Local Atomic Displacements and Sign of the Structural Transformation in Medium-Entropy Alloys Observed in Extended X-ray Absorption Fine Structure Spectra

Yoichi Ikeda; Yoshihiko Umemoto; Daiju Matsumura; Takuya Tsuji; Yuki Hashimoto; Takafumi Kitazawa; Masaki Fujita

doi:10.2320/matertrans.MT-M2023043

Abstract

Extended X-ray absorption fine structure (EXAFS) and neutron diffraction experiments were carried out to clarify the typical features of the local structure of a family of medium-entropy alloys (CrCoNi, MnCoNi, and FeCoNi). A simple random cluster model was constructed for analyzing EXAFS spectra, and static and dynamic components of the mean-square relative displacement (MSRD) were separately extracted. In our analysis, the static MSRD of the MnCoNi sample was slightly larger than those of the CrCoNi and FeCoNi samples, whereas the dynamic MSRDs of these samples were almost identical. Based on the complementary neutron diffraction data, we argued that the origin of the large static displacement in the MnCoNi alloy can be associated with a short-range structural transformation through long-term structural relaxation.

Fig. 6 Neutron diffraction profiles of CrCoNi (rectangles) and MnCoNi (circles) at room temperature. The open and closed symbols are the data of the as-grown and annealed samples, respectively. The bold bar symbols denote the Bragg positions for P4/mmm (the ratio of the c and a axes c/a ∼ 1). The backgrounds from the empty cell and air scattering were subtracted for clarity. The right panel structures, which were drawn using VESTA software,²⁹⁾ possibly explain the observed short-range structural transformation in the MnCoNi sample.

1. Introduction

The concept of high-entropy alloys to improve various kinds of material properties, not only in the field of traditional materials science¹^,²⁾ but also for the synthesis of new materials in chemistry and condensed matter physics,³^,⁴⁾ has gradually found global acceptance. An essential point of the concept is to utilize the stabilization of the solid-solution phase resulting from the increase in the configurational entropy in the total Gibbs energy to realize advanced properties, such as enhanced strength-ductility synergy,⁵⁾ high performance for catalysts,⁶⁾ and superconductivity.⁷⁾ The relationship between local structures and mechanical properties is of interest for improving the strength and ductility of high-entropy structural materials. Recent studies have highlighted the impact of local chemical ordering, also known as “short-range ordering”, on mechanical strength and noted an advanced material design for tuning stacking fault energies through atomic-scale segregation.⁸^,⁹⁾ A final conclusion about the impact of short-range ordering on strength, however, has not been reached because of the absence of any clear relationship between short-range ordering and strength based on reasonable experimental evidence.¹⁰^,¹¹⁾ The lack of experiments on short-range ordering and its evolution with heat treatment has also been noted.³^,⁴⁾

Moreover, the differences between local structures with and without chemical short-range ordering remain unclear. As references for the CrCoNi alloy, we chose a family of medium-entropy alloys (MnCoNi and FeCoNi), in which short-range ordering has not been identified, and examined the local structures of these alloys. For this purpose, we utilized the neutron total scattering technique and extended X-ray absorption fine structure (EXAFS) analysis, which are potentially effective probes for uncovering the differences in the subnanometer structures of multi-principal-element alloys. First, we focused on the general relationship between the critical resolved shear stress (CRSS) and mean-square atomic displacement (MSAD)¹²⁾ and checked its applicability by using the mean-square relative displacement (MSRD) evaluated from the EXAFS spectra. This quantity is a complementary value to the MSAD and may provide insights into the atomic motions and bonding states around absorbing atoms. In this paper, we report a simple method for separating the static and dynamic terms in the MSRD and verify its effectiveness as a measure of local structural instability in alloys. The results of the neutron diffraction experiments are described elsewhere.¹³⁾

2. Experimental Procedure

2.1 Sample preparation

Polycrystalline samples of a series of medium-entropy alloys, TrCoNi (Tr = Cr, Mn, and Fe), were prepared using the arc-melting method. The equiatomic ratio (Tr:Co:Ni = 1:1:1) was confirmed by qualitative X-ray fluorescence analysis. Using X-ray and neutron diffraction, the crystal structure was roughly confirmed to be a face-centered cubic structure. All samples for the EXAFS experiments were cut with electrical discharge machining and mechanically polished to a thickness of 10–20 µm. The mechanical stress in these film samples was removed by annealing at 1100 °C for 2 h in an argon atmosphere.

