Assignment:
Consider the thermal conductivity K of a pure synthetic sapphire crystal that has a diameter of 3mm. (For sapphire delta D -1000 K , speed of sound - 10^4ms^-1, and for T <
a. Discuss which scattering mechanism dominates the thermal conductivity K of the sapphire crystal at 20 k.
b. Discuss which scattering mechanism dominates the thermal conductivity K of the sapphire crystal at 1000 K.
c. Given that K - 1/3 c, vl where Cv is the specific heat capacity per unit volume, v is the speed of sound and l is the mean free path, and that the thermal conductivity K reaches a sharp maximum at a temperature of 30 K, estimate the maximum value of K.
d. Sketch K versus T for the temperature range 2K to 100 K.