Strength, elasticity, and equation of state of the nanocrystalline cubic silicon nitride γ-Si3N4 to 68 GPa

Lattice strains in nanocrystalline cubic silicon nitride were measured using an energy-dispersive x-ray diffraction technique under nonhydrostatic stress conditions up to a confining pressure of 68 GPa. The high-pressure elastic properties of γ-Si3N4 were also investigated theoretically using density-functional theory. The differential stress t between 30 and 68 GPa increases from 7 to 23 GPa and can be described beyond 40 GPa as t=7(4)+0.24(7)P where P is the pressure in GPa. The differential stress supported by γ-Si3N4 increases with pressure from 3.5% of the shear modulus at 21 GPa to 7.6% at 68 GPa. γ-Si3N4 is one of the strongest materials yet studied under extreme compression conditions. The elastic anisotropy of γ-Si3N4 is large and only weakly pressure dependent. The elastic anisotropy increases from A=1.4 to A=1.9 as the parameter α that characterizes stress-strain continuity across grain boundaries is decreased from 1 to 0.5. The high elastic anisotropy compares well with our first-principles calculations that lead to A=1.92-1.93 at ambient pressure and A=1.94-1.95 at 70 GPa. Using molybdenum as an internal pressure standard, the equation of state depends strongly on ψ, the direction between the diamond cell axis and the normal of the scattering plane. The bulk modulus increases from 224(3) GPa to 460(13) GPa as ψ varies from 0 deg. to 90 deg. This large variation highlights the need to account properly for deviatoric stresses in nonhydrostatic x-ray diffraction experiments carried out at angles other than the particular angle of ψ=54.7 deg., where deviatoric stress effects on the lattice vanish. At this angle we find a bulk modulus of 339(7) GPa (K0'=4, fixed). This result is in general agreement with our local density approximation calculations, K0=321 GPa, K0'=4.0, and previous shockwave and x-ray diffraction studies. However, our results are significantly lower than the recently reported bulk modulus of K0=685(45) GPa for nanocrystalline γ-Si3N4 below 40 GPa