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<div class="section" id="fix-phonon-command">
<span id="index-0"></span><h1>fix phonon command<a class="headerlink" href="#fix-phonon-command" title="Permalink to this headline">¶</a></h1>
<div class="section" id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
<div class="highlight-python"><div class="highlight"><pre>fix ID group-ID phonon N Noutput Nwait map_file prefix keyword values ...
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
<li>phonon = style name of this fix command</li>
<li>N = measure the Green&#8217;s function every this many timesteps</li>
<li>Noutput = output the dynamical matrix every this many measurements</li>
<li>Nwait = wait this many timesteps before measuring</li>
<li>map_file = <em>file</em> or <em>GAMMA</em></li>
</ul>
<pre class="literal-block">
<em>file</em> is the file that contains the mapping info between atom ID and the lattice indices.
</pre>
<pre class="literal-block">
<em>GAMMA</em> flags to treate the whole simulation box as a unit cell, so that the mapping
info can be generated internally. In this case, dynamical matrix at only the gamma-point
will/can be evaluated.
</pre>
<ul class="simple">
<li>prefix = prefix for output files</li>
<li>one or none keyword/value pairs may be appended</li>
<li>keyword = <em>sysdim</em> or <em>nasr</em></li>
</ul>
<pre class="literal-block">
<em>sysdim</em> value = d
d = dimension of the system, usually the same as the MD model dimension
<em>nasr</em> value = n
n = number of iterations to enforce the acoustic sum rule
</pre>
</div>
<div class="section" id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
<div class="highlight-python"><div class="highlight"><pre>fix 1 all phonon 20 5000 200000 map.in LJ1D sysdim 1
fix 1 all phonon 20 5000 200000 map.in EAM3D
fix 1 all phonon 10 5000 500000 GAMMA EAM0D nasr 100
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p>Calculate the dynamical matrix from molecular dynamics simulations
based on fluctuation-dissipation theory for a group of atoms.</p>
<p>Consider a crystal with <em>N</em> unit cells in three dimensions labelled <em>l
= (l&lt;sub&gt;1&lt;/sub&gt;,l&lt;sub&gt;2&lt;/sub&gt;,l&lt;sub&gt;3&lt;/sub&gt;)</em> where <em>l&lt;sub&gt;i&lt;/sub&gt;</em>
are integers. Each unit cell is defined by three linearly independent
vectors <a href="#id1"><span class="problematic" id="id2">**</span></a>a**&lt;sub&gt;1&lt;/sub&gt;, <a href="#id3"><span class="problematic" id="id4">**</span></a>a**&lt;sub&gt;2&lt;/sub&gt;, <a href="#id5"><span class="problematic" id="id6">**</span></a>a**&lt;sub&gt;3&lt;/sub&gt; forming a
parallelipiped, containing <em>K</em> basis atoms labelled <em>k</em>.</p>
<p>Based on fluctuation-dissipation theory, the force constant
coefficients of the system in reciprocal space are given by
(<a class="reference internal" href="#campana"><span>Campa&amp;ntilde;&amp;aacute;</span></a> , <a class="reference internal" href="#kong"><span>Kong</span></a>)
&lt;center&gt;&lt;b&gt;&amp;Phi;&lt;/b&gt;&lt;sub&gt;k&amp;alpha;,k&#8217;&amp;beta;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;) =
k&lt;sub&gt;B&lt;/sub&gt;T
&lt;b&gt;G&lt;/b&gt;&lt;sup&gt;-1&lt;/sup&gt;&lt;sub&gt;k&amp;alpha;,k&#8217;&amp;beta;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;),&lt;/center&gt;</p>
<p>where <strong>G</strong> is the Green&#8217;s functions coefficients given by</p>
<center><b>G</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>) =
<<b>u</b><sub>k&alpha;</sub>(<b>q</b>)&#149;<b>u</b><sub>k'&beta;</sub><sup>*</sup>(<b>q</b>)>,</center><p>where &lt;...&gt; denotes the ensemble average, and
&lt;center&gt;**u**&lt;sub&gt;k&amp;alpha;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;) = &amp;sum;&lt;sub&gt;l&lt;/sub&gt;
&lt;b&gt;u&lt;/b&gt;&lt;sub&gt;lk&amp;alpha;&lt;/sub&gt; exp(i**qr**&lt;sub&gt;l&lt;/sub&gt;)&lt;/center&gt;</p>
<p>is the &amp;alpha; component of the atomic displacement for the <em>k*th atom
in the unit cell in reciprocal space at **q*</em>. In practice, the Green&#8217;s
functions coefficients can also be measured according to the following
formula,</p>
<center><b>G</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>) =
<<b>R</b><sub>k&alpha;</sub>(<b>q</b>)&#149;<b>R</b><sup>*</sup><sub>k'&beta;</sub>(<b>q</b>)>
- <<b>R</b>><sub>k&alpha;</sub>(<b>q</b>)&#149;<<b>R</b>><sup>*</sup><sub>k'&beta;</sub>(<b>q</b>),
</center><p>where <strong>R</strong> is the instantaneous positions of atoms, and &lt;<strong>R</strong>&gt; is the
averaged atomic positions. It gives essentially the same results as
the displacement method and is easier to implement in an MD code.</p>
<p>Once the force constant matrix is known, the dynamical matrix <strong>D</strong> can
then be obtained by</p>
<center><b>D</b><sub>k&alpha;, k'&beta;</sub>(<b>q</b>) = (m<sub>k</sub>m<sub>k'</sub>)<sup>-1/2</sup> <b>&Phi;</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>)</center><p>whose eigenvalues are exactly the phonon frequencies at <strong>q</strong>.</p>
<p>This fix uses positions of atoms in the specified group and calculates
two-point correlations. To achieve this. the positions of the atoms
are examined every <em>Nevery</em> steps and are Fourier-transformed into
reciprocal space, where the averaging process and correlation
computation is then done. After every <em>Noutput</em> measurements, the
matrix <strong>G**(**q</strong>) is calculated and inverted to obtain the elastic
