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<div class="section" id="module-pymatgen.analysis.substrate_analyzer">
<span id="pymatgen-analysis-substrate-analyzer-module"></span><h1>pymatgen.analysis.substrate_analyzer module<a class="headerlink" href="#module-pymatgen.analysis.substrate_analyzer" title="Permalink to this headline">¶</a></h1>
<p>This module provides classes to identify optimal substrates for film growth</p>
<dl class="py class">
<dt id="pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer">
<em class="property">class </em><code class="sig-name descname">SubstrateAnalyzer</code><span class="sig-paren">(</span><em class="sig-param">zslgen=<pymatgen.analysis.substrate_analyzer.ZSLGenerator object></em>, <em class="sig-param">film_max_miller=1</em>, <em class="sig-param">substrate_max_miller=1</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L216-L399"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer" 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>This class applies a set of search criteria to identify suitable
substrates for film growth. It first uses a topoplogical search by Zur
and McGill to identify matching super-lattices on various faces of the
two materials. Additional criteria can then be used to identify the most
suitable substrate. Currently, the only additional criteria is the
elastic strain energy of the super-lattices</p>
<p>Initializes the substrate analyzer
:param zslgen: Defaults to a ZSLGenerator with standard</p>
<blockquote>
<div><p>tolerances, but can be fed one with custom tolerances</p>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>film_max_miller</strong> (<em>int</em>) – maximum miller index to generate for film
surfaces</p></li>
<li><p><strong>substrate_max_miller</strong> (<em>int</em>) – maximum miller index to generate for
substrate surfaces</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.calculate">
<code class="sig-name descname">calculate</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">film</span></em>, <em class="sig-param"><span class="n">substrate</span></em>, <em class="sig-param"><span class="n">elasticity_tensor</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">film_millers</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">substrate_millers</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">ground_state_energy</span><span class="o">=</span><span class="default_value">0</span></em>, <em class="sig-param"><span class="n">lowest</span><span class="o">=</span><span class="default_value">False</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L274-L345"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.calculate" title="Permalink to this definition">¶</a></dt>
<dd><p>Finds all topological matches for the substrate and calculates elastic
strain energy and total energy for the film if elasticity tensor and
ground state energy are provided:</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>film</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – conventional standard structure for the film</p></li>
<li><p><strong>substrate</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – conventional standard structure for the
substrate</p></li>
<li><p><strong>elasticity_tensor</strong> (<a class="reference internal" href="pymatgen.analysis.elasticity.elastic.html#pymatgen.analysis.elasticity.elastic.ElasticTensor" title="pymatgen.analysis.elasticity.elastic.ElasticTensor"><em>ElasticTensor</em></a>) – elasticity tensor for the film
in the IEEE orientation</p></li>
<li><p><strong>film_millers</strong> (<em>array</em>) – film facets to consider in search as defined by
miller indicies</p></li>
<li><p><strong>substrate_millers</strong> (<em>array</em>) – substrate facets to consider in search as
defined by miller indicies</p></li>
<li><p><strong>ground_state_energy</strong> (<em>float</em>) – ground state energy for the film</p></li>
<li><p><strong>lowest</strong> (<em>bool</em>) – only consider lowest matching area for each surface</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.calculate_3D_elastic_energy">
<code class="sig-name descname">calculate_3D_elastic_energy</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">film</span></em>, <em class="sig-param"><span class="n">match</span></em>, <em class="sig-param"><span class="n">elasticity_tensor</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">include_strain</span><span class="o">=</span><span class="default_value">False</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L347-L399"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.calculate_3D_elastic_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the multi-plane elastic energy. Returns 999 if no elastic
tensor was given on init</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>film</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – conventional standard structure for the film</p></li>
<li><p><strong>match</strong> (<em>dictionary</em>) – match dictionary from substrate analyzer</p></li>
<li><p><strong>elasticity_tensor</strong> (<a class="reference internal" href="pymatgen.analysis.elasticity.elastic.html#pymatgen.analysis.elasticity.elastic.ElasticTensor" title="pymatgen.analysis.elasticity.elastic.ElasticTensor"><em>ElasticTensor</em></a>) – elasticity tensor for the film</p></li>
<li><p><strong>include_strain</strong> (<em>bool</em>) – include strain in the output or not; changes
