No abstract

First‐principles molecular‐orbital calculations using the discrete‐variational Xα method have been made on model clusters of α‐Si3N4 and its solid solutions with lanthanide elements, which occupy interstitial sites in the structure. The formula is LnχSi12–4.5χAl4.5χO1.5χN16–1.5χ (Ln = La, Nd, Gd, Dy, Ho, Er, Tm, Yb), i.e., a Ln‐α‐SiAION solid solution. Covalent bond strength between Si and N, evaluated by overlap population, increases because of the presence of trivalent charges at the interstitial sites. When a Ln3+ ion is present, antibondings occur between Ln orbitals and N/Si orbitals, and they depend significantly on the ionic radius of Ln3+. The total overlap population for the whole cluster is determined by the balance of Si‐N bond reinforcement and Ln‐N/Si antibonding. Although no lattice relaxation around the Ln3+ ion is included in the present calculation, good correlation between maximum solubility and the total overlap population for the whole cluster is demonstrated for the first time.

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.

Two round robins (RRs) of the quantitative phase analysis (QPA) of silicon nitrides (Si 3 N 4 ) using the mean normalized intensity (MNI) method and the Rietveld method were conducted as one of the projects for establishing standard methods of characterizing advanced ceramic materials. Accuracy and precision of three techniques, namely the MNI method using peakheight intensity (MNI+P), the MNI method using integrated intensity (MNI+I) and the Rietveld method (R), were tested. Precision of the methods was found to follow the order R < MNI+I < MNI+P in the ®rst RR and MNI+I < R < MNI+P in the second RR. Resulting accuracy of the methods was ranked R 9 MNI+P < MNI+I in the ®rst RR and MNI+P < R 9 MNI+I in the second. The MNI+P method, which relies upon a simple and routine procedure for measuring peak-height intensities, gave the best precision in both RRs. Both the accuracy and the precision of the Rietveld method were the worst among the three techniques in the ®rst RR. They were, however, signi®cantly improved in the second RR. Although the precision of the MNI+I method was the worst in the second RR, it was better than that in the ®rst, and the accuracy was the best in both the ®rst and the second RR. The degree of improvement from the ®rst to the second RR, in both precision and accuracy, was MNI+P < MNI+I < R, coinciding with the ease of these three techniques in reverse order. This result is largely due to (i) a new protocol for experimental and analytical parameters and (ii) improved skill of the participants in data analysis in the second RR. Magnitudes and signs of the observed errors could be interpreted through results of the theoretical studies.

First-principles molecular-orbital calculations of ␣-and ␤-Si 3 N 4 with a trivalent lanthanide (Ln 3+ ) ion at the interstitial site are conducted using model clusters that are composed of 41-43 atoms, neglecting lattice relaxation effects. When an interstitial Ln 3+ ion is present, strong antibonding between the Ln 3+ ion and Si 3 N 4 is found. The magnitude of the antibonding is almost the same between the ␣-and ␤-Si 3 N 4 matrices. On the other hand, the Si−N bond around the Ln 3+ ion is notably reinforced in ␣-Si 3 N 4 but not so much in ␤-Si 3 N 4 . The different electronic response to the presence of the Ln 3+ ion for the Si−N bond is concluded to be the origin of the different solubilities of interstitial Ln 3+ ions between ␣-and ␤-SiAlONs that are reported experimentally. The contribution of the electric field that is induced by the presence of a trivalent charge at the interstitial site is examined in detail; we have found that the Si−N bond strength is not simply determined by the electric field but rather in a more complex manner.