Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites—A Review

Abstract

LÁ SZLÓ GRÁ NÁ SY, LÁ SZLÓ RÁ TKAI, ATTILA SZÁ LLÁ S, BÁ LINT KORBULY, GYULA I. TÓ TH, LÁ SZLÓ KÖ RNYEI, and TAMÁ S PUSZTAI Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.

Filling of three-dimensional space by two-dimensional sheet growth

“…Spherulites are spherical shapes occurring during crystallisation processes, assembled from outwardly-radiating fibres [38]. The structures presented here might be seen as an extension of this concept, where the essentially 1D fibres are replaced by 2D sheets.…”

Orientation-field models for polycrystalline solidification: Grain coarsening and complex growth forms

“…The mobilities M and Mc are defined in [13,20,21] and to allow for the freezing of orientational disorder in the solid, we used 3 multiplier in Eq. (10) compensates for the diverging driving force of orientational ordering, which emerges from the singular coupling function q() in Eq.…”

“…While the KWC model and its descendants have been widely used to address various aspects of polycrystalline solidification [13][14][15][16][17][18][19][20][21], there are only few studies [22] regarding the abilities of the HMP model in this area. Extending the orientation field to the liquid and making it fluctuate in time and space as in Ref.…”

“…In this situation, a comparison of different models may contribute to the identification of the governing phenomena. Along this line, herein, we investigate the LGSD emerging from phase-field models that rely on an orientation field, (r,t), to describe the crystallographic orientation of the individual grains [13].…”

Capillary effects in guided crystallization of organic thin films

“…Often such information is not known for materials other than metallic alloys. 10 An improved understanding of organic semiconductor molecular interactions and ordering behavior is also beneficial for better linking processing conditions to final structures. 11 In this paper, we investigate how the rate of guided crystal growth in an initially disordered thin film along a pre-patterned two-dimensional (2D) channel of fixed width w is reduced with decreasing channel widths due to capillary effects.…”