Combustion synthesis of metal carbides: Part II. Numerical simulation and comparison with experimental data
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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, Piazza d’Armi, 09123 Cagliari, Italy, and CRS4, Parco Scientifico e Tecnologico, POLARIS, Edificio 1, 09010 Pula (CA), Italy (Received 15 October 2004; accepted 8 February 2005)
Based on the general theoretical model proposed in Part I of this work [J. Mater. Res. 20, 1257 (2005)], a series of numerical simulations related to the self-propagating high-temperature synthesis in the Ti–C system is presented. A detailed and quantitative description of the various physical and chemical processes that take place during combustion synthesis processes is provided in Part II of this work. In particular, the proposed mathematical description of the system has been discussed by highlighting the relation between system macroscopic behavior obtained experimentally with the modeled phenomena taking place at the microscopic scale. Model reliability is tested by comparison with suitable experimental data being nucleation parameters adopted for the fitting procedure. The complex picture emerging as a result of the model sophistication indicates that the rate of conversion is essentially determined by the rate of nucleation and growth. In addition, comparison between model results and experimental data seems to confirm the occurrence of heterogeneous nucleation in product crystallization.
I. INTRODUCTION
Self-propagating high-temperature synthesis (SHS) processes have been widely investigated to prepare a large number of advanced ceramic, intermetallic, and composite materials.1 It is well known that SHS may be regarded as a complex process involving several interrelated phenomena such as the formation of molten phases as well as of final solid products and their subsequent microstructural evolution. Consequently, degree of sophistication of the mathematical description of SHS may be considerably high.2,3 As discussed in Part I of this work,4 several homogeneous and heterogeneous approaches have been adopted for modeling important features of SHS processes.5–9 However, since a comprehensive description of all the complex phenomena taking place was still missing, a novel mathematical model to thoroughly simulate SHS processes is proposed in Part I of this work.4 Based on a
Address all correspondence to these authors. a) e-mail: [email protected] b) e-mail: [email protected] DOI: 10.1557/JMR.2005.0153 J. Mater. Res., Vol. 20, No. 5, May 2005
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heterogeneous approach first presented by Stangle and co-workers,10–12 the proposed model simulates microstructural evolution using suitable population balances and properly evaluating the different driving forces from the relevant phase diagram. The main goal of this longterm approach is to establish an advanced modeling strategy for SHS processes, which not only provides a pro
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