Multiscale Modeling of Theta ' Precipitation in Al-Cu Binary Alloys

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2986 V. Vaithyanathan et al. / Acta Materialia 52 (2004) 2973–2987 average aspect ratio 20 18 16 14 12 10 8 6 4 information necessary to compare the effect of volume fraction on growth/coarsening kinetics. From the precipitate microstructure evolution in Figs. 10, 14(a) and (b) (corresponding to 2%, 3% and 4% Cu compositions, respectively), it is obvious that the number of precipitates which reach the growth stage from the nuclei stage increases with supersaturation and therefore, results in a larger precipitate density in the late stages of simulation. The real times for the evolution study corresponding to t ¼ 900 are 10 and 7.5 h for the 3% and 4% Cu compositions (due to difference in mobility M as a function of alloy composition), respectively, and the simulation size is 500 500 nm 2 . The average aspect ratio of h 0 precipitates decrease with increase in alloy composition (2–4% Cu) (see Fig. 15). This type of behavior is also observed in experiments [38], in which the reduction in aspect ratio with increase in alloy composition or supersaturation is caused by enhanced thickening. The multiscale model helps in understanding the physics behind the equilibrium h 0 precipitate morphology. The quantitative predictions of equilibrium aspect ratio of h 0 precipitates are in good agreement with experiments. In order to obtain a complete understanding of the non-equilibrium precipitate morphologies in experiments arising from interfacial kinetic anisotropy, a more sophisticated phase-field model that includes misfit defects and accounts for the ledge growth nature of the coherent interface of h 0 precipitates, is required. 6. Summary 2% 3% 4% 0 10 20 30 40 50 60 time (hrs) Fig. 15. Average aspect ratio evolution as a function of time compared for the Al–Cu alloys of three different compositions. The aspect ratio seems to decrease slightly with increase in composition, similar to the experimental results of Merle and Fouquet [38]. A multiscale approach is presented to study the precipitate morphology of h 0 precipitates in Al–Cu alloys. All of the energetic contributions required by the mesoscale phase-field (bulk, interfacial, and strain) are provided by atomic-scale first-principles calculations combined with cluster expansion and MC techniques. First-principles calculations provide the first reliable interfacial energy and misfit strain values for the coherent and semi-coherent interfaces of h 0 . From the multiscale simulation results, we demonstrate that the equilibrium plate-shaped morphology of h 0 is not solely governed by interfacial energy anisotropy as believed prevalently, but by the combination of interfacial and elastic energy anisotropies. The time evolution of the equilibrium precipitate features such as the length, thickness, and aspect ratio predicted by the simulation agrees qualitatively with the experimental observations, despite the fact that the model does not account for the non-equilibrium interfacial mobility anisotropy effects. We note that the first-principles/phase-field method proposed here is completely general and is not confined to the h 0 /Al case. It should be applicable to a wide variety of problems in microstructural evolution. References [1] Wolverton C, Ozolins V. Phys Rev Lett 2001;86:5518. [2] Hardy HK. J Inst Met 1951;79:321. [3] Hardy HK. J Inst Met 1953;82:236. [4] Laird C, Aaronson HI. Trans Metall Soc AIME 1968;242:1393. [5] Hornbogen E. Aluminium 1967;43:115. [6] Boyd JD, Nicholson RB. Acta Metall 1971;19:1379. [7] Doherty RD. Diffusive transformations in the solid state. In: Cahn RW, Haasen P, editors. Physical metallurgy. Amsterdam: Elsevier; 1996. p. 1363–505. [8] Stobbs WM, Purdy GR. 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Multiscale Modeling of Theta ' Precipitation in Al-Cu Binary Alloys

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