The samples for neutron diffraction experiments were prepared using the arc-melting method. CrCoNi and MnCoNi samples were cut into small ingots and annealed at 1100 °C for 2 h to remove mechanical stress. Some of these samples were further annealed at 400 °C for 400 h under an argon atmosphere. Herein, only samples that underwent the additional heat treatment at 400 °C for 400 h are labeled “annealed”.

2.2 EXAFS

K-edge EXAFS experiments were carried out for all constituent elements (Cr, Mn, Fe, Co, and Ni) utilizing the transmission mode at BL14B1 in SPring-8.¹⁴⁾ The incident X-ray was tuned using silicon (111) double-crystal monochromators and calibrated with the absorption edge energy of the standard samples. The spread of the incident X-ray beam was approximately 1 mm². The X-ray beam intensity was measured using ionization chambers installed before and after the sample. Film samples were mounted on a home-built through-hole copper holder with Apiezon-N grease and installed in a standard closed-cycle refrigerator. The temperature dependence of the EXAFS spectra between 20 K and 300 K was measured. In these experiments, the sample position was adjusted by using a two-axis goniometer to maximize the transmission ratio at each temperature. EXAFS data were analyzed using Demeter software (Athena and Artemis).¹⁵^,¹⁶⁾ The energy-dependent absorption coefficients μ(E) were normalized by the jump at the absorption edge Δμ_edge and converted to the EXAFS spectrum using χ(E) = [μ(E) − μ₀(E)]/Δμ_edge, where μ₀(E) is the background due to absorption and scattering from the bare atoms. The pre-edge μ_pre(E) and post-edge μ_post(E) backgrounds, μ₀(E) = μ_pre(E) + μ_post(E), were approximated using linear and spline interpolation, respectively. The normalized EXAFS spectra χ(k) were weighted by the square of the wavenumber k² and Fourier transformed using a Hanning-type window in the k range of 0.02–0.12 pm⁻¹. In this study, the Ni–K edge results of the FeCoNi sample were excluded because of the large systematic error in the EXAFS spectra.

2.3 Neutron diffraction

The neutron diffraction profiles of the CrCoNi and MnCoNi samples were measured at room temperature using a HERMES diffractometer installed on the T1-3 thermal guide tube at JRR-3.¹⁷⁾ The incident neutron was monochromatized with Ge (551) crystals and calibrated to λ = 134.219(7) pm using the NIST standard reference material^® 660c (La¹¹B₆). The samples were placed in a vanadium cylindrical cell. The backgrounds from the empty cell and air scattering were subtracted from the data.

3. Results

Figure 1 shows the weighted EXAFS spectra, k²χ(k), and the magnitude of the Fourier transformed spectra χ(R) of CrCoNi [Figs. 1(a)–(c), top], MnCoNi [Figs. 1(d)–(f), middle], and FeCoNi [Figs. 1(g)–(i), bottom] measured at selected temperatures (20, 100, 200, and 300 K). Figure 1 shows that the shapes of all the weighted EXAFS spectra and their Fourier transforms are qualitatively identical, indicating that the local environments around the absorbing atoms are quite similar in these alloys. In addition, no qualitative change in any spectra was observed during the temperature evolution down to 20 K, and thus, no remarkable structural phase transformations occurred in all the alloys.

