8.95058148e-04],\n [-7.27856464e-04, 5.72248779e-03, -8.95058148e-04],\n [-8.95058148e-04, -8.95058148e-04, 1.30276827e-02]],\n\n ...,\n\n [[-3.48139117e+00, -2.36186546e+00, 2.36468410e+00],\n [-2.36186546e+00, -3.48139117e+00, 2.36468410e+00],\n [ 2.36468410e+00, 2.36468410e+00, -3.48016416e+00]],\n\n [[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]],\n\n [[ 3.86955298e-03, 1.03899911e-04, 9.18164273e-03],\n [ 1.03899911e-04, -4.44967060e-03, -2.92254418e-03],\n [ 9.18164273e-03, -2.92254418e-03, 2.64253878e-03]]],\n\n\n [[[ 7.22093450e-03, 7.27856464e-04, 8.95058148e-04],\n [ 7.27856464e-04, -8.53720262e-03, -8.95058148e-04],\n [ 8.95058148e-04, -8.95058148e-04, 8.58955541e-03]],\n\n [[ 5.72248779e-03, -7.27856464e-04, -8.95058148e-04],\n [-7.27856464e-04, 5.72248779e-03, -8.95058148e-04],\n [-8.95058148e-04, -8.95058148e-04, 1.30276827e-02]],\n\n [[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]],\n\n ...,\n\n [[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]],\n\n [[-3.48139117e+00, -2.36186546e+00, 2.36468410e+00],\n [-2.36186546e+00, -3.48139117e+00, 2.36468410e+00],\n [ 2.36468410e+00, 2.36468410e+00, -3.48016416e+00]],\n\n [[-4.44967060e-03, 1.03899911e-04, -2.92254418e-03],\n [ 1.03899911e-04, 3.86955298e-03, 9.18164273e-03],\n [-2.92254418e-03, 9.18164273e-03, 2.64253878e-03]]],\n\n\n ...,\n\n\n [[[-4.44967060e-03, 1.03899911e-04, -2.92254418e-03],\n [ 1.03899911e-04, 3.86955298e-03, 9.18164273e-03],\n [-2.92254418e-03, 9.18164273e-03, 2.64253878e-03]],\n\n [[-3.48139117e+00, -2.36186546e+00, 2.36468410e+00],\n [-2.36186546e+00, -3.48139117e+00, 2.36468410e+00],\n [ 2.36468410e+00, 2.36468410e+00, -3.48016416e+00]],\n\n [[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]],\n\n ...,\n\n [[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]],\n\n [[ 5.72248779e-03, -7.27856464e-04, -8.95058148e-04],\n [-7.27856464e-04, 5.72248779e-03, -8.95058148e-04],\n [-8.95058148e-04, -8.95058148e-04, 1.30276827e-02]],\n\n [[ 7.22093450e-03, 7.27856464e-04, 8.95058148e-04],\n [ 7.27856464e-04, -8.53720262e-03, -8.95058148e-04],\n [ 8.95058148e-04, -8.95058148e-04, 8.58955541e-03]]],\n\n\n [[[ 3.86955298e-03, 1.03899911e-04, 9.18164273e-03],\n [ 1.03899911e-04, -4.44967060e-03, -2.92254418e-03],\n [ 9.18164273e-03, -2.92254418e-03, 2.64253878e-03]],\n\n [[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]],\n\n [[-3.48139117e+00, -2.36186546e+00, 2.36468410e+00],\n [-2.36186546e+00, -3.48139117e+00, 2.36468410e+00],\n [ 2.36468410e+00, 2.36468410e+00, -3.48016416e+00]],\n\n ...,\n\n [[ 5.72248779e-03, -7.27856464e-04, -8.95058148e-04],\n [-7.27856464e-04, 5.72248779e-03, -8.95058148e-04],\n [-8.95058148e-04, -8.95058148e-04, 1.30276827e-02]],\n\n [[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]],\n\n [[-8.53720262e-03, 7.27856464e-04, -8.95058148e-04],\n [ 7.27856464e-04, 7.22093450e-03, 8.95058148e-04],\n [-8.95058148e-04, 8.95058148e-04, 8.58955541e-03]]],\n\n\n [[[ 4.35320043e-03, -8.69200588e-04, 7.43830393e-03],\n [-8.69200588e-04, 4.35320043e-03, 7.43830393e-03],\n [ 7.43830393e-03, 7.43830393e-03, 1.98168743e-03]],\n\n [[ 3.86955298e-03, 1.03899911e-04, 9.18164273e-03],\n [ 1.03899911e-04, -4.44967060e-03, -2.92254418e-03],\n [ 9.18164273e-03, -2.92254418e-03, 2.64253878e-03]],\n\n [[-4.44967060e-03, 1.03899911e-04, -2.92254418e-03],\n [ 1.03899911e-04, 3.86955298e-03, 