Electronic and bonding analysis of hardness in pyrite-type transition-metal pernitrides

Abstract

Most commonly known hard transition-metal nitrides crystallize in rocksalt structure (B1). The discovery of ultraincompressible pyrite-type PtN 2 10 years ago has raised a question about the cause of its exceptional mechanical properties. We answer this question by a systematic computational analysis of the pyrite-type PtN 2 and other transition-metal pernitrides (MN 2) with density functional theory. Apart from PtN 2 , the three hardest phases are found among them in the 3d transition-metal period. They are MnN 2 , CoN 2 , and NiN 2 , with computed Vickers hardness (H V) values of 19.9 GPa, 16.5 GPa, and 15.7 GPa, respectively. Harder than all of these is PtN 2 , with a H V of 23.5 GPa. We found the following trends and correlations that explain the origin of hardness in these pernitrides. (a) Charge transfer from M to N controls the length of the N-N bond, resulting in a correlation with bulk modulus, dominantly by providing Coulomb repulsion between the pairing N atoms. (b) Elastic constant C 44 , an indicator of mechanical stability and hardness is correlated with total density of states at E F , an indicator of metallicity. (c) Often cited monotonic variation of H V and Pugh's ratio with valence electron concentration found in rocksalt-type early transition-metal nitrides is not evident in this structure. (d) The change in MM bond strength under a shearing strain indicated by crystal orbital Hamilton population is predictive of hardness. This is a direct connection between a specific bond and shear related mechanical properties. This panoptic view involving ionicity, metallicity, and covalency is essential to obtain a clear microscopic understanding of hardness.

Structural transition in the magnetoelectricZnCr2Se4spinel under pressure

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Pressure-induced phase transitions in the CdCr2Se4 spinel

“…The convergence criterion was set to 10 -5 eV in energy during the electronic iterations. For structural optimization, the cell shape and atomic positions were allowed to relax until stress was minimized and force on any atom was below 0.01 eV/Å, similar to earlier works [45][46][47][48][49][50][51] . The pressure dependence was determined by selecting a few volume points covering the equilibrium volumes corresponding to a range of 0 -30 GPa, optimizing the structures at those points and fitting the total energy vs volume to a B-M EoS 36 .…”

Pressure-induced transition in the multiferroicCoCr2O4spinel

“…The total density of states (TDOS) were calculated with k-points meshes of twice the division number than stated above. Bader charge transfer analysis [45][46][47] was done with the implementation following the theoretical guidelines 48,49 , as described elsewhere [50][51][52][53] . The fast Fourier transform grid for charges was set at 300 × 300 × 300.…”