Local lattice distortions and chemical short-range order in MoNbTaW

Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, $ \delta _{exp} $ δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO. GRAPHICAL ABSTRACT IMPACT STATEMENT A medium-entropy MoNbTaW bcc alloy annealed at 2273 K shows still signs of short-range ordering which relate to its segregational behavior at lower temperatures, corroborating observations on fcc alloys.


Introduction
The increasing need for more specialized and better performing structural materials has driven the discovery of many remarkable alloys.The harsher the service conditions, the more specific become material demands, where for example rockets and airplane turbines belong to the most challenging environments due to extreme temperatures, corrosive gases, and mechanical forces.For example, driven by increasing energy efficiency and therefore higher engine temperatures, commercial Ni-base superalloys have undergone a tremendous many-decades-long performance development.Noticeable efforts have been made both in terms of material development and component design, the latter of which includes cooling channels or thermal barrier coatings that push application temperatures by several hundred degrees.Alongside, new base CONTACT Andrea Fantin andrea.fantin@bam.deFederal Institute of Materials Research and Testing (BAM), Unter der Eichen 87, 12205 Berlin, Germany; Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, 14019 Berlin, Germany Supplemental data for this article can be accessed online at https://doi.org/10.1080/21663831.2024.2326014.materials, including Mo-based [1,2], Nb-based [3,4], Cobased [5][6][7][8], or noble metal superalloys [9,10] have been developed.Given their limited commercial and applicational viability, the search for novel candidate alloys continues.
A promising approach has been found at the beginning of the millennium with the introduction of so-called high-entropy alloys or multi-principle element alloys [11,12], exhibiting outperforming properties beyond conventional alloy design space.One of the core effects in this novel alloy class is their configurational entropy, which allows the solid solution to be single-phase, crystallizing in simple crystal structures such as face-centered cubic (fcc) [11,13], body-centered cubic (bcc) [14,15], and to a lesser extent to hexagonal close packed (hcp) lattices [16].
One of the most promising of these alloys, in terms of high-temperature properties, is the MoNbTaW alloy that was introduced by Senkov et al. in 2010 [14], and that has been studied experimentally [17][18][19][20][21][22] and with modeling [23][24][25][26] by several groups over the past decade.Investigating this alloy experimentally is a true challenge as its preparation, casting, powder metallurgical processing, as well as its homogenization, requires very high temperatures.As-cast, the alloy consistently shows segregation of the high-melting point elements W and Ta into dendritic cores, whereas the lower-melting point elements Nb and Mo segregate towards the interdendritic regions.Indeed, Senkov and co-workers [14,17] suggested these chemical fluctuations also to occur within the solid solution without having any influence on the overall lattice parameter of the alloy.Furthermore, no phaseformation was anticipated, a conclusion that to date has not been experimentally verified due to the challenges in tracking atomic-scale chemical order along very-high temperature isotherms.
Experimental evidence is, however, still scarce and methods to validate the theoretical findings are limited and highly specialized.One method that has proven a unique capacity in detecting local interatomic neighboring and preferences is extended X-ray absorption fine structure (EXAFS).In fact, EXAFS has recently shown that the assumed severe lattice distortion in the wellknown 'Cantor' CoCrMnFeNi alloy is much less pronounced than what initially was believed [37].Along the same line, earlier EXAFS studies on the six-component Al 8 Cr 17 Co 17 Cu 8 Fe 17 Ni 33 (at.%) system [38,39] showed that the formation of a second Al-Cu-Ni rich L1 2 structured phase could be foreshadowed by the determination of preferred nearest neighbor species for Al (Al-Ni, Al-Cu) in the single-phase region.Similarly, the established preference of Cr for smaller atoms as neighbors, such as Co, Fe and Ni [39,40], was correlated with the composition of the Co-Cr-Fe rich disordered matrix forming in the two-phase region.