9.18164273e-03],\n [-2.92254418e-03, 9.18164273e-03, 2.64253878e-03]],\n\n ...,\n\n [[ 7.22093450e-03, 7.27856464e-04, 8.95058148e-04],\n [ 7.27856464e-04, -8.53720262e-03, -8.95058148e-04],\n [ 8.95058148e-04, -8.95058148e-04, 8.58955541e-03]],\n\n [[-8.53720262e-03, 7.27856464e-04, -8.95058148e-04],\n [ 7.27856464e-04, 7.22093450e-03, 8.95058148e-04],\n [-8.95058148e-04, 8.95058148e-04, 8.58955541e-03]],\n\n [[ 1.47903370e+01, -7.27856464e-04, 8.95058148e-04],\n [-7.27856464e-04, 1.47903370e+01, 8.95058148e-04],\n [ 8.95058148e-04, 8.95058148e-04, 1.47889684e+01]]]])" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "calculation = Quasiparticle(trajectory)\n", "calculation.select_power_spectra_algorithm(2) # select FFT algorithm\n", "calculation.get_renormalized_phonon_dispersion_bands()\n", "renormalized_force_constants = (\n", " calculation.get_renormalized_force_constants().get_array()\n", ")\n", "renormalized_force_constants" ] }, { "cell_type": "markdown", "id": "2eb26d68-9d7e-45de-9b97-013a8e7e11bb", "metadata": {}, "source": "It calculates the re-normalized force constants which can then be used to calculate the finite temperature properties. " }, { "cell_type": "markdown", "id": "30bdcd29-a41b-4781-a2cd-6af0ba290883", "metadata": {}, "source": "In addition the [DynaPhoPy](https://abelcarreras.github.io/DynaPhoPy/) package can be used to directly compare the \nfinite temperature phonon spectrum with the 0K phonon spectrum calulated with the finite displacement method: " }, { "cell_type": "code", "execution_count": 16, "id": "8d8239ad-30eb-4f7a-a5aa-91e5030fa74d", "metadata": { "trusted": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": "
" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "calculation.plot_renormalized_phonon_dispersion_bands()" ] }, { "cell_type": "markdown", "id": "c5bada5c-706c-4d5c-9141-1d6bd146d445", "metadata": {}, "source": "### Langevin Thermostat \nIn addition to the molecular dynamics implemented in the LAMMPS simulation code, the `atomistics` package also provides\nthe `LangevinWorkflow` which implements molecular dynamics independent of the specific simulation code. \n" }, { "cell_type": "code", "execution_count": 17, "id": "fa69a7f8-940a-4fb9-aae3-1ac68d4255f2", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib_library_interface, get_potential_by_name\n", "from atomistics.workflows import LangevinWorkflow\n", "from pylammpsmpi import LammpsASELibrary\n", "\n", "steps = 300\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "workflow = LangevinWorkflow(\n", " structure=bulk(\"Al\", cubic=True).repeat([2, 2, 2]),\n", " temperature=1000.0,\n", " overheat_fraction=2.0,\n", " damping_timescale=100.0,\n", " time_step=1,\n", ")\n", "lmp = LammpsASELibrary(\n", " working_directory=None,\n", " cores=1,\n", " comm=None,\n", " logger=None,\n", " log_file=None,\n", " library=None,\n", " disable_log_file=True,\n", ")\n", "eng_pot_lst, eng_kin_lst = [], []\n", "for i in range(steps):\n", " task_dict = workflow.generate_structures()\n", " result_dict = evaluate_with_lammpslib_library_interface(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", " lmp=lmp,\n", " )\n", " eng_pot, eng_kin = workflow.analyse_structures(output_dict=result_dict)\n", " eng_pot_lst.append(eng_pot)\n", " eng_kin_lst.append(eng_kin)\n", "lmp.close()" ] }, { "cell_type": "markdown", "id": "d77f71c6-7afd-496d-a3bf-db517623d159", "metadata": {}, "source": "The