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Combustion synthesis of metal carbides: Part I. Model development

Published online by Cambridge University Press:  03 March 2011

A.M. Locci ,
A. Cincotti ,
F. Delogu ,
R. Orrù  and
G. Cao
A.M. Locci
Affiliation:
Dipartimento di Ingegneria Chimica e Materiali, Centro Studi sulle Reazioni Autopropaganti (CESRA), Unità di Ricerca del Consorzio Interuniversitario Nazionale di Scienza e Tecnologia dei Materiali (INSTM), Università degli Studi di Cagliari, 09123 Cagliari, Italy
A. Cincotti*
Affiliation:
Dipartimento di Ingegneria Chimica e Materiali, Centro Studi sulle Reazioni Autopropaganti (CESRA), Unità di Ricerca del Consorzio Interuniversitario Nazionale di Scienza e Tecnologia dei Materiali (INSTM), Università degli Studi di Cagliari, 09123 Cagliari, Italy
F. Delogu
Affiliation:
Dipartimento di Ingegneria Chimica e Materiali, Centro Studi sulle Reazioni Autopropaganti (CESRA), Unità di Ricerca del Consorzio Interuniversitario Nazionale di Scienza e Tecnologia dei Materiali (INSTM), Università degli Studi di Cagliari, 09123 Cagliari, Italy
R. Orrù
Affiliation:
Dipartimento di Ingegneria Chimica e Materiali, Centro Studi sulle Reazioni Autopropaganti (CESRA), Unità di Ricerca del Consorzio Interuniversitario Nazionale di Scienza e Tecnologia dei Materiali (INSTM), Università degli Studi di Cagliari, 09123 Cagliari, Italy
G. Cao*
Affiliation:
Dipartimento di Ingegneria Chimica e Materiali, Centro Studi sulle Reazioni Autopropaganti (CESRA), Unità di Ricerca del Consorzio Interuniversitario Nazionale di Scienza e Tecnologia dei Materiali (INSTM), Università degli Studi di Cagliari, 09123 Cagliari, Italy; and CRS4, Parco Scientifico e Tecnologico, POLARIS, 09010 Pula (CA), Italy
*
a)Address all correspondence to these authors. e-mail: cincotti@visnu.dicm.unica.it
b)Address all correspondence to these authors. e-mail: cao@visnu.dicm.unica.it
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Abstract

The definition of a rigorous theoretical framework for the appropriate physico-chemical description of self-propagating high-temperature synthesis (SHS) processes represents the main goal of this work which is presented in two sequential articles. In this article, a novel mathematical model to simulate SHS processes is proposed. By adopting a heterogeneous approach for the description of mass transfer phenomena, the model is based on appropriate mass and energy conservation equations for each phase present during the system evolution. In particular, it takes microstructural evolution into account using suitable population balances and properly evaluating the differentdriving forces from the relevant phase diagram. The occurrence of phase transitionsis treated on the basis of the so-called enthalpy approach, while a conventional nucleation-and-growth mechanistic scenario is adopted to describe quantitatively the formation of reaction products. The proposed mathematical model may be applied to the case of combustion synthesis processes involving a low melting point reactant and a refractory one, as for the synthesis of transition metal carbides from pure metal and graphite. Thus, the model can be profitably used to gain a deeper insight into the microscopic elementary phenomena involved in combustion synthesis processes through a suitable combination of experimental and modeling investigations, as it may be seen in Part II of this work [J. Mater. Res. 20, 1269 (2005)].

