Quantitative phase field simulations of polycrystalline solidification using a vector order parameter

Tatu Pinomaa, Nana Ofori-Opoku, Anssi Laukkanen, and Nikolas Provatas
Phys. Rev. E 103, 053310 – Published 24 May 2021
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Abstract

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-diffusion are quantitatively consistent with earlier theoretical work, with grain boundary energy being controlled through a simple solid-solid interaction parameter. Moreover, when considering polycrystalline aggregates and their coarsening, we show that the kinetics follow the expected parabolic growth law. Finally, we demonstrate how this vector order parameter model can be used to describe nucleation in polycrystalline systems via thermal fluctuations of the vector order parameter, a process that cannot be treated consistently with multiphase or multi-order-parameter based phase field models. The presented vector order parameter model serves as a practical and efficient computational tool for simulating polycrystalline materials. We also discuss the extension of the order parameter to higher dimensions as a simple method for modeling multiple solid phases.

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  • Received 12 February 2021
  • Accepted 21 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.053310

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tatu Pinomaa1, Nana Ofori-Opoku2, Anssi Laukkanen1, and Nikolas Provatas3

  • 1ICME Group, VTT Technical Research Centre of Finland Ltd., Espoo 02044, Finland
  • 2Computational Techniques Branch, Canadian Nuclear Laboratories, Chalk River, Ontario K0J 1J0, Canada
  • 3Department of Physics and Centre for the Physics of Materials, McGill University, Montreal, Quebec H3A 2T8, Canada

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Issue

Vol. 103, Iss. 5 — May 2021

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