# Fix heat kinetic energy went negative

Dear all

I want to calculate thermal conductivity in graphene. in input (metal
units), I have used :

fix 3h hot heat 1 0.01
fix 3c cold heat 1 -0.01

But I get this error:
"Fix heat kinetic energy went negative"

Thanks a lot
Farrokh

Dear all

I want to calculate thermal conductivity in graphene. in input (metal
units), I have used :

fix 3h hot heat 1 0.01
fix 3c cold heat 1 -0.01

But I get this error:
"Fix heat kinetic energy went negative"

think about it for a little bit and it should be obvious. you are
trying to remove more kinetic energy than what your (cold?) group
contains. this is impossible and thus your simulation setup must be
wrong. it is not a fix heat problem per se, but how you use it.

axel.

Farrokh
I prefer using two thermostats (at different temperatures) over the
fix heat for this type of calculations.
The main reason being that with the thermostats you know right away
what the temperature gradient is going to be in steady state. Remember
that you are ultimately interested in the low gradient limit (small
perturbation) as you are employing linear response theory to compute
the conductivity with this approach.
Carlos

Hi Farokkh,

You might also want to look into the RNEMD method implemented in LAMMPS (http://lammps.sandia.gov/doc/fix_thermal_conductivity.html) as well as the Green-Kubo method (http://lammps.sandia.gov/doc/compute_heat_flux.html), which will work for graphene since you have no formal charges (the Green-Kubo method in LAMMPS does not work using long-range electrostatic methods such as PPPM or Ewald sums, so cannot reasonably be applied to systems with charges on the atoms).

In addition be aware that the direct methods, such as you are trying or the RNEMD, require a sample size comparable to the scattering length of phonons in the material, which is going to be quite large in graphene. The Green-Kubo method is less sensitive. Of course, if you are interested in the thermal conductivity of a physically small piece of graphene, smaller than the scattering length, then this caution does not apply. Finally, the scattering length is strongly affected by the isotopic purity of the carbon. We almost always ignore isotopes when modeling because the effects are usually not significant. However in diamond, silicon, germanium and other pure elements the effect on the thermal conductivity can be very large, up to perhaps a factor of 10 at low temperatures. This will also occur in graphene, graphite and carbon nanotubes because they are composed of a single element and have high thermal conductivity, and hence long scattering lengths that may easily be on the order of a micrometer or more. Thus you need to consider the isotopic purity, even if you are interested in the thermal conductivity for nano sized pieces of graphene.

Hi Farokkh,

The PPPM contribution for heat flux (and stress) was added to LAMMPS about a year ago by Stan Moore, so Green-Kubo for TC can work with charges. As Paul said, finite size effects are very important. E.g., you could find the frequency-dependent thermal conductivity using G-K, but keep in mind that low frequency contributions could be missing due to finite box size.

Tim