Formulation of the anisotropic coarsening theory and applications to the liquid-phase sintering of Si3N4.
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We have developed a new coarsening theory that more completely describes grain growth of a system of anisotropic particles such as completely faceted crystals by Ostwald ripening. Our model takes the anisotropy of surface energies on dissimilar facets into account, and the particle sizes are described by a distribution function. The theory is applied to study the coarsening of ,B-silicon nitride in a liquid medium due to the anisotropic growth of grains in different crystallographic directions. A model of the growth of silicon nitride grains is obtained based on the numerical solution of the equations of the new theory. Computer experiments are performed to determine how the distribution function evolves, to investigate the influence of various parameters such as diffusion and interfacial reaction constants on grain growth and to extract grain growth exponents from this model in order to determine the growth mechanisms that are responsible for the anisotropic growth behaviour. Only preliminary numerical results are available thus far due to 1/r instabilities that occur in the theory as r → 0.