Q5: One dimensional chain like discrete Al sample with atomic mass (m) of 4.48x10-26 kg, length of L, density of atoms o

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Q5 One Dimensional Chain Like Discrete Al Sample With Atomic Mass M Of 4 48x10 26 Kg Length Of L Density Of Atoms O 1 (40.6 KiB) Viewed 13 times

Q5: One dimensional chain like discrete Al sample with atomic mass (m) of 4.48x10-26 kg, length of L, density of atoms of N and inter atomic distance of a is deformed elastically. a) Derive the dispersion relation between @ and k for longitudinal vibrations. b) If the vibration frequency is 25.8x10¹2Hz at the BZ boundaries, calculate the elastic constant, C. c) Show that the density of vibration modes is 2N g(@)= Here, @= √√4C/m_ is the maximum frequency of the vibrations. 'm π(0²-0²) ¹/2 m