Introduction to lattice dynamics and thermal properties of solids (60' lecture)
Ronald Cohen
Topics
- Why you need estimates of thermal corrections
- Thermodynamics of collection of oscillators
- Mathematical description of crystals (review)
- Atomic displacement waves (phonons)
- Dynamical matrix
- Secular equation (equations of motion)
- Densities of states
- Kieffer models
- Examples
- Ionic systems?non-analyticity
- Born effective charges
- Linear response
- Density functional perturbation theory
- Process for DFPT computations, short-range force constants
Prerequisite reading
- Ashcroft and Mermin, Chapters 21-23
Recommended reading
- Ashcroft and Mermin, Chapters 24-27
- Martin, Electronic Structure, Chapter 19
- Xavier Gonze, Adiabatic density-functional perturbation theory, Phys. Rev. A 52, 1096 (1995)
- Xavier Gonze, Perturbation expansion of variational principles at arbitrary order, Phys. Rev. A 52, 1086 (1995)
- Xavier Gonze and Changyol Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997)
- Baroni, S., et al., Phonons and related crystal properties from density-functional perturbation theory, Reviews of Modern Physics, 2001. 73(2): p. 515-48.
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