Defining and visualizing bulk systems

Built-in functions in ase

As with molecules, mod:ase provides several helper functions to create bulk structures. We highlight a few of them here. Particularly common ones are:

• mod:ase.lattice.cubic.FaceCenteredCubic

• mod:ase.lattice.cubic.BodyCenteredCubic

• mod:ase.lattice.hexagonal.Graphite

• mod:ase.lattice.compounds.NaCl

For others, see https://wiki.fysik.dtu.dk/ase/ase/lattice.html

We start with a simple example, fcc Ag. By default, mod:ase knows Ag is an fcc metal, and knows the experimental lattice constant. We have to specify the directions (vectors along each axis) to get something other than the default output. Here, the default fcc cell contains four atoms.

from ase.io import write
from ase.lattice.cubic import FaceCenteredCubic

atoms = FaceCenteredCubic('Ag')

write('images/Ag-fcc.png', atoms, show_unit_cell=2)

print(atoms)

Lattice(symbols='Ag4', pbc=True, cell=[4.09, 4.09, 4.09])

A mod:ase.lattice.bravais.Lattice object is returned! This is practically the same as as an mod:ase.atoms.Atoms object.

Here we specify the primitive unit cell, which only has one atom in it.

from ase.io import write
from ase.lattice.cubic import FaceCenteredCubic

atoms = FaceCenteredCubic('Ag', directions=[[0, 1, 1],
                                            [1, 0, 1],
                                            [1, 1, 0]])

write('images/Ag-fcc-primitive.png', atoms, show_unit_cell=2)

print(atoms)

Lattice(symbols='Ag', pbc=True, cell=[[2.892066735052979, 0.0, 0.0], [1.4460333675264898, 2.5046032619957996, 0.0], [1.4460333675264896, 0.8348677539985998, 2.3613626009855695]])

Lattice(symbols='Ag', positions=..., cell=[[2.892066735052979, 0.0, 0.0], [1.4460333675264898, 2.5046032619957996, 0.0], [1.4460333675264896, 0.8348677539985997, 2.3613626009855695]], pbc=[True, True, True])

Lattice(symbols='Ag', positions=..., cell=[[2.892066735052979, 0.0, 0.0], [1.4460333675264898, 2.5046032619957996, 0.0], [1.4460333675264896, 0.8348677539985997, 2.3613626009855695]], pbc=[True, True, True])

We can use these modules to build alloy unit cells. The basic strategy is to create the base unit cell in one element and then selectively change some atoms to different chemical symbols. Here we examine an Ag₃Pd alloy structure.

from ase.io import write
from ase.lattice.cubic import FaceCenteredCubic

atoms = FaceCenteredCubic(directions=[[1, 0, 0],
                                      [0, 1, 0],
                                      [0, 0, 1]],
                          size=(1, 1, 1),
                          symbol='Ag',
                          latticeconstant=4.0)

write('images/Ag-bulk.png', atoms, show_unit_cell=2)

# to make an alloy, we can replace one atom with another kind
atoms[0].symbol = 'Pd'
write('images/AgPd-bulk.png', atoms, show_unit_cell=2)

To create a graphite structure we use the following code. Note that we have to specify the lattice constants (taken from http://www.phy.ohiou.edu/~asmith/NewATOMS/HOPG.pdf) because mod:ase has C in the diamond structure by default. We show two views, because the top view does not show the spacing between the layers.

from ase.lattice.hexagonal import Graphite
from ase.io import write

atoms = Graphite('C', latticeconstant={'a': 2.4612,
                                       'c': 6.7079})
write('images/graphite.png',
      atoms.repeat((2, 2, 1)),
      rotation='115x', show_unit_cell=2)

write('images/graphite-top.png',
      atoms.repeat((2, 2, 1)),
      show_unit_cell=2)

To get a compound, we use the following code. We have to specify the basis atoms to the function generating the compound, and the lattice constant. For NaCl we use the lattice constant at (http://en.wikipedia.org/wiki/Sodium_chloride).

from ase.lattice.compounds import NaCl
from ase.io import write

atoms = NaCl(['Na', 'Cl'], latticeconstant=5.65)
write('images/NaCl.png', atoms, show_unit_cell=2, rotation='45x,45y,45z')

mod:ase.spacegroup

A final alternative to setting up bulk structures is mod:ase.spacegroup. This is a concise way to setup structures if you know the following properties of the crystal structure:

1. Chemical symbols

2. Coordinates of the non-equivalent sites in the unit cell

3. the spacegroup

4. the cell parameters (a, b, c, alpha, beta, gamma)

from ase.lattice.spacegroup import crystal
# FCC aluminum
a = 4.05
al = crystal('Al', [(0, 0, 0)],
             spacegroup=225,
             cellpar=[a, a, a, 90, 90, 90])
print(al)

Atoms(symbols='Al4', pbc=True, cell=[4.05, 4.05, 4.05], spacegroup_kinds=...)

