Segregation, precipitation, and $\alpha \text{−}{\alpha }^{\prime }$ phase separation in Fe-Cr alloys

Iron-chromium alloys, the base components of various stainless steel grades, have numerous technologically and scientifically interesting properties. However, these features are not yet sufficiently understood to allow their full exploitation in technological applications. In this work, we investigate segregation, precipitation, and phase separation in Fe-Cr systems analyzing the physical mechanisms behind the observed phenomena. To get a comprehensive picture of Fe-Cr alloys as a function of composition, temperature, and time the present investigation combines Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods have to be used. Using the exact muffin-tin orbitals method with the coherent potential approximation (CPA-EMTO) the effective chemical potential as a function of Cr content (0–15 at. % Cr) is calculated for a surface, second atomic layer, and bulk. At $\sim 10$ at. % Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr-containing surfaces are expected when the Cr content exceeds $\sim 10$ at. %. The second atomic layer forms about a 0.3 eV barrier for the migration of Cr atoms between the bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. However, for Cr concentration regions less than 10 at. %, the ab initio (CPA-EMTO) result of the important role of the second atomic layer to the surface is not reproducible from the large-scale Monte Carlo molecular dynamics (MCMD) simulation. On the other hand, for the nominal concentration of Cr larger than 10 at. % the MCMD simulations show the precipitation of Cr into isolated pockets in bulk Fe-Cr and the existence of the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer systems. For high Cr concentration alloys the performed spectroscopic measurements support the MCMD simulations. Hard x-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in the Fe/Cr double layer and ${\mathrm{Fe}}_{0.95}{\mathrm{Cr}}_{0.05}$ and ${\mathrm{Fe}}_{0.85}{\mathrm{Cr}}_{0.15}$ alloys. Initial oxidation of Fe-Cr was investigated experimentally at ${10}^{-8}$ Torr pressure of the spectrometers showing intense ${\mathrm{Cr}}_2{\mathrm{O}}_3$ signal. Cr segregation and the formation of Cr-rich precipitates were traced by analyzing the experimental atomic concentrations and chemical shifts with respect to annealing time, Cr content, and kinetic energy of the exited electron.

Figure 1

Calculated (EMTO) effective chemical potential $\mathrm{\Delta }\mu ={\mu }_{\mathrm{Fe}}-{\mu }_{\mathrm{Cr}}$ of the surface atomic layer (red squares), second atomic layer (blue diamonds), and bulk (black circles) as a function of Cr content of the homogeneous alloy. The open symbols are calculated points; the curves are guides to the eye. In the present calculations we have used larger unit cells, 12 atomic (100) layers separated by vacuum of thickness equivalent to 6 atomic layers, compared to the previous work [14], where 8 atomic layers of metal slab were separated by vacuum of thickness equivalent to 4 atomic layers.

Figure 2

Surface energies of low-index surfaces of bcc iron and chromium as predicted by the 2BEAM model. Results of ab initio calculations (open circles for Fe and open squares for Cr) are from Ref. [58]. Experimental values (open triangles for Fe and open diamonds for Cr) are from Ref. [60].

Figure 3

Segregation energy of a chromium atom in iron chromium alloy in the near-surface atomic layers for different chromium concentrations as predicted by the 2BEAM model (solid lines) and ab initio (dashed lines) calculations (Table 1). Curves are shifted by the marked amount for better visibility. The ab initio result for the pure iron from Ref. [21] is plotted with dotted line and open symbols.

Figure 4

Segregation energy of the three near-surface atomic layers as a function of bulk Cr concentration as predicted by the 2BEAM model. The ab initio data are the ones presented in Table 1.

Figure 5

Chromium concentration of near-surface atomic layers as a function of the average bulk concentration. Gray lines show the one-to-one relation between the bulk and layer concentrations. Note the different $y$ axis scale in the case of layer 1.

Figure 6

Snapshots of the simulated ${\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x$ systems at different temperatures and with different chromium concentrations $x$. Figure shows slices of thickness 15 Å in the (110) direction. Only chromium atoms are shown with color coding according to potential energy (blue color representing low potential energy). The top and bottom facets of the simulation box are open surfaces.

Figure 7

Chromium concentration depth profiles for different average chromium concentrations and simulation temperatures. Curves for 0.1% are multiplied by 10 for better visibility.

Figure 8

As in Fig. 7 but with chromium precipitates removed. Removing was done by discarding atoms whose average type during the last 60 000 simulation steps was larger than 1.5 where the value 1.0 corresponds to pure Fe and 2.0 to pure Cr.

Figure 9

Cr concentration profiles for the layer widths corresponding to different total Cr concentrations simulated in different temperatures. Thin dashed lines show the initial Cr profile.

Figure 10

Example of an AES spectrum of Fe/Cr interface (“o” curve) of Fe/Cr/Si sample. The sum spectrum (dashed curve) was obtained by principal component analysis (PCA) of CasaXPS 2.13.16 [63].

Figure 11

Left-hand side presents the Fe $2p$, Cr $2p$, and O $1s$ XPS spectra of a Fe/Cr bilayer sample before (topmost spectrum) and after annealing. These spectra were measured using Al $\mathrm{K}\alpha$ twin anode. Photoemission spectra clearly demonstrate the increase of Cr $2p$ intensity as a function of annealing time confirming the Cr diffusion into the Fe layer. The upper AES profile on the right is taken over the Fe/Cr interface before any heating was carried out starting sputtering from the surface represented by the uppermost XPS spectrum (blue) on the left. The lower AES depth profile on the right was taken after all the heating treatments starting from the surface concentration presented in the lowest (red) XPS spectrum on the left.

Figure 12

Overview HAXPES spectra of the Fe/Cr bilayer sample measured with 2300 eV photon energy before and after two heating treatments. In addition to the Cr $2s$ and Cr $2p$ spectra appearing after annealing, the increased intensity of Cr $2p$ as a comparison to Fe $2p$ after different annealing times demonstrates the Cr diffusion towards the surface. The intensity of Fe $2p_{3/2}$ of the presented spectra is normalized to 1 after setting background to zero.

Figure 13

Concentrations of Cr, Fe, and O in Fe/Cr/Si. Relative intensities are calculated by analyzing the area of Cr $2p$, Fe $2p$, and O $1s$ spectra.

Figure 14

Cr $2p$ spectra of Fe/Cr bilayer sample after 5 (open circles) and 60 min (solid line) heating (a) and Cr $2p$ spectra of ${\mathrm{Fe}}_{0.95}{\mathrm{Cr}}_{0.05}$ (b) and ${\mathrm{Fe}}_{0.85}{\mathrm{Cr}}_{0.15}$ (c) alloys before and after heating 10 minutes at 500 ${}^{\circ }\text{C}$. The lower spectra in (a), (b), and (c) are fitted using three components to represent signals from bulklike Cr, Cr from Fe-Cr alloy, and oxidized Cr. The simulated Cr $2p_{3/2}$ line shape for the Fe/Cr/Si sample at 2300 eV photon energy after 5 min heating is compared to the experimental spectrum which is a sum of Cr and Cr alloy components [inset of (a)].