**Physics-432**

**Homework Set (3)**

This homework set is due on Saturday (2^{nd} of Muharram) at 10.00
p.m. If you need help, please e-mail me or visit me in my office.

In __all__ homeworks, please solve fully and clearly, state
assumptions, circle final answers, and comment wisely (when applicable).

You are free to discuss with your colleagues, but makes sure your
solution is truly *yours*.

**Question #1:**

In class, we *qualitatively* discussed optical phonons due to
multi-atom basis lattices.

- Show in detail how optical phonons form with two-atom basis, assuming same force constant between atomic layers, different masses for atoms in neighboring layers, and repeat distance "a"; that is "a" is the distance between nearest identical planes.

- Show that this reduces to what we expect if the two atoms are taken to be identical.

- Show how the motion of the lattice points is different for optical phonons than for longitudinal phonons, in the limit K approaches zero, and how this justifies the naming (optical vs. acoustic).

**Question #2:**

In a few statements, describe how inelastic neutron scattering experiments can be used to experimentally measure phonon dispersion curves of crystals.

**Question
#3:**

In class, we assumed that the force constant between neighboring atomic planes is the same while atoms of neighboring planes are different.

Now consider the normal modes of a linear chain in which the force constant between nearest-neighbor planes are alternatively C and 10 C while the masses of all atoms in any plane are the same! Take the repeat distance to be "a". Find the phonon frequencies at K = 0 and also at K = p/a.

**Question #4:**

e-mail me (zhyamani@kfupm.edu.sa) two web-site URLs that animate longitudinal and transverse, acoustic and optical phonons.