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