324
Views
3
CrossRef citations to date
0
Altmetric
Special Issue Articles

Modeling of non-equilibrium solute diffusion upon rapid solidification: effective mobility versus kinetic energy

, , , &
Pages 1649-1657 | Received 12 Feb 2015, Accepted 17 Mar 2015, Published online: 12 Apr 2015

References

  • Herlach D. M.: ‘Non-equilibrium solidification of undercooled metallic melts’, Mater. Sci. Eng. Rep. R, 1994, R12, 177–272.
  • Hillert M.: ‘Solute drag, solute trapping and diffusional dissipation of Gibbs energy’, Acta Mater., 1999, 47, 4481–4505.
  • Wang H. F., Liu F., Zhai H. M. and Wang K.: ‘Application of the maximal entropy production principle to rapid solidification: a sharp interface model’, Acta Mater., 2012, 60, 1444–1454.
  • Steinbach I.: ‘Phase-field modelfor microstructure evolutionat the mesoscopic scale’, Annu. Rev. Mater. Res., 2013, 43, 89–107.
  • Zhang L. J., Danilova E. V., Steinbach I., Medvedev D. and Galenko P. K.: ‘Diffuse-interface modeling of solute trapping in rapid solidification: predictions of the hyperbolic phase-field model and parabolic model with finite interface dissipation’, Acta Mater., 2013, 61, 4155–4168.
  • Galenko P.: ‘Extended thermodynamical analysis of a motion of the solid–liquid interface in a rapidly solidifying alloy’, Phys. Rev. B, 2002, 65B, 144103.
  • Humadi H., Hoyt J. J. and Provatas N.: ‘Phase-field-crystal study of solute trapping’, Phys. Rev. E, 2013, 87E, 022404.
  • Sobolev S. L.: ‘Rapid solidification under local nonequilibrium conditions’, Phys. Rev. E, 1997, 55E, 6845–6854.
  • Jou D., Casas-Vázquez J. and Lebon G.: ‘Extended irreversible thermodynamics’; 2010, Berlin, Springer.
  • Sobolev S. L.: ‘Local-nonequilibrium model for rapid solidification of undercooled melts’, Phys. Lett. A, 1995, 199A, 383–386.
  • Sobolev S. L.: ‘Local non-equilibrium diffusion model for solute trapping duringrapid solidification’, Acta Mater., 2012, 60, 2711–2718.
  • Sobolev S. L.: ‘On the transition from diffusion-limited to kinetic-limited regimes of alloy solidification’, Acta Mater., 2013, 61, 7881–7888.
  • Galenko P. and Jou D.: ‘Diffuse-interface model for rapid phase transformations in nonequilibrium systems’, Phys. Rev. E, 2005, 71E, 046125.
  • Galenko P. K. and Danilov D. A.: ‘Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt’, Phys. Lett. A, 1997, 235, 271–280.
  • Galenko P. K. and Danilov D. A.: ‘Model for free dendritic alloy growth under interfacial and bulkphase nonequilibrium conditions’, J. Cryst. Growth, 1999, 197, 992–1002.
  • Galenko P.: ‘Solute trapping and diffusionless solidification in a binary system’, Phys. Rev. E, 2007, 76E, 031606.
  • Galenko P., Abramova E. V., Jou D., Danilov D. A., Lebedev V. G. and Herlach D. M.: ‘Solute trapping in rapid solidification of a binary dilute system: a phase-field study’, Phys. Rev. E, 2011, 84E, 041143.
  • Lebedev V. G., Abramova E. V., Danilov D. A. and Galenko P. K.: ‘Phase-field modeling of solute trapping comparative analysis of parabolic and hyperbolic models’, Int. J Mater. Res., 2010, 101, 473–479.
  • Galenko P. K. and Elder K. R.: ‘Marginal stability analysis of the phase field crystal model in one spatial dimension’, Phys. Rev. B, 2011, 83B, 06411.
  • Cheng M., Kundin J., Li D. and Emmerich H.: ‘Thermodynamic consistency and fast dynamics in phase-fieldcrystal modeling’, Philos. Mag. Lett., 2012, 92, 517–526.