Atoms(symbols='Al4', positions=..., cell=[[4.05, 0.0, 0.0], [2.4799097682733903e-16, 4.05, 0.0], [2.4799097682733903e-16, 2.4799097682733903e-16, 4.05]], pbc=[True, True, True])

Here is rutile TiO₂.

from ase.lattice.spacegroup import crystal

a = 4.6
c = 2.95
rutile = crystal(['Ti', 'O'], basis=[(0, 0, 0), (0.3, 0.3, 0.0)],
                 spacegroup=136, cellpar=[a, a, c, 90, 90, 90])
print(rutile)

Atoms(symbols='Ti2O4', pbc=True, cell=[4.6, 4.6, 2.95], spacegroup_kinds=...)

Atoms(symbols’Ti2O4’, positions=…, cell=[[4.6, 0.0, 0.0], [2.816687638038912e-16, 4.6, 0.0], [1.806354028742346e-16, 1.806354028742346e-16, 2.95]], pbc=[True, True, True]) =Atoms(symbols’Ti2O4’, positions=…, cell=[[4.6, 0.0, 0.0], [2.816687638038912e-16, 4.6, 0.0], [1.806354028742346e-16, 1.806354028742346e-16, 2.95]], pbc=[True, True, True]) =sho

Using http://materialsproject.org

The Materials Project offers web access to a pretty large number of materials (over 21,000 at the time of this writing), including structure and other computed properties. You must sign up for an account at the website, and then you can access the information. You can search for materials with lots of different criteria including formula, unit cell formula, by elements, by structure, etc… The website allows you to download the VASP files used to create the calculations. They also develop the pymatgen project (which requires python 2.7+).

For example, I downloaded this cif file for a RuO\(_2\) structure (Material ID 825).

#\#CIF1.1
##########################################################################
#               Crystallographic Information Format file
#               Produced by PyCifRW module
#
#  This is a CIF file.  CIF has been adopted by the International
#  Union of Crystallography as the standard for data archiving and
#  transmission.
#
#  For information on this file format, follow the CIF links at
#  http://www.iucr.org
##########################################################################

data_RuO2
_symmetry_space_group_name_H-M          'P 1'
_cell_length_a                          3.13970109
_cell_length_b                          4.5436378
_cell_length_c                          4.5436378
_cell_angle_alpha                       90.0
_cell_angle_beta                        90.0
_cell_angle_gamma                       90.0
_chemical_name_systematic               'Generated by pymatgen'
_symmetry_Int_Tables_number             1
_chemical_formula_structural            RuO2
_chemical_formula_sum                   'Ru2 O4'
_cell_volume                            64.8180127062
_cell_formula_units_Z                   2
loop_
  _symmetry_equiv_pos_site_id
  _symmetry_equiv_pos_as_xyz
   1  'x, y, z'

loop_
  _atom_site_type_symbol
  _atom_site_label
  _atom_site_symmetry_multiplicity
  _atom_site_fract_x
  _atom_site_fract_y
  _atom_site_fract_z
  _atom_site_attached_hydrogens
  _atom_site_B_iso_or_equiv
  _atom_site_occupancy
   O  O1  1  0.000000  0.694330  0.694330  0  .  1
   O  O2  1  0.500000  0.805670  0.194330  0  .  1
   O  O3  1  0.000000  0.305670  0.305670  0  .  1
   O  O4  1  0.500000  0.194330  0.805670  0  .  1
   Ru  Ru5  1  0.500000  0.500000  0.500000  0  .  1
   Ru  Ru6  1  0.000000  0.000000  0.000000  0  .  1

We can read this file in with func:ase.io.read. That function automatically recognizes the file type by the extension.

from ase.io import read, write

atoms = read('data/Ru2O4_1.cif')

write('images/Ru2O4.png', atoms, show_unit_cell=2)
print(atoms)

Atoms(symbols='O4Ru2', pbc=True, cell=[3.13970109, 4.5436378, 4.5436378], spacegroup_kinds=...)