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< 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’ 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
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info can be generated internally. In this case, dynamical matrix at only the gamma-point
will/can be evaluated.
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< / 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
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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
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< / 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
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fix 1 all phonon 20 5000 200000 map.in EAM3D
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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< sub> 1< /sub> ,l< sub> 2< /sub> ,l< sub> 3< /sub> )< / em > where < em > l< sub> i< /sub> < / em >
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are integers. Each unit cell is defined by three linearly independent
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vectors < a href = "#id1" > < span class = "problematic" id = "id2" > **< / span > < / a > a**< sub> 1< /sub> , < a href = "#id3" > < span class = "problematic" id = "id4" > **< / span > < / a > a**< sub> 2< /sub> , < a href = "#id5" > < span class = "problematic" id = "id6" > **< / span > < / a > a**< sub> 3< /sub> forming a
parallelipiped, containing < em > K< / em > basis atoms labelled < em > k< / em > .< / p >
< p > Based on fluctuation-dissipation theory, the force constant
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coefficients of the system in reciprocal space are given by
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(< a class = "reference internal" href = "#campana" > < span > Campa& ntilde;& aacute;< / span > < / a > , < a class = "reference internal" href = "#kong" > < span > Kong< / span > < / a > )
< center> < b> & Phi;< /b> < sub> k& alpha;,k’ & beta;< /sub> (< b> q< /b> ) =
k< sub> B< /sub> T
< b> G< /b> < sup> -1< /sup> < sub> k& alpha;,k’ & beta;< /sub> (< b> q< /b> ),< /center> < / p >
< p > where < strong > G< / strong > is the Green’ s functions coefficients given by< / p >
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< center > < b > G< / b > < sub > kα ,k'β < / sub > (< b > q< / b > ) =
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< < b > u< / b > < sub > kα < / sub > (< b > q< / b > )• < b > u< / b > < sub > k'β < / sub > < sup > *< / sup > (< b > q< / b > )>,< / center > < p > where < ...> denotes the ensemble average, and
< center> **u**< sub> k& alpha;< /sub> (< b> q< /b> ) = & sum;< sub> l< /sub>
< b> u< /b> < sub> lk& alpha;< /sub> exp(i**qr**< sub> l< /sub> )< /center> < / p >
< p > is the & 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’ s
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functions coefficients can also be measured according to the following
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formula,< / p >
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< center > < b > G< / b > < sub > kα ,k'β < / sub > (< b > q< / b > ) =
< < b > R< / b > < sub > kα < / sub > (< b > q< / b > )• < b > R< / b > < sup > *< / sup > < sub > k'β < / sub > (< b > q< / b > )>
- < < b > R< / b > >< sub > kα < / sub > (< b > q< / b > )• < < b > R< / b > >< sup > *< / sup > < sub > k'β < / sub > (< b > q< / b > ),
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< / center > < p > where < strong > R< / strong > is the instantaneous positions of atoms, and < < strong > R< / strong > > is the
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averaged atomic positions. It gives essentially the same results as
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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 > kα , k'β < / sub > (< b > q< / b > ) = (m< sub > k< / sub > m< sub > k'< / sub > )< sup > -1/2< / sup > < b > Φ < / b > < sub > kα ,k'β < / 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
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two-point correlations. To achieve this. the positions of the atoms
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are examined every < em > Nevery< / em > steps and are Fourier-transformed into
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reciprocal space, where the averaging process and correlation
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computation is then done. After every < em > Noutput< / em > measurements, the
matrix < strong > G**(**q< / strong > ) is calculated and inverted to obtain the elastic
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stiffness coefficients. The dynamical matrices are then constructed
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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
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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
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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 & Phi; at & 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
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indices and the atom IDs, which tells the code which atom sits at
which lattice point; the lattice indices start from 0. An auxiliary
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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
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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
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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 >
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points in the log file is in the units of the basis vectors of the
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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
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fix. You can use it to change the temperature compute from thermo_temp
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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
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mapping information) and the calculated dynamical matrices to the file
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< 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
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can be read by the post-processing tool in tools/phonon to compute the
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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
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temperature of the system should not exceed the melting temperature to
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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& ntilde;& aacute;)< / strong > C. Campa& ntilde;& aacute; and
M. H. M& uuml;ser, < 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. Campa& ntilde;& aacute;,
C. Denniston, and Martin H. M& uuml;ser, < 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. M& uuml;ser,
< em > An improved version of the Green’ 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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