Sintering Simplified: Surface Area, Density, and Grain Size Relations

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Abstract:

Sintering involves several interactions as particles bond and enable microstructure evolution toward a minimized energy condition, resulting in a complex interplay of measurement parameters. Overriding the evolution is energy minimization, and from that perspective some simple relations emerge. The natural progression is determined by energy reduction, measured by surface area, density, and grain boundary area (grain size). Contrary to the usual sintering analysis that starts with atomic level mass transport mechanisms, presented here is an approach that links to global energy reduction during sintering to simple monitors. Initially sintering converts surface area into lower energy grain boundary area. Subsequently grain growth annihilates grain boundary area. Thus, grain boundary area peaks at intermediate sintered densities, while surface area continuously declines. The trajectory follows a straightforward dependence on density as illustrated using data for a wide variety of materials and consolidation conditions.

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[1] R. M. German, Surface Area Reduction Kinetics during Intermediate Stage Sintering, J. Amer. Ceramic Soc., 61 (1978) 272-274.

DOI: 10.1111/j.1151-2916.1978.tb09301.x

Google Scholar

[2] J. Frenkel, Viscous Flow of Crystalline Bodies under the Action of Surface Tension, J. Phys., 9 (1945) 385-391.

Google Scholar

[3] G. C. Kuczynski, Self-Diffusion in Sintering of Metallic Particles, Trans. TMS-AIME, 185 (1949) 169-178.

Google Scholar

[4] R. M. German, Sintering Theory and Practice, Wiley, New York, (1996).

Google Scholar

[5] E. H. Aigeltinger, H. E. Exner, Stereological Characterization of the Interaction between Interfaces and its Application to the Sintering Process, Metall. Trans., 8A (1977) 421-424.

DOI: 10.1007/bf02661751

Google Scholar

[6] I. Nettleship, M. D. Lehigh, R. Sampathkumar, Microstructural Pathways for the Sintering of Alumina Ceramics, Scripta Mater., 37 (1997) 419-424.

DOI: 10.1016/s1359-6462(97)00131-0

Google Scholar

[7] N. J. Shaw, R. J. Brook, Structure and Grain Coarsening During the Sintering of Alumina, J. Amer. Ceramic Soc., 69 (1986) 107-110.

DOI: 10.1111/j.1151-2916.1986.tb04711.x

Google Scholar

[8] K. D. Zilnyk, G. S. Leite, H. R. Z. Sandim, P. R. Rios, Grain Growth Inhibition of Connected Porosity in Sintered Niobium, Acta Mater., 61 (2013) 5821-5828.

DOI: 10.1016/j.actamat.2013.06.027

Google Scholar

[9] R. M. German, Coarsening in Sintering: Grain Shape Distribution, Grain Size Distribution, and Grain Growth Kinetics in Solid-Pore Systems, Critical Rev. Solid State Mater. Sci., 35 (2010) 263-305.

DOI: 10.1080/10408436.2010.525197

Google Scholar

[10] R. L. Coble, T. K. Gupta, Intermediate Stage Sintering, in: G. C. Kuczynski, N. A. Hooton and C. F. Gibbon (eds. ), Sintering and Related Phenomena, Gordon and Breach, New York, 1967, pp.423-441.

Google Scholar

[11] R. T. Dehoff, R. A. Rummel, H. P. Labuff, F. N. Rhines, The Relationship Between Surface Area and Density in Second-Stage Sintering of Metals, in: H. H. Hausner (ed. ), Modern Developments in Powder Metallurgy, vol. 1, Plenum Press, New York, 1966, pp.310-331.

DOI: 10.1007/978-1-4684-7706-1_17

Google Scholar

[12] A. P. Sutton, R. W. Balluffi, General Aspects of Interfaces as Sources/Sinks, in: Interfaces in Crystalline Materials, Clarendon Press, Oxford, 1995, pp.599-621.

Google Scholar

[13] A. J. Markworth, On the Volume Diffusion Controlled Final Stage Densification of a Porous Solid, Scripta Metall., 6 (1972) 957-960.

DOI: 10.1016/0036-9748(72)90153-6

Google Scholar

[14] F. Wakai, D. Gomez-Garcia, A. Dominguez-Rodriguez, Pore Channel Closure in Sintering of a Ring of Three Spheres, J. Eur. Ceramic Soc., 27 (2007) 3365-3370.

DOI: 10.1016/j.jeurceramsoc.2007.02.188

Google Scholar

[15] J. Svoboda, H. Riedel, H. Zipse, Equilibrium Pore Surfaces, Sintering Stresses and Constitutive Equations for the Intermediate and Late Stages of Sintering - I Computation of Equilibrium Surfaces, Acta Metall. Mater., 42 (1994) 435-443.

DOI: 10.1016/0956-7151(94)90498-7

Google Scholar

[16] R. A. Gregg, F. N. Rhines, Surface Tension and the Sintering Force in Copper, Metall. Trans., 4 (1973) 1365-1374.

