# Calculating theoretical density

Just as the title states, I need to calculate the theoretical density of CaTiO3. These calculations need to come from the unit cell and ionic radii of each ion.

The CaTiO3 is like this http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture4/Lec4.html#anchor4 with the Ca2+ at the Corners, Ti4+ at the body center and O2- at the face centers.

So, my calculations go like this:

Total of each Ion:
Ca2+ -> 8 corners x (1/8 each corner) = 1 ion
Ti4+ ->  1 in center = 1 ion
O2-  -> 6 faces x (1/2 each face) = 3 ions

Total of 5 ions...

So, the "touching direction" is accross the face (since the center Ti ion is slighty off-center) so the Ionic distance there is:
2(Rca2+) + 2 (Ro2-) = 2(0.106) + 2(0.132) = 0.476 nm

If I give each side of the unit cell a lenth of "a" then the diagional is equal to root(2) x a. Thus a = 0.476 / root(2) = 0.336 nm

The volume of this unit cell is then a³ -> (0.336)³ = 0.03793

So the density is:

( (1atom x MassCa + 1atom x MassTi + 3atom x MassO) / (a³ x 0.6023x10^24) )  * (10^7 nm/cm)³
( (1 x 40.08 + 1 x 47.90 + 3 x 16) / (.336³ x 0.6023x10^24) ) * 10^21
= 5.92 g/cm³

Which is wrong. According to the book the density is 3.75 g/cm³

What silly mistake am I making?? :) - thx
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Asked:
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Commented:
where did you get the ionic radii numbers?
Author Commented:
There is a table of ionic radii in the back of our book and lists those values,

Ca2+ = 0.106 nm
O2- = 0.132 nm
Commented:
You should not use the diagonal for the calculation.

Try to find for the unit element the three dimensions. Note : they are not necessarily equal. Calculate the volume as the product of the three dimensions.

Take care of the form (if the cristal is oblique, use appropriate formulas).

Hope this helps
Commented:
The ionic radii you from the table will be the average radii. It will vary from crystal structure to crystal structure.
Author Commented:
As it turns out, the touching direction is directly accross the center of the unit cell.

Which gives the correct value needed.
Commented:
PAQed with points refunded (500)

CetusMOD
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