Energy Gap at the First Brillouin Zone

Note that there is a gap between the two allowable frequencies (Equation 16.22) the diatomic chain can support. Also note that values of k + irfa produce the same result as k, hence we can fold the dispersion curve into a reduced zone plot. 

As m — M, the solution for the diatomic chain reduces to o/ = ( /fi)[l cos(fca)]. The minus sign solution is identical to the solution for the chain of like atoms however, the plus sign solution only exists for the case of the diatomic chain. 

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