Creating structures in pyiron

This section gives a brief introduction about some of the tools available in pyiron to construct atomic structures.

For the sake of compatibility, our structure class is written to be compatible with the popular Atomistic Simulation Environment package (ASE). This makes it possible to use routines from ASE to help set-up structures.

Furthermore, pyiron uses the NGLview package to visualize the structures and trajectories interactively in 3D using NGLview-widgets.

As preparation for the following discussion we import a few python libraries

import numpy as np
%matplotlib inline
import matplotlib.pylab as plt

and create a pyiron project named ‘structures’:

from pyiron import Project
pr = Project(path='structures')

Bulk crystals

In this section we discuss various possibilities to create bulk crystal structures.

Using create_structure()

The simplest way to generate simple crystal structures is using the inbuilt create_structure() function specifying the element symbol, Bravais basis and the lattice constant(s)

Note: The output gives a cubic cell rather than the smallest non-orthogonal unit cell.

structure = pr.create_structure('Al',
                            bravais_basis='fcc',
                            lattice_constant=4.05)

To plot the structure interactively in 3D simply use:

structure.plot3d()

Using create_ase_bulk()

Another convenient way to set up structures is using the create_ase_bulk() function which is built on top of the ASE build package for bulk crystals. This function returns an object which is of the pyiron structure object type.

Example: fcc bulk aluminum in a cubic cell

structure = pr.create_ase_bulk('Al', cubic=True)
structure.plot3d()

Example: wurtzite GaN in a 3x3x3 repeated orthorhombic cell.

Note: - In contrast to new_structure = structure.repeat() which creates a new object, set_repeat() modifies the existing structure object. - Setting spacefill=False in the plot3d() method changes the atomic structure style to “ball and stick”.

structure = pr.create_ase_bulk('AlN',
                           crystalstructure='wurtzite',
                           a=3.5, orthorhombic=True)
structure.set_repeat([3,3,3])
structure.plot3d(spacefill=False)

Creating surfaces (using ASE)

Surfaces can be created using the create_surface() function which is also built on top of the ASE build package for surfaces

Example: Creating a 3x4 fcc Al(111) surface with 4 layers and a vacuum of 10 Ångström

Al_111 = pr.create_surface("Al", surface_type="fcc111",
                           size=(3, 4, 4), vacuum=10, orthogonal=True)
Al_111.plot3d()

Creating structures without importing the project class

In all the examples shown above, the structures are create from the pyiron Project object. It is also possible to do this without importing/initializing this object. For this the appropriate imports must be made.

from pyiron import create_ase_bulk, create_surface

structure = create_ase_bulk('AlN',
                            crystalstructure='wurtzite',
                            a=3.5, orthorhombic=True)
structure.set_repeat([3,3,3])
structure.plot3d(spacefill=False)

Al_111 = create_surface("Al", surface_type="fcc111",
                        size=(3, 4, 4), vacuum=10, orthogonal=True)
Al_111.plot3d()

Using the ASE spacegroup class

from ase.spacegroup import crystal
from pyiron import ase_to_pyiron

a = 9.04
skutterudite = crystal(('Co', 'Sb'),
                       basis=[(0.25, 0.25, 0.25), (0.0, 0.335, 0.158)],
                       spacegroup=204,
                       cellpar=[a, a, a, 90, 90, 90])
skutterudite = ase_to_pyiron(skutterudite)

skutterudite.plot3d()

Accessing the properties of the structure object

Using the bulk aluminum fcc example from before the structure object can be created by

structure = pr.create_ase_bulk('Al', cubic=True)

A summary of the information about the structure is given by using

print(structure)

Al: [0. 0. 0.]
Al: [0.    2.025 2.025]
Al: [2.025 0.    2.025]
Al: [2.025 2.025 0.   ]
pbc: [ True  True  True]
cell:
Cell([4.05, 4.05, 4.05])

The cell vectors of the structure object can be accessed and edited through

structure.cell

Cell([4.05, 4.05, 4.05])

The positions of the atoms in the structure object can be accessed and edited through

structure.positions

array([[0.   , 0.   , 0.   ],
       [0.   , 2.025, 2.025],
       [2.025, 0.   , 2.025],
       [2.025, 2.025, 0.   ]])

Point defects

Creating a single vacancy

We start by setting up a 4x4x4 supercell

structure = pr.create_ase_bulk('Al', cubic=True)
structure.set_repeat([4,4,4])

To create the vacancy at position index “0” simply use:

del structure[0]

