Posted by K on April 17, 2014, 1:38 pm
I was working through the problem of the diatomic chain (10.1 in the book), which we skipped in tutes first time round for some reason... All fine, til it says "describe the motion of the masses in each case". At k = 0, it's easy enough to solve the matrix equation (if I'm doing it right!). I get that the masses move with equal amplitude and in phase in the acoustic mode as k>0 (though there's no motion at k=0 because the frequency is 0), and in the optical mode they move in antiphase at k=0 with amplitudes in the ratio of the masses.(Is that right?) But for the zone boundaries, solving the equation just seems to give me a matrix full of zeros, from which I can't work out how to deduce the motion. I downloaded the program that shows the normal modes, and it looked like at the zone boundary, in the optical mode, the lighter mass would move while the heavier one was stationary, and vice versa in the acoustic mode. But I don't know if this is right, or how to show it from the equations... 
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