elastic properties at higher temperatures


I have seen the example for elastic constants at 0K in lammps examples

I would like to look at the elastic properties at various temperatures such as 300k, 500K and so on.
can you tell what modification to be made in the example script?


usually the calculation of the elastic constants can be donde by
different methods. First is a method that uses the fluctuation formula
at the finite temperature "J. R. Ray, Comp. Phys .Rep. 8 (1988),109"
. The other is the method that takes into account the internal
displacement in the range of the harmonic approximation J. W. Martin,
J. Phys. C, 8 (1975), 2858. At 0K the calculation of the elastic
constant is something trivial i.e just take the derivative of the
stress vs the displacement cijkl = sigma_ij/epsilon_kl. (dont forget
set the forces to zero). However for a finite pressure or temperaure
thing turns ugly ...

Oscar G.

Oscar is correct I believe, and Aidan may want to
comment on "ugly" ...


Yes, in theory the strain fluctuation formula can be used with NPT MD
sampling, but it practice it does not work. The stress fluctuation
counterpart does work, but it requires sampling second derivatives of
energy w.r.t. strain, while LAMMPS only computes.first derivatives i.e.
stress. The standard solution is to sample stress in NVT and N(V+epsilon)T
MD, where epsilon represents as small deformation. You have to run 6
different deformations to get all the elastic constants, or 12 if you do
both positive and negative deformations. That's pretty ugly. There is a
better method developed by Yubao Zhen[1] that is on our list of things to
do. Maybe in a few months.


[1] Yubao Zhen *, Chengbiao Chu, A deformation–fluctuation hybrid method
for fast evaluation of elastic constants with many-body potentials,
Computer Physics Communications 183 (2012) 261–265,