Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.

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The Theory of Ostwald Ripening

Ostwald ripening theory: applications to fluorocarbon emulsion stability

The Lifshitz-Slyozof-Wagner (LSW) theory, which corresponds to a zero volume fraction approximation, was developed to model kinetics of precipitate growth from supersaturated solid solutions. The subsequent modifications of the LSW theory for the incorporations of various factors including volume fractions of precipitates to fit the experimental data from the coarsening precipitates were made by various workers during last twenty five years. The LSW theory and its modifications have been applied on the diffusion-controlled Ostwald ripening of the γ′ precipitate particles [Ni3(Al,Ti)] in nickel-based superalloys. The important Ostwald ripening theories were reviewed in the part I of this paper, and the coarsening characteristics of the γ′-precipitates in Ni-base high temperature superalloys are presented in detail in relation to these theories in the present part. A model developed by D. McLean can be used to predict the γ′ particle growth over service lifetimes in the case of relatively Al-rich nickel-base superalloys. Additional fundamental data (such as the precipitate-matrix interfacial energy, diffusivity of the component species of the particle, and the equilibrium solubility with a particle in nickel-based superalloys) can be obtained from experimental results for coarsening, if the concentration changes during coarsening can be measured precisely, using the methods developed by A. J. Ardell. Furthermore, the factors affecting the shape changes and splitting of the γ′ precipitate particles during the coarsening were also considered seperately since the classical Ostwald ripening theories can not explain the morphological changes.

Review Progress in Ostwald ripening theories and their applications to the γ′-precipitates in nickel-base superalloys Part II Nickel-base superalloys

Thermal stability and coarsening of coherent particles in a precipitation-hardened (NiCoFeCr)94Ti2Al4 high-entropy alloy

Temperature dependence of γ-γ' lattice mismatch in Nickel-base superalloys

Etude de la precipitation entre 673 et 973 K par microscopie optique et microscopie electronique en transmission

Precipitation in Ni-Co-Al alloys: Part 1 continuous precipitation

http://rd.springer.com/content/pdf/10.1007%2FBF00553059.pdf

Precipitation in Ni-Co-AI alloys Part 2 Discontinuous precipitation

Continuous precipitation of γ′ in Ni-Co-Al alloys has been studied using X-ray diffraction, scanning electron microscopy and transmission electron microscopy The precipitation sequence is observed to be a change of morphology from spheres → cube → plates The γ∣γ′ lattice parameter mismatch is of the order of 03% The γ′ particle growth rate has been determined over a range of temperatures for alloys containing a range of cobalt contents from 0 to 55 at % In all cases the particle size varies att1/3 and the particle number density ast−1 The growth rate varies very little with increasing volume fraction of γ′ The measured particle growth rate decreases with increasing cobalt content, probably as a result of partitioning of cobalt between particle and matrix Electron micro-probe analysis, volume fraction measurements and X-ray analyses were used to determine the γ∣(γ + γ′) boundary in the Ni-Co-Al ternary system at temperatures between 973 and 1073 K It is clear from the position of the boundary that a significant beneficial effect of cobalt is in decreasing the solubility of the γ′ phase in γ for any temperature up to 1073 K Histograms of particle size were constructed and compared with both the Lifshitz-Slyozov-Wagner and the Lifshitz-Slyozov encounter modified (LSEM) predicted distributions The LSEM theory for particle coarsening was shown to be a much better fit to the experimental particle size distributions

L. C. Yap

Papers

Precipitation in Ni-Co-Al alloys: Part 1 continuous precipitation

Precipitation in Ni-Co-AI alloys Part 2 Discontinuous precipitation

Precipitation in Ni-Co-Al alloys