Crystal

Added in version 0.7.

For the full reference see Crystal module

Crystal is a base class, which store the structure. It is defined as a combination of the the Lattice and the set of Atoms. For the detailed description of the Lattice and Atom see:

• Lattice
  • Bravais lattices
  • References
  • Creation
  • Identification of the lattice
  • Reference attributes
  • Lattice parameters
  • Variation of the lattice
  • Plotting of the lattice
  • K points
• Atom
  • Creation and basic attributes
  • Properties
• K points
  • Creation
  • Settings
  • Properties for calculation
  • Properties for plotting

Creation of the Crystal

Crystal constructor take two optional arguments:

• lattice - instance of the Lattice class, which defines the unit cell.

• atoms - list of the Atom instances, which defines the set of atoms in the unit cell.

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice(3.0, 3.0, 3.0, 90.0, 90.0, 90.0)
>>> atoms = [Atom('Si', (0.0, 0.0, 0.0))]
>>> crystal = Crystal(lattice, atoms)

By default the Crystal is created with the cubic lattice (\(a = 1\)) and and no atoms.

>>> from radtools import Crystal
>>> crystal = Crystal()
>>> crystal.lattice.cell
array([[1, 0, 0],
       [0, 1, 0],
       [0, 0, 1]])
>>> crystal.lattice.identify()
'CUB'
>>> crystal.atoms
[]

Identification of the Bravais lattice type

Warning

Primitive cell identification is not implemented yet. Any cell is interpreted as primitive.

When arbitrary crystal structure is considered the Crystal.lattice is an instance of the general Lattice class, where unit cell is interpreted as a primitive one and the type of the Bravais lattice is not defined. The process of the definition of the crystal type is divided in two steps:

• Define primitive cell of the Crystal

  Crystal.find_primitive_cell()

• Define the type of the Bravais lattice.

  Crystal.identify()

This routine is implemented in Crystal.identify() method. It calls for the Crystal.find_primitive_cell() internally.

Adding and removing atoms

Adding atoms to the crystal is straightforward:

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)))
>>> for atom in crystal.atoms:
...    print(atom.fullname, atom.position)
...
Cr__1 [0. 0. 0.]
Cr__2 [0.5 0.5 0.5]

By default atom coordinates are interpreted as absolute. In order to add atom in the fractional coordinates the relative keyword argument should be set to True:

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice(3.0, 3.0, 3.0, 90.0, 90.0, 90.0)
>>> crystal = Crystal(lattice)
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)), relative=True)
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)), relative=True)
>>> for atom in crystal.atoms:
...    print(atom.fullname, atom.position)
...
Cr__1 [0. 0. 0.]
Cr__2 [1.5 1.5 1.5]

Removing atoms is also straightforward:

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom("Cr", (0.0, 0.0, 0.0)))
>>> atom = Atom("Cr", (0.5, 0.5, 0.5))
>>> crystal.add_atom(atom)
>>> crystal.remove_atom("Cr__1")
>>> for atom in crystal.atoms:
...    print(atom.fullname, atom.position)
...
Cr__2 [0.5 0.5 0.5]
>>> crystal.remove_atom(atom)
>>> crystal.atoms
[]
>>> crystal.add_atom(Atom("Cr", (0.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom("Cr", (1.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom("Cr", (1.0, 1.0, 0.0)))
>>> crystal.add_atom(Atom("Cr", (1.0, 1.0, 1.0)))
>>> # Same as len(crystal.atoms)
>>> len(crystal)
4
>>> # You can remove all atoms with the same name at once
>>> crystal.remove_atom("Cr")
>>> len(crystal)
0

Note

The Crystal.remove_atom() method can take either the string literal or the atom instance as an argument. String literal is interpreted as the Atom.name if only one atom with that name is present in the crystal. Otherwise it is interpreted as the Atom.fullname.

Atom getters

There is a number of properties involving atom of the crystal you have access to:

• Crystal.atoms - list of the Atom instances in the crystal.

• Crystal.get_atom - get atom by name or by fullname.

..doctest:

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)))
>>> atom1 = crystal.get_atom('Cr')
>>> atom1.name
'Cr'
>>> atom1.position
array([0., 0., 0.])
>>> atom1.index
1
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)))
>>> atom2 = crystal.get_atom('Cr')
Traceback (most recent call last):
...
ValueError: Multiple matches found for name = Cr, index = None
>>> atom2 = crystal.get_atom('Cr__2')
>>> atom2.index
2

• Crystal.get_atom_coordinates - get coordinates of the atom by name or by fullname.

