Concept:
Nucleation is the first step in phase transformation where a stable nucleus of a new phase is formed. The energy barrier for nucleation is called activation free energy.
There are two types:
• Homogeneous nucleation (inside bulk)
• Heterogeneous nucleation (at surfaces/interfaces)
Step 1: Homogeneous nucleation energy barrier.
In homogeneous nucleation:
• nucleus forms in bulk material
• requires high energy barrier
• no assistance from surfaces
So activation energy is maximum.
Step 2: Heterogeneous nucleation.
In heterogeneous nucleation:
• occurs on container walls, grain boundaries, impurities
• surface reduces interfacial energy
• lowers energy barrier
Step 3: Comparison.
\[
\Delta G^*_{heterogeneous} < \Delta G^*_{homogeneous}
\]
Thus heterogeneous nucleation is energetically easier.
Final Answer:
\[
\boxed{\text{Lower}}
\]