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 aproximate formula to calculate the atomic form factor for many elements.

 

[paranormal]

Hello,

Calculating the atomic form factor for crystals can be a complex task, as it involves understanding the structure and properties of the crystal lattice. However, I can provide some guidance to help you with your calculations.

Firstly, it is important to understand that the atomic form factor is a function of the scattering vector (K) and the atomic properties of the crystal. The formula you have provided is correct, where fj(K) represents the atomic form factor for a specific atom in the crystal.

To calculate the atomic form factor for a particular crystal, you will need to know the atomic positions and the atomic properties of each atom in the unit cell. This information can be found in crystal structure databases or in textbooks on crystallography.

Once you have this information, you can use the formula you have provided to calculate the atomic form factor for each atom in the unit cell. Then, you can sum up these individual atomic form factors to obtain the total atomic form factor for the crystal.

It is also important to note that the atomic form factor can vary depending on the type of x-ray scattering being used (e.g. elastic or inelastic scattering), the energy of the x-rays, and the orientation of the crystal. Therefore, it is important to consider these factors when calculating the atomic form factor.

I hope this helps you with your calculations. If you need further assistance, I would recommend consulting with a crystallography expert or your instructor for more guidance. Good luck with your homework!