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

The hardness, elastic moduli, and fracture toughness of the spinel phases, γ-Ge₃N₄ and 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-Ge₃N₄ and γ-Sn₃N₄ were found to be 295 and 167 GPa, respectively. The nanohardnesses of γ-Ge₃N₄ and γ-Sn₃N₄ were found to be 31 and 13 GPa, respectively. The shear moduli G₀ and Poisson's ratios v₀ were derived using theoretical bulk moduli B₀ obtained from density-functional theory calculations. The calculated values were B₀ = 260 GPa, G₀ = 146 GPa, v₀ = 0.26 for γ-Ge₃N₄, and B₀ = 186 GPa, G₀ = 64 GPa, v₀ = 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