Phase field theory of polycrystalline solidification in three dimensions

TL;DR

This paper develops a three-dimensional phase field model for polycrystalline solidification, capturing nucleation and anisotropic grain growth with multiple orientation fields, and demonstrates its application to various growth morphologies.

Contribution

It introduces a 3D phase field framework with multiple orientation fields based on Euler parameters, extending previous 2D models to better simulate realistic grain growth.

Findings

Successfully models dendritic, needle, and spherulitic growth morphologies.

Incorporates anisotropic grain boundary energies based on Euler angle differences.

Provides a basis for more accurate 3D polycrystalline solidification simulations.

Abstract

A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the two-dimensional case, where a single orientation field suffices, in three dimensions, minimum three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four symmetric Euler parameters. The equations of motion for these fields are obtained from variational principles. Illustrative calculations are performed for polycrystalline solidification with dendritic, needle and spherulitic growth morphologies.