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358 • Chapter 10 / Phase Transformations

simple diffusion-dependent transformations in which there is no change in either the
number or composition of the phases present. These include solidification of a pure
metal, allotropic transformations, and recrystallization and grain growth (see Sections
7.12 and 7.13).
In another type of diffusion-dependent transformation, there is some alteration in
phase compositions and often in the number of phases present; the final microstructure
typically consists of two phases. The eutectoid reaction described by Equation 9.19 is of
this type; it receives further attention in Section 10.5.
The third kind of transformation is diffusionless, in which a metastable phase is pro-
duced. As discussed in Section 10.5, a martensitic transformation, which may be induced
in some steel alloys, falls into this category.

10.3 THE KINETICS OF PHASE TRANSFORMATIONS
With phase transformations, normally at least one new phase is formed that has dif-
ferent 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 in-
crease in size until the transformation has reached completion. The progress of a phase
nucleation, growth 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 at-
tained. We now discuss the mechanics of these two processes and how they relate to
solid-state transformations.

Nucleation
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 ho-
mogeneous type, nuclei of the new phase form uniformly throughout the parent phase,
whereas for the heterogeneous type, nuclei form preferentially at structural inhomoge-
neities, 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.

Homogeneous Nucleation
A discussion of the theory of nucleation involves a thermodynamic parameter
free energy 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 discus-
sion 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 G; a transformation occurs spontaneously only when G has a nega-
tive value.
For the sake of simplicity, let us first consider the solidification of a pure material,
assuming that nuclei of the solid phase form in the interior of the liquid as atoms cluster
together so as to form a packing arrangement similar to that found in the solid phase.