Icosahedral particle¶

class
wulffpack.
Icosahedron
(surface_energies, twin_energy, primitive_structure=None, natoms=1000, tol=1e05)[source]¶ An Icosahedron object is a generalized Wulff construction of an icosahedral particle.
 Parameters
surface_energies (
Dict
[tuple
,float
]) – A dictionary with surface energies, where keys are Miller indices and values surface energies (per area) in a unit of choice, such as J/m^2.twin_energy (
float
) – Energy per area for twin boundariesprimitive_structure (
Optional
[Atoms
]) – Primitive cell to define the atomic structure used if an atomic structure is requested. By default, an Au FCC structure is used. The crystal has to have cubic symmetry.natoms (
int
) – Together with lattice_parameter, this parameter defines the volume of the particle. If an atomic structure is requested, the number of atoms will as closely as possible match this value.tol (
float
) – Numerical tolerance parameter.
Example
The following example illustrates some possible uses of an Icosahedron object:
>>> from wulffpack import Icosahedron >>> from ase.build import bulk >>> from ase.io import write >>> surface_energies = {(1, 1, 1): 1.0, (1, 0, 0): 1.14} >>> particle = Icosahedron(surface_energies, ... twin_energy=0.03, ... primitive_structure=bulk('Au')) >>> particle.view() >>> write('icosahedron.xyz', particle.atoms) # Writes atomic structure

property
area
¶ Returns total area of the surface of the particle (not including twin boundaries).
 Return type

property
atoms
¶ Returns an ASE Atoms object
 Return type
Atoms

property
average_surface_energy
¶ Average surface energy for the Wulff construction, i.e., a weighted average over all the facets, where the weights are the area fraction of each facet.
 Return type

property
facet_fractions
¶ Returns a dict specifying fraction of each form (not including twin boundaries).

get_continuous_color_scheme
(base_colors=None, normalize=False)¶ Returns a dictionary with RGB colors for each form. The colors smoothly interpolate between three base colors, corresponding to (1, 1, 1), (1, 1, 0) and (1, 0, 0). Note that this is sensible primarily for cubic systems.
 Parameters
 Return type

get_strain_energy
(shear_modulus, poissons_ratio)[source]¶ Return a strain energy as estimated with the formula provided in A. Howie and L. D. Marks in Phil. Mag. A 49, 95 (1984) [HowMar84] (Eq. 23), which assumes an inhomogeneous strain in the particle.
Warning
This value is only approximate. If the icosahedron is heavily truncated, the returned strain energy may be highly inaccurate.
 Parameters
shear_modulus – Shear modulus of the material
poissons_ratio – Poisson’s ratio of the material

make_plot
(ax, alpha=0.85, linewidth=0.3, colors=None)¶ Plot a particle in an axis object. This function can be used to make customized plots of particles.
 Parameters
Example
In the following example, three different particles are plotted in the same figure:
>>> from wulffpack import SingleCrystal, Decahedron, Icosahedron >>> import matplotlib.pyplot as plt >>> from mpl_toolkits.mplot3d import Axes3D >>> >>> surface_energies = {(1, 1, 1): 1.0, ... (1, 0, 0): 1.1, ... (1, 1, 0): 1.15, ... (3, 2, 1): 1.15} >>> twin_energy = 0.05 >>> >>> fig = plt.figure(figsize=(3*4.0, 4.0)) >>> ax = fig.add_subplot(131, projection='3d') >>> particle = SingleCrystal(surface_energies) >>> particle.make_plot(ax) >>> >>> ax = fig.add_subplot(132, projection='3d') >>> particle = Decahedron(surface_energies, ... twin_energy=0.05) >>> particle.make_plot(ax) >>> >>> ax = fig.add_subplot(133, projection='3d') >>> particle = Icosahedron(surface_energies, ... twin_energy=0.05) >>> particle.make_plot(ax) >>> >>> plt.subplots_adjust(top=1, bottom=0, left=0, ... right=1, wspace=0, hspace=0) >>> plt.savefig('particles.png')

property
natoms
¶ The approximate number of atoms in the particle (implicitly defining the volume).

property
number_of_corners
¶ Returns the number of corners (vertices) on the particle.
 Return type

rotate_particle
(rotation)¶ Rotate the particle.
 Parameters
rotation (
ndarray
) – Rotation matrix

property
standardized_structure
¶ The standardized atomic structure that defines the geometry and thus the meaning of the Miller indices. Also forms the building blocks when particle.atoms is called.
 Return type
Atoms

property
surface_energy
¶ The total surface energy of the particle (including twin boundaries).
 Return type

translate_particle
(translation)¶ Translate the particle.
 Parameters
translation (list of 3 floats) – Translation vector

view
(alpha=0.85, linewidth=0.3, colors=None, legend=True, save_as=None)¶ Use matplotlib to view a rendition of the particle.
 Parameters
alpha (
float
) – Opacity of the faceslinewidth (
float
) – Thickness of lines between facescolors (
Optional
[dict
]) – Allows custom colors for facets of all or a subset of forms, example {(1, 1, 1): ‘#FF0000’}legend (
bool
) – Whether or not to show a legend with facetcolor definitionssave_as (
Optional
[str
]) – Filename to save figure as. If None, show the particle with the GUI instead.