stiffness coefficients. The dynamical matrices are then constructed
and written to <em>prefix</em>.bin.timestep files in binary format and to the
file <em>prefix</em>.log for each wavevector <strong>q</strong>.</p>
<p>A detailed description of this method can be found in
(<a class="reference internal" href="#kong2011"><span>Kong2011</span></a>).</p>
<p>The <em>sysdim</em> keyword is optional. If specified with a value smaller
than the dimensionality of the LAMMPS simulation, its value is used
for the dynamical matrix calculation. For example, using LAMMPS ot
model a 2D or 3D system, the phonon dispersion of a 1D atomic chain
can be computed using <em>sysdim</em> = 1.</p>
<p>The <em>nasr</em> keyword is optional. An iterative procedure is employed to
enforce the acoustic sum rule on &amp;Phi; at &amp;Gamma;, and the number
provided by keyword <em>nasr</em> gives the total number of iterations. For a
system whose unit cell has only one atom, <em>nasr</em> = 1 is sufficient;
for other systems, <em>nasr</em> = 10 is typically sufficient.</p>
<p>The <em>map_file</em> contains the mapping information between the lattice
indices and the atom IDs, which tells the code which atom sits at
which lattice point; the lattice indices start from 0. An auxiliary
code, <a class="reference external" href="http://code.google.com/p/latgen">latgen</a>, can be employed to
generate the compatible map file for various crystals.</p>
<p>In case one simulates an aperiodic system, where the whole simulation box
is treated as a unit cell, one can set <em>map_file</em> as <em>GAMMA</em>, so that the mapping
info will be generated internally and a file is not needed. In this case, the
dynamical matrix at only the gamma-point will/can be evaluated. Please keep in
mind that fix-phonon is designed for cyrstals, it will be inefficient and
even degrade the performance of lammps in case the unit cell is too large.</p>
<p>The calculated dynamical matrix elements are written out in
<a class="reference internal" href="units.html"><em>energy/distance^2/mass</em></a> units. The coordinates for <em>q</em>
points in the log file is in the units of the basis vectors of the
corresponding reciprocal lattice.</p>
</div>
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
<h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
<p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
fix. You can use it to change the temperature compute from thermo_temp
to the one that reflects the true temperature of atoms in the group.</p>
<p>No global scalar or vector or per-atom quantities are stored by this
fix for access by various <span class="xref std std-ref">output commands</span>.</p>
<p>Instead, this fix outputs its initialization information (including
mapping information) and the calculated dynamical matrices to the file
<em>prefix</em>.log, with the specified <em>prefix</em>. The dynamical matrices are
also written to files <em>prefix</em>.bin.timestep in binary format. These
can be read by the post-processing tool in tools/phonon to compute the
phonon density of states and/or phonon dispersion curves.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords
of the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
<p>This fix assumes a crystalline system with periodical lattice. The
temperature of the system should not exceed the melting temperature to
keep the system in its solid state.</p>
<p>This fix is part of the USER-PHONON package. It is only enabled if
LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
<p>This fix requires LAMMPS be built with an FFT library. See the
<a class="reference internal" href="Section_start.html#start-2"><span>Making LAMMPS</span></a> section for more info.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
<p><a class="reference internal" href="compute_msd.html"><em>compute msd</em></a></p>
</div>
<div class="section" id="default">
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
<p>The option defaults are sysdim = the same dimemsion as specified by
the <a class="reference external" href="dimension">dimension</a> command, and nasr = 20.</p>
<hr class="docutils" />
<p id="campana"><strong>(Campa&amp;ntilde;&amp;aacute;)</strong> C. Campa&amp;ntilde;&amp;aacute; and
M. H. M&amp;uuml;ser, <em>Practical Green&#8217;s function approach to the
simulation of elastic semi-infinite solids</em>, <a class="reference external" href="http://dx.doi.org/10.1103/PhysRevB.74.075420">Phys. Rev. B [74], 075420 (2006)</a></p>
<p id="kong"><strong>(Kong)</strong> L.T. Kong, G. Bartels, C. Campa&amp;ntilde;&amp;aacute;,
C. Denniston, and Martin H. M&amp;uuml;ser, <em>Implementation of Green&#8217;s
function molecular dynamics: An extension to LAMMPS</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2008.12.035">Computer Physics Communications [180](6):1004-1010 (2009).</a></p>
<p>L.T. Kong, C. Denniston, and Martin H. M&amp;uuml;ser,
<em>An improved version of the Green&#8217;s function molecular dynamics
method</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2010.10.006">Computer Physics Communications [182](2):540-541 (2011).</a></p>
<p id="kong2011"><strong>(Kong2011)</strong> L.T. Kong, <em>Phonon dispersion measured directly from
molecular dynamics simulations</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2011.04.019">Computer Physics Communications [182](10):2201-2207, (2011).</a></p>
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