Fig. 1

Weighted EXAFS spectra k²χ (a), (d), (g) and their Fourier transformed spectra |χ(R)| (b), (e), (h) of CrCoNi, MnCoNi, and FeCoNi measured at 20 (blue), 100 (light green), 200 (orange), and 300 K (red). The right panel figures display the Fourier transformed spectra |χ(R)| of each sample measured at 20 K. The absorbing atoms are denoted by the legends in the figure.

The local structures were examined using the FEFF-6 code in Artemis software by calculating the backscattering contributions and phase shift in the EXAFS formula.¹⁵^,¹⁶⁾ Here, we utilized a simple fcc cluster model (space group: Fm–3m) as a first approximation, in which the size of the cluster was approximately 800 pm and the arrangement of 176 atoms around the absorbing atom was based on the normal distribution. To calculate the EXAFS spectra, scattering paths up to 600 pm were considered. In this local structural analysis, we used the following EXAFS formula:¹⁸⁾

\begin{align} \chi(k)k^{2} &= S_{0}{}^{2} \Sigma_{j} N(R_{j})t_{j}(k) (k/R_{j}{}^{2}) \exp [-2\{k^{2}\sigma_{j}{}^{2} \\ &\quad + R_{j}/\varLambda\}]\sin\{2kR_{j} + \delta_{j}(k)\}. \end{align}

(1)

Here, R_j is the distance between the absorbing and j-th scattering atoms, and S₀² is the damping factor. N(R_j) is the coordination number at R_j, which is fixed at an appropriate value, as predicted from the fcc structure. t_j(k) and δ_j(k) are the backscattering factor and the phase shift parameter, respectively, as a function of photoelectron wavenumber k. The effective mean free path Λ was also considered, while its k dependence was ignored for simplicity. Both S₀² and Λ were determined by averaging the fitting results of the room-temperature and base-temperature (20 K) data for each absorbing atom. Subsequently, both parameters were fixed to the evaluated values for fitting to the sample data to reduce the scattering of the fitting results. The typical values of S₀² and Λ were evaluated to be 1.2–1.4 and 200–600 pm, respectively. The real-space range of Fourier filtering was fixed at 100–575 pm for all datasets. The observed EXAFS spectra were fitted using Artemis software, in which the bond length R_j and parallel MSRD σ_j² values were refined at each temperature. Typical fit results are displayed in Figs. 2(a)–(c), in which the blue and red lines depict the observed and calculated spectra, respectively, and the black lines show the residuals between the observed and calculated values for the real part of χ(R). For simplicity, the deviations from the crystallographic bond length and σ_j² were assumed to be identical for all scattering paths. In this simple treatment, the scattering path dependence of these values is averaged; therefore, both R_j and σ_j² could be a measure of the discrepancy between the actual structure and the calculation. Hereafter, the scattering path label (j) on R_j and σ_j² is omitted for simplicity.

Fig. 2

(a)–(c) Typical results of a fit with the simple random structure model. In the left panels, the blue, red, and black lines denote the observed, calculated, and residual values, respectively. The right panels (d)–(f) show the atomic coordination number at each neighboring site of the constructed fcc cluster model.

The evaluated bond lengths and MSRDs are displayed in Figs. 3 and 4, respectively, as functions of temperature. The temperature dependence of the bond length was reasonably consistent with that evaluated from the diffraction experiment¹³⁾ within the experimental accuracy. This result indicates that our simple analysis is suitable for investigating local structures. The MSRDs of all the samples showed a monotonic increase with increasing temperature. Note that the magnitudes of these MSRDs at room temperature are close to the previously reported values for a ternary alloy [CrCoNi: 20–100(400) pm²]¹⁹^,²⁰⁾ and a quinary high-entropy alloy [CrMnFeCoNi: 60–70(1) pm²].²¹⁾ To separate the static σ₀² and dynamic (temperature-dependent) σ_T²(T) terms in the MSRD, the temperature dependence of the MSRD was analyzed using the following correlated Einstein model:²²^,²³⁾

\begin{align} \sigma^{2}(T) &= \sigma_{0}{}^{2} + \sigma_{T}{}^{2}(T) \\ &= \sigma_{0}{}^{2} + \{ \hbar^{2}/(2m_{\text{r}}k_{\text{B}}\varTheta_{\text{E}})\}\coth \{ \varTheta_{\text{E}}/(2T)\}, \end{align}

