Consider a diffusion couple composed of two semi-infinite solids of the same metal and that each side of the diffusion couple has a different concentration of the same elemental impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion couple. For this situation, the solution to Fick's second law (assuming that the diffusion coefficient for the impurity is independent of concentration) is as follows:

(5.15)

The schematic diffusion profile in Figure 5.13 shows these concentration parameters as well as concentration profiles at times t = 0 and t > 0. Please note that at t = 0, the x = 0 position is taken as the initial diffusion couple interface, whereas C1 is the impurity concentration for x 0.
Consider a diffusion couple composed of pure nickel and a 55 wt% Ni-45 wt% Cu alloy (similar to the couple shown in Figure 5.1). Determine the time this diffusion couple must be heated at 1000°C (1273 K) in order to achieve a composition of 56.5 wt% Ni a distance of 15 μm into the Ni-Cu alloy referenced to the original interface. Values for the pre-exponential and activation energy for this diffusion system are 2.3 × 10-4 m2/s and 252,000 J/mol?

Transcribed Image Text:

х 1- erf Dt Cx = C2 + 2 2-