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The Effect of Undercooling on Solidification of YSZ Splats

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Abstract

We consider the rapid solidification of a molten YSZ particle, by solving the so-called hyperbolic equations for heat and mass transfer. The hyperbolic model predicts the interface undercooling (due to thermal and solutal effects) and velocity as a function of time, as well as the yttria redistribution within the solid phase. Results are then compared to corresponding ones that we obtained from a parabolic model, to assess the extent to which YSZ solidification is influenced by nonequilibrium effects. Results indicate that these effects are limited to the early part of the solidification process when undercooling is most significant. At this stage, the interface velocity is unsteady, and solute redistribution is most evident. As solidification decelerates, the nonequilibrium effects wane and solidification can then be properly modeled as an equilibrium process.

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Abbreviations

C :

concentration (wt.%)

C 0 :

initial concentration (wt.%)

C p :

specific heat capacity (J kg−1 K−1)

b :

splat thickness (m)

D :

mass diffusivity (m2 s−1)

h :

heat transfer coefficient (W m−2 K−1)

J C :

concentration flux (wt.% m s−1)

k f :

nonequilibrium partition coefficient

k e :

equilibrium partition coefficient

m :

slope of nonequilibrium liquidus (K wt.%−1)

m e :

slope of equilibrium liquidus (K wt.%−1)

Q :

latent heat of solidification (J kg−1)

T :

temperature (K)

T m :

equilibrium melting temperature (K)

T 0 :

initial temperature (K)

V D :

mass diffusion velocity (m s−1)

V i :

interface velocity (m s−1)

α:

thermal diffusivity (m2 s−1)

κ:

thermal conductivity (W m−1 K−1)

μ:

linear kinetics coefficient (m s−1 K−1)

ρ:

density (kg m−3)

τ:

relaxation time (s)

i:

interface

j:

solid or liquid phase

−:

liquid interface

 + :

solid interface

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering and Centre for Advanced Coating Technologies, University of Toronto, 5 King’s College Road, Toronto, ON, Canada, M5S 3G8

    Haibo Liu, Markus Bussmann & Javad Mostaghimi

Authors
  1. Haibo Liu
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  2. Markus Bussmann
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  3. Javad Mostaghimi
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Corresponding author

Correspondence to Markus Bussmann.

Additional information

This article is an invited paper selected from presentations at the 2008 International Thermal Spray Conference and has been expanded from the original presentation. It is simultaneously published in Thermal Spray Crossing Borders, Proceedings of the 2008 International Thermal Spray Conference, Maastricht, The Netherlands, June 2-4, 2008, Basil R. Marple, Margaret M. Hyland, Yuk-Chiu Lau, Chang-Jiu Li, Rogerio S. Lima, and Ghislain Montavon, Ed., ASM International, Materials Park, OH, 2008.

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Liu, H., Bussmann, M. & Mostaghimi, J. The Effect of Undercooling on Solidification of YSZ Splats. J Therm Spray Tech 17, 646–654 (2008). https://doi.org/10.1007/s11666-008-9238-5

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  • DOI: https://doi.org/10.1007/s11666-008-9238-5

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