Thermal conductivity : Green Kubo

Hi Lammps users:

I have couple of questions regarding Green Kubo approach for computing thermal conductivity. I am trying to compute thermal conductivity for bulk silicon crystal (666 at 1000k) using Stillinger-Weber potential. I collect the heat flux data from lammps simulation (15 ns with data collected at every 0.5 fs ) and do the autocorrelation using matlab . I computed thermal conductivity with different correlation window to check the convergence. >From my calculation I see that 500ps is sufficient for convergence. For 15 ns calculation I can easily average over 30 such intervals. To even get better statistic I did 3 independent 15 ns calculations. If I look at the average thermal conductivity it varied from 40 to 70 W/m-K for the three runs. In addition to that the x, y, and z component of the thermal conductivity varies from 20 to 100W/m-K. This variation is after averaging over the 15 ns runs. If a look at values from individual correlation window the variation is even larger.

My questions is, is this variation normal for these calculations? From literature I understand that the system size I am using should be sufficient. Also some of the reported thermal conductivity values for silicon does not show this much variation (Physical review B 81, 214305 (2010)).

I have seen a similar question by Baoling Huang in lammps forum, but couldn’t find many responses for that query.

If somebody has any experience in computing thermal conductivity of Silicon using Green Kubo approach in lammps, could you please comment on this question.

Thanks a lot

Deena

I don't think what you are asking is a LAMMPS question per se,
especially if you are post-processing the data yourself.

Maybe Reese can comment on the overall approach you are using.

Steve

The results for Si with SW potential for T=1000 K calculated using
LAMMP are published in J of Nucl. Mater. 418 (2011) 174.
There is not significant size effect for this temperature.
German

hi Deena
   there is also Schelling's often cited PRB 2002 and I know of another careful study by a colleague that should appear soon.
    You can also take a look at my publication
http://jcp.aip.org/resource/1/jcpsa6/v136/i15/p154102_s1
where you can estimate the variation by the simple formula
relative errror ~ 2 sqrt( correlation time / total run time)
    The variations you see are large but might be on the high end of reasonable.
Reese

Reese Jones
Sandia National Laboratories
P.O. Box 969, MS 9404
Livermore, CA 94551
(925) 294-4744 or 800 4SANDIA x2944744

German:

Thanks a lot for the information.

Could you please give me the following information regarding the Si MD runs.

Did you use NVT or NVE during the Heat flux calculation. Also the error mentioned in your calculation is from one long MD, but based on three calculations with different time shift, is that correct?

Thanks again
Deena

Hi Reese:

Thanks for the reply and information. I do see slightly larger variation in thermal conductivity compared to your paper. I did refer Schelling's paper and the error reported there is somewhat similar to what I see.

I am doing NVE compared to NVT that your paper refer to. My logic was to avoid influence of the thermostat. Is there any reason why you chose NVT compared to NVE?

Thanks
Deena

Deena,

1) Did you use NVT or NVE during the Heat flux calculation?
I did NVE.

2) Also the error mentioned in your calculation is from one long MD,
but based on three calculations with different time shift, is that
correct?

Yes, it's correct.

German