  • Wang H. F., Kuang W. W., Xiao Z. and Liu F.: ‘A hyperbolic phase-field model for rapid solidification of a binary alloy’, J. Mater. Sci., 2015, 50, 1277–1286.
  • Wang H. F., Liu F., Ehlen G. J. and Herlach D. M.: ‘Application of the maximal entropy production principle torapid solidification: a multi-phase-field model’, Acta Mater., 2013, 61, 2617–2627.
  • Wang H. F., Galenko P. K., Zhang X., Kuang W. W., Liu F. and Herlach D. M.: ‘Phase-field modeling of an abrupt disappearance of solute drag in rapid solidification’, Acta Mater., 2015, 90, 282–291.
  • Yang Y., Humadi H., Buta D., Laird B. B., Sun D., Hoyt J. J. and Asta M.: ‘Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts’, Phys. Rev. Lett., 2011, 107, 025505.
  • Cahn J. W. and Hilliard J.: ‘Free energy of a nonuniform system. I: interface free energy’, J. Chem. Phys., 1958, 28, 258–267.
  • Aziz M. J.: ‘Model for solute redistribution during rapid solidification’, J Appl. Phys., 1982, 53, 1158–1168.
  • Aziz M. J. and Kaplan T.: ‘Continuous growth model for interface motion during alloy solidification’, Acta Metall., 1988, 36, 2335–2347.
  • Fischer F. D. and Simha N. K.: ‘Influence of material flux on the jump relations at a singular interface in a multicomponent solid’, Acta Mech., 2004, 171, 213–223.
  • Hillert M. and Rettenmayr M.: ‘Deviation from local equilibrium at migrating phaseinterfaces’, Acta Mater., 2003, 51, 2803–2809.
  • Hillert M., Odqvist J. and Ågren J.: ‘Interface conditions during diffusion-controlled phase transformations’, Scr. Mater., 2004, 50, 547–550.
  • Onsager L.: ‘Reciprocal relations in irreversible processes I’, Phys. Rev., 1930, 37, 405–426.
  • Ziegler H.: ‘An introduction to thermodynamics’; 1983, Amsterdam, North-Holland.
  • Martyushev L. M. and Seleznev V. D.: ‘Maximum entropy production principle in physics, chemistry and biology’, Phys. Rep., 2006, 426, 1–45.
  • Svoboda J. and Turek I.: ‘On diffusion-controlled evolution of closed solid-state thermodynamicsystems at constant temperature and pressure’, Philos. Mag. B, 1991, 64B, 749–759.
  • Svoboda J., Turek I. and Fischer F. D.: ‘Application of the thermodynamic extremal principle tomodeling of thermodynamic processes in material sciences’, Philos. Mag., 2005, 85, 3699–3707.
  • Svoboda J., Fischer F. D., Fratzl P. and Kroupa A.: ‘Diffusion in multi-component systems with no or dense sources and sinks for vacancies’, Acta Mater., 2002, 50, 1369–1381.
  • Fischer F. D., Svoboda J. and Petryk H.: ‘Thermodynamic extremal principles for irreversible processesin materials science’, Acta Mater., 2014, 67, 1–20.
  • Steinbach I., Zhang L. J. and Plapp M.: ‘Phase-field model with finite interface dissipation’, Acta Mater., 2012, 60, 2689–2701.
  • Zhang L. J. and Steinbach I.: ‘Phase-field model with finite interface dissipation: extension to multi-component multi-phase alloys’, Acta Mater., 2012, 60, 2702–2710.
  • Steinbach I.: ‘Phase-field models in materials science’, Modell. Simul. Mater. Sci. Eng., 2009, 17, 073001.
  • Wang H. F., Zhang X., Lai C., Kuang W. and Liu F.: ‘Thermodynamic principles for phase-field modeling of alloy solidification’, Curr. Opin. Chem. Eng., 2015, 7, 6–15.
  • Peng Z. C., Xie F. Q., Wu X. Q. and Zhang J.: ‘Study of grain refinement and eutectic transformation of undercooled IN718 superalloy’, Mater. Sci. Technol., 2013, 29, 931–936.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.