Homogeneous and Heterogeneous Nucleation

Although solid-state transformations are frequently sensitive to lattice defects in the parent phase and thus tend to nucleate heterogeneously, evidence of homogeneous nucleation has been convincingly demonstrated in the past two years in selected alloy systems.85,86 Copper-cobalt alloys are particularly appropriate for this objective in that both the copper-rich parent phase and the cobalt-rich precipitate phase have the same face-centered cubic crystal structure and are mutually coherent, thereby exhibiting low interfacial energy and simplifying its calculation. The corresponding nucleation rates for precipitation in a copper-1 atomic percent cobalt alloy are plotted in Figure 46, as determined experimentally by electron microscopy and as calculated from classical homogeneous nucleation theory involving thermal fluctuations surmounting an interface-related free-energy barrier.85 The indicated agreement, assuming diffusivities based on vacancy concentrations characteristic of the solutionizing temperature, provides good support for the validity of homogeneous nucleation theory. Similar findings have been obtained for more dilute copper-cobalt alloys.85 This signifies that, even though the smallest precipitated particles detected by electron microscopy (approximately 50 angstroms) were considerably larger than the critical nucleus size, the increasing particle-number density versus time was small enough (yet measurable) to permit unimpeded growth of the individual particles to detectable sizes before encountering overlapping diffusion fields between nearest-neighbor precipitates.

On the other hand, with higher supersaturations (e.g., copper-2.7 atomic

FIGURE 46 Calculated and experimental nucleation rates from homogeneous precipitation in a copper-1 atomic percent cobalt alloy as a function of temperature, normalized to the solvus temperature (Tc), after solutionizing at 870°C. From LeGoues and Aaronson.85 Reprinted with permission.

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