Normal Modes in a Diatomic Chain

Applying periodic boimdary conditions to the wave equations in Equation 16.13, we see that k = 27rjjL as in Equation 16.9. But now the first Brillouin zone extends from — n/Ta to a/la 

Source From Kittel, C., Introduction to Solid State Physics, 7th edn., John Wiley Sons, New York, 1966. 

Dispersion relaKons for NaCl in the reduced zone scheme for the various modes of oscillation longitudinal optical (LO), transverse optical (TO), longitudinal acoustic, and transverse acoustic. The curves were computed from Equation 16.19 using the elastic coefficients for NaCl given in Table 16.1. It should be noted that the a in this figure is the distance between the individual ions. Usually this dispersion relation is shown plotted between —-ir/fl and -ir/fl where a is taken as the distance between ion pairs. 

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