A. calculate the diffusion coefficient for magnesium in aluminum at 450°c.
what time will be required at 550°c550°c to produce the same diffusion result (in terms of concentration at a specific point) as for 15 h at 450°c?

a) D = 4.88 * 10^(-14) m^2 / s

b)   t = 1.1 hr

Solution:

a) Magnesium in Aluminum diffusion:

D = Do * exp(-Qd / RT)

  =  (1.2 * 10^(-4) m^2 / s) * exp ( - 130,000 / 8.31 * 723.15)

  = 4.88 * 10^(-14) m^2 / s

D = 4.88 * 10^(-14) m^2 / s

b) The composition remains same at say the distance Xo:

(Cx - Co) / (Cs - Co) = Constant

Xo^2 / D_{550} * t = Xo^2 / D_{450} * 15

D_{550} * t = D_{450} * 15

(1.2 * 10^(-4) m^2 / s) * exp ( - 130,000 / 8.31 * 723.15) * t

(4.88 * 10^(-14) m^2 / s) * 15

by, solving for t we get:

 t = 1.1 hr

So, the time required is 1.1 hr.