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@ -159,6 +159,10 @@ listed above.
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4.18 <A HREF = "Section_howto.html#4_18">Elastic constants</A>
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<BR>
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4.19 <A HREF = "Section_howto.html#4_19">Library interface to LAMMPS</A>
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<BR>
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4.20 <A HREF = "Section_howto.html#4_20">Calculating thermal conductivity</A>
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<BR>
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4.21 <A HREF = "Section_howto.html#4_21">Calculating viscosity</A>
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<BR></UL>
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<LI><A HREF = "Section_example.html">Example problems</A>
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@ -295,6 +299,10 @@ listed above.
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|
|
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@ -113,7 +113,9 @@ listed above.
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4.16 "Thermostatting, barostatting, and compute temperature"_4_16 :b
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4.17 "Walls"_4_17 :b
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4.18 "Elastic constants"_4_18 :b
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4.19 "Library interface to LAMMPS"_4_19 :ule,b
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4.19 "Library interface to LAMMPS"_4_19 :b
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4.20 "Calculating thermal conductivity"_4_20 :b
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4.21 "Calculating viscosity"_4_21 :ule,b
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"Example problems"_Section_example.html :l
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"Performance & scalability"_Section_perf.html :l
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"Additional tools"_Section_tools.html :l
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@ -176,6 +178,8 @@ listed above.
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:link(4_17,Section_howto.html#4_17)
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:link(4_18,Section_howto.html#4_18)
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:link(4_19,Section_howto.html#4_19)
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:link(4_20,Section_howto.html#4_20)
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:link(4_21,Section_howto.html#4_21)
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:link(9_1,Section_python.html#9_1)
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:link(9_2,Section_python.html#9_2)
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|
|
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@ -32,7 +32,9 @@ LAMMPS.
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4.16 <A HREF = "#4_16">Thermostatting, barostatting and computing temperature</A><BR>
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4.17 <A HREF = "#4_17">Walls</A><BR>
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4.18 <A HREF = "#4_18">Elastic constants</A><BR>
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4.19 <A HREF = "#4_19">Library interface to LAMMPS</A> <BR>
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4.19 <A HREF = "#4_19">Library interface to LAMMPS</A><BR>
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4.20 <A HREF = "#4_20">Calculating thermal conductivity</A><BR>
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4.21 <A HREF = "#4_21">Calculating viscosity</A> <BR>
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<P>The example input scripts included in the LAMMPS distribution and
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highlighted in <A HREF = "Section_example.html">this section</A> also show how to
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|
|
@ -1707,6 +1709,184 @@ grab data from LAMMPS, change it, and put it back into LAMMPS.
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</P>
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<HR>
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<A NAME = "4_20"></A><H4>4.20 Calculating thermal conductivity
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</H4>
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<P>The thermal conductivity kappa of a material can be measured in at
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least 3 ways using various options in LAMMPS. (See <A HREF = "Section_howto.html#4_21">this
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section</A> of the manual for an analogous
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discussion for viscosity). The thermal conducitivity tensor kappa is
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a measure of the propensity of a material to transmit heat energy in a
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diffusive manner as given by Fourier's law
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</P>
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<P>J = -kappa grad(T)
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</P>
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<P>where J is the heat flux in units of energy per area per time and
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grad(T) is the spatial gradient of temperature. The thermal
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conductivity thus has units of energy per distance per time per degree
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K and is often approximated as an isotropic quantity, i.e. as a
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scalar.
