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This commit is contained in:
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doc/Eqs/fix_ttm.jpg
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doc/Eqs/fix_ttm.tex
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\documentclass[12pt]{article}
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\begin{document}
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$$
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C_e \rho_e \frac{\partial T_e}{\partial t} =
|
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|
\bigtriangledown (\kappa_e \bigtriangledown T_e) -
|
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|
g_p (T_e - T_a) + g_s T_a'
|
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$$
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\end{document}
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doc/fix_ttm.html
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<HTML>
|
||||||
|
<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
|
||||||
|
</CENTER>
|
||||||
|
|
||||||
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|
||||||
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<HR>
|
||||||
|
|
||||||
|
<H3>fix ttm command
|
||||||
|
</H3>
|
||||||
|
<P><B>Syntax:</B>
|
||||||
|
</P>
|
||||||
|
<PRE>fix ID group-ID ttm seed e_specific_heat e_density e_thermal_conductivity gamma_p gamma_s v_0 nxnodes nynodes nznodes T_infile N T_outfile
|
||||||
|
</PRE>
|
||||||
|
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
|
||||||
|
<LI>ttm = style name of this fix command
|
||||||
|
<LI>seed = random number seed to use for white noise (positive integer)
|
||||||
|
<LI>e_specific_heat = electronic specific heat (energy/(electron*temperature) units)
|
||||||
|
<LI>e_density = electronic density (electrons/volume units)
|
||||||
|
<LI>e_thermal_conductivity = electronic thermal conductivity (energy/(time*distance*temperature) units)
|
||||||
|
<LI>gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
|
||||||
|
<LI>gamma_s = friction coefficient due to electronic stopping (mass/time units)
|
||||||
|
<LI>v_0 = electronic stopping critical velocity (velocity units)
|
||||||
|
<LI>nxnodes = number of thermal solve grid points in the x-direction (positive integer)
|
||||||
|
<LI>nynodes = number of thermal solve grid points in the y-direction (positive integer)
|
||||||
|
<LI>nznodes = number of thermal solve grid points in the z-direction (positive integer)
|
||||||
|
<LI>T_infile = filename to read initial electronic temperature from
|
||||||
|
<LI>N = dump TTM temperatures every this many timesteps, 0 = no dump
|
||||||
|
<LI>T_outfile = filename to write TTM temperatures to (only needed if N > 0)
|
||||||
|
</UL>
|
||||||
|
<P><B>Examples:</B>
|
||||||
|
</P>
|
||||||
|
<PRE>fix 2 all ttm 699489 1.0 1.0 10 0.1 0.0 2.0 1 12 1 initialTs 1000 T.out
|
||||||
|
fix 2 all ttm 123456 1.0 1.0 1.0 1.0 1.0 5.0 5 5 5 Te.in 1 Te.out
|
||||||
|
</PRE>
|
||||||
|
<P><B>Description:</B>
|
||||||
|
</P>
|
||||||
|
<P>Use a two-temperature model (TTM) to represent heat transfer through
|
||||||
|
and between electronic and atomic subsystems. LAMMPS models the
|
||||||
|
atomic subsystem as usual with a molecular dynamics model and the
|
||||||
|
classical force field specified by the user, but the electronic
|
||||||
|
subsystem is modeled as a continuum, or a background "gas", on a
|
||||||
|
regular grid. Energy can be transferred spatially within the grid
|
||||||
|
representing the electrons. Energy can also be transferred between
|
||||||
|
the electronic and the atomic subsystems. The algorithm underlying
|
||||||
|
this fix was derived by D. M. Duffy and A. M. Rutherford and is
|
||||||
|
discussed in two J Physics: Condensed Matter papers: <A HREF = "#Duffy">(Duffy)</A>
|
||||||
|
and <A HREF = "#Rutherford">(Rutherford)</A>. They used this algorithm in cascade
|
||||||
|
simulations where a primary knock-on atom (PKA) was initialized with a
|
||||||
|
high velocity to simulate a radiation event.