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice([[2,0,0],[0,2,0],[0,0,2]])
>>> crystal = Crystal(lattice)
>>> crystal.add_atom(Atom('Cr', (0.0, 0.5, 0.0)))
>>> crystal.get_atom_coordinates('Cr')
array([0. , 0.5, 0. ])
>>> crystal.Cr.position
array([0. , 0.5, 0. ])
>>> crystal.get_atom_coordinates('Cr', relative=True)
array([0.  , 0.25, 0.  ])

• Crystal.get_vector - get vector from the atom1 to atom2 by name or by fullname.

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice([[2,0,0],[0,2,0],[0,0,2]])
>>> crystal = Crystal(lattice)
>>> crystal.add_atom(Atom('Cr', (0.0, 0.5, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.0, 0.0)))
>>> crystal.get_vector('Cr__1', 'Cr__2')
array([ 0.5, -0.5,  0. ])
>>> crystal.get_vector('Cr__1', 'Cr__2', relative=True)
array([ 0.25, -0.25,  0.  ])

• Crystal.get_distance - get distance between atom1 and atom2 by name or by fullname.

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice([[2,0,0],[0,2,0],[0,0,2]])
>>> crystal = Crystal(lattice)
>>> crystal.add_atom(Atom('Cr', (0.0, 0.5, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.0, 0.0)))
>>> print(f"{crystal.get_distance('Cr__1', 'Cr__2'):.4f}")
0.7071

Magnetic dipole-dipole interaction energy

If spins of crystal`s atoms are defined, the magnetic dipole-dipole interaction energy can be calculated.

Two functions are used for this purpose:

• Crystal.mag_dipdip_energy() - calculate the energy of the magnetic dipole-dipole interaction.

  It returns energy in meV if atom`s positions are in Angstroms and magnetic moments are in Bohr magnetons.

>>> from radtools import Crystal, Lattice, Atom
>>> lattice = Lattice([[2,0,0],[0,2,0],[0,0,2]])
>>> crystal = Crystal(lattice)
>>> crystal.add_atom(Atom('Cr', (0.0, 0.5, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.0, 0.0)))
>>> energy = crystal.mag_dipdip_energy(1,1,1, progress_bar=False)
Traceback (most recent call last):
...
ValueError: There are no magnetic atoms in the crystal.
>>> crystal.Cr__1.magmom = [0,0,1]
>>> crystal.Cr__2.magmom = [0,0,1]
>>> energy = crystal.mag_dipdip_energy(1,1,1, progress_bar=False)
>>> print(f"{energy:.8f}")
0.07591712
>>> crystal.Cr__1.magmom = [0,1,0]
>>> energy = crystal.mag_dipdip_energy(1,1,1, progress_bar=False)
>>> print(f"{energy:.8f}")
0.00000000
>>> crystal.Cr__2.magmom = [1,0,0]
>>> energy = crystal.mag_dipdip_energy(1,1,1, progress_bar=False)
>>> print(f"{energy:.8f}")
0.11387568

• Crystal.converge_mag_dipdip_energy() - converge the energy of the magnetic dipole-dipole interaction.

Iterations and stuff

Crystal class is iterable over the atoms of the crystal.

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)))
>>> for atom in crystal:
...    print(atom.fullname)
...
Cr__1
Cr__2

You can check if the atom is in the crystal:

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> atom = Atom('Cr', (0.0, 0.0, 0.0))
>>> crystal.add_atom(atom)
>>> atom in crystal
True
>>> "Cr" in crystal
True
>>> 'Cr__1' in crystal
True
>>> 'Cr__3' in crystal
False
>>> "Br" in crystal
False

You can get an atom object by its name or fullname (it is identical to passing the name to the Crystal.get_atom() method with return_all=False):

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)))
>>> atom = crystal.Cr__1
>>> atom.fullname
'Cr__1'
>>> atom = crystal.Cr__2
>>> atom.fullname
'Cr__2'
>>> crystal.Cr
Traceback (most recent call last):
...
AttributeError: 'Crystal' object has no attribute 'Cr'

Similar method (it is identical to passing the name to the Crystal.get_atom() method with return_all=True):

>>> from radtools import Crystal, Lattice, Atom
>>> crystal = Crystal()
>>> crystal.add_atom(Atom('Cr', (0.0, 0.0, 0.0)))
>>> crystal.add_atom(Atom('Cr', (0.5, 0.5, 0.5)))
>>> atoms = crystal["Cr__1"]
>>> atoms[0].fullname
'Cr__1'
>>> atoms = crystal["Cr__2"]
>>> atoms[0].fullname
'Cr__2'
>>> atoms = crystal["Cr"]
>>> for atom in atoms:
...    print(atom.fullname)
...
Cr__1
Cr__2

Note

Second method returns a list of atoms, while the first one returns a single atom.