Packing fraction for multi-atom basis

[james477]

Hi,

I understand that the maximum packing fraction for a particular atomic structure can be calculated assuming the nearset neighbours are touching but my question is how can the maximum packing fraction be calculated for a basis containing two different types of atoms?

Thanks, James

 

[alxm]

Well, begin with a unit cell.
Does http://en.wikipedia.org/wiki/Atomic_packing_factor" example clarify matters?

 

[james477]

Well, begin with a unit cell.
Does http://en.wikipedia.org/wiki/Atomic_packing_factor" example clarify matters?

So say I have a unit cell containing 1 atom of type X and 1 of type Y - this means that i can find the total volume of atoms per unit cell and i know the volume of the cell. But how would i go about finding the radii of these atoms which results in the maximum packing fraction? This is where i get lost..

Thanks, James

 

[kanato]

There is no unique way to do it. You could simply choose R_x = R_y = R_NN/2 where R_NN is the nearest neighbor distance. Or you could work out the packing fraction analytically, and then maximize it with respect to R_x and R_y subject to the constraint that R_x + R_y = R_NN.

 

[james477]

There is no unique way to do it. You could simply choose R_x = R_y = R_NN/2 where R_NN is the nearest neighbor distance. Or you could work out the packing fraction analytically, and then maximize it with respect to R_x and R_y subject to the constraint that R_x + R_y = R_NN.

Thanks, That makes sense - not quite sure how i would go about it but i'll give it some more thought.