# Thermal conductivity calculation of Argon gas using Green-Kubo formalism

Hi there,

I’m trying to compute the thermal conductivity of Argon gas at STP using the Green-Kubo method as described in the related documentation page. I used the same sample script for solid Argon given at the end of the page. The temperature was set to 70K. And it computed the thermal conductivity as 0.31 W/mK, very close to the reference value given on the page.

I’ve changed the lattice spacing and the volume of the simulation box accordingly, as well as the temperature. I also increased the total number of steps. As a result, the lammps-calculated properties of the system are as follows:
pressure = 0.96 atm,
density = 1.708 kg/m^3 (at STP , it should be 1,783kg/m^3)
temperature = 273K

As you can see, the system is very close to the standard conditions. However, Green-Kubo computes the average thermal conductivity of Ar as 0.0003795 W/mK, which is two orders of magnitudes lower than the expected value of 0.0165 W/mK.

What do you think about the possible reasons for this discrepancy? What is the problem here? I’ve seen many studies using this method for solids and liquids, but I haven’t encountered such computation for gases. Can we use Green-Kubo for gases? If not, why?

The example provided at the end of the doc page is a toy example designed to be run on laptop with a very low number of atoms.

For an idea on how to set-up a simulation of gas phase and compute diffusion using GK, you can refer to the literature. Note that velocity autocorrelation and stress autocorrelation can be relatively long (several ps) due to the low diffusion through collision and gas. See for example: Molecular Dynamics Simulation Study of Transport Properties of Diatomic Gases -Bulletin of the Korean Chemical Society | Korea Science

Have you tried changing each of these properties individually? Try one simulation with a different lattice spacing but same values of everything else, one with a different volume but same everything else, etc. Then try changing two things, then three. Eventually, you’ll find the answer as to what change caused the discrepancy.

It is well known that measured self-diffusivity is lower in smaller boxes due to finite size effects (e.g. https://www.tandfonline.com/doi/full/10.1080/08927022.2020.1810685). It would not be surprising if thermal conductivity was also somehow similarly affected.

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