Skip to main content
SpringerLink
Log in

The evolution of microcrystalline structures in supercooled metal powders

  • Published:
Metallurgical Transactions A Aims and scope Submit manuscript

Abstract

A numerical model has been developed to study the relative effects of nucleation and growth kinetics on the evolution of ultrafine grain structures observed in some supercooled metal powders. The thermal history during solidification is analyzed using a Newtonian heat transfer formulation coupled to classical models for homogeneous nucleation and continuous growth with a diffuse interface. The results indicate that decreasing particle size increases both the supercooling prior to solidification and the thermal excursion beyond the nucleation temperature. After the first nucleus appears, a compctition is established between the formation of new nuclei and the growth of the existing one(s). There is a range of particle sizes in which the achievable supercoolings are high enough to produce massive nucleation before any significant growth—and the ensuing recalescence—can take place. The probability of multiple nucleation may be evaluated from a dimensionless parameter combining the characteristic frequencies of the nucleation, growth, and heat transfer processes at the moment of nucleation. Calculations for Al and Ni model systems confirm the experimental observation that the latter has a stronger tendency to supercool and develop microcrystalline structures.

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

Similar content being viewed by others

Abbreviations

a :

atomic diameter

C :

molar heat capacity

d x :

grain size

D :

diffusion coefficient

E v :

activation energy for viscous flow

f :

fraction solid

H :

molar enthalpy relative to the solid atT M ,H SM 0

ΔH M :

molar heat of fusion

h :

heat transfer coefficient between the droplet and the environment

h P :

Planck's constant

I :

nucleation rate integrated over time

J :

nucleation frequency, taken as homogeneous

k B :

Boltzmann's constant

N :

number of nuclei or grains in a polycrystalline powder

N A :

Avogadro's number

R :

gas constant

r 0 :

radius of droplet or powder

T :

temperature

T G :

temperature of cooling environment

T g :

glass transition temperature

T M :

melting temperature

T N :

nucleation temperature

T r :

reduced temperature,T/T M

T :

cooling rate

ΔT :

bath supercooling

ΔT :

kinetic supercooling

ΔT H :

characteristic supercooling to hypercool the liquid, ΔM/CL

ΔT r :

reduced supercooling, ΔT/TM

t :

time

V :

interface velocity

V G :

gas/particle relative velocity

α :

thermal diffusivity

β :

kinetic parameter reflecting the ease of interfacial rearrangement

ε :

emissivity

η :

viscosity of the liquid metal

υ :

kinematic viscosity

γ :

solid-liquid interfacial energy

ρ :

Stefan-Boltzmann's constant

Ω :

molar volume

References

  1. P. Joly and R. Mehrabian:J. Mater. Sci., 1974, vol. 9, pp. 1446–55.

    Article  CAS  Google Scholar 

  2. S. R. Coriell and R. F. Sekerka: inRapid Solidification Processing, Principles and Technologies II, R. Mehrabian, B.H. Kear, and M. Cohen, eds., Claitor's Publishing Division, Baton Rouge, LA, 1980, pp. 35–49.

    Google Scholar 

  3. W. J. Boettinger, S. R. Coriell, and R. K. Trivedi: inRapid Solidification Processing, Principles and Technologies IV, Proceedings of a Conference at the University of California, Santa Barbara, CA, Dec. 15-18, 1986, in press.

  4. T. Z. Kattamis and R. Mehrabian:J. Vac. Sci. Technol., 1974, vol. 11, pp. 1118–22.

    Article  CAS  Google Scholar 

  5. T. Z. Kattamis:J. Crystal Growth, 1976, vol. 34, pp. 215–20.

    Article  CAS  Google Scholar 

  6. H. Jones:Rep. Prog. Phys., 1973, vol. 36, p. 1425.

    Article  CAS  Google Scholar 

  7. J. J. Valencia, C. G. Levi, and R. Mehrabian: inProcessing of Structural Metals by Rapid Solidification, F. H. Froes and S. J. Savage, eds., ASM INTERNATIONAL, Metals Park, OH, 1987, pp. 1–12.

    Google Scholar 

  8. P. Ramachandrarao, M.G. Scott, and G.A. Chadwick:Phil. Mag., 1972, vol. 25, p. 961.

    Article  CAS  Google Scholar 

  9. R. D. Field, E. H. Aigeltinger, and H. L. Fraser: inRapid Solidification Processing, Principles and Technologies II, R. Mehrabian, B.H. Kear, and M. Cohen, eds., Claitor's Publishing Division, Baton Rouge, LA, 1980, pp. 93–99.

