The so-called LSW (Lifshitz, Slezov and Wagner) theory of precipitate
coarsening, or Ostwald ripening, contains physical parameters that are often
difficult to evaluate independently. This is especially true of the free energy,
σ, of the interface between the majority
(matrix) phase and the minority (precipitate or dispersed) phases. It is also
true to a lesser extent of the chemical diffusion coefficient, Dc, in
the majority phase, and of the limit of solubility of the solute atoms, Xeq.
The LSW theory provides rate laws for the growth of the average precipitate and
the kinetics of solute depletion. When both processes can be experimentally
measured independently it is possible to extract from the data values of
σ and Dc which are independent of
each other; data on Xeq are obtained independently from analysis of
the kinetics of solute depletion. In binary Ni-base alloys with Al, Ga, Ge, Si
or Ti the kinetics of precipitate growth are obtained using transmission
electron microscopy and the kinetics of solute depletion are obtained by
measuring the change in ferromagnetic Curie temperature as a function of time.
Experiments conducted over many years, and judicious analysis of the data, have
provided the most reliable estimates of σ
available to date. The data on Dc obtained from these measurements
are generally in excellent agreement with data from conventional diffusion
experiments (mostly extrapolated from much higher temperatures), and data on Xeq
have proved to be invaluable in evaluating coherent solubility limits of the
solutes in these alloys. Nevertheless, the community is entitled to be somewhat
skeptical of these results because the LSW theory applies, strictly speaking, to
the coarsening of precipitates in a fluid matrix in the limit of zero phase
fraction of the dispersed phase. The dispersed coherent, crystallographically
ordered Ni3X precipitates, where X represents the solute atoms noted
above, all have different lattice mismatches with the majority phase, which
introduces complications such as non-constant morphologies and pronounced
spatial correlations among the precipitates. Furthermore, their phase fractions
vary from as little as 0.03 to greater than 0.50. In this talk I will present
the data on σ, Dc and Xeq
for the 5 alloys, will compare, where possible, the results with values expected
from different sources, including first-principles calculations and other
experiments, and will provide justification, largely from the results of recent
computer simulation experiments, for the accuracy of the values extracted from
data on coarsening. This work is supported by the National Science Foundation.
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