Atoms playground 2

Continuing from the previous section, let us become more familiar with Atoms through examples of its manipulation.

from ase import Atoms
from ase.build import molecule, bulk

from pfcc_extras.visualize.view import view_ngl

Super cell

As already explained, the structure of a periodic system can be increased in cell size by using repeat method or multiplication by “*” notation.

atoms = bulk("Si") * (2, 3, 4)
atoms222 = atoms * (2, 2, 2)
view_ngl(atoms222, w=400, h=300)

Cell

The periodic structure atoms has a cell property, which is defined in a special class called the Cell class, which has some additional methods.

# atoms = bulk("Fe", cubic=True)
atoms = bulk("Fe") * (2, 2, 2)
view_ngl(atoms, w=400, h=300)

atoms.cell

Cell([[-2.87, 2.87, 2.87], [2.87, -2.87, 2.87], [2.87, 2.87, -2.87]])

Cite from Fractional coordinates

The crystal cell can be represented by a 3x3 array showing the vectors of the a-, b-, and c-axes, respectively, but using fractional coordinates, it can also be represented by the lengths a, b, and c of the axes and the angles α, β, and γ of the axes. Each of the following methods returns the following values

• cellpar(): (a, b, c, α, β, γ)

• lengths(): (a, b, c)

• angles(): (α, β, γ)

print("cellpar(): ", atoms.cell.cellpar())
print("lengths(): ", atoms.cell.lengths())
print("angles() : ", atoms.cell.angles())

cellpar():  [  4.97098582   4.97098582   4.97098582 109.47122063 109.47122063
 109.47122063]
lengths():  [4.97098582 4.97098582 4.97098582]
angles() :  [109.47122063 109.47122063 109.47122063]

To access a 3x3 array, use array to get a numpy array.

atoms.cell.array

array([[-2.87,  2.87,  2.87],
       [ 2.87, -2.87,  2.87],
       [ 2.87,  2.87, -2.87]])

cell can also use numpy functions. For example, the following uses the diagonal method of numpy to get only the diagonal components.

atoms.cell.diagonal()

array([-2.87, -2.87, -2.87])

You can also get the Bravais lattice with get_bravais_lattice and the bandpath with bandpath method.

atoms.cell.get_bravais_lattice()

BCC(a=5.7400000000000002132)

atoms.cell.bandpath()

BandPath(path='GHNGPH,PN', cell=[3x3], special_points={GHNP}, kpts=[25x3])

The standard_form() method computes the cell form rcell which is standardized to the lower triangular matrix and the rotation matrix Q to make it so.

rcell, Q = atoms.cell.standard_form()
rcell

Cell([[4.970985817722678, 0.0, 0.0], [-1.6569952725742265, 4.686690374525147, 0.0], [-1.6569952725742256, -2.3433451872625737, 4.058792924010784]])

Element substitution

If you want to create a structure for a crystal with a small amount of an additive, you can model it by substituting atoms after creating the base crystal.

The following example shows the addition of V in Fe metal.

*In the bcc111 method, which generates a surface structure, you can specify the length of the vacuum layer along the z-axis by specifying vacuum. The periodic boundary condition is also applied in the z-axis direction by setting periodic=True. Note that if you do not specify this, the cell size will not be fixed, and nglviewer visualization will raise an error.

from ase.build import bcc111
from ase.visualize import view

atoms = bcc111("Fe", size=(4, 4, 6), periodic=True)
view_ngl(atoms, w=400, h=300)

At first, the atoms is all Fe (atomic number 26).

numbers = atoms.get_atomic_numbers()
numbers

array([26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
       26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
       26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
       26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
       26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
       26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26])

This time we will randomly change 5 atoms to V (atomic number 23).

import numpy as np

replace_index = np.random.choice(np.arange(len(numbers)), size=5, replace=False)
print(f"Replace {replace_index} atom")
numbers[replace_index] = 23
atoms.set_atomic_numbers(numbers)

Replace [17 25 36 23 52] atom

view_ngl(atoms, w=400, h=300)

If you want to know the atomic number of each element, you can refer to ase.data.atomic_numbers.

from ase.data import atomic_numbers
print("atomic_numbers: ", atomic_numbers)

print(f"V's atomic number is", atomic_numbers['V'])

atomic_numbers:  {'X': 0, 'H': 1, 'He': 2, 'Li': 3, 'Be': 4, 'B': 5, 'C': 6, 'N': 7, 'O': 8, 'F': 9, 'Ne': 10, 'Na': 11, 'Mg': 12, 'Al': 13, 'Si': 14, 'P': 15, 'S': 16, 'Cl': 17, 'Ar': 18, 'K': 19, 'Ca': 20, 'Sc': 21, 'Ti': 22, 'V': 23, 'Cr': 24, 'Mn': 25, 'Fe': 26, 'Co': 27, 'Ni': 28, 'Cu': 29, 'Zn': 30, 'Ga': 31, 'Ge': 32, 'As': 33, 'Se': 34, 'Br': 35, 'Kr': 36, 'Rb': 37, 'Sr': 38, 'Y': 39, 'Zr': 40, 'Nb': 41, 'Mo': 42, 'Tc': 43, 'Ru': 44, 'Rh': 45, 'Pd': 46, 'Ag': 47, 'Cd': 48, 'In': 49, 'Sn': 50, 'Sb': 51, 'Te': 52, 'I': 53, 'Xe': 54, 'Cs': 55, 'Ba': 56, 'La': 57, 'Ce': 58, 'Pr': 59, 'Nd': 60, 'Pm': 61, 'Sm': 62, 'Eu': 63, 'Gd': 64, 'Tb': 65, 'Dy': 66, 'Ho': 67, 'Er': 68, 'Tm': 69, 'Yb': 70, 'Lu': 71, 'Hf': 72, 'Ta': 73, 'W': 74, 'Re': 75, 'Os': 76, 'Ir': 77, 'Pt': 78, 'Au': 79, 'Hg': 80, 'Tl': 81, 'Pb': 82, 'Bi': 83, 'Po': 84, 'At': 85, 'Rn': 86, 'Fr': 87, 'Ra': 88, 'Ac': 89, 'Th': 90, 'Pa': 91, 'U': 92, 'Np': 93, 'Pu': 94, 'Am': 95, 'Cm': 96, 'Bk': 97, 'Cf': 98, 'Es': 99, 'Fm': 100, 'Md': 101, 'No': 102, 'Lr': 103, 'Rf': 104, 'Db': 105, 'Sg': 106, 'Bh': 107, 'Hs': 108, 'Mt': 109, 'Ds': 110, 'Rg': 111, 'Cn': 112, 'Nh': 113, 'Fl': 114, 'Mc': 115, 'Lv': 116, 'Ts': 117, 'Og': 118}
V's atomic number is 23

