Analysis of microwave sintering of ceramics

Abstract

The use of microwaves to process ceramics has been an active area of research over the past three decades. The literature on microwave (MW) sintering is largely experimental in nature. Although models for microwave heating have been developed (Ayappa et?al., 1991, 1992), models specifically for microwave sintering have yet to appear in the literature. In this work, a finite?element model is developed to predict temperature, microwave power, porosity, and grain?size distributions for ceramic slabs exposed to microwaves. The dielectric and thermal properties of the ceramic are assumed to be temperature independent. The microwave power, derived from Maxwell’s equations, and the porosity and grain?size evolution equations for the late stages of sintering (Svoboda and Riedel, 1992) are incorporated into the model. During sintering, the porosity of the medium continuously changes. The effective dielectric and thermal properties are therefore functions of the evolving porosity. Dielectric properties are assumed to follow nonlinear mixture rules, while thermal properties are assumed to follow linear mixture rules. Microwave heating studies of slabs of Al?O? and SiC were carried out and their heating rates compared. It was found that the microwave power absorbed by SiC is much greater than that absorbed by Al?O? due to the higher dielectric loss of SiC. As a result, the temperature rise in SiC samples is also higher. The penetration depth in Al?O? is very large compared to the sample sizes studied, and therefore no attenuation is observed in the power?absorption profiles of Al?O? slabs. Microwave heating studies of cylindrical samples of Al?O? and SiC exposed to TMz?polarized plane waves were also conducted, and the heating rates were compared with those of slabs. Heating rates in cylinders were generally found to be higher than those in slabs, except in cases where resonance occurs for a particular slab length but not in the cylinder. Microwave heating studies of Al?O? slabs with dielectric properties varying with temperature were also performed. A thermal runaway effect was observed when the material was maintained at temperatures higher than a critical temperature. The influence of temperature, grain?boundary diffusion coefficient, and initial grain size on the late stages of sintering was studied by solving the evolution equations for porosity and grain diameter. Densification rates were found to be faster at higher grain?boundary diffusion coefficients, which retards grain growth. At higher temperatures, densification slows down, allowing grains to grow more rapidly. Microwave sintering studies for Al?O? slabs during the late stages of sintering were performed, and the effect of sample size was investigated. Sintering time was observed to be greater for slabs in which power absorption and temperature were higher. This result agrees with trends observed in conventional sintering. High power absorption at specific sample lengths is attributed to resonance effects. Microwave sintering was also compared with conventional sintering under identical heating?rate conditions. It was observed that the time required to reach final densification was the same in both cases. This outcome arises because microwaves were used solely as a heat source in the present model, and no additional microwave?specific effects were considered.