3. A block of pure iron needs to be converted to steel. The density of iron is 7

Question

3. A block of pure iron needs to be converted to steel. The density of iron is 7.86x10A3kg/m 3, and the atomic weight is 0.0558kg/mol. The concentration of carbon at position A is 4x10 26 at/m43. The carbon atomic weight is 0.012kg/mol. Carbon must be diffused into the iron to convert it to steel. It is desired to have 1025 atoms of carbon per m3 at point B. Position A is 1mm from position B. Assume that you have 1m^3 of iron. You heat the material uniformly to 1200oC. D0, carbon = 79x10-6 m2/sec, Ea = 83kJ/mol, and the density of carbon is 2260kg/m^3. (10pts) 1mm Fe block i. What is Dcarbon at 1200°C in m2/sec? li. Calculate the FLUX (J) of carbon atoms in atoms per m2-sec at 1

Explanation / Answer

(1)

At 1200oC

ln(D) = ln(Do) - Ea/RT

where

Do = 79*10-6 m2/sec

Ea = 83000 j/mol

T = 1200oC = 1473 K

ln(D) = ln( 79*10-6 ) - 8300/8.31*1473

Dcarbon = e-16.226

at 1200oC , Dcarbon = 8.97*10-8 m2/s

(2)

Concentration at A = 4*1026 at/m3

B = 1025 at/m3

xB - xA = 1 mm = 0.001 m

J = -D = CB -CA / xB -xA

J = -8.97*10-8 * (1025 - 4*1026) / 0.001

J = 3.49*1022 atoms/m2-sec

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