Conversely, if you want to know the symbol/name of an element from its number, you can use chemical_symbols and atomic_names.

from ase.data import atomic_names, chemical_symbols
print("chemical_symbols: ", chemical_symbols)
print("atomic_names    : ", atomic_names)

print(f"atomic number 23 is", chemical_symbols[23], atomic_names[23])

chemical_symbols:  ['X', 'H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'Ar', 'K', 'Ca', 'Sc', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'Ga', 'Ge', 'As', 'Se', 'Br', 'Kr', 'Rb', 'Sr', 'Y', 'Zr', 'Nb', 'Mo', 'Tc', 'Ru', 'Rh', 'Pd', 'Ag', 'Cd', 'In', 'Sn', 'Sb', 'Te', 'I', 'Xe', 'Cs', 'Ba', 'La', 'Ce', 'Pr', 'Nd', 'Pm', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu', 'Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au', 'Hg', 'Tl', 'Pb', 'Bi', 'Po', 'At', 'Rn', 'Fr', 'Ra', 'Ac', 'Th', 'Pa', 'U', 'Np', 'Pu', 'Am', 'Cm', 'Bk', 'Cf', 'Es', 'Fm', 'Md', 'No', 'Lr', 'Rf', 'Db', 'Sg', 'Bh', 'Hs', 'Mt', 'Ds', 'Rg', 'Cn', 'Nh', 'Fl', 'Mc', 'Lv', 'Ts', 'Og']
atomic_names    :  ['', 'Hydrogen', 'Helium', 'Lithium', 'Beryllium', 'Boron', 'Carbon', 'Nitrogen', 'Oxygen', 'Fluorine', 'Neon', 'Sodium', 'Magnesium', 'Aluminium', 'Silicon', 'Phosphorus', 'Sulfur', 'Chlorine', 'Argon', 'Potassium', 'Calcium', 'Scandium', 'Titanium', 'Vanadium', 'Chromium', 'Manganese', 'Iron', 'Cobalt', 'Nickel', 'Copper', 'Zinc', 'Gallium', 'Germanium', 'Arsenic', 'Selenium', 'Bromine', 'Krypton', 'Rubidium', 'Strontium', 'Yttrium', 'Zirconium', 'Niobium', 'Molybdenum', 'Technetium', 'Ruthenium', 'Rhodium', 'Palladium', 'Silver', 'Cadmium', 'Indium', 'Tin', 'Antimony', 'Tellurium', 'Iodine', 'Xenon', 'Caesium', 'Barium', 'Lanthanum', 'Cerium', 'Praseodymium', 'Neodymium', 'Promethium', 'Samarium', 'Europium', 'Gadolinium', 'Terbium', 'Dysprosium', 'Holmium', 'Erbium', 'Thulium', 'Ytterbium', 'Lutetium', 'Hafnium', 'Tantalum', 'Tungsten', 'Rhenium', 'Osmium', 'Iridium', 'Platinum', 'Gold', 'Mercury', 'Thallium', 'Lead', 'Bismuth', 'Polonium', 'Astatine', 'Radon', 'Francium', 'Radium', 'Actinium', 'Thorium', 'Protactinium', 'Uranium', 'Neptunium', 'Plutonium', 'Americium', 'Curium', 'Berkelium', 'Californium', 'Einsteinium', 'Fermium', 'Mendelevium', 'Nobelium', 'Lawrencium', 'Rutherfordium', 'Dubnium', 'Seaborgium', 'Bohrium', 'Hassium', 'Meitnerium', 'Darmastadtium', 'Roentgenium', 'Copernicium', 'Nihonium', 'Flerovium', 'Moscovium', 'Livermorium', 'Tennessine', 'Oganesson']
atomic number 23 is V Vanadium

Creation of vacancies

It is industrially important to study the behavior of defects in crystal structures.

In ASE, the pop method can be used to delete atoms of a particular index. (Alternatively, the del method can also be used.)

The following is an example of creating a defect structure without the 13th Si atom from a Si crystal.

atoms = bulk("Si") * (2, 2, 2)
# `del atoms[13]` also works
atoms.pop(13)
view_ngl(atoms, representations=["ball+stick"], w=400, h=300)

These are just a few examples of how atoms can be handled by looking at the various methods implemented in ASE.

From here on, let’s learn by practice, together with calculation methods and examples.