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 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
LVL 11
Who is Participating?
I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

where did you get the ionic radii numbers?
bingieAuthor 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
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
HTML5 and CSS3 Fundamentals

Build a website from the ground up by first learning the fundamentals of HTML5 and CSS3, the two popular programming languages used to present content online. HTML deals with fonts, colors, graphics, and hyperlinks, while CSS describes how HTML elements are to be displayed.

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

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

Community Support Moderator

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
It's more than this solution.Get answers and train to solve all your tech problems - anytime, anywhere.Try it for free Edge Out The Competitionfor your dream job with proven skills and certifications.Get started today Stand Outas the employee with proven skills.Start learning today for free Move Your Career Forwardwith certification training in the latest technologies.Start your trial today
Math / Science

From novice to tech pro — start learning today.