Benchmarking Erhart-Albe (EA) Tersoff potential

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1

Dear lammps users,

Is there anybody who checked the EA Tersoff potential in lammps?
I obtained same results(lattice constant, cohesive energy, and bulk modulus) for bulk Si with those in the original reference, but some deviations found:

e.g. elastic constants (GPa):
c11 = 177, c12 = 56, c44 = 60
cf) c11 = 167, c12 = 65, c44 = 60 in the EA paper

I used the script in the EXAMPLE folder for the calculation of elastic constants.
Thanks for any comments in advance.

Joe

2

Dear lammps users,

Is there anybody who checked the EA Tersoff potential in lammps?
I obtained same results(lattice constant, cohesive energy, and bulk
modulus) for bulk Si with those in the original reference, but some
deviations found:

e.g. elastic constants (GPa):
    c11 = 177, c12 = 56, c44 = 60
cf) c11 = 167, c12 = 65, c44 = 60 in the EA paper

I used the script in the EXAMPLE folder for the calculation of elastic
constants.
Thanks for any comments in advance.

i don't know anything about the potential parameters
and the paper, but i would like to remind you that
everything under "example" is just that: an example
for how to do something, and not necessary a
demonstration of best practices that can be copied
without adapting it for specific needs.

for example, have you checked for convergence
of your raw data? many examples are very abbreviated
runs for the sake of showing the workflow.

axel.

3

In addition to Axel's comments, Tersoff has multiple papers on Si,
each with different parameter set and different elastic constants.
You might want to check which reference you are citing, and which
parameter set is provided in the Si.tersoff potential file.

Cheers,
Ray

4

Thank you all.

I found the reason of deviation in elastic constants.

In this case, It does not comes from non-convergence of data in a series of displacement-minimization process as Axel mentioned, but from orientation of the structure.

For bulk property such as bulk modulus, it doesn’t matter.
But, elastic constants are affected by orientation of the structure.

e.g.
Let me say z indicate (001), then x and y orientation can have arbitrary orientations if both are perpendicular and satisfied with the right-hand rule.

Consider following two cases:

  1. orient x 1 -1 0 orient y 1 1 0 orient z 0 0 1
  2. rotated 1) by 45 degrees along z direction

c11(cxx) would be different between 1) and 2).

all the best,

Joe

5

Hi Joe,

I don't think I agree with you. Comments below, thanks.

In this case, It does not comes from non-convergence of data in a series of
displacement-minimization process as Axel mentioned, but from orientation of
the structure.

Elastic constants always depend on orientation. Strain X then measure
stress in X gives you C11, while straining YZ then measure stress in
XY gives you C46, etc.

For bulk property such as bulk modulus, it doesn't matter.
But, elastic constants are affected by orientation of the structure.

Elastic constants are also bulk properties, which by definition are
intensive properties of the system that does not depend on the size.

e.g.
Let me say z indicate (001), then x and y orientation can have arbitrary
orientations if both are perpendicular and satisfied with the right-hand
rule.

Consider following two cases:
1) orient x 1 -1 0 orient y 1 1 0 orient z 0 0 1

What you think is c11 is actually C66, which is equal to C44 for a
diamond cubic. C11 is a notation for C1111, while C66 is C1212
(meaning straining xy then measuring stress in xy). In the above
scenario, X is orientated along [1-10], which is the same as xy. So
that "c11" is actually C1212 = C66.

2) rotated 1) by 45 degrees along z direction

Does not this rotate the crystal back to its normal orientation? X is
aligned with [100], Y [010], or the opposite. So that this C11 is the
true C11, or C22. But again, C11 = C22 for a diamond cubic.

c11(cxx) would be different between 1) and 2).

Yes, they are different, but only because one is C66 and the other C11.

Cheers,
Ray

6

Hi,

As a bonus : Rotational elastic constant are relate via a rotational tranformation , So once you find the elastic constant along [100] , then its easily to find it along different cyrstalographycs indices .

A good reference that is worth to read : “Young’s modulus surface and Poisson’s ratio curve for cubic metals”

Link:
http://www.sciencedirect.com/science/article/pii/S0022369707000133

Cheers
Oscar G.

7

Hi,

Thank you so much, Ray and Oscar.
I am learning a lot from those like you in this mailing list.

All the very best,

Joe