|
||||||
|
</P>
|
||||||
|
<P>Heat transfer between the electronic and atomic subsystems is carried
|
||||||
|
out via an inhomogeneous Langevin thermostat. This thermostat differs
|
||||||
|
from the regular Langevin thermostat (<A HREF = "fix_langevin.html">fix
|
||||||
|
langevin</A>) in three important ways. First, the
|
||||||
|
Langevin thermostat is applied uniformly to all atoms in the
|
||||||
|
user-specified group, whereas the TTM fix applies Langevin
|
||||||
|
thermostatting locally within the volumes represented by the
|
||||||
|
user-specified grid points. Second, the Langevin thermostat couples
|
||||||
|
the temperature of the atoms to an infinite heat reservoir, whereas
|
||||||
|
the heat reservoir for fix TTM is finite and represents the local
|
||||||
|
electrons. Third, the TTM fix allows users to specify not just one
|
||||||
|
friction coefficient, but rather two independent friction
|
||||||
|
coefficients: one for the electron-ion interactions and one for
|
||||||
|
electron stopping.
|
||||||
|
</P>
|
||||||
|
<P>When the friction coefficient due to electron stopping, <I>gamma_s</I>, is
|
||||||
|
non-zero, electron stopping effects are included for atoms moving
|
||||||
|
faster than the electron stopping critical velocity, <I>v_0</I>. For
|
||||||
|
further details about this algorithm, see <A HREF = "#Duffy">(Duffy)</A> and
|
||||||
|
<A HREF = "#Rutherford">(Rutherford)</A>.
|
||||||
|
</P>
|
||||||
|
<P>Energy transport within the electronic subsystem is solved according
|
||||||
|
to the heat diffusion equation with added source terms for heat
|
||||||
|
transfer between the subsystems:
|
||||||
|
</P>
|
||||||
|
<CENTER><IMG SRC = "Eqs/fix_ttm.jpg">
|
||||||
|
</CENTER>
|
||||||
|
<P>where C is the specific heat, rho is the density, kappa is the thermal
|
||||||
|
conductivity, and the "e" and "a" subscripts represent the electronic
|
||||||
|
and atomic subsystems respectively. g_p is the coupling constant for
|
||||||
|
the electron-ion interaction, and g_s is the electron stopping
|
||||||
|
coupling parameter. The form of the heat diffusion equation used here
|
||||||
|
is almost the same as that in equation 6 of <A HREF = "#Duffy">(Duffy)</A>, with the
|
||||||
|
exception that the electronic density is explicitly reprensented,
|
||||||
|
rather than being part of the the specific heat parameter.
|
||||||
|
</P>
|
||||||
|
<P>Currently, this fix assumes that none of the user-supplied parameters
|
||||||
|
will vary with temperature. This assumption can be relaxed by
|
||||||
|
modifying the source code to include the desired temperature
|
||||||
|
dependency and functional form for any of the parameters. Note that
|
||||||
|
<A HREF = "#Duffy">(Duffy)</A> used a tanh() functional form for the temperature
|
||||||
|
dependence of the electronic specific heat, but ignored temperature
|
||||||
|
dependencies of any of the other parameters.
|
||||||
|
</P>
|
||||||
|
<P>This fix requires use of periodic boundary conditions and a 3D
|
||||||
|
simulation. Periodic boundary conditions are also used in the heat
|
||||||
|
equation solve for the electronic subsystem. This varies from the
|
||||||
|
approach of <A HREF = "#Rutherford">(Rutherford)</A> where the atomic subsystem was
|
||||||
|
embedded within a larger continuum representation of the electronic
|
||||||
|
subsystem.
|
||||||
|
</P>
|
||||||
|
<P>The initial electronic temperature input file, <I>T_infile</I>, is a text
|
||||||
|
file LAMMPS reads in with no header and with four numeric columns
|
||||||
|
(ix,iy,iz,Temp) and with a number of rows equal to the number of
|
||||||
|
user-specified grid points (nxnodes*nynodes*nznodes). The ix,iy,iz
|
||||||
|
are node indices from 0 to nxnodes-1, etc. For example, the initial
|
||||||
|
electronic temperatures on a 1 by 2 by 3 grid could be specified in a
|
||||||
|
<I>T_infile</I> as follows:
|
||||||
|
</P>
|
||||||
|
<PRE>0 0 0 1.0
|
||||||
|
0 0 1 1.0
|
||||||
|
0 0 2 1.0
|
||||||
|
0 1 0 2.0
|
||||||
|
0 1 1 2.0
|
||||||
|
0 1 2 2.0
|
||||||
|
</PRE>
|
||||||
|
<P>where the electronic temperatures along the nynodes=0 plane have been
|
||||||
|
set to 1.0, and the electronic temperatures along the nynodes=1 plane
|
||||||
|
have been set to 2.0. The order of lines in this file is unimportant.
|
||||||
|
If all the nodal values are not specified, LAMMPS will generate an
|
||||||
|
error.
|
||||||
|
</P>
|
||||||
|
<P>The temperature output file, <I>T_oufile</I>, is created and written by
|
||||||
|
this fix. Temperatures for both the electronic and atomic subsystems
|
||||||
|
at every node and every N timesteps are output. If N is specified as
|
||||||
|
zero, no output is generated, and no output filename is needed. The
|
||||||
|
format of the output is as follows. One long line is written every
|
||||||
|
output timestep. The timestep itself is given in the first column.
|
||||||
|
The next nxnodes*nynodes*nznodes columns contain the temperatures for
|
||||||
|
the atomic subsystem, and the final nxnodes*nynodes*nznodes columns
|
||||||
|
contain the temperatures for the electronic subsystem. The ordering
|
||||||
|
of the nxnodes*nynodes*nznodes columns is with the z index varing
|
||||||
|
fastest, y the next fastest, and x the slowest.
|
||||||
|
</P>
|
||||||
|
<P>This fix does not change the coordinates of its atoms; it only scales
|
||||||
|
their velocities. Thus a time integration fix (e.g. <A HREF = "fix_nve.html">fix
|
||||||
|
nve</A>) should still be used to time integrate the affected
|
||||||
|
atoms. This fix should not normally be used on atoms that have their
|
||||||
|
temperature controlled by another fix - e.g. <A HREF = "fix_nvt.html">fix nvt</A> or
|
||||||
|
<A HREF = "fix_langevin.html">fix langevin</A>.
|
||||||
|
</P>
|
||||||
|
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
|
||||||
|
</P>
|
||||||
|
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
|
||||||
|
files</A>. None of the <A HREF = "fix_modify.html">fix_modify</A> options
|
||||||
|
are relevant to this fix. No global scalar or vector or per-atom
|
||||||
|
quantities are stored by this fix for access by various <A HREF = "Section_howto.html#4_15">output
|
||||||
|
commands</A>. No parameter of this fix can be
|
||||||
|
used with the <I>start/stop</I> keywords of the <A HREF = "run.html">run</A> command.
|
||||||
|
This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
|
||||||
|
</P>
|
||||||
|
<P><B>Restrictions:</B>
|
||||||
|
</P>
|
||||||
|
<P>This fix can only be used for 3d simulations and orthogonal
|
||||||
|
simlulation boxes. You must use periodic <A HREF = "doc/boundary.html">boundary</A>
|
||||||
|
conditions with this fix.
|
||||||
|
</P>
|
||||||
|
<P><B>Related commands:</B>
|
||||||
|
</P>
|
||||||
|
<P><A HREF = "fix_langevin.html">fix langevin</A>, <A HREF = "fix_dt_reset.html">fix dt/reset</A>
|
||||||
|
</P>
|
||||||
|
<P><B>Default:</B> none
|
||||||
|
</P>
|
||||||
|
<A NAME = "Duffy"></A>
|
||||||
|
|
||||||
|
<P><B>(Duffy)</B> D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
|
||||||
|
016207-016218 (2007).
|
||||||
|
</P>
|
||||||
|
<A NAME = "Rutherford"></A>
|
||||||
|
|
||||||
|
<P><B>(Rutherford)</B> A M Rutherford and D M Duffy, J. Phys.:
|
||||||
|
Condens. Matter, 19, 496201-496210 (2007).
|
||||||
|
</P>
|
||||||
|
</HTML>
|
||||||
171
doc/fix_ttm.txt
Normal file
171
doc/fix_ttm.txt
Normal file
@ -0,0 +1,171 @@
|
|||||||
|
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
|
||||||
|
|
||||||
|
:link(lws,http://lammps.sandia.gov)
|
||||||
|
:link(ld,Manual.html)
|
||||||
|
:link(lc,Section_commands.html#comm)
|
||||||
|
|
||||||
|
:line
|
||||||
|
|
||||||
|
fix ttm command :h3
|
||||||
|
|
||||||
|
[Syntax:]
|
||||||
|
|
||||||
|
fix ID group-ID ttm seed e_specific_heat e_density e_thermal_conductivity gamma_p gamma_s v_0 nxnodes nynodes nznodes T_infile N T_outfile :pre
|
||||||
|
|
||||||
|
ID, group-ID are documented in "fix"_fix.html command
|
||||||
|
ttm = style name of this fix command
|
||||||
|
seed = random number seed to use for white noise (positive integer)
|
||||||
|
e_specific_heat = electronic specific heat (energy/(electron*temperature) units)
|
||||||
|
e_density = electronic density (electrons/volume units)
|
||||||
|
e_thermal_conductivity = electronic thermal conductivity (energy/(time*distance*temperature) units)
|
||||||
|
gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
|
||||||
|
gamma_s = friction coefficient due to electronic stopping (mass/time units)
|
||||||
|
v_0 = electronic stopping critical velocity (velocity units)
|
||||||
|
nxnodes = number of thermal solve grid points in the x-direction (positive integer)
|
||||||
|
nynodes = number of thermal solve grid points in the y-direction (positive integer)
|
||||||
|
nznodes = number of thermal solve grid points in the z-direction (positive integer)
|
||||||
|
T_infile = filename to read initial electronic temperature from
|
||||||
|
N = dump TTM temperatures every this many timesteps, 0 = no dump
|
||||||
|
T_outfile = filename to write TTM temperatures to (only needed if N > 0) :ul
|
||||||
|
|
||||||
|
[Examples:]
|
||||||
|
|
||||||
|
fix 2 all ttm 699489 1.0 1.0 10 0.1 0.0 2.0 1 12 1 initialTs 1000 T.out
|
||||||
|
fix 2 all ttm 123456 1.0 1.0 1.0 1.0 1.0 5.0 5 5 5 Te.in 1 Te.out :pre
|
||||||
|
|
||||||
|
[Description:]
|
||||||
|
|
||||||
|
Use a two-temperature model (TTM) to represent heat transfer through
|
||||||
|
and between electronic and atomic subsystems. LAMMPS models the
|
||||||
|
atomic subsystem as usual with a molecular dynamics model and the
|
||||||
|
classical force field specified by the user, but the electronic
|
||||||
|
subsystem is modeled as a continuum, or a background "gas", on a
|
||||||
|
regular grid. Energy can be transferred spatially within the grid
|
||||||
|
representing the electrons. Energy can also be transferred between
|
||||||
|
the electronic and the atomic subsystems. The algorithm underlying
|
||||||
|
this fix was derived by D. M. Duffy and A. M. Rutherford and is
|
||||||
|
discussed in two J Physics: Condensed Matter papers: "(Duffy)"_#Duffy
|
||||||
|
and "(Rutherford)"_#Rutherford. They used this algorithm in cascade
|
||||||
|
simulations where a primary knock-on atom (PKA) was initialized with a
|
||||||
|
high velocity to simulate a radiation event.
|
||||||
|
|
||||||
|
Heat transfer between the electronic and atomic subsystems is carried
|
||||||
|
out via an inhomogeneous Langevin thermostat. This thermostat differs
|
||||||
|
from the regular Langevin thermostat ("fix
|
||||||
|
langevin"_fix_langevin.html) in three important ways. First, the
|
||||||
|
Langevin thermostat is applied uniformly to all atoms in the
|
||||||
|
user-specified group, whereas the TTM fix applies Langevin
|
||||||
|
thermostatting locally within the volumes represented by the
|
||||||
|
user-specified grid points. Second, the Langevin thermostat couples
|
||||||
|
the temperature of the atoms to an infinite heat reservoir, whereas
|
||||||
|
the heat reservoir for fix TTM is finite and represents the local
|
||||||
|
electrons. Third, the TTM fix allows users to specify not just one
|
||||||
|
friction coefficient, but rather two independent friction
|
||||||
|
coefficients: one for the electron-ion interactions and one for
|
||||||
|
electron stopping.
|
||||||
|
|
||||||
|
When the friction coefficient due to electron stopping, {gamma_s}, is
|
||||||
|
non-zero, electron stopping effects are included for atoms moving
|
||||||
|
faster than the electron stopping critical velocity, {v_0}. For
|
||||||
|
further details about this algorithm, see "(Duffy)"_#Duffy and
|
||||||
|
"(Rutherford)"_#Rutherford.
|
||||||
|
|
||||||
|
Energy transport within the electronic subsystem is solved according
|
||||||
|
to the heat diffusion equation with added source terms for heat
|
||||||
|
transfer between the subsystems:
|
||||||
|
|
||||||
|
:c,image(Eqs/fix_ttm.jpg)
|
||||||
|
|
||||||
|
where C is the specific heat, rho is the density, kappa is the thermal
|
||||||
|
conductivity, and the "e" and "a" subscripts represent the electronic
|
||||||
|
and atomic subsystems respectively. g_p is the coupling constant for
|
||||||
|
the electron-ion interaction, and g_s is the electron stopping
|
||||||
|
coupling parameter. The form of the heat diffusion equation used here
|
||||||
|
is almost the same as that in equation 6 of "(Duffy)"_#Duffy, with the
|
||||||
|
exception that the electronic density is explicitly reprensented,
|
||||||
|
rather than being part of the the specific heat parameter.
|
||||||
|
|
||||||
|
Currently, this fix assumes that none of the user-supplied parameters
|
||||||
|
will vary with temperature. This assumption can be relaxed by
|
||||||
|
modifying the source code to include the desired temperature
|
||||||
|
dependency and functional form for any of the parameters. Note that
|
||||||
|
"(Duffy)"_#Duffy used a tanh() functional form for the temperature
|
||||||
|
dependence of the electronic specific heat, but ignored temperature
|
||||||
|
dependencies of any of the other parameters.
|
||||||
|
|
||||||
|
This fix requires use of periodic boundary conditions and a 3D
|
||||||
|
simulation. Periodic boundary conditions are also used in the heat
|
||||||
|
equation solve for the electronic subsystem. This varies from the
|
||||||
|
approach of "(Rutherford)"_#Rutherford where the atomic subsystem was
|
||||||
|
embedded within a larger continuum representation of the electronic
|
||||||
|
subsystem.
|
||||||
|
|
||||||
|
The initial electronic temperature input file, {T_infile}, is a text
|
||||||
|
file LAMMPS reads in with no header and with four numeric columns
|
||||||
|
(ix,iy,iz,Temp) and with a number of rows equal to the number of
|
||||||
|
user-specified grid points (nxnodes*nynodes*nznodes). The ix,iy,iz
|
||||||
|
are node indices from 0 to nxnodes-1, etc. For example, the initial
|
||||||
|
electronic temperatures on a 1 by 2 by 3 grid could be specified in a
|
||||||
|
{T_infile} as follows:
|
||||||
|
|
||||||
|
0 0 0 1.0
|
||||||
|
0 0 1 1.0
|
||||||
|
0 0 2 1.0
|
||||||
|
0 1 0 2.0
|
||||||
|
0 1 1 2.0
|
||||||
|
0 1 2 2.0 :pre
|
||||||
|
|
||||||
|
where the electronic temperatures along the nynodes=0 plane have been
|
||||||
|
set to 1.0, and the electronic temperatures along the nynodes=1 plane
|
||||||
|
have been set to 2.0. The order of lines in this file is unimportant.
|
||||||
|
If all the nodal values are not specified, LAMMPS will generate an
|
||||||
|
error.
|
||||||
|
|
||||||
|
The temperature output file, {T_oufile}, is created and written by
|
||||||
|
this fix. Temperatures for both the electronic and atomic subsystems
|
||||||
|
at every node and every N timesteps are output. If N is specified as
|
||||||
|
zero, no output is generated, and no output filename is needed. The
|
||||||
|
format of the output is as follows. One long line is written every
|
||||||
|
output timestep. The timestep itself is given in the first column.
|
||||||
|
The next nxnodes*nynodes*nznodes columns contain the temperatures for
|
||||||
|
the atomic subsystem, and the final nxnodes*nynodes*nznodes columns
|
||||||
|
contain the temperatures for the electronic subsystem. The ordering
|
||||||
|
of the nxnodes*nynodes*nznodes columns is with the z index varing
|
||||||
|
fastest, y the next fastest, and x the slowest.
|
||||||
|
|
||||||
|
This fix does not change the coordinates of its atoms; it only scales
|
||||||
|
their velocities. Thus a time integration fix (e.g. "fix
|
||||||
|
nve"_fix_nve.html) should still be used to time integrate the affected
|
||||||
|
atoms. This fix should not normally be used on atoms that have their
|
||||||
|
temperature controlled by another fix - e.g. "fix nvt"_fix_nvt.html or
|
||||||
|
"fix langevin"_fix_langevin.html.
|
||||||
|
|
||||||
|
[Restart, fix_modify, output, run start/stop, minimize info:]
|
||||||
|
|
||||||
|
No information about this fix is written to "binary restart
|
||||||
|
files"_restart.html. None of the "fix_modify"_fix_modify.html options
|
||||||
|
are relevant to this fix. No global scalar or vector or per-atom
|
||||||
|
quantities are stored by this fix for access by various "output
|
||||||
|
commands"_Section_howto.html#4_15. No parameter of this fix can be
|
||||||
|
used with the {start/stop} keywords of the "run"_run.html command.
|
||||||
|
This fix is not invoked during "energy minimization"_minimize.html.
|
||||||
|
|
||||||
|
[Restrictions:]
|
||||||
|
|
||||||
|
This fix can only be used for 3d simulations and orthogonal
|
||||||
|
simlulation boxes. You must use periodic "boundary"_doc/boundary.html
|
||||||
|
conditions with this fix.
|
||||||
|
|
||||||
|
[Related commands:]
|
||||||
|
|
||||||
|
"fix langevin"_fix_langevin.html, "fix dt/reset"_fix_dt_reset.html
|
||||||
|
|
||||||
|
[Default:] none
|
||||||
|
|
||||||
|
:link(Duffy)
|
||||||
|
[(Duffy)] D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
|
||||||
|
016207-016218 (2007).
|
||||||
|
|
||||||
|
:link(Rutherford)
|
||||||
|
[(Rutherford)] A M Rutherford and D M Duffy, J. Phys.:
|
||||||
|
Condens. Matter, 19, 496201-496210 (2007).
|
||||||
Reference in New Issue
Block a user