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</P>
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<P>The first method is to setup two thermostatted regions at opposite
|
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ends of a simulation box, or one in the middle and one at the end of a
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periodic box. By holding the two regions at different temperatures
|
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with a <A HREF = "Section_howto.html#4_13">thermostatting fix</A>, the energy added
|
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to the hot region should equal the energy subtracted from the cold
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region and be proportional to the heat flux moving between the
|
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regions. See the paper by <A HREF = "#Ikeshoji">Ikeshoji and Hafskjold</A> for
|
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details of this idea. Note that thermostatting fixes such as <A HREF = "fix_nh.html">fix
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nvt</A>, <A HREF = "fix_langevin.html">fix langevin</A>, and <A HREF = "fix_temp_rescale.html">fix
|
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temp/rescale</A> store the cumulative energy they
|
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add/subtract. Alternatively, the <A HREF = "fix_heat.html">fix heat</A> command can
|
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used in place of thermostats on each of two regions, and the resulting
|
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temperatures of the two regions monitored with the "compute
|
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temp/region" command or the temperature profile of the intermediate
|
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region monitored with the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> and
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<A HREF = "compute_ke_atom.html">compute ke/atom</A> commands.
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</P>
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<P>The second method is to perform a reverse non-equilibrium MD
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simulation using the <A HREF = "fix_thermal_conductivity.html">fix
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thermal/conductivity</A> command which
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implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is
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swapped between atoms in two different layers of the simulation box.
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This induces a temperature gradient between the two layers which can
|
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be monitored with the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> and
|
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<A HREF = "compute_ke_atom.html">compute ke/atom</A> commands. The fix tallies the
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cumulative energy transfer that it performs. See the <A HREF = "fix_thermal_conductivity.html">fix
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thermal/conductivity</A> command for
|
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details.
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</P>
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<P>The third method is based on the Green-Kubo (GK) formula which relates
|
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the ensemble average of the auto-correlation of the heat flux to
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kappa. The heat flux can be calculated from the fluctuations of
|
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per-atom potential and kinetic energies and per-atom stress tensor in
|
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a steady-state equilibrated simulation. This is in contrast to the
|
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two preceding non-equilibrium methods, where energy flows continuously
|
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between hot and cold regions of the simulation box.
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</P>
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<P>The <A HREF = "compute_heat_flux.html">compute heat/flux</A> command can calculate
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the needed heat flux and describes how to implement the Green_Kubo
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formalism using additional LAMMPS commands, such as the <A HREF = "fix_ave_correlate.html">fix
|
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ave/correlate</A> command to calculate the needed
|
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auto-correlation. See the doc page for the <A HREF = "compute_heat_flux.html">compute
|
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heat/flux</A> command for an example input script
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that calculates the thermal conductivity of solid Ar via the GK
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formalism.
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</P>
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<HR>
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<A NAME = "4_21"></A><H4>4.21 Calculating viscosity
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</H4>
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<P>The shear viscosity eta of a fluid can be measured in at least 3 ways
|
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using various options in LAMMPS. (See <A HREF = "Section_howto.html#4_">this
|
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section</A>??? of the manual for an analogous
|
||||
discussion for thermal conductivity). Eta is a measure of the
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propensity of a fluid to transmit momentum in a direction
|
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perpendicular to the direction of velocity or momentum flow.
|
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Alternatively it is the resistance the fluid has to being sheared. It
|
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is given by
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</P>
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<P>J = -eta grad(Vstream)
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</P>
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<P>where J is the momentum flux in units of momentum per area per time.
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and grad(Vstream) is the spatial gradient of the velocity of the fluid
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moving in another direction, normal to the area through which the
|
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momentum flows. Viscosity thus has units of pressure-time.
|
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</P>
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<P>The first method is to perform a non-equlibrium MD (NEMD) simulation
|
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by shearing the simulation box via the <A HREF = "fix_deform.html">fix deform</A>
|
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command, and using the <A HREF = "fix_nvt_sllod.html">fix nvt/sllod</A> command to
|
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thermostat the fluid via the SLLOD equations of motion. The velocity
|
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profile setup in the fluid by this procedure can be monitored by the
|
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<A HREF = "fix_ave_spatial.html">fix ave/spatial</A> command, which determines
|
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grad(Vstream) in the equation above. E.g. the derivative in the
|
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y-direction of the Vx component of fluid motion or grad(Vstream) =
|
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dVx/dy. In this case, the Pxy off-diagonal component of the pressure
|
||||
or stress tensor, as calculated by the <A HREF = "compute_pressure.html">compute
|
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pressure</A> command, can also be monitored, which
|
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is the J term in the equation above. See <A HREF = "Section_howto.html#4_13">this
|
||||
section</A> of the manual for details on NEMD
|
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simulations.
