Need help using the atomic form factor

[Lemenks]

Homework Statement

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
f_h+k+l = 4(f_a+f_b)

h+k+l = 2n+1
f_h+k+l = 4(f_a-f_b)

Homework Equations

S_k = ∑ f_j(K)*e^{(iK.d_j )}

where f_j(K) = atomic form factor = ∑p e^{(iK.r_p )}

d_j = distance between to lattice points

r_p = distance between to basis points

K = wavenumber

The Attempt at a Solution

For the geometrical form factor:

S_k= ∑e^{(iK.d_h+k+l )}

D(k-k`)=2πm or e<sup>i(k-k`)</sup>D=1

S_k= 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).

S_k = ∑ ∑ e^{(iK.r_p )}*e^{(iK.d_j )}

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?