forked from lijiext/lammps
333 lines
14 KiB
Plaintext
333 lines
14 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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fix ttm command :h3
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fix ttm/mod command :h3
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[Syntax:]
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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
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fix ID group-ID ttm/mod seed init_file Nx Ny Nz T_infile N T_outfile :pre
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ID, group-ID are documented in "fix"_fix.html command :ulb,l
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style = {ttm} or {ttm_mod} :l
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seed = random number seed to use for white noise (positive integer) :l
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remaining arguments for fix ttm: :l
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C_e = electronic specific heat (energy/(electron*temperature) units)
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rho_e = electronic density (electrons/volume units)
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kappa_e = electronic thermal conductivity (energy/(time*distance*temperature) units)
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gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
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gamma_s = friction coefficient due to electronic stopping (mass/time units)
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v_0 = electronic stopping critical velocity (velocity units)
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Nx = number of thermal solve grid points in the x-direction (positive integer)
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Ny = number of thermal solve grid points in the y-direction (positive integer)
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Nz = number of thermal solve grid points in the z-direction (positive integer)
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T_infile = filename to read initial electronic temperature from
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N = dump TTM temperatures every this many timesteps, 0 = no dump
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T_outfile = filename to write TTM temperatures to (only needed if N > 0) :pre
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remaining arguments for fix ttm/mod: :l
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init_file = file with the parameters to TTM
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Nx = number of thermal solve grid points in the x-direction (positive integer)
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Ny = number of thermal solve grid points in the y-direction (positive integer)
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Nz = number of thermal solve grid points in the z-direction (positive integer)
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T_infile = filename to read initial electronic temperature from
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N = dump TTM temperatures every this many timesteps, 0 = no dump
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T_outfile = filename to write TTM temperatures to (only needed if N > 0) :pre
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:ule
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[Examples:]
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fix 2 all ttm 699489 1.0 1.0 10 0.1 0.0 2.0 1 12 1 initialTs 1000 T.out
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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
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fix 2 all ttm/mod 34277 parameters.txt 5 5 5 T_init 10 T_out :pre
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[Description:]
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Use a two-temperature model (TTM) to represent heat transfer through
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and between electronic and atomic subsystems. LAMMPS models the
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atomic subsystem as usual with a molecular dynamics model and the
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classical force field specified by the user, but the electronic
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subsystem is modeled as a continuum, or a background "gas", on a
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regular grid. Energy can be transferred spatially within the grid
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representing the electrons. Energy can also be transferred between
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the electronic and the atomic subsystems. The algorithm underlying
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this fix was derived by D. M. Duffy and A. M. Rutherford and is
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discussed in two J Physics: Condensed Matter papers: "(Duffy)"_#Duffy
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and "(Rutherford)"_#Rutherford. They used this algorithm in cascade
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simulations where a primary knock-on atom (PKA) was initialized with a
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high velocity to simulate a radiation event.
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The description in this sub-section applies to both fix ttm and fix
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ttm/mod. Fix ttm/mod adds options to account for external heat
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sources (e.g. at a surface) and for specifying parameters that allow
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the electronic heat capacity to depend strongly on electronic
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temperature. It is more expensive computationally than fix ttm
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because it treats the thermal diffusion equation as non-linear. More
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details on fix ttm/mod are given below.
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Heat transfer between the electronic and atomic subsystems is carried
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out via an inhomogeneous Langevin thermostat. This thermostat differs
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from the regular Langevin thermostat ("fix
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langevin"_fix_langevin.html) in three important ways. First, the
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Langevin thermostat is applied uniformly to all atoms in the
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user-specified group for a single target temperature, whereas the TTM
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fix applies Langevin thermostatting locally to atoms within the
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volumes represented by the user-specified grid points with a target
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temperature specific to that grid point. Second, the Langevin
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thermostat couples the temperature of the atoms to an infinite heat
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reservoir, whereas the heat reservoir for fix TTM is finite and
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represents the local electrons. Third, the TTM fix allows users to
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specify not just one friction coefficient, but rather two independent
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friction coefficients: one for the electron-ion interactions
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({gamma_p}), and one for electron stopping ({gamma_s}).
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When the friction coefficient due to electron stopping, {gamma_s}, is
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non-zero, electron stopping effects are included for atoms moving
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faster than the electron stopping critical velocity, {v_0}. For
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further details about this algorithm, see "(Duffy)"_#Duffy and
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"(Rutherford)"_#Rutherford.
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Energy transport within the electronic subsystem is solved according
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to the heat diffusion equation with added source terms for heat
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transfer between the subsystems:
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:c,image(Eqs/fix_ttm.jpg)
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where C_e is the specific heat, rho_e is the density, kappa_e is the
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thermal conductivity, T is temperature, the "e" and "a" subscripts
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represent electronic and atomic subsystems respectively, g_p is the
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coupling constant for the electron-ion interaction, and g_s is the
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electron stopping coupling parameter. C_e, rho_e, and kappa_e are
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specified as parameters to the fix. The other quantities are derived.
