Zirconium
and hafnium nitrides are charmingly hard superconductors
[X. J. Chen et al. Proc. Natl. Acad. Sci. U.S.A., 2005, 102, 3198] with specific application
under extreme conditions. Understanding the intrinsic hardness, especially
under Vickers indentation deformation, in these superconductors is
very important. Here, we perform first-principles studies of the stress–strain
relations and deformation mechanisms of ZrN and HfN under compressive,
tensile, pure shear, and indentation strains. The results offer a
comprehensive description of their versatile stress responses, and
the calculated indentation shear strengths for ZrN and HfN agree well
with experimental results. The superior performance characteristics
of HfN, compared to the isostructural ZrN, is attributed to the higher
valence electron concentration that strengthens the Hf–N bonds.
These results reveal the atomistic mechanisms for the mechanical properties
of ZrN and HfN, providing insights for further exploration of hard
and ultrahard transition-metal compounds.