Problem building a unit cell of bulk tio2

[zhySarah]

Hi,

I am trying to build a unit cell of bulk TiO₂ anatase as is shown in the first attachment (a). However I am only able to build one as shown in the second attachment. I am wondering if these two are equivalent when doing calculations? If not, how can I build the other model?

Thanks in advance!

[Umberto Martinez]

Yes, the structure looks exactly the same.
You can use Bulk Tools->Repeat to repeat your structure one more time along the A or B directions to build the structure reported in (b).

[zhySarah]

Yes, the structure looks exactly the same.
You can use Bulk Tools->Repeat to repeat your structure one more time along the A or B directions to bale the structure reported in (b).

Thanks for your reply Umberto! That is to say that in my unit cell there are as well 4 Ti atoms and 8 O atoms as in reported structure (a)?   Or it is only the atoms shown in the cell that counts for the total number of atoms in the unit cell? It matters because I need to know the impurity concentration in the (b) like structure.

PS: what if I repeat my structure in all three dimensions first and then delete all the atoms outside the unit cell to make a structure exactly like the one in (a). What difference it will make compared to the one I have now.

[Jess Wellendorff]

Dear zhySarah. The image from the article is cheating you a bit, and it is important that you understand why: The key concept is that of the "repeted cell" for calculations on bulk structures. You should always try to do calculations for the smallest unit cell possible and account for periodicity by using k-point sampling - this is simply most efficient in terms of CPU hours. The structure you have built is the minimal cell: If you repeat it along all directions, you see that it really does form anatase TiO2.

The authors of the article have tried to make it easy to interpret the image and recognize the TiO2 bulk by repeating the cell and cutting away the atoms outside the unit cell. This is perfectly fine for illustrations, but in their calculations they have certainly used the minimal cell. You should do so too.

[zh]

If you understand the periodic boundary of unit cell, your problem will be easily gotten answer.

1). Some atoms in (a) are equivalent. For example, the atoms in the vertexal points of the cell; the atoms in the middle of a and b lattice vectors.

2). The size of two cells are different, even you make the same numbers of atom in two cells.

[zhySarah]

Dear zhySarah. The image from the article is cheating you a bit, and it is important that you understand why: The key concept is that of the "repeted cell" for calculations on bulk structures. You should always try to do calculations for the smallest unit cell possible and account for periodicity by using k-point sampling - this is simply most efficient in terms of CPU hours. The structure you have built is the minimal cell: If you repeat it along all directions, you see that it really does form anatase TiO2.

The authors of the article have tried to make it easy to interpret the image and recognize the TiO2 bulk by repeating the cell and cutting away the atoms outside the unit cell. This is perfectly fine for illustrations, but in their calculations they have certainly used the minimal cell. You should do so too.

Thanks for your answer, Jess! Yet I have gotten another problem and hope that you can share your opinion on it.
I have used the unit cell to calculate the band structure of the bulk tio2 and the resulting band gap is only 1.807eV. I have referred to many literatures using the same settings (GGA+PBE) and almost all claim the calculated band gap in the range of 2.1-2.2eV. Can you suggest what the problem could be? (The mesh cut off energy of 75Hartree and k-sampling of 5*5*5 are used after convergence test.) I have also tried to do the calculation in a 2*2*1 supercell and the result is slightly different 1.862 vs. 1.807eV)

Thanks in advance!

[zhySarah]

If you understand the periodic boundary of unit cell, your problem will be easily gotten answer.

1). Some atoms in (a) are equivalent. For example, the atoms in the vertexal points of the cell; the atoms in the middle of a and b lattice vectors.

2). The size of two cells are different, even you make the same numbers of atom in two cells.

Thank you for your answer zh! I can see the equivalence of some atoms, and they are not shown in my model compared to (a). But my question is should we count them when doing calculation Let me put it this way so that you can understand my confusion better: If I substitute one atom with an impurity atom in the unit cell, is the concentration of the impurity 1/12 or?

And as you mentioned about the size of the cell, I wonder also does it affect the calculated band gap of the bulk material?