advantage of this implementation is that the user can directly interact with the simulation between the individual\nmolecular dynamics simulation steps. This provides a lot of flexibility to prototype new simulation methods. The input\nparameters of the `LangevinWorkflow` are:\n\n* `structure` the `ase.atoms.Atoms` object which is used as initial structure for the molecular dynamics calculation \n* `temperature` the temperature of the molecular dynamics calculation given in Kelvin\n* `overheat_fraction` the over heating fraction of the Langevin thermostat\n* `damping_timescale` the damping timescale of the Langevin thermostat \n* `time_step` the time steps of the Langevin thermostat\n" }, { "cell_type": "markdown", "id": "6944d8c5-718d-4d87-956c-d456c151c331", "metadata": {}, "source": "## Harmonic Approximation \nThe harmonic approximation is implemented in two variations, once with constant volume and once including the volume \nexpansion at finite temperature also known as quasi-harmonic approximation. Both of these are based on the [phonopy](https://phonopy.github.io/phonopy/)\npackage. " }, { "cell_type": "markdown", "id": "4f699026-d1a8-47a3-b354-6c8572550a50", "metadata": {}, "source": "### Phonons \nTo calculate the phonons at a fixed volume the `PhonopyWorkflow` is used:" }, { "cell_type": "code", "execution_count": 18, "id": "7ac74f80-d613-4a96-b841-5a2973b949a9", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import PhonopyWorkflow\n", "from phonopy.units import VaspToTHz\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "workflow = PhonopyWorkflow(\n", " structure=bulk(\"Al\", cubic=True),\n", " interaction_range=10,\n", " factor=VaspToTHz,\n", " displacement=0.01,\n", " dos_mesh=20,\n", " primitive_matrix=None,\n", " number_of_snapshots=None,\n", ")\n", "task_dict = workflow.generate_structures()\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "phonopy_dict = workflow.analyse_structures(output_dict=result_dict)" ] }, { "cell_type": "markdown", "id": "0528bcb2-55ea-4df0-a0b6-71c99dbd9f57", "metadata": {}, "source": "The `PhonopyWorkflow` takes the following inputs: \n\n* `structure` the `ase.atoms.Atoms` object to calculate the phonon spectrum\n* `interaction_range` the cutoff radius to consider for identifying the interaction between the atoms\n* `factor` conversion factor, typically just `phonopy.units.VaspToTHz` \n* `displacement` displacement to calculate the forces \n* `dos_mesh` mesh for the density of states \n* `primitive_matrix` primitive matrix\n* `number_of_snapshots` number of snapshots to calculate\n\nIn addition to the phonon properties, the `PhonopyWorkflow` also enables the calculation of thermal properties: " }, { "cell_type": "code", "execution_count": 19, "id": "467a9752-e842-43ef-9233-96663b7086dd", "metadata": { "trusted": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": "{'temperatures': array([1.000e+00, 5.100e+01, 1.010e+02, 1.510e+02, 2.010e+02, 2.510e+02,\n 3.010e+02, 3.510e+02, 4.010e+02, 4.510e+02, 5.010e+02, 5.510e+02,\n 6.010e+02, 6.510e+02, 7.010e+02, 7.510e+02, 8.010e+02, 8.510e+02,\n 9.010e+02, 9.510e+02, 1.001e+03, 1.051e+03, 1.101e+03, 1.151e+03,\n 1.201e+03, 1.251e+03, 1.301e+03, 1.351e+03, 1.401e+03, 1.451e+03,\n 1.501e+03]), 'volumes': array([66.430125, 66.430125, 66.430125, 66.430125, 66.430125, 