Here we will continue to leverage the power of EXAFS to unravel element-specific atomic ordering in the high-temperature bcc MoNbTaW alloy.Subjected to an unprecedented heat treatment at 2273 K for 24 h, we find that short-range order persists around W, preferring 4d elements in the two nearest-neighbor shells.At the same time, a Nb-W ordering is revealed that gives a strong high-temperature signature of the ordered B2 (Mo-Ta) or B32 (Nb-W) phases, otherwise associated with the medium temperature range below the order-disorder transition.This new insight suggests that high-temperature local ordering is generally indicative of lower temperature ordered phase-formation, as now established for both fcc and bcc solid solutions.Besides low temperature phase-formation predictions, modeling correctly SRO at higher temperatures may contribute in better determining its influence on dislocation behavior, as discussed for MoNbTaW [41] and similar refractory HEAs [42,43].

Materials and methods
The MoNbTaW was cast via arc melting and remelted four times to ensure maximum homogeneity.A heat treatment of 2273 K for 24 h in Ar was subsequently applied at the University of Bayreuth to the specimen, which was then mechanically ground and polished (200 nm sized colloidal SiO 2 suspension) for scanning-electron microscopy (SEM, Zeiss LEO 1530 with a Gemini I column), laboratory X-ray diffraction (XRD, Bruker D8 diffractometer) investigations, and synchrotron experiments.Note that the long annealing made the MoNbTaW ingot react with the ceramic support, inducing an oxygen gradient in its near-surface parts.The specimen used in the present work, approximately 1 cm 2 area × 1 mm thickness, was taken from the ingot's core.Energy dispersive X-ray spectroscopy (EDS) was performed at 5 and 20 keV, while a Cu Kα 1/2 radiation was employed for XRD data acquisition.The MoNbTaW sample was measured at the LISA beamline (BM08, ESRF) using a pair of Si (311) flat monochromator crystals, acquiring EXAFS spectra at Ta L 3 (9881 eV), W L 3 (10207 eV), Nb K (18986 eV), and Mo K (20000 eV) edges.Higher harmonics rejection was obtained through Si-coated (Ta, W L 3 , E cutoff ≈ 15 keV) and Pt-coated (Nb, Mo K) collimating/focusing mirrors.Spectra were measured in fluorescence mode (13-channel Germanium Detector), at room temperature, employing a fixed k step of 0.05 Å −1 up to a maximum value of about k max = 15 Å −1 , except for Ta (k max = 9.1 Å −1 ) due to intrinsic range limitations because of the presence of the Z + 1 element W (Z: atomic number) in the alloy.Data on references (Nb, Mo, W and Ta metal foils) was collected in transmission mode up to k max = 18 Å −1 .

Results and discussion
One of the challenges lies in the extremely high melting points of the MoNbTaW alloy (ca.3200 K) and of all its components, above 2700 K, which implies the need for special furnaces when it comes to its homogenization.The heat treatment chosen in this study, 2273 K for 24 h, is the most extreme in terms of the combination of temperature and holding time so far for this alloy.
Figures 1(a and b) show the SEM overview images of the as-cast (AC) and the heat-treated (HT) alloy.Both states are characterized by 50-300 μm sized grains and internal segregations, with a slightly reduced segregation behavior in the HT case.80 μm long EDS-linescans performed through one grain show relevant elemental fluctuations of Nb, Mo and W in the AC state (cf.histograms) and of W in the HT state, contrary to Ta that shows the least fluctuations and is rather uniformly distributed in the dendritic cores and in the interdendritic regions.The peak concentrations in the EDS-linescans for the AC state are especially high for Nb and W and significantly damped in the HT state.Self-diffusion and impurity diffusion data gathered from Ref. [44] allowed calculating the maximum diffusion length for all elements imposing the diffusion time (t = 24 h) as the heat-treating time (cf.Table S1, S.I.).Within 24 h and at T = 2273 K, all elements diffuse the most in Nb, between 24 (W) and 50 (Nb) μm, and the least in W, ca. 1 μm (Mo, Nb, Ta) or even less (W).These numbers are in good agreement with the experimental observation of a two-fold oscillationperiod increase of the EDS line-scans between the AC and the HT state, indicating that the diffusion behavior in the MoNbTaW matrix is reasonably well extrapolated by impurity diffusion of its pure elements.Achieving a fully uniform distribution of the elements would require, however, significantly longer isotherms than pursued here, which due to technical reasons was not possible.This is in line with earlier reported heat treatments, such as at 1673 K for 19 h by Senkov et al. [17] or 2073K for 7 days by Zou et al. [45], both of which were also not able to homogenize the dendritic segregation.
