4. Given is a two-atomic linear chain with lattice constant a - 4A and \"spring

Question

4. Given is a two-atomic linear chain with lattice constant a - 4A and "spring constant" 10 N/m. The masses of the linear chain elements are Mi-40 mu and M2-80 mu (mu is the atomic mass unit). The chain has a length L with N elementary cells, the temperature is T- 300 K. (a) Give an expression for the dispersion curves o(q) for the acoustic and optical branch of the linear chain. Make a graph with mathematica (or a different program) showing the frequencies (q) as a function of wavevector q inA-lea (b) Give an expression for the average phonon occupation number

Explanation / Answer

lattice constant

a = 4 X 10-8 cm

we have

d = a / ( h2 + k2 + l2 )

h k l = miller indices

d = interplanar distance

a = lattice constant

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