A model for microwave processing of compositionally changing ceramic systems

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A finite-difference model was used to simulate the temperature and composition distributions produced inside a specimen heated with microwave energy during a process involving a change in composition. The dielectric properties of the specimen change with composition, resulting in nonuniform microwave power absorption and steady-state temperature gradients. When the specimen becomes less lossy as it reacts, or if the changes in the microwave heating properties are gradual, the reaction proceeds relatively uniformly and the volumetric microwave heating creates an inside-out reaction profile leading to increased conversions for processes such as reaction bonding and chemical vapor infiltration (CVI). If the specimen becomes more lossy as it reacts, then the reaction proceeds nonuniformly with rapid reaction rates in the hottest parts of the specimen and little or no reaction in the cooler areas. The process may then occur as a reaction front which moves along the specimen, as with combustion synthesis. This type of processing has potential advantages and disadvantages depending on the system.

I. INTRODUCTION Microwave heating provides a potentially useful way to process ceramic materials.1'2 It can provide rapid heating rates and volumetric heating, in contrast to the slow heating rates and surface heating obtained with conventional heating. Although ceramic materials can be sintered rapidly using microwave energy, carefully designed insulation and susceptor configurations must be used to ensure near-uniform heating. 34 Materials that possess a large temperature dependence of the dielectric loss are particularly difficult to heat in a stable manner.5 These factors, together with the high capital cost of microwave equipment, have tended to limit the application of microwave heating to ceramic processing. On the other hand, processes that require that reactants be transported from outside the specimen into the interior through a diminishing pore structure can benefit most from microwave heating. Isothermal heating of these processes often results in unreacted material or incomplete densification in the specimen interior. Examples are reaction-bonding and chemical vapor infiltration. The steady-state temperature gradients inside the specimen can create an inside-to-outside chemical reaction, which results in increased conversion or densification of the final product before the outer pores close. In many cases, such as sintering and annealing, the composition of the ceramic materials being processed remains constant. In contrast, most of the processes that benefit from the temperature gradients created by microwave heating involve changes in composition via a chemical reaction with a gas. Because the rate of reaction 3160

J. Mater. Res., Vol. 10, No. 12, Dec 1995

depends on both temperature and reactant gas composition, density and composition gradients which affect the microwave heating characteristics will develop. This will lead to undesirable nonuniform microstructures. In the microwave-assisted chemical vapor infi