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< title > fix ti/spring command — LAMMPS documentation< / title >
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< li > fix ti/spring command< / li >
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< span id = "index-0" > < / span > < h1 > fix ti/spring command< a class = "headerlink" href = "#fix-ti-spring-command" title = "Permalink to this headline" > ¶< / a > < / h1 >
< div class = "section" id = "syntax" >
< h2 > Syntax< a class = "headerlink" href = "#syntax" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < pre > fix ID group-ID ti/spring K t_switch t_equil keyword value ...
< / pre > < / div >
< / div >
< ul class = "simple" >
< li > ID, group-ID are documented in < a class = "reference internal" href = "fix.html" > < em > fix< / em > < / a > command< / li >
< li > ti/spring = style name of this fix command< / li >
< li > K = spring constant (force/distance units)< / li >
< li > t_switch/t_equil = number of steps of the switching/equilibration procedure< / li >
< li > zero or more keyword/value pairs may be appended to args< / li >
< li > keyword = < em > function< / em > < / li >
< / ul >
< pre class = "literal-block" >
< em > function< / em > value = function-ID
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function-ID = ID of the switching function (1 or 2)
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< / pre >
< p > < strong > Example:< / strong > < / p >
< div class = "highlight-python" > < div class = "highlight" > < pre > fix ref all ti/spring 50.0 2000 1000 function 2
< / pre > < / div >
< / div >
< / div >
< div class = "section" id = "description" >
< h2 > Description< a class = "headerlink" href = "#description" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > This fix allows you to compute the free energy of solids by performing
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a thermodynamic integration between the solid of interest and an
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Einstein crystal < a class = "reference internal" href = "#frenkel" > < span > (Frenkel)< / span > < / a > . The thermodynamic integration
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is performed using the nonequilibrium method of Adiabatic Switching
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< a class = "reference internal" href = "#watanabe" > < span > (Watanabe,< / span > < / a > < a class = "reference internal" href = "#dekoning96" > < span > de Koning96)< / span > < / a > .< / p >
< p > A spring force is applied independently to each atom in the group to
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tether it to its initial position. The initial position for each atom
is its location at the time the fix command was issued. More details
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about the springs are available in < a class = "reference internal" href = "fix_spring_self.html" > < em > fix spring/self< / em > < / a > . The forces on the atoms are
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dynamically scaled during the simulation, the rescaling is done in the
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following manner:< / p >
< img alt = "_images/fix_ti_spring_force.jpg" class = "align-center" src = "_images/fix_ti_spring_force.jpg" / >
< p > where F_harm is the force due to the springs, F_solid is the total
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force on the atoms due to the interatomic potential and lambda is the
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coupling parameter of the thermodynamic integration.< / p >
< p > The fix acts as follows: during the first < em > t_equil< / em > steps after the
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fix is defined the value of lambda is zero, this is the period to
equilibrate the system in the lambda = 0 state. After this the value
of lambda changes continuously from 0 to 1 according to the function
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defined using the keyword < em > function< / em > (described below), this is done
in < em > t_switch< / em > steps. Then comes the second equilibration period of
< em > t_equil< / em > to equilibrate the system in the lambda = 1 state. After
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that the switching back to the lambda = 0 state is made using
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< em > t_switch< / em > timesteps and following the same switching function. After
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this period the value of lambda is kept equal to zero and the fix has
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no action in the dynamics of the system anymore.< / p >
< p > The description of thermodynamic integration in both directions is
done in < a class = "reference internal" href = "#dekoning97" > < span > de Koning97< / span > < / a > , the main reason is to try to
eliminate the dissipated heat due to the nonequilibrium process.< / p >
< p > The < em > function< / em > keyword allows the use of two different switching
rates, the option < em > 1< / em > results in a constant rescaling where the lambda
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parameter changes at a constant rate during the switching time
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according to the switching function< / p >
< img alt = "_images/fix_ti_spring_function_1.jpg" class = "align-center" src = "_images/fix_ti_spring_function_1.jpg" / >
< p > where tau is the scaled time variable t/t_switch. The option number
< em > 2< / em > performs the switching at a rate defined by the following
switching function< / p >
< img alt = "_images/fix_ti_spring_function_2.jpg" class = "align-center" src = "_images/fix_ti_spring_function_2.jpg" / >
< p > This function has zero slope as lambda approaches its extreme values
