Combustion synthesis of metal carbides: Part I. Model development
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. Caob) 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 (Received 15 October 2004; accepted 8 February 2005)
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 different driving forces from the relevant phase diagram. The occurrence of phase transitions is 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)].
I. INTRODUCTION
It is well known that the large heat release associated with the chemical conversion of reactants in products in highly exothermic systems can give rise to selfsustaining reactions.1 Irrespective of the gaseous, liquid, or solid nature of reactant species, the experimental setup can be suitably arranged to allow the generation of hightemperature combustion waves. Due to system exothermicity and consequent self-sustaining characteristics of the process, combustion waves are able to self-propagate along directions which depend upon experimental conditions.2 The combustion process involving solid phase reactants and products is generally referred to as self-
Address all correspondence to these authors. a) e-mail: [email protected] b) e-mail: [email protected] DOI: 10.1557/JMR.2005.0152 J. Mater. Res., Vol. 20, No. 5, May 2005
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propagating high-temperature synthesis (SHS). Since the early 1970s, it has been used for the preparation of advanced materials, such as intermetallics, ceramics, and composites.3 According to the picture emerging from about three decades of inten
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