|
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</P>
|
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<P>The second method is to perform a reverse non-equilibrium MD
|
||||
simulation using the <A HREF = "fix_viscosity.html">fix viscosity</A> command which
|
||||
implements the rNEMD algorithm of Muller-Plathe. Momentum in one
|
||||
dimension is swapped between atoms in two different layers of the
|
||||
simulation box in a different dimension. This induces a velocity
|
||||
gradient which can be monitored with the <A HREF = "fix_ave_spatial.html">fix
|
||||
ave/spatial</A> command. The fix tallies the
|
||||
cummulative momentum transfer that it performs. See the <A HREF = "fix_viscosity.html">fix
|
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viscosity</A> command for details.
|
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</P>
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<P>The third method is based on the Green-Kubo (GK) formula which relates
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the ensemble average of the auto-correlation of the stress/pressure
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tensor to eta. This can be done in a steady-state equilibrated
|
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simulation which is in contrast to the two preceding non-equilibrium
|
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methods, where momentum flows continuously through the simulation box.
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</P>
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<P>Here is an example input script that calculates the viscosity of
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liquid Ar via the GK formalism:
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</P>
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<PRE># Sample LAMMPS input script for viscosity of liquid Ar
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</PRE>
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<PRE>units real
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variable T equal 86.4956
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variable V equal vol
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variable dt equal 4.0
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variable p equal 400 # correlation length
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variable s equal 5 # sample interval
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variable d equal $p*$s # dump interval
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</PRE>
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<PRE># convert from LAMMPS real units to SI
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</PRE>
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<PRE>variable kB equal 1.3806504e-23 # [J/K/</B> Boltzmann
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variable atm2Pa equal 101325.0
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variable A2m equal 1.0e-10
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variable fs2s equal 1.0e-15
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variable convert equal ${atm2Pa}*${atm2Pa}*${fs2s}*${A2m}*${A2m}*${A2m}
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</PRE>
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<PRE># setup problem
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</PRE>
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<PRE>dimension 3
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boundary p p p
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lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
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region box block 0 4 0 4 0 4
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create_box 1 box
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create_atoms 1 box
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mass 1 39.948
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pair_style lj/cut 13.0
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pair_coeff * * 0.2381 3.405
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timestep ${dt}
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thermo $d
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</PRE>
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<PRE># equilibration and thermalization
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</PRE>
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<PRE>velocity all create $T 102486 mom yes rot yes dist gaussian
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fix NVT all nvt temp $T $T 10 drag 0.2
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run 8000
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</PRE>
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<PRE># viscosity calculation, switch to NVE if desired
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</PRE>
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<PRE>#unfix NVT
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#fix NVE all nve
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</PRE>
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<PRE>reset_timestep 0
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variable pxy equal pxy
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variable pxz equal pxz
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variable pyz equal pyz
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fix SS all ave/correlate $s $p $d &
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v_pxy v_pxz v_pyz type auto file S0St.dat ave running
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variable scale equal ${convert}/(${kB}*$T)*$V*$s*${dt}
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variable v11 equal trap(f_SS[3/</B>)*${scale}
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variable v22 equal trap(f_SS[4/</B>)*${scale}
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variable v33 equal trap(f_SS[5/</B>)*${scale}
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thermo_style custom step temp press v_pxy v_pxz v_pyz v_v11 v_v22 v_v33
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run 100000
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variable v equal (v_v11+v_v22+v_v33)/3.0
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variable ndens equal count(all)/vol
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print "average viscosity: $v [Pa.s/</B> @ $T K, ${ndens} /A^3"
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</PRE>
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<HR>
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<HR>
|
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|
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<A NAME = "Berendsen"></A>
|
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|
|
@ -1724,6 +1904,11 @@ Spellmeyer, Fox, Caldwell, Kollman, JACS 117, 5179-5197 (1995).
