A mass transport equation which takes into account parallel diffusion paths for both anions and cations was derived and applied to the diffusional creep of polycrystalline ionic solids. From the results of the analysis, several limiting conditions were found for grain-boundary- and lattice-diffusion-controlled kinetics. These conditions depend on temperature, grain size, and type and concentration of cation impurities. Examples of these limiting situations are given for the creep of polycrystalline Fe-doped MgO and transition-metal-doped Al2O3.

Summary
A mass transport equation which takes into account parallel diffusion paths for anions and cations was derived and applied to the diffusional creep of polycrystalline ionic solids. The effect of grain size and cation impurities of variable valence in solid solution on the relative contributions of lattice and grain-boundary diffusion of different ionic species in polycrystalline MgO and Al2O3 was examined. Depending on the temperature, grain size, impurity level, and O2 partial pressure, several limiting conditions were found:

Limit I: At very small grain sizes and reasonably small cation lattice diffusivities the creep rate will be controlled by the slower-moving ion in the grain-boundary regions (i.e. Coble creep).

Limit II: For intermediate grain sizes and cation lattice diffusivities the creep rate will be controlled by cation lattice diffusion when anion transport is significantly faster near grain boundaries than in the lattice (i.e. Nabarro-Herring creep).

Limit III: For an appropriate combination of large grain size and high cation lattice diffusivity the creep rate will be controlled by anion boundary diffusion (i.e. Coble creep).

Well-defined examples of limits I and II have been observed in the creep of Fe-doped polycrystalline MgO, and tentative evidence exists for limit III. Most results of studies of creep in polycrystalline Al2O3 (doped and undoped) fall within limit II, with some overlap with limit III.

The model developed in the present work explains much of the data in the literature in which creep rates correspond to cation lattice mobilities. It is concluded that in the creep of polycrystalline ionic solids anion transport near grain boundaries is rapid and can, in some circumstances, be rate-controlling. It should also be possible to apply this model to sintering and thermal-grooving data for such systems, particularly for Al2O3, in which cation lattice diffusion is frequently observed to be rate-controlling.32

Mass Transport in the Diffusional Creep of Ionic Solids

Influence of MnO and TiO2 additives on density, microstructure and mechanical properties of Al2O3

The effect of TiO2 and MnO2 on densification and microstructural development of alumina

Alumina powders with varying iron oxide contents were prepared by coprecipitation. The powders were spheroidized by passing them through an oxygen-acetylene flame. The spheres were sized, annealed, and sintered in air and in N2 with 132 ppm O2. Isothermal studies were combined with constant-rate-of-heating studies to identify the mechanism of sintering and to calculate the diffusion coefficients. The contribution of surface diffusion during initial-stage sintering of Fe-doped Al2O3 was estimated by combining shrinkage and neck-growth data. The effect of Ti on the sintering rate of Fe-doped Al2O3 was also studied. Both Fe2+ and Ti4+ ions enhanced the sintering rate of Al2O3. A defect model for corundum is proposed to explain the sintering data for transition-metal-ion-doped Al2O3.

Effect of Iron Oxide on the Sintering Kinetics of Al2O3

The effect of doping simultaneously with iron and titanium was studied in dense, polycrystalline alumina over a range of grain sizes (10 to 100 μm) and temperatures (1250° to 1550°C). In the double-doped system, the titanium concentration was varied between 0.05 and 0.15 cation %, whereas the iron-dopant level was varied between 0.05 and 6 cation %. For iron concentrations below about 2 to 3%, the aluminum vacancy concentration was dominated by the presence of quadrivalent titanium in substitutional solid solution and Nabarro-Herring diffusional creep at 1450°C was rate-limited by aluminum lattice diffusion. As the iron-dopant level was increased, the concentration of divalent iron became comparable to that of quadrivalent titanium, leading to a suppression in the cation lattice diffusivity at an iron-to-titanium ratio of ∼60. These results suggested that, at the dopant levels and temperatures studied, more than 98% of the iron was in the trivalent state. The diffusional creep of polycrystalline alumina doped with a single iron impurity (0.2 to 2%) was reinterpreted in terms of simultaneous contributions of aluminum lattice and grain-boundary diffusion, consistent with a grain-size dependence corresponding to a mixture of Nabarro-Herring and Coble creep. Aluminum grain-boundary diffusion was found to be significantly enhanced by the presence of iron in solid solution. Evidence is presented to suggest that the diffusional creep of polycrystalline Al2O3 doped with a single titanium dopant is interface-controlled. Interfacial kinetics can be promoted by several factors, including (1) a small grain size, (2) a high cation lattice diffusivity, (3) slow cation grain-boundary diffusion, and (4) the presence of a grain-boundary second phase.

Effect of Doping Simultaneously with Iron and Titanium on the Diffusional Creep of Polycrystalline A12O3

Effects of manganese oxide on the initial sintering kinetics of compacts of 5-μ diameter alumina were studied by isothermal shrinkage measurements from 1450° to 1650°C. The observed rates were characterized by assuming a volume-diffusion mechanism. Variations in sintering rate with both oxygen partial pressure in the furnace and impurity concentration, as well as the observed activation energy, indicated oxygen-ion diffusion was the rate-limiting step during densification.

J. R. Keski

Papers

Initial Sintering of MnXO-Al2O3