Geology Reference
In-Depth Information
during growth of the new phase are individually uncoordinated (as in diffusion) or
are cooperative (as in mechanical twinning). In metallurgy, the terms ''nucleation
and growth'' and ''martensitic'' are commonly used for the two types, respectively,
while in mineralogy they are often referred to as ''reconstructive'' and ''displa-
cive''. The second type is commonly characterized by significant shape change,
leading to the term ''shear transformation'', and by the tendency for non-hydro-
static stress to play an important role. The label ''diffusionless'' is also used for the
second type (Zhang and Kelly
2009
).
The formal kinetic theory of solid-state reactions is usually based on either a
nucleation and growth model, where a nucleation stage is identifiable, or on a
simple growth model where a nucleation stage does not enter, as in spinodal
decomposition. Nucleation is commonly heterogeneous, occurring at grain
boundaries, dislocations, etc.; see Flynn (
1972
), Christian (
1975
), and Kirkpatrick
(
1981
) for general theory on nucleation. Once an interface is established, the local
rate of growth is generally controlled either by processes at the interface itself
(interface control) or by the rate at which material is transported to the reaction site
(diffusion control). In the case of interface control, after a local steady state is
established, the growth tends to be linear with time. In spinodal decomposition
cases where a laminar structure grows by edgewise propagation, a linear growth
law also tends to apply. However, in common cases of diffusion control, as where
the reacting material reaches the interface through a thickening layer of product
material or the depletion of the reactants has to be taken into account, the growth
tends to be proportional to the square root of time (parabolic growth). Instability in
growth rate may also arise at an interface, with important results for the mor-
phology of product phases (c.f. dendritic structures). In a global view, covering
both nucleation and whatever type of growth control that pertains, it is often
possible, as in the case of recrystallization, to describe the overall kinetics by an
Avrami relation of the type (
3.13
) with a suitable choice of n, the value of which
may vary from less than 1 to more than 4 (Christian
1975
, p. 542).
The mechanisms of the reactions or diffusion processes are important in
determining the actual kinetic coefficients. Crystal defects are usually involved,
point defects, dislocations, or planar defects (''shear planes'') having roles in
particular cases. The defects may play an important part in the formation of an
activated complex where such can be recognized or usefully postulated.
In solid-state reactions, two other factors also influence the kinetics to an
important degree. The first is local volume or shape change. This gives rise to
internal stresses, and the associated strain energy has to be taken into account as
work to be provided during the transformation. The magnitude of the internal
stresses will be influenced by whether the reaction products are crystallographi-
cally coherent with the matrix or not. The stresses may also directly interact with
the reaction mechanism if shearing is involved. The second factor is the
impingement of reaction zones associated with separate nuclei or sites of reaction.
The impingement may involve either a meeting of the actual reaction interfaces or
an overlap of the zones of depletion from which diffusion is recurring.
