5.Evaluation Via homework assignments,thinking questions in class.quizzes Chapter 5 Phonon II.Thermal Properties 1.Teaching Aim In this hapter students study the density of states and the thermal Students are required to derive the heat capacities of phonons in the Einstein and the Debye models.Comparing the results with those obtained in classical gases.students should understand the quantum effects on thermal properties and the result of zero point energy. 2.Difficult Points Understand the density of states and use itin the calculation of thermal properties.Obtain th total energy by integrating the energies of phonons and derive the limit at low and high temperatures. 3.Teaching Contents Section 1.Phonon Heat capacity (1)Bose-Einstein(Plank)Distribution Key points:Be familiar with the Bose-Einstein(Plank)Distribution for phonons. (2)Normal Mode Enumeration Key points:Transfer the summation over states into integration with the density of states (3)Density of States in One Dimension Key points:Density of states in energy space can be derived from the constant density of states in k-space.Theyare the group velocity which can be obtained from the dispersion. (4)Density of States in Three Dimension Key points:Similarly.density of states in three dimension is obtained from the constant density of states in k-space and dispersion. (5)Debye Model for Density of States Key points:Density of states in obtained by assuming linear dispersion or constant sound velocity. Key points:Heat capacity is proportionl to cubic power of temperature in the Debye model (7)Einstein Model of the Density of States 5. Evaluation Via homework assignments, thinking questions in class, quizzes. Chapter 5 Phonon II. Thermal Properties 1. Teaching Aim In this chapter students study the density of states and the thermal properties of phonons. Students are required to derive the heat capacities of phonons in the Einstein and the Debye models. Comparing the results with those obtained in classical gases, students should understand the quantum effects on thermal properties and the result of zero point energy. 2. Difficult Points Understand the density of states and use it in the calculation of thermal properties. Obtain the total energy by integrating the energies of phonons and derive the limit at low and high temperatures. 3. Teaching Contents Section 1. Phonon Heat capacity (1) Bose-Einstein (Plank) Distribution Key points: Be familiar with the Bose-Einstein (Plank) Distribution for phonons. (2) Normal Mode Enumeration Key points: Transfer the summation over states into integration with the density of states. (3) Density of States in One Dimension Key points: Density of states in energy space can be derived from the constant density of states in k-space. They are connected by the group velocity which can be obtained from the dispersion. (4) Density of States in Three Dimension Key points: Similarly, density of states in three dimension is obtained from the constant density of states in k-space and dispersion. (5) Debye Model for Density of States Key points: Density of states in obtained by assuming linear dispersion or constant sound velocity. (6) Debye T3 Law Key points: Heat capacity is proportional to cubic power of temperature in the Debye model. (7) Einstein Model of the Density of States