Effects of Space Charge, Grain‐Boundary Segregation, and Mobility Differences Between Grain Boundary and Bulk on the Conductivity of Polycrystalline Al₂O₃

Abstract

The potential difference between grain boundary and bulk and the concentrations of native and foreign point defects in the bulk, the grain boundary (gb), and the subgrain boundary space‐charge region (sg) of polycrystalline Al2O3 doped with acceptors are computed for the case that the dopants segregate at the grain boundaries, with either the ionized or the nonionized acceptor as the dominant species. Expressions are derived for the effective dc conductivity of a polycrystalline material on the basis of a model in which the grain has one or two shells with conductivities different from that of the bulk. Combination of the two results yields expressions for the effective ionic and electronic conductivity of doped A12O3 as a function of grain size with distribution coefficients gb/sg, mobility ratios in the various regions, and equilibrium constants as parameters. At impurity concentrations normally found in ceramics, the contribution by subgrain boundaries to conductivity may be neglected. The theoretical results are compared to published data for Al2O3:Mg, Fe, and Ti.

Experiment and Theory of Diffusion in Alumina

“…With aliovalent impurities, the grain boundary could be charged and this, together with the compensating space-charge region, should be considered (a discussion is given in Ref. 15).…”

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“…Because the electron potential at the metal phase is sufficiently higher than that of oxide phase, the negative potential at grain boundary reference to the bulk (6 0 < 6 1 ¼ 0) may be developed and the curvature of which is related to the charge density and thus the defect concentration according to the Poisson's equation [21]. The concentration of the effectively positive charged protons may increase in the grain boundary layer (space charge layer).…”

Solute and defect segregation at the space charge layers of Fe-doped fine-grained Al2O3: Effect on the creep rate

“…The segregation of these defects in the grain boundary or subgrain boundary regions alters defect concentrations at the grain boundary, in the subgrain boundary space charge and in the bulk. 8 It is now well accepted that both the ionic size difference (resulting in elastic misfit strain energy) as well the valence (resulting in charge compensation) contribute to the driving force for segregation. Considering only the ionic charge (i.e.…”