[yomi]

What are the coordination numbers of calcium and titanium, respectively, in perovskite?
The unit cell is shown below.
How to calculate it?

[Dan]

How to calculate it?

Just count, very simple.

E.g. ABA - coordination number of B is 2

        A
E.g. ABA - coordination number of B is 4
        A

For Ti, you will have to visualise 4 unit cells.

[yomi]

But the answer is "12 and 6"
Can you explain again more clearly?

[Dan]

Ok notice how the unit cell is divided up into 8 small cubes, the face of each of these I will call a "small square".

If you look at Ca, the closest O is a distance of "1 diagonal of a small square". There are 12 O at this distance away (all of them).
If you consider Ti, it is easier to visualise if you extend the unit cell in your head - the unit cell is the simplest reapeating unit of the lattice. You can see that the closest O is "1 edge of a small square" away, and there are 6 - two on each axis x, y, z.

Alternatively, we can say that the unit cell is divided up into 8 small cubes with edge length A, so an edge of the whole unit cell is 2A. The closest O is SQRT(2A²) away, and all the O in the unit cell is SQRT(2A²) from Ca.

For Ti, the Ti-O distance is A, and O surrounds Ti in an octahedral arrangement.

Does this help? I don't have time to draw a picture right now but I can if you want.

[yomi]

Yeah, I got it. Thanks a lot!