lattpy

Package for modeling Bravais lattices and finite lattice structures.

Submodules

`lattpy.atom`	Objects for representing atoms and the unitcell of a lattice.
`lattpy.basis`	Basis object for defining the coordinate system and unit cell of a lattice.
`lattpy.data`	This module contains objects for low-level representation of lattice systems.
`lattpy.disptools`	Tools for dispersion computation and plotting.
`lattpy.lattice`	This module contains the main Lattice object.
`lattpy.shape`	Objects for representing the shape of a finite lattice.
`lattpy.spatial`	Spatial algorithms and data structures.
`lattpy.structure`	Lattice structure object for defining the atom basis and neighbor connections.
`lattpy.utils`	Contains miscellaneous utility methods.

lattpy.simple_chain(a=1.0, atom=None, neighbors=1)[source]

Creates a 1D lattice with one atom at the origin of the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.simple_chain()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.alternating_chain(a=1.0, atom1=None, atom2=None, x0=0.0, neighbors=1)[source]

Creates a 1D lattice with two atoms in the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atom1str or Atom, optional: The first atom to add to the lattice. If a string is passed, a new Atom instance is created.
atom2str or Atom, optional: The second atom to add to the lattice. If a string is passed, a new Atom instance is created.
x0float, optional: The offset of the atom positions in x-direction.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.alternating_chain()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.simple_square(a=1.0, atom=None, neighbors=1)[source]

Creates a square lattice with one atom at the origin of the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.simple_square()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.simple_rectangular(a1=1.5, a2=1.0, atom=None, neighbors=2)[source]

Creates a rectangular lattice with one atom at the origin of the unit cell.

Parameters

a1float, optional: The lattice constant in the x-direction.
a2float, optional: The lattice constant in the y-direction.
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (2).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.simple_rectangular()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.simple_hexagonal(a=1.0, atom=None, neighbors=1)[source]

Creates a hexagonal lattice with one atom at the origin of the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.simple_hexagonal()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.honeycomb(a=1.0, atom=None)[source]

Creates a honeycomb lattice with two identical atoms in the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.honeycomb()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.graphene(a=1.0)[source]

Creates a hexagonal lattice with two atoms in the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vectors).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.graphene()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.simple_cubic(a=1.0, atom=None, neighbors=1)[source]

Creates a cubic lattice with one atom at the origin of the unit cell.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.simple_cubic()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.nacl_structure(a=1.0, atom1='Na', atom2='Cl', neighbors=1)[source]

Creates a NaCl lattice structure.

Parameters

afloat, optional: The lattice constant (length of the basis-vector).
atom1str or Atom, optional: The first atom to add to the lattice. If a string is passed, a new Atom instance is created. The default name is Na.
atom2str or Atom, optional: The second atom to add to the lattice. If a string is passed, a new Atom instance is created.. The default name is Cl.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).

Returns

lattLattice: The configured lattice instance.

Examples

>>> import matplotlib.pyplot as plt
>>> latt = lp.nacl_structure()
>>> latt.plot_cell()
>>> plt.show()

(png, pdf)

lattpy.finite_hypercubic(s, a=1.0, atom=None, neighbors=1, primitive=True, periodic=None)[source]

Creates a d-dimensional finite lattice model with one atom in the unit cell.

Parameters

sfloat or Sequence[float] or AbstractShape: The shape of the finite lattice. This also defines the dimensionality.
afloat, optional: The lattice constant (length of the basis-vectors).
atomstr or Atom, optional: The atom to add to the lattice. If a string is passed, a new Atom instance is created.
neighborsint, optional: The number of neighbor-distance levels, e.g. setting to 1 means only nearest neighbors. The default is nearest neighbors (1).
primitivebool, optional: If True the shape will be multiplied by the cell size of the model. The default is True.
periodicbool or int or (N, ) array_like: One or multiple axises to apply the periodic boundary conditions. If the axis is None no perodic boundary conditions will be set.

Returns

lattLattice: The configured lattice instance.

Examples

Simple chain:

>>> import matplotlib.pyplot as plt
>>> latt = lp.finite_hypercubic(4)
>>> latt.plot()
>>> plt.show()

(png, pdf)

Simple square:

>>> import matplotlib.pyplot as plt
>>> latt = lp.finite_hypercubic((4, 2))
>>> latt.plot()
>>> plt.show()

(png, pdf)