2016-05-10 01:33:12 +08:00
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< li > fix phonon command< / 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 >
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< pre class = "literal-block" >
fix ID group-ID phonon N Noutput Nwait map_file prefix keyword values ...
< / pre >
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< 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’ 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’ s functions coefficients given by< / p >
< div class = "math" >
\[\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) = \left< \mathbf{u}_{k\alpha}(\mathbf{q}) \bullet \mathbf{u}_{k^\prime \beta}^*(\mathbf{q}) \right> \end{equation}\]< / div >
< p > where < span class = "math" > \(\left< \ldots \right> \)< / 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’ s
functions coefficients can also be measured according to the following
formula,< / p >
< div class = "math" >
\[\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) =
\left< \mathbf{R}_{k \alpha}(\mathbf{q}) \bullet \mathbf{R}^*_{k^\prime \beta}(\mathbf{q}) \right>
- \left< \mathbf{R}\right> _{k \alpha}(\mathbf{q}) \bullet \left< \mathbf{R}\right> ^*_{k^\prime \beta}(\mathbf{q})\end{equation}\]< / div >
< p > where < span class = "math" > \(\mathbf{R}\)< / span > is the instantaneous positions of atoms, and < span class = "math" > \(\left< \mathbf{R}\right> \)< / 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
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
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< a class = "reference internal" href = "units.html" > < span class = "doc" > energy/distance^2/mass< / span > < / a > units. The coordinates for < em > q< / em >
2016-05-10 01:33:12 +08:00
points in the log file is in the units of the basis vectors of the
corresponding reciprocal lattice.< / p >
2016-09-14 23:35:03 +08:00
< p > < strong > Restart, fix_modify, output, run start/stop, minimize info:< / strong > < / p >
2016-05-10 01:33:12 +08:00
< 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
2016-09-01 12:02:40 +08:00
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 >
2016-05-10 01:33:12 +08:00
< 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 >
< / 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’ 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
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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