DOI: 10.1007/bf02644534

Google Scholar

[17] R. M. German, Manipulation of Strength during Sintering as a Basis for Obtaining Rapid Densification without Distortion, Mater. Trans., 42 (2001) 1400-1410.

DOI: 10.2320/matertrans.42.1400

Google Scholar

[18] R. Watanabe, Y. Masuda, Quantitative Estimation of Structural Change in Carbonyl Iron Powder Compacts during Sintering, Trans. Japan Inst. Met., 13 (1972) 134-139.

DOI: 10.2320/matertrans1960.13.134

Google Scholar

[19] W. Beers, The Sintering and Morphology of Interconnected Porosity in UO2 Powder Compacts, J. Mater. Sci., 8 (1973) 1717-1724.

DOI: 10.1007/bf02403522

Google Scholar

[20] R. M. German, Z. A. Munir, Morphology Relations during Bulk-Transport Sintering, Metall. Trans., 6A (1975) 2229-2234.

DOI: 10.1007/bf02818648

Google Scholar

[21] J. P. Jernot, M. Coster, J. L. Chermant, Model of Variation of the Specific Surface Area during Sintering, Powder Tech., 30 (1981) 21-29.

DOI: 10.1016/0032-5910(81)85023-1

Google Scholar

[22] S. Prochazka, R. L. Coble, Surface Diffusion in the Initial Sintering of Alumina Part 2. Surface Measurement, Phys. Sint., 2 (1970) 1-14.

Google Scholar

[23] R. M. German, Identification of the Common Densification Pathway for Metal Powder Compaction, Sintering, and Pressure-Assisted Densification, in: Advances in Powder Metallurgy and Particulate Materials - 2014, Metal Powder Industries Federation, Princeton, 2014, Part 1, pp.132-149.

DOI: 10.2298/sos0601095u

Google Scholar

[24] A. S. Watwe, R. T. Dehoff, Metric and Topological Characterization of the Advanced Stages of Loose Stack Sintering, Metall. Trans., 21A (1990) 2935-2941.

DOI: 10.1007/bf02647214

Google Scholar

[25] E. H. Aigeltinger, R. T. Dehoff, Quantitative Determination of Topological and Metric Properties during Sintering of Copper, Metall. Trans., 6A (1975) 1853-1862.

DOI: 10.1007/bf02646849

Google Scholar

[26] R. M. German, Analysis of Surface Diffusion Sintering Using a Morphology Model, Sci. Sint., 14 (1982) 13-19.

Google Scholar

[27] A. C. Nyce, W. M. Shafer, The Relationship of B.E.T. Surface Area to the Sintering Behavior of Spherical Copper Particles, Inter. J. Powder Metall., 8 (1972) 171-180.

Google Scholar

[28] R. M. German, Z. A. Munir, Morphology Relations during Surface-Transport Controlled Sintering, Metall. Trans., 6B (1975) 289-294.

DOI: 10.1007/bf02913572

Google Scholar

[29] R. M. German, Coordination number changes during powder densification, Powder Tech., 243 (2014) 368-376.

DOI: 10.1016/j.powtec.2013.12.006

Google Scholar

[30] R. L. Coble, Sintering Crystalline Solids. 1. Intermediate and Final State Diffusion Models, J. Appl. Phys., 32 (1961) 787-792.

DOI: 10.1063/1.1736107

Google Scholar

[31] C. S. Smith, Further Notes on the Shape of Metal Grains: Space-Filling Polyhedra with Unlimited Sharing of Corners and Faces, Acta Metall., 1 (1953) 295-300.

DOI: 10.1016/0001-6160(53)90102-3

Google Scholar

[32] D. A. Aboav, Foam and Polycrystal, Metallog., 5 (1972) 251-263.

Google Scholar

[33] R. M. German, Z. A. Munir, Surface Area Reduction during Isothermal Sintering, J. Amer. Ceramic Soc., 59 (1976) 379-383.

DOI: 10.1111/j.1151-2916.1976.tb09500.x

Google Scholar

[34] T. M. Hare, Statistics of Early Sintering and Rearrangement by Computer Simulation, in: G. C. Kuczynski (ed. ), Sintering Processes, Plenum Press, New York, 1980, pp.77-93.

DOI: 10.1007/978-1-4899-5301-8_6

Google Scholar

[35] J. V. Kumar, The Hypothesis of Constant Relative Responses and Its Application to the Sintering Process of Spherical Powders, Solid State Phen., 8 (1989) 125-134.

DOI: 10.4028/www.scientific.net/ssp.8-9.125

Google Scholar

[36] R. M. German, The Contiguity of Liquid Phase Sintered Microstructures, Metall. Trans., 16A (1985) 1247-1252.

DOI: 10.1007/bf02670329

Google Scholar

[37] S. H. Hillman, R. M. German, Constant Heating Rate Analysis of Simultaneous Sintering Mechanisms in Alumina, J. Mater. Sci., 27 (1992) 2641-2648.