|
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<P><B>(Horn)</B> Horn, Swope, Pitera, Madura, Dick, Hura, and Head-Gordon,
|
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J Chem Phys, 120, 9665 (2004).
|
||||
</P>
|
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<A NAME = "Ikeshoji"></A>
|
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|
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<P><B>(Ikeshoji)</B> Ikeshoji and Hafskjold, Molecular Physics, 81, 251-261
|
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(1994).
|
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</P>
|
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<A NAME = "MacKerell"></A>
|
||||
|
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<P><B>(MacKerell)</B> MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
|
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|
|
|
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|
|
@ -29,7 +29,9 @@ LAMMPS.
|
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4.16 "Thermostatting, barostatting and computing temperature"_#4_16
|
||||
4.17 "Walls"_#4_17
|
||||
4.18 "Elastic constants"_#4_18
|
||||
4.19 "Library interface to LAMMPS"_#4_19 :all(b)
|
||||
4.19 "Library interface to LAMMPS"_#4_19
|
||||
4.20 "Calculating thermal conductivity"_#4_20
|
||||
4.21 "Calculating viscosity"_#4_21 :all(b)
|
||||
|
||||
The example input scripts included in the LAMMPS distribution and
|
||||
highlighted in "this section"_Section_example.html also show how to
|
||||
|
|
@ -1693,6 +1695,184 @@ have example C++ and C and Python codes which show how a driver code
|
|||
can link to LAMMPS as a library, run LAMMPS on a subset of processors,
|
||||
grab data from LAMMPS, change it, and put it back into LAMMPS.
|
||||
|
||||
:line
|
||||
|
||||
4.20 Calculating thermal conductivity :link(4_20),h4
|
||||
|
||||
The thermal conductivity kappa of a material can be measured in at
|
||||
least 3 ways using various options in LAMMPS. (See "this
|
||||
section"_Section_howto.html#4_21 of the manual for an analogous
|
||||
discussion for viscosity). The thermal conducitivity tensor kappa is
|
||||
a measure of the propensity of a material to transmit heat energy in a
|
||||
diffusive manner as given by Fourier's law
|
||||
|
||||
J = -kappa grad(T)
|
||||
|
||||
where J is the heat flux in units of energy per area per time and
|
||||
grad(T) is the spatial gradient of temperature. The thermal
|
||||
conductivity thus has units of energy per distance per time per degree
|
||||
K and is often approximated as an isotropic quantity, i.e. as a
|
||||
scalar.
|
||||
|
||||
The first method is to setup two thermostatted regions at opposite
|
||||
ends of a simulation box, or one in the middle and one at the end of a
|
||||
periodic box. By holding the two regions at different temperatures
|
||||
with a "thermostatting fix"_Section_howto.html#4_13, the energy added
|
||||
to the hot region should equal the energy subtracted from the cold
|
||||
region and be proportional to the heat flux moving between the
|
||||
regions. See the paper by "Ikeshoji and Hafskjold"_#Ikeshoji for
|
||||
details of this idea. Note that thermostatting fixes such as "fix
|
||||
nvt"_fix_nh.html, "fix langevin"_fix_langevin.html, and "fix
|
||||
temp/rescale"_fix_temp_rescale.html store the cumulative energy they
|
||||
add/subtract. Alternatively, the "fix heat"_fix_heat.html command can
|
||||
used in place of thermostats on each of two regions, and the resulting
|
||||
temperatures of the two regions monitored with the "compute
|
||||
temp/region" command or the temperature profile of the intermediate
|
||||
region monitored with the "fix ave/spatial"_fix_ave_spatial.html and
|
||||
"compute ke/atom"_compute_ke_atom.html commands.
|
||||
|
||||
The second method is to perform a reverse non-equilibrium MD
|
||||
simulation using the "fix
|
||||
thermal/conductivity"_fix_thermal_conductivity.html command which
|
||||
implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is
|
||||
swapped between atoms in two different layers of the simulation box.
