A new theory of the solid-state growth of embryos during nucleation: the fundamental role of interfacial mobility

Figures & data

Figure 1. Variation of free energy with the size of a precipitate when nucleating (a) homogeneously, (b) on a grain boundary and (c) on a dislocation.

Figure 2. Time evolution of the number (i) of atoms in one cluster. “Reprinted (Fig. 7b) with permission from [9] Copyright (2000) by the American Physical Society”.

Figure 3. Illustration of the exchange mechanism for interface controlled kinetics. Repetition of the same sequence will produce coarsening and reduction of the free energy.

Figure 4. Solute concentration profile near the interface under different regimes.

Figure 5. Evolution of a cluster size distribution from time t ₀ to t ₁. Adapted from [23].

Figure 6. On the left: An isolated subcritical embryo experiencing a net loss of atoms. On the right: A cloud of subcritical embryos.

Figure 7. Left: A cloud containing a high number density of embryos. Right: One of the dissolving embryos located at periphery.

Figure 8. Plot of the factor F vs. time.

Figure 9. Evolution of the number density of embryos with respect of the radius of the embryos. Calculations were made with C ₀ = 1 × 10²² m⁻³, r ₀ = 2 nm and υ = 0.01 nm/s.

Table 1. Comparison between the classical nucleation theory and the subcritical growth theory (this contribution).

	Classical nucleation theory	Subcritical growth theory
Frequency Factor: β ^*
Incubation time: τ
Dissolution of embryos	Zeldovitch factor: Z	Negative source term in the equation:

Figure 10. Schematized events captured by Liu et al. [11] during the precipitation of θ′ in an Al-5.7 wt.%Cu specimen. Precipitates 1 and 3 are created and are then dissolved under the influence of precipitates 2 and 4. The boxes indicate the time in hours and minutes.

F. Soisson and G. Martin , Monte Carlo simulations of the decomposition of metastable solid solutions: Transient and steady-state nucleation kinetics , Phys. Rev. B 62 (2000), pp. 203–214.10.1103/PhysRevB.62.203

 Web of Science ®Google Scholar

G. Martin , The theories of unmixing kinetics of solid solutions, in Solid State Phase Transformation in Metals and Alloys , Les Éditions de Physique (1979), pp. 337–406.

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C. Liu , S.K. Malladi , Q. Xu , J. Chen , F.D. Tichelaar , X. Zhuge , and H.W. Zandbergen , In-situ STEM imaging of growth and phase change of individual CuAlX precipitates in Al alloy , Sci Rep. 7 (2017). Available at https://www.nature.com/articles/s41598-017-02081-9#author-information.10.1038/s41598-017-02081-9

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