Step 1: Understand the crystallization process.
Crystallization is the process by which atoms or molecules arrange into a highly ordered solid structure called a crystal. This process involves two main steps: nucleation (formation of stable nuclei) and crystal growth (enlargement of these nuclei).
Step 2: Analyze the role of different types of energy in crystallization.
During nucleation, a small cluster of atoms forms. For this cluster to become a stable nucleus (and not just redissolve), it must overcome an energy barrier. This energy barrier is related to two competing factors:
- Volume free energy (driving force): The reduction in bulk free energy as the solid forms from the liquid. This term is negative and favors nucleation.
- Surface free energy (retarding force): The energy required to create new solid-liquid interfaces (surfaces). This term is positive and opposes nucleation, effectively "retarding" it.
Only when the reduction in volume free energy outweighs the increase in surface free energy can a stable nucleus form.
Let's evaluate the given options:
(1) Free surface energy: This is the energy associated with the creation of new surfaces. In crystallization, the formation of a new solid phase requires creating interfaces between the solid and the surrounding liquid. This interfacial energy (or surface energy) is always positive and acts as an energy barrier that must be overcome for nucleation to occur. Therefore, it retards the nucleation and growth process by resisting the formation of new surfaces.
(2) Kinetic energy: This is the energy of motion of atoms or molecules. While atoms must have sufficient kinetic energy to move and arrange themselves into a crystal lattice, kinetic energy itself doesn't directly retard the process in the context of an energy barrier.
(3) Vibration energy: This refers to the vibrational energy of atoms within a solid lattice. It's related to the internal energy but not the primary retarding energy barrier in the context of nucleation.
(4) Activation energy: This is a general term for the minimum energy required to initiate a chemical reaction or physical process. While nucleation does involve an activation energy barrier, this barrier is largely attributed to the creation of the new surface (free surface energy). So, "free surface energy" is a more specific and direct answer to what retards the process by being an energetic penalty.
Step 3: Conclude which energy retards the process.
The free surface energy is the positive energy barrier that opposes the formation of stable nuclei, thus retarding the crystallization process.
The final answer is $\boxed{\text{1}}$.