To plot the structure that now contains a vacancy run:

structure.plot3d()

Creating multiple vacancies

# First create a 4x4x4 supercell
structure = pr.create_ase_bulk('Al', cubic=True)
structure.set_repeat([4,4,4])
print('Number of atoms in the repeat unit: ',structure.get_number_of_atoms())

Number of atoms in the repeat unit:  256

The del command works for passing a list of indices to the structure object. For example, a random set of n\(_{\text{vac}}\) vacancies can be created by using

# Generate a list of indices for the vacancies
n_vac = 24
vac_ind_lst = np.random.permutation(len(structure))[:n_vac]

# Remove atoms according to the "vac_ind_lst"
del structure[vac_ind_lst]

# Visualize the structure
print('Number of atoms in the repeat unit: ',structure.get_number_of_atoms())
structure.plot3d()

Number of atoms in the repeat unit:  232

Random substitutial alloys

# Create a 4x4x4 supercell
structure = pr.create_ase_bulk('Al', cubic=True)
structure.set_repeat([4,4,4])

Substitutional atoms can be defined by changing the atomic species accessed through its position index.

Here, we set \(n_{\text{sub}}\) magnesium substitutional atoms at random positions

n_sub = 24
structure[np.random.permutation(len(structure))[:n_sub]] = 'Mg'

# Visualize the structure and print some additional information about the structure
print('Number of atoms in the repeat unit: ',structure.get_number_of_atoms())
print('Chemical formula: ',structure.get_chemical_formula())
structure.plot3d()

Number of atoms in the repeat unit:  256
Chemical formula:  Al232Mg24

Explicit definition of the structure

You can also set-up structures through the explicit input of the cell parameters and positions

cell = 10.0 * np.eye(3) # Specifying the cell dimensions
positions = [[0.25, 0.25, 0.25], [0.75, 0.75, 0.75]]
elements = ['O', 'O']

# Now use the Atoms class to create the instance.
O_dimer = pr.create_atoms(elements=elements, scaled_positions=positions, cell=cell)

O_dimer.plot3d()

Importing from cif/other file formats

Parsers from ASE can be used to import structures from other formats. In this example, we will download and import a Nepheline structure from the Crystallography Open Database (COD)

# The COD structures can be accessed through their unique COD identifier
cod = 1008753
filename = '{}.cif'.format(cod)
url = 'http://www.crystallography.net/cod/{}'.format(filename)

cif_structure = """\
#------------------------------------------------------------------------------
#$Date: 2015-01-27 21:58:39 +0200 (Tue, 27 Jan 2015) $
#$Revision: 130149 $
#$URL: svn://www.crystallography.net/cod/cif/1/00/87/1008753.cif $
#------------------------------------------------------------------------------
#
# This file is available in the Crystallography Open Database (COD),
# http://www.crystallography.net/
#
# All data on this site have been placed in the public domain by the
# contributors.
#
data_1008753
loop_
_publ_author_name
'Buerger, M J'
'Klein, G E'
'Donnay, G'
_publ_section_title
;
Determination of the crystal structure of nepheline
;
_journal_coden_ASTM              AMMIAY
_journal_name_full               'American Mineralogist'
_journal_page_first              805
_journal_page_last               818
_journal_volume                  39
_journal_year                    1954
_chemical_formula_structural     'K Na3 Al4 Si4 O16'
_chemical_formula_sum            'Al4 K Na3 O16 Si4'
_chemical_name_mineral           Nepheline
_chemical_name_systematic        'Potassium trisodium tetraaluminium silicate'
_space_group_IT_number           173
_symmetry_cell_setting           hexagonal
_symmetry_Int_Tables_number      173
_symmetry_space_group_name_Hall  'P 6c'
_symmetry_space_group_name_H-M   'P 63'
_cell_angle_alpha                90
_cell_angle_beta                 90
_cell_angle_gamma                120
_cell_formula_units_Z            2
_cell_length_a                   10.01
_cell_length_b                   10.01
_cell_length_c                   8.405
_cell_volume                     729.4
_cod_database_code               1008753
loop_
_symmetry_equiv_pos_as_xyz
x,y,z
-y,x-y,z
y-x,-x,z
-x,-y,1/2+z
y,y-x,1/2+z
x-y,x,1/2+z
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
_atom_site_attached_hydrogens
_atom_site_calc_flag
K1 K1+ 2 a 0. 0. 0. 1. 0 d
Al1 Al3+ 2 b 0.3333 0.6667 0.18 1. 0 d
Si1 Si4+ 2 b 0.3333 0.6667 0.82 1. 0 d
O1 O2- 2 b 0.3333 0.6667 0. 1. 0 d
Na1 Na1+ 6 c 0.008 0.432 0. 1. 0 d
Al2 Al3+ 6 c 0.092 0.33 0.67 1. 0 d
Si2 Si4+ 6 c 0.092 0.33 0.33 1. 0 d
O2 O2- 6 c 0.02 0.33 0.5 1. 0 d
O3 O2- 6 c 0.18 0.5 0.75 1. 0 d
O4 O2- 6 c 0.17 0.53 0.25 1. 0 d
O5 O2- 6 c 0.23 0.28 0.25 1. 0 d
O6 O2- 6 c 0.23 0.28 0.75 1. 0 d
loop_
_atom_type_symbol
_atom_type_oxidation_number
K1+ 1.000
Al3+ 3.000
Si4+ 4.000
O2- -2.000
Na1+ 1.000"""

