Lecture 3: Reciprocal Lattice

We review lattice planes, and talk about how to construct the corresponding Miller indices. We define the reciprocal lattice: Think of this as the Fourier wavevectors of the original lattice. It turns out that the reciprocal lattice of a Bravais lattice is itself a Bravais lattice. We define the first Brillouin zone. We calculate the dispersion (frequency vs. wavevector) for phonons in a 1D crystal in the harmonic approximation, and encounter our first instance of Goldstone's theorem: Since crystals break the continuous translational symmetry of free space, there is a corresponding Goldstone mode (the phonons, or vibrations of the crystal), which has the important property that the frequency goes continuously to zero.

Be sure and play with the Solid State Simulations package by Cornell, available at: http://www.ruph.cornell.edu/sss/sss.html

Demos: Today, we used the "Bravais" SSS program in class.
Visual Aid: The squishy crystal model -- actual balls and springs.

Audio