Core components¶
Base particle¶

class
wulffpack.core.
BaseParticle
(forms, standardized_structure, natoms, ngrains=1, volume_scale=1.0, tol=1e05)[source]¶ Base class for Wulff constructions, useful for systems of (almost) any symmetry.
The Wulff construction calculates the vertices of the dual, calculates the convex hull of those vertices using scipy’s ConvexHull, and then converts the dual back to the Wulff shape.
 Parameters
forms (
List
[Form
]) – List of forms belonging to the system at handstandardized_structure (
Atoms
) – The structural unit implicitly carrying information about basis vectors etc.natoms (
int
) – Used as a target number of atoms if an atomistic structure is requested. Together with standardized_structure, natoms also defines the volume of the particle.ngrains (
int
) – If only a part of a complete particle is to be constructed, for example a fifth of a decahedron, this should be reflected by this parameter.volume_scale (
int
) – Decahedral and icosahedral particle need to be strained to fill space. With this parameter, the volume is scaled such that the volume of the particle is correct after this straining.tolerance – Numerical tolerance

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

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)[source]¶ 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

make_plot
(ax, alpha=0.85, linewidth=0.3, colors=None)[source]¶ 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)[source]¶ 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)[source]¶ Translate the particle.
 Parameters
translation (list of 3 floats) – Translation vector

view
(alpha=0.85, linewidth=0.3, colors=None, save_as=None)[source]¶ 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’}save_as (
Optional
[str
]) – Filename to save figure as. If None, show the particle with the GUI instead.
Form¶

class
wulffpack.core.
Form
(miller_indices, energy, cell, symmetries, parent_miller_indices)[source]¶ A Form object contains all facets that are equivalent by the symmetry of the system under consideration. For a cubic system, this means that the form with Miller indices {100} will contain the facets with normals [100], [100], [010] etc.
 Parameters
miller_indices (
tuple
) – Miller indices for a representative member of the form.energy (
float
) – The surface energy per area for a facet in this form.cell (
ndarray
) – The cell, with the basis vectors as columns.symmetries (
List
[ndarray
]) – Symmetry elements of the system. If symmetry is broken by, e.g., the presence of an interface, this list should only contain the symmetries surviving.parent_miller_indices (
tuple
) – If symmetry is broken, it may still be of interest to know what its form would be had not the symmetry been broken. This attribute contains the Miller indices for a representative of such a form.

property
surface_energy
¶ Returns the total surface energy of the facets in this form.
 Return type
Facet¶

class
wulffpack.core.
Facet
(normal, energy, symmetry, original_grain=True, tol=1e05)[source]¶ A Facet carries information about a particular facet, i.e., only one facet out of potentially several that are equivalent by symmetry.
 Parameters
normal (
Union
[List
[float
],Tuple
[float
]]) – The normal to the surface in Cartesian coordintesenergy (
float
) – Surface energy (in units of energy per surface area)rotation – Symmetry operation (acting on scaled coordinates) that carried an arbtriraily defined “parent facet” to this facet
original_grain (
bool
) – If True, this facet is part of an “original grain”, i.e., in the case of decahedron/icosahedron, it is part of the first created tetrahedrontol (
float
) – Numerical tolerance

add_vertex
(vertex)[source]¶ Add a vertex to the list of vertices. This function checks that there is not already such a vertex, to ensure that no vertex is duplicated. It is also checked that the vertex lies in the expected plane (as defined by the first vertex and the surface normal).

property
face_as_triangles
¶ Given N 3D coordinates, ABCD…N, split them into triangles that do not overlap. Two of the vertices of each triangle will be vertices of the face, the third vertex will be the origin.

get_volume
(origin=None)[source]¶ Calculate the volume formed by the pyramid having the face as its base and the specified origin as its tip.
 Parameters
origin (list of 3 ints) – The origin
 Returns
 Return type
The total volume

property
ordered_vertices
¶ Returns the vertices ordered such that they enclose a polygon. The first/last vertex occurs twice.
It is assumed (but not checked) that the coordinates lie in a plane and that they form a convex polygon.
 Return type
List
[ndarray
]