return from just the energy to a tuple with the energy and strain
in voigt notation</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.generate_surface_vectors">
<code class="sig-name descname">generate_surface_vectors</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">film_millers</span></em>, <em class="sig-param"><span class="n">substrate_millers</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L243-L272"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.SubstrateAnalyzer.generate_surface_vectors" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates the film/substrate slab combinations for a set of given
miller indicies</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>film_millers</strong> (<em>array</em>) – all miller indices to generate slabs for
film</p></li>
<li><p><strong>substrate_millers</strong> (<em>array</em>) – all miller indicies to generate slabs
for substrate</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt id="pymatgen.analysis.substrate_analyzer.ZSLGenerator">
<em class="property">class </em><code class="sig-name descname">ZSLGenerator</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">max_area_ratio_tol</span><span class="o">=</span><span class="default_value">0.09</span></em>, <em class="sig-param"><span class="n">max_area</span><span class="o">=</span><span class="default_value">400</span></em>, <em class="sig-param"><span class="n">max_length_tol</span><span class="o">=</span><span class="default_value">0.03</span></em>, <em class="sig-param"><span class="n">max_angle_tol</span><span class="o">=</span><span class="default_value">0.01</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L28-L213"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.ZSLGenerator" 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>This class generate matching interface super lattices based on the methodology
of lattice vector matching for heterostructural interfaces proposed by
Zur and McGill:
Journal of Applied Physics 55 (1984), 378 ; doi: 10.1063/1.333084
The process of generating all possible matching super lattices is:
1.) Reduce the surface lattice vectors and calculate area for the surfaces
2.) Generate all super lattice transformations within a maximum allowed area</p>
<blockquote>
<div><p>limit that give nearly equal area super-lattices for the two
surfaces - generate_sl_transformation_sets</p>
</div></blockquote>
<dl>
<dt>3.) For each superlattice set:</dt><dd><p>1.) Reduce super lattice vectors
2.) Check length and angle between film and substrate super lattice</p>
<blockquote>
<div><p>vectors to determine if the super lattices are the nearly same
and therefore coincident - get_equiv_transformations</p>
</div></blockquote>
</dd>
<dt>Intialize a Zur Super Lattice Generator for a specific film and</dt><dd><p>substrate</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>max_area_ratio_tol</strong> (<em>float</em>) – Max tolerance on ratio of
super-lattices to consider equal</p></li>
<li><p><strong>max_area</strong> (<em>float</em>) – max super lattice area to generate in search</p></li>
<li><p><strong>max_length_tol</strong> – maximum length tolerance in checking if two
vectors are of nearly the same length</p></li>
<li><p><strong>max_angle_tol</strong> – maximum angle tolerance in checking of two sets
of vectors have nearly the same angle between them</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.ZSLGenerator.generate_sl_transformation_sets">
<code class="sig-name descname">generate_sl_transformation_sets</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">film_area</span></em>, <em class="sig-param"><span class="n">substrate_area</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L87-L114"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.ZSLGenerator.generate_sl_transformation_sets" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates transformation sets for film/substrate pair given the
area of the unit cell area for the film and substrate. The
transformation sets map the film and substrate unit cells to super
lattices with a maximum area
:param film_area: the unit cell area for the film
:type film_area: int
:param substrate_area: the unit cell area for the substrate
:type substrate_area: int</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p><dl class="simple">
<dt>a set of transformation_sets defined as:</dt><dd><p>1.) the transformation matricies for the film to create a
super lattice of area i*film area
2.) the tranformation matricies for the substrate to create
a super lattice of area j*film area</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>transformation_sets</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.ZSLGenerator.get_equiv_transformations">
<code class="sig-name descname">get_equiv_transformations</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">transformation_sets</span></em>, <em class="sig-param"><span class="n">film_vectors</span></em>, <em class="sig-param"><span class="n">substrate_vectors</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L116-L152"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.ZSLGenerator.get_equiv_transformations" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the transformation_sets to the film and substrate vectors
to generate super-lattices and checks if they matches.
Returns all matching vectors sets.
