Here is the CIF file of CeO2 (http://www.crystallography.net/cod/1562989.html). One of the paper mentioned that they have used 192 CeO2 atoms constructed by 444 primitive cells. To generate the coordinates, I have opened it using Vesta and make 444 supercell. But, I got 128 atoms from there (Not 192). Would you please suggest me how can I get the 192 atoms coordinates? Thanks for your time Best Jahid Hasan
1 Answer
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The paper you link to identifies 4 Ce atoms and 8 O atoms per unit cell, which has the correct stoichiometry and seems a reasonable density for CeO2, so what is going wrong? The issue is that you have the fully symmetry-reduced coordinates in the CIF file, and Vesta has not applied the symmetry operations to generate all the atomic sites.
The CIF file places them at the Wyckoff sites, but to convert this into all the symmetry-equivalent sites you need to apply the symmetry operations. If you look in Table 1 of the paper to which you link, Ce is at site 4a and O is at site 8c, i.e the unit cell has 4 Ce atoms and 8 O atoms (12 atoms in total). Perhaps Vesta hasn't detected the correct symmetry? The symmetry you want in this case is Fm-3m (this is also in the paper you link, Table 1; it's space group 225).
As a quick test, I created your cell by hand in Vesta. I made a new unit cell, space group 225 (Fm-3m) with 5.407 Angstrom lattice constant. Then I added Ce at (0,0,0) and O at (1/4,1/4,1/4) and it correctly populated all the symmetry-equivalent sites, giving me 4 Ce and 8 O in total:
When you construct the supercell, however, this should not be a supercell of this conventional cubic cell; the conventional cell has 12 atoms, so the supercell of that would give you $12\times 4\times 4\times 4 = 768$ atoms! You first want to reduce it to the primitive cell, which only has 3 atoms, and then do a supercell of that.
Vesta lets you convert to the Niggli cell when you export the data. For example, since you added the VASP tag to your question you might want the data in that format; simply choose "File", "Export Data" pick a filename and then when you save it a dialogue box will open with the option to convert to the Niggli reduced cell. Choose this, and it will save the primitive cell for you:
For the supercell, you can simply read this back in and then create the $4\times 4\times 4$ supercell.
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$\begingroup$ Thank you so much for your detailed explanation and time. I have a question regarding the exporting data. In the dialogue box I have seen " Convert to primitive cell" "convert to the niggli reduced cell" . You suggested to select later on. However, can you explain me what the difference between these? I have checked the fractional coordinates both ways and have found small differences. Which one should I use? Thanks again! $\endgroup$ Commented May 15 at 14:57
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2$\begingroup$ @Md.JahidHasanSagor a primitive cell is defined as the minimum volume cell, but in fact there are many different possible primitive cells with the same volume. Niggli defined a "reduced cell" in a way which is unique, so it gives one particular primitive cell. See, for example, nvlpubs.nist.gov/nistpubs/sp958-lide/188-190.pdf $\endgroup$ Commented May 15 at 21:30
code block. Also, adding a reference to the paper you mentioned will be helpful in answering your question. $\endgroup$