X-ray diffraction patterns of the AC and the HT MoNbTaW are shown in Figure 2. In Figure S1, an enlarged view of high 2θ values (HT state), together with SEM maps and optical microscopy images show the absence of secondary bcc phases and the remainders of a Ta-O rich segregation mainly present at the grain boundaries, undistinguishable in the XRD patterns.The refined lattice parameters using a bcc structure model (s.g.Im 3m) and the LeBail method [46] are consistent for both specimens: a AC = 3.222(1) Å and a HT = 3.223(1) Å, both of which are in good agreement with literature data on the heat-treated MoNbTaW alloy (2073 K, 7 d), a = 3.222(1) Å [45].A single bcc phase was indexed in Figure 2 except for a small peak at about 2θ : 72°, which is ascribed to a pure W reflection. Areas of unmolten W can be distinguished in SEM (not shown here) and are a common feature in W containing alloys.Refined lattice parameters are close to the lattice constant predicted via Vegard's law, a VEG = 3.226 Å, and close to the 2 nd shell bond distances extracted by the EXAFS analysis (reference foils' results: Table S2; MoNbTaW fits: Figure S2), presented in Table S3 together with XRD values.
In EXAFS fitting, a binary model with two gray atoms was used for modeling the spectra: one atom represents a 4d average, and one represents a 5d average, labeled 4d and 5d, respectively.According to this binary approach, 1 st and 2 nd shells were fitted with two paths each, defined as Abs -4d and Abs -5d (Abs: absorbing atom).In this way, two distances per shell are determined, the Abs -4d (1 st , 2 nd ) and Abs -5d (1 st , 2 nd ) bond lengths, depicted in Figure 3 together with the averaged 1 st and 2 nd shell obtained from XRD data and those obtained from the Vegard's law.The XRD 1 st shell was calculated assuming that, in an undistorted bcc structure, the 1 st shell distance is √ 3/2a, where a is the lattice constant.The disorder in EXAFS spectra was modeled using the Debye approximation, with only one free parameter left free, the Debye Temperature θ D , used to compute every mean-square variation in path lengths for each path in the EXAFS fit.
