cubic lattices and unit cells

[sarahsbs]

Hi, I am having trouble with a problem involving unit cells and crystal lattices. The problem looks like this:

Consider a collection of hard spherical atoms arranged at the lattice pts of a primitive cubic lattice. A unit cell is constructed so that 1/8 of the corner atoms lie within the unit cell. Compute the fraction of the volume of the unit cell that is empty if the atoms are in contact along the edge of the cell.

My solutins manual claims that this also means that the atoms are in contact along the diagonal of the cell. How can this be? I am having trouble picturing how the cells can be incontact along the edges and along the cubic diagonal. Am I maybe missing comething? Is it implied somewhere that this is a body centered cubic cell? Even so, then wouldnt that mean that the atoms werene tin contact along the edges?

The book further says that there are 2 atoms per unit cell.

Can anyone shed some light on this?

thansk so much
sarah

[RobJim]

I don't think that the atoms should be in contact along any diagonal either. And I believe that there should only be one atom per cell - 8 x 1/8.

My inorganic book agrees with me that there is only 1 atom per unit cell for a primitive cubic cell. For the record, such a unit cell is 52.4% full of atom and the rest is empty space.

I suspect your solutions manual is wrong. That happens sometimes.