Skip to main content
SpringerLink
Log in

Reduced critical solidification front velocity of particle engulfment due to an interface active solute in the liquid metal

  • Communications
  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Abbreviations

a :

atomic diameter of the liquid atoms (m)

h 0 :

the smallest separation between the solidification front and the particle (Eq. [5]) (m)

k :

distribution coefficient of the solute [wt pct solid/wt pct liquid]

k ML :

the numerical coefficient of the Mukai and Lin equation (Eq. [6a])

m :

semiempirical coefficient used in Eq. [9] (J/m2)

n :

semiempirical coefficient used in Eq. [9] (1/wt pct)

v :

velocity of the interface (m/s)

v cr :

critical interface velocity of engulfment (Eq. [13]) (m/s)

v /0 cr :

standard critical interface velocity of engulfment at Mu = 0 (Eq. [1] (m/s))

x :

direction measured perpendicular to the originally planar solidification front, toward the liquid metal, through the center of the particle (Fig. 1)

C :

concentration of the solute in the liquid metal as function of parameter x (wt pct) (at x → 0, C → C o/k)

C 0 :

bulk concentration of the solute in liquid metal far from the solidification front (wt pct)

D :

diffusion coefficient of the interface active solute in the liquid metal (m2/s)

F σ :

interfacial force (N)

F grad :

interfacial gradient force (N)

F drag :

drag force (N)

MMC:

metal matrix composites

Mu :

dimensionless number (the Mukai number) defined by Eq. [12], being the ratio of the interfacial gradient force to the drag force near the interface and determining (among other things) the correction to the critical velocity of PET due to the solute field

PET:

pushing engulfment transition

R :

radius of the spherical particle (m)

R i :

radius of curvature of the solid-liquid interface in the “shadow” of the particle (m)

V :

molar volume of the liquid metal (m3/mol)

α = R/R i :

the ratio of the radii of the particle and the interface (m/m)

η :

dynamic viscosity of the liquid metal (Pa · s)

σ jk :

interfacial energy between phases j and k (J/m2)

σ /0 cl :

the ceramic/liquid metal interfacial energy at C = 0 (Eq. [9])

Δσ :

a complex quantity, proportional to the interfacial force F σ (Eqs. [3] and [A1]) (J/m2)

Θ:

contact angle of the liquid metal on the ceramic (deg)

c :

solid ceramics

cr :

critical

i :

interface

j, k :

general numbering of phases

l :

liquid metal

s :

solid metal

v :

vacuum or vapor

References

  1. G. Kaptay: Metall. Mater. Trans. A, 2001, vol. 32A, pp. 993–1006.

    CAS  Google Scholar 

  2. A.A. Chernov and D.E. Temkin: in 1976 Crystal Growth and Materials, E. Kaldis and H.J. Scheel, eds., North Holland Publ. Co., Amsterdam, Holland, 1977, pp. 3–77.

    Google Scholar 

  3. D.M. Stefanescu, F.R. Juretzko, B.K. Dhindaw, A. Catalina, S. Sen, and P.A. Curreri: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 1697–1706.

    Article  CAS  Google Scholar 

  4. K. Mukai and W. Lin: Tetsu-to-Hagané, 1994, vol. 80, pp. 527–32.

    CAS  Google Scholar 

  5. Z. Wang, K. Mukai, and I.J. Lee: Iron Steel Inst. Jpn. Int., 1999, vol. 39, pp. 553–62.

    CAS  Google Scholar 

  6. G. Kaptay and K.K. Kelemen: Iron Steel Inst. Jpn. Int., 2001, vol. 41, pp. 305–07.

    CAS  Google Scholar 

  7. K. Mukai, Z. Wang, and W. Lin: Iron Steel Inst. Jpn. Int. 2001, vol. 41, pp. 308–10.

    CAS  Google Scholar 

  8. W. Kurz and D.J. Fisher: Fundamentals of Solidification, Trans Tech Publications Ltd., Aedermannsdorf, Switzerland, 1989.

    Google Scholar 

  9. K. Mukai and W. Lin: Tetsu-to-Hagane, 1994, vol. 80, pp. 533–38.

    CAS  Google Scholar 

  10. Y. Waseda and W.A. Miller: Trans. JIM, 1978, vol. 19, pp. 546–52.

    CAS  Google Scholar 

  11. T. Iida and R.I.L. Guthrie: Physical Properties of Liquid Metals, Clarendon Press, Oxford, U.K., 1993.

    Google Scholar 

  12. W.D. Kingery: J. Amer. Cer. Soc., 1942, vol. 37, pp. 42–45.

    Article  Google Scholar 

  13. G. Kaptay, E. Báder, and L. Bolyán: Mater. Science Forum, 2000, vols. 329–330, pp. 151–56.

    Article  Google Scholar 

  14. H. Shibata, H. Yin, S. Yoshinaga, T. Emi, and M. Suzuki: Iron Steel Inst. Jpn. Int., 1998, vol. 38, pp. 149–56.

    CAS  Google Scholar 

  15. S. Kimura, Y. Nabeshima, K. Nakajima, and S. Mizoguchi: Metall. Mater. Trans. A, 2000, vol. 31B, pp. 1013–21.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physical Chemistry, University of Miskolc, Miskolc, Hungary

    G. Kaptay (Professor and Head Dean)

  2. Faculty of Materials and Metallurgical Engineering, University of Miskolc, Miskolc, Hungary

    G. Kaptay (Professor and Head Dean)

Authors
  1. G. Kaptay
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kaptay, G. Reduced critical solidification front velocity of particle engulfment due to an interface active solute in the liquid metal. Metall Mater Trans A 33, 1869–1873 (2002). https://doi.org/10.1007/s11661-002-0198-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-002-0198-y

Keywords

Search

Navigation