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The form of the heat diffusion equation used here is almost the same
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as that in equation 6 of "(Duffy)"_#Duffy, with the exception that the
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electronic density is explicitly reprensented, rather than being part
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of the the specific heat parameter.
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Currently, fix ttm assumes that none of the user-supplied parameters
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will vary with temperature. Note that "(Duffy)"_#Duffy used a tanh()
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functional form for the temperature dependence of the electronic
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specific heat, but ignored temperature dependencies of any of the
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other parameters. See more discussion below for fix ttm/mod.
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These fixes require use of periodic boundary conditions and a 3D
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simulation. Periodic boundary conditions are also used in the heat
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equation solve for the electronic subsystem. This varies from the
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approach of "(Rutherford)"_#Rutherford where the atomic subsystem was
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embedded within a larger continuum representation of the electronic
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subsystem.
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The initial electronic temperature input file, {T_infile}, is a text
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file LAMMPS reads in with no header and with four numeric columns
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(ix,iy,iz,Temp) and with a number of rows equal to the number of
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user-specified grid points (Nx by Ny by Nz). The ix,iy,iz are node
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indices from 0 to nxnodes-1, etc. For example, the initial electronic
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temperatures on a 1 by 2 by 3 grid could be specified in a {T_infile}
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as follows:
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0 0 0 1.0
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0 0 1 1.0
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0 0 2 1.0
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0 1 0 2.0
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0 1 1 2.0
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0 1 2 2.0 :pre
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where the electronic temperatures along the y=0 plane have been set to
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1.0, and the electronic temperatures along the y=1 plane have been set
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to 2.0. The order of lines in this file is no important. If all the
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nodal values are not specified, LAMMPS will generate an error.
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The temperature output file, {T_oufile}, is created and written by
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this fix. Temperatures for both the electronic and atomic subsystems
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at every node and every N timesteps are output. If N is specified as
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zero, no output is generated, and no output filename is needed. The
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format of the output is as follows. One long line is written every
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output timestep. The timestep itself is given in the first column.
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The next Nx*Ny*Nz columns contain the temperatures for the atomic
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subsystem, and the final Nx*Ny*Nz columns contain the temperatures for
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the electronic subsystem. The ordering of the Nx*Ny*Nz columns is
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with the z index varing fastest, y the next fastest, and x the
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slowest.
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These fixes do not change the coordinates of their atoms; they only
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scales their velocities. Thus a time integration fix (e.g. "fix
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nve"_fix_nve.html) should still be used to time integrate the affected
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atoms. The fixes should not normally be used on atoms that have their
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temperature controlled by another fix - e.g. "fix nvt"_fix_nh.html or
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"fix langevin"_fix_langevin.html.
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IMPORTANT NOTE: The current implementations of these fixes create a
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copy of the electron grid that overlays the entire simulation domain,
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for each processor. Values on the grid are summed across all
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processors. Thus you should insure that this grid is not too large,
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else your simulation could incur high memory and communication costs.
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:line
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[Additional details for fix ttm/mod]
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Fix ttm/mod uses the heat diffusion equation with possible external
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heat sources (e.g. laser heating in ablation simulations):
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:c,image(Eqs/fix_ttm_mod.jpg)
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where theta is the Heaviside step function, I_0 is the (absorbed)
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laser pulse intensity for ablation simulations, l_skin is the depth
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of skin-layer, and all other designations have the same meaning as in
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the former equation. The duration of the pulse is set by the parameter
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{tau} in the {init_file}.
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Fix ttm/mod also allows users to specify the dependencies of C_e and
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kappa_e on the electronic temperature. The specific heat is expressed
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as
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:c,image(Eqs/fix_ttm_ce.jpg)
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where {X} = T_e/1000, and the thermal conductivity is defined as
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kappa_e = D_e*rho_e*C_e, where D_e is the thermal diffusion
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coefficient.
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Electronic pressure effects are included in the TTM model to account
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for the blast force acting on ions because of electronic pressure
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gradient (see "(Chen)"_Chen, "(Norman)"_#Norman). The total force
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acting on an ion is:
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:c,image(Eqs/fix_ttm_blast.jpg)
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where F_langevin is a force from Langevin thermostat simulating
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electron-phonon coupling, and nabla P_e/n_ion is the electron blast
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force.
