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<div class="section" id="module-pymatgen.analysis.wulff">
<span id="pymatgen-analysis-wulff-module"></span><h1>pymatgen.analysis.wulff module<a class="headerlink" href="#module-pymatgen.analysis.wulff" title="Permalink to this headline">¶</a></h1>
<p>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.</p>
<p>The lattice is from the conventional unit cell, and (hkil) for hexagonal
lattices.</p>
<p>If you use this code extensively, consider citing the following:</p>
<p>Tran, R.; Xu, Z.; Radhakrishnan, B.; Winston, D.; Persson, K. A.; Ong, S. P.
(2016). Surface energies of elemental crystals. Scientific Data.</p>
<dl class="class">
<dt id="pymatgen.analysis.wulff.WulffFacet">
<em class="property">class </em><code class="descname">WulffFacet</code><span class="sig-paren">(</span><em>normal</em>, <em>e_surf</em>, <em>normal_pt</em>, <em>dual_pt</em>, <em>index</em>, <em>m_ind_orig</em>, <em>miller</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#WulffFacet"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.WulffFacet" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>Helper container for each Wulff plane.</p>
</dd></dl>
<dl class="class">
<dt id="pymatgen.analysis.wulff.WulffShape">
<em class="property">class </em><code class="descname">WulffShape</code><span class="sig-paren">(</span><em>lattice</em>, <em>miller_list</em>, <em>e_surf_list</em>, <em>symprec=1e-05</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#WulffShape"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>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.</p>
<p>Wulff shape is the convex hull.
Based on:
<a class="reference external" href="http://scipy.github.io/devdocs/generated/scipy.spatial.ConvexHull.html">http://scipy.github.io/devdocs/generated/scipy.spatial.ConvexHull.html</a></p>
<dl class="simple">
<dt>Process:</dt><dd><ol class="arabic simple">
<li><p>get wulff simplices</p></li>
<li><p>label with color</p></li>
<li><p>get wulff_area and other properties</p></li>
</ol>
</dd>
</dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.debug">
<code class="descname">debug</code><span class="sig-paren">(</span><em>bool</em><span class="sig-paren">)</span><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.debug" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.alpha">
<code class="descname">alpha</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.alpha" title="Permalink to this definition">¶</a></dt>
<dt id="pymatgen.analysis.wulff.WulffShape.transparency">
<code class="descname">transparency</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.transparency" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.color_set">
<code class="descname">color_set</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.color_set" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.grid_off">
<code class="descname">grid_off</code><span class="sig-paren">(</span><em>bool</em><span class="sig-paren">)</span><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.grid_off" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.axis_off">
<code class="descname">axis_off</code><span class="sig-paren">(</span><em>bool</em><span class="sig-paren">)</span><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.axis_off" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.show_area">
<code class="descname">show_area</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.show_area" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.off_color">
<code class="descname">off_color</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.off_color" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">color of facets off wulff</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.structure">
<code class="descname">structure</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.structure" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">Structure object, input conventional unit cell (with H ) from lattice</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.miller_list">
<code class="descname">miller_list</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.miller_list" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">list of input miller index, for hcp in the form of hkil</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.hkl_list">
<code class="descname">hkl_list</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.hkl_list" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">modify hkill to hkl, in the same order with input_miller</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.e_surf_list">
<code class="descname">e_surf_list</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.e_surf_list" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">list of input surface energies, in the same order with input_miller</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.lattice">
<code class="descname">lattice</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.lattice" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">Lattice object, the input lattice for the conventional unit cell</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.facets">
<code class="descname">facets</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.facets" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">[WulffFacet] for all facets considering symm</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.dual_cv_simp">
<code class="descname">dual_cv_simp</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.dual_cv_simp" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">simplices from the dual convex hull (dual_pt)</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.wulff_pt_list">
<code class="descname">wulff_pt_list</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.wulff_pt_list" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.wulff_cv_simp">
<code class="descname">wulff_cv_simp</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.wulff_cv_simp" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">simplices from the convex hull of wulff_pt_list</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.on_wulff">
<code class="descname">on_wulff</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.on_wulff" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">list for all input_miller, True is on wulff.</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.color_area">
<code class="descname">color_area</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.color_area" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">list for all input_miller, total area on wulff, off_wulff = 0.</code></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.miller_area">
<code class="descname">miller_area</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.miller_area" title="Permalink to this definition">¶</a></dt>
<dt>
<code class="descname">($hkl$): area for all input_miller</code></dt>
<dd></dd></dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>lattice</strong> – Lattice object of the conventional unit cell</p></li>
<li><p><strong>miller_list</strong> (<em>[</em><em>(</em><em>hkl</em>) – list of hkl or hkil for hcp</p></li>
<li><p><strong>e_surf_list</strong> (<em>[</em><em>float</em><em>]</em>) – list of corresponding surface energies</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – for recp_operation, default is 1e-5.</p></li>
</ul>
</dd>
</dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.anisotropy">
<code class="descname">anisotropy</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.anisotropy" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns:
(float) Coefficient of Variation from weighted surface energy
