Question

The diffusion process of oxygen in titanium lattice is considered at
the temperature T1=300 K. The activation energy is 202 kJ/mole and the
exponential factor is 1.6 cm2/s. In what time the temperature should be risen to
increase the average penetration depth of oxygen in titanium in 4 times?

Answer 1

The Diffusion coefficient increases with temperature T and activation energy E_a as:-

D=D_oexp(-E_a/RT) ----------(1)

where D=diffusion coefficient

D_o=pre-exponential= 1.6 cm²/s= 1.6*10^-4 m²/s

E_a= activation energy= 202 KJ/mole= 202*10³ J/mole

R=Rydberg's constant= 8.314 J/mole

T=300K

Using these in equation (1),

D=1.6*10^-4*exp(-202*10³/8.314*300)=1.08*10^-39 m²/s

=(8Dt)^1/2 ----------(2)

where t=time

Here, =4(given)

Thus, substituting D in (2):-

Thus, t=1.85*10³⁹secs