A micromechanistic model of the combustion synthesis process: Part I. Theoretical development
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A theoretical model of the combustion synthesis process has been developed. In particular, a set of nonlinear and interrelated partial differential equations is given that accounts for all of the relevant physical and chemical processes that occur during the combustion synthesis process. The appropriate conservation equations for thermal energy, mass, and momentum densities are correctly described—for each phase at each point in the sample—at all times during the process. In addition, details of the necessary interphase transfer terms are expressed in a number of constitutive relationships, in which the dependence of an independent variable upon its dependent variable(s) is given explicitly. In doing so, microstructural details are accounted for, derived primarily from percolation concepts as applied to disordered porous media. All assumptions that are incorporated into the theoretical model have been tabulated in detail. This theoretical model establishes an approach to the development of a sound, quantitative, and fundamental understanding of the combustion synthesis process, particularly with respect to the processing-microstructure-properties relationship. It also provides a point of departure for conducting detailed, quantitative computer experiments of the combustion synthesis process.
I. INTRODUCTION The reaction synthesis process can be used to fabricate a large number of advanced ceramic, intermetallic, and composite materials.1"14 The combustion synthesis (or self-propagating high-temperature synthesis [SHS]) process is a significant subclass of reaction synthesis processes that exploit a rapid and exothermic chemical reaction.2-5'61011 The process derives the thermal energy that is required to drive the process from this internal source, rather than from an external and usually expensive source (e.g., a furnace). Several advantages of the combustion synthesis process include (i) materials can be made that are difficult to produce by other synthesis methods; (ii) external heating requirements are minimal, thus underscoring a principal economic advantage; (iii) self-purification may occur, since the high temperatures involved may cause volatilization of impurities; and (iv) the method can compete economically with existing commercial materials synthesis processes. Empirical studies have demonstrated that combustion synthesis can indeed produce useful materials.15"21 A complete, quantitative connection between (i) the type, amount, and distribution of constituent phases and pores in the as-synthesized product material and (ii) the size, purity, and distribution of the starting materials has not been rigorously established. Thermodynamic studies merely give equilibrium phase distributions for a distinctly nonequilibrium process.22"24 Kinetic studies 2592
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J. Mater. Res., Vol. 9, No. 10, Oct 1994
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have only begun to focus on one or more of the important subprocesses.17 Theoretical modeling studies are only as accurate as the physical picture upon which
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