Skip to main content
Book cover

Approximation and Computation pp 409–424Cite as

Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to Gravity-Induced Skeletal Settling

Part of the Springer Optimization and Its Applications book series (SOIA,volume 42)

Abstract

In this paper we will investigate numerically densification due to gravity-induced skeletal settling during liquid phase sintering. For domain definition we will use small identical cubic elements, voxels, of finite size. Solid skeleton formation will be introduced by defining skeleton units and by their time evolution and formation of large solid skeleton arranged in a long chain of connected solid-phase domains. As it will be assumed that under gravity condition Stokes’s law settling usually dominates microstructure formation, the settling procedure as well as the settling time will be used for computation of average migration distance during a given time interval. Thus, gravity-induced solid-phase domain evolution will be simulated by simultaneous computation of the displacement of the center of the mass and mass transport due to dissolution and precipitation at the interfaces between solid-phase domains and liquid matrix. The new methodology will be applied to the simulation of microstructural evolution of a regular multidomain model.

Keywords

  • Liquid Phase Sinter
  • Normal Gravity
  • Solid Skeleton
  • Liquid Matrix
  • Microgravity Environment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-1-4419-6594-3_27
  • Chapter length: 16 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-6594-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)
Hardcover Book
USD   109.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ardell, A.J.: The effect of volume fraction on particle coarsening: Theoretical considerations. Acta Metall. 20, 61–71 (1972)

    CrossRef  Google Scholar 

  2. Cocks, A.C.F., Gill, S.P.: A variational approach to two dimensional grain growth - I. Theory. Acta Mater. 44 [12], 4765–4775 (1996)

    Google Scholar 

  3. Courtney, T.H.: Microstructural evolution during liquid phase sintering: Part I. Development of microstructure. Metall. Trans. 8A, 679–684 (1977)

    CrossRef  Google Scholar 

  4. Courtney, T.H.: Gravitational effects on microstructural development in liquid phase sintered materials. Scripta Mater. 35 [5], 567–571 (1996)

    Google Scholar 

  5. Dehoff, R.T.: A geometrically general theory of diffusion controlled coarsening. Acta Metall 39 [10], 2349–2360 (1991)

    Google Scholar 

  6. Freundlich, H.: Kapillarchemie. Leipzig (1922)

    Google Scholar 

  7. German, R.M., Liu, Y.: Grain agglomeration in liquid phase sintering. J. Mater. Sci. Engng. 4, 23–34 (1996)

    Google Scholar 

  8. Greenwood, G.W.: The growth of dispersed precipitates in solutions. Acta Metall. 4, 243–248 (1956)

    CrossRef  Google Scholar 

  9. Hansen, M., Anderko, K.: Constitution of Binary Alloys. McGraw-Hill, New York (1958)

    Google Scholar 

  10. Heaney, D.F., German, R.M., Ahn, I.S.: The gravitational effects on low solid-volume fraction liquid-phase sintering. J. Mater. Sci. 30, 5808–5812 (1995)

    CrossRef  Google Scholar 

  11. Huppmann, W.J., Petzow, G.: The role of grain and phase boundaries in liquid phase sintering. Ber. Bunsenges. Phys. Chem. 82, 308–312 (1978)

    Google Scholar 

  12. Kipphut, C.M., Bose, A., Farooq, S., German, R.M.: Gravity and configurational energy induced microstructural changes in liquid phase sintering. Metall. Trans. A, 19A, 1905–1913 (1988)

    Google Scholar 

  13. Lifshitz, I.M., Slyozov, V.V.: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids. 119 [12], 35–50 (1961)

    Google Scholar 

  14. Liu, Y., Heaney, D.F., German, R.M.: Gravity induced solid grain packing during liquid phase sintering. Acta Metall. Mater. 43, 1587–1592 (1995)

    CrossRef  Google Scholar 

  15. Marder, M.: Correlations and droplet growth. Phys. Rev. Lett. 55, 2953–2956 (1985)

    CrossRef  Google Scholar 

  16. Niemi, A.N., Courtney, T.H.: Settling in solid–liquid systems with specific application to liquid phase sintering. Acta Metall. 31 [9], 1393–1401 (1983)

    Google Scholar 

  17. Nikolić, Z.S.: Computer simulation of grain growth by grain boundary migration during liquid phase sintering. J. Mater. Sci. 34 [4], 783–794 (1999)

    Google Scholar 

  18. Nikolić, Z.S.: Liquid phase sintering – I. Computer study of skeletal settling and solid phase extrication in normal gravity environment. Science of Sintering 40, 3–12 (2008)

    Google Scholar 

  19. Nikolić, Z.S.: Liquid phase sintering – II. Computer study of skeletal settling and solid phase extrication in microgravity environment. Sci. Sintering 40, 107–116 (2008)

    Google Scholar 

  20. Nikolić, Z.S.: Numerical simulation of gravity induced skeletal settling during liquid phase sintering. Math. Comp. Model. 51, 1146–1153 (2010)

    CrossRef  Google Scholar 

  21. Ono, Y., Shigematsu, T.: Diffusion of Vanadium, Cobalt, and Molybdenum in molten Iron. J. Jpn. Inst. Met. 41, 62–68 (1977)

    Google Scholar 

  22. Saetre, T.O., Ryum, N.: Dynamic simulation of grain boundary migration. J. Sci. Comp. 3, 189–199 (1988)

    CrossRef  Google Scholar 

  23. Taylor, J.E.: II-mean curvature and weighted mean curvature. Acta Metall. Mater. 40 [7], 1475–1485 (1992)

    Google Scholar 

  24. Tewari, A., Gokhale, A.M., German, R.M.: Effect of gravity on three-dimensional coordination number distribution in liquid phase sintered microstructures. Acta Mater. 47 [13], 3721–3734 (1999)

    Google Scholar 

  25. Tewari, A., Gokhale, A.M.: Application of three-dimensional digital image processing for reconstruction of microstructural volume from serial sections. Mater. Charact. 44, 259–269 (2000)

    CrossRef  Google Scholar 

  26. Voorhees, P.W., Glicksman, M.E.: Solution to the multi-particle diffusion problem with applications to Ostwald ripening – I. Theory. Acta Metall 32 [11] 2001–2011 (1984)

    Google Scholar 

  27. Wagner, C.: Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung). Z Elektrochem. 65, 581–591 (1961)

    Google Scholar 

Download references

Acknowledgements

This work was performed under the project No. 142011G supported financially by the Ministry of Science and Technological Development of the Republic of Serbia.

Author information

Authors and Affiliations

  1. Faculty of Electronic Engineering, Department of Microelectronics, University of Niš, Aleksandra Medvedeva 14, 18000, Niš, Serbia

    Zoran S. Nikolić

Authors
  1. Zoran S. Nikolić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zoran S. Nikolić .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Walter Gautschi

  2. Dipto. Matematica, Università Basilicata, Contrada Macchia Romana, Potenza, 85100, Italy

    Giuseppe Mastroianni

  3. Zagoras Street 4, Athens, 151 25, Greece

    Themistocles M. Rassias

Additional information

Dedicated to the 60-th anniversary of Professor Gradimir V. Milovanovic

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Nikolić, Z.S. (2010). Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to Gravity-Induced Skeletal Settling. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_27

Download citation