# Download and save the structure file locally
# import urllib
# urllib.request.urlretrieve(url=url, filename='strucs.'+filename);
with open('strucs.'+filename, "w") as f:
    f.writelines(cif_structure)

# Using ase parsers to read the structure and then convert to a pyiron instance
import ase
from pyiron import ase_to_pyiron

structure = ase_to_pyiron(ase.io.read(filename='strucs.'+filename,
                                      format='cif'))
structure.info["cod"] = cod

/srv/conda/envs/notebook/lib/python3.7/site-packages/ase/io/cif.py:380: UserWarning: crystal system 'hexagonal' is not interpreted for space group Spacegroup(173, setting=1). This may result in wrong setting!
  setting_name, spacegroup))

structure.plot3d()

Structures can be stored indepently from jobs in HDF5 by using the special StructureContainer job. To save to disk, call run().

container = pr.create_job(pr.job_type.StructureContainer, "nepheline")
container.structure = structure
container.run()

The job nepheline was saved and received the ID: 1

It’s also possible to store multiple structures in one container and to store directly from a job. Let’s use this here to store the equilibrated structures at finite temperatures.

al_container = pr.create_job(pr.job_type.StructureContainer, "al_temp", delete_existing_job=True)
for T in (400, 600, 800):
    j = pr.create_job(pr.job_type.Lammps, "T_{}".format(T))
    j.structure = pr.create_ase_bulk("Al", cubic = True)
    j.potential = j.list_potentials()[0]
    j.calc_md(temperature=T, n_ionic_steps=1000, pressure=0)
    j.run()
    structure = j.get_structure(-1)
    structure.info["T"] = T
    structure.info["P"] = 0
    al_container.append(structure)

al_container.run()

This group does not exist in the HDF5 file al_temp
The job T_400 was saved and received the ID: 2
The job T_600 was saved and received the ID: 3
The job T_800 was saved and received the ID: 4
The job al_temp was saved and received the ID: 5

al_container.structure_lst[0].info

{'T': 400, 'P': 0}

al_container.structure_lst

InputList([Al: [0.13389146 3.96541338 4.05893092]
Al: [3.99018226 2.0071096  1.95618182]
Al: [1.98560236 3.88778884 2.0465924 ]
Al: [2.04906472 2.05913422 0.09311447]
pbc: [ True  True  True]
cell:
Cell([[4.079370396328773, 2.497893949200251e-16, 2.497893949200251e-16], [0.0, 3.973148678151775, 2.4328519056175543e-16], [0.0, 0.0, 4.077409804014059]])
, Al: [0.0070279  4.03832899 0.08383998]
Al: [4.08339864 2.06533333 2.03444326]
Al: [2.20534808 4.07618808 1.94632881]
Al: [1.91118709 2.15964157 0.05514228]
pbc: [ True  True  True]
cell:
Cell([[4.103480856873612, 2.5126573483663535e-16, 2.5126573483663535e-16], [0.0, 4.11316398781314, 2.5185865560217624e-16], [0.0, 0.0, 4.119754328387385]])
, Al: [3.7382874  0.12171228 4.27645154]
Al: [0.05199557 1.91099383 2.20493355]
Al: [1.92074788 0.03592662 2.13915097]
Al: [1.89264518 1.93451826 0.04368514]
pbc: [ True  True  True]
cell:
Cell([[3.8018380195130206, 2.3279543807366664e-16, 2.3279543807366664e-16], [0.0, 4.003150985990483, 2.451223020748408e-16], [0.0, 0.0, 4.332110602330072]])
])