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This paper aims to elucidate the role of interface energy anisotropy in orientation selection during nucleation of new grains in a polycrystalline film growth. An assessment of (heterogeneous) nucleation probability as function of orientation of both the bottom grain and of the nucleus was developed (using the concepts of classical nucleation theory). Novel solutions to the generalized Winterbottom construction were described in cases of very strong anisotropy and arbitrary orientations. In order to demonstrate the effect on the film crystallographic texture, a 2D Monte Carlo algorithm for anisotropic polycrystalline growth was used to simulate growth of films with columnar microstructure. The effect of strength of anisotropy, the deposition rate and initial texture were investigated. Results showed that with larger strength of anisotropy, the nucleation rate is less dependent on the driving force, but more dependent on the initial texture. With certain initial textures, the anisotropic nucleation may even be either impossible or having probability close to one irrespective of the driving force. Depending on the conditions, the anisotropic nucleation could hasten the evolution towards the interface-energy minimizing texture or retard it. Based on these insights, a hypothesis was offered to explain a peculiar texture evolution in electrodeposited nickel., Comment: 18 pages, 14 figures, 1 table Submitted in September 2023 to Computational Materials Science, Elsevier

Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be a reliable simulation tool. Nevertheless, their efficiency and accuracy still depend on the homogenization scheme used to interpolate the elastic properties in the interfacial regions. In this paper, we present a phase-field model for multi-phase and multi-component solids using a partial rank-one homogenization scheme that enforces static and kinematic compatibilities in the interfacial regions. To this end, we first extend the rank-one homogenization scheme to multi-phase systems. Moreover, for computational efficiency, we analytically solve the static compatibility equations for linear elastic three-phase solids. For quantitative accuracy, a coupling technique is used to extract the prerequisite thermodynamic and kinetic properties from CALPHAD databases. The model is solved numerically in an open source finite-element framework. As numerical applications, the microstructure of two elastically stressed intermetallic-containing three-phase alloys: Ni-Al and Al-Cr-Ni, are simulated. The accuracy of the model is verified against analytically obtained solutions for planar and concentric ring interfaces. We show that the simulation results remain unaltered with varying interface width. Except for one simulation, all cases show better or nearly equal convergence using the partial rank-one scheme compared to the Voigt-Taylor scheme.

This paper presents an efficient and quantitative phase-field model for elastically heterogeneous alloys that ensures the two mechanical compatibilities$\unicode{x2014}$static and kinematic, in conjunction with chemical equilibrium within the interfacial region. Our model contrasts with existing phase-field models that either violate static compatibility or interfacial chemical equilibrium or are computationally costly. For computational efficiency, the partial rank-one homogenization (PRH) scheme is employed to enforce both static and kinematic compatibilities at the interface. Moreover, interfacial chemical equilibrium is ensured by replacing the composition field with the diffusion potential field as the independent variable of the model. Its performance is demonstrated by simulating four single-particle and one multi-particle cases for two binary two-phase alloys: Ni-Al $\gamma^{\prime}/\gamma$ and UO$_2$/void. Its accuracy is then investigated against analytical solutions. For the single-particle $\gamma^{\prime}/\gamma$ alloy, we find that the accuracy of the phase-field results remains unaffected for both planar and non-planar geometries when the PRH scheme is employed. Fortuitously, in the UO$_2$/void simulations, despite a strong elastic heterogeneity$\unicode{x2014}$the ratio of Young's modulus of the void phase to that of the UO$_2$ phase is $10^{-4}\unicode{x2014}$we find that the PRH scheme shows significantly better convergence compared to the Voigt-Taylor scheme (VTS) for both planar and non-planar geometries. Nevertheless, for the same interface width range as in the $\gamma^{'}/\gamma$ case, the interface migration in these simulations shows dependence on interface width. Contrary to the $\gamma^{\prime}/\gamma$ simulations, we also find that the simulated elastic fields show deviations from the analytical solution in the non-planar UO$_2$/void case using the PRH scheme.

Two benchmark problems for quantitative assessment of anisotropic curvature driving force in phase field method were developed and introduced. Both benchmarks contained an anisotropically shrinking grain in homogeneous matrix. The first benchmark was a shrinking Wulff shape and in the second, such inclination dependence of the kinetic coefficient was added so that the shrinkage was isotropic. In both cases the match to the expected shape was quantified by means of Hausdorff distance and the shrinkage rate was analytically expressed. Three different ways of interface energy anisotropy inclusion in a multi-phase field model were compared. Because their performance was comparable, they were tested in an additional benchmark problem, which concerned direct measurement of equilibrium triple junction angles. Based on this benchmark, only one of the three strategies to include anisotropy was reliable in strongly anisotropic systems., Comment: 19 pages, 9 figures, 6 tables (main text and Supplemental Material merged). Link to the used MATLAB code in the references. In response to reviewers' comments, the main message of the paper changed and the sections Title, Abstract, Introduction, Methodology and Conclusion underwent major revision. The results are consistent with the first version