# How can I find the smaller symmetric structure from big crystal unit cell?

It appeared as triclinic cell, but if you download CIF file and open it from softwares like Avogadro or VESTA, it appeared as a orthogonal simple cubic (a=b=c, alpha = beta = gamma = 90 degree). I also checked that this geometry is the same with what I downloaded from American Mineralogy Material Database.

Now, I wish to run DFT or quantum calculations for them. So, I excluded atoms in periodic boundary, unit cell contains total 160 atoms. I'm afraid this might be too big, might takes too long time to calculate via DFT or any other quantum simulations. All I need to do is just geometry optimizations, but still, 160 atoms seems too big.

Using VESTA or Avogadro or any other software, is this possible to find the symmetric structure inside this or other "big" unit cell, and make a smaller / simpler version of unit cell for faster calculation?

Or, can I manually cut this unit cell in 1/4 size, 40 atom system with 1/2 size for x, y, and z direction, and run the minimization? It seems that the Pyrope unit cell have some sort of repeating structure inside the big unit cell. But I'm not sure if it is "safe" to find symmetry and divide the unit cell manually.

Thank you

• A fully ab initio geometry optimisation of pyrope has already been done: pubs.acs.org/doi/pdf/10.1021/jp050316z Commented Jul 1, 2019 at 22:38
• @IanBush Thank you, but I need to do some other things, like volumetric expansion and compression and etc.... which requires good amount of computational resources. Commented Jul 2, 2019 at 0:40
• You don't cut unit cell in half out of the blue. It would be about as sensible as cutting your car in half, in the hope that it will still be able to carry half the load, say, yourself and one passenger. (Besides, cutting a cell in half along x, y, and z would give you 1/8, not 1/4 the volume.) Also, pyrope is definitely neither triclinic not orthogonal nor simple cubic. As for the symmetry, it is written right there in the CIF file, as plain as it gets, and is pretty high (think of 1/48, not 1/8). Whether your software of choice can read and properly account for it is another question. Commented Jul 2, 2019 at 6:34
• @exsonic01 Note the paper referenced calculated the full phonon spectrum of pyrope as well as the structural optimisation, and is14 years old. 160 atoms should be reasonably routine nowadays on a small cluster, people are doing well over 1000 atoms in optimisations. I've just submitted a paper with around 2800 atoms in the structure, studying the structure and properties as a function of the metal at the heart. That required a fairly chunky machine, but only ~2000 cores which is not outrageous. Commented Jul 2, 2019 at 8:17
• @IanBush Well, not all research centers have affluent amount of computational resources, and I have other guys in my lap to run some simulations... Oh well, I will see what I can do. Thanks anyway. Commented Jul 3, 2019 at 2:00

The structure contains 4 independent atoms, Mg, Al, Si and O. The space group is a cubic one containing 96 asymmetric units. If you place an atom on a general position, it will appear 96 times in the unit cell. Mg, Al, and Si are located in various special positions, i.e. lie on symmetry elements. Placing the Mg and the Si atom will result in 24 atoms in unit cell, while placing the Al atom in its position (on the origin) will result in 16 atoms in the unit cell (on a three-fold and on the center of inversion).

So you could say that the asymmetric unit contains one oxygen atom, one quarter Mg and Si atom respectively (24/96), and one sixth Al atom (16/96). One of the sites you cited in a previous question gives the fractional coordinates as:

Si: 0.3750 0.0000 0.2500

Al: Origin

Mg: 0.1250 0.0000 0.2500

O: 0.0341 0.0490 0.6530

If you look at the space group, http://img.chem.ucl.ac.uk/sgp/large/230az1.gif,

you can see that Al, Mg, and Si are on special positions (you can either find the locations on the diagram or apply the 96 operations (48 combined with the I-centering) listed on the right to the coordinates and see how many unique locations you get), while oxygen is not.

can I manually cut this unit cell in 1/4 size, 40 atom system with 1/2 size for x, y, and z direction, and run the minimization?

If you software is aware of crystallographic symmetry, it is a very simple system with 4 degrees of freedom (the oxygen position and the lattice parameter a). Everything else is fixed if you impose the symmetry of garnet.

I have Pyrope (Mg3Al2(SiO4)3) crystal structure, downloaded from materialsproject: https://materialsproject.org/materials/mp-6073/#. It appeared as triclinic cell...

There are some inconsistencies in the way the site shows the data. The space group is (correctly) given as Ia3d. The 3D image does not show a body-centered cubic cell, but instead the primitive rhombohedral cell (the smallest unit that recreates the entire crystal through three translations). In one iteration ("primitive"), the coordinate file lists the symmetry as 1, applied the Ia3d operators to the atomic positions (maybe to "not to confuse" users unaware of crystal symmetry), and switched to the rhombohedral cell.

No, the unit cell is the smallest translational repeating unit, and any truncation of that would mean that you're calculating a different solid which may or may not exist. 160 atoms is a decent sized unit cell, but is still routinely doable with the right resources. (The materials project page you link to is in fact an automated DFT geometry optimization of that solid, so you could use that)

If you still want to do the calculation yourself then you have to use the whole cell; however, if the unit cell has some additional symmetry (e.g. center of inversion), then a good DFT program will take advantage of that to speed up the calculation.

• Thanks. But I have a question, the unitcell CIF file I downloaded from materials project (and american mineralogy) actually have Mg24 Al16 Si24 O96. But we know the original formula of structure is Mg3 Al2 Si3 O12. Material database one actually 8 times bigger than formula. That was why I was thinking it might be possible to devide the unit cell. Commented Jul 2, 2019 at 0:46
• Speaking of DFT, I'm using Quantum Espresso 6.4.1, and as far as I know default option consider the symmetry... Commented Jul 2, 2019 at 0:50
• The ‘actual’ formula you’ve mentioned above is the empirical formula and not the structural formula, so you cannot do what you are proposing. (webmineral.com/data/Pyrope.shtml)
– PJ R
Commented Jul 2, 2019 at 5:55
• OK, thanks to let me know, I'm checking CIF file and now I know I was totally wrong. Purpose of my questions was, I just wished if such things are possible, just in case to check. Commented Jul 3, 2019 at 2:12
• If you want to impose symmetry restraints (i.e. keep the symmetry), there are only 4 unique atoms, and most of their coordinates are fixed. The asymmetric unit (in this case 1/48th of the unit cell) is the unique volume, not the unit cell.
– Karsten
Commented Jul 5, 2019 at 13:00