|
||||
This induces a temperature gradient between the two layers which can
|
||||
be monitored with the "fix ave/spatial"_fix_ave_spatial.html and
|
||||
"compute ke/atom"_compute_ke_atom.html commands. The fix tallies the
|
||||
cumulative energy transfer that it performs. See the "fix
|
||||
thermal/conductivity"_fix_thermal_conductivity.html command for
|
||||
details.
|
||||
|
||||
The third method is based on the Green-Kubo (GK) formula which relates
|
||||
the ensemble average of the auto-correlation of the heat flux to
|
||||
kappa. The heat flux can be calculated from the fluctuations of
|
||||
per-atom potential and kinetic energies and per-atom stress tensor in
|
||||
a steady-state equilibrated simulation. This is in contrast to the
|
||||
two preceding non-equilibrium methods, where energy flows continuously
|
||||
between hot and cold regions of the simulation box.
|
||||
|
||||
The "compute heat/flux"_compute_heat_flux.html command can calculate
|
||||
the needed heat flux and describes how to implement the Green_Kubo
|
||||
formalism using additional LAMMPS commands, such as the "fix
|
||||
ave/correlate"_fix_ave_correlate.html command to calculate the needed
|
||||
auto-correlation. See the doc page for the "compute
|
||||
heat/flux"_compute_heat_flux.html command for an example input script
|
||||
that calculates the thermal conductivity of solid Ar via the GK
|
||||
formalism.
|
||||
|
||||
:line
|
||||
|
||||
4.21 Calculating viscosity :link(4_21),h4
|
||||
|
||||
The shear viscosity eta of a fluid can be measured in at least 3 ways
|
||||
using various options in LAMMPS. (See "this
|
||||
section"_Section_howto.html#4_??? of the manual for an analogous
|
||||
discussion for thermal conductivity). Eta is a measure of the
|
||||
propensity of a fluid to transmit momentum in a direction
|
||||
perpendicular to the direction of velocity or momentum flow.
|
||||
Alternatively it is the resistance the fluid has to being sheared. It
|
||||
is given by
|
||||
|
||||
J = -eta grad(Vstream)
|
||||
|
||||
where J is the momentum flux in units of momentum per area per time.
|
||||
and grad(Vstream) is the spatial gradient of the velocity of the fluid
|
||||
moving in another direction, normal to the area through which the
|
||||
momentum flows. Viscosity thus has units of pressure-time.
|
||||
|
||||
The first method is to perform a non-equlibrium MD (NEMD) simulation
|
||||
by shearing the simulation box via the "fix deform"_fix_deform.html
|
||||
command, and using the "fix nvt/sllod"_fix_nvt_sllod.html command to
|
||||
thermostat the fluid via the SLLOD equations of motion. The velocity
|
||||
profile setup in the fluid by this procedure can be monitored by the
|
||||
"fix ave/spatial"_fix_ave_spatial.html command, which determines
|
||||
grad(Vstream) in the equation above. E.g. the derivative in the
|
||||
y-direction of the Vx component of fluid motion or grad(Vstream) =
|
||||
dVx/dy. In this case, the Pxy off-diagonal component of the pressure
|
||||
or stress tensor, as calculated by the "compute
|
||||
pressure"_compute_pressure.html command, can also be monitored, which
|
||||
is the J term in the equation above. See "this
|
||||
section"_Section_howto.html#4_13 of the manual for details on NEMD
|
||||
simulations.
|
||||
|
||||
The second method is to perform a reverse non-equilibrium MD
|
||||
simulation using the "fix viscosity"_fix_viscosity.html command which
|
||||
implements the rNEMD algorithm of Muller-Plathe. Momentum in one
|
||||
dimension is swapped between atoms in two different layers of the
|
||||
simulation box in a different dimension. This induces a velocity
|
||||
gradient which can be monitored with the "fix
|
||||
ave/spatial"_fix_ave_spatial.html command. The fix tallies the
|
||||
cummulative momentum transfer that it performs. See the "fix
|
||||
viscosity"_fix_viscosity.html command for details.
