Interfacial free energy anisotropy driven faceting of precipitates

Abstract

During solid–solid precipitation, interface free energy anisotropy is known to drive faceting of precipitates. In this paper, using a recently developed phase field formulation based on higher order tensor terms, we develop and implement a family of phase field models and indicate the parameter choices which lead to faceted precipitate morphologies. We also indicate how to choose the parameters given either the known precipitate morphology or the interfacial free energy anisotropy. Specifically, we study the faceting of precipitates in systems with cubic and hexagonal anisotropies; in 2 and 3D implementation of our phase field model, the precipitates do show facets in accordance with the Wulff plot – including cases where the Wulff plot predicts facets made up of more than one family of planes. We also indicate the possible extensions of our model to study other problems of interest.

Keywords:

• Phase field modelling
• faceted precipitates
• interfacial energy anisotropy
• cubic anisotropy
• hexagonal anisotropy
• Wulff plot

Acknowledgements

We thank T. A. Abinandanan for useful discussions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Industrial Research and Consultancy Centre, IIT Bombay [grant number 09IRCC16]; Computational facilities of PARAM-YUVA at CDAC, Pune, Nebula, Dendrite (DST-FIST facility), and Spinode are acknowledged. One of us (AR) thank DST [grant number 14DST017].