Consider a diffused couple between pure Beryllium and a Stee

Consider a diffused couple between pure Beryllium and a Steel Alloy with 0.05 wt% Be. At 700 degree C, how long must you allow diffusion to increase the concentration of Beryllium to 1.3 wr% up to a depth of 3 mm into your steel alloy? The pre-exponential and activation energy for Beryllium diffusion into Steel at 700 degree C are 3.2 Times 10^-4 m^2/s and 123,456 J/mol.

Solution

Given:

pre exponential = 3.2 x 10^-4 m² s^-1; Activation energy = 123456 J mol^-1

Equation:

Diffusion coefficient

J = -D (dc / dx) ;J - Diffusion coefficient;

Diffusion coefficient is the measure of mobility of diffusing species. (for example, this problem diffusion with metal with alloy, called \"Atomic Diffusion\").

Diffusion Coefficient:

D = D₀ exp ( - Q_d / RT); where D₀ -temperature independent pre exponential, Q_d - the activation energy for diffusion, R - gas constant 8.314 Jmol^-1 K^-1 , T - absolute Temperature (K)

Diffusion Couple (C):

C = [((C₁ + C₂ ) /2) - ((C_{1 -}C₂) / 2) erf(x / 2 * sqrt (Dt))];

where C₁ - Concentration of metal, C₂ - Concentration of alloy.