|
||||
|
||||
The third method is based on the Green-Kubo (GK) formula which relates
|
||||
the ensemble average of the auto-correlation of the stress/pressure
|
||||
tensor to eta. This can be done in a steady-state equilibrated
|
||||
simulation which is in contrast to the two preceding non-equilibrium
|
||||
methods, where momentum flows continuously through the simulation box.
|
||||
|
||||
Here is an example input script that calculates the viscosity of
|
||||
liquid Ar via the GK formalism:
|
||||
|
||||
# Sample LAMMPS input script for viscosity of liquid Ar :pre
|
||||
|
||||
units real
|
||||
variable T equal 86.4956
|
||||
variable V equal vol
|
||||
variable dt equal 4.0
|
||||
variable p equal 400 # correlation length
|
||||
variable s equal 5 # sample interval
|
||||
variable d equal $p*$s # dump interval :pre
|
||||
|
||||
# convert from LAMMPS real units to SI :pre
|
||||
|
||||
variable kB equal 1.3806504e-23 # \[J/K/] Boltzmann
|
||||
variable atm2Pa equal 101325.0
|
||||
variable A2m equal 1.0e-10
|
||||
variable fs2s equal 1.0e-15
|
||||
variable convert equal $\{atm2Pa\}*$\{atm2Pa\}*$\{fs2s\}*$\{A2m\}*$\{A2m\}*$\{A2m\} :pre
|
||||
|
||||
# setup problem :pre
|
||||
|
||||
dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 39.948
|
||||
pair_style lj/cut 13.0
|
||||
pair_coeff * * 0.2381 3.405
|
||||
timestep $\{dt\}
|
||||
thermo $d :pre
|
||||
|
||||
# equilibration and thermalization :pre
|
||||
|
||||
velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000 :pre
|
||||
|
||||
# viscosity calculation, switch to NVE if desired :pre
|
||||
|
||||
#unfix NVT
|
||||
#fix NVE all nve :pre
|
||||
|
||||
reset_timestep 0
|
||||
variable pxy equal pxy
|
||||
variable pxz equal pxz
|
||||
variable pyz equal pyz
|
||||
fix SS all ave/correlate $s $p $d &
|
||||
v_pxy v_pxz v_pyz type auto file S0St.dat ave running
|
||||
variable scale equal $\{convert\}/($\{kB\}*$T)*$V*$s*$\{dt\}
|
||||
variable v11 equal trap(f_SS\[3/])*$\{scale\}
|
||||
variable v22 equal trap(f_SS\[4/])*$\{scale\}
|
||||
variable v33 equal trap(f_SS\[5/])*$\{scale\}
|
||||
thermo_style custom step temp press v_pxy v_pxz v_pyz v_v11 v_v22 v_v33
|
||||
run 100000
|
||||
variable v equal (v_v11+v_v22+v_v33)/3.0
|
||||
variable ndens equal count(all)/vol
|
||||
print "average viscosity: $v \[Pa.s/] @ $T K, $\{ndens\} /A^3" :pre
|
||||
|
||||
:line
|
||||
:line
|
||||
|
||||
|
|
@ -1708,6 +1888,10 @@ Spellmeyer, Fox, Caldwell, Kollman, JACS 117, 5179-5197 (1995).
|
|||
[(Horn)] Horn, Swope, Pitera, Madura, Dick, Hura, and Head-Gordon,
|
||||
J Chem Phys, 120, 9665 (2004).
|
||||
|
||||
:link(Ikeshoji)
|
||||
[(Ikeshoji)] Ikeshoji and Hafskjold, Molecular Physics, 81, 251-261
|
||||
(1994).
|
||||
|
||||
:link(MacKerell)
|
||||
[(MacKerell)] MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
|
||||
Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).
|
||||
|
|
|
|||
|
|
@ -89,8 +89,8 @@ integral estimated, and the Green-Kubo formula above evaluated.
