Abstract
The stability of closed pores in two and three dimensions has been discussed and it is found that the stability of pores in two dimension can be determined mathematically from their particle coordination number and dihedral angle; while those in three dimension can be approximately determined by a spherical pore model. This model is set up by first excluding the effect of interface tension, so the pore was supposed to be spherical, and then the tensile stress arising from the interface tension was allowed to act on this hypothesized spherical pore. On the basis of the spherical pore model, pore microstructure models for real powder compacts were set up and the densification equations for the intermediate and final stages of sintering were derived. The criterion for pore shrinkage, and the effect of pore size distribution and green density were discussed according to the derived equations. The densification equations for pressureless solid state sintering can be easily extended to describe the densification behaviour during hot-pressing or hot-isostatic-pressing. Densification characteristics in liquid state sintering were also considered from the result of solid state sintering.
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References
Herring, J. Appl. Phys. 21 (1950) 301.
G. C. Kuczynski, N. A. Hootenand G. N. Gilbson (ed.), “Sintering and Related Phenomena” (Gorden & Breach, New York, 1967).
G. C. Kuczynski(ed.), “Sintering and Related Phenomena, ” Mater. Sci. Res., Vol. 6 (Plenum, New York, 1973).
A. R. Cooperand A. H. Heuer(eds.), “Mass Transport Phenomena in Ceramics, ” Mater. Sci. Res., Vol. 9 (Plenum Press, New York and London, 1975).
G. C. Kuczynski(ed.), “Sintering and Catalysis, ” Mater. Sci. Res., Vol. 10 (Plenum Press, New York and London, 1978).
Idem., (ed.), “Sintering Process, ” Mater. Sci. Res., Vol. 13 (Plenum Press, New York and London, 1980).
J. Paskand A. Evans(eds.), “Surfaces and Interfaces in Ceramic and Ceramic Metal Systems, ” Mater. Sci. Res., Vol. 14 (Plenum Press, New York and London, 1981).
D. Kolar, S. Pejovnikand M. M. Ristic(eds.), “Sintering–Theory and Practice, ” Mater. Sci. Monographs, Vol. 14 (Elsevier, Amsterdam, 1982).
M. M. Risticand B. Kidric(eds.), “Physics of Sintering, ” Vol. 5 (Institute of Nuclear Science, Beograd, Yugoslavia, 1973).
S. Somiyaand Shimada(eds.), “Sintering 87” (Elsevier Applied Science, London, 1988).
S. Somiyaand Y. Moriyoshi(eds.), “Sintering, Key Papers” (Elsevier Applied Science, London, 1987).
R. L. Coble, J. Applied Physics 32(5) (1961) 787–793.
Idem.,ibid. 32(5) (1961) 793.
G. C. Kuczynski, AIME 85 (1949) 169–178.
Idem., in “Sintering, Key Papers, ” edited by S. Somiya and Y. Moriyoshi (Elsevier Applied Science, London, 1987) pp. 501–508.
W. D. Kingeryand M. Berg, J. Appl. Phys. 26(10) (1955) 1205–1212.
J. A. Pask, in “Sintering, Key Papers, ” edited by S. Somiya and Y. Moriyoshi (Elsevier Applied Science, London, 1987) pp. 567–678.
H. E. Exner, Powder Metallurgy 4 (1980) 203–209.
H. E. Exnerand E. Arzt, in “Physical Metallurgy, ” edited by R.W. Cahn and P. Haasan, 3rd ed. (Elsevier Science Publishers BV, 1983) Chap. 10, pp. 1185–1912; in “Sintering, Key Papers, ” edited by S. Somiya and Y. Moriyoshi (Elsevier Applied Science, London, 1987) pp. 157–184.
W. S. Coblenz, J. M. Dynys, R. M. Cannonand R. L. Coble, in “Sintering Process, ” Mater. Sci. Res., Vol. 13, edited by G. C. Kuczynski (Plenum Press, New York and London, 1980) pp. 141–157.
D. L. Johnson, J. Amer. Ceram. Soc. 53(10) (1970) 574–577.
J. L. Shiand Z. X. Lin, Ceram. Int. 15 (1989) 107–112.
J. M. Vieiraand R. J. Brook, J. Amer. Ceram. Soc. 67(2) (1984) 245–249.
Idem., ibid. 67(7) (1984) 450–454.
H. E. Exnerand G. Petzow, in “Sintering Processes, ” Mater. Sci. Res., Vol. 13, edited by G. C. Kuczynski (Plenum, New York, 1980) pp. 107–120.
S. Pejovnik, V. Smolej, D. Susnikand D. Kolar, Powder Metall. Int. 11 (1979) 22–24.
M. H. Tikkanenand S. A. Makipirtti, Int. J. Powd. Met. 1(1) (1965) 15–22.
M. P. Harmer, H. M. Chanand D. M. Smyth, in “Defect Properties and Processing of High-Technology Nonmetallic Materials, ” edited by Y. Chen, W. D. Kingery and R. J. Stokes (Materials Research Society, Pittsburgh, Pennsylvania, 1986) pp. 125–134.