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The electronic pressure is taken to be P_e = B*rho_e*C_e*T_e
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The current fix ttm/mod implementation allows TTM simulations with a
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vacuum. The vacuum region is defined as the grid cells with zero
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electronic temperature. The numerical scheme does not allow energy
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exchange with such cells. Since the material can expand to previously
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unoccupied region in some simulations, the vacuum border can be
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allowed to move. It is controlled by the {surface_movement} parameter
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in the {init_file}. If it is set to 1, then "vacuum" cells can be
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changed to "electron-filled" cells with the temperature {T_e_min} if
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atoms move into them (currently only implemented for the case of
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1-dimensional motion of flat surface normal to the X axis). The
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initial borders of vacuum can be set in the {init_file} via {lsurface}
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and {rsurface} parameters. In this case, electronic pressure gradient
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is calculated as
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:c,image(Eqs/fix_ttm_blast1.jpg)
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where lambda is the electron mean free path (see "(Norman)"_#Norman,
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"(Pisarev)"_#Pisarev)
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The fix ttm/mod parameter file {init_file} has the following syntax/
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Every line with the odd number is considered as a comment and
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ignored. The lines with the even numbers are treated as follows:
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a_0, energy/(temperature*electron) units
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a_1, energy/(temperature^2*electron) units
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a_2, energy/(temperature^3*electron) units
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a_3, energy/(temperature^4*electron) units
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a_4, energy/(temperature^5*electron) units
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C_0, energy/(temperature*electron) units
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A, 1/temperature units
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rho_e, electrons/volume units
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D_e, length^2/time units
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gamma_p, mass/time units
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gamma_s, mass/time units
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v_0, length/time units
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I_0, energy/(time*length^2) units
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lsurface, electron grid units (positive integer)
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rsurface, electron grid units (positive integer)
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l_skin, length units
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tau, time units
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B, dimensionless
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lambda, length units
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n_ion, ions/volume units
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surface_movement: 0 to disable tracking of surface motion, 1 to enable
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T_e_min, temperature units :pre
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:line
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[Restart, fix_modify, output, run start/stop, minimize info:]
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These fixes write the state of the electronic subsystem and the energy
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exchange between the subsystems to "binary restart
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files"_restart.html. See the "read_restart"_read_restart.html command
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for info on how to re-specify a fix in an input script that reads a
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restart file, so that the operation of the fix continues in an
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uninterrupted fashion.
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Because the state of the random number generator is not saved in the
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restart files, this means you cannot do "exact" restarts with this
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fix, where the simulation continues on the same as if no restart had
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taken place. However, in a statistical sense, a restarted simulation
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should produce the same behavior.
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None of the "fix_modify"_fix_modify.html options are relevant to these
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fixes.
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Both fixes compute 2 output quantities stored in a vector of length 2,
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which can be accessed by various "output
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commands"_Section_howto.html#howto_15. The first quantity is the
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total energy of the electronic subsystem. The second quantity is the
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energy transferred from the electronic to the atomic subsystem on that
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timestep. Note that the velocity verlet integrator applies the fix ttm
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forces to the atomic subsystem as two half-step velocity updates: one
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on the current timestep and one on the subsequent timestep.
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Consequently, the change in the atomic subsystem energy is lagged by
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half a timestep relative to the change in the electronic subsystem
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energy. As a result of this, users may notice slight fluctuations in
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the sum of the atomic and electronic subsystem energies reported at
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the end of the timestep.
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The vector values calculated are "extensive".
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No parameter of the fixes can be used with the {start/stop} keywords
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of the "run"_run.html command. The fixes are not invoked during
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"energy minimization"_minimize.html.
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[Restrictions:]
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Fix {ttm} is part of the MISC package. It is only enabled if LAMMPS
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was built with that package. Fix {ttm/mod} is part of the USER-MISC
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package. It is only enabled if LAMMPS was built with that package.
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See the "Making LAMMPS"_Section_start.html#start_3 section for more
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info.
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These fixes can only be used for 3d simulations and orthogonal
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simlulation boxes. You must also use periodic
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"boundary"_boundary.html conditions.
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[Related commands:]
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"fix langevin"_fix_langevin.html, "fix dt/reset"_fix_dt_reset.html
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[Default:] none
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:line
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:link(Duffy)
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[(Duffy)] D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
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016207-016218 (2007).
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:link(Rutherford)
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[(Rutherford)] A M Rutherford and D M Duffy, J. Phys.:
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Condens. Matter, 19, 496201-496210 (2007).
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:link(Chen)
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[(Chen)] J Chen, D Tzou and J Beraun, Int. J. Heat
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Mass Transfer, 49, 307-316 (2006).
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:link(Norman)
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[(Norman)] G E Norman, S V Starikov, V V Stegailov et al., Contrib.
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Plasma Phys., 53, 129-139 (2013).
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:link(Pisarev)
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[(Pisarev)] V V Pisarev and S V Starikov, J. Phys.: Condens. Matter, 26,
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475401 (2014).
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