Question

The product particles having radius less than critical radius ($r_c$) during nucleation are known as

• A. Nuclei
• B. Embryos
• C. Elements
• D. Atoms

Hint:

Embryos are unstable clusters; only when they exceed the critical radius do they become stable nuclei.

Answer 1

The Correct Option is B

The total free energy change on forming a cluster of radius \( r \) is \[ \Delta G = -\frac{4}{3}\pi r^3 \Delta G_v + 4\pi r^2 \gamma \] where \( \Delta G_v \) is the free-energy change per unit volume favouring the new phase and \( \gamma \) is the surface energy per unit area.

1. Step 1: For small \( r \), the surface term \( 4\pi r^2 \gamma \) dominates, so \( \Delta G \) increases as \( r \) grows, meaning small clusters are unstable and shrink back.
2. Step 2: This unstable, sub-critical behaviour defines the clusters as embryos rather than stable nuclei.
3. Step 3: Beyond \( r_c \), the volume term dominates and \( \Delta G \) decreases with further growth, giving stable nuclei instead.

So particles with \( r < r_c \) are called embryos.

Answer 2

It helps to line up the exact terminology metallurgists use at each stage of nucleation and match the given condition to the right term.

1. Nuclei: this term is reserved for clusters that have crossed \( r_c \) and become thermodynamically stable, continuing to grow into the new phase. Since the question specifies radius less than \( r_c \), this term does not apply.
2. Embryos: this is the specific term metallurgists use for sub-critical clusters, those with radius less than \( r_c \), which are unstable and constantly forming and redissolving in the parent phase due to thermal fluctuations, until by chance one exceeds \( r_c \) and becomes a true nucleus.
3. Elements: not a nucleation-stage term at all, it refers to chemical species, unrelated to cluster size.
4. Atoms: refers to the individual constituent particles, not the multi-atom cluster being described, so it does not fit either.

The standard metallurgical term for a sub-critical cluster, exactly matching the given condition of radius less than \( r_c \), is embryo.

Therefore, the correct answer is Embryos.