Volume of Brillouin zone show that the volume of the first Brillouin zone is (2π)3/Vc, where Vc is the volume of a crystal primitive cell. Recall the vector identity (e x a) x (a x b) = (e ∙ a x b)a.
Answer to relevant QuestionsWidth of diffraction maximum we suppose that in a linear crystal there are identical point scattering centers at every lattice point pm = ma, where m is an integer. By analogy with (20), the total scattered radiation ...Cohesive energy of bcc and fcc neon. Using the Lenard-Jones potential, calculate the ratio of the cohesive energies of neon in the bcc and fcc structures (Ans, 0.958). The lattice sums for the bcc structures are Longitudinal wave velocity, show that the velocity of a longitudinal wave in the  direction of a cubic crystal is given by vs = [1/3(C11 + 2C12 + 4C44)/p]1/2. Basis of two unlike atoms for the problem treated by (18) to (26), find the amplitude ratios u/v for the two branches at K max = π/a. Show that at this value of K the two lattices act as if decoupled: one lattice ...Gruneisen constant (a) Show that the free energy of a phonon mode of frequency w is kBT in [2sinh (hw/2kBT)]. It is necessary to retain the zero-point energy ½hw to obtain this result. (b) If Δ is the fractional ...
Post your question