equal thermal conductivity in 3 directions

Dear lammps users,
I am running lammps to calculate the thermal conductivity of bulk graphite using Tersoff potential and Green-Kubo method. I have used ppp, pps, and even ssp boundary conditions and in all cases I get exactly equal value for thermal conductivity in x,y and z directions. Is something wrong with settings of commands?What setting gives me different thermal conductivities. The thermal conductivity in z-direction should be much less respect to x and y directions.
Any help would be appreciated.

Best regards,
Nima Pirouzmand

Since you’re using GK for bulk, why should

you get a different answer depending on the

boundary condition or the direction? There

are no gradients.

Steve

There’s a strong anisotropy in the thermal conductivity of graphite due to the nature of interlayer binding (compared to in-plane sp2 bonds), which should be observed in MD regardless of the method used - with or without a temperature gradient. There’s probably something wrong with your structure or with your input script, but it’s hard to tell what if you don’t send files.

Arthur

Dear Steve,

Thank you for your response. Do you mean that the GK essentially gives equal thermal conductivities in all directions?

So, how can I get direction-dependent thermal conductivity for a bulk system using GK?

Do I have to use NEMD to get direction-dependent thermal conductivity for a bulk system?

Best regards,

Nima Pirouzmand

I didn’t see the work graphene in your original post, just Tersoff,
so I assumed a simple crystal. So there could be directional
effects, though I don’t know that classical MD would be good
at picking them up. As I recall there have been papers on this
topic recently. I don’t think however that periodic vs non-periodic
BC will make a difference. There is nothing in the GK method
that would know anything about the boundaries, I don’t think.

Steve

Nimra was referring to graphite in the first post, where strong anisotropy in the thermal conductivity, consistent with the structural anisotropy, is observed. And as I said this can be (and is) observed in MD regardless of the method used.

Boundaries are also an important choice, again for any type of method (EMD, NEMD, etc), depending on the system under interest. Fixed boundaries lead to phonon-boundary scattering, which, depending on what you are studying, can be irrelevant (eg. for bulk materials). Depending on the size of your system and on the nature of the vibrational modes carrying heat (eg. long or short wavelengths, etc), this additional scattering can have negligible or substantial effect on the thermal conductivity (see ballistic/diffusive transport regimes).

Arthur

Dear Arthur,

Thank you very much for your informative response. I much appreciate it if you introduce appropriate references.

Best regards,

Nima Pirouzmand

These are broad topics, but you can probably find insights in these:

By the way, instead of “fixed boundaries”, I meant “any type of non-periodic boundaries” (including fixed ones).

Arthur

Thank you very much for your help and advice Arthur.

Best regards,

Nima Pirouzmand

yes, you’re getting much better answers from Arthur than me.

Ignore what I said before after not reading your post

carefully enough, and then mis-reading graphene/graphite a 2nd time!

Steve