Advertisement

Metallurgical and Materials Transactions B

, Volume 50, Issue 6, pp 2843–2852 | Cite as

Influence of Particle Size on Apparent Diffusivity During Spark Plasma Sintering of Crystalline Powders

  • X. X. Li
  • C. YangEmail author
  • Z. Liu
  • F. Wang
  • Y. Y. Li
  • O. M. Ivasishin
Article
  • 63 Downloads

Abstract:

A theoretical framework is presented to determine an apparent diffusivity D during powder sintering and further elucidate the underlying interrelation between D and shrinkage behaviors of powders. Furthermore, to eliminate the influence of crystalline defects that are typically present in raw powders, complete crystallization of metallic glass powders is performed to allow the investigation of the influence of particle size solely on powder densification. Furthermore, to validate the framework developed, Ti40.6Zr9.4Cu37.5Ni9.4Sn3.1 crystalline alloy powders constituting particles with different sizes are examined to establish a correlation between D and the sintering behaviors of the powders. The findings show that the value of the apparent diffusivity D increases with the increasing particle size, which accelerates powder densification during spark plasma sintering. Furthermore, the results quantitatively support the argument that particle size can affect atomic diffusion during powder sintering.

Nomenclature

ρ

Relative density

ρ0

Initial relative density

H

Powder height (mm)

H0

Initial powder height (mm)

\( \dot{\rho } \)

Densification rate (s−1)

T

Time (s)

γ

Surface energy (J/m2)

L

Average particle size (μm)

ΔH/H0

Powder shrinkage

B

Geometry factor (constant)

η

Viscosity, (pa s)

P

The applied pressure (MPa)

a

Average grain size (nm)

D

Diffusivity (m2/s)

δ

Atom diameter (Å)

k

Boltzmann constant (J/K)

T

Temperature (K)

D0

Diffusion constant (m2/s)

\( Q \)

Diffusion activation energy (kJ/mol)

C

Heating rate (K/s)

\( D^{P} \)

Pressure-related diffusivity (m2/s)

\( D_{0}^{P} \)

Pressure-related diffusion constant (m2/s)

\( D_{0}^{T} \)

Total diffusion constant (m2/s)

\( \Delta T \)

The localized overheating (K)

X

Distance from the surface of a powder (μm)

R

The radius of powder particle, (μm)

I

Current (A)

\( \rho_{r} \)

Electrical resistivity (Ω cm)

\( \Delta t \)

Pulse time (s)

\( C_{V} \)

Heat capacity (J/K/mol)

\( \rho_{m} \)

Density (g/cm3)

Φ

Inner diameter of the die (mm)

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 51574128), the Guangdong Natural Science Foundation for Research Team (No. 2015A030312003), the Guangdong Application-oriented Special Funds for Science and Technology R&D (No. 2016B090931002), and the Fundamental Research Funds for the Central Universities (No. 2017PY014). We thank The Editing Team from Liwen Bianji, Edanz Editing China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript.

Supplementary material

11663_2019_1715_MOESM1_ESM.docx (131 kb)
Supplementary material 1 (DOCX 130 kb)

