Understanding Bragg's Law: The Relationship Between Wavelength & Atomic Order

[MintyPanda]

Hello,

My teacher was talking about Bragg's law and mentioned how there was a relationship between the wavelength of light and a solid's order of separations.

I'm still confused about this, actually. Can someone please help me clear up what he said? What is the order of separations in a solid, and how does this relate to a particle's wavelength?

I do know that de Broglie's equation relates a particle's wavelength, a solid's atomic lattice spacing, the order, and the resulting diffraction angle. I'm just having trouble putting this all together.

I emailed them but I wanted to see if this community could generate a better response for me to digest.

Much thanks,
Steve

 

[jtbell]

a solid's order of separations

Usually, when we say "order" in connection with Bragg diffraction, we mean the number 'n' in the equation nλ = 2d sin θ. Is that what you are referring to here? However, I've never seen it called the "solid's order of separations", so I'm wondering whether you're referring to something else, or you simply mis-heard something, or it's a garbled translation from some other language into English (we get a lot of that around here).

 

[MintyPanda]

Usually, when we say "order" in connection with Bragg diffraction, we mean the number 'n' in the equation nλ = 2d sin θ. Is that what you are referring to here?

Thanks for the quick reply. Yes, I believe that is what he was referring to in this case, considering we just talked about said equation last class! He gave us work sheets that said "... on the order of the separations between the atoms in a solid". Hope this cleared up any confusion I may have posted earlier!

 

[jtbell]

That n has nothing to do with the solid itself (or rather its crystal structure). That's why your instructor's phrase confused me. It is a property of the interference (diffraction) process itself that you get diffracted beams at multiple angles (for the same crystal), corresponding to different values of n.

 

[MintyPanda]

Ah, so maybe he was referring to the spacing between lattices represented by "d" in this equation?

Which means there can be a relationship between a particle's wavelength and the spacing, correct?

Please take my sincere apologies, as this is all new material to me...I would just like to make sure I understand this concept!

 

[jtbell]

Which means there can be a relationship between a particle's wavelength and the spacing, correct?

If you know the atomic-plane spacing in the crystal, d, and you measure the diffraction angle θ, then you can calculate some possible values for the wavelength λ, for various values of n. Is that what you're trying to get at?

 

[MintyPanda]

Yep! I guess ultimately, if you can explain this conceptually, why is there a relationship between a particle's wavelength and the atomic-place spacing in the crystal? Is this where electron diffraction comes into play?

 

[jtbell]

The mathematics of electron diffraction is the same as with classical electromagnetic waves. The theory of Bragg diffraction originated in the study of X rays, in fact, treating them as electromagnetic radiation without reference to photons, I think. In general, with diffraction, the characteristics of the diffraction depend on the ratio between the wavelength and the size of the slits or spacing of crystal planes or whatever. See the treatment of diffraction in any decent optics book.

 

[MintyPanda]

Fantastic! Thank you jtbell for your help and for pointing me in the right direction for further research. As a student I definitely appreciate it!Minty