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Coarsening of polyhedral grains in a liquid matrix

Published online by Cambridge University Press:  31 January 2011

Yang-Il Jung ,
Suk-Joong L. Kang  and
Duk Yong Yoon
Suk-Joong L. Kang*
Affiliation:
Center for NanoInterface Technology, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
Duk Yong Yoon
Affiliation:
Center for NanoInterface Technology, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea; and Korea Research Institute of Standards and Science, Daejeon 305-340, and Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
*
a) Address all correspondence to this author. e-mail: [email protected]
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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.

Keywords

Crystal growthGrain boundariesPolycrystal
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 9 , September 2009 , pp. 2949 - 2959
Copyright
Copyright © Materials Research Society 2009

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References

1Kang, S-J.L. and Han, S-M.: Grain-growth in Si3N4-based material. MRS Bull. 20, 33 (1995).Google Scholar
2Park, Y.J., Hwang, N.M. and Yoon, D.Y.: Abnormal growth of faceted WC grains in a Co liquid matrix. Metall. Mater. Trans. A 27, 2809 (1996).Google Scholar
3Seabaugh, M.M., Kerscht, I.H. and Messing, G.L.: Texture development by templated grain growth in liquid-phase-sintered a-alumina. J. Am. Ceram. Soc. 80, 1181 (1997).Google Scholar
4Oh, K-S., Jun, J-Y., Kim, D-Y. and Hwang, N.M.: Shape dependence of the coarsening behavior of niobium carbide grains dispersed in a liquid iron matrix. J. Am. Ceram. Soc. 83, 3117 (2000).Google Scholar
5Choi, K., Hwang, N.M. and Kim, D-Y.: Effect of grain shape on abnormal grain growth in liquid-phase-sintered Nb1x TixC–Co alloys. J. Am. Ceram. Soc. 85, 2313 (2002).CrossRefGoogle Scholar
6Wallace, J.S., Huh, J.M., Blendell, J.E. and Handwerker, C.A.: Grain growth and twin formation in 0.74PMN–0.26PT. J. Am. Ceram. Soc. 85, 1581 (2002).Google Scholar
7Jang, C-W., Kim, J. and Kang, S-J.L.: Effect of sintering atmosphere on grain shape and grain growth in liquid-phase-sintered silicon carbide. J. Am. Ceram. Soc. 85, 1281 (2002).CrossRefGoogle Scholar
8Chung, S-Y., Yoon, D.Y. and Kang, S-J.L.: Effects of donor concentration and oxygen partial pressure on interface morphology and grain growth behavior in SrTiO3. Acta Mater. 50, 3361 (2002).Google Scholar
9Park, C.W. and Yoon, D.Y.: Abnormal grain growth in alumina with anorthite liquid and the effect of MgO addition. J. Am. Ceram. Soc. 85, 1585 (2002).Google Scholar
10Cho, Y.K., Yoon, D.Y. and Kim, B-K.: Surface roughening transition and coarsening of NbC grains in liquid cobalt-rich matrix. J. Am. Ceram. Soc. 87, 443 (2004).CrossRefGoogle Scholar
11Fisher, J.G., Kim, M-S., Lee, H. and Kang, S-J.L.: 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).Google Scholar
12Yoon, B-K., Lee, B-A. and Kang, S-J.L.: Growth behavior of rounded (Ti,W)C and faceted WC grains in a Co matrix during liquid phase sintering. Acta Mater. 53, 4677 (2005).CrossRefGoogle Scholar
13Gorzkowski, E.P., Chan, H.M. and Harmer, M.P.: 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).Google Scholar
14Jo, W., Kim, D-Y. and Hwang, N.M.: Effect of interface structure on the microstructural evolution of ceramics. J. Am. Ceram. Soc. 89, 2369 (2006).CrossRefGoogle Scholar
15Chang, J. and Kang, S-J.L.: Step free-energy change and microstructural development in BaTiO3–SiO2. Key Eng. Mater. 352, 25 (2007).CrossRefGoogle Scholar
16Moon, K.S. and Kang, S-J.L.: Coarsening behavior of round-edged cubic grains in the Na1/2Bi1/2TiO3–BaTiO3 system. J. Am. Ceram. Soc. 91, 3191 (2008).Google Scholar
17Kang, S-J.L., Lee, M-G. and An, S-M.: Microstructural evolution during sintering with control of the interface structure. J. Am. Ceram. Soc. 92, 1464 (2009).Google Scholar