References

  1. 1.
    S.J.L. Kang (ed.), Sintering: Densification, Grain Growth and Microstructure, Elsevier Butterworth-Heinemann, Oxford, 2005.Google Scholar
  2. 2.
    M. Schnabel, C. Weiss, M. Canino, T. Rachow, P. Löper, C. Summonte, S. Mirabella, S. Janz, P.R. Wilshaw: Appl. Phys. Lett., 2014, vol. 104, pp. 213108–213122.CrossRefGoogle Scholar
  3. 3.
    Z.A. Munir, U. Anselmi-Tamburini, M. Ohyanagi: J. Mater. Sci., 2006, vol. 41, pp. 763-777.CrossRefGoogle Scholar
  4. 4.
    Z.H. Zhang, Z.F. Liu, J.F. Lu, X.B. Shen, F.C. Wang, Y.D. Wang: Scr. Mater., 2014, vol. 81, pp. 56-59.CrossRefGoogle Scholar
  5. 5.
    L.H. Liu, C. Yang, Y.G. Yao, F. Wang, W.W. Zhang, Y. Long, Y.Y. Li: Intermetallics., 2015, vol. 66, pp. 1-7.CrossRefGoogle Scholar
  6. 6.
    R.T. Li, Z.L. Dong, K.A. Khor: Scr. Mater., 2016, vol. 144, pp. 88-92.CrossRefGoogle Scholar
  7. 7.
    7. Z. Trzaska, G. Bonnefont, G. Fantozzi, J.-P. Monchoux: Acta Mater., 2017, vol. 135, pp. 1-13.CrossRefGoogle Scholar
  8. 8.
    C. Yang, M.D. Zhu, X. Luo, L.H. Liu, W.W. Zhang, Y. Long, Z.Y. Xiao, Z.Q. Fu, L.C. Zhang, E.J. Lavernia: Scr. Mater., 2017, vol. 139, pp. 96-99.CrossRefGoogle Scholar
  9. 9.
    Z. Trzaska, A. Couret, J.-P. Monchoux: Acta Mater., 2016, vol. 118, pp. 100-108.CrossRefGoogle Scholar
  10. 10.
    J.E. Alaniz, A.D. Dupuy, Y. Kodera, J.E. Garay: Scr. Mater., 2014, vol. 92, pp. 7-10.CrossRefGoogle Scholar
  11. 11.
    T. Paul, S.P. Harimkar: Scr. Mater., 2017, vol. 126, pp. 37-40.CrossRefGoogle Scholar
  12. 12.
    S. Xie, R. Li, T. Yuan, M. Zhang, M. Wang, H. Wu, F. Zeng: Scr. Mater., 2018, vol. 149, pp. 125-128.CrossRefGoogle Scholar
  13. 13.
    V.V. Dabhade, T.R.R. Mohan, P. Ramakrishnan: Mater. Res. Bull., 2007, vol. 42, pp. 1262-1268.CrossRefGoogle Scholar
  14. 14.
    N. Chawake, P. Ghosh, L. Raman, A.K. Srivastav, T. Paul, S.P. Harimkar, J. Eckert, R.S. Kottada: Scr. Mater., 2019, vol. 161, pp. 36-39.CrossRefGoogle Scholar
  15. 15.
    X. Song, X. Liu, J. Zhang: J. Am. Ceram. Soc., 2006, vol. 89, pp. 494-500.CrossRefGoogle Scholar
  16. 16.
    S. Diouf, A. Molinari: Powder Technol., 2012, vol. 221, pp. 220-227.CrossRefGoogle Scholar
  17. 17.
    C. Yang, Y.J. Zhao, L.M. Kang, D.D. Li, W.W. Zhang, L.C. Zhang: Mater. Lett., 2018, vol. 210, pp. 169-172.CrossRefGoogle Scholar
  18. 18.
    M.B. Shongwe, M.M. Ramakokovhu, S. Diouf, M.O. Durowoju, B.A. Obadele, R. Sule, M.L. Lethabane, P.A. Olubambi: J. Alloy. Compd., 2016, vol. 678, pp. 241-248.CrossRefGoogle Scholar
  19. 19.
    Z. Zhang, F. Wang, L. Wang, S. Li, S. Osamu: Mater. Lett., 2008, vol. 62, pp. 3987-3990.CrossRefGoogle Scholar
  20. 20.
    T. Paul, N. Chawake, R.S. Kottada, S.P. Harimkar: J. Alloy. Compd., 2018, vol. 738, pp. 10-15.CrossRefGoogle Scholar
  21. 21.
    S. Decker, S. Martin, L. Krüger: Metall. Mater. Trans. A, 2015, vol. 47, pp. 170-177.Google Scholar
  22. 22.
    P. Heitjans, J. Kärger (ed.), Diffusion in Condensed Matter, Springer Verlag, Berlin Heidelberg, 2005.Google Scholar
