Atomic Form Factor Homework: NaCl, LiF, GaP, Si

[Lemenks]

Homework Statement

I am trying to calculate the atomic form factor for various crystals (NaCl, LiF, GaP, Si) in an x-ray diffraction experiment.

There seems to be very little information on this topic anywhere.

Homework Equations

[/B]
I understand how to derive the geometric form factor Sk = sum of exp[i.pi.K.r]

And the atomic form factor is Sk = ∑exp[i.pi.K.r].fj

Where fj(K) = -1/e ∫dr exp[i.K.r].pj(r)

The Attempt at a Solution

For a BCC lattice Sk = 1+(-1)^n1+n2+n3 -monatomic
My guess is that I sub in Sk = f1(1) + f2(-1)^n1+n2+n3

I am not sure if this is correct and how I can generalize it, any help would be appreciated. Thanks.

 

[nasu]

The atomic form factor does not depend on the type of crystal. Is a characteristic of the atom. You can find it in literature or databases, for each atom, as a function of angle and wavelength.

It looks like you are trying to calculate the structure factor of various lattices and not the atomic form factor. Isn't that so?

 

[Lemenks]

Ohh, I actually made a mistake,

And the atomic form factor is Sk = ∑exp[i.pi.K.r].fj

Where fj(K) = -1/e ∫dr exp[i.K.r].pj(r)

fj(K) is the actual atomic form factor, I solved the geometric form factor for a BCC lattice but I am struggling to add in the atomic form factor. ~ I guessed that I simply multiply each geometric form factor answer for a BCC lattice by each atomic form factor but honestly I don't really know and I can't find any texts on it.

 

[nasu]

This may be useful
http://lamp.tu-graz.ac.at/~hadley/ss1/crystaldiffraction/atomicformfactors/formfactors.php

It gives an approximate formula to calculate the atomic form factor for many elements.