Commit b275cb13 by psd

### Exercise-10

parent 6f005725
 { "cells": [], "metadata": {}, "nbformat": 4, "nbformat_minor": 2 }
 { "cells": [ { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "import itertools\n", "import numpy as np\n", "from numpy.linalg import norm\n", "import spglib\n", "from glob import glob\n", "\n", "from ase import Atoms\n", "from ase.io import read\n", "from ase.spacegroup import crystal\n", "from ase.spacegroup import Spacegroup\n", "from ase.data import atomic_numbers, atomic_names\n", "import nglview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Crystallographic point groups" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14 P 21/c\n", " setting 1\n", " centrosymmetric 1\n", " primitive vectors\n", " 1.0000000000 0.0000000000 0.0000000000\n", " 0.0000000000 1.0000000000 0.0000000000\n", " 0.0000000000 0.0000000000 1.0000000000\n", " reciprocal vectors\n", " 1 0 0\n", " 0 1 0\n", " 0 0 1\n", " 1 subtranslations\n", " 0.0000000000 0.0000000000 0.0000000000\n", " 2 symmetry operations (rot+trans)\n", " 1 0 0 0 1 0 0 0 1 0.0000000000 0.0000000000 0.0000000000\n", " -1 0 0 0 1 0 0 0 -1 0.0000000000 0.5000000000 0.5000000000\n", "\n", "\n" ] } ], "source": [ "a=5.117\n", "b=5.175\n", "c=5.291\n", "alpha=90\n", "beta=99.22\n", "gamma=90\n", "thespacegroup=14\n", "print(Spacegroup(thespacegroup))\n", "\n", "hfo2 = crystal(symbols=['Hf','O','O'],\n", " basis=[(0.276,0.04,0.208),(0.074,0.332,0.347),(0.449,0.758,0.480)],\n", " spacegroup=thespacegroup, \n", " cellpar=[a, b, c, alpha, beta, gamma])\n", "#hfo2.write('hfo2.xyz')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "bondatoms = []\n", "symbols = hfo2.get_chemical_symbols()\n", "for i in range(len(hfo2)):\n", " for j in range(i):\n", " if (symbols[i] == 'Hf' and symbols[j] == 'O' and hfo2.get_distance(i, j) < 2.6):\n", " bondatoms.append((i, j))\n", " elif (symbols[i] == 'O' and symbols[j] == 'Hf' and hfo2.get_distance(i, j) < 2.6):\n", " bondatoms.append((i, j))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "173ee9fd9ff14be7a76bdd69a69afbe2", "version_major": 2, "version_minor": 0 }, "text/plain": [ "NGLWidget()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nglview.show_ase(hfo2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Questions:\n", "\n", " -how many atoms are contained in the unit cell?\n", " -compute the volume of the unit cell " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def ase_to_spgcell(ase_atoms=None, cell=None, inverse=False):\n", " if not inverse:\n", " assert ase_atoms is not None\n", " return (ase_atoms.get_cell(),\n", " ase_atoms.get_scaled_positions(),\n", " ase_atoms.get_atomic_numbers())\n", " else:\n", " assert cell is not None\n", " return Atoms(cell=cell[0],\n", " scaled_positions=cell[1],\n", " numbers=cell[2])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def a_equiv_b(a,b):\n", " \"\"\"Function that identifies whether two crystals are equivalent\"\"\"\n", "\n", " # getting symmetry datasets for both crystals\n", " cryst_a = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=a), symprec=1e-5, angle_tolerance=-1.0, hall_number=0)\n", " cryst_b = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=b), symprec=1e-5, angle_tolerance=-1.0, hall_number=0)\n", "\n", " samecell = np.allclose(cryst_a['std_lattice'], cryst_b['std_lattice'], atol=1e-5)\n", " samenatoms = len(cryst_a['std_positions']) == len(cryst_b['std_positions'])\n", " samespg = cryst_a['number'] == cryst_b['number']\n", " \n", " def test_rotations_translations(cryst_a, cryst_b, repeat):\n", " cell = cryst_a['std_lattice']\n", " pristine = crystal('Mg', [(0, 0., 0.)], \n", " spacegroup=int(cryst_a['number']),\n", " cellpar=[cell[0]/repeat[0], cell[1]/repeat[1], cell[2]/repeat[2]]).repeat(repeat)\n", "\n", " sym_set_p = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=pristine), symprec=1e-5,\n", " angle_tolerance=-1.0, hall_number=0)\n", "\n", " for _,trans in enumerate(zip(sym_set_p['rotations'], sym_set_p['translations'])):\n", " pnew=(np.matmul(trans[0],cryst_a['std_positions'].T).T + trans[1]) % 1.0\n", " fulln = np.concatenate([cryst_a['std_types'][:, None], pnew], axis=1)\n", " fullb = np.concatenate([cryst_b['std_types'][:, None], cryst_b['std_positions']], axis=1)\n", " sorted_n = np.array(sorted([ list(row) for row in list(fulln) ]))\n", " sorted_b = np.array(sorted([ list(row) for row in list(fullb) ]))\n", " if np.allclose(sorted_n, sorted_b, atol=1e-5):\n", " return True\n", " return False\n", "\n", " if samecell and samenatoms and samespg:\n", " cell = cryst_a['std_lattice']\n", " rng1 = range(1, int(norm(cell[0])/2.))