Non-equilibrium Thermodynamical Description of Superfluid Transition in Liquid Helium

Since the growth velocity can be comparable with or even larger than the solute diffusion velocity in the bulk phases, modeling of rapid solidification with non-equilibrium solute diffusion becomes quite an important topic. In this paper, an effective mobility approach was proposed to derive the current phase field model (PFM). In contrast with the previous PFMs that were derived by the so-called kinetic energy approach, diffusionless solidification happens not only in the bulk phases but also inside the interface when the growth velocity is equal to the solute diffusion velocity in liquid. A good agreement between the model predictions and experimental results is obtained for rapid solidification of Si-9at.%As alloy.

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Thermodynamic Model Formulations for Inhomogeneous Solids with Application to Non-isothermal Phase Field Modelling

Journal of Non-Equilibrium Thermodynamics ◽

10.1515/jnet-2015-0062 ◽

2016 ◽

Vol 41 (2) ◽

Cited By ~ 1

Author(s):

Svyatoslav Gladkov ◽

Julian Kochmann ◽

Stefanie Reese ◽

Markus Hütter ◽

Bob Svendsen

Keyword(s):

Phase Field ◽

Thermodynamic Model ◽

Field Model ◽

Phase Field Model ◽

Antiphase Boundary ◽

Diffuse Interface ◽

Equilibrium Thermodynamics ◽

Field Methods ◽

Macroscopic Theory ◽

Non Equilibrium

AbstractThe purpose of the current work is the comparison of thermodynamic model formulations for chemically and structurally inhomogeneous solids at finite deformation based on “standard” non-equilibrium thermodynamics [SNET: e. g. S. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, 1962] and the general equation for non-equilibrium reversible–irreversible coupling (GENERIC) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley Interscience, 2005]. In the process, non-isothermal generalizations of standard isothermal conservative [e. g. J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial energy. J. Chem. Phys. 28 (1958), 258–267] and non-conservative [e. g. S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979), 1085–1095; A. G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983] diffuse interface or “phase-field” models [e. g. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Modern Phys. 49 (1977), 435–479; N. Provatas and K. Elder, Phase Field Methods in Material Science and Engineering, Wiley-VCH, 2010.] for solids are obtained. The current treatment is consistent with, and includes, previous works [e. g. O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D 43 (1990), 44–62; O. Penrose and P. C. Fife, On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field model. Phys. D 69 (1993), 107–113] on non-isothermal systems as a special case. In the context of no-flux boundary conditions, the SNET- and GENERIC-based approaches are shown to be completely consistent with each other and result in equivalent temperature evolution relations.

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