Question

7. (8 points) Carburization is an industrial process to harden steel components through diffusion. It is done at elevated temperature because a. Steels have high yield strength b. Catoms can penetrate into the component's surface through vacancy diffusion c. Catoms can penetrate into the component's surface through interstitial diffusion d. Diffusivity is high at elevated temperature 8. (15 Points) The bonding energy Ex between two atoms is a function of interatomic distance r as follows: where A, B, and n are constants. Derive the modulus of elasticity E (at the equilibrium spacing ro). 9. (15 Points) Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the surface concentration is maintained at 0.1 wt% N, what will be the concentration 1 mm from the surface after 10 h? The diffusion coefficient for nitrogen in iron at 700°C is 2.5 x 10 m/s.

Please answer all the three questions.. Please please

Answer 1

7. Carburizing is done at elevated temperatures because, diffusivity is high at elevated temperatures. Hence, it will take lesser time for C atoms to diffuse into the metal.

D = Do * exp(-Q/RT)

In the equation above, Q is activation energy and D is diffusivity at a temperature T. Do is a constant. As we can see, diffusivity increase with temperature exponentially.

8 and 9:

w E= A + B slope - de - & (Ar' + B7") - Arz- nB genul At equilibrium slope = 0, saro o = Arz - nBronn 2 - Aro - -n-1 Bro. -n-1t2 her -1+2 NB i-nti so = (4 juti = (nejhi In an atomic setup, d²E I at raro drz /ro dZE E = (^r2-nB in-) drz - -2A3 + n(n+1) Brn-2

= -2A7 + n(n+1) B - 2 - ZA3 + n(n+1) Brone E = - 2A -- - + n(n+1) Bron-3 T=700'c = 700+ 273.15 = 973.15k = 0.1 x=1mm = 10 m talous = 10x3600 = 36000 s D = 2.5x101 mis By Ficks second law: l-en ) -0 Cs-Co Co = x = 0.1 (1-ext (2.638 x 10) = 0+ (1 -0.002413) 6x = 0.0997