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Investigating nucleation using the phase-field method

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journal contribution
posted on 03.11.2017 by Frigyes Podmaniczky, Gyula Toth, Tamas Pusztai, Laszlo Granasy
The first order phase transitions, like freezing of liquids, melting of solids, phase separation in alloys, vapor condensation, etc., start with nucleation, a process in which internal fluctuations of the parent phase lead to formation of small seeds of the new phase. Owing to different size dependence of (negative) volumetric and (positive) interfacial contributions to work of formation of such seeds, there is a critical size, at which the work of formation shows a maximum. Seeds that are smaller than the critical one decay with a high probability, while the larger ones have a good chance to grow further and reach a macroscopic size. Putting it in another way, to form the bulk new phase, the system needs to pass a thermodynamic barrier via thermal fluctuations. When the fluctuations of the parent phase alone lead to transition, the process is called homogeneous nucleation. Such a homogeneous process is, however, scarcely seen and requires very specific conditions in nature or in the laboratory. Usually, the parent phase resides in a container and/or it incorporates floating heterogeneities (solid particles, droplets, etc.). The respective foreign surfaces lead to ordering of the adjacent liquid layers, which in turn may assist the formation of the seeds, a process termed heterogeneous nucleation. Herein, we review how the phase-field techniques contributed to the understanding of various aspects of crystal nucleation in undercooled melts, and its role in microstructure evolution. We recall results achieved using both conventional phase-field techniques that rely on spatially averaged (coarse grained) order parameters in capturing the phase transition, as well as molecular scale phase-field approaches that employ time averaged fields, as happens in the classical density functional theories, including the recently developed phase-field crystal models.

Funding

This work has been supported by National Agency for Research, Development, and Innovation (NKFIH), Hungary under contract No. OTKA-K-115959, by the EU FP7 Collaborative Project “EXOMET” (contract no. NMP-LA-2012–280421, co-funded by ESA), and by the ESA MAP/PECS projects “MAGNEPHAS III” (ESTEC Contract No. 40000110756/11/NL/KML) and “GRADECET” (ESTEC Contract No. 40000 110759/11/NL/KML).

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of the Indian Institute of Science

Volume

96

Issue

3

Pages

161 - 178

Citation

PODMANICZKY, F. ...et al., 2016. Investigating nucleation using the phase-field method. Journal of the Indian Institute of Science, 96(3), pp. 161- 178.

Publisher

© Indian Institute of Science

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

This paper was published in the Journal of the Indian Institute of Science and the definitive version can be found: http://journal.library.iisc.ernet.in/index.php/iisc/article/view/4618

ISSN

0019-4964

Language

en

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