:param transformation_sets: an array of transformation sets:</p>
<blockquote>
<div><p>each transformation set is an array with the (i,j)
indicating the area multipes of the film and subtrate it
corresponds to, an array with all possible transformations
for the film area multiple i and another array for the
substrate area multiple j.</p>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>film_vectors</strong> (<em>array</em>) – film vectors to generate super lattices</p></li>
<li><p><strong>substrate_vectors</strong> (<em>array</em>) – substrate vectors to generate super
lattices</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.ZSLGenerator.is_same_vectors">
<code class="sig-name descname">is_same_vectors</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">vec_set1</span></em>, <em class="sig-param"><span class="n">vec_set2</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L70-L85"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.ZSLGenerator.is_same_vectors" title="Permalink to this definition">¶</a></dt>
<dd><p>Determine if two sets of vectors are the same within length and angle
tolerances
:param vec_set1: an array of two vectors
:type vec_set1: array[array]
:param vec_set2: second array of two vectors
:type vec_set2: array[array]</p>
</dd></dl>
<dl class="py method">
<dt id="pymatgen.analysis.substrate_analyzer.ZSLGenerator.match_as_dict">
<code class="sig-name descname">match_as_dict</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">film_sl_vectors</span></em>, <em class="sig-param"><span class="n">substrate_sl_vectors</span></em>, <em class="sig-param"><span class="n">film_vectors</span></em>, <em class="sig-param"><span class="n">substrate_vectors</span></em>, <em class="sig-param"><span class="n">match_area</span></em>, <em class="sig-param"><span class="n">film_transformation</span></em>, <em class="sig-param"><span class="n">substrate_transformation</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L188-L213"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.ZSLGenerator.match_as_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns dict which contains ZSL match
:param film_miller:
:type film_miller: array
:param substrate_miller:
:type substrate_miller: array</p>
</dd></dl>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.fast_norm">
<code class="sig-name descname">fast_norm</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">a</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L444-L448"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.fast_norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Much faster variant of numpy linalg norm</p>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.gen_sl_transform_matricies">
<code class="sig-name descname">gen_sl_transform_matricies</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">area_multiple</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L402-L423"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.gen_sl_transform_matricies" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates the transformation matricies that convert a set of 2D
vectors into a super lattice of integer area multiple as proven
in Cassels:</p>
<p>Cassels, John William Scott. An introduction to the geometry of
numbers. Springer Science & Business Media, 2012.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>area_multiple</strong> (<em>int</em>) – integer multiple of unit cell area for super</p></li>
<li><p><strong>area</strong> (<em>lattice</em>) – </p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>transformation matricies to covert unit vectors to
super lattice vectors</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>matrix_list</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.get_factors">
<code class="sig-name descname">get_factors</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L487-L493"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.get_factors" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate all factors of n</p>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.reduce_vectors">
<code class="sig-name descname">reduce_vectors</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">a</span></em>, <em class="sig-param"><span class="n">b</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L467-L484"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.reduce_vectors" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate independent and unique basis vectors based on the
methodology of Zur and McGill</p>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.rel_angle">
<code class="sig-name descname">rel_angle</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">vec_set1</span></em>, <em class="sig-param"><span class="n">vec_set2</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L433-L441"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.rel_angle" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate the relative angle between two vector sets</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>vec_set1</strong> (<em>array</em><em>[</em><em>array</em><em>]</em>) – an array of two vectors</p></li>
<li><p><strong>vec_set2</strong> (<em>array</em><em>[</em><em>array</em><em>]</em>) – second array of two vectors</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.rel_strain">
<code class="sig-name descname">rel_strain</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">vec1</span></em>, <em class="sig-param"><span class="n">vec2</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L426-L430"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.rel_strain" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate relative strain between two vectors</p>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.vec_angle">
<code class="sig-name descname">vec_angle</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">a</span></em>, <em class="sig-param"><span class="n">b</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L451-L457"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.vec_angle" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate angle between two vectors</p>
</dd></dl>
<dl class="py function">
<dt id="pymatgen.analysis.substrate_analyzer.vec_area">
<code class="sig-name descname">vec_area</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">a</span></em>, <em class="sig-param"><span class="n">b</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2021.1.28/pymatgen/analysis/substrate_analyzer.py#L460-L464"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.substrate_analyzer.vec_area" title="Permalink to this definition">¶</a></dt>
<dd><p>Area of lattice plane defined by two vectors</p>
</dd></dl>
</div>
</div>
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