|
|||
the autocorrelation. The trap() function in the
|
||||
<A HREF = "variable.html">variable</A> command can calculate the integral.
|
||||
</P>
|
||||
<P>An an example LAMMPS input script for solid Ar is appended below.
|
||||
The result should be: average conductivity ~0.29 in W/mK.
|
||||
<P>An example LAMMPS input script for solid Ar is appended below. The
|
||||
result should be: average conductivity ~0.29 in W/mK.
|
||||
</P>
|
||||
<HR>
|
||||
|
||||
|
|
@ -128,24 +128,29 @@ energy/area/time <A HREF = "units.html">units</A>
|
|||
</P>
|
||||
<HR>
|
||||
|
||||
<H4>Sample LAMMPS input script
|
||||
</H4>
|
||||
<PRE>atom_style atomic
|
||||
units real
|
||||
variable kB equal 1.3806504e-23 # [J/K] Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
<PRE># Sample LAMMPS input script for thermal conductivity of solid Ar
|
||||
</PRE>
|
||||
<PRE>units real
|
||||
variable T equal 70
|
||||
variable V equal vol
|
||||
variable dt equal 4.0
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval
|
||||
</PRE>
|
||||
<PRE># convert from LAMMPS real units to SI
|
||||
</PRE>
|
||||
<PRE>variable kB equal 1.3806504e-23 # [J/K] Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
variable A2m equal 1.0e-10
|
||||
variable fs2s equal 1.0e-15
|
||||
variable convert equal ${kCal2J}*${kCal2J}/${fs2s}/${A2m}
|
||||
</PRE>
|
||||
<PRE># setup problem
|
||||
</PRE>
|
||||
<P># ---------------------------------------------------------
|
||||
</P>
|
||||
<PRE>dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
|
|
@ -155,34 +160,35 @@ pair_coeff * * 0.2381 3.405
|
|||
timestep ${dt}
|
||||
thermo $d
|
||||
</PRE>
|
||||
<P># ------------- equilibration and thermalization ----------------
|
||||
</P>
|
||||
<PRE>velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000
|
||||
<PRE># equilibration and thermalization
|
||||
</PRE>
|
||||
<P># -------------- flux calculation, switch to NVE if desired --------
|
||||
</P>
|
||||
<PRE>#unfix NVT
|
||||
#fix NVE all nve
|
||||
<PRE>velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000
|
||||
</PRE>
|
||||
<PRE>reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux[1]/vol
|
||||
variable Jy equal c_flux[2]/vol
|
||||
variable Jz equal c_flux[3]/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
|
||||
variable scale equal ${kCal2J}*${kCal2J}/${kB}/$T/$T/$V*$s*${dt}*1.0e25
|
||||
variable k11 equal trap(f_JJ[3])*${scale}
|
||||
variable k22 equal trap(f_JJ[4])*${scale}
|
||||
variable k33 equal trap(f_JJ[5])*${scale}
|
||||
<PRE># thermal conductivity calculation, switch to NVE if desired
|
||||
</PRE>
|
||||
<PRE>#unfix NVT
|
||||
#fix NVE all nve
|
||||
</PRE>
|
||||
<PRE>reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux[1]/vol
|
||||
variable Jy equal c_flux[2]/vol
|
||||
variable Jz equal c_flux[3]/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
|
||||
variable scale equal ${convert}/${kB}/$T/$T/$V*$s*${dt}
|
||||
variable k11 equal trap(f_JJ[3])*${scale}
|
||||
variable k22 equal trap(f_JJ[4])*${scale}
|
||||
variable k33 equal trap(f_JJ[5])*${scale}
|
||||
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
print "average conductivity: $k [W/mK]"
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
variable ndens equal count(all)/vol
|
||||
print "average conductivity: $k[W/mK] @ $T K, ${ndens} /A^3"
|
||||
</PRE>
|
||||
</HTML>
|
||||
|
|
|
|||
|
|
@ -86,8 +86,8 @@ The "fix ave/correlate"_fix_ave_correlate.html command can calclate
|
|||
the autocorrelation. The trap() function in the
|
||||
"variable"_variable.html command can calculate the integral.
