# Thermal Conductivity of Diamond Calculation

Hi all,

using lammps version from March 3, 2020.

I’m trying to do a simple calculation of diamond thermal conductivity by adapting the example for the ehex calculations to diamond. I’m not looking for an exact answer just playing around to master the technique.

I think it’s working fine and looks like it’s stabilizing. I’m trying to understand the equation in the README file. I am a bit confused on the time units and delta Time.

Note: Using Metal Units

In the end my calculation for dT = 0.008
This is in eV (from metal units) so I divide by Boltzmann factor to get into kelvin:
dT = 0.008 eV / (8.617E-5 eV/K) = 92 K
The distance dZ is 140 units of the lattice constant(3.615 Ang):
dZ = 140*3.567E-10 m

Now for the heat flux, we use the equation given in the Wirnsberger paper so that (as in the README file) the energy flux is 10 eV.
This is where I become confused. On the ehex documentation page it says the rate is in (energy / time units).
So then:
F = 10 eV / ps

The total heat flux is then in 70000 steps of run time and cross section of (103.567E-10)^2 :
__dQ = (10 eV / ps) * 70000 steps / 70000 steps / (10
3.567E-10 m)^2 (1/2)__
and converting to J/(s
m^2)
dQ = (10 eV / 1ps)(1.6E-19 J/eV) / (10^-12 s/ps) / (103.567E-10 m)^2 *(1/2)

Note: I’m not sure about the time steps. In the README file for ehex it has that the steps cancel out which I assume is true whenever using ehex. So that all you’re left with is F value.
Additionally, I’m not sure where the default timestep of 0.001 ps kicks in. This should obviously be included in the above 7000 steps but it doesn’t matter if it cancels out?

Multiplying out the factors:
dQ * dZ / dT = 33 W/(m*K)

According to Morelli et al this is low but the plots show that the phonon mean free path is in the hundreds of nanometers between 200-350K (the temperature of my system), while my system is only 50 nm long.
Which is as expected, again, I’m not looking for a legitimate answer to the thermal conductivity just hoping to learn and verify that I’m doing the ehex calculations correctly.

So any insight would be helpful. Below is the input file and output.

DiamondKappa141F.in (2.15 KB)

log.lammps (19.6 KB)

profile141F.ehex (569 KB)