Which one of the following options is correct?
In a binary alloy system, during spinodal decomposition, uphill diffusion occurs:
In a binary alloy system, during spinodal decomposition, uphill diffusion occurs:
Show Hint
- From higher to lower concentration and from higher to lower chemical potential
- From higher to lower concentration and from lower to higher chemical potential
- From lower to higher concentration and from lower to higher chemical potential
- From lower to higher concentration and from higher to lower chemical potential
The Correct Option is D
Solution and Explanation
Diffusion is not really driven by a concentration gradient. It is driven by a gradient in chemical potential (\(\mu\)). Atoms always move so as to lower the total free energy of the system, which means flux flows from a region of higher chemical potential to a region of lower chemical potential.
\[ J \propto -\frac{\partial \mu}{\partial x} \]
Step 2: Recall Fick's first law in terms of chemical potential.
For a normal (stable) solution, \(\mu\) increases with concentration, so a drop in chemical potential lines up with a drop in concentration, and diffusion moves atoms from high concentration to low concentration, exactly as intuition suggests.
Step 3: Understand what is different inside the spinodal region.
Inside the spinodal region of a phase diagram, the free energy curve is concave down:
\[ \frac{\partial^2 G}{\partial c^2} < 0 \]
This makes \(\frac{\partial \mu}{\partial c}\) negative, so chemical potential now DECREASES as concentration INCREASES. The system is unstable to any small composition fluctuation.
Step 4: Work out the direction of flux.
Since atoms still move from high \(\mu\) to low \(\mu\) (this rule never changes), and since \(\mu\) is now lower where concentration is higher, atoms move toward the region that already has more solute. Concentration keeps climbing in the solute rich zone and keeps falling in the solute poor zone. This is uphill diffusion: atoms travel from lower concentration to higher concentration, while still travelling from higher chemical potential to lower chemical potential.
Step 5: Analyze the options.
(A) Higher to lower concentration, higher to lower chemical potential: this is normal downhill diffusion, not what happens inside the spinodal. Incorrect.
(B) Higher to lower concentration, lower to higher chemical potential: chemical potential never rises in the direction of flux. Incorrect.
(C) Lower to higher concentration, lower to higher chemical potential: again puts flux going toward higher chemical potential, which cannot happen. Incorrect.
(D) Lower to higher concentration, higher to lower chemical potential: matches the spinodal decomposition mechanism exactly. Correct.
Final Answer:
Uphill diffusion during spinodal decomposition moves atoms from lower to higher concentration, but this still happens from higher to lower chemical potential.
\[ \boxed{\text{From lower to higher concentration and from higher to lower chemical potential}} \]
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