# Solid State Physics, FCC or BCC and why?

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1. Sep 7, 2016

### Alvis

1. The problem statement, all variables and given/known data
Based on sizes for Na(.97 Angstroms), Cs(1.67 Angstroms), and Cl(1.81 Angstroms), which lattice type would you expect for NaCl and CsCl and why?

2. Relevant equations
My equation for the hole size for a bcc is (4/sqrt(3))(radius)-2(radius), I assume you put in the radius of Cl in since the positive ions are the ones that fill the holes?

For fcc I got 2(sqrt(2))(radius)-2(radius), again, (assuming this equation is correct) I think you input the Cl as radius.

3. The attempt at a solution
So I know NaCl is supposed to be fcc and CsCl is bcc. For NaCl, I got the hole size (using fcc formula) to be 1.49 Angstroms and that is bigger than .97 Ang for Na.

For CsCl, I got the hole size to be 5.6x10^-11 using bcc forumula. The ion Cs is much bigger than the hole size which is what we want I believe.

I'm not sure NaCl and CsCl are the structure they are? my prof said it was based off of the hole size and my equation for bcc one is correct but not sure about fcc.

2. Sep 12, 2016