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)

Bases: object

Helper container for each Wulff plane.

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

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))

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)

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)

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)

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

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