X-ray Powder Diffraction: Determine Structure of Crystal

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X-ray powder diffraction is an effective method for determining crystal structures, specifically face-centered cubic (fcc), body-centered cubic (bcc), or diamond structures. By plotting the square root of sine of the diffraction angles against the square root of the sum of the squares of the Miller indices, a straight line can indicate the crystal structure. To perform this analysis, a series of Miller indices for each structure is needed. The discussion emphasizes the importance of understanding the structure factor in this context. Resources for obtaining the necessary Miller indices series were requested for further assistance.
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Hello! X-ray powder diffraction can be used to determine the structure of crystal. I am given the diffraction angles (theta) for a sample and I am supposed to see if it has fcc, bcc or diamond structure. I read that if one plots sqr(sin(theta)) against ( sqr(h) +sqr(k) +sqr(l) ) where h, k, l are Miller indices one gets a straight line. So what I should do is plot for the series of Miller indices for fcc, bcc and diamond and see which gives a straight line. But I have no idea where to get the miller indices series from. Could you please help me? Thank you!
 
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bosti said:
Hello! X-ray powder diffraction can be used to determine the structure of crystal. I am given the diffraction angles (theta) for a sample and I am supposed to see if it has fcc, bcc or diamond structure. I read that if one plots sqr(sin(theta)) against ( sqr(h) +sqr(k) +sqr(l) ) where h, k, l are Miller indices one gets a straight line.
Correct. Do you understand why this is true, or what equation it is derived from?

So what I should do is plot for the series of Miller indices for fcc, bcc and diamond and see which gives a straight line. But I have no idea where to get the miller indices series from. Could you please help me? Thank you!
You must have learned about structure factor. If you have forgotten, look it up.
 

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