M. P. Harmer, in“Advances in Ceramics, ” Vol. 10 (American Ceramic Society, Columbus, OH, 1985) pp. 679–696.
F. V. Level, in “Sintering, Key Papers, ” edited by S. Somiya and Y. Moriyoshi (Elsevier Applied Science, London, 1987), pp. 543–566.
G. C. Kuczynski, in “Sintering–Theory and Practice, ” Mater. Sci. Monographs, Vol. 14 (Elsevier, Amsterdam, 1982) pp. 37–44.
T. T. Fangand H. Palmer III, Ceram. Int. 15 (1989) 329–335.
W. D. Kingeryand B. Francois, in “Sintering and Related Phenomena, ” edited by G. C. Kuczynski, N. A. Hooten and G. N. Gilbson (Gorden & Breach, New York, 1967) pp. 471–498.
F. F. Lange, J. Amer. Ceram. Soc. 67 (1984) 83.
J. L. Shi, J. H. Gao, Z. X. Linand T. S. Yen, ibid. 74(5) (1991) 994–997.
F. F. Langeand B. J. Kellet, ibid. 72(5) (1989) 735–741.
B. J. Kelletand F. F. Lange, in “Advanced Ceramic Processing and Technology, ” Vol. 1, edited by J. G. P. Binner (Noyes Publications, 1990) pp. 1–38.
T. K. Gupta, J. Amer. Cera. Soc. 55(5) (1972) 176–177.
J. L. Shi, “Solid State Sintering of Ceramics: Experimental Tests on Grain Growth, Pore Growth and Densification of Superfine Zirconia Powders, ” to be published.
C. Herring, in “The Physics of Powder Metallurgy, ” edited by T. E. Kingston (McGraw-Hill, New York, 1951) chap. 8, p. 143.
R. L. Eadieand G. C. Weatherly, in “Sintering and Catalysis, ” edited by G. C. Kuczynski (Plenum Press, New York, 1978) pp. 239–248.
D. L. Johnson, in “Sintering Processes, ” Mater. Sci. Res., Vol. 13, edited by G. C. Kuczynski (Plenum, New York, 1980) pp. 97–104.
Idem., in “Processing of Crystalline Ceramics, ” Materials Science Research, Vol. 11, edited by H. Palmour III, R. F. Davis and T. M. Hare (Plenum Press, New York, 1978) pp. 137–149.
J. Zhengand J. S. Reed, J. Amer. Ceram. Soc. 72(5) (1989) 810–817.
J. L. Shi, Z. X. Linand T. S. Yen, J. Mater. Sci. 28(2) (1993) 342–348.
B. Francoisand W. D. Kingery, “Physical Metallurgy, ” edited by R. W. Cohn and P. Haasan, 3rd ed. (Elsevier Science Publishers BV, 1983) pp. 499–525.
J. Zhaoand M. P. Harmer, J. Amer. Ceram. Soc. 71(7) (1988) 530–539.
A. G. Evans, ibid. 65(10) (1982) 498–506.
O. J. Whittemoreand J. A. Varela, in “Sintering–Key Papers, ” edited by S. Somiya and Y. Moriyoshi (Elsevier Applied Science, London 1987) pp. 777–793.
J. A. Varela, O. J. Whittemoreand E. Longo, Ceram. Int. 16 (1990) 177–189.
F. F. Lange, in “Ceramic Transactions Vol. 1, Ceramic Powder Science, ” edited by G. L. Messing, E. R. Fuller and H. Hausner (The American Ceramic Soc. Westerville, OH, 1987) pp. 1069–1083.
J. L. Shiand T. S. Yen, J. Europ. Ceram. Soc. 15(4) (1995) 363–369.
J. L. Shi, Z. X. Linand T. S. iYen, J. Mater. Sci. 28(2) (1993) 342–348.
J. L. Shiand T. S. Yen, J. Europ. Ceram. Soc. 14 (1994) 505–510.
R. M. Spriggs, in “Sintering and Related Phenomena, ” Mater. Sci. Res., Vol. 6, edited by G. C. Kuczynski (Plenum, New York, 1973) pp. 369–379.
R. L. Coble, J. Appl. Phys. 41(12) (1970) 4798–4807.
F. R. N. Nabarro, The Physical Soc. (1948) 75–90.
W. D. Kingery, J. Appl. Phys. 30(3) (1959) 301–306.
G. Petzowand W. A. Kaysser, in “Sintered Metal-Ceramic Composites, ” edited by G. S. Upadhyaya (1984) pp. 51–70.
J. L. Shi, T. S. Yenand H. Schubert, J. Mater. Sci. 32 (1997) 1341–1346.
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Shi, J.L. Solid state sintering of ceramics: pore microstructure models, densification equations and applications. Journal of Materials Science 34, 3801–3812 (1999). https://doi.org/10.1023/A:1004600816317
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DOI: https://doi.org/10.1023/A:1004600816317