2.2 声子热容简明固体物理.pdf

Chapter 2 Crystal Dynamics 2.1 Lattice Vibration 2.2 Phonon Heat Capacity 2.2.1 Dulong-Petit Law 2.2.2 Einstein Heat Capacity Model 2.2.3 Debye Heat Capacity Model Dulong-Petit Law Einstein Heat Capacity Model Debye Heat Capacity Model ·Heat capacity ·Dispersion relation / Phonon spectrum Heat capacity C  lim Q The energy in a solid includes: T 0 T  The energy given to lattice According to first law of thermodynamics vibrations dominant Q  U  pV contribution to the heat capacity in most solids. V  0  The energy given to electrons’ movement. UV U  C  lim  V   T 0 T  T V  Calculation of the lattice energy and heat capacity of a solid falls into two steps:  the evaluation of the contribution of lattice waves with the frequency of ω  the summation over all frequency distribution of lattice waves. Dulong-Petit Law Einstein Heat Capacity Model Debye Heat Capacity Model ·Heat capacity ·Dispersion relation / Phonon spectrum UV U  C  lim  V   T 0 T  T V 3P  m 1 m j  E E E (T )  g ω d  g ω d 0