# Need help using the atomic form factor

1. Nov 3, 2014

### Lemenks

1. The problem statement, all variables and given/known data

I need to calculate interference peaks using the atomic form factor for several lattice types for a lab report. I was given the expected answers but told I should also be able to calculate them.

Expected results for rocksalt (eg NaCl):

h+k+l = 2n
fh+k+l = 4(fa+fb)

h+k+l = 2n+1
fh+k+l = 4(fa-fb)

2. Relevant equations

Sk = ∑ fj(K)*e(iK.dj )

where fj(K) = atomic form factor = ∑p e(iK.rp )

dj = distance between to lattice points

rp = distance between to basis points

K = wavenumber

3. The attempt at a solution

For the geometrical form factor:

Sk= ∑e(iK.dh+k+l )

D(k-k)=2πm or ei(k-k)D=1

Sk= 1+ (-1)((n1+n2+n3))

This is the answer for a mono-atomic BCC lattice.

NaCl has atoms at basis points Na(0,0,0) and Cl 1/2(1,1,1).

Sk = ∑ ∑ e(iK.rp )*e(iK.dj )

2. Nov 8, 2014