Skip to main content
Log in

Coarsening of polyhedral grains in a liquid matrix

  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The coarsening of polyhedral grains in a liquid matrix was calculated using crystal growth and dissolution equations used in crystal growth theories for faceted crystals. The coarsening behavior was principally governed by the relative value of the maximum driving force for growth (Δgmax), which is determined by the average size and size distribution, to the critical driving force for appreciable growth (Δgc). When Δgmax was much larger than Δgc, pseudonormal grain coarsening occurred. With a reduction of Δgmax relative to Δgc, abnormal grain coarsening (AGC, when Δgmax ≥ Δgc) and stagnant grain coarsening (SGC, when Δgmax < Δgc) were predicted. The observed cyclic AGC and incubation for AGC in real systems with faceted grains were explained in terms of the relative value between Δgmax and Δgc. The effects of various processing and physical parameters, such as the initial grain size and distribution, the liquid volume fraction, step free energy, and temperature, were also evaluated. The calculated results were in good agreement with previous experimental observations.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S-J.L. Kang and S-M. Han: Grain-growth in Si3N4-based material. MRS Bull. 20, 33 (1995).

    CAS  Google Scholar 

  2. Y.J. Park, N.M. Hwang and D.Y. Yoon: Abnormal growth of faceted WC grains in a Co liquid matrix. Metall. Mater. Trans. A 27, 2809 (1996).

    Article  Google Scholar 

  3. M.M. Seabaugh, I.H. Kerscht and G.L. Messing: Texture development by templated grain growth in liquid-phase-sintered a-alumina. J. Am. Ceram. Soc. 80, 1181 (1997).

    Article  CAS  Google Scholar 

  4. K-S. Oh, J-Y. Jun, D-Y. Kim and N.M. Hwang: Shape dependence of the coarsening behavior of niobium carbide grains dispersed in a liquid iron matrix. J. Am. Ceram. Soc. 83, 3117 (2000).

    Article  CAS  Google Scholar 

  5. K. Choi, N.M. Hwang and D-Y. Kim: Effect of grain shape on abnormal grain growth in liquid-phase-sintered Nb1−x TixC–Co alloys. J. Am. Ceram. Soc. 85, 2313 (2002).

    Article  CAS  Google Scholar 

  6. J.S. Wallace, J.M. Huh, J.E. Blendell and C.A. Handwerker: Grain growth and twin formation in 0.74PMN–0.26PT. J. Am. Ceram. Soc. 85, 1581 (2002).

    Article  CAS  Google Scholar 

  7. C-W. Jang, J. Kim and S-J.L. Kang: Effect of sintering atmosphere on grain shape and grain growth in liquid-phase-sintered silicon carbide. J. Am. Ceram. Soc. 85, 1281 (2002).

    Article  CAS  Google Scholar 

  8. S-Y. Chung, D.Y. Yoon and S-J.L. Kang: Effects of donor concentration and oxygen partial pressure on interface morphology and grain growth behavior in SrTiO3. Acta Mater. 50, 3361 (2002).

    Article  CAS  Google Scholar 

  9. C.W. Park and D.Y. Yoon: Abnormal grain growth in alumina with anorthite liquid and the effect of MgO addition. J. Am. Ceram. Soc. 85, 1585 (2002).

    Article  CAS  Google Scholar 

  10. Y.K. Cho, D.Y. Yoon and B-K. Kim: Surface roughening transition and coarsening of NbC grains in liquid cobalt-rich matrix. J. Am. Ceram. Soc. 87, 443 (2004).

    Article  CAS  Google Scholar 

  11. J.G. Fisher, M-S. Kim, H. Lee and S-J.L. Kang: Effect of LiO2and PbO additions on abnormal grain growth in the PbMg1/3Nb2/3 O3–35 mol% PbTiO3 system. J. Am. Ceram. Soc. 87, 937 (2004).

    Article  CAS  Google Scholar 

  12. B-K. Yoon, B-A. Lee and S-J.L. Kang: Growth behavior of rounded (Ti,W)C and faceted WC grains in a Co matrix during liquid phase sintering. Acta Mater. 53, 4677 (2005).

