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

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SUMMARY

The discussion focuses on calculating the atomic form factor for crystals such as NaCl, LiF, GaP, and Si in x-ray diffraction experiments. The atomic form factor is defined as Sk = ∑exp[iπKr]fj, where fj(K) is derived from the integral fj(K) = -1/e ∫dr exp[iKr]pj(r). Participants clarify that the atomic form factor is a characteristic of the atom and does not depend on the crystal type. A resource for approximating atomic form factors is provided, which can assist in calculations for various elements.

PREREQUISITES
  • Understanding of x-ray diffraction principles
  • Familiarity with geometric and atomic form factors
  • Knowledge of BCC lattice structures
  • Basic calculus for evaluating integrals
NEXT STEPS
  • Research the derivation of the atomic form factor for specific elements
  • Explore the use of the provided resource for calculating atomic form factors
  • Learn about the structure factor in crystallography
  • Investigate the impact of wavelength and angle on atomic form factors
USEFUL FOR

Students and researchers in materials science, crystallography, and solid-state physics who are involved in x-ray diffraction experiments and need to calculate atomic form factors for various crystals.

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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.
 
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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?
 
Ohh, I actually made a mistake,

Lemenks said:
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.
 

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