(2)

where ħ is the reduced Planck constant; k_B is the Boltzmann constant; m_r = (m_am_s)/(m_a + m_s) is the reduced mass of the pair of absorbing and scattering atoms; σ₀² is the temperature-independent term in MSRD σ²; and Θ_E is the Einstein temperature corresponding to the effective force constant k_E (= m_rk_B²Θ_E²ħ⁻²) in the interatomic pair potential energy. The temperature evolution of the MSRD can be described using the Einstein model, as shown in Fig. 4, in which the fitting curves are represented by solid lines. The evaluated σ₀² and Θ_E values are presented in Figs. 5(a) and 5(b), respectively.

Fig. 3

Temperature dependence of the bond length between the absorbing and nearest-neighbor scattering atoms in (a) CrCoNi, (b) MnCoNi, and (c) FeCoNi. The black diamond symbols show the bond lengths evaluated from the neutron diffraction data.¹³⁾ Data were cited from Ref. 13). The thin-solid and broken lines are guides to the eye.

Fig. 4

Temperature dependence of the mean-square relative displacement MSRD for (a) CrCoNi, (b) MnCoNi, and (c) FeCoNi. The solid lines are the result of fits with the correlated Einstein model. The dotted (Cr/Mn/Fe), dashed (Co), and broken (Ni) lines show the dynamic component of the MSRD.

Fig. 5

Evaluated (a) static component of the mean-square relative displacement MSRD and (b) Einstein temperature for CrCoNi, MnCoNi, and FeCoNi. The shaded bars in (a) show twice the average MSADs cited from Ref. 28).

4. Discussions

4.1 Validation of the structural model

First, we checked whether our simple cluster model can approximate the local structures of the measured samples. In general, the slight deviations among the peak top positions in the raw data (Fig. 1) for each absorbing atom cannot directly reflect the difference in the bond lengths. For example, the 1st-shell profile can be described by tuning the parameters in the EXAFS formula [eq. (1)], even with an extreme model (e.g., all Co ligands). Therefore, a structural model with appropriate constraints is required to investigate the local structure around the absorbing atoms. Here, we used the following constraint: The bond length R_EXAFS is larger than the crystallographic bond length R_D evaluated from the diffraction data.¹³⁾ This constraint is based on the following relationship: The EXAFS bond length R_EXAFS is approximated by R_EXAFS ≒ R_D + MSRD_perp/2R_D, where MSRD_perp is the MSRD perpendicular to the bond direction and is a measure of the anisotropy of atomic displacement. Because this value is always positive, the bond length R_EXAFS is larger than R_D owing to the contribution of MSRD_perp. The constructed random model satisfies the above constraint within the fitting error, as shown in Fig. 3. From this result, we conclude that our models are suitable for our purpose, which is to examine the deviation from an average fcc structure. However, to analyze MSRD_perp, high accuracy (∼0.1 pm) is required for both the diffraction and EXAFS experiments. For this reason, we decided not to evaluate MSRD_perp in this analysis. Note that the evaluated MSRD was qualitatively unchanged within the fitting error even when the bond length R_EXAFS was fixed at R_D.

Figures 2(d)–(f) show possible sets of the atomic coordination numbers of the 1st, 2nd, 3rd, 4th, and 5th nearest-neighbor sites in the constructed simple fcc structural model. As seen in Fig. 2(a)–(c), the experimental data were satisfactorily reproduced even though these models contain deviations from the equiatomic distribution. However, the quantitative reliability of the atomic ratio is low because of the poor approximation of the EXAFS parameters, including S₀², δ_j(k), and Λ(k). Similarly, the fitting results remained qualitatively unchanged (i.e., the reliability factor R was almost identical within a few percent) even when the atomic coordination number was slightly modified from the indicated structural model in Figs. 2(d)–(f). This is due to the low sensitivity of the EXAFS experiment and implies that the chemical short-range ordering is difficult to determine from only EXAFS data. Nevertheless, we believe that EXAFS experiments have the potential to enable examination of the degree of deviation from the average structure around the target elements, as discussed later.

