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<div class="section" id="fix-ttm-command">
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<span id="index-0"></span><h1>fix ttm command<a class="headerlink" href="#fix-ttm-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="fix-ttm-mod-command">
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<h1>fix ttm/mod command<a class="headerlink" href="#fix-ttm-mod-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><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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fix ID group-ID ttm/mod seed init_file Nx Ny Nz T_infile N T_outfile
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
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<li>style = <em>ttm</em> or <em>ttm_mod</em></li>
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<li>seed = random number seed to use for white noise (positive integer)</li>
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<li>remaining arguments for fix ttm:</li>
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</ul>
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<div class="highlight-python"><div class="highlight"><pre>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)
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</pre></div>
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</div>
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<ul class="simple">
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<li>remaining arguments for fix ttm/mod:</li>
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</ul>
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<div class="highlight-python"><div class="highlight"><pre>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)
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</pre></div>
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</div>
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</div>
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<div class="section" id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><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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fix 2 all ttm/mod 34277 parameters.txt 5 5 5 T_init 10 T_out
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
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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 class="reference internal" href="#duffy"><span>(Duffy)</span></a>
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and <a class="reference internal" href="#rutherford"><span>(Rutherford)</span></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.</p>
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<p>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.</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 class="reference internal" href="fix_langevin.html"><em>fix langevin</em></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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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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(<em>gamma_p</em>), and one for electron stopping (<em>gamma_s</em>).</p>
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<p>When the friction coefficient due to electron stopping, <em>gamma_s</em>, 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, <em>v_0</em>. For
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further details about this algorithm, see <a class="reference internal" href="#duffy"><span>(Duffy)</span></a> and
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<a class="reference internal" href="#rutherford"><span>(Rutherford)</span></a>.</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:</p>
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<img alt="_images/fix_ttm.jpg" class="align-center" src="_images/fix_ttm.jpg" />
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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 class="reference internal" href="#duffy"><span>(Duffy)</span></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.</p>
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<p>Currently, fix ttm assumes that none of the user-supplied parameters
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will vary with temperature. Note that <a class="reference internal" href="#duffy"><span>(Duffy)</span></a> 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.</p>
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<p>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 <a class="reference internal" href="#rutherford"><span>(Rutherford)</span></a> where the atomic subsystem was
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embedded within a larger continuum representation of the electronic
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subsystem.</p>
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<p>The initial electronic temperature input file, <em>T_infile</em>, 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 <em>T_infile</em>
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as follows:</p>
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<div class="highlight-python"><div class="highlight"><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></div>
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</div>
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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.</p>
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<p>The temperature output file, <em>T_oufile</em>, 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.</p>
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<p>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. <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>) 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. <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or
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<a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>.</p>
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<div class="admonition warning">
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<p class="first admonition-title">Warning</p>
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<p class="last">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.</p>
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</div>
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<hr class="docutils" />
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<p><strong>Additional details for fix ttm/mod</strong></p>
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<p>Fix ttm/mod uses the heat diffusion equation with possible external
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heat sources (e.g. laser heating in ablation simulations):</p>
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<img alt="_images/fix_ttm_mod.jpg" class="align-center" src="_images/fix_ttm_mod.jpg" />
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<p>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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<em>tau</em> in the <em>init_file</em>.</p>
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<p>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</p>
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<img alt="_images/fix_ttm_ce.jpg" class="align-center" src="_images/fix_ttm_ce.jpg" />
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<p>where <em>X</em> = 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.</p>
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<p>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 <a class="reference internal" href="#chen"><span>(Chen)</span></a>, <a class="reference internal" href="#norman"><span>(Norman)</span></a>). The total force
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acting on an ion is:</p>
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<img alt="_images/fix_ttm_blast.jpg" class="align-center" src="_images/fix_ttm_blast.jpg" />
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<p>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.</p>
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<p>The electronic pressure is taken to be P_e = B*rho_e*C_e*T_e</p>
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<p>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 <em>surface_movement</em> parameter
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in the <em>init_file</em>. If it is set to 1, then “vacuum” cells can be
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changed to “electron-filled” cells with the temperature <em>T_e_min</em> 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 <em>init_file</em> via <em>lsurface</em>
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and <em>rsurface</em> parameters. In this case, electronic pressure gradient
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is calculated as</p>
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<img alt="_images/fix_ttm_blast1.jpg" class="align-center" src="_images/fix_ttm_blast1.jpg" />
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<p>where lambda is the electron mean free path (see <a class="reference internal" href="#norman"><span>(Norman)</span></a>,
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<a class="reference internal" href="#pisarev"><span>(Pisarev)</span></a>)</p>
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<p>The fix ttm/mod parameter file <em>init_file</em> 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:</p>
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<div class="highlight-python"><div class="highlight"><pre>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
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</pre></div>
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</div>
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</div>
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<hr class="docutils" />
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<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
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<h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
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<p>These fixes write the state of the electronic subsystem and the energy
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exchange between the subsystems to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>. See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></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.</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.</p>
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<p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to these
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fixes.</p>
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<p>Both fixes compute 2 output quantities stored in a vector of length 2,
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which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>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 <a class="reference internal" href="run.html"><em>run</em></a> command. The fixes are not invoked during
|
|
<a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
|
|
</div>
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
|
|
<p>Fix <em>ttm</em> is part of the MISC package. It is only enabled if LAMMPS
|
|
was built with that package. Fix <em>ttm/mod</em> is part of the USER-MISC
|
|
package. It is only enabled if LAMMPS was built with that package.
|
|
See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more
|
|
info.</p>
|
|
<p>These fixes can only be used for 3d simulations and orthogonal
|
|
simlulation boxes. You must also use periodic
|
|
<a class="reference internal" href="boundary.html"><em>boundary</em></a> conditions.</p>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
|
|
<p><a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a></p>
|
|
<p><strong>Default:</strong> none</p>
|
|
<hr class="docutils" />
|
|
<p id="duffy"><strong>(Duffy)</strong> D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
|
|
016207-016218 (2007).</p>
|
|
<p id="rutherford"><strong>(Rutherford)</strong> A M Rutherford and D M Duffy, J. Phys.:
|
|
Condens. Matter, 19, 496201-496210 (2007).</p>
|
|
<p id="chen"><strong>(Chen)</strong> J Chen, D Tzou and J Beraun, Int. J. Heat
|
|
Mass Transfer, 49, 307-316 (2006).</p>
|
|
<p id="norman"><strong>(Norman)</strong> G E Norman, S V Starikov, V V Stegailov et al., Contrib.
|
|
Plasma Phys., 53, 129-139 (2013).</p>
|
|
<p id="pisarev"><strong>(Pisarev)</strong> V V Pisarev and S V Starikov, J. Phys.: Condens. Matter, 26,
|
|
475401 (2014).</p>
|
|
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