2009-04-06 23:58:28 +08:00
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<HTML>
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<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>
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<HR>
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<H3>fix ttm command
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</H3>
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<P><B>Syntax:</B>
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</P>
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2009-04-07 04:34:43 +08:00
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<PRE>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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2009-04-06 23:58:28 +08:00
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>ttm = style name of this fix command
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<LI>seed = random number seed to use for white noise (positive integer)
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2009-04-07 04:32:46 +08:00
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<LI>C_e = electronic specific heat (energy/(electron*temperature) units)
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<LI>rho_e = electronic density (electrons/volume units)
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<LI>kappa_e = electronic thermal conductivity (energy/(time*distance*temperature) units)
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2009-04-06 23:58:28 +08:00
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<LI>gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
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<LI>gamma_s = friction coefficient due to electronic stopping (mass/time units)
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<LI>v_0 = electronic stopping critical velocity (velocity units)
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2009-04-07 04:34:43 +08:00
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<LI>Nx = number of thermal solve grid points in the x-direction (positive integer)
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<LI>Ny = number of thermal solve grid points in the y-direction (positive integer)
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<LI>Nz = number of thermal solve grid points in the z-direction (positive integer)
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2009-04-06 23:58:28 +08:00
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<LI>T_infile = filename to read initial electronic temperature from
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<LI>N = dump TTM temperatures every this many timesteps, 0 = no dump
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<LI>T_outfile = filename to write TTM temperatures to (only needed if N > 0)
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>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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</PRE>
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<P><B>Description:</B>
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</P>
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<P>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: <A HREF = "#Duffy">(Duffy)</A>
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and <A HREF = "#Rutherford">(Rutherford)</A>. 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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</P>
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<P>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 (<A HREF = "fix_langevin.html">fix
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langevin</A>) in three important ways. First, the
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Langevin thermostat is applied uniformly to all atoms in the
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2009-04-07 04:32:46 +08:00
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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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2009-04-07 05:03:10 +08:00
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friction coefficients: one for the electron-ion interactions
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2009-04-07 04:55:03 +08:00
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(<I>gamma_p</I>), and one for electron stopping (<I>gamma_s</I>).
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2009-04-06 23:58:28 +08:00
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</P>
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<P>When the friction coefficient due to electron stopping, <I>gamma_s</I>, 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, <I>v_0</I>. For
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further details about this algorithm, see <A HREF = "#Duffy">(Duffy)</A> and
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<A HREF = "#Rutherford">(Rutherford)</A>.
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</P>
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<P>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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</P>
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<CENTER><IMG SRC = "Eqs/fix_ttm.jpg">
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</CENTER>
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2009-04-07 04:32:46 +08:00
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<P>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 <A HREF = "#Duffy">(Duffy)</A>, 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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2009-04-06 23:58:28 +08:00
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</P>
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<P>Currently, this fix assumes that none of the user-supplied parameters
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will vary with temperature. This assumption can be relaxed by
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modifying the source code to include the desired temperature
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dependency and functional form for any of the parameters. Note that
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<A HREF = "#Duffy">(Duffy)</A> used a tanh() functional form for the temperature
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dependence of the electronic specific heat, but ignored temperature
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dependencies of any of the other parameters.
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</P>
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<P>This fix requires 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 <A HREF = "#Rutherford">(Rutherford)</A> 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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</P>
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<P>The initial electronic temperature input file, <I>T_infile</I>, 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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2009-04-07 04:34:43 +08:00
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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 <I>T_infile</I>
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as follows:
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2009-04-06 23:58:28 +08:00
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</P>
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<PRE>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
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</PRE>
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2009-04-07 04:34:43 +08:00
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<P>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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2009-04-06 23:58:28 +08:00
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</P>
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<P>The temperature output file, <I>T_oufile</I>, 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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2009-04-06 23:58:28 +08:00
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</P>
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<P>This fix does not change the coordinates of its atoms; it only scales
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their velocities. Thus a time integration fix (e.g. <A HREF = "fix_nve.html">fix
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nve</A>) should still be used to time integrate the affected
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atoms. This fix should not normally be used on atoms that have their
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temperature controlled by another fix - e.g. <A HREF = "fix_nvt.html">fix nvt</A> or
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<A HREF = "fix_langevin.html">fix langevin</A>.
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</P>
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2009-06-04 04:33:21 +08:00
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<P>This fix computes 2 output quantities stored in a vector of
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length 2, which can be accessed by various <A HREF = "Section_howto.html#4_15">output
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commands</A>. The first quantity is
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the total energy of the electronic subsystem. The second quantity
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is the energy transferred from the electronic to the atomic subsystem
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on that timestep. Note that the velocity verlet integrator applies the
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fix ttm forces to the atomic subsystem as two half-step velocity
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updates: one 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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</P>
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<P>The vector values calculated by this fix are "extensive",
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meaning they scale with the number of atoms in the simulation.
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</P>
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2009-04-07 05:03:10 +08:00
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<P>IMPORTANT NOTE: The current implementation creates a copy of the
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electron grid that overlays the entire simulation domain, for each
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processor. Values on the grid are summed across all processors. Thus
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you should insure that this grid is not too large, else your
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simulation could incur high memory and communication costs.
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</P>
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2009-04-06 23:58:28 +08:00
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<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
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</P>
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2009-09-05 04:50:48 +08:00
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<P>This fix writes the state of the electronic subsystem and the energy
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exchange between the subsystems to <A HREF = "restart.html">binary restart
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files</A>. See the <A HREF = "read_restart.html">read_restart</A> 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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</P>
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<P>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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</P>
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<P>None of the <A HREF = "fix_modify.html">fix_modify</A> options
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are relevant to this fix. No global scalar or vector or per-atom
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quantities are stored by this fix for access by various <A HREF = "Section_howto.html#4_15">output
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commands</A>. No parameter of this fix can be
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used with the <I>start/stop</I> keywords of the <A HREF = "run.html">run</A> command.
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This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
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</P>
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<P><B>Restrictions:</B>
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</P>
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<P>This fix can only be used for 3d simulations and orthogonal
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simlulation boxes. You must use periodic <A HREF = "doc/boundary.html">boundary</A>
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conditions with this fix.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_langevin.html">fix langevin</A>, <A HREF = "fix_dt_reset.html">fix dt/reset</A>
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</P>
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<P><B>Default:</B> none
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</P>
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2009-06-04 04:33:21 +08:00
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<HR>
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2009-04-06 23:58:28 +08:00
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<A NAME = "Duffy"></A>
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<P><B>(Duffy)</B> D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
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016207-016218 (2007).
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</P>
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<A NAME = "Rutherford"></A>
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<P><B>(Rutherford)</B> A M Rutherford and D M Duffy, J. Phys.:
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Condens. Matter, 19, 496201-496210 (2007).
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</P>
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</HTML>
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