4.2 Dynamic MSRD and Θ_E

Next, we examine the dynamic MSRD and Θ_E. The total magnitudes of the MSRDs of the measured samples were on the order of 40–80 pm² at low temperatures, in which the dynamic MSRDs of the CrCoNi, MnCoNi, and FeCoNi samples (broken lines in Fig. 4) were almost identical (σ_T² = 30 pm² at 20 K). Note that the finite σ_T²(T = 0) is due to quantum stretching behavior and depends on m_r and Θ_E (e.g., 30 pm² for m_r = 4.8 × 10⁻²⁶ kg and Θ_E = 280 K). Indeed, the evaluated Einstein temperatures of these alloys are quite similar, as shown in Fig. 5(b). The similar Θ_Es of these samples are associated with the similar atomic weights and metallic bonding forces in these alloys.

The effective force constants (k_E = m_rk_B²Θ_E²ħ⁻²) of the measured alloys were calculated to be 4–5 eV Å⁻² (60–80 J m⁻²) and depended on the core element. The difference between the effective force constants of these alloys possibly causes broadening of the phonon spectrum and element-pair-dependent thermal expansion. However, the small difference in k_E values implies that the influence is not significant in these medium-entropy alloys. Furthermore, the variation in the effective force constant can be used to measure the degree of systematic deviation of the atomic distribution. In this context, the close k_E values of the measured alloys imply that the statistically significant deviation of the atomic distributions is presumably small, even if atomic-scale segregation exists. In other words, these results show the resolution required to identify the difference in the atomic distributions between multi-principal-element alloys and the limitations of our simple analysis. To further extract scattering-path-dependent information of multi-principal-element alloys, advanced model-free analyses, such as sparse modeling,²⁴⁾ might be effective.

4.3 Static MSRD and MSAD

As shown in Fig. 5(a), the additional static components of the MSRDs of the measured alloys were evaluated to be approximately 20–50 pm². These values are larger than those of normal metals, in which the σ₀² for copper is almost negligible,²⁵⁾ indicating the existence of static local distortions around the absorbing atoms in these samples. In this analysis, the static MSRDs of the measured alloys increased in the order of the CrCoNi, FeCoNi, and MnCoNi samples. As a result, the general relationship between the CRSS and MSAD seems to be broken, which predicts that the MSAD is proportional to the CRSS (FeCoNi ≤ MnCoNi < CrCoNi), as demonstrated by Okamoto et al.¹²⁾ Here, we should comment on the relationship between the MSRD and MSAD while referencing Ref. 18). The MSRD between two atoms labeled A and B is approximated as MSRD_AB = MSAD_A + MSAD_B − 2DCF_AB, where MSAD_A and MSAD_B are the atomic displacement parameters of atoms A and B, respectively, and DCF_AB is the displacement correlation function between them. DCF_AB is a measure of the real-space correlation between two atoms and may become large for coherent vibrational motions owing to covalent bonding and small for incoherent motions, such as individual thermal vibrations, as reported elsewhere.¹⁸^,²⁶^,²⁷⁾ In the measured alloys, the atomic weight of atom A is similar to that of atom B, and these atoms can randomly occupy only one crystallographic site in the fcc structure. Consequently, MSAD_A is considered to be almost identical to MSAD_B for the measured alloys, and the above relationship can be approximated as MSRD_AB = 2MSAD − 2DCF_AB. The meaning of this relationship is that the DCF term is essential for verifying the CRSS-MSAD relationship with the MSRD and might provide complementary information about the bonding states in alloys.