66.430125,\n 66.430125, 66.430125, 66.430125, 66.430125, 66.430125, 66.430125,\n 66.430125, 66.430125, 66.430125, 66.430125, 66.430125, 66.430125,\n 66.430125, 66.430125, 66.430125, 66.430125, 66.430125, 66.430125,\n 66.430125, 66.430125, 66.430125, 66.430125, 66.430125, 66.430125,\n 66.430125]), 'free_energy': array([ 0.14914132, 0.14837894, 0.13954171, 0.11738723, 0.08264779,\n 0.03712237, -0.01759836, -0.08025513, -0.14986079, -0.22563203,\n -0.30693668, -0.39325592, -0.48415731, -0.57927552, -0.67829812,\n -0.78095507, -0.88701079, -0.99625805, -1.10851315, -1.22361223,\n -1.3414082 , -1.46176834, -1.58457228, -1.70971039, -1.8370824 ,\n -1.96659625, -2.09816715, -2.23171671, -2.3671723 , -2.5044664 ,\n -2.64353611]), 'entropy': array([1.10364016e-08, 5.98829810e+00, 2.96478195e+01, 5.54593816e+01,\n 7.80099308e+01, 9.71787932e+01, 1.13608521e+02, 1.27894607e+02,\n 1.40492150e+02, 1.51738264e+02, 1.61883985e+02, 1.71119149e+02,\n 1.79589851e+02, 1.87410480e+02, 1.94672040e+02, 2.01447985e+02,\n 2.07798389e+02, 2.13772961e+02, 2.19413270e+02, 2.24754417e+02,\n 2.29826293e+02, 2.34654555e+02, 2.39261386e+02, 2.43666089e+02,\n 2.47885561e+02, 2.51934678e+02, 2.55826598e+02, 2.59573021e+02,\n 2.63184393e+02, 2.66670075e+02, 2.70038493e+02]), 'heat_capacity': array([1.78544597e-07, 1.73410821e+01, 5.37349237e+01, 7.35976295e+01,\n 8.34733324e+01, 8.87978444e+01, 9.19287453e+01, 9.39060819e+01,\n 9.52277477e+01, 9.61520364e+01, 9.68225162e+01, 9.73237288e+01,\n 9.77079209e+01, 9.80087218e+01, 9.82485402e+01, 9.84427587e+01,\n 9.86022130e+01, 9.87347097e+01, 9.88459861e+01, 9.89403338e+01,\n 9.90210141e+01, 9.90905402e+01, 9.91508741e+01, 9.92035655e+01,\n 9.92498509e+01, 9.92907269e+01, 9.93270039e+01, 9.93593459e+01,\n 9.93883017e+01, 9.94143276e+01, 9.94378055e+01])}\n" } ], "source": [ "tp_dict = workflow.get_thermal_properties(\n", " t_min=1,\n", " t_max=1500,\n", " t_step=50,\n", " temperatures=None,\n", " cutoff_frequency=None,\n", " pretend_real=False,\n", " band_indices=None,\n", " is_projection=False,\n", ")\n", "print(tp_dict)" ] }, { "cell_type": "markdown", "id": "d8c4ac48-293a-45f9-bf77-cca3cc275e52", "metadata": {}, "source": "The calculation of the thermal properties takes additional inputs: \n\n* `t_min` minimum temperature\n* `t_max` maximum temperature\n* `t_step` temperature step \n* `temperatures` alternative to `t_min`, `t_max` and `t_step` the array of temperatures can be defined directly\n* `cutoff_frequency` cutoff frequency to exclude the contributions of frequencies below a certain cut off\n* `pretend_real` use the absolute values of the phonon frequencies\n* `band_indices` select bands based on their indices \n* `is_projection` multiplies the squared eigenvectors - not recommended\n\nFurthermore, also the dynamical matrix can be directly calculated with the `PhonopyWorkflow`:\n" }, { "cell_type": "code", "execution_count": 20, "id": "0856938b-b1cd-40ce-95b7-4605f10ee7a4", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "array([[ 1.72794621e-01, 6.42929783e-20, -6.22838227e-20,\n -1.55150365e-18, 1.42759084e-35, -1.50515236e-19,\n 4.11475061e-18, 4.82197337e-20, 9.98736570e-02,\n 8.87128656e-18, -1.02675017e-33, -1.50493730e-19],\n [ 6.42929783e-20, 1.40379905e-01, 6.83112895e-20,\n 2.05216191e-35, 8.80589092e-18, 1.94854949e-33,\n 1.60732446e-20, 1.02868765e-18, -1.60732446e-20,\n -1.10192213e-34, 