In: Physics
Consider a one-dimensional lattice with a basis of two non-equivalent atoms of masses M_1and M_2.
1. Find the dispersion relations (ω versus k).
2. Sketch the normal modes in the first Brillouin zone.
3. Show that the ratio of the displacements of the two atoms u/v for the k = 0 optical mode is given by:u/v=-M_2/M_1