Unfortunately, we could not determine the MSADs of the measured alloys through neutron experiments because of the influence of the crystal texture. Therefore, we used the reported values for comparison. Through first-principles calculations, the MSADs of CrCoNi, MnCoNi, and FeCoNi alloys were calculated to be 27.6 (32.08), 21.9 (18.41), and 16.3 (11.56) pm², respectively.¹²^,²⁸⁾ The values of twice these MSADs slightly deviate from the total values of the MSRDs at 20 K measured from the EXAFS experiments. Although the accuracy of these MSRDs and calculated MSADs should be carefully verified, the slight difference between them is intriguing in the context of the bonding states in medium-entropy alloys. In particular, the slightly negative deviation (total or static MSRD ≤ 2MSAD) in the CrCoNi sample signifies a finite DCF term, which results in a decrease in the MSRD and implies the existence of anomalous covalent-like local motion and coherent local strain. In contrast, the positive deviation (total MSRD ≥ 2MSAD) in the MnCoNi and FeCoNi samples is difficult to interpret. The positive deviation in these samples may be due to poor assumptions in our analysis, in which the fitting parameters (R_j and σ_j²) were assumed to be identical for all scattering paths. Therefore, the observed large MSRDs may have resulted from a mismatch between the constructed and actual structures. In other words, the actual structure may be distorted from the fcc structure, as mentioned in the next subsection.

We discuss another possible explanation for the difference between the MSRD and calculated MSAD. Because first-principles calculations may be carried out with a completely stable structure through structural relaxation, the calculated MSAD can be considered the value at the lowest energy. However, as demonstrated in the next subsection, the average structure of the MnCoNi sample changes from fcc to a lower-symmetry structure through long-term structural relaxation. This indicates that a metastable structure can be realized in high- and medium-entropy alloys that is possibly different from the ground-state structure treated in first-principles calculations. Therefore, the experimental values of MSRD/MSAD may become larger than the calculated values.

4.4 Local structural instability

Let us now consider the origin of the large MSRD observed in the MnCoNi sample. Figure 6 shows the neutron diffraction profiles of CrCoNi and MnCoNi samples measured at room temperature. The filled blue rectangles and filled green circles depict the results of the annealed samples, whereas the light-blue open rectangles and red open circles show the results of the as-grown samples. The sharp peaks at approximately 37° and 43° correspond to the fundamental Bragg reflections (111 and 200) of the fcc lattice. Additional diffuse scatterings around the 100, 110, and 210 forbidden reflection points were observed in the MnCoNi sample, including the as-grown sample, clearly indicating a structural transformation from the fcc lattice to a structure with lower symmetry (e.g., a primitive tetragonal lattice P4/mmm, L1₀). After heat treatment at 400 °C for 400 h, the diffuse scattering signal showed a clear increase, and the width of the profile decreased. These results are indicative of long-term structural relaxation in the MnCoNi sample, and the large MSRD can be associated with such local structural instabilities. The width of the diffuse scattering profile is rather large after long-term annealing. The spatial correlation lengths in the as-grown and annealed samples were roughly evaluated to be 1 nm and 5 nm, respectively, indicating that the superlattice structure maintained short-range correlation. Further investigation of the short-range structural transformation in the MnCoNi sample is in progress.

Fig. 6

Neutron diffraction profiles of CrCoNi (rectangles) and MnCoNi (circles) at room temperature. The open and closed symbols are the data of the as-grown and annealed samples, respectively. The bold bar symbols denote the Bragg positions for P4/mmm (the ratio of the c and a axes c/a ∼ 1). The backgrounds from the empty cell and air scattering were subtracted for clarity. The right panel structures, which were drawn using VESTA software,²⁹⁾ possibly explain the observed short-range structural transformation in the MnCoNi sample.

