Winterbottom construction¶

class
wulffpack.
Winterbottom
(surface_energies, interface_direction, interface_energy, primitive_structure=None, natoms=1000, tol=1e05)[source]¶ A Winterbottom object is a Winterbottom construction, i.e., the lowest energy shape adopted by a single crystalline particle in contact with an interface.
 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.interface_direction (
tuple
) – Miller indices for the interface facet.interface_energy (
float
) – Energy per area for twin boundaries.primtive_structure – primitive structure to implicitly define the point group as well as the atomic structure used if an atomic structure is requested. By default, an Au FCC structure is used.
natoms (
int
) – Together with primitive_structure, 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 a Winterbottom object:
>>> from wulffpack import Winterbottom >>> from ase.build import bulk >>> from ase.io import write >>> surface_energies = {(1, 1, 0): 1.0, (1, 0, 0): 1.08} >>> prim = bulk('Fe', a=4.1, crystalstructure='bcc') >>> particle = Winterbottom(surface_energies=surface_energies, ... interface_direction=(3, 2, 1), ... interface_energy=0.4, ... primitive_structure=prim) >>> particle.view() >>> write('winterbottom.xyz', particle.atoms) # Writes atomic structure to file

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

property
atoms
¶ Returns an ASE Atoms object

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

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.