<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
<p>where <span class="math">\(\mathbf{R}\)</span> is the instantaneous positions of atoms, and <span class="math">\(\left<\mathbf{R}\right>\)</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
<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>
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<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 <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>.</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 <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">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 class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<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’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’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’s function molecular dynamics
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