\n", " rng2 = range(1, int(norm(cell[1])/2.))\n", " rng3 = range(1, int(norm(cell[2])/2.))\n", "\n", " for repeat in itertools.product(rng1, rng2, rng3):\n", " if test_rotations_translations(cryst_a, cryst_b, repeat):\n", " return True\n", "\n", " return False" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 1" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7261855ebc41485c8822834f33016a8d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "NGLWidget()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "atoms = read('./quartz_alpha.xyz')\n", "nglview.show_ase(atoms)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "cell = ase_to_spgcell(ase_atoms=atoms)\n", "lattice, scaled_positions, numbers = spglib.find_primitive(cell, symprec=1e-5)\n", "reduced = ase_to_spgcell(cell=(lattice, scaled_positions, numbers),inverse=True)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c0b014720e3d4c09b7430432c38b0056", "version_major": 2, "version_minor": 0 }, "text/plain": [ "NGLWidget()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nglview.show_ase(reduced)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 2" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "versions = [read(atoms) for atoms in glob('./quartz_alpha*')]\n", "\n", "for outer in range(len(versions)-1):\n", " for inner in range(outer+1,len(versions)):\n", " print('Comparing: ',outer,inner)\n", " print('Equivalent: ',a_equiv_b(versions[outer],versions[inner]))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }
 %% Cell type:code id: tags: ``` python import itertools import numpy as np from numpy.linalg import norm import spglib from glob import glob from ase import Atoms from ase.io import read from ase.spacegroup import crystal from ase.spacegroup import Spacegroup from ase.data import atomic_numbers, atomic_names import nglview ``` %% Cell type:markdown id: tags: ## Crystallographic point groups %% Cell type:code id: tags: ``` python a=5.117 b=5.175 c=5.291 alpha=90 beta=99.22 gamma=90 thespacegroup=14 print(Spacegroup(thespacegroup)) hfo2 = crystal(symbols=['Hf','O','O'], basis=[(0.276,0.04,0.208),(0.074,0.332,0.347),(0.449,0.758,0.480)], spacegroup=thespacegroup, cellpar=[a, b, c, alpha, beta, gamma]) #hfo2.write('hfo2.xyz') ``` %%%% Output: stream 14 P 21/c setting 1 centrosymmetric 1 primitive vectors 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 reciprocal vectors 1 0 0 0 1 0 0 0 1 1 subtranslations 0.0000000000 0.0000000000 0.0000000000 2 symmetry operations (rot+trans) 1 0 0 0 1 0 0 0 1 0.0000000000 0.0000000000 0.0000000000 -1 0 0 0 1 0 0 0 -1 0.0000000000 0.5000000000 0.5000000000 %% Cell type:code id: tags: ``` python bondatoms = [] symbols = hfo2.get_chemical_symbols() for i in range(len(hfo2)): for j in range(i): if (symbols[i] == 'Hf' and symbols[j] == 'O' and hfo2.get_distance(i, j) < 2.6): bondatoms.append((i, j)) elif (symbols[i] == 'O' and symbols[j] == 'Hf' and hfo2.get_distance(i, j) < 2.6): bondatoms.append((i, j)) ``` %% Cell type:code id: tags: ``` python nglview.show_ase(hfo2) ``` %%%% Output: display_data %% Cell type:markdown id: tags: Questions: -how many atoms are contained in the unit cell? -compute the volume of the unit cell %% Cell type:markdown id: tags: ## %% Cell type:code id: tags: ``` python def ase_to_spgcell(ase_atoms=None, cell=None, inverse=False): if not inverse: assert ase_atoms is not None return (ase_atoms.get_cell(), ase_atoms.get_scaled_positions(), ase_atoms.get_atomic_numbers()) else: assert cell is not None return Atoms(cell=cell[0], scaled_positions=cell[1], numbers=cell[2]) ``` %% Cell type:code id: tags: ``` python def a_equiv_b(a,b): """Function that identifies whether two crystals are equivalent""" # getting symmetry datasets for both crystals cryst_a = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=a), symprec=1e-5, angle_tolerance=-1.0, hall_number=0) cryst_b = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=b), symprec=1e-5, angle_tolerance=-1.0, hall_number=0) samecell = np.allclose(cryst_a['std_lattice'], cryst_b['std_lattice'], atol=1e-5) samenatoms = len(cryst_a['std_positions']) == len(cryst_b['std_positions']) samespg = cryst_a['number'] == cryst_b['number'] def test_rotations_translations(cryst_a, cryst_b, repeat): cell = cryst_a['std_lattice'] pristine = crystal('Mg', [(0, 0., 