(a) A 2D hexagonal lattice of lattice spacing a = 3 A has isotropic speed of sound v = 1 10³ m/s. Starting from the basic assumptions of the Debye model, show that the Debye frequency cop is 1.27 x 10¹3s-¹, and find the magnitude of the Debye wave vector Kp (hint: think about how you will accommodate the correct number of phonon modes).
(a) A 2D hexagonal lattice of lattice spacing a = 3 A has isotropic speed of sound v = 1 10³ m/s. Starting from the basic assumptions of the Debye model, show that the Debye frequency cop is 1.27 x 10¹3s-¹, and find the magnitude of the Debye wave vector Kp (hint: think about how you will accommodate the correct number of phonon modes).
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Transcribed Image Text:(a) A 2D hexagonal lattice of lattice spacing a = 3 Å has isotropic speed of sound v = 10³
m/s. Starting from the basic assumptions of the Debye model, show that the Debye
frequency OD is 1.27 x 10¹3s-¹, and find the magnitude of the Debye wave vector KD
(hint: think about how you will accommodate the correct number of phonon modes).
(b) Na (sodium) has a body-centered cubic structure with lattice constant a = 4.225 Å
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