Question

After a 34-hour heat treatment at 1080°C (and subsequent cooling to room temperature), the concentration of A is 3.4 wt% at the 13.6-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, this time at 890°C for 34 hours, at what position will the composition be 3.4 wt% A? The preexponential and activation energy values for the diffusion of A in B are 3.4 × 10-5 m2/s and 156 kJ/mol, respectively.

Answer 1

After a 34-hour heat treatment at 1080°C (and subsequent cooling to room temperature), the concentration of A is 3.4 wt% at the 13.6-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, this time at 890°C for 34 hours, at what position will the composition be 3.4 wt% A? The pre-exponential and activation energy values for the diffusion of A in B are 3.4 × 10-5 m2/s and 156 kJ/mol, respectively.

1080+273=1353 K

890+273= 1163 K

13.6 mm

3.4 %

N_A= D(ΔC)/z= N_A= 3.4x10^-5 m²/s (3.4kg_A-0)/13.6x10^-3m

D_A= 3.4x10^-5m²/s x e^{-(156000J/mol) /(8.314 J/mol K * 1353K)}

D_A=3.4x10^-5m²/s x 9.48x10^-7= 3.226 x10^-11 m²/s

D_A= 3.4x10^-5m²/s x e^{-(156000J/mol) /(8.314 J/mol K * 1163K)}

D_A=3.4x10^-5m²/s x 9.84x10^-8= 3.347 x10^-12 m²/s

N_A=3.226 x10^-11 m²/s x (3,4-0)kg_A / 13.6 x 10^-3 m

N_A= 3.047x10^-8 kg/ms

z_A=3.347 x10^-12 m²/s x (3,4-0)kg_A / 3.047x10^-8 kg/ms

z_A=3.74 x10^-4 m