A series of molecular-dynamics simulations using a many-body interatomic potential has been performed to investigate the behavior under load of several ͗001͘ and ͗011͘ symmetrical tilt grain boundaries ͑GB's͒ in diamond. Cohesive energies, the work for fracture, maximum stresses and strains, and toughness as a function of GB type are evaluated. Results indicate that special short-period GB's possess higher strengths and greater resistance to crack propagation than GB's in nearby misorientation angles. Based on dynamic simulations, it was found that the mechanism of interface failure for GB's without preexisting flaws is not that implied by Orovan's criterion, but rather GB strength is defined by GB type instead of cleavage energy. In simulations of crack propagation within GB's on the other hand, it was found that critical stresses for crack propagation from atomistic simulation and from the Griffith criterion are consistent, indicating that GB cleavage energy is an important characteristic of GB toughness. Crack propagation in polycrystalline diamond samples under an applied load was also simulated and found to be predominantly transgranular rather than intergranular.

Molecular dynamics simulations of approximately 15 Å thick intergranular films (IGFs) containing SiO 2 and CaO in contact with two surface terminations of the prism (1010) and basal planes (0001) of Si 3 N 4 were performed using a multibody interatomic potential. Samples with the same composition (1.5 mol% CaO) and number of atoms but different crystal planes (i.e., the prism and basal planes of Si 3 N 4 ) were studied. In both the prism and basal cases, the IGF in the final configuration is well-ordered in the interface region. A small number of N ions from the crystal moved into the IGF near the interface, and O ions moved into the N sites in the crystal, indicating the formation of a Si-O-N interface. In addition, Ca ions do not segregate to the IGF-crystal interface. The bonding characteristics of the O ions at the interface with neighbor Si ions are different in the prism and basal cases. Such difference may be explained by the difference in the two crystal Si 3 N 4 surfaces. The Si-O bond length of the IGF has a range from 1.62 Å to 1.64 Å, consistent with recent experimental findings.

The electronic structure and bonding of a realistic model of an intergranular glassy film ͑IGF͒ was studied with multiple computational methods. The model has a Si-O-N glassy region sandwiched between crystalline basal planes of ␤-Si 3 N 4 and contains a total of 798 atoms. It was constructed with periodic boundary conditions via classical molecular dynamics ͑MD͒ techniques using an accurate multibody atomic potential. The model was then further relaxed by the VASP ͑Vienna ab initio simulation package͒ program. It is shown that the VASP-relaxed structure reduces the total energy from the MD-relaxed structure by only 47.38 eV, validating the accuracy of the multiatom potential used. The calculated electronic structure shows the IGF model to be an insulator with a sizable gap of almost 3 eV. Quasidefectlike states can be identified near the band edges arising from the more strained Si-N and Si-O bonds at the interface. Calculation of the Mulliken effective charge and bond order values indicates that the bonds in the glassy region and at the interface can be enhanced and weakened by distortions in the bond length and bond angle. The states at the top of the valence band are derived mostly from the crystalline part of the Si-N bonding while the states at the bottom of the conduction band are dominated by the Si-O bonding in the glassy region. Calculation of the electrostatic potential across the interface shows an average band offset of about 1.5 eV between the crystalline ␤-Si 3 N 4 and the glassy Si-O-N region which could be related to the space charge model for IGF.

Molecular dynamics simulations of intergranular films (IGFs) containing Si, O, N, and Ca in contact with three different types of surface terminations of Si 3 N 4 were performed using a multi-body interatomic potential. IGFs with the same Ca concentration (12 mol% CaO) but different nitrogen concentrations [N/(N+O)= 0, 15, 30, and 50%] were studied. In all 12 IGFs, Ca ions do not compete with the first adsorbed layer of Si at the IGF/basal crystal interface, but do so at the IGF/prism crystal interface. The simulations show the epitaxial adsorption of Si, O, and N from the IGF onto the basal and prism crystal surfaces. While it is expected to see more adsorbed N as nitrogen concentration increases, there is a significantly larger number of N adsorbed to the basal surface than to the prism surface. It is found that Ca ions sit closer to the prism surface than the basal surface, but move closer to the crystal at both surfaces with the increasing nitrogen concentration, although the effect is more pronounced at the basal interface. With the increase of nitrogen concentration, the percentage of two-coordinated oxygen remains about the same, but there is a change in the type of defect oxygen present. In all the simulations, the central position of the first peak in the Si-O PDF ranges from 1.63 Å to 1.65 Å, and those of Si-N PDF ranges from 1.71 Å to 1.73 Å, both consistent with experimental findings. Furthermore, the first peak of both the Si-O and Si-N PDF shifts to larger values as the nitrogen concentration increases, indicating the elongation of the Si-O and Si-N bond in the IGF with the increase of nitrogen concentration. Both the elongation of the Si-N and Si-O bonds could lead to weakening of the IGF as nitrogen concentration increases, although competing changes in bonding of the O complicate the effect of N addition on the strength of the IGF.

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