# Homework Help: Crystal physics problem

1. Nov 5, 2005

### Reshma

The problem here is to find the maximum radius of the interstitial sphere that could just fit into the void space of cubic crystalline structures of:
the simple cube
body centered cubic
face centered cubic

My question is how is position of the void space determined in these structures?

2. Nov 5, 2005

### inha

Use the hard sphere model ie. there are spheres of radius r at the lattice points and their radius and the lattice constant are connected via a relation for each of the unit cells.

3. Nov 5, 2005

### Reshma

I'm aware of relationship between the lattice constant and the atomic radius.
Let 'a' be the lattice constant and 'r' be the atomic radius 'r'.
For simple cubic structure: $$r = \frac{a}{2}$$

For body centered:$$r = a\frac{\sqrt{3}}{4}$$

For face centered: $$r = a\frac{\sqrt{2}}{4}$$

But how is the position of the void determined exactly(using geometry)?

Last edited: Nov 5, 2005
4. Nov 5, 2005

### inha

Pick a lattice plane and draw the spheres for visual aid. It shouldn't be difficult to see where you can fit an interstitial atom. Then draw another sphere of unknown radius r' and solve for it in the same manner the a-r relations are normally solved.

5. Nov 8, 2005

### PrinceOfDarkness

In simple cubic's case, it is quite simple.

For BCC: Consider the body diagonal. It's length is aXsqrt3 (Pythagorus Theorem!).

For FCC: Consider the face diagonal. It's length is aXsqrt2 (Pythagorus again!).

6. Nov 9, 2005

### armandowww

And now: what about diamond bonding angle?

7. Nov 9, 2005