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<title>pymatgen.analysis.quasiharmonic module — pymatgen 2019.5.1 documentation</title>
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<div class="section" id="module-pymatgen.analysis.quasiharmonic">
<span id="pymatgen-analysis-quasiharmonic-module"></span><h1>pymatgen.analysis.quasiharmonic module<a class="headerlink" href="#module-pymatgen.analysis.quasiharmonic" title="Permalink to this headline">¶</a></h1>
<p>This module implements the Quasi-harmonic Debye approximation that can
be used to compute thermal properties.</p>
<p>See the following papers for more info:</p>
<blockquote>
<div><p><a class="reference external" href="http://doi.org/10.1016/j.comphy.2003.12.001">http://doi.org/10.1016/j.comphy.2003.12.001</a> (2004)
<a class="reference external" href="http://doi.org/10.1103/PhysRevB.90.174107">http://doi.org/10.1103/PhysRevB.90.174107</a> (2014)</p>
</div></blockquote>
<dl class="class">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox">
<em class="property">class </em><code class="descname">QuasiharmonicDebyeApprox</code><span class="sig-paren">(</span><em>energies</em>, <em>volumes</em>, <em>structure</em>, <em>t_min=300.0</em>, <em>t_step=100</em>, <em>t_max=300.0</em>, <em>eos='vinet'</em>, <em>pressure=0.0</em>, <em>poisson=0.25</em>, <em>use_mie_gruneisen=False</em>, <em>anharmonic_contribution=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox" 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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>energies</strong> (<em>list</em>) – list of DFT energies in eV</p></li>
<li><p><strong>volumes</strong> (<em>list</em>) – list of volumes in Ang^3</p></li>
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.structure.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – </p></li>
<li><p><strong>t_min</strong> (<em>float</em>) – min temperature</p></li>
<li><p><strong>t_step</strong> (<em>float</em>) – temperature step</p></li>
<li><p><strong>t_max</strong> (<em>float</em>) – max temperature</p></li>
<li><p><strong>eos</strong> (<em>str</em>) – <p>equation of state used for fitting the energies and the
volumes.
options supported by pymatgen: “quadratic”, “murnaghan”, “birch”,</p>
<blockquote>
<div><p>”birch_murnaghan”, “pourier_tarantola”, “vinet”,
“deltafactor”, “numerical_eos”</p>
</div></blockquote>
</p></li>
<li><p><strong>pressure</strong> (<em>float</em>) – in GPa, optional.</p></li>
<li><p><strong>poisson</strong> (<em>float</em>) – poisson ratio.</p></li>
<li><p><strong>use_mie_gruneisen</strong> (<em>bool</em>) – whether or not to use the mie-gruneisen
formulation to compute the gruneisen parameter.
The default is the slater-gamma formulation.</p></li>
<li><p><strong>anharmonic_contribution</strong> (<em>bool</em>) – whether or not to consider the anharmonic
contribution to the Debye temperature. Cannot be used with
use_mie_gruneisen. Defaults to False.</p></li>
</ul>
</dd>
</dl>
<dl class="staticmethod">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.debye_integral">
<em class="property">static </em><code class="descname">debye_integral</code><span class="sig-paren">(</span><em>y</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.debye_integral"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.debye_integral" title="Permalink to this definition">¶</a></dt>
<dd><p>Debye integral. Eq(5) in doi.org/10.1016/j.comphy.2003.12.001</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>y</strong> (<em>float</em>) – debye temperature/T, upper limit</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>unitless</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.debye_temperature">
<code class="descname">debye_temperature</code><span class="sig-paren">(</span><em>volume</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.debye_temperature"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.debye_temperature" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the debye temperature.
