How can (220) in bcc diffract?

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SUMMARY

The discussion centers on the diffraction pattern of body-centered cubic (bcc) structures, specifically addressing the (220) planes. It is established that the (220) reflection is a second-order diffraction of the (110) plane, meaning that the (220) plane does not contribute directly to the diffraction pattern. The confusion arises from various sources that incorrectly list (220) as a diffracting plane, while the correct understanding is that the (110) plane produces the second-order diffraction peaks.

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  • Basic concepts of constructive interference in wave physics
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Sveto
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Dear xrd experts,

I need help in explaining the diffraction pattern of bcc structure. Specifically, (220) is listed among the planes that give constructive interference since (h2 + k2 + l2) = 8; (h+k+l) = even number. But I am blind to see a single atom on a (220) planes in bcc structure: attached is a picture illustrating (220) planes. I am missing something here. In advance, greatly thankful for helping me.

Sveto
 

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Dear all,

I came across the same type of question concerned with 200 reflection of simple cubic structure at https://www.physicsforums.com/showthread.php?t=465354. Since 220 is a second order diffraction of (110) plane it means there is no need for a (220) plane; like a harmonic in waves. So, all is clear!

The confusion came from the sources that use language like:
"Diffracting planes in BCC crystals: 110,200,211,220,222" See "Materials science for engineering students" By Traugott E. Fischer, p. 544.. There are more textbooks like this one.

Thus, it is not 220 plane that is diffracting , but 110 plane that gives a 2-nd order (and higher orders) diffraction peaks.
 

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