An impurity diffusing through a solid metal has an activatio

An impurity diffusing through a solid metal has an activation energy for diffusion of 12 kJ/mole, Do for this impurity in the solid metal is 0.11 mm2/sec. Calculate the following:
a. Diffusion coefficient for the impurity at 25, 100 and 300°C.
b. Characteristic time for the molecule to diffuse distances of 1, 10 and 100 micrometers. Calculate the time at all three temperatures.

Solution

Answer:

An impurity diffusing through a solid metal has an activation energy for diffusion of 12 kJ/mole, D_o for this impurity in the solid metal is 0.11 mm²/sec.

Diffusion coefficient (D) is the measure of mobility of diffusing species.

D = D₀ exp (- Q_d / RT ) ,

where , D₀ – temperature-independent pre exponential (m²/s)

Qd – the activation energy for diffusion (J/mol or eV/atom)

R – the gas constant (8.31 J/mol-K or 8.62×10-5 eV/atom-K)

T – absolute temperature (K)

a. Diffusion coefficient for the impurity at 25, 100 and 300°C.

D = D₀ exp (- Q_d / RT )

D₀ = 0.11 mm²/sec = 0.11 X 10^-6 m² /sec, R = 8.31 J/mol-K, Q_{d =} 12 kJ/mole

For T = 25⁰ C or (273+25) K or 298K

D = D₀ exp (- Q_d / RT ) = 0.11 X 10^-6 exp ( -12 / 8.31 X 298 )

So also for other temperature points diffusion coefficient can be calculated.