The engulfment of a precipitated particle in a saturated melt during solidification

Yutao Tao, Jeffrey J. Derby

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A rigorous, finite-element model is employed to study the engulfment of a precipitated solid particle during solidification in a saturated melt, in which solute segregation, compositional effects on melting temperature, and reaction of the solute with the particle occur. The case of a silicon carbide (SiC) particle approaching a solid–liquid interface in a silicon melt supersaturated with carbon is specifically considered. Critical engulfment velocities are computed for particles with different surface reaction rates, as characterized by the Damköhler number, a dimensionless ratio of reaction to diffusion. Consistent with prior studies, an inert particle is predicted to be less likely to be engulfed when solute effects are present. However, a particle with fast surface reaction is more likely to be engulfed than in a system without solute effects, which is likely relevant for SiC particles during silicon crystal growth. Most interestingly, a particle for which the surface reaction is characterized by a Damköhler number of order unity is predicted to never be engulfed.

Original languageEnglish (US)
Article number126400
JournalJournal of Crystal Growth
StatePublished - Jan 1 2022

Bibliographical note

Funding Information:
This work was supported in part by U.S. National Aeronautics and Space Administration, NNX10AR70G, and the U.S. National Science Foundation, CMMI-1760689. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. We acknowledge the significant input of A. Yeckel, who developed and provided support for the Cats2D code at the University of Minnesota.

Publisher Copyright:
© 2021 Elsevier B.V.


  • A1. Computer simulation
  • A1. Fluid flows
  • A1. Heat transfer
  • A2. Particle engulfment
  • B2. Multicrystalline silicon
  • B3. Solar cells


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