Eur. Phys. J. E (2020) 43: 28
https://doi.org/10.1140/epje/i2020-11950-3

Regular Article

Phase-field modeling of complex dendritic structures in constrained growth of hexagonal close-packed crystals

¹ College of Materials Science and Engineering, Zhengzhou University, 450001, Zhengzhou, P.R. China
² State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, 710072, Xi’an, P.R. China
³ State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, P.R. China

^* e-mail: dxl881112@zzu.edu.cn
^** e-mail: zhlwkr@zzu.edu.cn

Received: 17 November 2019
Accepted: 21 April 2020
Published online: 27 May 2020

Abstract

We perform the phase-field modeling to investigate the growth pattern selections of the complex dendritic structures in constrained growth with different solidification and orientation conditions. The results show that hexagonal close-packed (hcp) crystals emerge as dendritic and cellular arrays in different planes, originating from the specific hcp anisotropy that allows different growth preferences between the basal and cylindrical planes. A morphological transition of the titled dendrites to tip-splitting dendrites arises reflecting the competition between the preferred orientation induced primary growth and the misorientation induced sidebranching formation. Furthermore, the dendritic patterns exhibit sharper tips and the more significant sidebranches, while the cellular pattern is changed from the symmetric cells to the tip-splitting cells, and to seaweeds with the increase of anisotropy strength, indicating the competitive mechanism of the in-plane anisotropy induced growth promotion and the out-plane anisotropy induced growth restriction. We expect to understand the growth competition, the morphology selection, as well as the orientation dependence of the complex dendritic structures in the three-dimensional (3D) constrained growth.