Problem 6
A disk of Ti-40at.%V is bonded to a disk of pure Ti with inert marker placed at the plane of bonding. The
diffusion couple is then annealed at 1300°C in an inert atmosphere for 1 hour. After diffusion couple
experiment, the inert markers are identified at a distance of 13.2 µm from the Matano plane ($x_o$). The
vanadium concentration at the marker plane is 19.5 at.% and the intrinsic diffusion coefficient, $D_V$ and $D_{Ti}$,
at the marker composition are $3.9 \times 10^{-8}$ cm²/sec and $2.0 \times 10^{-8}$ cm²/sec, respectively. Assume a constant
molar volume ($\bar{V}$) of 9.5 cm³/g-mole.
(a) Draw a schematic diagram of the concentration profiles ($C_V$ and $C_{Ti}$ vs. x) and identify the
areas that represent the cumulative intrinsic fluxes of V and Ti.
(b) Evaluate the intrinsic flux, $J_V$ and $J_{Ti}$ at t = 1 hour.
(c) Evaluate the interdiffusion flux $\bar{J}$ at the marker plane at t = 1hour.
(d) Determine the position and velocity of the marker plane expected at t = 6 hours.
Note on conversion of flux units:
$\text{Flux} = \frac{[\text{atf} \cdot \text{cm}]}{\text{sec}} = \frac{1}{100 \cdot \bar{V}} \left[\frac{\text{moles}}{\text{cm}^2 \cdot \text{sec}}\right]$ where \"atf\" refers to the atom fraction
