A discussion of the theory of nucleation involves a
thermodynamic parameter called free energy (or Gibbs free energy), G. In brief, free energy is a
function of other thermodynamic parameters, of which one is the internal energy
of the system (i.e., the enthalpy,
H), and another is a
measurement of the randomness or disorder of the atoms or molecules (i.e., the entropy, S). It is not our purpose here to provide a detailed discussion of
the principles of thermodynamics as they apply to materials systems. However,
relative to phase transformations, an important thermodynamic parameter is the
change in free energy a transformation will occur spontaneously only when has a
negative value. For the sake of simplicity, let us first consider

Homogeneous Nucleation

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There are two types of nucleation: homogeneous and heterogeneous. The distinction between them is made according to
the site at which nucleating events occur. For the homogeneous type, nuclei of
the new phase form uniformly throughout the parent phase, whereas for the
heterogeneous type, nuclei form preferentially at structural inhomogeneities,
such as container surfaces, insoluble impurities, grain boundaries,
dislocations, and so on. We begin by discussing homogeneous nucleation because
its description and theory are simpler to treat. These principles are then
extended to a discussion of the heterogeneous type.



With phase transformations, normally at least one
new phase is formed that has different physical/chemical characteristics and/or
a different structure than the parent phase. Furthermore, most phase
transformations do not occur instantaneously. Rather, they begin by the
formation of numerous small particles of the new phase(s), which increase in
size until the transformation has reached completion. The progress of a phase
transformation may be broken down into two distinct stages: nucleation and growth. Nucleation involves the appearance of very small particles,
or nuclei of the new phase (often consisting of only a few hundred atoms), which
are capable of growing. During the growth stage these nuclei increase in size, which
results in the disappearance of some (or all) of the parent phase. The
transformation reaches completion if the growth of these new phase particles is
allowed to proceed until the equilibrium fraction is attained. We now discuss
the mechanics of these two processes, and how they relate to solid-state