Question

At eutectic point, degree of freedom is:

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

Invariant points ($F = 0$) on binary alloy phase diagrams include:
- Eutectic points
- Eutectoid points
- Peritectic points
- Peritectoid points

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the number of degrees of freedom (variance) at a eutectic point in a binary phase diagram.

Step 2: Key Formula or Approach:
We use Gibbs Phase Rule for condensed systems (where pressure is held constant, typically at $1\text{ atm}$):
\[ F = C - P + 1 \]
where:
$F$ is the degrees of freedom.
$C$ is the number of components.
$P$ is the number of phases in equilibrium.

Step 3: Detailed Explanation:

• A eutectic reaction occurs in a binary system, meaning the number of components is $C = 2$.

• At the eutectic point, three phases coexist in equilibrium: the liquid phase ($L$) and two distinct solid phases ($\alpha$ and $\beta$). Thus, $P = 3$.

• Substituting these values into the condensed phase rule:
\[ F = 2 - 3 + 1 = 0 \]

• A degree of freedom of $0$ means the system is invariant.

• This implies that the eutectic reaction can only occur at a single, unique temperature and a specific composition. Changing either temperature or composition will cause at least one of the three phases to disappear.

Step 4: Final Answer:
At the eutectic point, the degree of freedom is 0.