0.)], spacegroup=int(cryst_a['number']), cellpar=[cell[0]/repeat[0], cell[1]/repeat[1], cell[2]/repeat[2]]).repeat(repeat) sym_set_p = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=pristine), symprec=1e-5, angle_tolerance=-1.0, hall_number=0) for _,trans in enumerate(zip(sym_set_p['rotations'], sym_set_p['translations'])): pnew=(np.matmul(trans[0],cryst_a['std_positions'].T).T + trans[1]) % 1.0 fulln = np.concatenate([cryst_a['std_types'][:, None], pnew], axis=1) fullb = np.concatenate([cryst_b['std_types'][:, None], cryst_b['std_positions']], axis=1) sorted_n = np.array(sorted([ list(row) for row in list(fulln) ])) sorted_b = np.array(sorted([ list(row) for row in list(fullb) ])) if np.allclose(sorted_n, sorted_b, atol=1e-5): return True return False if samecell and samenatoms and samespg: cell = cryst_a['std_lattice'] rng1 = range(1, int(norm(cell[0])/2.)) rng2 = range(1, int(norm(cell[1])/2.)) rng3 = range(1, int(norm(cell[2])/2.)) for repeat in itertools.product(rng1, rng2, rng3): if test_rotations_translations(cryst_a, cryst_b, repeat): return True return False ``` %% Cell type:markdown id: tags: ## Task 1 %% Cell type:code id: tags: ``` python atoms = read('./quartz_alpha.xyz') nglview.show_ase(atoms) ``` %%%% Output: display_data %% Cell type:code id: tags: ``` python cell = ase_to_spgcell(ase_atoms=atoms) lattice, scaled_positions, numbers = spglib.find_primitive(cell, symprec=1e-5) reduced = ase_to_spgcell(cell=(lattice, scaled_positions, numbers),inverse=True) ``` %% Cell type:code id: tags: ``` python nglview.show_ase(reduced) ``` %%%% Output: display_data %% Cell type:markdown id: tags: ## Task 2 %% Cell type:code id: tags: ``` python versions = [read(atoms) for atoms in glob('./quartz_alpha*')] for outer in range(len(versions)-1): for inner in range(outer+1,len(versions)): print('Comparing: ',outer,inner) print('Equivalent: ',a_equiv_b(versions[outer],versions[inner])) ```
 { "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import itertools\n", "import numpy as np\n", "from numpy.linalg import norm\n", "import spglib\n", "from glob import glob\n", "\n", "from ase import Atoms\n", "from ase.io import read\n", "from ase.spacegroup import crystal\n", "from ase.spacegroup import Spacegroup\n", "from ase.data import atomic_numbers, atomic_names\n", "import nglview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Crystallographic point groups" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a=...\n", "b=...\n", "c=...\n", "alpha=...\n", "beta=...\n", "gamma=...\n", "thespacegroup=...\n", "print Spacegroup(thespacegroup)\n", "\n", "hfo2 = crystal(['...','...','...'],basis=[(...,...,...),(...,...,...),(...,...,...)], \n", " spacegroup=thespacegroup, cellpar=[a, b, c, alpha, beta, gamma])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bondatoms = []\n", "symbols = hfo2.get_chemical_symbols()\n", "for i in range(len(hfo2)):\n", " for j in range(i):\n", " if (symbols[i] == 'Hf' and symbols[j] == 'O' and hfo2.get_distance(i, j) < 2.6):\n", " bondatoms.append((i, j))\n", " elif (symbols[i] == 'O' and symbols[j] == 'Hf' and hfo2.get_distance(i, j) < 2.6):\n", " bondatoms.append((i, j))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Questions:\n", "\n", " -how many atoms are contained in the unit cell?\n", " -compute the volume of the unit cell " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def ase_to_spgcell(ase_atoms=None, cell=None, inverse=False):\n", " if not inverse:\n", " assert ase_atoms is not None\n", " return (ase_atoms.get_cell(),\n", " ase_atoms.get_scaled_positions(),\n", " ase_atoms.get_atomic_numbers())\n", " else:\n", " assert cell is not None\n", " return Atoms(cell=cell[0],\n", " scaled_positions=cell[1],\n", " numbers=cell[2])" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def a_equiv_b(a,b):\n", " \"\"\"Function that identifies whether two crystals are equivalent\"\"\"\n", "\n", " # getting symmetry datasets for both crystals\n", " cryst_a = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=a), symprec=1e-5, angle_tolerance=-1.0, hall_number=0)\n", " cryst_b = spglib.get_symmetry_dataset(ase_to_spgcell(ase_atoms=b), symprec=1e-5, angle_tolerance=-1.0, hall_number=0)\n", "\n", " samecell = np.allclose(cryst_a['std_lattice'], cryst_b['std_lattice'], atol=1e-5)\n", " samenatoms = len(cryst_a['std_positions']) == len(cryst_b['std_positions'])\n", " samespg = cryst_a['number'] == cryst_b['number']\n", " \n", " def test_rotations_translations(cryst_a, cryst_b, repeat):\n",