pymatgen.analysis.wulff module

This module define a WulffShape class to generate the Wulff shape from a lattice, a list of indices and their corresponding surface energies, and the total area and volume of the wulff shape,the weighted surface energy, the anisotropy and shape_factor can also be calculated. In support of plotting from a given view in terms of miller index.

The lattice is from the conventional unit cell, and (hkil) for hexagonal lattices.

If you use this code extensively, consider citing the following:

Tran, R.; Xu, Z.; Radhakrishnan, B.; Winston, D.; Persson, K. A.; Ong, S. P. (2016). Surface energies of elemental crystals. Scientific Data.

class WulffFacet(normal, e_surf, normal_pt, dual_pt, index, m_ind_orig, miller)[source]

Bases: object

Helper container for each Wulff plane.

class WulffShape(lattice, miller_list, e_surf_list, symprec=1e-05)[source]

Bases: object

Generate Wulff Shape from list of miller index and surface energies, with given conventional unit cell. surface energy (Jm^2) is the length of normal.

Wulff shape is the convex hull. Based on: http://scipy.github.io/devdocs/generated/scipy.spatial.ConvexHull.html

Process:
  1. get wulff simplices
  2. label with color
  3. get wulff_area and other properties
debug(bool)
alpha
transparency
color_set
grid_off(bool)
axis_off(bool)
show_area
off_color
color of facets off wulff
structure
Structure object, input conventional unit cell (with H ) from lattice
miller_list
list of input miller index, for hcp in the form of hkil
hkl_list
modify hkill to hkl, in the same order with input_miller
e_surf_list
list of input surface energies, in the same order with input_miller
lattice
Lattice object, the input lattice for the conventional unit cell
facets
[WulffFacet] for all facets considering symm
dual_cv_simp
simplices from the dual convex hull (dual_pt)
wulff_pt_list
wulff_cv_simp
simplices from the convex hull of wulff_pt_list
on_wulff
list for all input_miller, True is on wulff.
color_area
list for all input_miller, total area on wulff, off_wulff = 0.
miller_area
($hkl$): area for all input_miller
Parameters:
  • lattice – Lattice object of the conventional unit cell
  • miller_list ([(hkl) – list of hkl or hkil for hcp
  • e_surf_list ([float]) – list of corresponding surface energies
  • symprec (float) – for recp_operation, default is 1e-5.
anisotropy

Returns – (float) Coefficient of Variation from weighted surface energy The ideal sphere is 0.

area_fraction_dict

**Returns* – (dict)* – {hkl: area_hkl/total area on wulff}

get_plot(color_set='PuBu', grid_off=True, axis_off=True, show_area=False, alpha=1, off_color='red', direction=None, bar_pos=(0.75, 0.15, 0.05, 0.65), bar_on=False, legend_on=True, aspect_ratio=(8, 8))[source]

Get the Wulff shape plot.

Parameters:
  • color_set – default is ‘PuBu’
  • grid_off (bool) – default is True
  • axis_off (bool) – default is Ture
  • show_area (bool) – default is False
  • alpha (float) – chosen from 0 to 1 (float), default is 1
  • off_color – color_legend for off_wulff facets on show_area legend
  • direction – default is (1, 1, 1)
  • bar_pos – default is [0.75, 0.15, 0.05, 0.65]
  • bar_on (bool) – default is False
  • legend_on (bool) – default is True
  • aspect_ratio – default is (8, 8)
Returns:

(matplotlib.pyplot)

miller_area_dict

Returns {hkl – area_hkl on wulff}

miller_energy_dict

Returns {hkl – surface energy_hkl}

shape_factor

This is useful for determining the critical nucleus size. A large shape factor indicates great anisotropy. See Ballufi, R. W., Allen, S. M. & Carter, W. C. Kinetics

of Materials. (John Wiley & Sons, 2005), p.461
Returns:(float) Shape factor.
show(*args, **kwargs)[source]

Show the Wulff plot.

Parameters:
  • *args – Passed to get_plot.
  • **kwargs – Passed to get_plot.
surface_area

Total surface area of Wulff shape.

volume

Volume of the Wulff shape

weighted_surface_energy

Returns – sum(surface_energy_hkl * area_hkl)/ sum(area_hkl)

get_tri_area(pts)[source]

Given a list of coords for 3 points, Compute the area of this triangle.

Parameters:pts – [a, b, c] three points
hkl_tuple_to_str(hkl)[source]

Prepare for display on plots “(hkl)” for surfaces Agrs:

hkl: in the form of [h, k, l] or (h, k, l)