Local order in Cr-Fe-Co-Ni: Experiment and electronic structure calculations

A quenched-in state of thermal equilibrium (at 723 K) in a single crystal of Cr-Fe-Co-Ni close to equal atomic percent was studied. Atom probe tomography revealed a single-phase state with no signs of long-range order. The presence of short-range order (SRO) was established by diffuse x-ray scattering exploiting the variation in scattering contrast close to the absorption edges of the constituents: At the incoming photon energies of 5969, 7092, and 8313 eV, SRO maxima that result from the linear superposition of the six partial SRO scattering patterns, were always found at $X$ position. Electronic structure calculations showed that this type of maximum stems from the strong Cr-Ni and Cr-Co pair correlations, that are furthermore connected with the largest scattering contrast at 5969 eV. The calculated effective pair interaction parameters revealed an order-disorder transition at approximately 500 K to a $L{1}_2$-type (Fe,Co,Ni)${}_3\mathrm{Cr}$ structure. The calculated magnetic exchange interactions were dominantly of the antiferromagnetic type between Cr and any other alloy component and ferromagnetic between Fe, Co, and Ni. They yielded a Curie temperature ($T_{\mathrm{C}}$) of 120 K, close to experimental findings. Despite the low value of $T_{\mathrm{C}}$, the global magnetic state strongly affects chemical and elastic interactions in this system. In particular, it significantly increases the ordering tendency in the ferromagnetic state compared to the paramagnetic one.

Figure 1

Normalized resistivity from Cr-Fe-Co-Ni versus aging temperature for two samples. At the end of the aging path RT (as-grown state) $\to$ 1073 K $\to$ 623 K (holding time of 24 h for any aging temperature), sample 1 was additionally heat treated at 673 K for 119 days, sample 2 at 723 K for 16 days.

Figure 2

(a) Reconstruction of the evaporated volume from Cr-Fe-Co-Ni (as grown). Only Cr atoms are marked. (b) Cross-correlated density profiles with Ni as reference atom and Cr, Fe, Co, Ni at the 002 pole. An increase in the field evaporation strength Cr $\to$ Ni $\to$ Co $\to$ Fe is noted. (c) This evaporation sequence results in an apparent Cr fraction increase along [001] as revealed by the red isosurface of 26.5 at.% Cr that confines the high-Cr region around the 002 pole.

Figure 3

Energy-resolved spectra (a) at the Cr edge, (b) Fe edge (scale: 1 ch. $\approx 2.0$ eV), and (c) Ni edge (1 ch. $\approx 5.0$ eV) around the lines that contain elastic scattering of energy $E$. To provide an average view, the spectra at all h positions (in black) were added. The $K-L_{\mathrm{II}}{L}_{\mathrm{III}}$ resonant Raman scattering is shown in red. Channel numbers refer to the maximum position of the respective lines, with theoretical energy values in parentheses.

Figure 4

Elastic diffuse scattering at ($h_x,h_y,0$) positions in Laue units as measured (upper triangles, $h_x<h_y$) and as fitted (lower triangles, $h_x>h_y$): (a) at the Cr edge, (b) at the Fe edge, and (c) at the Ni edge.

Figure 5

SRO scattering at ($h_x,h_y,0$) positions as determined from diffuse scattering based on Table 2 (lower triangles) and from the present electronic structure calculations at 720 K [(top sectors) and (left sectors) based on Table 2]: (a) at the Cr edge, (b) at the Fe edge, and (c) at the Ni edge.

Figure 6

Total energies of random fcc and hcp ${\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}$ alloys from ELSGF calculations, as function of the Wigner-Seitz radius.

Figure 7

Electronic density of states in random fcc ${\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}$ from the ELSGF and EMTO-CPA calculations.

Figure 8

Local magnetic moments of random fcc ${\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}$ from the ELSGF DLM-LSF calculations at 130 K shown for all the atoms in the supercell using their site indexes. Thick lines show the average magnitudes for each alloy component.

Figure 9

Atomic SRO parameters ${\alpha }_{lmn}^{ij}$ at the first and second coordination shell from Monte Carlo simulations with the effective interactions at 750 K. The dashed line shows the order-disorder transition.

Figure 10

Atomic SRO parameters ${\alpha }_{lmn}^{ij}$ at the first and second coordination shell from Monte Carlo simulations with the effective interactions at 500 K. The dashed line shows the order-disorder transition.

Figure 11

A snapshot of a $12\times 12\times 12(\times 4)$ Monte Carlo simulation box at 700 K obtained with the 750 K interactions, 330 K above the order-disorder phase transition. Cr atoms are dark blue, Co light blue, Ni gray, and Fe yellow.

Figure 12

A snapshot of a $12\times 12\times 12(\times 4)$ Monte Carlo simulation box at 500 K obtained with the 500 K interactions, just 30 K below the order-disorder phase transition. The colors of atoms are the same as in Fig. 11.

Figure 13

Configurational entropy of ${\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}$ from Monte Carlo simulations.

Figure 14

SRO scattering at ($h_x,h_y,0$) positions for 720 K separately for the six partial SRO parameter sets ${\alpha }_{lmn}^{ij}$ as determined by the present electronic structure calculations.