Phys 460 Lecture 11

1. From previous lectures:
   • Typical Crystal Structures
   • Diffraction, Fourier Analysis, and the Reciprocal Lattice
   • Crystal binding, elastic waves
   • Vibration waves in crystals: dispersion curves, quantization
2. Last Lecture: Thermal properties, first part
   • Planck disptribution, Bose-Einstein Statistics
   • Density of states, Internal energy, Heat capacity
   • Normal mode enumeration -- # k points = number of cells
   • Debye Model - T³ law at low T
   • Einstein Model
3. Anharmonicity - treated cursorily
   • Anharmonicity is responsible for:
     • Scattering of phonons
     • Thermal expansion
   • Gruneisen Constant
4. Thermal conductivity
   • Basic law: j = - K dT/dx, where K = thermal conductivity. This describes flow of energy (power per unit area) in the direction of minus the thermal gradient
   • For particles (gas of ordinary molecules or phonons), K = (1/3) C v L, where C = heat capacity, v = mean velocity, L = mean free path
   • Essential point: particles scatter to come to local thermal eqilibrium
   • Heat flow in a solid involves transport of energy by phonons
   • Phonons scatter and come to local thermal equilibrium in each local region (scattering due to anharmonicity and to defects)
     • Formulas in lecture for low temperature( K~T³) and high temperature ( K~T^-1)
     • Maximum at intermediate temperature
     • Special role of Umklapp scattering (G unequal 0)
5. Additional topics (extra material not required)
   • Recent results with isotopically pure crystals
   • Nanostructures - atomic wires, nanotubes, etc.

Summary of Part I of course