The diffusion coefficient D for carbon C in alpha iron are k

The diffusion coefficient D for carbon (C) in alpha -iron are known at two different temperatures: At T=500 degree C, D_500=2.4 times 10^-12 m^2/s. and at 900 degree C D_900 =1.7 times 10^-10 m^2/s. Calculate the values of D_0 and Q_d for this pair of materials (C and alpha -iron) Find the magnitude of the activation energy for diffusion Q_d at 700 degree C

Solution

Given,

diffusion coefficient at a temperature of 500⁰ C ( 773 K ) = D₅₀₀ = 2.4 *10^-12 m² /s

diffusion coefficient at a temperature of 900⁰ C ( 1173 K ) =D₉₀₀ = 1.7 * 10^-10 m²/s

ln D = ln D_o - ( Q_d / RT )

ln D₅₀₀ = ln Do - ( Q_d / ( R * T₁ ) ) ( eq 1)

ln D₉₀₀ = ln Do - ( Q_d / ( R * T₂ ) ) (eq 2)

Solving them

Q_d = ( ln D₁ - ln D₂ ) / ( 1/T₁ - 1/T₂ )

Q_d = ( ln 2.4 *10^-12 - ln 1.7 * 10^-10 ) / (1/ 773 -1/1173 ) = 9577.32

substitute in eq 1

ln D₅₀₀ = ln Do - ( Q_d / ( R * T₁ ) )

-26.75 = ln D₀ - ( 9577.32 / (8.31 *773) )

D₀ =1.07 * 10^-11 m²/s

At temperature =700 ⁰ C = 973 K

ln D = ln D0 - (Q/ (R * 973 ) )

ln D = - 25.26 - ( 9577.32 / (8.31 *973) )

D₇₀₀ = 3.2 * 10^-12 m²/s