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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

          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

$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 (xo). The vanadium concentration at the marker plane is 19.5 at.% and the intrinsic diffusion coefficient, $DV$ and $D{Ti}$, at the marker composition are 3.9 × 10^-8 cm²/sec and 2.0 × 10^-8 cm²/sec, respectively. Assume a constant molar volume (V̅) of 9.5 cm³/g-mole. (a) Draw a schematic diagram of the concentration profiles (CV and CTi vs. x) and identify the areas that represent the cumulative intrinsic fluxes of V and Ti. (b) Evaluate the intrinsic flux, JV and JTi at t = 1 hour. (c) Evaluate the interdiffusion flux J̅ 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: Flux = ([atf·cm])/(sec) = (1)/(100 ·V̅)[(moles)/(cm^2 ·sec)] where ätfr̈efers to the atom fraction$

Added by Jacqueline N.

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