Defect and solute properties in dilute Fe-Cr-Ni austenitic alloys from first principles

We present results of an extensive set of first-principles density functional theory calculations of point defect formation, binding, and clustering energies in austenitic Fe with dilute concentrations of Cr and Ni solutes. A large number of possible collinear magnetic structures were investigated as appropriate reference states for austenite. We found that the antiferromagnetic single- and double-layer structures with tetragonal relaxation of the unit cell were the most suitable reference states and highlighted the inherent instabilities in the ferromagnetic states. Test calculations for the presence and influence of noncollinear magnetism were performed but proved mostly negative. We calculate the vacancy formation energy to be between 1.8 and 1.95 eV. Vacancy cluster binding was initially weak at 0.1 eV for divacancies but rapidly increased with additional vacancies. Clusters of up to six vacancies were studied and a highly stable octahedral cluster and stacking fault tetrahedron were found with total binding energies of 2.5 and 2.3 eV, respectively. The $\langle 100\rangle$ dumbbell was found to be the most stable self-interstitial with a formation energy of between 3.2 and 3.6 eV and was found to form strongly bound clusters, consistent with other fcc metals. Pair interaction models were found to be capable of capturing the trends in the defect cluster binding energy data. Solute-solute interactions were found to be weak in general, with a maximal positive binding of 0.1 eV found for Ni-Ni pairs and maximum repulsion found for Cr-Cr pairs of $-$0.1 eV. Solute cluster binding was found to be consistent with a pair interaction model, with Ni-rich clusters being the most stable. Solute-defect interactions were consistent with Ni and Cr being modestly oversized and undersized solutes, respectively, which is exactly opposite to the experimentally derived size factors for Ni and Cr solutes in type 316 stainless steel and in the pure materials. Ni was found to bind to the vacancy and to the $\langle 100\rangle$ dumbbell in the tensile site by 0.1 eV and was repelled from mixed and compressive sites. In contrast, Cr showed a preferential binding to interstitials. Calculation of tracer diffusion coefficients found that Ni diffuses significantly more slowly than both Cr and Fe, which is consistent with the standard mechanism used to explain radiation-induced segregation effects in Fe-Cr-Ni austenitic alloys by vacancy-mediated diffusion. Comparison of our results with those for bcc Fe showed strong similarity for pure Fe and no correlation with dilute Ni and Cr.

Figure 1

Energy difference per atom, $\Delta E$, between distinct magnetic reference states for austenitic Fe (open symbols) and the bcc fm ground state (black solid circles) versus atomic volume, $V_{\mathrm{atom}}$. We include ferromagnetic (fm, black circles), nonmagnetic (nm, red squares), and antiferromagnetic (001) single-layer (afmI, green upward triangles), double-layer (afmD, blue downward triangles), and triple layer (afmT, purple right-facing triangles) orderings. Also shown is a magnetic (001) layered structure with a spin-up, spin-up, spin-down ordering (uud, beige left-facing triangles), an antiferromagnetic (111) single-layer structure (afmI${}_{111}$, orange stars), and a magnetic ordering formed by taking a four-atom fcc unit cell with three spin up atoms and one spin down atom (fm-flip, cyan diamonds). We distinguish between fcc (solid curves) and fct (dashed curves) for the same magnetic (001) structures.

Figure 2

(a) (Self-)Interstitial defect positions (black circles) in the fcc/fct afmD magnetically ordered structure. (b) A-B interactions between on-site defects and solutes in the fcc/fct afmD magnetically ordered structure. Species A is shown in black, species B in gray, and the surrounding Fe atoms in white. Arrows indicate local moments in both figures and the magnetic planes are shown to aid visualization. The afmD state has been shown here to uniquely identify all of its distinct defect configurations. The higher symmetry afmI and fm-HS states share this set of configurations, although many (e.g., tetra uu and tetra ud) will be symmetry equivalent.

Figure 3

Lattice site numbering used to identify clusters of point defects and solutes. The afmD magnetic state is shown to identify its clusters unambiguously but the numbering is equally valid for the other magnetic states considered here (where no ambiguity exists).

Figure 4

Total binding energies, $E_{\mathrm{b}}$, in eV for (a) vacancy clusters and (b) self-interstitial dumbbell clusters. Data have been shifted horizontally for clarity. Configurations of defects are considered clusters when all defects can be connected by chains of 1NN bonds.

Figure 5

Plots of binding energies from the pairwise bond model, $E_{\mathrm{b}}^{\left(\mathrm{m}\right)}$, versus ab initio fit data, $E_{\mathrm{b}}$, for defect clusters in the fct afmI and afmD states. The results of fits performed to data from a single magnetic state or simultaneously to both are shown, as labeled. The simultaneous fit results have been separated into those for afmI and afmD states in order to allow the effect of a combined fit to be directly compared with the single-fit results. The $E_{\mathrm{b}}^{\left(\mathrm{m}\right)}=E_{\mathrm{b}}$ line is included to indicate a perfect fit. Horizontal lines indicate representative error bars for the averaging over both magnetic states in the combined fits.

Figure 6

Comparison of point defect formation and binding energies between austenitic and ferritic Fe. Interstitial formation energies for the two datasets have been associated with one another in order from lowest to highest energy. The black line is included to indicate an exact agreement.

Figure 7

Plots of binding energies from the pairwise bond model, $E_{\mathrm{b}}^{\left(\mathrm{m}\right)}$, versus ab initio data, $E_{\mathrm{b}}$, for solute clusters in the fct afmI and afmD states. The $E_{\mathrm{b}}^{\left(\mathrm{m}\right)}=E_{\mathrm{b}}$ line is included to indicate a perfect fit.

Figure 8

Ratios of tracer diffusion coefficients versus temperature, $T$, for vacancy-mediated diffusion of Ni and Cr solutes and self-diffusion in the fct afmI and afmD Fe reference states. The two curves for each reference state were evaluated with $H_{\mathrm{b},1}^{\mathrm{B}}–\mathrm{TS}=\pm 0.5$ eV and provide a conservative measure of the uncertainty resulting from that parameter.

Figure 9

Comparison of solute properties in austenitic and ferritic Fe. The dataset consists of the substitutional formation energy, solute-vacancy binding energies, and solute-interstitial binding energies for the most stable self-interstitial, in eV. The black line is included to indicate an exact agreement.

Figure 10

The vacancy wind, $G$, versus temperature, $T$, for a number of distinct values for $H_{\mathrm{b},1}^{\mathrm{B}}–\mathrm{TS}$, which are used to label the corresponding curves. The line $G=-1$ is shown to distinguish the vacancy drag regime from the regime where solute flux is opposite to vacancy flux.