8.80589092e-18, 2.23061078e-36],\n [-6.22838227e-20, 6.83112895e-20, 1.72794621e-01,\n -1.50493730e-19, 1.25694783e-34, 8.87128656e-18,\n 9.98736570e-02, 3.21464892e-20, 0.00000000e+00,\n -1.50515236e-19, 1.47219713e-35, -1.55150365e-18],\n [-1.55150365e-18, 2.05216191e-35, -1.50493730e-19,\n 1.72794621e-01, -6.63021339e-20, 6.42929783e-20,\n 8.87128656e-18, -1.03065371e-33, -1.50493730e-19,\n 1.85163778e-17, 8.03662229e-20, 9.98736570e-02],\n [ 1.42759084e-35, 8.80589092e-18, 1.25694783e-34,\n -6.63021339e-20, 1.40379905e-01, 6.42929783e-20,\n -2.28392231e-33, 8.80589092e-18, 2.67635707e-36,\n 0.00000000e+00, 0.00000000e+00, -1.60732446e-20],\n [-1.50515236e-19, 1.94854949e-33, 8.87128656e-18,\n 6.42929783e-20, 6.42929783e-20, 1.72794621e-01,\n -1.50515236e-19, -4.46122155e-37, -1.55150365e-18,\n 9.98736570e-02, 0.00000000e+00, -1.85163778e-17],\n [ 4.11475061e-18, 1.60732446e-20, 9.98736570e-02,\n 8.87128656e-18, -2.28392231e-33, -1.50515236e-19,\n 1.72794621e-01, 6.63021339e-20, -6.42929783e-20,\n -1.55150365e-18, 6.24500783e-36, -1.50493730e-19],\n [ 4.82197337e-20, 1.02868765e-18, 3.21464892e-20,\n -1.03065371e-33, 8.80589092e-18, -4.46122155e-37,\n 6.63021339e-20, 1.40379905e-01, 6.83112895e-20,\n 1.07069317e-35, 8.80589092e-18, -6.89481791e-34],\n [ 9.98736570e-02, -1.60732446e-20, 0.00000000e+00,\n -1.50493730e-19, 2.67635707e-36, -1.55150365e-18,\n -6.42929783e-20, 6.83112895e-20, 1.72794621e-01,\n -1.50515236e-19, 1.81950725e-33, 8.87128656e-18],\n [ 8.87128656e-18, -1.10192213e-34, -1.50515236e-19,\n 1.85163778e-17, 0.00000000e+00, 9.98736570e-02,\n -1.55150365e-18, 1.07069317e-35, -1.50515236e-19,\n 1.72794621e-01, 6.42929783e-20, -6.22838227e-20],\n [-1.02675017e-33, 8.80589092e-18, 1.47219713e-35,\n 8.03662229e-20, 0.00000000e+00, 0.00000000e+00,\n 6.24500783e-36, 8.80589092e-18, 1.81950725e-33,\n 6.42929783e-20, 1.40379905e-01, 6.83112895e-20],\n [-1.50493730e-19, 2.23061078e-36, -1.55150365e-18,\n 9.98736570e-02, -1.60732446e-20, -1.85163778e-17,\n -1.50493730e-19, -6.89481791e-34, 8.87128656e-18,\n -6.22838227e-20, 6.83112895e-20, 1.72794621e-01]])" }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat = workflow.get_dynamical_matrix()\n", "mat" ] }, { "cell_type": "markdown", "id": "93bc3fbe-fe43-42d4-aaf9-12ef9994e923", "metadata": {}, "source": "Or alternatively the hesse matrix:" }, { "cell_type": "code", "execution_count": 21, "id": "c3154b6d-50c1-4327-b7cc-00f48b31fd37", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "array([[ 4.50127147e-02, -1.92714960e-33, 8.52306995e-33, ...,\n -6.63514216e-05, 8.82979633e-06, 5.93920137e-05],\n [-5.07378488e-34, 4.50127147e-02, 5.07378488e-34, ...,\n 8.82979633e-06, -6.63514216e-05, 5.93920137e-05],\n [ 5.07378488e-34, -5.07378488e-34, 4.50127147e-02, ...,\n 5.93659141e-05, 5.93659141e-05, 1.73512126e-05],\n ...,\n [-6.63514216e-05, 8.82979633e-06, 5.93920137e-05, ...,\n 4.50127147e-02, -1.92714960e-33, 8.52306995e-33],\n [ 8.82979633e-06, -6.63514216e-05, 5.93920137e-05, ...,\n -5.07378488e-34, 4.50127147e-02, 5.07378488e-34],\n [ 5.93659141e-05, 5.93659141e-05, 1.73512126e-05, ...,\n 5.07378488e-34, -5.07378488e-34, 4.50127147e-02]])" }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat = workflow.get_hesse_matrix()\n", "mat" ] }, { "cell_type": "markdown", "id": "ebc0a064-af95-42e4-854e-67bdb1065ac6", "metadata": {}, "source": "Finally, also