Elastic moduli of hard c-Zr$_{3}$N$_{4}$ and $\eta $-Ta$_{2}$N$_{3}$, a tough self-healing material, via laser ultrasonics and nanoindentation

Bulk and shear moduli ($B_{0}$ and $G_{0})$ of the dense polycrystalline oxygen bearing c-Zr$_{3}$N$_{4}$ and $\eta $-Ta$_{2}$N$_{3}$ were determined from the laser ultrasonic (LU) measurements on highly porous samples having the volume fraction porosity of 0.23 and 0.18, respectively. Dense samples of these high-pressure (HP) materials are today not available due to their very high hardness and absence of a densification procedure. Combining the LU data with a numerical analysis of the sample porosity, the ``true'' isotropic moduli were determined to be $B_{0}=$217(20) GPa and $G_{0}=$163(9) GPa, for c-Zr$_{3}$N$_{4}$, and $B_{0}=$281(15) GPa and $G_{0}=$123(2) GPa, for $\eta $-Ta$_{2}$N$_{3}$. For both HP-nitrides the $B_{0}$ values agree with those obtained earlier via the HP compression measurements in a diamond anvil cell. Also, the self-healing behavior of $\eta $-Ta$_{2}$N$_{3}$ by mechanical polishing was confirmed by two independent methods. Finally, the results obtained for $\eta $-Ta$_{2}$N$_{3}$ via the LU method were compared with our nanoindentation measurements. The high $G_{0}$ value of c-Zr$_{3}$N$_{4}$ suggests that this material could vie with $\gamma $-Si$_{3}$N$_{4}$ for the rank of the third hardest material after diamond and c-BN.