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The chemical bonding states of GeO 2 and/or TiO 2 -doped tetragonal zirconia polycrystal (TZP) are calculated by a first principle molecular orbital method using model clusters. It is clarified that Ge 4+ and Ti 4+ ions, which are substituted into a lattice of TZP, have a high covalent bond with oxygen ions rather than Zr-O bond. Covalency of TZP is more increased by solution of germanium ions than that of titanium ones. In superplastic deformation of TZP, an addition of GeO 2 or TiO 2 enhances tensile ductility of TZP. Germanium ion is more effective to improve ductility than titanium. The increment of covalency is in a good agreement with the improvement of elongation to failure in doped TZP. Dopant cations segregate at grain boundaries and form no secondary phase. Assuming that a dopant effect on chemical bonding states in grain boundaries is similar to that in grain interior, segregation of germanium or titanium ion increases covalent bonding strength nearby grain boundaries. Such increasing of covalency is likely to enhance cohesion of grain boundaries. The enhancement of grain boundary cohesion suppresses intergranular failure during tensile deformation at elevated temperatures. This must be the reason why an addition of GeO 2 and TiO 2 is effective to improve the high temperature ductility of TZP. Our calculation suggests that the covalency nearby grain boundaries have a critical role in the tensile ductility of TZP.

Fine-grained 3Y-TZP has been known to show high superplasticity. Addition of a small amount of metal oxide influences the superplastic behavior in 3Y-TZP. In this study, 3Y-TZP doped with 1 mol% GeO 2 , TiO 2 or BaO were fabricated, and respective grain boundary energy has been systematically measured by a thermal grooving technique with atomic force microscopy. It has been found that addition of Ge 4þ or Ti 4þ ions decreases the grain boundary energy to stabilize the grain boundaries in TZP whereas doping of Ba 2þ ion increases the grain boundary energy to destabilize the grain boundaries. A change in the grain boundary energy should be due to segregation of dopant at grain boundaries. It has been also found that the elongation to failure of cation-doped 3Y-TZP is directly proportional to the stability of grain boundary. Grain boundary energy is thus one of the principal factors to determine the tensile ductility of TZP. In order to reveal the effect of dopant on the grain boundary energy, lattice static calculations and first principles molecular orbital calculations have been performed for supercells and model clusters including the present dopant, respectively. A series of results shows that substitution of Ge 4þ or Ti 4þ ion for Zr 4þ ion increases the covalency of TZP, but the covalency of TZP is reduced by addition of Ba 2þ ions. The grain boundary energy is found to have a relationship with covalency nearby grain boundaries in TZP.

Simple and accurate rules similar to that of Tchebycheff. A numerical example is given for a sine curve and the result compared with those by Gauss', Tchebycheff's, Simpson's and Trapezoidal rules.

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