    Google Scholar 

  10. C. G. Levi and R. Mehrabian:Metall. Trans. A, 1982, vol. 13A, pp. 13–23.

    CAS  Google Scholar 

  11. O. Salas: M.S. Thesis, University of California, Santa Barbara, CA, 1987.

    Google Scholar 

  12. L. A. Bendersky and S. D. Ridder:J. Mater. Res., 1986, vol. 1, pp. 405–14.

    CAS  Google Scholar 

  13. J. P. Hirth:Metall. Trans. A, 1978, vol. 9A, pp. 401–04.

    CAS  Google Scholar 

  14. P. G. Boswell and G. A. Chadwick:Scripta Metall., 1977, vol. 11, pp. 459–65.

    Article  CAS  Google Scholar 

  15. H. Reiss and J. L. Katz: inRapid Solidification Processing, Principles and Technologies, R. Mehrabian, B.H. Kear, and M. Cohen, eds., Claitor's Pub. Div., Baton Rouge, LA, 1978, pp. 64–77.

    Google Scholar 

  16. T.W. Clyne:Metall. Trans. B, 1984, vol. 15B, pp. 369–81.

    Article  CAS  Google Scholar 

  17. W. J. Boettinger and J. H. Perepezko: inRapidly Solidified Crystalline Alloys, S.K. Das, B.H. Kear, and C. M. Actam, eds., TMS- AIME, Warrendale, PA, 1985, pp. 21–58.

    Google Scholar 

  18. K. N. Ishihara, M. Maeda, and P.H. Shingu:Acta Metall., 1985, vol. 33, pp. 2113–17.

    Article  CAS  Google Scholar 

  19. J. H. Perepezko, B. A. Mueller, and K. Ohsaka: inUndercooled Alloy Phases, E. W. Collings and C. C. Koch, eds., TMS-AIME, Warrendale, PA, 1986, pp. 289–320.

    Google Scholar 

  20. C. G. Levi and R. Mehrabian: inUndercooled Alloy Phases, E. W. Collings and C. C. Koch, eds., TMS-AIME, Warrendale, PA, 1986, pp. 345–74.

    Google Scholar 

  21. M. Cohen, B.H. Kear, and R. Mehrabian: inRapid Solidification Processing, Principles and Technologies II, R. Mehrabian, B.H. Kear, and M. Cohen, eds., Claitor's Publishing Division, Baton Rouge, LA, 1980, pp. 1–23.

    Google Scholar 

  22. G. Horvay: inProc. 4th National Congress of Applied Mechanics, ASME, 1962, p. 1315.

  23. J. L. Walker:Trans. Vacuum Met. Conf., American Vacuum Soc.iety, 1963.

  24. R. Mehrabian: inRapid Solidification Processing, Principles and Technologies, R. Mehrabian, B.H. Kear, and M. Cohen, eds., Claitor's Publishing Division, Baton Rouge, LA, 1978, pp. 9–27.

    Google Scholar 

  25. G. H. Geiger and D. R. Poirier:Transport Phenomena in Metallurgy, Addison Wesley, Reading, MA, 1980.

    Google Scholar 

  26. D. Turnbull and J. C. Fisher:J. Chem. Phys., 1949, vol. 17, p. 71.

    Article  CAS  Google Scholar 

  27. J. W. Christian:The Theory of Transformations in Metals and Alloys, 2nd ed., Pergamon Press, Oxford, U.K., 1975, ch. 10.

    Google Scholar 

  28. D. Turnbull:Contemp. Phys., 1969, vol. 10, p. 473.

    Article  CAS  Google Scholar 

  29. F. Spaepen:Acta Metall., 1975, vol. 23, pp. 729–43.

    Article  CAS  Google Scholar 

  30. D. Turnbull:J. Appl. Phys., 1950, vol. 21, p. 1022.

    Article  CAS  Google Scholar 

  31. R. T. Beyer and E. M. Ring: inLiquid Metals: Chemistry and Physics, S. Z. Beer, ed., Marcel Dekker, Inc., New York, NY, 1972, p. 450.

    Google Scholar 

  32. D. Turnbull:Metall. Trans. B, 1981, vol. 12B, pp. 217–29.

    Article  CAS  Google Scholar 

  33. J. W. Cahn, W.B. Hillig, and G. W. Sears:Acta Metall., 1964, vol. 12, pp. 1421–39.

    Article  CAS  Google Scholar 

  34. N. Eustathopoulos, L. Courdurier, J. C. Joud, and P. Desdre:J. Crystal Growth, 1976, vol. 33, pp. 105–15.

    Article  CAS  Google Scholar 

  35. C. G. Levi:Metall. Trans. A, 1988, vol. 19A, pp. 687–97.

    CAS  Google Scholar 

  36. J. Perel, J. F. Mahoney, S. Taylor, Z. Shanfield, and C. G. Levi: inRapid Solidification Processing, Principles and Technologies III, R. Mehrabian, ed., National Bureau of Standards, 1982, pp. 458-63.

Download references

Author information

Authors and Affiliations

  1. Materials Department and Department of Mechanical and Environmental Engineering, University of California, 93106, Santa Barbara, CA

    Carlos G. Levi (Assistant Professor)

Authors
  1. Carlos G. Levi
    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

Levi, C.G. The evolution of microcrystalline structures in supercooled metal powders. Metall Trans A 19, 699–708 (1988). https://doi.org/10.1007/BF02649284

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02649284

Keywords

Search

Navigation