Chapter 4 Phonon I.Crystal Vibrations 1.Teaching Aim In this chapter students study the dynamics of atoms in crystals and derive vibration modes of atoms in simple cases students are required to understand the physical origin of the adiabatic ion,be able toex act the Hook constant from the crystals.Students should also establish the connection between the degree of freedom and the mode number and understand the reason why only the modes are distributed in the first Brillouin zone. 2.Difficult Points Switch between real space and k-space when discussing atomic dynamics in crystals. Distinguish the group velocity from the phase velocity. 3.Teaching Contents Section 1.Vibrations of Crystals with Monatomic Basis (1)First Brillouin Zone Key points:Establish the dynamic equation of atoms connected via spring to neighbors in the one-dimensional monatomic crystal chain,and derive the vibration modes in the first Brillouin zone. (2)Group Velocity Key points:Figure out the dispersion relation of vibration modes and derive the group velocity of each mode. (3)Long Wavelength Limit Key points:In the long wavelength limit estimate the sound velocity and compare it with the result of elastic wave. Section 2.Two Atoms per Primitive Basis Key points:Derive the phonon dispersion for one-dimensional diatomic chain Section 3.Quantization of Elastic Waves Key points:Phonon is quasi-particle due to the quantization of vibration wave. Section 4.Phonon Momentum Key points:Understand the phonon momentum and know how to use it 4.Teaching method PPTlectures,Handwritten derivation in class,discussion in class,tutorial after class.Chapter 4 Phonon I. Crystal Vibrations 1. Teaching Aim In this chapter students study the dynamics of atoms in crystals and derive vibration modes of atoms in simple cases. Students are required to understand the physical origin of the adiabatic approximation and the harmonic approximation, be able to extract the Hook constant from the interatomic coupling, and be familiar with the derivation of vibration modes in one-dimensional crystals. Students should also establish the connection between the degree of freedom and the mode number and understand the reason why only the modes are distributed in the first Brillouin zone. 2. Difficult Points Switch between real space and k-space when discussing atomic dynamics in crystals. Distinguish the group velocity from the phase velocity. 3. Teaching Contents Section 1. Vibrations of Crystals with Monatomic Basis (1) First Brillouin Zone Key points: Establish the dynamic equation of atoms connected via spring to neighbors in the one-dimensional monatomic crystal chain, and derive the vibration modes in the first Brillouin zone. (2) Group Velocity Key points: Figure out the dispersion relation of vibration modes and derive the group velocity of each mode. (3) Long Wavelength Limit Key points: In the long wavelength limit estimate the sound velocity and compare it with the result of elastic wave. Section 2. Two Atoms per Primitive Basis Key points: Derive the phonon dispersion for one-dimensional diatomic chain. Section 3. Quantization of Elastic Waves Key points: Phonon is quasi-particle due to the quantization of vibration wave. Section 4. Phonon Momentum Key points: Understand the phonon momentum and know how to use it. 4. Teaching method PPT lectures, Handwritten derivation in class, discussion in class, tutorial after class, self-directed learning