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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="calculate-diffusion-coefficients">
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<h1><span class="section-number">8.3.8. </span>Calculate diffusion coefficients<a class="headerlink" href="#calculate-diffusion-coefficients" title="Link to this heading"></a></h1>
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<p>The diffusion coefficient <span class="math notranslate nohighlight">\(D\)</span> of a material can be measured in at least
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2 ways using various options in LAMMPS. See the <code class="docutils literal notranslate"><span class="pre">examples/DIFFUSE</span></code>
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directory for scripts that implement the 2 methods discussed here for
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a simple Lennard-Jones fluid model.</p>
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<p>The first method is to measure the mean-squared displacement (MSD) of
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the system, via the <a class="reference internal" href="compute_msd.html"><span class="doc">compute msd</span></a> command. The slope
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of the MSD versus time is proportional to the diffusion coefficient.
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The instantaneous MSD values can be accumulated in a vector via the
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<a class="reference internal" href="fix_vector.html"><span class="doc">fix vector</span></a> command, and a line fit to the vector to
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compute its slope via the <a class="reference internal" href="variable.html"><span class="doc">variable slope</span></a> function, and
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thus extract <span class="math notranslate nohighlight">\(D\)</span>.</p>
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<p>The second method is to measure the velocity auto-correlation function
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(VACF) of the system, via the <a class="reference internal" href="compute_vacf.html"><span class="doc">compute vacf</span></a>
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command. The time-integral of the VACF is proportional to the
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diffusion coefficient. The instantaneous VACF values can be
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accumulated in a vector via the <a class="reference internal" href="fix_vector.html"><span class="doc">fix vector</span></a> command,
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and time integrated via the <a class="reference internal" href="variable.html"><span class="doc">variable trap</span></a> function,
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and thus extract <span class="math notranslate nohighlight">\(D\)</span>.</p>
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