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Ind. Eng. Chem. Res. 1998, 37, 2246-2249
Influence of Reaction Mixture Porosity on the Effective Kinetics of Gasless Combustion Synthesis Cynthia R. Kachelmyer and Arvind Varma* Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
Alexander S. Rogachev and Alexander E. Sytschev Institute of Structural Macrokinetics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia
The effective activation energies for the self-propagating high-temperature synthesis of Ti5Si3 were determined for samples with porosities ranging from 30% to 62%. A low-activation-energy regime was found for highly porous samples, while relatively high effective activation energies of 200-250 kJ/mol were measured for samples with porosity less than 50%. The same effect was also observed in two other systems, involving syntheses of TiC and MoSi2. The limiting role of interparticle heat transfer in propagation of the combustion front for highly porous samples is suggested as a possible explanation for the observed phenomenon. E dη ) φ(η)k0 exp dt RT
Introduction It is a great pleasure to participate in this felicitation for Professor L. K. Doraiswamy. We hope that our discussion of effective kinetics in the context of gasless combustion synthesis will appeal to him, especially since he has made seminal contributions to our understanding of solid-solid reactions (cf. Tamhankar and Doraiswamy, 1979). Combustion synthesis is a promising technique to synthesize a wide variety of advanced materials that include powders and near-net shape products of ceramics, intermetallics, composites, and functionally gradient materials (Merzhanov, 1994; Varma et al., 1998). This process is based on the self-sustained propagation of a chemical exothermic reaction wave through a heterogeneous mixture of metal and nonmetal powders. Gasless combustion synthesis is realized when all initial reactants and intermediate and final products remain in a condensed (solid or liquid) state during the course of the process. Only a negligible amount of gas is released in the combustion wave, consisting of vapors of metals and, possibly, volatilized impurities. Due to evolution of the high reaction heat, the process results in a significant (up to 3500 K) and very rapid (104-106 K/s) increase in temperature. Conversion of the reactants into the final product at such high temperatures occurs in a time scale of seconds, which complicates investigations of the combustion synthesis kinetics and mechanism. A study of the effective kinetics for materials produced by combustion synthesis has great significance for further development of the method. The determination of kinetic parameters (especially the energy of activation, E) and their comparison with known elementary processes may provide an insight into the controlling steps of the combustion synthesis mechanism. The most common method to determine the effective energy of activation is based on the assumption that the controlling step is described by Arrhenius-type kinetics: * To whom correspondence should be addressed.
(
)
(1)
where η is the degree of reactant conversion and the other quantities are defined in the Nomenclature section. In this case, the combustion velocity, U, can be expressed by the following formula (Zeldovich and Frank-Kamenetskii, 1938; Merzhanov, 1977):
U)
[
( )]
RTC2 k0 λ E exp -∆HrF E f(η) RTC
1/2
(2)
Thus, a plot of ln(U/Tc) as a function of 1/Tc yields a straight line, where the effective energy of activation, E, can be obtained from the slope. This procedure becomes more complicated in the case of combustion with broad zones, phase transitions (e.g., melting), or multistage reactions; however, the general principle still applies. This method for determining the energy of activation was first applied in combustion synthesis by Borovinskaya et al. (1974) and has been followed in numerous subsequent investigations. It was shown previously for the Ti-C system that the value of E can vary with the combustion temperature due to a change in the rate-limiting step during the course of the exothermic chemical reaction (Kirdyashkin et al., 1981; Dunmead et al., 1989). The present work is focused on studying the influence of green mixture porosity on the combustion synthesis kinetics, and by following the approach mentioned above, determining the effective E values. The systems studied include TiC, Mo-Si, and Ti-Si in which the metal, nonmetal, or both reactants melt, respectively, at the combustion temperature when no diluent is present. Experimental Section High-purity fine elemental reactant powders of Ti (99.5% purity,