Keywords

Combustion synthesisSelf-propagating high-temperature synthesis (SHS)Nucleation & growth
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 5 , May 2005 , pp. 1257 - 1268
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1.Booth, F.: The theory of self-propagating exothermic reactions in solid systems. Trans. Faraday Soc. 49, 272 (1953).CrossRefGoogle Scholar
2.Walton, J.D. and Poulos, N.E.: Cermets from thermite reactions. J. Am. Ceram. Soc. 42, 40 (1959).CrossRefGoogle Scholar
3.Merzhanov, A.G. and Borovinskaya, I.P.: Self-propagating high-temperature synthesis of refractory inorganic compounds. Dokl. Akad. Nauk SSSR 204, 366 (1972).Google Scholar
4.Varma, A., Rogachev, A.S., Mukasyan, A.S. and Hwang, S.: Combustion synthesis of advanced materials: Principles and applications. Adv. Chem. Eng. 24, 79 (1998).CrossRefGoogle Scholar
5.Moore, J.J. and Feng, H.J.: Combustion synthesis of Advanced Materials: Part I. Reaction parameters. Prog. Mater. Sci. 39, 243 (1995).CrossRefGoogle Scholar
6.Moore, J.J. and Feng, H.J.: Combustion synthesis of Advanced Materials: Part II. Classification, application and modeling. Prog. Mater. Sci. 39, 275 (1995).CrossRefGoogle Scholar
7.Novozhilov, B.V.: The rate of propagation of the front of an exothermic reaction in a condensed phase. Dokl. Akad. Nauk SSSR. 141, 151 (1961).Google Scholar
8.Khaikin, B.I. and Merzhanov, A.G.: Theory of thermal propagation of a chemical reaction front. Fiz. Goreniya Vzryva. 2(3), 36 (1966).Google Scholar
9.Merzhanov, A.G.: New elementary model of the second kind. Dokl. Akad. Nauk SSSR 233(6), 1130 (1977).Google Scholar
10.Margolis, S.B.: An asymptotic theory of condensed two-phase flame propagation. SIAM J. Appl. Math. 43, 351 (1983).CrossRefGoogle Scholar
11.Cao, G. and Varma, A.: A new expression for velocity of the combustion front during self-propagating high-temperature synthesis. Combust. Sci. Technol. 102, 181 (1994).CrossRefGoogle Scholar
12.Makhviladze, G.M. and Novozilov, B.V.: Two-dimensional stability of combustion of condensed systems. Zh. Prikl. Mekh. I Tekhn. Fiz. 5, 51 (1971).Google Scholar
13.Shkadinskii, K.G., Khaikin, B.I. and Merzhanov, A.G.: Propagation of a pulsating exothermic reaction front in the condensed phase. Fiz. Goreniya Vzryva. 8, 202 (1971).Google Scholar
14.Aldushin, A.P., Lugovoi, V.D., Merzhanov, A.G. and Khaikin, B.I.: Conditions of stationary combustion wave degradation. Dokl. Akad. Nauk SSSR 243, 1434 (1978).Google Scholar
15.Matkowsky, B.J. and Sivanshinsky, G.L.: Propagation of a pulsating reaction front in solid fuel combustion. SIAM J. Appl. Math. 35, 465 (1978).CrossRefGoogle Scholar
16.Puszynski, J.A., Degreve, J. and Hlavacek, V.: Modeling of exothermic solid-solid noncatalytic reactions. Ind. Eng. Chem. Res. 26, 1424 (1987).CrossRefGoogle Scholar
17.Kanury, A.M.: A kinetic model for metal + nonmetal reactions. Metall. Trans. 23A, 2349 (1992).CrossRefGoogle Scholar
18.Bhattacharya, A.K.: Temperature enthalpy approach to the modeling of self-propagating combustion synthesis of materials. J. Mater. Sci. 27(11), 3050 (1992).CrossRefGoogle Scholar
19.Astapchik, A.S., Podvoisky, E.P., Chebotko, I.S., Khusid, B.M., Merzhanov, A.G. and Khina, B.B.: Stochastic model for wavelike isothermal reaction in condensed heterogeneous systems. Phys. Rev. E 47(1), 319 (1993).CrossRefGoogle Scholar
20.Hwang, S., Mukasyan, A.S., Rogachev, A.S. and Varma, A.: Combustion wave microstructure in gas-solid system: Experiments and theory. Combust. Sci. Technol. 123, 165 (1997).CrossRefGoogle Scholar
21.Nekrasov, E.A., Maksimov, Y.M. and Aldushin, A.P.: Mathematical model of combustion of a titanium-carbon system. Fiz. Goreniya Vzryva. 17(5), 39 (1981).Google Scholar
22.Makino, A.: Fundamental aspects of the heterogeneous flame in the self-propagating high-temperature synthesis (SHS) process. Prog. Energy Combust. Sci. 27(1), 1 (2001).CrossRefGoogle Scholar
