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3D phase-field simulations of lamellar and fibrous growth during discontinuous precipitation

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Abstract

3D phase field simulations have been used to investigate the effect of the third dimension on morphological instabilities of lamellar growing precipitates during discontinuous precipitation. 3D simulations offer the possibility to act on the reaction front as a surface. However, no changes would be expected, in the system’s behavior along the third dimension, with regard to 2D systems’ in terms of translation invariance. The effect of a numerically induced noise, on the behavior of the growing precipitate, as a Saffman–Taylor finger in the presence of volume diffusion is reported. The numerical noise consists of breaking symmetry by acting on the reaction front as a surface. As our 3D system consists of a set of planes forming the growing \(\beta\) precipitate along with the \(\alpha\) depleted lamellar phase, a certain part of the reaction front (1 or more given planes) have been allowed to grow faster than the others; which has resulted in a symmetry breaking leading to fibrous growth. It turns out that even with breaking symmetry the oscillatory instability is systematically followed by a tip-splitting and that fibers are rather due to the decrease in steady state velocity associated to the lamellar thickness increase. A new method to tune the steady state velocity is suggested.

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Acknowledgements

Thanks are due to Mathis Plapp for his great assistance and for all the fruitful discussions. A. R.L would like to thank Mathis Plapp for providing means to perform some of the expensive runs. L. A. thanks Pawel Zeiba for his fruitful discussions.

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  1. Laboratoire de Physique Théorique, Faculté de Physique, U.S.T.H.B, BP 32, El-Alia, BabEzzouar, 16311, Alger, Algeria

    Aniss Ryad Ladjeroud & Lynda Amirouche

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  2. Lynda Amirouche
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Correspondence to Lynda Amirouche.

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Ladjeroud, A.R., Amirouche, L. 3D phase-field simulations of lamellar and fibrous growth during discontinuous precipitation. Appl. Phys. A 128, 582 (2022). https://doi.org/10.1007/s00339-022-05710-x

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