18Hirth, J.P. and Pound, G.M.: Condensation and evaporation, nucleation and growth kinetics, in Progress in Material Science, Vol. 11, edited by Chalmers, B. (Pergamon Press, Oxford, 1963).Google Scholar
19Howe, J.M.: Interfaces in Materials (John Wiley & Sons, New York, 1997).Google Scholar
20Lifshitz, I.M. and Slyozov, V.V.: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35 (1961).Google Scholar
21Wagner, C.: Theory of precipitate change by redissolution (Ostwald ripening). Z. Elektrochem. 65, 581 (1961).Google Scholar
22Ardell, A.J.: The effect of volume fraction on particle coarsening: Theoretical considerations. Acta Metall. 20, 61 (1972).CrossRefGoogle Scholar
23Brailsford, A.D. and Wynblatt, P.: The dependence of Ostwald ripening kinetics on particle volume fraction. Acta Metall. 27, 489 (1979).Google Scholar
24Voorhees, P.W. and Glicksman, M.E.: Ostwald ripening during liquid phase sintering—Effect of volume fraction on coarsening kinetics. Metall. Trans. A 15, 1081 (1984).CrossRefGoogle Scholar
25Marsh, S.P. and Glicksman, M.E.: Kinetics of phase coarsening in dense systems. Acta Mater. 44, 3761 (1996).Google Scholar
26German, R.M. and Olevsky, E.A.: Modeling grain growth dependence on the liquid content in liquid-phase-sintered materials. Metall. Mater. Trans. A 29, 3057 (1998).Google Scholar
27Snyder, V.A., Alkemper, J. and Voorhees, P.W.: The development of spatial correlations during Ostwald ripening: A test of theory. Acta Mater. 48, 2689 (2000).Google Scholar
28Burton, W.K., Cabrera, N. and Frank, F.C.: The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. R. Soc. London, Ser. A 243, 299 (1951).Google Scholar
29Peteves, S.D. and Abbaschian, R.: Growth kinetics of solid-liquid Ga interfaces: Part II. Theoretical. Metall.Trans.A 22, 1271 (1991).CrossRefGoogle Scholar
30Yoon, D.Y., Park, C.W. and Koo, J.B.: The step growth hypothesis for abnormal grain growth, in Ceramic Interfaces 2, edited by Yoo, H-I. and Kang, S-J.L. (Institute of Materials, London, 2001), p. 3.Google Scholar
31Wynblatt, P. and Gjostein, N.A.: Particle growth in model supported metal catalysts—I. Theory. Acta Metall. 24, 1165 (1976).Google Scholar
32Rohrer, G.S., Rohrer, C.L. and Mullins, W.W.: Coarsening of faceted crystals. J. Am. Ceram. Soc. 85, 675 (2002).Google Scholar
33Kang, M-K., Kim, D-Y. and Hwang, N.M.: 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).CrossRefGoogle Scholar
34Rohrer, G.S., Rohrer, C.L. and Mullins, W.W.: Nucleation energy barriers for volume-conserving shape changes of crystals with nonequilibrium morphologies. J. Am. Ceram. Soc. 84, 2099 (2001).Google Scholar
35Kang, S-J.L.: Sintering: Densification, Grain Growth and Micro-structure (Elsevier, Oxford, 2005).Google Scholar
36Kang, S-J.L., Jung, Y-I. and Moon, K-S.: Principles of microstructural design in two-phase systems. Mater. Sci. Forum 827–834, 558 (2007).Google Scholar
37Bennema, P. and Eerden, J.P. van der: Crystal graphs, connected nets, roughening transition and the morphology of crystals, in Morphology of Crystals, edited by Sunagawa, I. (Terra Scientific Publishing Company, Tokyo, Japan, 1987), p. 1.Google Scholar
38Kang, M-K., Yoo, Y-S., Kim, D-Y. and Hwang, N.M.: Growth of BaTiO3 seed grains by the twin-plane reentrant edge mechanism. J. Am. Ceram. Soc. 83, 385 (2000).Google Scholar
39Schreiner, M., Schmitt, Th., Lassner, E. and Lux, B.: On the origins of discontinuous grain growth during liquid phase sintering of WC–Co cemented carbides. Powder Metall. Inter. 16, 180 (1984).Google Scholar
40Jung, Y-I., Choi, S-Y. and Kang, S-J.L.: Grain-growth behavior during stepwise sintering of barium titanate in hydrogen gas and air. J. Am. Ceram. Soc. 86, 2228 (2003).CrossRefGoogle Scholar
41Moon, H., Kim, B-K. and Kang, S-J.L.: Growth mechanism of round-edged NbC grains in Co liquid. Acta Mater. 49, 1293 (2001).CrossRefGoogle Scholar
