Syntax:
compute ID group-ID heat/flux pe-ID
Examples:
compute myFlux all heat/flux myPE
Description:
Define a computation that calculates the heat flux vector based on interactions between atoms in the specified group. This can be used by itself to measure the heat flux between a hot and cold reservoir of particles or to calculate a thermal conductivity using the Green-Kubo formalism.
See the fix thermal/conductivity command for details on how to compute thermal conductivity in an alternate way, via the Muller-Plathe method.
The compute takes a pe-ID argument which is the ID of a compute pe/atom that calculates per-atom potential energy. Normally, it should be defined for the same group used by compute heat/flux, though LAMMPS does not check for this.
The Green-Kubo formulas relate the ensemble average of the auto-correlation of the heat flux J to the thermal conductivity kappa.
Ei is the per-atom energy (potential and kinetic). The potential portion is calculated by the compute pe-ID specified as an argument to the compute heat/flux command.
IMPORTANT NOTE: The per-atom potential energy calculated by the pe-ID compute should only include pairwise energy, to be consistent with the second virial-like term in the formula for J. Thus if any bonds, angles, etc exist in the system, the compute should limit its calculation to only the pair contribution. E.g. it could be defined as follows. Note that if pair is not listed as the last argument, it will be included by default, but so will other contributions such as bond, angle, etc.
compute myPE all pe/atom pair
The second term of the heat flux equation for J is calculated by compute heat/flux for pairwise interactions for any I,J pair where one of the 2 atoms in is the compute group.
These quantities can be output every so many timesteps (e.g. via the thermo_style custom command). Then as post-processing steps, an autocorrelation can be performed, its integral estimated, and the Green-Kubo formula evaluated.
Here is an example of this procedure. First a LAMMPS input script for solid Ar is appended below. A Python script correlate.py is also given, which calculates the autocorrelation of the flux output in the logfile flux.log, produced by the LAMMPS run. It is invoked as
correlate.py flux.log -c 3 -s 200
The resulting data lists the autocorrelation in column 1 and the integral of the autocorrelation in column 2. The integral of the correlation needs to be multiplied by V/(kB T^2) times the sample interval and the appropriate unit conversion factors. For real units in LAMMPS, this is 2917703220.0 in this case. The final thermal conductivity value obtained is 0.25 W/mK.
The 6 components of the vector calculated by this compute are as follows. The first 3 components are the x, y, z components of the full heat flux. The next 3 components are the x, y, z components of just the convective portion of the flux, which is the energy per atom times the velocity of the atom.
Output info:
This compute calculates a global vector of length 6 (heat flux vector), which can be accessed by indices 1-6. These values can be used by any command that uses global vector values from a compute as input. See this section for an overview of LAMMPS output options.
The vector values calculated by this compute are "extensive". They should be divided by the appropriate volume to get a flux. The vector values will be in energy*velocity units.
Restrictions:
Only pairwise interactions, as defined by the pair_style command, are included in this calculation.
This compute requires you to use the communicate vel yes option so that velocites are stored by ghost atoms.
Related commands:
Default: none
atom_style atomic communicate single vel yes units real 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 group every region box velocity all create 70 102486 mom yes rot yes dist gaussian timestep 4.0 thermo 10
# ------------- Equilibration and thermalisation ----------------
fix NPT all npt 70 70 10 xyz 0.0 0.0 100.0 drag 0.2 run 8000 unfix NPT
# --------------- Equilibration in nve -----------------
fix NVE all nve run 8000
# -------------- Flux calculation in nve ---------------
reset_timestep 0 compute myPE all pe/atom pair compute flux all heat/flux myPE log flux.log variable J equal c_flux[1]/vol thermo_style custom step temp v_J run 100000