    Article  CAS  Google Scholar 

  13. E.P. Gorzkowski, H.M. Chan and M.P. Harmer: Effect of PbO on the kinetics of 001 Pb(Mg1/3Nb2/3)O3–35 mol% PbTiO3 single crystals grown into fully dense matrices. J. Am. Ceram. Soc. 89, 856 (2006).

    Article  CAS  Google Scholar 

  14. W. Jo, D-Y. Kim and N.M. Hwang: Effect of interface structure on the microstructural evolution of ceramics. J. Am. Ceram. Soc. 89, 2369 (2006).

    Article  CAS  Google Scholar 

  15. J. Chang and S-J.L. Kang: Step free-energy change and microstructural development in BaTiO3–SiO2. Key Eng. Mater. 352, 25 (2007).

    Article  CAS  Google Scholar 

  16. K.S. Moon and S-J.L. Kang: Coarsening behavior of round-edged cubic grains in the Na1/2Bi1/2TiO3–BaTiO3 system. J. Am. Ceram. Soc. 91, 3191 (2008).

    Article  CAS  Google Scholar 

  17. S-J.L. Kang, M-G. Lee and S-M. An: Microstructural evolution during sintering with control of the interface structure. J. Am. Ceram. Soc. 92, 1464 (2009).

    Article  CAS  Google Scholar 

  18. J.P. Hirth and G.M. Pound: Condensation and evaporation, nucleation and growth kinetics, in Progress in Material Science, Vol. 11, edited by B. Chalmers (Pergamon Press, Oxford, 1963).

    Google Scholar 

  19. J.M. Howe: Interfaces in Materials (John Wiley & Sons, New York, 1997).

    Google Scholar 

  20. I.M. Lifshitz and V.V. Slyozov: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35 (1961).

    Article  Google Scholar 

  21. C. Wagner: Theory of precipitate change by redissolution (Ostwald ripening). Z. Elektrochem. 65, 581 (1961).

    CAS  Google Scholar 

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

    Article  Google Scholar 

  23. A.D. Brailsford and P. Wynblatt: The dependence of Ostwald ripening kinetics on particle volume fraction. Acta Metall. 27, 489 (1979).

    Article  CAS  Google Scholar 

  24. P.W. Voorhees and M.E. Glicksman: Ostwald ripening during liquid phase sintering—Effect of volume fraction on coarsening kinetics. Metall. Trans. A 15, 1081 (1984).

    Article  Google Scholar 

  25. S.P. Marsh and M.E. Glicksman: Kinetics of phase coarsening in dense systems. Acta Mater. 44, 3761 (1996).

    Article  CAS  Google Scholar 

  26. R.M. German and E.A. Olevsky: Modeling grain growth dependence on the liquid content in liquid-phase-sintered materials. Metall. Mater. Trans. A 29, 3057 (1998).

    Article  Google Scholar 

  27. V.A. Snyder, J. Alkemper and P.W. Voorhees: The development of spatial correlations during Ostwald ripening: A test of theory. Acta Mater. 48, 2689 (2000).

    Article  CAS  Google Scholar 

  28. W.K. Burton, N. Cabrera and F.C. Frank: The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. R. Soc. London, Ser. A 243, 299 (1951).

    Article  Google Scholar 

  29. S.D. Peteves and R. Abbaschian: Growth kinetics of solid-liquid Ga interfaces: Part II. Theoretical. Metall.Trans.A 22, 1271 (1991).

    Article  Google Scholar 

  30. D.Y. Yoon, C.W. Park and J.B. Koo: The step growth hypothesis for abnormal grain growth, in Ceramic Interfaces 2, edited by H-I. Yoo and S-J.L. Kang (Institute of Materials, London, 2001), p. 3.

    Google Scholar 

  31. P. Wynblatt and N.A. Gjostein: Particle growth in model supported metal catalysts—I. Theory. Acta Metall. 24, 1165 (1976).

    Article  CAS  Google Scholar 

  32. G.S. Rohrer, C.L. Rohrer and W.W. Mullins: Coarsening of faceted crystals. J. Am. Ceram. Soc. 85, 675 (2002).

    Article  CAS  Google Scholar 

  33. M-K. Kang, D-Y. Kim and N.M. Hwang: Ostwald ripening kinetics of angular grains dispersed in a liquid phase by two-dimensional nucleation and abnormal grain growth. J. Eur. Ceram. Soc. 22, 603 (2002).

