The creep rate (ė) predicted by the boundary diffusion (Db) model is ė≃150σDbWΩ/(GS)3kT, where σ is the stress, W is the boundary width, (GS) is the average grain size, and Ω is vacancy volume. The stress dependence is the same as the lattice diffusion model, given by C. Herring, while the grain size dependence and the numerical constant are greater for boundary diffusion. Discussion of the mechanism of creep in polycrystalline alumina is based on the differences between the lattice and boundary diffusion models.

Photomicrographs of pore and grain boundary structures in

Porous structures having a continuous solid phase with isolated pores were prepared by the addition of different amounts of crushed naphthalene to an alumina casting slip. Samples of from 5 to 500/, porosity were fired together for comparable grain development, eliminating structural variables except porosity. Eff ects of porosity and temperature on strength, elastic modulus, modulus of rigidity, and coefficient of thermal expansion were investigated. Effects of porosity on thermal stress resistance and torsional creep properties were studied at constant temperature.

Experimental measurements of the rate of shrinkage of pressed A1203 compacts, the neck growth between single-crystal A1203 spheres and plates, and the effect of particle size on neck growth between single-crystal AlzOa spheres and plates are mutually consistent with the bulk diffusion sintering model. Tbe temperature dependence of the rate of shrinkage and neck growth in AizOJ is characterized by an activation energy of 165 kcal. per mole. Apparent diffusion coefficients and temperature dependence calculated from the shrinkage of pressed compacts of Fez03 agree with measured diffusion coefficients for the diffusion of Fe in Fez03.

Models for initial-, intermediate-, and final-stage densification under pressure have been developed, which explicitly include both the surface energy and applied pressure as driving forces. For the initial stage, the time dependences and size effects given by the integrated equations are identical to those reported earlier for surface energy (alone) as the driving force. The only modification is that the surface energy (γ) is expanded into (γ+PaR/π), where Pa is the applied pressure and R is the particle radius. For the intermediate stage of the process, the Nabarro-Herring and Coble creep models may be adapted to give approximate (∼4×) densification rates for lattice and boundary diffusion models, respectively. In these cases the complex driving force is written as: (Pa/D+γk), where D is the relative density, and k is the pore surface curvature. At the final stage of the process those models are invalid; an alternate model is developed based on diffusive transport between concentric spherical shells which will give a better assessment of the time dependence of densification high density (>95%); the driving force is (Pa/D+γk) in this case also. Because of the fact that the pore size is some unknown function of density, the rate equations cannot be integrated without further information. It is shown that of the various relations which have been assumed in development of models for hot pressing, for the effective stress in relationship to the applied stress and the porosity, (Pa/D) is the only form which satifies the criteria demanded by self-consistency in generation of steady-state diffusion models.