Transcript Applications of Normal Modes

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 1.66053886 × 10-27 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 infrared.
• This means they absorb thermal
radiation very well
• Especially certain molecules like CO2
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.