Hardness, elasticity, and fracture toughness of polycrystalline spinel germanium nitride and tin nitride

The hardness, elastic moduli, and fracture toughness of the spinel phases, γ–Ge₃N₄and γ–Sn₃N₄, were determined using indentation data and theoretical calculations. Measurements were performed on polycrystalline specimens using the technique of nanoindentation to determine the reduced moduli and hardnesses from the unloading portion of the indent curves. Reduced moduli of γ–Ge₃N₄and γ–Sn₃N₄were found to be 295 and 167 GPa, respectively. The nanohardnesses of γ–Ge₃N₄and γ–Sn₃N₄were found to be 31 and 13 GPa, respectively. The shear moduliG₀and Poisson’s ratios ν₀were derived using theoretical bulk moduliB₀obtained from density-functional theory calculations. The calculated values wereB₀= 260 GPa,G₀= 146 GPa, ν₀= 0.26 for γ–Ge₃N₄, andB₀= 186 GPa,G₀= 64 GPa, ν₀= 0.34 for γ–Sn₃N₄. Fracture toughness was estimated by direct measurement of radial cracks emanating from Vickers microindents. It was determined that for γ–Ge₃N₄,K_IC= 2.3 MPa(m)^1/2, while for γ–Sn₃N₄,K_IC= 1.4 MPa(m).^1/2