part C only A2-hour carburizing (i.e. adding carbon) heat treatment of a steel s

Question

part C only

A2-hour carburizing (i.e. adding carbon) heat treatment of a steel sample at 250 degree C will raise the carbon concentration to 0.40 wt% (weight %) at a depth of 4.0 mm from the surface. How much time is required to achieve the same concentration at a depth of 16.0 mm for a carburizing heat treatment at 250 degree C? In aluminum, assume the activation energy for vacancy formation is 0.80eV/atom. Estimate the fraction of atomic sites that are vacant at 300 degree C. Estimate the volume of a unit cell of chromium.

Explanation / Answer

Cr favours BCC metal structure in crystal formation

=> BCC has 2 atoms ( 1 resides completely in unit cell while another is 1/8*8 =1 from corners)

=> In BCC, principal body diagonal is given as:R= sqrt(3)*a => a =R/sqrt(3)

and radius of atom r & principal body diagonal R are related as: r+2*r+r =R => R=4*r

radius of Cr is 140 pm or 1.4 A

=>r= 1.4*10^-10m => R= 4*1.4*10^-10 = 5.6*10^-10m

=> a =R/sqrt(3) = 5.6*10^-10/sqrt(3) =3.233*10^-10m

=> Volume of unit cell V= a^3 =(3.233*10^-10)^3 =3.379*10^-29 m^3

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