Explore BrainMass

Scattering Mechanism in Metals

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

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 <<delta D, cv - 10^-1 T^8 J M K^-1, delta D is the Debye temperature and T is the temperature).

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.

See attachment for better formula representation.

© BrainMass Inc. brainmass.com October 24, 2018, 7:50 pm ad1c9bdddf


Solution Preview

For a metal the collision or scattering mechanisms affects the thermal conductivities. these collissions can be classified as 1. Collision of a phonon with other phonons. 2. Collision of a phonon with imperfections of a crystal. 3. Collision of the phonon with external boundaries of the ...

Solution Summary

This solution looks at the scattering mechanism in metals and uses concepts of thermal conductivity, specific heat capacity and thermal range

See Also This Related BrainMass Solution

Rate Limiting Steps in Metal Oxide Epitaxy

On the bottom right-hand side of the third page of the pdf attached (page 2 of the article), the author states:

"Metal deposition rates are easily converted into the oxide growth rate under the assumption that the metal arrival rates are the rate limiting steps, which is true for growth under oxygen- rich conditions."

I am having trouble understanding this, so please answer the following questions to clarify it for me.

(a) What is meant by metal arrival rates being "rate limiting steps?" (Does this refer to oxidation?)

(b) Why is this true? (Why are metal arrival rates rate limiting steps?)

(c) What exactly is meant by an "oxygen-rich environment?" I haven't seen a technical definition of an "oxygen-rich environment" anywhere in the literature.

View Full Posting Details