23.Yukhvid, V.I., Makladov, S.V., Zhirkov, P.V., Gorshkov, V.A., Timokhin, N.I. and Dovzhenko, A.Y.: Combustion synthesis and structure formation in a model Cr–CrO3 self-propagating high-temperature synthesis system. J. Mater. Sci. 32, 1915 (1997).CrossRefGoogle Scholar
24.Zhang, Y. and Stangle, G.C.: A micromechanistic model of the combustion synthesis process: Part I. Theoretical development. J. Mater. Res. 9, 2582 (1994).Google Scholar
25.Zhang, Y. and Stangle, G.C.: A micromechanistic model of the combustion synthesis process: Part II. Numerical simulation. J. Mater. Res. 9, 2605 (1994).CrossRefGoogle Scholar
26.Zhang, Y. and Stangle, G.C.: A micromechanistic model of microstructure development during the combustion synthesis process. J. Mater. Res. 10, 962 (1995).CrossRefGoogle Scholar
27.Locci, A.M., Cincotti, A., Delogu, F., Orrù, R. and Cao, G.: Combustion synthesis of metal carbides: Part II. Numerical simulation and comparison with experimental data. J. Mater. Res. 20, 1269 (2005).CrossRefGoogle Scholar
28.Locci, A.M., Cincotti, A., Delogu, F., Orrù, R. and Cao, G.: Modeling of Self-propagating reaction: past approaches and future directions. Int. J. of SHS 12, 61 (2003).Google Scholar
29.Locci, A.M., Cincotti, A., Delogu, F., Orrù, R. and Cao, G.: Advanced modeling of self-propagating high-temperature synthesis: the case of the Ti–C system. Chem. Eng. Sci. 59, 5121 (2004).CrossRefGoogle Scholar
30.Fan, H., Chai, H. and Jin, Z.: Dual-solution precipitation mechanism of combustion synthesis of TiC-Fe cermet with finer Ti powder. J. Mater. Sci. 36, 5559 (2001).CrossRefGoogle Scholar
31.Fan, H., Chai, H. and Jin, Z.: Dissolution-precipitation mechanism of self-propagating high-temperature synthesis of mononickel aluminide. Intermetallics 9, 609 (2001).CrossRefGoogle Scholar
32.Holt, J.B. and Munir, Z.A.: Combustion synthesis of titanium carbide: Theory and experiment. J. Mater. Sci. 21, 251 (1986).CrossRefGoogle Scholar
33.Binary Phase Diagrams, edited by Massalski, T.B. (American Society for Metals, Metals Park, OH, 1986).Google Scholar
34.Dirksen, J.A. and Ring, T.A.: Fundamental of crystallization: Kinetic effects on particle size distributions and morphology. Chem. Eng. Sci. 46, 2389 (1991).CrossRefGoogle Scholar
35.Randolph, A.D. and Larson, M.A.: Theory of Particulate Process: Analysis and Techniques of Continuous Crystallization, 2nd ed. (Academic Press, San Diego, CA, 1988).Google Scholar
36.Ramkrishna, D.: Population Balances, Theory and Application to Particulate System in Engineering (Academic Press, London, U.K., 2000).Google Scholar
37.Hulburt, H.M. and Katz, S.: Some problem in particle technology: A statistical mechanical formulation. Chem. Eng. Sci. 19, 555 (1964).CrossRefGoogle Scholar
38.Clavaguera-Mora, M.T., Clavaguera, N., Crespo, D. and Pradell, T.: Crystallization kinetics and microstructure development in metallic systems. Prog. Mater. Sci. 47, 559 (2002).CrossRefGoogle Scholar
39.Gatica, J.E., Dimitriou, P.A., Puszynski, J.A. and Hlavacek, V.: Melting effects on reaction front propagation in gasless combustion. Int. J. SHS 4, 123 (1995).Google Scholar
40.Bird, R.B., Stewart, W.E. and Lightfoot, E.N.: Transport Phenomena (Wiley, New York, NY, 1960).Google Scholar
41.Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure, 2nd ed. (Academic Press Inc., San Diego, CA, 1992).Google Scholar
42.Szekely, J. and Themelis, N.J.: Rate Phenomena in Process Metallurgy (John Wiley & Sons, New York, NY, 1971).Google Scholar
43.Luikov, A.V., Shashkov, A.G., Vasiliev, L.L. and Fraiman, Y.E.: Thermal conductivity of porous systems. Int. J. Heat Mass Transf. 11, 117 (1968).CrossRefGoogle Scholar
44.Hsu, C.T., Cheng, P. and Wong, K.W.: Modified Zehner–Schlunder models for stagnant thermal conductivity of porous media. Int. J. Heat Mass Transf. 37, 2751 (1994).CrossRefGoogle Scholar
45.Singh, B.P. and Kaviany, M.: Effect of solid conductivity on radiative heat transfer in packed beds. Int. J. Heat Mass Transfer. 37, 2579 (1994).CrossRefGoogle Scholar