the function to calculate the band structure is directly available on the `PhonopyWorkflow`: " }, { "cell_type": "code", "execution_count": 22, "id": "a9655fa5-bf39-47f2-ae30-0450b40bf252", "metadata": { "trusted": true }, "outputs": [], "source": [ "band_structure = workflow.get_band_structure(\n", " npoints=101, with_eigenvectors=False, with_group_velocities=False\n", ")" ] }, { "cell_type": "markdown", "id": "e8d2dcce-a5c6-4301-8c0e-bf0ca11043e9", "metadata": {}, "source": "This band structure can also be visualised using the built-in plotting function: " }, { "cell_type": "code", "execution_count": 23, "id": "4ad1f1e4-9496-4e99-afa0-fd67c72c26f4", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "" }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": "
" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "workflow.plot_band_structure()" ] }, { "cell_type": "markdown", "id": "ae251474-875a-4af2-9290-74e9785490cd", "metadata": {}, "source": "Just like the desnsity of states which can be plotted using:" }, { "cell_type": "code", "execution_count": 24, "id": "82da60b3-3930-4ff1-879e-65895112aecb", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "" }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": "
" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "workflow.plot_dos()" ] }, { "cell_type": "markdown", "id": "93e6fb35-cc50-4235-9885-406c41c6a486", "metadata": {}, "source": "### Quasi-harmonic Approximation \nTo include the volume expansion with finite temperature the `atomistics` package implements the `QuasiHarmonicWorkflow`:" }, { "cell_type": "code", "execution_count": 25, "id": "9387e3aa-b349-49a9-b7b9-0ac1d7f209d5", "metadata": { "trusted": true }, "outputs": [], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import QuasiHarmonicWorkflow\n", "\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "workflow = QuasiHarmonicWorkflow(\n", " structure=bulk(\"Al\", cubic=True),\n", " num_points=11,\n", " vol_range=0.05,\n", " interaction_range=10,\n", " factor=VaspToTHz,\n", " displacement=0.01,\n", " dos_mesh=20,\n", " primitive_matrix=None,\n", " number_of_snapshots=None,\n", ")\n", "task_dict = workflow.generate_structures()\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=task_dict,\n", " potential_dataframe=potential_dataframe,\n", ")\n", "fit_dict = workflow.analyse_structures(output_dict=result_dict)" ] }, { "cell_type": "markdown", "id": "b5167f8d-c90f-4bf0-a7c0-fd4dfdd35667", "metadata": {}, "source": "The `QuasiHarmonicWorkflow` is a combination of the `EnergyVolumeCurveWorkflow` and the `PhonopyWorkflow`. Consequently, \nthe inputs are a superset of the inputs of these two workflows. " }, { "cell_type": "markdown", "id": "169ddaf9-7f5d-4126-babf-9f2de3793128", "metadata": {}, "source": "Based on the `QuasiHarmonicWorkflow` the thermal properties can be calculated:" }, { "cell_type": "code", "execution_count": 26, "id": "07cc0818-15a8-4508-ba97-c3a95eaa72b1", "metadata": { "trusted": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": "{'temperatures': array([1.000e+00, 5.100e+01, 1.010e+02, 1.510e+02, 2.010e+02, 2.510e+02,\n 3.010e+02, 3.510e+02, 4.010e+02, 4.510e+02, 5.010e+02, 5.510e+02,\n 6.010e+02, 6.510e+02, 7.010e+02, 7.510e+02, 8.010e+02, 8.510e+02,\n 9.010e+02, 9.510e+02, 1.001e+03, 1.051e+03, 1.101e+03, 1.151e+03,\n 1.201e+03, 1.251e+03, 1.301e+03, 1.351e+03, 