SPAM - Science, Pizza And Mathematics

Extended phase-field crystal models of solidification

Presenter: Maik Punke

Abstract: The modeling of crystalline materials requires the resolution of microscopic details on large length and time scales to guarantee the description of lattice-dependent features as well as the dynamics of solidification. The so-called phase-field crystal (PFC) model emerged as a prominent framework to model crystalline systems [1, 2]. Indeed, it describes crystalline materials through a continuous order parameter related to the atomic number density and its dynamic at relatively large (diffusive) time scales. It describes solidification and crystal growth, including capillarity, elasticity, nucleation, and motion of defects. We discuss several extensions of the classical PFC model such as the coupling with thermal transport, enabling the description of a temperature-dependent lattice parameter [3] and the coupling with a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations [4]. We examine how those model extensions influence short- and long range behaviour of the elastic field through a wide range of test cases. Especially, we look at solidification problems in undercooled melts, grain boundary evolution for different crystal symmetries and benchmarks like the Eshelby inclusion problem. Overall, it is shown that the PFC model thanks to its extensions accurately predicts elasticity effects at the mesoscale.

[1] K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Modeling Elasticity in Crystal Growth, Physical Review Letters 88, 245701 (2002)
[2] K.R. Elder, M. Grant, Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals, Physical Review E 70, 051605 (2004)
[3] M. Punke, S. M. Wise, A. Voigt, M. Salvalaglio, Explicit temperature coupling in phase-field crystal models of solidification, Modelling and Simulation in Materials Science and Engineering 30, 074004 (2022)
[4] V. Skogvoll, M. Salvalaglio, L. Angheluta, Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks, Modelling and Simulation in Materials Science and Engineering 30, 084002 (2022)

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