Applications of Normal Modes Physics 213 Lecture 20

What are normal modes? ``Characteristic’’ motions of the system All parts of the system move with same frequency As many normal modes as number of oscillators in the system. But are masses coupled by springs really that interesting?

All matter is made of atoms, and our first model for an atom is: M M = Atomic mass x × kg

But atoms group together to form molecules by forming ``Atomic Bonds’’ H H O What are ``Atomic Bonds’’?

An atomic bond means there is a stable equilbrium of the two atoms: Energy Position of atoms We know that around a stable equilibrium you can have oscillations.

Vibrational motions of molecules See Wikipedia The frequencies of the normal mode motions of molecules are in the infra- red. This means they absorb thermal radiation very well Especially certain molecules like CO 2

What else? If we put lots of molecules together we get a solid. Solids have a lattice structure:

Lattice vibrations: normal modes Solids can be metals, insulators, semiconductors, superconductors What decides which is which? The lattice structure will have normal modes of oscillation (like the beads on the string in this weeks assignment) These normal modes tell us EVERYTHING about the lattice vibrations

Lattice vibration - phonons Lattice vibrations interact with the electrons in the solid This interaction determines whether the material is a metal, insulator or semiconductor We call the normal modes ``phonons’’ - as if they were a new kind of particle If the electrons keep crashing into phonons - we expect bad conduction But it gets weirder……..

Superconductors Electron A and Electron B can ``talk’’ to each other by A exciting a phonon, and sending it off to B. This can make the electrons interact In some materials the electrons pair up, and the materials become superconducting.