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

Abstract

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.

Effect of Rare Earth Oxide Additives on the Phase Transformation Rates of Si3N4

“…In contrast, the rest of the elements showed the atomic bonding of atoms along the prismatic plane of Si 3 N 4 that is periodic and occurred at two very specific atomic sites, A and B. Sm atoms bond in single‐atom configuration to both positions, whereas Er, Yb, and Lu atoms bond in pairs at A site and singly at B site. Thus, it could be concluded that the segregation tendency of RE ions at the interface increases with increasing atomic number (decreasing ionic radius), which agrees well with the prediction made from the first principle molecular orbital calculations performed by the discrete variation (DV) Xα method: the total chemical bonding strength evaluated by the total overlap population increased by the presence of any RE 3+ at the interface, and it strengthened with increasing atomic number of RE (decreasing ionic radius) 8 …”

“…Thus, it could be concluded that the segregation tendency of RE ions at the interface increases with increasing atomic number (decreasing ionic radius), which agrees well with the prediction made from the first principle molecular orbital calculations performed by the discrete variation (DV) Xa method: the total chemical bonding strength evaluated by the total overlap population increased by the presence of any RE 31 at the interface, and it strengthened with increasing atomic number of RE (decreasing ionic radius). 8 The next fundamental question is what the ''catalytic effect'' is. Segregation/adsorption occurs as a result of decreasing the free energy of the total system.…”

Atomic Resolution Transmission Electron Microscopy of the Intergranular Structure of a Y2O3‐Containing Silicon Nitride Ceramic

“…The results of Nakayasu et al 10 demonstrate how Ln 3ϩ ions are more stable at the interfaces and less stable in the Si 3 N 4 matrix. Benco 9 states that oxygen present along grain boundaries in Si 3 N 4 has a destabilizing effect on the bonding characteristics if associated antibonding interactions are not prevented.…”

“…8 -14 Using a Hartree-Fock periodic approach with extended Hückel tight-binding approximation 8,9 and molecular dynamic calculations with a pair-potential set approach, 10 atomic positions and grain-boundary bonding characteristics have been determined for a variety of interface-atom coordinations. 8 -14 Using a Hartree-Fock periodic approach with extended Hückel tight-binding approximation 8,9 and molecular dynamic calculations with a pair-potential set approach, 10 atomic positions and grain-boundary bonding characteristics have been determined for a variety of interface-atom coordinations.…”

High-Resolution Interface Atomic Structure Analysis in Silicon Nitride Ceramics

“…Additionally, this new information about the atomic structure and bonding characteristics will help verify and refine atomic-structure calculations performed in the past [16][17][18][19][20][21]. A double peak (102eV and 103.5eV) appears in the spectrum taken from atom position A.…”