Eq(6) in doi.org/10.1016/j.comphy.2003.12.001. Thanks to Joey.</p>
<p>Eq(6) above is equivalent to Eq(3) in doi.org/10.1103/PhysRevB.37.790
which does not consider anharmonic effects. Eq(20) in the same paper
and Eq(18) in doi.org/10.1016/j.commatsci.2009.12.006 both consider
anharmonic contributions to the Debye temperature through the Gruneisen
parameter at 0K (Gruneisen constant).</p>
<p>The anharmonic contribution is toggled by setting the anharmonic_contribution
to True or False in the QuasiharmonicDebyeApprox constructor.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>volume</strong> (<em>float</em>) – in Ang^3</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>debye temperature in K</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.get_summary_dict">
<code class="descname">get_summary_dict</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.get_summary_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.get_summary_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a dict with a summary of the computed properties.</p>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.gruneisen_parameter">
<code class="descname">gruneisen_parameter</code><span class="sig-paren">(</span><em>temperature</em>, <em>volume</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.gruneisen_parameter"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.gruneisen_parameter" title="Permalink to this definition">¶</a></dt>
<dd><dl>
<dt>Slater-gamma formulation(the default):</dt><dd><dl>
<dt>gruneisen paramter = - d log(theta)/ d log(V)</dt><dd><p>= - ( 1/6 + 0.5 d log(B)/ d log(V) )
= - (1/6 + 0.5 V/B dB/dV),</p>
<blockquote>
<div><p>where dB/dV = d^2E/dV^2 + V * d^3E/dV^3</p>
</div></blockquote>
</dd>
</dl>
</dd>
<dt>Mie-gruneisen formulation:</dt><dd><p>Eq(31) in doi.org/10.1016/j.comphy.2003.12.001
Eq(7) in Blanco et. al. Joumal of Molecular Structure (Theochem)</p>
<blockquote>
<div><p>368 (1996) 245-255</p>
</div></blockquote>
<dl class="simple">
<dt>Also se J.P. Poirier, Introduction to the Physics of the Earth’s</dt><dd><p>Interior, 2nd ed. (Cambridge University Press, Cambridge,
2000) Eq(3.53)</p>
</dd>
</dl>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – temperature in K</p></li>
<li><p><strong>volume</strong> (<em>float</em>) – in Ang^3</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>unitless</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.optimize_gibbs_free_energy">
<code class="descname">optimize_gibbs_free_energy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.optimize_gibbs_free_energy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.optimize_gibbs_free_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the gibbs free energy as a function of V, T and P i.e
G(V, T, P), minimize G(V, T, P) wrt V for each T and store the
optimum values.</p>
<dl class="simple">
<dt>Note: The data points for which the equation of state fitting fails</dt><dd><p>are skipped.</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.optimizer">
<code class="descname">optimizer</code><span class="sig-paren">(</span><em>temperature</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.optimizer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.optimizer" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate G(V, T, P) at the given temperature(and pressure) and
minimize it wrt V.</p>
<ol class="arabic simple">
<li><p>Compute the vibrational helmholtz free energy, A_vib.</p></li>
<li><dl class="simple">
<dt>Compute the gibbs free energy as a function of volume, temperature</dt><dd><p>and pressure, G(V,T,P).</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>Preform an equation of state fit to get the functional form of</dt><dd><p>gibbs free energy:G(V, T, P).</p>
</dd>
</dl>
</li>
<li><p>Finally G(V, P, T) is minimized with respect to V.</p></li>
</ol>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>temperature</strong> (<em>float</em>) – temperature in K</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>G_opt(V_opt, T, P) in eV and V_opt in Ang^3.</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float, float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.thermal_conductivity">
<code class="descname">thermal_conductivity</code><span class="sig-paren">(</span><em>temperature</em>, <em>volume</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.thermal_conductivity"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.thermal_conductivity" title="Permalink to this definition">¶</a></dt>
<dd><p>Eq(17) in 10.1103/PhysRevB.90.174107</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – temperature in K</p></li>
<li><p><strong>volume</strong> (<em>float</em>) – in Ang^3</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>thermal conductivity in W/K/m</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.vibrational_free_energy">
<code class="descname">vibrational_free_energy</code><span class="sig-paren">(</span><em>temperature</em>, <em>volume</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.vibrational_free_energy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.vibrational_free_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Vibrational Helmholtz free energy, A_vib(V, T).
Eq(4) in doi.org/10.1016/j.comphy.2003.12.001</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – temperature in K</p></li>
<li><p><strong>volume</strong> (<em>float</em>) – </p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>vibrational free energy in eV</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
<dl class="method">
<dt id="pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.vibrational_internal_energy">
<code class="descname">vibrational_internal_energy</code><span class="sig-paren">(</span><em>temperature</em>, <em>volume</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pymatgen/analysis/quasiharmonic.html#QuasiharmonicDebyeApprox.vibrational_internal_energy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pymatgen.analysis.quasiharmonic.QuasiharmonicDebyeApprox.vibrational_internal_energy" title="Permalink to this definition">¶</a></dt>
<dd><p>Vibrational internal energy, U_vib(V, T).
Eq(4) in doi.org/10.1016/j.comphy.2003.12.001</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>temperature</strong> (<em>float</em>) – temperature in K</p></li>
<li><p><strong>volume</strong> (<em>float</em>) – in Ang^3</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>vibrational internal energy in eV</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</div>
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