<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: <aclass="reference internal"href="#duffy"><spanclass="std std-ref">(Duffy)</span></a>
and <aclass="reference internal"href="#rutherford"><spanclass="std std-ref">(Rutherford)</span></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>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.</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 (<aclass="reference internal"href="fix_langevin.html"><spanclass="doc">fix langevin</span></a>) 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
(<em>gamma_p</em>), and one for electron stopping (<em>gamma_s</em>).</p>
<p>When the friction coefficient due to electron stopping, <em>gamma_s</em>, is
non-zero, electron stopping effects are included for atoms moving
faster than the electron stopping critical velocity, <em>v_0</em>. For
further details about this algorithm, see <aclass="reference internal"href="#duffy"><spanclass="std std-ref">(Duffy)</span></a> and
<p>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.</p>
<p>The temperature output file, <em>T_oufile</em>, 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.</p>
<p>These fixes do not change the coordinates of their atoms; they only
scales their velocities. Thus a time integration fix (e.g. <aclass="reference internal"href="fix_nve.html"><spanclass="doc">fix nve</span></a>) 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. <aclass="reference internal"href="fix_nh.html"><spanclass="doc">fix nvt</span></a> or
<p>where <em>X</em> = 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.</p>
<p>Electronic pressure effects are included in the TTM model to account
for the blast force acting on ions because of electronic pressure
gradient (see <aclass="reference internal"href="#chen"><spanclass="std std-ref">(Chen)</span></a>, <aclass="reference internal"href="#norman"><spanclass="std std-ref">(Norman)</span></a>). The total force
<p>The fix ttm/mod parameter file <em>init_file</em> 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:</p>
<preclass="literal-block">
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
</pre>
<hrclass="docutils"/>
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>These fixes write the state of the electronic subsystem and the energy
exchange between the subsystems to <aclass="reference internal"href="restart.html"><spanclass="doc">binary restart files</span></a>. See the <aclass="reference internal"href="read_restart.html"><spanclass="doc">read_restart</span></a> 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.</p>
<p>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.</p>
<p>None of the <aclass="reference internal"href="fix_modify.html"><spanclass="doc">fix_modify</span></a> options are relevant to these
fixes.</p>
<p>Both fixes compute 2 output quantities stored in a vector of length 2,
which can be accessed by various <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">output commands</span></a>. 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.</p>
<p>The vector values calculated are “extensive”.</p>
<p>No parameter of the fixes can be used with the <em>start/stop</em> keywords
of the <aclass="reference internal"href="run.html"><spanclass="doc">run</span></a> command. The fixes are not invoked during
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