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# Structure factor question (CMP) watch

1. Hello, I'm abit stuck with a question on structure factor, hope someone can help.

Basically I have to calculate the structure factor for NaCl,
The Atom coords are as followed

Na at
0, 0, 0
0.5, 0.5, 0
0.5, 0, 0.5 <= Which is a fcc
0, 0.5, 0.5

Cl
0.5, 0.5, 0.5
0, 0, 0.5
0, 0.5, 0
0.5, 0, 0.5

I have done it for the Na, where Fhkl = f(1 + e^iπ(h+k) + e^iπ(h+l) + e^iπ(k+l))

However i can seem to do it for Cl
I know what is should be as seen from slide 10 here
http://bama.ua.edu/~mweaver/courses/..._Class_18b.pdf

But I don't understand how to make the exponentials?
For example, why is it
Fhkl = f(e^iπ(h+k+l) + e^iπ(h) + e^iπ(k) + e^iπ(l) )

Hope someone can help cheers
2. (Original post by JackFarr)
Basically I have to calculate the structure factor for NaCl,
The Atom coords are as followed

Na at
0, 0, 0
0.5, 0.5, 0
0.5, 0, 0.5 <= Which is a fcc
0, 0.5, 0.5

Cl
0.5, 0.5, 0.5
0, 0, 0.5
0, 0.5, 0
0.5, 0, 0.5

I have done it for the Na, where Fhkl = f(1 + e^iπ(h+k) + e^iπ(h+l) + e^iπ(k+l))

However i can seem to do it for Cl
I know what is should be as seen from slide 10 here
http://bama.ua.edu/~mweaver/courses/..._Class_18b.pdf

But I don't understand how to make the exponentials?
For example, why is it
Fhkl = f(e^iπ(h+k+l) + e^iπ(h) + e^iπ(k) + e^iπ(l) )

If you are asking how to go from the second equation to the third equation shown in the picture. Below is the explanation.

Take for instance

h and k are integers, it does not matter whether they are both odd, even or one odd and the other even, 2h + 2k will be even. Then use the relation given in page 4 of the pdf file that you have posted.

Thus,

I believe you can handle the rest of the term.

However, if I misinterpret your question, let me know.

Cheers.
3. (Original post by Eimmanuel)

If you are asking how to go from the second equation to the third equation shown in the picture. Below is the explanation.

Take for instance

h and k are integers, it does not matter whether they are both odd, even or one odd and the other even, 2h + 2k will be even. Then use the relation given in page 4 of the pdf file that you have posted.

Thus,

I believe you can handle the rest of the term.

However, if I misinterpret your question, let me know.

Cheers.
Cheers, im still unsure on how to get the first equation?
4. (Original post by JackFarr)
Cheers, im still unsure on how to get the first equation?
You said you did it for Na in the first post. How did you do it for Na?

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