The ideal sphere is 0.</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.area_fraction_dict">
<code class="descname">area_fraction_dict</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.area_fraction_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns:
(dict): {hkl: area_hkl/total area on wulff}</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.effective_radius">
<code class="descname">effective_radius</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.effective_radius" title="Permalink to this definition">¶</a></dt>
<dd><p>Radius of the Wulffshape when the
Wulffshape is approximated as a sphere.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>(float) radius.</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.wulff.WulffShape.get_line_in_facet">
<code class="descname">get_line_in_facet</code><span class="sig-paren">(</span><em>facet</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#WulffShape.get_line_in_facet"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.get_line_in_facet" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the sorted pts in a facet used to draw a line</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.wulff.WulffShape.get_plot">
<code class="descname">get_plot</code><span class="sig-paren">(</span><em>color_set='PuBu'</em>, <em>grid_off=True</em>, <em>axis_off=True</em>, <em>show_area=False</em>, <em>alpha=1</em>, <em>off_color='red'</em>, <em>direction=None</em>, <em>bar_pos=(0.75</em>, <em>0.15</em>, <em>0.05</em>, <em>0.65)</em>, <em>bar_on=False</em>, <em>units_in_JPERM2=True</em>, <em>legend_on=True</em>, <em>aspect_ratio=(8</em>, <em>8)</em>, <em>custom_colors={}</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#WulffShape.get_plot"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.get_plot" title="Permalink to this definition">¶</a></dt>
<dd><p>Get the Wulff shape plot.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>color_set</strong> – default is ‘PuBu’</p></li>
<li><p><strong>grid_off</strong> (<em>bool</em>) – default is True</p></li>
<li><p><strong>axis_off</strong> (<em>bool</em>) – default is Ture</p></li>
<li><p><strong>show_area</strong> (<em>bool</em>) – default is False</p></li>
<li><p><strong>alpha</strong> (<em>float</em>) – chosen from 0 to 1 (float), default is 1</p></li>
<li><p><strong>off_color</strong> – Default color for facets not present on the Wulff shape.</p></li>
<li><p><strong>direction</strong> – default is (1, 1, 1)</p></li>
<li><p><strong>bar_pos</strong> – default is [0.75, 0.15, 0.05, 0.65]</p></li>
<li><p><strong>bar_on</strong> (<em>bool</em>) – default is False</p></li>
<li><p><strong>legend_on</strong> (<em>bool</em>) – default is True</p></li>
<li><p><strong>aspect_ratio</strong> – default is (8, 8)</p></li>
<li><p><strong>(</strong><strong>{</strong><strong>(</strong><strong>h</strong><strong>,</strong><strong>k</strong><strong>,</strong><strong>l}</strong> (<em>custom_colors</em>) – [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.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(matplotlib.pyplot)</p>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.miller_area_dict">
<code class="descname">miller_area_dict</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.miller_area_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>area_hkl on wulff}</p>
<dl class="field-list simple">
<dt class="field-odd">Type</dt>
<dd class="field-odd"><p>Returns {hkl</p>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.miller_energy_dict">
<code class="descname">miller_energy_dict</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.miller_energy_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>surface energy_hkl}</p>
<dl class="field-list simple">
<dt class="field-odd">Type</dt>
<dd class="field-odd"><p>Returns {hkl</p>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.shape_factor">
<code class="descname">shape_factor</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.shape_factor" title="Permalink to this definition">¶</a></dt>
<dd><p>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</p>
<blockquote>
<div><p>of Materials. (John Wiley & Sons, 2005), p.461</p>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>(float) Shape factor.</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.wulff.WulffShape.show">
<code class="descname">show</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#WulffShape.show"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.show" title="Permalink to this definition">¶</a></dt>
<dd><p>Show the Wulff plot.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>*args</strong> – Passed to get_plot.</p></li>
<li><p><strong>**kwargs</strong> – Passed to get_plot.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.surface_area">
<code class="descname">surface_area</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.surface_area" title="Permalink to this definition">¶</a></dt>
<dd><p>Total surface area of Wulff shape.</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.tot_corner_sites">
<code class="descname">tot_corner_sites</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.tot_corner_sites" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the number of vertices in the convex hull.
Useful for identifying catalytically active sites.</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.tot_edges">
<code class="descname">tot_edges</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.tot_edges" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the number of edges in the convex hull.
Useful for identifying catalytically active sites.</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.total_surface_energy">
<code class="descname">total_surface_energy</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.total_surface_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Total surface energy of the Wulff shape.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>(float) sum(surface_energy_hkl * area_hkl)</p>
</dd>
</dl>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.volume">
<code class="descname">volume</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.volume" title="Permalink to this definition">¶</a></dt>
<dd><p>Volume of the Wulff shape</p>
</dd></dl>
<dl class="attribute">
<dt id="pymatgen.analysis.wulff.WulffShape.weighted_surface_energy">
<code class="descname">weighted_surface_energy</code><a class="headerlink" href="#pymatgen.analysis.wulff.WulffShape.weighted_surface_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns:
sum(surface_energy_hkl * area_hkl)/ sum(area_hkl)</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.wulff.get_tri_area">
<code class="descname">get_tri_area</code><span class="sig-paren">(</span><em>pts</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#get_tri_area"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.get_tri_area" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a list of coords for 3 points,
Compute the area of this triangle.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>pts</strong> – [a, b, c] three points</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="pymatgen.analysis.wulff.hkl_tuple_to_str">
<code class="descname">hkl_tuple_to_str</code><span class="sig-paren">(</span><em>hkl</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/wulff.html#hkl_tuple_to_str"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.wulff.hkl_tuple_to_str" title="Permalink to this definition">¶</a></dt>
<dd><p>Prepare for display on plots
“(hkl)” for surfaces
Agrs:</p>
<blockquote>
<div><p>hkl: in the form of [h, k, l] or (h, k, l)</p>
</div></blockquote>
</dd></dl>
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