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A phase in material science refers to a region of a material with uniform physical and chemical properties, such as a specific crystal structure and composition. When a material undergoes a phase transformation, its crystal structure or composition changes, resulting in particles of a new phase.

Nucleation is the first step in the formation of particles of a new phase. During this stage, a small number of atoms or molecules come together to form a stable nucleus. This usually occurs when the material is cooled or subjected to a change in pressure or composition, which makes the existing phase unstable. The stable nucleus exhibits the properties of the new phase and acts as a template for further growth.

Once nucleation has occurred, the second stage, growth, takes place. During this stage, the stable nucleus formed in the nucleation stage begins to grow as additional atoms or molecules join the nucleus. This process continues until the new phase completely replaces the original phase or reaches a stable equilibrium with it. The rate of growth depends on the driving force behind the phase transformation, such as temperature, pressure, or compositional changes. In conclusion, the two stages involved in the formation of particles of a new phase are nucleation, during which a stable nucleus of the new phase forms, and growth, during which the nucleus grows and eventually replaces or reaches equilibrium with the original phase.