1.401e+03, 1.451e+03,\n 1.501e+03]), 'volumes': [66.71710763927429, 66.7217721669909, 66.7588030456557, 66.82252047263532, 66.89849494958942, 66.9796340113892, 67.06260790999332, 67.14571406293086, 67.22800412575396, 67.30891433769602, 67.38809533263267, 67.46532691223801, 67.54047194450261, 67.61344961442688, 67.68421888050003, 67.7527676376025, 67.81910525012583, 67.88325718224746, 67.94526099996934, 68.00516331349996, 68.06301739227649, 68.11888127927111, 68.1728162874363, 68.22488579579438, 68.27515428480372, 68.32368656530063, 68.3705471654382, 68.41579984727981, 68.45950723009813, 68.50173050155158, 68.54252920118272], 'free_energy': array([ 0.14903662, 0.14826796, 0.13934608, 0.1169922 , 0.08193524,\n 0.03597463, -0.01929655, -0.08261538, -0.15299036, -0.22963345,\n -0.31190757, -0.39928889, -0.49134004, -0.5876908 , -0.68802399,\n -0.79206502, -0.89957393, -1.01033927, -1.12417341, -1.24090869,\n -1.36039449, -1.48249475, -1.60708597, -1.73405557, -1.86330055,\n -1.99472628, -2.12824554, -2.26377775, -2.40124816, -2.54058732,\n -2.6817305 ]), 'entropy': array([1.02970750e-08, 5.98072651e+00, 2.96865053e+01, 5.55852668e+01,\n 7.82409727e+01, 9.75218995e+01, 1.14065625e+02, 1.28465273e+02,\n 1.41174728e+02, 1.52530436e+02, 1.62783056e+02, 1.72122199e+02,\n 1.80693841e+02, 1.88612312e+02, 1.95968600e+02, 2.02836175e+02,\n 2.09275150e+02, 2.15335286e+02, 2.21058222e+02, 2.26479132e+02,\n 2.31627991e+02, 2.36530543e+02, 2.41209060e+02, 2.45682935e+02,\n 2.49969156e+02, 2.54082691e+02, 2.58036788e+02, 2.61843234e+02,\n 2.65512561e+02, 2.69054215e+02, 2.72476702e+02]), 'heat_capacity': array([1.67065980e-07, 1.73540235e+01, 5.38037700e+01, 7.36871465e+01,\n 8.35644372e+01, 8.88841670e+01, 9.20085315e+01, 9.39792227e+01,\n 9.52946945e+01, 9.62133951e+01, 9.68788951e+01, 9.73756862e+01,\n 9.77559504e+01, 9.80532534e+01, 9.82899463e+01, 9.84813619e+01,\n 9.86382931e+01, 9.87685101e+01, 9.88777197e+01, 9.89701872e+01,\n 9.90491516e+01, 9.91171073e+01, 9.91760000e+01, 9.92273651e+01,\n 9.92724273e+01, 9.93121724e+01, 9.93474017e+01, 9.93787712e+01,\n 9.94068224e+01, 9.94320054e+01, 9.94546967e+01])}\n" } ], "source": [ "tp_dict = workflow.get_thermal_properties(\n", " t_min=1,\n", " t_max=1500,\n", " t_step=50,\n", " temperatures=None,\n", " cutoff_frequency=None,\n", " pretend_real=False,\n", " band_indices=None,\n", " is_projection=False,\n", " quantum_mechanical=True,\n", ")\n", "print(tp_dict)" ] }, { "cell_type": "markdown", "id": "1fb5c6e3-83a4-4503-a0f1-4958ebc6361c", "metadata": {}, "source": "This requires the same inputs as the calculation of the thermal properties `get_thermal_properties()` with the \n`PhonopyWorkflow`. The additional parameter `quantum_mechanical` specifies whether the classical harmonic oscillator or \nthe quantum mechanical harmonic oscillator is used to calculate the free energy. " }, { "cell_type": "markdown", "id": "3e6cc3bd-5f7c-4462-8083-5111dc5d4577", "metadata": {}, "source": "And finally also the thermal expansion can be calculated:" }, { "cell_type": "code", "execution_count": 27, "id": "76426cc0-38c8-480e-9fd1-fbcb41c8afec", "metadata": { "trusted": true }, "outputs": [], "source": [ "tp_dict = workflow.get_thermal_properties(\n", " t_min=1,\n", " t_max=1500,\n", " t_step=50,\n", " temperatures=None,\n", " cutoff_frequency=None,\n", " pretend_real=False,\n", " band_indices=None,\n", " is_projection=False,\n", " quantum_mechanical=True,\n", " output_keys=[\"free_energy\", \"temperatures\", \"volumes\"],\n", ")\n", "temperatures, volumes = tp_dict[\"temperatures\"], tp_dict[\"volumes\"]" ] }, { "cell_type": "markdown", "id": "3cf34091-d7f5-464a-b386-9b81c1fa853a", "metadata": {}, "source": "## Structure Optimization \nIn analogy to the molecular dynamics calculation also the structure optimization could in principle be defined inside \nthe simulation code or on the python level. Still currently the `atomistics` package only supports the structure \noptimization defined inside the simulation codes. " }, { "cell_type": "markdown", "id": "e58b5d2e-8839-48c6-b72e-0fa09ace20ce", "metadata": {}, "source": "### Volume and Positions \nTo optimize both the volume of the supercell as well as the positions inside the supercell the `atomistics` package\nimplements the `optimize_positions_and_volume()` workflow:" }, { "cell_type": "code", "execution_count": 28, "id": "a7f38a78-11b9-41c2-82c9-7c30b3a9b005", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "Atoms(symbols='Al4', pbc=True, cell=[[4.05000466219724, 2.4799126230458533e-16, 2.4799126230458533e-16], [0.0, 4.05000466219724, 2.4799126230458533e-16], [0.0, 0.0, 4.05000466219724]])" }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import optimize_positions_and_volume\n", "\n", "structure = bulk(\"Al\", a=4.0, cubic=True)\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=optimize_positions_and_volume(structure=structure),\n", " potential_dataframe=potential_dataframe,\n", ")\n", "structure_opt = result_dict[\"structure_with_optimized_positions_and_volume\"]\n", "structure_opt" ] }, { "cell_type": "markdown", "id": "c375f310-78c2-426a-8f77-669e9bec855f", "metadata": {}, "source": "The result is the optimized atomistic structure as part of the result dictionary. " }, { "cell_type": "markdown", "id": "6d4ef070-f0f1-4f56-afff-ff6322d3729a", "metadata": {}, "source": "### Positions \nThe optimization of the positions inside the supercell without the optimization of the supercell volume is possible with\nthe `optimize_positions()` workflow:" }, { "cell_type": "code", "execution_count": 29, "id": "9a50125b-a97a-4445-b140-b8019c035902", "metadata": { "trusted": true }, "outputs": [ { "data": { "text/plain": "Atoms(symbols='Al4', pbc=True, cell=[4.0, 4.0, 4.0])" }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ase.build import bulk\n", "from atomistics.calculators import evaluate_with_lammpslib, get_potential_by_name\n", "from atomistics.workflows import optimize_positions\n", "\n", "structure = bulk(\"Al\", a=4.0, cubic=True)\n", "potential_dataframe = get_potential_by_name(\n", " potential_name=\"1999--Mishin-Y--Al--LAMMPS--ipr1\", resource_path=\"static/lammps\"\n", ")\n", "result_dict = evaluate_with_lammpslib(\n", " task_dict=optimize_positions(structure=structure),\n", " potential_dataframe=potential_dataframe,\n", ")\n", "structure_opt = result_dict[\"structure_with_optimized_positions\"]\n", "structure_opt" ] }, { "cell_type": "markdown", "id": "d027161c-abd3-4267-a10f-cb404c3ebbfd", "metadata": {}, "source": "The result is the optimized atomistic structure as part of the result dictionary. " }, { "cell_type": "code", "execution_count": null, "id": "a84ef4fc-a9a7-4386-921f-7b77af81a166", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }