forked from lijiext/lammps
380 lines
15 KiB
Plaintext
380 lines
15 KiB
Plaintext
.. index:: fix ttm
|
|
|
|
fix ttm command
|
|
===============
|
|
|
|
fix ttm/mod command
|
|
===================
|
|
|
|
Syntax
|
|
""""""
|
|
|
|
.. parsed-literal::
|
|
|
|
fix ID group-ID ttm seed C_e rho_e kappa_e gamma_p gamma_s v_0 Nx Ny Nz T_infile N T_outfile
|
|
fix ID group-ID ttm/mod seed init_file Nx Ny Nz T_infile N T_outfile
|
|
|
|
* ID, group-ID are documented in :doc:`fix <fix>` command
|
|
* style = *ttm* or *ttm_mod*
|
|
* seed = random number seed to use for white noise (positive integer)
|
|
* remaining arguments for fix ttm:
|
|
.. parsed-literal::
|
|
|
|
C_e = electronic specific heat (energy/(electron*temperature) units)
|
|
rho_e = electronic density (electrons/volume units)
|
|
kappa_e = 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)
|
|
Nx = number of thermal solve grid points in the x-direction (positive integer)
|
|
Ny = number of thermal solve grid points in the y-direction (positive integer)
|
|
Nz = 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)
|
|
|
|
* remaining arguments for fix ttm/mod:
|
|
.. parsed-literal::
|
|
|
|
init_file = file with the parameters to TTM
|
|
Nx = number of thermal solve grid points in the x-direction (positive integer)
|
|
Ny = number of thermal solve grid points in the y-direction (positive integer)
|
|
Nz = 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)
|
|
|
|
|
|
|
|
Examples
|
|
""""""""
|
|
|
|
.. parsed-literal::
|
|
|
|
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
|
|
fix 2 all ttm/mod 34277 parameters.txt 5 5 5 T_init 10 T_out
|
|
|
|
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: :ref:`(Duffy) <Duffy>`
|
|
and :ref:`(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.
|
|
|
|
The description in this sub-section applies to both fix ttm and fix
|
|
ttm/mod. Fix ttm/mod adds options to account for external heat
|
|
sources (e.g. at a surface) and for specifying parameters that allow
|
|
the electronic heat capacity to depend strongly on electronic
|
|
temperature. It is more expensive computationally than fix ttm
|
|
because it treats the thermal diffusion equation as non-linear. More
|
|
details on fix ttm/mod are given below.
|
|
|
|
Heat transfer between the electronic and atomic subsystems is carried
|
|
out via an inhomogeneous Langevin thermostat. This thermostat differs
|
|
from the regular Langevin thermostat (:doc:`fix langevin <fix_langevin>`) in three important ways. First, the
|
|
Langevin thermostat is applied uniformly to all atoms in the
|
|
user-specified group for a single target temperature, whereas the TTM
|
|
fix applies Langevin thermostatting locally to atoms within the
|
|
volumes represented by the user-specified grid points with a target
|
|
temperature specific to that grid point. 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
|
|
(\ *gamma_p*\ ), and one for electron stopping (\ *gamma_s*\ ).
|
|
|
|
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 :ref:`(Duffy) <Duffy>` and
|
|
:ref:`(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:
|
|
|
|
.. image:: Eqs/fix_ttm.jpg
|
|
:align: center
|
|
|
|
where C_e is the specific heat, rho_e is the density, kappa_e is the
|
|
thermal conductivity, T is temperature, the "e" and "a" subscripts
|
|
represent 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. C_e, rho_e, and kappa_e are
|
|
specified as parameters to the fix. The other quantities are derived.
|
|
The form of the heat diffusion equation used here is almost the same
|
|
as that in equation 6 of :ref:`(Duffy) <Duffy>`, with the exception that the
|
|
electronic density is explicitly reprensented, rather than being part
|
|
of the the specific heat parameter.
|
|
|
|
Currently, fix ttm assumes that none of the user-supplied parameters
|
|
will vary with temperature. Note that :ref:`(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. See more discussion below for fix ttm/mod.
|
|
|
|
These fixes require 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 :ref:`(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 (Nx by Ny by Nz). 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:
|
|
|
|
.. parsed-literal::
|
|
|
|
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
|
|
|
|
where the electronic temperatures along the y=0 plane have been set to
|
|
1.0, and the electronic temperatures along the y=1 plane have been set
|
|
to 2.0. The order of lines in this file is no important. 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 Nx*Ny*Nz columns contain the temperatures for the atomic
|
|
subsystem, and the final Nx*Ny*Nz columns contain the temperatures for
|
|
the electronic subsystem. The ordering of the Nx*Ny*Nz columns is
|
|
with the z index varing fastest, y the next fastest, and x the
|
|
slowest.
|
|
|
|
These fixes do not change the coordinates of their atoms; they only
|
|
scales their velocities. Thus a time integration fix (e.g. :doc:`fix nve <fix_nve>`) should still be used to time integrate the affected
|
|
atoms. The fixes should not normally be used on atoms that have their
|
|
temperature controlled by another fix - e.g. :doc:`fix nvt <fix_nh>` or
|
|
:doc:`fix langevin <fix_langevin>`.
|
|
|
|
.. note::
|
|
|
|
The current implementations of these fixes create a copy of the
|
|
electron grid that overlays the entire simulation domain, for each
|
|
processor. Values on the grid are summed across all processors. Thus
|
|
you should insure that this grid is not too large, else your
|
|
simulation could incur high memory and communication costs.
|
|
|
|
|
|
----------
|
|
|
|
|
|
**Additional details for fix ttm/mod**
|
|
|
|
Fix ttm/mod uses the heat diffusion equation with possible external
|
|
heat sources (e.g. laser heating in ablation simulations):
|
|
|
|
.. image:: Eqs/fix_ttm_mod.jpg
|
|
:align: center
|
|
|
|
where theta is the Heaviside step function, I_0 is the (absorbed)
|
|
laser pulse intensity for ablation simulations, l_skin is the depth
|
|
of skin-layer, and all other designations have the same meaning as in
|
|
the former equation. The duration of the pulse is set by the parameter
|
|
*tau* in the *init_file*\ .
|
|
|
|
Fix ttm/mod also allows users to specify the dependencies of C_e and
|
|
kappa_e on the electronic temperature. The specific heat is expressed
|
|
as
|
|
|
|
.. image:: Eqs/fix_ttm_ce.jpg
|
|
:align: center
|
|
|
|
where *X* = T_e/1000, and the thermal conductivity is defined as
|
|
kappa_e = D_e*rho_e*C_e, where D_e is the thermal diffusion
|
|
coefficient.
|
|
|
|
Electronic pressure effects are included in the TTM model to account
|
|
for the blast force acting on ions because of electronic pressure
|
|
gradient (see :ref:`(Chen) <Chen>`, :ref:`(Norman) <Norman>`). The total force
|
|
acting on an ion is:
|
|
|
|
.. image:: Eqs/fix_ttm_blast.jpg
|
|
:align: center
|
|
|
|
where F_langevin is a force from Langevin thermostat simulating
|
|
electron-phonon coupling, and nabla P_e/n_ion is the electron blast
|
|
force.
|
|
|
|
The electronic pressure is taken to be P_e = B*rho_e*C_e*T_e
|
|
|
|
The current fix ttm/mod implementation allows TTM simulations with a
|
|
vacuum. The vacuum region is defined as the grid cells with zero
|
|
electronic temperature. The numerical scheme does not allow energy
|
|
exchange with such cells. Since the material can expand to previously
|
|
unoccupied region in some simulations, the vacuum border can be
|
|
allowed to move. It is controlled by the *surface_movement* parameter
|
|
in the *init_file*\ . If it is set to 1, then "vacuum" cells can be
|
|
changed to "electron-filled" cells with the temperature *T_e_min* if
|
|
atoms move into them (currently only implemented for the case of
|
|
1-dimensional motion of flat surface normal to the X axis). The
|
|
initial borders of vacuum can be set in the *init_file* via *lsurface*
|
|
and *rsurface* parameters. In this case, electronic pressure gradient
|
|
is calculated as
|
|
|
|
.. image:: Eqs/fix_ttm_blast1.jpg
|
|
:align: center
|
|
|
|
where lambda is the electron mean free path (see :ref:`(Norman) <Norman>`,
|
|
:ref:`(Pisarev) <Pisarev>`)
|
|
|
|
The fix ttm/mod parameter file *init_file* has the following syntax/
|
|
Every line with the odd number is considered as a comment and
|
|
ignored. The lines with the even numbers are treated as follows:
|
|
|
|
.. parsed-literal::
|
|
|
|
a_0, energy/(temperature*electron) units
|
|
a_1, energy/(temperature^2*electron) units
|
|
a_2, energy/(temperature^3*electron) units
|
|
a_3, energy/(temperature^4*electron) units
|
|
a_4, energy/(temperature^5*electron) units
|
|
C_0, energy/(temperature*electron) units
|
|
A, 1/temperature units
|
|
rho_e, electrons/volume units
|
|
D_e, length^2/time units
|
|
gamma_p, mass/time units
|
|
gamma_s, mass/time units
|
|
v_0, length/time units
|
|
I_0, energy/(time*length^2) units
|
|
lsurface, electron grid units (positive integer)
|
|
rsurface, electron grid units (positive integer)
|
|
l_skin, length units
|
|
tau, time units
|
|
B, dimensionless
|
|
lambda, length units
|
|
n_ion, ions/volume units
|
|
surface_movement: 0 to disable tracking of surface motion, 1 to enable
|
|
T_e_min, temperature units
|
|
|
|
|
|
----------
|
|
|
|
|
|
Restart, fix_modify, output, run start/stop, minimize info
|
|
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
|
|
|
|
These fixes write the state of the electronic subsystem and the energy
|
|
exchange between the subsystems to :doc:`binary restart files <restart>`. See the :doc:`read_restart <read_restart>` command
|
|
for info on how to re-specify a fix in an input script that reads a
|
|
restart file, so that the operation of the fix continues in an
|
|
uninterrupted fashion.
