The phase field simulation of autocatalytic nucleation

Precipitation of metastable θ′ phase is a well known process that underlies age-hardening of Al-Cu alloys. The strength acquired is very sensitive to the morphology and spatial distribution of θ′, with the peak hardness corresponding to a fine distribution of precipitates with high length-to-thickness aspect ratio. Therefore, an understanding of the transformation mechanism between the matrix and θ′ and the factors affecting the nucleation barriers associated with its formation are crucial for an effective alloy design. Although the behaviour of the Al-Cu system has been a focus of intensive research for the large part of a century, the need still exists to elucidate the atomic mechanism of transformation. θ′ was traditionally considered to be a purely diffusional transformation product; however, several mechanisms have been proposed (Dahmen and Westmacott, Nie and Muddle) that recognised the existence of lattice correspondence between the Al-Cu matrix and θ′. The important feature of these mechanisms was a large shear component in the transformation strain, suggesting that the transformation may be diffusional-displacive in nature. This project was undertaken to investigate the special mode of transformation, autocatalytic nucleation, which features distinctive clusters of precipitates arranged into linear inclined stacks and cross-like arrays. The hypothesis tested was that such clustering of precipitates is the result of interaction between the shear component of the strain of the nucleus with the pre-existing microstructure, and that autocatalytic structures potentially reveal the nature of transformation strain. The thesis presents an assessment of the nucleation barriers associated with the formation of platelike inclusions, representative of a wide class of strengthening precipitates (θ′ and T₁ in Al-Cu and Al-Cu-Li, γ/γ′ in Al-Ag). It is demonstrated that existing estimates of interfacial energies and chemical driving forces do not explain the difficulty of precipitation in these systems, and that the influence of the shear component on the magnitude of the nucleation barrier is crucial and must be accounted in the model of the transformation mechanism. Further, a simple elastic interaction model based on earlier work of Perovic, Purdy and Brown is employed to demonstrate that the elastic interaction energy between the sheared nucleus and pre-existing large precipitate has the symmetry consistent with the distribution of θ′ in autocatalytic arrays. Finally, a diffuse interface phase field model is developed for the coherent nucleation and microstructure evolution in Al-Cu. The model takes into account the effect of local stress on the nucleation rate in an attempt to dynamically track how the nucleation of subsequent precipitates is facilitated by elastic interaction with the pre-existing microstructure. It is demonstrated that the traditional model of purely tetragonal transformation strain rules out the possibility of strain induced nucleation, due to weak interaction and the effective suppression of driving forces by matrix depletion. In the case of a sheared nucleus it was not possible to answer conclusively whether autocatalysis may be caused by the elastic interaction. Some precipitate clustering was evident, but characteristic linear stacks and cross-like arrays observed in experiments were not reproduced in the simulations. The results suggest that inhomogeneous distributions, when they occur, are the product of association with inhomogeneities, such as dislocations or grain boundaries, rather than a self-stimulating chain of strain induced nucleation events.