I am working on an assignment here;(adsbygoogle = window.adsbygoogle || []).push({});

A linear chain with a two-atom primitive basis, both atoms of the same mass but different nearest neighbor separation and thus different force constants.

I have made a rigorous calculation in order to find the dispersion relation ω(k), with extensive help from Kittel's book. But I wonder if there is a way to predict ω(k) qualitatively(?)

Anyway, I plugged in some values for the constants in my formula for ω(k) and drew the graps in mathematica. I (obviously) get different curves when I choose the plus sign and the minus sign in the quadratic formula. How should I interpret that? Are those the acoustical and optical branches?

I am asked to say something about the relative motion of the atoms at the brillouin zone boundary, within a cell AND from cell to cell, and relate that to the group velocity. Again, what can be qualitatively deducted here?

I know that the group velocity is the derivative of ω(k) so if my curves have a horizontal tangent at k =[itex]\pm[/itex] [itex]\pi[/itex]/a the group velocity is zero there. I have read the wikipedia entry on group velocity but I can't figure out how that applies to the relative motion of the atoms. Are the cells seen as wave packages here?

Please help :shy:

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# Group velocity at Brillouin zone boundary

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