Assuming that the mobility of B, , is positive, prove that the diffusivity of B, ,
in the phase is negative at a temperature of 500 °C for a composition xx=0.5.
2. Consider a diffusion couple between pure FCC Ni and FCC Ni containing 25 mol % Cu.
Successive experiments at five different temperatures yielded the following results for the
diffusivity of Cu in Ni:
T (°C) D (m²/s)
200 5.00×10-33
300 5.56×10-29
400 2.90×10-24
600 4.34×10-20
800 2.11×10-17
a. Determine and for Cu diffusion in Ni.
b. The diffusion couple is heated to 1000 °C, held for 50 hours, then cooled to room
temperature.
i. Determine the equation for the composition profile across the diffusion couple
interface. Plot this composition profile.

ii. Determine the width of the diffusion zone, i.e., the distance between where the
composition reaches 0.01 mol % Cu (pure Ni) on one side of the couple and
reaches 24.99 mol % Cu (Ni-25 mol % Cu) on the other side. Assume that
Cu =Ni. You can assume the molar volumes of Cu and Ni are the same,
7.5×10-6 mol/m³.
c. After being annealed at 1000 °C for 50 hours (i.e., it now has a composition profile
across the interface given by the equation determined in part b-i), the diffusion couple
in part b is then instantaneously heated to a temperature of 1100 °C. What is the flux
of Cu atoms at a point 1 μm from the original interface into the pure Ni-side of the
couple?
d. It is now realized that the diffusivity of Ni at 1000 °C is 1.8 ×10-16 m²/s. For the
diffusion couple from part b:
i. Determine the net flux of vacancies at the original couple interface after 50
hours at 1000 °C. Be sure to indicate the direction relative to the two couple
ends.
ii. What is the interdiffusion coefficient, �, at the original couple interface after 50
hours at 1000 °C?