(0 and 1), according to (< a class = "reference internal" href = "#dekoning96" > < span > de Koning96)< / span > < / a > this results in
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smaller fluctuations on the integral to be computed on the
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thermodynamic integration.< / p >
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< div class = "admonition note" >
< p class = "first admonition-title" > Note< / p >
< p class = "last" > It is importante to keep the center of mass fixed during the
thermodynamic integration, a non-zero total velocity will result in
divergencies during the integration due to the fact that the atoms are
‘ attatched’ to its equilibrium positions by the Einstein
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crystal. Check the option < em > zero< / em > of < a class = "reference external" href = "fix_langevin_html" > fix langevin< / a >
and < a class = "reference internal" href = "velocity.html" > < em > velocity< / em > < / a > . The use of the Nose-Hoover thermostat
(< code class = "xref doc docutils literal" > < span class = "pre" > fix< / span > < span class = "pre" > nvt< / span > < / code > ) is NOT recommended due to its well documented
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issues with the canonical sampling of harmonic degrees of freedom
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(notice that the < em > chain< / em > option will NOT solve this problem). The
Langevin thermostat (< a class = "reference external" href = "fix_langevin.html"" > fix langevin< / a > ) works fine.< / p >
< / div >
< / div >
< div class = "section" id = "restart-fix-modify-output-run-start-stop-minimize-info" >
< 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 >
< p > This fix writes the original coordinates of tethered atoms to < a class = "reference internal" href = "restart.html" > < em > binary restart files< / em > < / a > , so that the spring effect will be the
same in a restarted simulation. See the < a class = "reference internal" href = "read_restart.html" > < em > read restart< / em > < / a > command for info on how to re-specify a fix
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in an input script that reads a restart file, so that the operation of
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the fix continues in an uninterrupted fashion.< / p >
< p > The < a class = "reference internal" href = "fix_modify.html" > < em > fix modify< / em > < / a > < em > energy< / em > option is supported by this
fix to add the energy stored in the per-atom springs to the system’ s
potential energy as part of < a class = "reference internal" href = "thermo_style.html" > < em > thermodynamic output< / em > < / a > .< / p >
< p > This fix computes a global scalar and a global vector quantities which
can be accessed by various < a class = "reference internal" href = "Section_howto.html#howto-15" > < span > output commands< / span > < / a > . The scalar is an energy which
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is the sum of the spring energy for each atom, where the per-atom
energy is 0.5 * K * r^2. The vector has 2 positions, the first one is
the coupling parameter lambda and the second one is the time
derivative of lambda. The scalar and vector values calculated by this
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fix are “ extensive” .< / p >
< p > No parameter of this fix can be used with the < em > start/stop< / em > keywords of
the < a class = "reference internal" href = "run.html" > < em > run< / em > < / a > command.< / p >
< p > The forces due to this fix are imposed during an energy minimization,
invoked by the < a class = "reference internal" href = "minimize.html" > < em > minimize< / em > < / a > command.< / p >
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< div class = "admonition note" >
< p class = "first admonition-title" > Note< / p >
< p class = "last" > If you want the per-atom spring energy to be included in the
total potential energy of the system (the quantity being minimized),
you MUST enable the < a class = "reference internal" href = "fix_modify.html" > < em > fix modify< / em > < / a > < em > energy< / em > option for
this fix.< / p >
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< / div >
< p > An example script using this command is provided in the
examples/USER/misc/ti directory.< / 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_spring.html" > < em > fix spring< / em > < / a > , < a class = "reference internal" href = "fix_ti_rs.html" > < em > fix ti/rs< / em > < / a > < / p >
< / div >
< div class = "section" id = "restrictions" >
< h2 > Restrictions< a class = "headerlink" href = "#restrictions" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > This command is part of the USER-MISC package. It is only enabled if
LAMMPS was built with those packages. See the < a class = "reference internal" href = "Section_start.html#start-3" > < span > Making LAMMPS< / span > < / a > section for more info.< / p >
< / div >
< div class = "section" id = "default" >
< h2 > Default< a class = "headerlink" href = "#default" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > The keyword default is function = 1.< / p >
< hr class = "docutils" / >
< p id = "frenkel" > < strong > (Frenkel)< / strong > Daan Frenkel and Anthony J. C. Ladd, J. Chem. Phys. 81, 3188
(1984).< / p >
< p id = "watanabe" > < strong > (Watanabe)< / strong > M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).< / p >
< p id = "dekoning96" > < strong > (de Koning 96)< / strong > M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).< / p >
< p id = "dekoning97" > < strong > (de Koning 97)< / strong > M. de Koning and A. Antonelli, Phys Rev B, 55, 735 (1997).< / p >
< / div >
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