- #1
Niles
- 1,866
- 0
Hi all.
I have two questions, which I hope you can help me with:
1) In my book (Solid State Physics by Ashcroft and Mermin) it says on page 436 that:
"When the wavevector k is equal to pi/a (where a is the lattice constant), then the motion in neighboring cells are 180 degrees out of phase. "
This is when the basis consists of two ions. I cannot see what the argument is for this statement?2) At the boundary of the Brilliouin zone (i.e. k = pi/a), the group velocity is zero and the vibrational wave creates a standing wave. Here the wavelength is 2a, and with a Bragg angle of pi/2, the Bragg condition is satisfied:
[tex]
\theta = \frac{\pi}{2}, \,\,\,\, d = a, \,\,\,\, k = 2\pi/\lambda, \,\,\,\, n=1, \,\,\,\, \lambda = 2a \,\,\,\,\,\, \text{from}\,\,\,\,\,\, 2d\sin \theta = n\lambda
[/tex]
But what does this mean? That there are standing waves being reflected between the ends of the Brillouin zone? If yes, then what is does this physically mean?
I have two questions, which I hope you can help me with:
1) In my book (Solid State Physics by Ashcroft and Mermin) it says on page 436 that:
"When the wavevector k is equal to pi/a (where a is the lattice constant), then the motion in neighboring cells are 180 degrees out of phase. "
This is when the basis consists of two ions. I cannot see what the argument is for this statement?2) At the boundary of the Brilliouin zone (i.e. k = pi/a), the group velocity is zero and the vibrational wave creates a standing wave. Here the wavelength is 2a, and with a Bragg angle of pi/2, the Bragg condition is satisfied:
[tex]
\theta = \frac{\pi}{2}, \,\,\,\, d = a, \,\,\,\, k = 2\pi/\lambda, \,\,\,\, n=1, \,\,\,\, \lambda = 2a \,\,\,\,\,\, \text{from}\,\,\,\,\,\, 2d\sin \theta = n\lambda
[/tex]
But what does this mean? That there are standing waves being reflected between the ends of the Brillouin zone? If yes, then what is does this physically mean?