The crystal structure for Ba2TiO explained with symmetries

[Beyar]

Hello!

I would love to get help on this particular question that I find extremely difficult to answer.

-"Bariumtitanate can under a certain set of conditions crystallize in the given structure. With the help of the compounds symmetries, explain how it is possible for it to achieve such a crystallization structure.

No equations are given for the specific problem so I am leaning towards that one has to use translation/reflection symmetries etc. to be able to solve this specific problem.

The given crystallized structure (transparent octahedron shape) can be seen in the picture.

 

[TeethWhitener]

It might help to label the species in the picture and then think about what happens if you try to move the center ion out of its place.

 

[Beyar]

I believe that this species has undergone translation from either heat or cooling, which in turn has moved the Ti-ion (center ion) and caused the hexagon-shaped face to appear. Because from the start, the Ba2Tio species has a unit cell of a perovskite, which in turn is ideally face-centered cubic I believe. But I don't know how to translate this into "symmetry words", so to say..

 

[TeethWhitener]

I believe that this species has undergone translation from either heat or cooling,

What do you mean by translation? Do you mean the Ti⁴⁺ has moved to the center of an octahedron?

If you start with the cubic crystal structure in the picture you attached, what happens when you move the Ti⁴⁺ away from the center?