Thanks

[Umberto Martinez]

Thanks for your answer, Jess! Yet I have gotten another problem and hope that you can share your opinion on it.
I have used the unit cell to calculate the band structure of the bulk tio2 and the resulting band gap is only 1.807eV. I have referred to many literatures using the same settings (GGA+PBE) and almost all claim the calculated band gap in the range of 2.1-2.2eV. Can you suggest what the problem could be? (The mesh cut off energy of 75Hartree and k-sampling of 5*5*5 are used after convergence test.) I have also tried to do the calculation in a 2*2*1 supercell and the result is slightly different 1.862 vs. 1.807eV)

Thanks in advance!

did you optimize the lattice parameters?
Uncheck "constrain cell" in Optimize Geometry and set a stress tolerance to something like 0.002/0.001 eV/A^3 

[zh]

When you estimate the impurity concentration, the symmetry nonequivalent atoms in the unit cell should be used.

"And as you mentioned about the size of the cell, I wonder also does it affect the calculated band gap of the bulk material?"
For example, Si, the use of a primitive unit cell (face centered cubic) and a conventional unit cell (simple cubic) would give the same band gap if the k-points used in k-point sampling are symmetry equivalent.

[zhySarah]

Thanks for your answer, Jess! Yet I have gotten another problem and hope that you can share your opinion on it.
I have used the unit cell to calculate the band structure of the bulk tio2 and the resulting band gap is only 1.807eV. I have referred to many literatures using the same settings (GGA+PBE) and almost all claim the calculated band gap in the range of 2.1-2.2eV. Can you suggest what the problem could be? (The mesh cut off energy of 75Hartree and k-sampling of 5*5*5 are used after convergence test.) I have also tried to do the calculation in a 2*2*1 supercell and the result is slightly different 1.862 vs. 1.807eV)

Thanks in advance!

did you optimize the lattice parameters?
Uncheck "constrain cell" in Optimize Geometry and set a stress tolerance to something like 0.002/0.001 eV/A^3

Hi Umberto,

I did optimize the structure, but only with the quick optimizer with the max force 0.01eV/Å right after building the model. I will try with the optimize geometry right now and let you know how it works. But which potential settings I should choose (I don't see the Tersoff potential in my version 2014.0 as is used in one of your tutorials)? And the value of the stress tolerance you suggested, should I do the convergence test and make adjustment too?

Regards

[zhySarah]

When you estimate the impurity concentration, the symmetry nonequivalent atoms in the unit cell should be used.

"And as you mentioned about the size of the cell, I wonder also does it affect the calculated band gap of the bulk material?"
For example, Si, the use of a primitive unit cell (face centered cubic) and a conventional unit cell (simple cubic) would give the same band gap if the k-points used in k-point sampling are symmetry equivalent.

Thanks

[Umberto Martinez]

Optimize with DFT-PBE which is the functional you are using to calculate the electronic properties.
It won't take long time.
Yes, you can test the stress tolerance parameters. the value I suggested is a good start.

Also, update to ATK/VNL 2014.3 which is the latest stable version:
http://quantumwise.com/publications/quantumwise-news/item/894
http://quantumwise.com/download/pkgs/archive/

Finally notice that ATK and VNL 2015 has been released. You can consider upgrading to this latest version as well (depending on your license)
http://quantumwise.com/publications/quantumwise-news/item/908-vnl-atk-2015-released.

[zhySarah]

Optimize with DFT-PBE which is the functional you are using to calculate the electronic properties.
It won't take long time.
Yes, you can test the stress tolerance parameters. the value I suggested is a good start.

Also, update to ATK/VNL 2014.3 which is the latest stable version:
http://quantumwise.com/publications/quantumwise-news/item/894
http://quantumwise.com/download/pkgs/archive/

Finally notice that ATK and VNL 2015 has been released. You can consider upgrading to this latest version as well (depending on your license)
http://quantumwise.com/publications/quantumwise-news/item/908-vnl-atk-2015-released.

Hi Umberto

Thanks for your suggestion. The result is finally acceptable.
One more thing that confuses me though. What decides the distance between fermi Level and CB(or VB) in the band structure. It seems that my fermi Level lies almost in the middle of the band gap, while I saw in many Reference papers the fermi Level stays right on top of the valence band.

[zh]

In the DFT simulation of bulk semiconductor or insulator, the Fermi level is set at the top of valence bands or at the middle of band gap. Both of them are acceptable.  See the following discussion:
https://www.researchgate.net/post/Why_does_the_Fermi_energy_level_lie_in_the_centre_of_the_energy_band_gap_of_a_semiconductor

[Umberto Martinez]

Exactly. I suggest you to always specify in your papers/figures the definition of the Fermi level you use for an undoped semiconductor or insulator, top of the valence band or middle of the band gap. Even though it is clear from the picture which definition you pick.