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Lattice Vibration III, Only the first neighbour interaction is considered,…
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Two equations of motion, M and m, equation of motion :
Two different types of atoms move in opposite direction, thus further complicating the model
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As n does not appear in above equation indicates that our assumed solution is of the correct form and may be rewritten in the form:
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two values of ω for each value of k, thus two branches (corresponds to positive and negative signs of dispersion relation);
