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.

Parameters

• normal –

• e_surf –

• normal_pt –

• dual_pt –

• index –

• m_ind_orig –

• miller –

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.

property anisotropy

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

property area_fraction_dict

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

property effective_radius

Radius of the Wulffshape when the Wulffshape is approximated as a sphere.

Returns

(float) radius.

get_line_in_facet(facet)

Returns the sorted pts in a facet used to draw a line

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, units_in_JPERM2=True, legend_on=True, aspect_ratio=(8, 8), custom_colors={})

Get the Wulff shape plot.

Parameters

• color_set – default is ‘PuBu’

• grid_off (bool) – default is True

• axis_off (bool) – default is True

• show_area (bool) – default is False

• alpha (float) – chosen from 0 to 1 (float), default is 1

• off_color – Default color for facets not present on the Wulff shape.

• 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)

• ({(h (custom_colors) – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• k – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• l} – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• units_in_JPERM2 (bool) – Units of surface energy, defaults to Joules per square meter (True)

Returns

(matplotlib.pyplot)

get_plotly(color_set='PuBu', off_color='red', alpha=1, custom_colors={}, units_in_JPERM2=True)

Get the Wulff shape as a plotly Figure object.

Parameters

• color_set – default is ‘PuBu’

• alpha (float) – chosen from 0 to 1 (float), default is 1

• off_color – Default color for facets not present on the Wulff shape.

• ({(h (custom_colors) – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• k – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• l} – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

• units_in_JPERM2 (bool) – Units of surface energy, defaults to Joules per square meter (True)

Returns

(plotly.graph_objs.Figure)

property miller_area_dict

area_hkl on wulff}

Type

Returns {hkl

property miller_energy_dict

surface energy_hkl}

Type

Returns {hkl

property 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.

property surface_area

Total surface area of Wulff shape.

property tot_corner_sites

Returns the number of vertices in the convex hull. Useful for identifying catalytically active sites.

property tot_edges

Returns the number of edges in the convex hull. Useful for identifying catalytically active sites.

property total_surface_energy

Total surface energy of the Wulff shape.

Returns

(float) sum(surface_energy_hkl * area_hkl)

property volume

Volume of the Wulff shape

property 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)