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

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.