Answer Happy

5 x 1013 (100) [110] [111] 4 LA LA LA TA2 3 TA 2 TA TA1 1 1.84 0 1.51 0.87 1.74 0 b 0.92 0.755 Fig. 1. Dispersion curves in Copper (Cu) Q.1. a) In Fig. 1(a-c) above, describe which properties are represented by the symbols o and k. b) What are the distinguishing features of the dispersion curve of a diatomic material such as KBr as opposed to Cu, which is mono-atomic? [Hint: Comment on the difference in behavior of the two types of dispersion curves near k=0 and k=r/a] c) What properties of a crystal are represented by the numbers in the square brackets such as [100], [110] and [111] in Fig.1(a-c)? d) Describe what mechanisms in Cu are represented by LA and TA in Fig. 1(a-c). e) Why do you have two TA curves in Fig. 1b while la and lc have just one each? f) From the dispersion curves in Fig. 1(a-c), calculate the velocities of the LA and TA sound waves in copper along the [100] direction. Show the coordinates on the figure (by drawing dotted lines) that you have used in your calculations.