# Homework Help: Discuss how the resultant phonon should be designated in the First Brillouin Zone

1. Feb 15, 2012

### blueyellow

1. The problem statement, all variables and given/known data

In a simple cubic lattice of spacing 0.2nm a phonon travelling in the {1 0 0} direction with wavelength 0.42nm collides with another phonon of the same wavelength which is travelling in the {1 1 0} direction. Draw a reciprocal space diagram to show the magnitude and direction of the resultant phonon and discuss how the resulting phonon should be designated in the First Brillouin Zone.

Explain how such processes can be responsible for the finding that certain crystals have a maximum in their thermal conductivity as a function of temperature?

3. The attempt at a solution

So I just draw the first phonon going along the positive h-direction, and the second phonon is at an angle of 45 degrees to that? So the resultant phonon is at an angle of 22.5 degrees to the horizontal? But how do I work out what the wavelength of the resultant phonon is? Is there going to be constructive or destructive inteference? Do I just add the wavelengths of the two phonons?

What does it mean by 'discuss how the resulting phonon should be designated in the First Brillouin Zone'? Please help, since my notes and textbooks tell me hardly anything.