Question

solid state physics

1. Consider a 1-dimensional chain of atoms with mass m. The force constant between atoms are alternately C and 10C. The distances between the nearest neighbors are a/2. Let u, and v, be the displacements of the s-th pair of atoms as shown in the figure below. lu lu Us lu s-1 s-1 s+1 s+1 10C 100 10C (a) Write down the equations of motion for u, and v,. [5] (b) Look for solutions in the form u, = ueikae-out, etc. and find a(K). Sketch the curve o(K) for the first Brillouin zone. [10] (c) Find the relative displacement of neighboring atoms when K-0. [5]

Answer 1

Us+ Us US-2 gth atouu the equaton tt Selulin Vestos U-Amtld ude, a lallue.pcwarutei Prom 2a h e.

2- 2. C) Relahne Displace ment at K20 means k=ax ka m. ym ri S-2 と--, a → ea St. I-

where χ=S,a 2 f rom Pavt