|
||||
|
||||
An an example LAMMPS input script for solid Ar is appended below.
|
||||
The result should be: average conductivity ~0.29 in W/mK.
|
||||
An example LAMMPS input script for solid Ar is appended below. The
|
||||
result should be: average conductivity ~0.29 in W/mK.
|
||||
|
||||
:line
|
||||
|
||||
|
|
@ -125,24 +125,29 @@ energy/area/time "units"_units.html
|
|||
|
||||
:line
|
||||
|
||||
Sample LAMMPS input script :h4
|
||||
# Sample LAMMPS input script for thermal conductivity of solid Ar :pre
|
||||
|
||||
atom_style atomic
|
||||
units real
|
||||
variable kB equal 1.3806504e-23 # \[J/K\] Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
variable T equal 70
|
||||
variable V equal vol
|
||||
variable dt equal 4.0
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval :pre
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval :pre
|
||||
|
||||
# ---------------------------------------------------------
|
||||
# convert from LAMMPS real units to SI :pre
|
||||
|
||||
variable kB equal 1.3806504e-23 # \[J/K\] Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
variable A2m equal 1.0e-10
|
||||
variable fs2s equal 1.0e-15
|
||||
variable convert equal $\{kCal2J\}*$\{kCal2J\}/$\{fs2s\}/$\{A2m\} :pre
|
||||
|
||||
# setup problem :pre
|
||||
|
||||
dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
|
|
@ -152,32 +157,33 @@ pair_coeff * * 0.2381 3.405
|
|||
timestep $\{dt\}
|
||||
thermo $d :pre
|
||||
|
||||
# ------------- equilibration and thermalization ----------------
|
||||
# equilibration and thermalization :pre
|
||||
|
||||
velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000 :pre
|
||||
velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000 :pre
|
||||
|
||||
# -------------- flux calculation, switch to NVE if desired --------
|
||||
# thermal conductivity calculation, switch to NVE if desired :pre
|
||||
|
||||
#unfix NVT
|
||||
#fix NVE all nve :pre
|
||||
#unfix NVT
|
||||
#fix NVE all nve :pre
|
||||
|
||||
reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux\[1\]/vol
|
||||
variable Jy equal c_flux\[2\]/vol
|
||||
variable Jz equal c_flux\[3\]/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux\[1\] c_flux\[2\] c_flux\[3\] type auto file J0Jt.dat ave running
|
||||
variable scale equal $\{kCal2J\}*$\{kCal2J\}/$\{kB\}/$T/$T/$V*$s*$\{dt\}*1.0e25
|
||||
variable k11 equal trap(f_JJ\[3\])*$\{scale\}
|
||||
variable k22 equal trap(f_JJ\[4\])*$\{scale\}
|
||||
variable k33 equal trap(f_JJ\[5\])*$\{scale\}
|
||||
reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux\[1\]/vol
|
||||
variable Jy equal c_flux\[2\]/vol
|
||||
variable Jz equal c_flux\[3\]/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux\[1\] c_flux\[2\] c_flux\[3\] type auto file J0Jt.dat ave running
|
||||
variable scale equal $\{convert\}/$\{kB\}/$T/$T/$V*$s*$\{dt\}
|
||||
variable k11 equal trap(f_JJ\[3\])*$\{scale\}
|
||||
variable k22 equal trap(f_JJ\[4\])*$\{scale\}
|
||||
variable k33 equal trap(f_JJ\[5\])*$\{scale\}
|
||||
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
print "average conductivity: $k \[W/mK\]" :pre
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
variable ndens equal count(all)/vol
|
||||
print "average conductivity: $k\[W/mK\] @ $T K, $\{ndens\} /A^3" :pre
|
||||
|
|
|
|||
Loading…
Reference in New Issue