Theoretical models for the combustion of alloyable materials
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INTRODUCTION
THIS article is principally concerned with the flame propagation induced by the exothermic interdiffusion of two solid substances (usually metals). Systems of this class are potentially important to the production of highquality ceramics and belong to the larger topic of combustion synthesis. In a previous article, ~1] a theoretical model showed that lamina of alloyable substances would give rise to a self-propagating combustion wave. It was shown that an activation energy barrier in the diffusion coefficient would behave much as the chemical-reaction activation barrier in well-known models of premixed gas flames, t21 Diffusion in the SHS systems is essential, however, since there is no analogue to a "premixed" flame here. An activation energy barrier to interdiffusion keeps the differentiated particles of alloyable material distinct until the thermal wave raises the temperature to the point that interdiffusion can contribute to its propagation. Though both of these systems can have aspects of mass diffusion and reaction, the gas flame derives its propagation mechanism from exothermic, locally homogeneous chemical reaction, while the alloying reaction relies on mixing one constituent with another. Afterburning refers to the general characteristic exhibited by many of these systems that, after the thin flame zone has passed, a residual quantity of material continues to react long after. Ceramics have desirable properties for use in combustion machinery, such as turbine blades in jet engines. However, they are notoriously difficult to reform (by grinding, etc.), and thus, it would be of considerable use to form the shape of the desired product first and then undergo a combustion process to the desired ceramic ROBERT ARMSTRONG, Technical Staff Member, is with the Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551. This article is based on a presentation made in the symposium "Reaction Synthesis of Materials" presented during the TMS Annual Meeting, New Orleans, LA, February 17-21, 1991, under the auspices of the TMS Powder Metallurgy Committee. METALLURGICAL TRANSACTIONS A
in situ.[3] The final strength and other properties are dependent on the details of the interdiffusion process during the time that the flame passes. [4] Typically, the dynamics of the flame involve a balancing between the large length-scale parameters (temperature, etc.) and microscopic parameters (particle size, diffusion, etc.). There are a number of investigations that treat the powder media in a "mesoscopic" fashion, deriving global rate of conversion of reactants by treating the microscopic geometry of the powder as a phenomenological continuum, tSl Aldushin and Khaikin, t6] on the other hand, have studied the "flat particle" problem, in which the geometry of the alloying system is idealized. Their model assumes that the powdered media is equivalent to alternating laminae of alloyable material. This simplification allows the analytic calculation of a flame speed while keeping all of the microscop
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