    Article  CAS  Google Scholar 

  34. G.S. Rohrer, C.L. Rohrer and W.W. Mullins: Nucleation energy barriers for volume-conserving shape changes of crystals with nonequilibrium morphologies. J. Am. Ceram. Soc. 84, 2099 (2001).

    Article  CAS  Google Scholar 

  35. S-J.L. Kang: Sintering: Densification, Grain Growth and Micro-structure (Elsevier, Oxford, 2005).

    Google Scholar 

  36. S-J.L. Kang, Y-I. Jung and K-S. Moon: Principles of microstructural design in two-phase systems. Mater. Sci. Forum 827–834, 558 (2007).

    Google Scholar 

  37. P. Bennema and J.P. van der Eerden: Crystal graphs, connected nets, roughening transition and the morphology of crystals, in Morphology of Crystals, edited by I. Sunagawa (Terra Scientific Publishing Company, Tokyo, Japan, 1987), p. 1.

    Google Scholar 

  38. M-K. Kang, Y-S. Yoo, D-Y. Kim and N.M. Hwang: Growth of BaTiO3 seed grains by the twin-plane reentrant edge mechanism. J. Am. Ceram. Soc. 83, 385 (2000).

    Article  CAS  Google Scholar 

  39. M. Schreiner, Th. Schmitt, E. Lassner and B. Lux: On the origins of discontinuous grain growth during liquid phase sintering of WC–Co cemented carbides. Powder Metall. Inter. 16, 180 (1984).

    Google Scholar 

  40. Y-I. Jung, S-Y. Choi and S-J.L. Kang: Grain-growth behavior during stepwise sintering of barium titanate in hydrogen gas and air. J. Am. Ceram. Soc. 86, 2228 (2003).

    Article  CAS  Google Scholar 

  41. H. Moon, B-K. Kim and S-J.L. Kang: Growth mechanism of round-edged NbC grains in Co liquid. Acta Mater. 49, 1293 (2001).

    Article  CAS  Google Scholar 

  42. H. Gabrisch, L. Kjeldgaard, E. Johnson and U. Dahmen: Equilibrium shape and interface roughening of small liquid Pb inclusions in solid Al. Acta Mater. 49, 4259 (2001).

    Article  CAS  Google Scholar 

  43. C. Steimer, M. Giesen, L. Verheij and H. Ibach: Experimental determination of step energies from island shape fluctuations: A comparison to the equilibrium shape method for Cu(100), Cu (111), and Ag(111). Phys. Rev. B 64, 085416 (2001).

    Article  CAS  Google Scholar 

  44. Y-W. Kim, M. Mitomo, H. Emoto and J-G. Lee: Effect of initial a-phase content on microstructure and mechanical properties of sintered silicon carbide. J. Am. Ceram. Soc. 81, 3136 (1998).

    Article  CAS  Google Scholar 

  45. C.W. Park and D.Y. Yoon: Effects of SiO2, CaO, and MgO additions on the grain growth of alumina. J. Am. Ceram. Soc. 83, 2605 (2000).

    Article  CAS  Google Scholar 

  46. C.W. Park, D.Y. Yoon, J.E. Blendell and C.A. Handwerker: Singular grain boundaries in alumina and their roughening transition. J. Am. Ceram. Soc. 86, 603 (2003).

    Article  CAS  Google Scholar 

  47. T. Motohashi and T. Kimura: Formation of homo-template grains in Bi0.5Na0.5TiO3 prepared by the reactive-templated grain growth process. J. Am. Ceram. Soc. 91, 3889 (2008).

    Article  CAS  Google Scholar 

  48. P. Shen, H. Fujii, T. Matsumoto and K. Nogi: The influence of surface structure on wetting of a-Al2O3 by aluminum in a reduced atmosphere. Acta Mater. 51, 4897 (2003).

    Article  CAS  Google Scholar 

  49. C.A. Bateman, S.J. Bennison and M.P. Harmer: Mechanism for the role of magnesia in the sintering of alumina containing small amounts of a liquid phase. J. Am. Ceram. Soc. 72, 1241 (1989).

