The outer surface of an steel alloy is to be hardened by increasing its carbon c

Question

The outer surface of an steel alloy is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 868°C for 10 min increases the carbon concentration to 0.75 wt% at a position 1.4 mm below the surface. Estimate the diffusion time required at 660°C to achieve this same concentration also at a 1.4 mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. The preexponential and activation energy values for the diffusion of carbon in the iron are 6.1 × 10-7 m2/s and 71.4 kJ/mol, respectively.

Explanation / Answer

Diffusion coefficient D(868) at 868 oC = Do e^(-Qd/RT)

with,

Qd = 71.4 kJ/mol

Do = 6.1 x 10^-7 m^2/s

R = gas constant

T(868) = 868 + 273 = 1141 K

T(660) = 660 + 273 = 933 K

we get,

D(868) = 6.1 x 10^-7 x e^(-71400/8.314 x 1141) = 3.3 x 10^-10 m^2/s

D(660) = 6.1 x 10^-7 x e^(-71400/8.314 x 933) = 6.1 x 10^-11 m^2/s

Using,

D(860) x t(860) = D(660) x t(660)

with,

t(860) = 10 min

So, diffurion time t(660) = 3.3 x 10^-10 x 10/6.1 x 10^-11 = 54.10 min

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