Which one of the following options is correct? In a binary alloy system, during spinodal decomposition, uphill diffusion occurs:
Show Hint
Diffusion always runs from high to low chemical potential; inside the spinodal region, chemical potential falls as concentration rises, so atoms move to higher concentration.
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
Show Solution
The Correct Option isD
Solution and Explanation
Concept: Diffusion really follows chemical potential, not concentration.
The textbook picture "atoms move from crowded areas to empty areas" is only true because, in a normal stable solution, chemical potential $\mu$ rises together with concentration $c$. The real rule, valid everywhere, is that atoms move to cut down the free energy of the whole system, so flux always runs from high $\mu$ to low $\mu$.
Step 1: Look at the shape of the free energy curve.
Plot the molar free energy $G$ of the alloy against composition. Outside the spinodal region this curve is concave up, $\dfrac{\partial^2G}{\partial c^2}>0$, so $\mu$ and $c$ move together. Inside the spinodal region the curve bends the other way, $\dfrac{\partial^2G}{\partial c^2}<0$.
Step 2: See what the sign flip does to $\mu$.
Because $\mu$ is basically the slope of the $G$ curve, a negative curvature means $\mu$ now falls as $c$ rises. A solute rich pocket has a LOWER chemical potential than the surrounding solute poor material.
Step 3: Apply the flux rule.
Atoms in the solute poor region sit at a higher $\mu$ than atoms already in the solute rich pocket. Since flux runs from high $\mu$ to low $\mu$, atoms move into the already solute rich pocket. Concentration there gets even higher, while the surrounding region gets even more depleted. This is exactly uphill diffusion in terms of concentration, even though it is completely normal downhill diffusion in terms of chemical potential.
Step 4: Match this against the four options.
The concentration part of the flux is from lower to higher (uphill), which rules out both options that say "higher to lower concentration". Between the two remaining choices, the chemical potential part must still be from higher to lower, since that never changes; the option pairing "lower to higher concentration" with "lower to higher chemical potential" gets the second half backwards.
Step 5: Conclude.
Spinodal decomposition drives atoms from lower to higher concentration, powered by a fall from higher to lower chemical potential.
\[ \boxed{\text{From lower to higher concentration and from higher to lower chemical potential}} \]
