Calculation of Grain-Boundary Bonding in Rare-Earth-Doped β-Si3N4

First-principles molecular orbital calculations are performed by the discrete variational Xalpha method using model clusters of rare-earth-doped β-Si₃N₄ and the interface between prismatic planes of β-Si₃N₄ and intergranular glassy films. On the basis of the total overlap population of each cluster, the rare-earth ions are implied to be stable in the grain-boundary model, while they are not stable in the bulk model. These results are consistent with experimental observations showing significant segregation of Ln³⁺ ions at the grain boundary and no solubility of Ln³⁺ into bulk β-Si₃N₄. Grain-boundary bonding is weakened with an increase of the ionic radius of the rare-earth ions, which provides a reasonable explanation for the ionic size dependence of the crack propagation behaviors as well as the growth rate of the prismatic plane in the rare-earth-doped β-Si₃N₄ during liquid-phase sintering.