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<li><a class="reference internal" href="#">fix phonon command</a><ul>
<li><a class="reference internal" href="#syntax">Syntax</a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
<li><a class="reference internal" href="#description">Description</a></li>
<li><a class="reference internal" href="#restart-fix-modify-output-run-start-stop-minimize-info">Restart, fix_modify, output, run start/stop, minimize info</a></li>
<li><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li><a class="reference internal" href="#related-commands">Related commands</a></li>
<li><a class="reference internal" href="#default">Default</a></li>
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<div class="section" id="fix-phonon-command">
<span id="index-0"></span><h1>fix phonon command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">phonon</span> <span class="n">N</span> <span class="n">Noutput</span> <span class="n">Nwait</span> <span class="n">map_file</span> <span class="n">prefix</span> <span class="n">keyword</span> <span class="n">values</span> <span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></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</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">phonon</span> <span class="mi">20</span> <span class="mi">5000</span> <span class="mi">200000</span> <span class="nb">map</span><span class="o">.</span><span class="ow">in</span> <span class="n">LJ1D</span> <span class="n">sysdim</span> <span class="mi">1</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">phonon</span> <span class="mi">20</span> <span class="mi">5000</span> <span class="mi">200000</span> <span class="nb">map</span><span class="o">.</span><span class="ow">in</span> <span class="n">EAM3D</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">phonon</span> <span class="mi">10</span> <span class="mi">5000</span> <span class="mi">500000</span> <span class="n">GAMMA</span> <span class="n">EAM0D</span> <span class="n">nasr</span> <span class="mi">100</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</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 <span class="math">\(N\)</span> unit cells in three dimensions labelled <span class="math">\(l = (l_1, l_2, l_3)\)</span> where <span class="math">\(l_i\)</span>
are integers. Each unit cell is defined by three linearly independent
vectors <span class="math">\(\mathbf{a}_1\)</span>, <span class="math">\(\mathbf{a}_2\)</span>, <span class="math">\(\mathbf{a}_3\)</span> forming a
parallelipiped, containing <span class="math">\(K\)</span> basis atoms labeled <span class="math">\(k\)</span>.</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 class="std std-ref">Campana</span></a> , <a class="reference internal" href="#kong"><span class="std std-ref">Kong</span></a>)</p>
<div class="math">
\[\begin{equation}\mathbf{\Phi}_{k\alpha,k^\prime \beta}(\mathbf{q}) = k_B T \mathbf{G}^{-1}_{k\alpha,k^\prime \beta}(\mathbf{q})\end{equation}\]</div>
<p>where <span class="math">\(\mathbf{G}\)</span> is the Green&#8217;s functions coefficients given by</p>
<div class="math">
\[\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) = \left&lt; \mathbf{u}_{k\alpha}(\mathbf{q}) \bullet \mathbf{u}_{k^\prime \beta}^*(\mathbf{q}) \right&gt;\end{equation}\]</div>
<p>where <span class="math">\(\left&lt; \ldots \right&gt;\)</span> denotes the ensemble average, and</p>
<div class="math">
\[\begin{equation}\mathbf{u}_{k\alpha}(\mathbf{q}) = \sum_l \mathbf{u}_{l k \alpha} \exp{(i\mathbf{qr}_l)}\end{equation}\]</div>
<p>is the <span class="math">\(\alpha\)</span> component of the atomic displacement for the <span class="math">\(k\)</span> th atom
in the unit cell in reciprocal space at <span class="math">\(\mathbf{q}\)</span>. In practice, the Green&#8217;s
functions coefficients can also be measured according to the following
formula,</p>
<div class="math">
\[\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) =
\left&lt; \mathbf{R}_{k \alpha}(\mathbf{q}) \bullet \mathbf{R}^*_{k^\prime \beta}(\mathbf{q}) \right&gt;
- \left&lt;\mathbf{R}\right&gt;_{k \alpha}(\mathbf{q}) \bullet \left&lt;\mathbf{R}\right&gt;^*_{k^\prime \beta}(\mathbf{q})\end{equation}\]</div>
<p>where <span class="math">\(\mathbf{R}\)</span> is the instantaneous positions of atoms, and <span class="math">\(\left&lt;\mathbf{R}\right&gt;\)</span> 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 <span class="math">\(\mathbf{D}\)</span> can
then be obtained by</p>
<div class="math">
\[\begin{equation}\mathbf{D}_{k\alpha, k^\prime\beta}(\mathbf{q}) =
(m_k m_{k^\prime})^{-\frac{1}{2}} \mathbf{\Phi}_{k \alpha, k^\prime \beta}(\mathbf{q})\end{equation}\]</div>
<p>whose eigenvalues are exactly the phonon frequencies at <span class="math">\(\mathbf{q}\)</span>.</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 <span class="math">\(\mathbf{G}(\mathbf{q})\)</span> 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 <span class="math">\(\mathbf{q}\)</span>.</p>
<p>A detailed description of this method can be found in
(<a class="reference internal" href="#kong2011"><span class="std std-ref">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 <span class="math">\(\Phi\)</span> at <span class="math">\(\Gamma\)</span>, 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"><span class="doc">energy/distance^2/mass</span></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</h2>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>.</p>
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></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"><span class="doc">run</span></a> command.</p>
<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</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 <span class="xref std std-ref">Making LAMMPS</span> section for more info.</p>
<p>This fix requires LAMMPS be built with an FFT library. See the
<span class="xref std std-ref">Making LAMMPS</span> section for more info.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="compute_msd.html"><span class="doc">compute msd</span></a></p>
</div>
<div class="section" id="default">
<h2>Default</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>(Campana)</strong> C. Campana and
M. H. Muser, <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. Campana,
C. Denniston, and Martin H. Muser, <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. Muser,
<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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