42Gabrisch, H., Kjeldgaard, L., Johnson, E. and Dahmen, U.: Equilibrium shape and interface roughening of small liquid Pb inclusions in solid Al. Acta Mater. 49, 4259 (2001).Google Scholar
43Steimer, C., Giesen, M., Verheij, L. and Ibach, H.: 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).CrossRefGoogle Scholar
44Kim, Y-W., Mitomo, M., Emoto, H. and Lee, J-G.: Effect of initial a-phase content on microstructure and mechanical properties of sintered silicon carbide. J. Am. Ceram. Soc. 81, 3136 (1998).Google Scholar
45Park, C.W. and Yoon, D.Y.: Effects of SiO2, CaO, and MgO additions on the grain growth of alumina. J. Am. Ceram. Soc. 83, 2605 (2000).Google Scholar
46Park, C.W., Yoon, D.Y., Blendell, J.E. and Handwerker, C.A.: Singular grain boundaries in alumina and their roughening transition. J. Am. Ceram. Soc. 86, 603 (2003).Google Scholar
47Motohashi, T. and Kimura, T.: Formation of homo-template grains in Bi0.5Na0.5TiO3 prepared by the reactive-templated grain growth process. J. Am. Ceram. Soc. 91, 3889 (2008).Google Scholar
48Shen, P., Fujii, H., Matsumoto, T. and Nogi, K.: The influence of surface structure on wetting of a-Al2O3 by aluminum in a reduced atmosphere. Acta Mater. 51, 4897 (2003).CrossRefGoogle Scholar
49Bateman, C.A., Bennison, S.J. and Harmer, M.P.: 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).CrossRefGoogle Scholar
50Thompson, C.V., Frost, H.J. and Spaepen, F.: The relative rates of secondary and normal grain growth. Acta Metall. 35, 887 (1987).Google Scholar
51Yoo, Y-S., Kang, M-K., Han, J-H., Kim, H. and Kim, D-Y.: Fabrication of BaTiO3 single crystals by using the exaggerated grain growth method. J. Eur. Ceram. Soc. 17, 1725 (1997).Google Scholar
52Khan, A., Meschke, F.A., Li, T., Scotch, A.M., Chan, H.M. and Harmer, M.P.: 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).Google Scholar
53Rehrig, P.W., Messing, G.L. and Trolier-McKinstry, S.: Templated grain growth of barium titanate single crystals. J. Am. Ceram. Soc. 83, 2654 (2000).Google Scholar
54Sabolsky, E.M., Messing, G.L. and Trolier-McKinstry, S.: Kinetics of templated grain growth of 0.65Pb(Mg1/3Nb2/3)O3–0.35PbTiO3. J. Am. Ceram. Soc. 84, 2507 (2001).Google Scholar
55King, P.T., Gorzkowski, E.P., Scotch, A.M., Rockosi, D.J., Chan, H.M. and Harmer, M.P.: 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).Google Scholar
56Choi, S-Y., Yoon, D.Y. and Kang, S-J.L.: Kinetic formation and thickening of intergranular amorphous films at grain boundaries in barium titanate. Acta Mater. 52, 3721 (2004).Google Scholar
57Kim, M-S., Fisher, J.G. and Kang, S-J.L.: 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).Google Scholar
58Yoon, B-K., Choi, S-Y., Yamamoto, T., Ikuhara, Y. and Kang, S-J.L.: Grain boundary mobility and grain growth behavior in polycrystals with faceted wet and dry boundaries. Acta Mater. 57, 2128 (2009).Google Scholar
59Chen, C.P., Yang, H.Z., Gao, J.X., Sun, H.W. and Hu, X.: Densification behavior and microstructural evolution of TiO2/CAS-incorporated alumina. Ceram. Int. 35, 585 (2009).Google Scholar
60Kosterlitz, J.M.: The critical properties of the two-dimensional xy model. J. Phys. C: Solid State Phys. 7, 1046 (1974).CrossRefGoogle Scholar
61Beijeren, H. van: Exactly solvable model for the roughening transition of a crystal surface. Phys. Rev. Lett. 38, 993 (1977).CrossRefGoogle Scholar
62Beijeren, H. van and Nolden, I.: The roughening transition, in Structure and Dynamics of Surfaces II, Vol 43 of Topics in Current Physics, edited by Schommers, W. and Blanckenhagen, P. von (Springer-Verlag, Berlin, 1987), p. 259.Google Scholar
63Wortis, M.: Equilibrium crystal shapes and interfacial phase transitions, in Chemistry and Physics of Solid Surfaces, Vol. 7, edited by Banselow, R. and Howe, R.F. (Springer Verlag, Berlin, Germany, 1988), p. 367.Google Scholar