Atomic defects and dopants in ternary Z-phase transition-metal nitrides $\mathbf{Cr}\mathit{M}\mathbf{N}$ with $\mathit{M}=\mathbf{V}$, Nb, Ta investigated with density functional theory

A density functional theory study of atomic defects and dopants in ternary Z-phase transition-metal nitrides $\mathrm{Cr}M\mathrm{N}$ with $M=\mathrm{V}$, Nb, or Ta is presented. Various defect formation energies of native point defects and of substitutional atoms of other metal elements which are abundant in the steel as well are evaluated. The dependence thereof on the thermodynamic environment, i.e., the chemical conditions of a growing Z-phase precipitate, is studied, and different growth scenarios are compared. The results obtained may help to relate results of experimental atomic-scale analysis by atom probe tomography or transmission electron microscopy to the theoretical modeling of the formation process of the Z phase from binary transition-metal nitrides.

Figure 1

Z-phase structure with an alternating sequence of two bcc-like layers of Cr atoms (red) and two rocksalt-like nitride layers where V/Nb/Ta atoms are shown in gray and N atoms are shown in blue. The 192-atom supercell (right) used for the study of point defects consists of $4\times 4\times 2$ primitive cells (left) of six atoms each.

Figure 2

Range of possible values for the relative chemical potentials $\mathrm{\Delta }{\mu }_{\mathrm{Cr}},\mathrm{\Delta }{\mu }_{\mathrm{Nb}}$, and $\mathrm{\Delta }{\mu }_{\mathrm{N}}$ under the boundary conditions (5) and (6) for the case of the CrNbN Z phase, given in units of $-\mathrm{\Delta }{H}_f^{\left(0\right)}\left[\mathrm{CrNbN}\right]$. The points $\mathcal{A}\text{–}\mathcal{G}$ and the respective connecting red lines mark special limiting cases which are discussed in detail in the text.

Figure 3

Variation of defect formation energies of native point defects ($v_{\mathrm{Cr}},{\mathrm{Cr}}_M,v_M$, and $M_{\mathrm{Cr}}$) in the $\mathrm{Cr}M\mathrm{N}$ Z phase in thermodynamic contact with $M\mathrm{N}$ (left column) or ${\mathrm{Cr}}_2\mathrm{N}$ (right column) precipitates as a function of the relative chemical potential $\mathrm{\Delta }{\mu }_{\mathrm{N}}$ of nitrogen. The variation in relative chemical potentials ($x$ axis) corresponds to the variation along lines $\overline{\mathcal{D}\mathcal{E}}$ and $\overline{\mathcal{F}\mathcal{G}}$ of Fig. 2, respectively.

Figure 4

Compilation of the data from Tables 2 and 3 showing the general trend observed for the formation energies $E_f^{\left(0\right)}$ of substitutional defects (a) on host-metal sites $X_M$ and (b) on Cr sites $X_{\mathrm{Cr}}$, evaluated for $M$-rich/Cr-rich conditions.

Figure 5

Calculated chemical potentials of (a) individual Cr atoms dissolved on substitutional sites in a bcc Fe crystal and (b) individual N atoms located on octahedral interstitial sites as a function of the supercell size (number of atoms $n$) which is used for the calculation.