|
|
|
|
Because the state of the random number generator is not saved in the
|
|
restart files, this means you cannot do "exact" restarts with this
|
|
fix, where the simulation continues on the same as if no restart had
|
|
taken place. However, in a statistical sense, a restarted simulation
|
|
should produce the same behavior.
|
|
|
|
None of the :doc:`fix_modify <fix_modify>` options are relevant to these
|
|
fixes.
|
|
|
|
Both fixes compute 2 output quantities stored in a vector of length 2,
|
|
which can be accessed by various :ref:`output commands <howto_15>`. The first quantity is the
|
|
total energy of the electronic subsystem. The second quantity is the
|
|
energy transferred from the electronic to the atomic subsystem on that
|
|
timestep. Note that the velocity verlet integrator applies the fix ttm
|
|
forces to the atomic subsystem as two half-step velocity updates: one
|
|
on the current timestep and one on the subsequent timestep.
|
|
Consequently, the change in the atomic subsystem energy is lagged by
|
|
half a timestep relative to the change in the electronic subsystem
|
|
energy. As a result of this, users may notice slight fluctuations in
|
|
the sum of the atomic and electronic subsystem energies reported at
|
|
the end of the timestep.
|
|
|
|
The vector values calculated are "extensive".
|
|
|
|
No parameter of the fixes can be used with the *start/stop* keywords
|
|
of the :doc:`run <run>` command. The fixes are not invoked during
|
|
:doc:`energy minimization <minimize>`.
|
|
|
|
Restrictions
|
|
""""""""""""
|
|
|
|
|
|
Fix *ttm* is part of the MISC package. It is only enabled if LAMMPS
|
|
was built with that package. Fix *ttm/mod* is part of the USER-MISC
|
|
package. It is only enabled if LAMMPS was built with that package.
|
|
See the :ref:`Making LAMMPS <start_3>` section for more
|
|
info.
|
|
|
|
These fixes can only be used for 3d simulations and orthogonal
|
|
simlulation boxes. You must also use periodic
|
|
:doc:`boundary <boundary>` conditions.
|
|
|
|
Related commands
|
|
""""""""""""""""
|
|
|
|
:doc:`fix langevin <fix_langevin>`, :doc:`fix dt/reset <fix_dt_reset>`
|
|
|
|
**Default:** none
|
|
|
|
|
|
----------
|
|
|
|
|
|
.. _Duffy:
|
|
|
|
|
|
|
|
**(Duffy)** D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
|
|
016207-016218 (2007).
|
|
|
|
.. _Rutherford:
|
|
|
|
|
|
|
|
**(Rutherford)** A M Rutherford and D M Duffy, J. Phys.:
|
|
Condens. Matter, 19, 496201-496210 (2007).
|
|
|
|
.. _Chen:
|
|
|
|
|
|
|
|
**(Chen)** J Chen, D Tzou and J Beraun, Int. J. Heat
|
|
Mass Transfer, 49, 307-316 (2006).
|
|
|
|
.. _Norman:
|
|
|
|
|
|
|
|
**(Norman)** G E Norman, S V Starikov, V V Stegailov et al., Contrib.
|
|
Plasma Phys., 53, 129-139 (2013).
|
|
|
|
.. _Pisarev:
|
|
|
|
|
|
|
|
**(Pisarev)** V V Pisarev and S V Starikov, J. Phys.: Condens. Matter, 26,
|
|
475401 (2014).
|
|
|
|
|
|
.. _lws: http://lammps.sandia.gov
|
|
.. _ld: Manual.html
|
|
.. _lc: Section_commands.html#comm
|