In addition, no diffuse scattering was observed at room temperature in the CrCoNi sample. This result indicates that no remarkable structural relaxation occurred in the CrCoNi sample, even though significant static local distortions exist in the sample, as predicted in Fig. 5(a). The qualitative difference in the structural transformations of the MnCoNi, CrCoNi, and FeCoNi samples may be due to the difference in the structural transformation temperature T_s values of these samples, namely, T_s may be high for the MnCoNi sample and low for the CrCoNi (and FeCoNi) samples. The short-range structural transformation observed in the MnCoNi sample may belong to a diffusional type with rearrangement of the atomic distribution. In general, such diffusional transformation requires a large atomic diffusion coefficient at low temperatures below T_s. For this reason, the formation of atomic-scale segregation (chemical short-range ordering) in the CrCoNi and FeCoNi samples can be frozen at high temperatures, at which an almost random structure must be preferred due to the effect of the configurational entropy term in the total Gibbs energy. Furthermore, the lower melting temperature of the MnCoNi sample (1462 °C), as reported by Wu et al.,²⁾ than that of the CrCoNi (1690 °C) and FeCoNi (1720 °C) alloys may serve as a reference for this interpretation. Alternatively, the many vacancies due to the high vapor pressure of Mn may drive rearrangement of the atomic distribution in the MnCoNi sample. We believe that the introduction of vacancies is a promising method for tuning the degree of short-range ordering at low temperatures, even in the CrCoNi sample.

5. Summary and Conclusion

We have presented the results of EXAFS and neutron diffraction experiments on a family of ternary medium-entropy alloys (CrCoNi, MnCoNi, and FeCoNi). The EXAFS spectra were analyzed using a simple random cluster model, which was carefully constructed such that the appropriate constraint on the bond length (R_EXAFS ≥ R_D) was conserved. We succeeded in separating the static and dynamic MSRD components by analyzing the temperature evolution of the MSRD using the correlated Einstein model. The evaluated static MSRDs increased in the order of the CrCoNi, FeCoNi, and MnCoNi samples. In contrast, the dynamic MSRDs of these alloys were almost identical, resulting from their similar atomic weights and metallic bonding forces. We discussed the origin of the difference between the MSRD and MSAD and considered the implications of the DCF term arising from the influence of the bonding states and local structural instability in alloys. Finally, we investigated the origin of the large MSRD in the MnCoNi sample and demonstrated the crucial results of neutron diffraction experiments, which indicated the emergence of a short-range structural transformation through long-term structural relaxation.

We conclude that EXAFS experiments are effective for examining the local structures in multi-principal-element alloys. In particular, MSRDs are useful for detecting structural instabilities in alloys. Further developments in structural modeling and model-free analyses of EXAFS spectra are essential for examining the state of chemical short-range ordering in multi-principal-element alloys.

Acknowledgments

One of the authors (YI) thanks Dr. M. Enoki and Prof. H. Ohtani for their helpful advice. We also thank Mr. M. Ohkawara and Assoc. Prof. Y. Nambu for their kind support in the neutron diffraction experiments at T1-3 HERMES. This work was supported by Grants-in-Aid for Scientific Research on Innovative Areas on High Entropy Alloys (grant numbers JP19H05164 and JP21H00139). We wish to thank the Analytical Research Core for Advanced Materials at the Institute for Materials Research, Tohoku University for the experimental support in the chemical composition analysis with the XRF spectrometer. EXAFS experiments were carried out at the BL14B1 beamline of SPring-8 (Proposal No. 2020A-E03, JPMXP09A20AE0003, JASRI-2020A3647) with the support of the “Nanotechnology Platform” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan and the approval of the Japan Synchrotron Radiation Research Institute (JASRI). The neutron diffraction experiments were performed under the Joint-Use Research Program for Neutron Scattering, Institute for Solid State Physics (ISSP), University of Tokyo, at the Japan Research Reactor JRR-3 (Proposal No. 21576). We gratefully acknowledge the support from the Center of Neutron Science for Advanced Materials, Institute for Materials Research, Tohoku University.

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