Kittel Chapter 7: Explaining Energy Gaps with First Brillioun Zone

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[SOLVED] kittel chapter 7

Homework Statement


This question relates to Kittel's solid-state physics book. I have edition 8.

I just do not understand how the first Brillioun zone relates to energy gaps. For example, in Figure 2, I do not understand the shape of the curve in Figure 2. I do understand what is going on in Figure 3, but it seems to me like that is a completely different way of explaining energy gaps.

In the caption below figure 2, what exactly does it that the "energy gap E_g is associated with the first Bragg reflection at ... " ? I thought Bragg reflection had to do with light getting diffracted when you send a beam of it into the crystal (e.g. x-ray diffraction). I have absolutely no idea why Bragg reflection is is being talked about here!

Homework Equations


The Attempt at a Solution

 
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Bragg reflection can be done with ANY wave. So anything that have a k-vector can be bragg reflected.

remember that the section about light diffraction in ch 2, nothing was said what the wave was composed of.

And this is why you are lead to impose the standing waves, and fig 3.. as a helped you with earlier this week.