    Article  CAS  Google Scholar 

  50. C.V. Thompson, H.J. Frost and F. Spaepen: The relative rates of secondary and normal grain growth. Acta Metall. 35, 887 (1987).

    Article  CAS  Google Scholar 

  51. Y-S. Yoo, M-K. Kang, J-H. Han, H. Kim and D-Y. Kim: Fabrication of BaTiO3 single crystals by using the exaggerated grain growth method. J. Eur. Ceram. Soc. 17, 1725 (1997).

    Article  CAS  Google Scholar 

  52. A. Khan, F.A. Meschke, T. Li, A.M. Scotch, H.M. Chan and M.P. Harmer: Growth of Pb(Mg1/3Nb2/3)O3–35 mol% PbTiO3 single crystals from (111) substrates by seeded polycrystal conversion. J. Am. Ceram. Soc. 82, 2958 (1999).

    Article  CAS  Google Scholar 

  53. P.W. Rehrig, G.L. Messing and S. Trolier-McKinstry: Templated grain growth of barium titanate single crystals. J. Am. Ceram. Soc. 83, 2654 (2000).

    Article  CAS  Google Scholar 

  54. E.M. Sabolsky, G.L. Messing and S. Trolier-McKinstry: Kinetics of templated grain growth of 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3. J. Am. Ceram. Soc. 84, 2507 (2001).

    Article  CAS  Google Scholar 

  55. P.T. King, E.P. Gorzkowski, A.M. Scotch, D.J. Rockosi, H.M. Chan and M.P. Harmer: Kinetics of 001 Pb(Mg1/3Nb2/3) O3–35 mol% PbTiO3 single crystals grown by seeded polycrystal conversion. J. Am. Ceram. Soc. 86, 2182 (2003).

    Article  CAS  Google Scholar 

  56. S-Y. Choi, D.Y. Yoon and S-J.L. Kang: Kinetic formation and thickening of intergranular amorphous films at grain boundaries in barium titanate. Acta Mater. 52, 3721 (2004).

    Article  CAS  Google Scholar 

  57. M-S. Kim, J.G. Fisher and S-J.L. Kang: Grain growth control and solid-state crystal growth by Li2O/PbO addition and dislocation introduction in the PMN–35PT system. J. Am. Ceram. Soc. 89, 1237 (2006).

    Article  CAS  Google Scholar 

  58. B-K. Yoon, S-Y. Choi, T. Yamamoto, Y. Ikuhara and S-J.L. Kang: Grain boundary mobility and grain growth behavior in polycrystals with faceted wet and dry boundaries. Acta Mater. 57, 2128 (2009).

    Article  CAS  Google Scholar 

  59. C.P. Chen, H.Z. Yang, J.X. Gao, H.W. Sun and X. Hu: Densification behavior and microstructural evolution of TiO2/CAS-incorporated alumina. Ceram. Int. 35, 585 (2009).

    Article  CAS  Google Scholar 

  60. J.M. Kosterlitz: The critical properties of the two-dimensional xy model. J. Phys. C: Solid State Phys. 7, 1046 (1974).

    Article  Google Scholar 

  61. H. van Beijeren: Exactly solvable model for the roughening transition of a crystal surface. Phys. Rev. Lett. 38, 993 (1977).

    Article  Google Scholar 

  62. H. van Beijeren and I. Nolden: The roughening transition, in Structure and Dynamics of Surfaces II, Vol 43 of Topics in Current Physics, edited by W. Schommers and P. von Blanckenhagen (Springer-Verlag, Berlin, 1987), p. 259.

    Chapter  Google Scholar 

  63. M. Wortis: Equilibrium crystal shapes and interfacial phase transitions, in Chemistry and Physics of Solid Surfaces, Vol. 7, edited by R. Banselow and R.F. Howe (Springer Verlag, Berlin, Germany, 1988), p. 367.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Suk-Joong L. Kang.

Additional information

This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/jmr_policy

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jung, YI., Yoon, D.Y. & Kang, SJ.L. Coarsening of polyhedral grains in a liquid matrix. Journal of Materials Research 24, 2949–2959 (2009). https://doi.org/10.1557/jmr.2009.0356

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2009.0356

Navigation