  23. 23.
    A. Inoue: Acta Mater., 2000, vol. 48, pp. 279-306.CrossRefGoogle Scholar
  24. 24.
    H. Zhu, R.S. Averback: Mater. Sci. Eng. A, 1995, vol. 204, pp. 96-100.CrossRefGoogle Scholar
  25. 25.
    R.S. Averback, H. Zhu, R. Tao, H. Hofler, in: D.L. Bourell (Ed.), Synthesis and Processing of Nanocrystalline Powder, TMS, Warrendale, 1996, p. 203.Google Scholar
  26. 26.
    S.Y. Gómez, D. Hotza: J. Eur. Ceram. Soc, 2018, vol. 38, pp. 1736-1741.CrossRefGoogle Scholar
  27. 27.
    V.V. Dabhade, T.R. Mohan, P. Ramakrishnan: Mater. Sci. Eng. A, 2007, 452-453, 386-394.CrossRefGoogle Scholar
  28. 28.
    J.R. Groza, C.C. Koch (Ed.), Nanostructured Materials: Processing, Properties and Applications, Noyes Publication, New York, 2002, pp. 123–124.CrossRefGoogle Scholar
  29. 29.
    Q. Chen, C.Y. Tang, K.C. Chan, L. Liu: J. Alloy. Compd., 2013, vol. 557, pp. 98-101.CrossRefGoogle Scholar
  30. 30.
    X.X. Li, C. Yang, T. Chen, Z.Q. Fu, Y.Y. Li, O.M. Ivasishin, E.J. Lavernia: Scr. Mater., 2018, vol. 151, pp. 47-52.CrossRefGoogle Scholar
  31. 31.
    J. Frenkel: J. Phys., 1945, vol. 9, pp. 385-391.Google Scholar
  32. 32.
    X.X. Li, C. Yang, T. Chen, Z.Q. Fu, Y.Y. Li, O.M. Ivasishin, E.J. Lavernia: Materialia., 2019, vol. 6, pp. 100334–100338.CrossRefGoogle Scholar
  33. 33.
    A. Antonelli, J. Bernholc: Phys. Rev. B., 1989, vol. 40, pp. 10643–10646.CrossRefGoogle Scholar
  34. 34.
    B.Y. Pines: J. Techn. Physics., 1946, vol. 16, p.737.Google Scholar
  35. 35.
    P.Y. Huang (ed.), Principle of Power Metallurgy, Metallurgical industry press, Beijing, 2008.Google Scholar
  36. 36.
    X.X. Li, C. Yang, H.Z. Lu, X. Luo, Y.Y. Li, O.M. Ivasishin: J. Alloy. Compd., 2019, vol. 787, pp. 112-122.CrossRefGoogle Scholar
  37. 37.
    R.M. German (ed.), Sintering Theory and Practice, Wiley, New York, 1996.Google Scholar
  38. 38.
    38. V.A. Khonik, N.P. Kobelev: Phys. Rev. B, 2008, vol. 77, pp. 133203–133205.CrossRefGoogle Scholar
  39. 39.
    L.M. Kang, C. Yang: Adv. Eng. Mater., 2019, https://doi.org/10.1002/adem.201801359CrossRefGoogle Scholar
  40. 40.
    T. Paul, S.P. Harimkar: J. Phys. D: Appl. Phys., 2017, 50, pp. 27LT01–27LT04CrossRefGoogle Scholar
  41. 41.
    M. Köppers, C. Herzig, M. Friesel, Y. Mishin: Acta Mater., 1997, vol. 45, pp. 4181-4191.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • X. X. Li
    • 1
    • 2
  • C. Yang
    • 1
    • 2
    Email author
  • Z. Liu
    • 1
  • F. Wang
    • 1
  • Y. Y. Li
    • 3
  • O. M. Ivasishin
    • 4
  1. 1.National Engineering Research Center of Near-Net-Shape Forming for Metallic MaterialsSouth China University of TechnologyGuangzhouP.R. China
  2. 2.Guangdong Key Laboratory for Processing and Forming of Advanced Metallic MaterialsSouth China University of TechnologyGuangzhouP.R. China
  3. 3.School of Material Science and EngineeringHuazhong University of Science and TechnologyWuhanP.R. China
  4. 4.Institute for Metal PhysicsKievUkraine

Personalised recommendations