# parameters of Vashishta potential for Al2O3

Dear LAMMPS users,
I started testing Vashishta potential for Al2O3. I took the potential file from LAMMPS and changed the parameters according to the article, Journal of Applied Physics 103, 083504 (2008); https://doi.org/10.1063/1.2901171. Having looked at the LAMMPS documentation and source code for the potential, I see that the formulation of the potential is implemented in Lammps as it is given in the article. I used LAMMPS example scripts to calculate the elastic constants. The obtained elastic constants are not close to what were expected according to the article. I do not know what I am missing here; however, started having doubt about the values of D, the coefficient in 3rd term in 2-body interaction!
Could you provide some information on the values of D in the potential file? To be more specific; should it be D (as reported in the article) or D/2, or am I missing something else here?

Regards,
Shyamal

Hi,

Perhaps you need to take care of the units. Vashishta liked to use the Gauss units, where 1/4/pi/epsilon_0=1. So you need to do the following to convert the parameter D in the paper to that in the LAMMPS potential file (I assume that you use the “metal” units in LAMMPS):

D -> D/ 1.441959e+1 # from Gauss to SI

because 1/4/pi/epsilon_0 = 1.441959e+1 eV A /e^2.

Perhaps you also need to further divide D by 2. I am not sure about this. You need to consult the LAMMPS manual and/or the example potential file you have.

Bruce

Sorry that I have a typo. It should be:

D -> D*1.441959e+1 # from Gauss to SI

Best,

Bruce

Hello Bruce,

Yes, the units are in LAMMPS “metal” units, and the unit (eV*Angstroms^4) of D is taken care of.

Thanks,
Shyamal

I am afraid that eV*Angstroms^4 is not in SI unit system. This is still in Gauss units. You need to multiply D by 1.441959e+1 to convert it the SI unit system with the LAMMPS metal units.

Bruce

I have just checked a Vashishta potential file in LAMMPS and it indeed requires converting the value of D from Gauss to SI. In Vahishita’s 2007-JAP paper on SiC, D = 2.1636 e^2 A^3. By multiplying this with the factor
1/4/pi/epsilon_0 = 1.441959e+1 eV A /e^2 and then divide the result by 2, you will get a value D’ = 15.575 eV A^4, which is close to that in this file:

https://github.com/lammps/lammps/blob/master/potentials/SiC.vashishta

Bruce

According to the Lammps documentation there is no 1/2 factor in the third term in 2-body interaction potential formulation, https://lammps.sandia.gov/doc/pair_vashishta.html. However, there is a 1/2 factor in the third term in formulation in the paper DOI:10.1063/1.2724570 as you mentioned for SiC. So, in order to be consistent with the Lammps and the article, one should provide half of the value of D (as reported in the article) in the Lammps potential file as you have suggested. The unit should be changed to eV*A^4 as you also have suggested.

I was refereeing to the article for Al2O3 (alumina), Journal of Applied Physics 103, 083504 (2008); https://doi.org/10.1063/1.2901171. There is no 1/2 factor in the third term, which is exactly the same formulation implemented in Lammps. Therefore, the value of D should be provided in the Lammps potential file as it is given in the article. The unit of D needs not to be changed as the article provides it in eV*A^4. The obtained elastic constants, in this case, are not even close to the values mentioned in the article! Having said that, just out of curiosity, I used half of D for a test simulation, and the elastic constants are appearing to be the ones as mentioned in the article. This is bothering me, knowing that I am providing apparently wrong value (in this case D/2 instead of D) and getting apparently good results! So there must be something else that is missing here and I have no idea what it is!

Regards,
Shyamal

Hi Shyamal,