In Si3N4 ceramics sintered with Al2O3, the interfacial strength between the intergranular glass and the reinforcing grains has been observed to increase with increases in the aluminum and oxygen content of the epitaxial beta-Si6-zAlzOzN layer that forms on the Si3N4 grains. This has been attributed to the formation of a network of strong bonds (cross bonds) that span the glass-crystalline interface. This proposed mechanism is considered further in light of first-principles atomic cluster calculations of the relative stabilities of bridge and threefold-bonded atomic fragments chosen to represent compositional changes at the glass/Si3N4, grain interface. Calculated binding energies Indicate Al-N binding is favorable at the Si3N4 grain surface, where aluminum occupancy can promote the growth of SiAlON, further enhancing the cross-bonding mechanism of interfacial strengthening.