DOI: 10.1007/bf00540683

Google Scholar

[38] W. D. Kingery, M. Berg, Study of the Initial Stages of Sintering Solids by Viscous Flow, Evaporation-Condensation, and Self-Diffusion, J. Appl. Phys., 26 (1955) 1205-1212.

DOI: 10.1063/1.1721874

Google Scholar

[39] P. V. Hobbs, B. J. Mason, The Sintering and Adhesion of Ice, Phil. Mag., 9 (1964) 181-197.

Google Scholar

[40] R. D. McIntyre, The Effect of HCl-H2 Sintering Atmospheres on the Properties of Compacted Iron Powder, Trans. Quart. ASM, 57 (1964) 351-354.

Google Scholar

[41] R. D. McIntyre, The Effect of HCl-H2 Sintering Atmospheres on Properties of Compacted Tungsten Powder, Trans. Quart. ASM, 56 (1963) 468-476.

Google Scholar

[42] M. J. Readey, D. W. Readey, Sintering of ZrO2 in HCl Atmospheres, J. Amer. Ceramic Soc., 69 (1986) 580-582.

DOI: 10.1111/j.1151-2916.1986.tb04797.x

Google Scholar

[43] M. J. Readey, D. W. Readey, Sintering of TiO2 in HCl Atmospheres, J. Amer. Ceramic Soc., 70 (1987) 358-361.

DOI: 10.1111/j.1151-2916.1987.tb04919.x

Google Scholar

[44] T. Quadir, D. W. Readey, Microstructure Development of Zinc Oxide in Hydrogen, J. Amer. Ceramic Soc., 72 (1989) 297-302.

DOI: 10.1111/j.1151-2916.1989.tb06118.x

Google Scholar

[45] D. W. Readey, D. J. Aldrich, M. A. Ritland, Vapor Transport and Sintering, in: R. M. German, G. L. Messing, R. G. Cornwall (eds. ), Sintering Technology, Marcel Dekker, New York, 1996, pp.53-60.

Google Scholar

[46] J. Svoboda, H. Riedel, H. Zipse, Equilibrium Pore Surfaces, Sintering Stresses and Constitutive Equations for the Intermediate and Late Stages of Sintering - I Computation of Equilibrium Surfaces, Acta Metall. Mater., 42 (1994) 435-443.

DOI: 10.1016/0956-7151(94)90498-7

Google Scholar

[47] C. Toennes, R. M. German, Density and Microstructure Control in a Martensitic Stainless Steel through Enhanced Sintering, Powder Metall. Inter., 24 (1992) 151-157.

Google Scholar

[48] C. A. Bruch, Sintering Kinetics for the High Density Alumina Process, Ceram. Bull., 41 (1962) 799-806.

Google Scholar

[49] R. M. German, Sintering: From Empirical Observations to Scientific Principles, Elsevier, Oxford, (2014).

Google Scholar

[50] H. Y. Suzuki, K. Shinozaki, M. Murai, H. Kuroki, Quantitative Analysis of Microstructure Development During Sintering of High Purity Alumina Made by High Speed Centrifugal Compaction Process, J. Japan Soc. Powder Metall., 45 (1998) 1122-1130.

DOI: 10.2497/jjspm.45.1122

Google Scholar

[51] M. Zadra, F. Casari, L. Girardini, A. Molinari, Microstructure and Mechanical Properties of CP Titanium Produced by Spark Plasma Sintering, Powder Metall., 51 (2008) 59-65.

DOI: 10.1179/174329008x277000

Google Scholar

[52] R. M. German, R. W. Mar, J. C. Hastings, Sintering Behavior of Boron, Ceramic Bull., 54 (1975) 178-181.

Google Scholar

[53] S. C. Coleman, W. Beere, The Sintering of Open and Closed Porosity in UO2, Phil. Mag., 31 (1975) 1403-1413.

Google Scholar

[54] W. H. Lee, H. E. Kim, S. J. Cho, Microstructural Evolution of Gas-Pressure Sintered Si3N4 with Yb2O3 as a Sintering Aid, J Amer. Ceramic Soc., 1997, vol. 80, pp.2737-2740.

DOI: 10.1111/j.1151-2916.1997.tb03187.x

Google Scholar

[55] J. B. Moser, D. H. Whitmore, Kinetics of Sintering of Sodium Chloride in the Presence of an Inert Gas, J. Appl. Phys., 31 (1960) 488-493.

DOI: 10.1063/1.1735615

Google Scholar

[56] F. Amar, J. Bernholc, R. S. Berry, J. Jellinek, P. Salamon, The Shapes of First-Stage Sinters, J. Appl. Phys., 15 (1989) 3219-3225.

DOI: 10.1063/1.342674

Google Scholar

[57] A. S. A. Chinelatto, R. Tomasi, Influence of Processing Atmosphere on the Microstructural Evolution of Submicron Alumina Powder during Sintering, Ceramics Inter., 35 (2009) 2915-2920.

DOI: 10.1016/j.ceramint.2009.03.037

Google Scholar