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P. Lazar, R. Podloucky, E. Kozeschnik, J. Redinger:
"Density functional theory study of ternary V-Cr-N compounds";
Physical Review B, 78 (2008), 1342021 - 1342028.

The Z-phase VCrN is important for steel technology because of its harmful influence on the mechanical
properties of 9%-12% Cr steel with V additions. The thermodynamical stability of the Z phase and related
ternary compounds with respect to the decomposition into binary Cr- and V-nitride phases is studied. By
application of the density functional theory DFT approach we investigate the ground-state properties of a
variety of binary V-N and Cr-N compounds, and we propose the existence of a different phase V4N5. Concerning
ternary phases, we studied the compounds VCrN, V2Cr2N3, and VCrN2 for two structural variants,
namely, for an alternating single-layer V-N / Cr-N 100 stacked rocksalt structure and for a double-layer
V-N V-N / Cr-N Cr-N 100 stacked tetragonal structure. For the Z-phase VCrN, the tetragonal structure with
pure Cr layers is most stable, whereas for the composition VCrN2 both structural variants are almost degenerate.
The intermediate phase V2Cr2N3 is unstable against a decomposition into VCrN and VCrN2. Comparing
the formation energies of ternary and binary nitrides, we find that the Z-phase VCrN is always stable whereas
VCrN2 is less stable than a mixture of V4N5 and Cr2N. Assuming nonequilibrium conditions for which
nitrogen might be abundant, also the Z-phase VCrN can decompose into binary nitrides. Applying an empirical
temperature-dependent approach to study the formation of nitrides of Cr and V dissolved in Fe, the DFT data
are corroborated concerning the Z-phase VCrN and VN. For Cr2N the empirical approach yields a formation
energy which is about 20% more stable than the DFT data. The DFT data are, however, in good agreement with
a corresponding measured value.\