forked from lijiext/lammps
195 lines
7.1 KiB
HTML
195 lines
7.1 KiB
HTML
<HTML>
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>compute heat/flux command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>compute ID group-ID heat/flux ke-ID pe-ID stress-ID
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>heat/flux = style name of this compute command
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<LI>ke-ID = ID of a compute that calculates per-atom kinetic energy
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<LI>pe-ID = ID of a compute that calculates per-atom potential energy
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<LI>stress-ID = ID of a compute that calculates per-atom stress
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>compute myFlux all heat/flux myKE myPE myStress
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Define a computation that calculates the heat flux vector based on
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contributions from atoms in the specified group. This can be used by
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itself to measure the heat flux into or out of a reservoir of atoms,
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or to calculate a thermal conductivity using the Green-Kubo formalism.
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</P>
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<P>See the <A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
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command for details on how to compute thermal conductivity in an
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alternate way, via the Muller-Plathe method. See the <A HREF = "fix_heat.html">fix
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heat</A> command for a way to control the heat added or
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subtracted to a group of atoms.
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</P>
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<P>The compute takes three arguments which are IDs of other
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<A HREF = "compute.html">computes</A>. One calculates per-atom kinetic energy
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(<I>ke-ID</I>), one calculates per-atom potential energy (<I>pe-ID)</I>, and the
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third calcualtes per-atom stress (<I>stress-ID</I>). These should be
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defined for the same group used by compute heat/flux, though LAMMPS
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does not check for this.
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</P>
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<P>The Green-Kubo formulas relate the ensemble average of the
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auto-correlation of the heat flux J to the thermal conductivity kappa:
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</P>
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<CENTER><IMG SRC = "Eqs/heat_flux_J.jpg">
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</CENTER>
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<CENTER><IMG SRC = "Eqs/heat_flux_k.jpg">
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</CENTER>
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<P>Ei in the first term of the equation for J is the per-atom energy
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(potential and kinetic). This is calculated by the computes <I>ke-ID</I>
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and <I>pe-ID</I>. Si in the second term of the equation for J is the
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per-atom stress tensor calculated by the compute <I>stress-ID</I>. The
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tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a
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vector. Note that as discussed below, the 1/V scaling factor in the
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equation for J is NOT included in the calculation performed by this
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compute; you need to add it for a volume appropriate to the atoms
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included in the calculation.
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</P>
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<P>IMPORTANT NOTE: The <A HREF = "compute_pe_atom.html">compute pe/atom</A> and
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<A HREF = "compute_stress_atom.html">compute stress/atom</A> commands have options
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for which terms to include in their calculation (pair, bond, etc).
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The heat flux calculation will thus include exactly the same terms.
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Normally you should use <A HREF = "compute_stress_atom.html">compute stress/atom
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virial</A> so as not to include a kinetic energy
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term in the heat flux. Note that neither of those computes is able to
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include a long-range Coulombic contribution to the per-atom energy or
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stress.
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</P>
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<P>This compute calculates 6 quantities and stores them in a 6-component
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vector. The first 3 components are the x, y, z components of the full
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heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x,
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y, z components of just the convective portion of the flux, i.e. the
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first term in the equation for J above.
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</P>
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<HR>
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<P>The heat flux can be output every so many timesteps (e.g. via the
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<A HREF = "thermo_style.html">thermo_style custom</A> command). Then as a
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post-processing operation, an autocorrelation can be performed, its
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integral estimated, and the Green-Kubo formula above evaluated.
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</P>
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<P>Here is an example of this procedure. First a LAMMPS input script for
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solid Ar is appended below. A Python script
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<A HREF = "Scripts/correlate.py">correlate.py</A> is also given, which calculates
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the autocorrelation of the flux output in the logfile flux.log,
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produced by the LAMMPS run. It is invoked as
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</P>
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<PRE>correlate.py flux.log -c 3 -s 200
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</PRE>
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<P>The resulting data lists the autocorrelation in column 1 and the
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integral of the autocorrelation in column 2. After running the
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correlate.py script, the value of the integral is ~9e-11. This has to
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be multiplied by V/(kB T^2) times the sample interval and the
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appropriate unit conversion factors. For real <A HREF = "units.html">units</A> in
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LAMMPS,
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</P>
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<PRE>kappa (KCal/(mol fmsec Ang K)) = V/(k_B*(T^2)) x "thermo" output frequency x timestep x Integral value
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</PRE>
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<P>where
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</P>
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<PRE>V = 10213.257 Angs^3
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k_B = 1.98721e-3 KCal/(mol K)
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T = ~70K
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</PRE>
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<P>Therefore, lamda = 3.7736e-6 (KCal/(mol fs A K)).
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</P>
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<P>Converting to W/mK gives:
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</P>
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<PRE>3.7736e-6 * (4182 / (1e-15 * 1e-10 * N_Avogradro)) =
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3.7736e-6 * 69443.837 =
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~0.26 W/mK
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</PRE>
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<HR>
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<P><B>Output info:</B>
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</P>
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<P>This compute calculates a global vector of length 6 (total heat flux
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vector, followed by conductive heat flux vector), which can be
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accessed by indices 1-6. These values can be used by any command that
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uses global vector values from a compute as input. See <A HREF = "Section_howto.html#4_15">this
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section</A> for an overview of LAMMPS output
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options.
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</P>
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<P>The vector values calculated by this compute are "extensive", meaning
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they scale with the number of atoms in the simulation. They can be
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divided by the appropriate volume to get a flux, which would then be
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an "intensive" value, meaning independent of the number of atoms in
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the simulation. Note that if the compute is "all", then the
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appropriate volume to divide by is the simulation box volume.
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However, if a sub-group is used, it should be the volume containing
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those atoms.
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</P>
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<P>The vector values will be in energy*velocity <A HREF = "units.html">units</A>. Once
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divided by a volume the units will be that of flux, namely
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energy/area/time <A HREF = "units.html">units</A>
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</P>
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<P><B>Restrictions:</B> none
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<H4>Sample LAMMPS input script
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</H4>
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<PRE>atom_style atomic
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units real
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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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group every region box
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velocity all create 70 102486 mom yes rot yes dist gaussian
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timestep 4.0
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thermo 10
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</PRE>
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<PRE># ------------- Equilibration and thermalisation ----------------
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</PRE>
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<PRE>fix NPT all npt 70 70 10 xyz 0.0 0.0 100.0 drag 0.2
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run 8000
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unfix NPT
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</PRE>
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<PRE># --------------- Equilibration in nve -----------------
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</PRE>
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<PRE>fix NVE all nve
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run 8000
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</PRE>
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<PRE># -------------- Flux calculation in nve ---------------
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</PRE>
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<PRE>reset_timestep 0
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compute myKE all ke/atom
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compute myPE all pe/atom
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compute myStress all stress/atom virial
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compute flux all heat/flux myKE myPE myStress
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log flux.log
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variable J equal c_flux[1]/vol
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thermo_style custom step temp v_J
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run 100000
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</PRE>
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</HTML>
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