Stress increase due to point defect is negative

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siying_li
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Stress increase due to point defect is negative

#1 Post by siying_li » Mon Nov 27, 2023 12:14 am

I was trying to calculate the stress increase in the HCP Ti system, after atomic relaxation, due to the introduction of an oxygen atom into the hexahedral site. I first fully relaxed the HCP Ti cell, and then introduced the hexahedral oxygen and allow atomic relaxation. The stress components XX, YY, ZZ (in kB) I obtained from systems with increasing number of atoms are shown below. Note that 5x5x3 means the periodicity in the a, b, and c directions in the HCP cell are 5 by 5 by 3.

system #atoms XX YY ZZ
6x6x2 144 5.93828 5.93828 -0.14642
5x5x3 150 5.17143 5.17143 1.17534
7x7x2 196 4.09788 4.09788 0.59545
5x5x4 200 4.02149 4.02149 0.91526
6x6x3 216 3.65289 3.65289 0.85778
6x6x4 288 3.15212 3.15212 -0.21246

The results show that as the system size increases, the XX and YY stress components decreases, which is what I expected. However, the ZZ component became negative for 6x6x2 and 6x6x4 cells and smaller than the normal trend for 7x7x2. I'm wondering if anyone can explain why this happened? Thank you!

Below is my INCAR
ISTART = 0
ICHARG = 2
PREC = Accurate
ENCUT = 900.00
ALGO = Fast
NELM = 80
EDIFF = 1E-8
SIGMA = 0.05
ISMEAR = 1
EDIFFG = -1E-4
NSW = 200
IBRION = 1
POTIM = 0.5
ISIF = 2
LCHARG = .FALSE.
LWAVE = .FALSE.
LSCALAPACK = .FALSE.
LREAL = .FALSE.
KPAR = 1
NPAR = 16

I've tried to use IBRION=2, but the results remain the same for all system sizes.

fabien_tran1
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Re: Stress increase due to point defect is negative

#2 Post by fabien_tran1 » Mon Nov 27, 2023 2:53 pm

Hi,

Difficult to say. However, note that the ZZ component is one order of magnitude smaller than XX an YY, and the unexpected trends observed for ZZ may possibly be just due to fluctuations (and the sign of no real physical importance). Actually, do you think that the ZZ values would stay the same if a tighter criterion like -1E-5 is used for EDIFFG? Also, what is the ZZ value for the HCP Ti without defect?

siying_li
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Re: Stress increase due to point defect is negative

#3 Post by siying_li » Mon Nov 27, 2023 8:58 pm

Thank you for the suggestions!

The stress components seem to converge well with EDIFFG = -1E-4. But I can try tighter criterion.
The ZZ value for the HCP Ti cell without the defect is negligible (less than 0.01kB).

It is possible that the sign has no physical meaning - just fluctuation of the stress. I was actually hoping to use stress to compute elastic dipole tensor with the residual stress method: Pij = Vσij, where Pij are components of elastic dipole tensor, σij are the stress increase due to the point defect, and V is the volume of the pristine Ti cell. I was expecting that as the system size increases, V increases and σij decreases, leading to converging Pij values (there might be small variations due to periodic interaction of the point defect). However, using the stress output, I got the following Pij values (unit: eV).

system #atoms P11 P22 P33
6x6x2 144 9.26 9.26 -0.23
5x5x3 150 8.41 8.41 1.90
7x7x2 196 8.70 8.70 1.26
5x5x4 200 8.73 8.73 1.96
6x6x3 216 8.58 8.58 1.98
6x6x4 288 9.84 9.84 -0.66

Clearly, the 6x6x2 and 6x6x4 cells experienced some "Poisson-like" effect, with larger P11 and P22 and negative P33. It is possible that the fluctuation of the stress leads to problems when computing elastic dipole tensor with the residual stress method. I'm open to any suggestions/thoughts!

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