Link to HTML version of Power Point Slides for Lecture 3
Reading: Text: Chapter 4 and part of Chapter 10.
This lecture is a review of material from a basic course on solid state physics, with perhaps a different emphasis and way of proving the theorems.
- Crystal Periodicity
- Crystal Structure = Lattice + Basis
- Translation symmetry
- Reciprocal Lattice
- Brilluoin Zone
- Point symmetries - very short discussion
- Computer program for crystal structure
- Example of approach to programs in this class
- Modular structure of program in Fortran 90
- Input of information
- Calculation of basic structure-related quantities
- Ability to include in other programs as a module
- Bloch Theorem for excitations in crystals
- Proof by group theory
- Proof by Fourier Expansion
- Applies to any excitations - phonons, electrons, etc.
- Qualitative discussion of Bloch functions. Zone center, Zone boundary
- The first qualitative estimates of band widths in solids
- How to predict band widths in a crystal knowing only atomic wavefunctions
- Already this information shows why covalent materials tend to be wide-band materials, transition metals are likely to be magnetic, expected properties of rare earths, ...
- Conclusions