By averaging the 1 st shell atomic distances to nearest neighbors, a contraction of 0.8(7) % to the average 1 st shell distance derived by XRD fits (XRD 1 st = 2.791(1) Å) is found.2 nd shell distances determined by EXAFS are also slightly contracted by 1(1)% compared to those determined from the XRD data.Taking a closer look, the Nb 1 st shell is closest to the average structure compared to Mo, Ta and W, while Ta's 1 st , 2 nd and W 2 nd shells are within the uncertainty of the average structure lattice value.A net distinction between local lattice distortions of bcc and fcc compounds is reported in literature [21,47,48], where it is generalized that in bcc the local lattice distortion distances extend up to 4 Å, compared to fcc systems where it remains below 3 Å.The results from Figure 4 show that the bcc MoNbTaW system exhibits slight distortions at least up to the 2 nd shell, even though at the 1 st shell level distortions are close to those found in an fcc alloy (0.9(2)% [39]).This hints that distortions are more related to the alloying elements' properties than to the crystal structure.MoNbTaW is reported to have a nominal low overall lattice distortion compared to several other quaternary high-entropy alloys [49,50].A root mean square displacement (RMSD) from ideal lattice sites of ca.0.1 Å was established by Monte Carlo/Molecular Dynamics simulations at 300 K [49], in line with the averaged value extracted from EXAFS, 0.10(1) Å.However, through EXAFS an element specific RMSD can be calculated, which spans from 0.01(3) Å (W) to 0.15(7) Å (Ta), showing that the calculated size-mismatch parameter δ calc or the lattice strain index λ * , , and with c i (c j ) and r i (r j ) the relative concentration (from EDS, Table S4) and the metallic radii (from lattice parameters, Table S5) of the species i(j), grasp only partially the complexity of atomic level distortions.In the interdendritic and the dendritic regions in both the homogenized and as-cast states, δ calc = 2.3-2.4% and λ * = 5%, much below the critical values of 6% and 16% [51], respectively, indicating a low elastic driving force for a phase decomposition in this alloy.The corresponding elastic energy in the homogenized state is e = qδ 2 calc = 210 MPa [51], with q = 2μ (1+ν) (1−ν) = 337 GPa computed based on DFT calculations [52].An experimental size-mismatch parameter δ exp can also be estimated for the homogenized MoNbTaW assuming that with r EXAFS being the observed EXAFS bond length of each absorber (cf.Table S3) and a XRD is the 'average' value from XRD. c XAS is the relative weight of each bond length, which is assumed to be equal for every alloying element.In this way, δ exp = 1.1% (2 nd shell), a ca.50% sizemismatch decrease with respect to δ calc is obtained that occurs due to the electrochemical interaction between species to stabilize the structure by reducing its distortions.EXAFS allows calculating δ exp also for the 1 st shell (δ exp = 0.9%).Such decrease is ascribed in literature to a charge transfer [47] or electronic rearrangements including a mixture of directional bonding and metallic bonding [38][39][40].Non-negligible lattice distortions in the 2 nd shell also indicate the significance of ternary interactions, i.e. the additional effect of third element on pair interactions.
Simulations of MoNbTaW preferred nearest neighbors were carried out previously [30,33,35,36,41,49], indicating order at lower temperatures (T < 800 K-1000 K), where intergroup near neighbor correlations remain above the inter-row correlation.These in turn remain above the self (e.g.Ta-Ta) correlations, following the proposed bond interaction strengths.For higher temperatures, the -T S part of the Gibbs Free Energy becomes relevant enough to substantially decrease such nearest neighbor correlations, as it can be observed for the simulations performed at 1800 K [30].Assuming the alloy retained the structure at 2273 K before cooling, comparison with simulations should be made around this temperature, with Widom et al. [30] reporting the closest state to the present experimental conditions.Recent works [35,36] established Warren-Cowley (WC) order parameters as a function of temperature, showing that at 1773 K Ta-Mo and Nb-Mo (competition), then Ta-W and finally Nb-W pairs have negative WC parameters.Summarizing the predicted behavior of short-range order (SRO) with temperature, MoNbTaW segregates at low temperatures in B2(Mo,Ta) and B32(Nb,W) phases [25,27,28], orders into a B2(Mo,W;Ta,Nb) phase with preferred pairs above 350-400 K until an order-disorder transition occurs [25,26,[29][30][31][32][33], above which the system slowly tends to a fully disordered solid solution.In Figure 4 is becomes evident that at 2273 K Nb has no preferences in the 1st shell and slight preferences in the 2nd shell for 5d metals.On the other hand, non-negligible ordering appears around Mo and W on both the 1 st and 2 nd shells, preferring 4d elements.Note that chemical fluctuations observed by SEM (μm-scale) and atomic preferences by EXAFS (Åscale) cannot be directly related, as EXAFS resolves the SRO on much smaller length scales.As such, the effects of SEM-resolved chemical fluctuations on the SRO can essentially be neglected.
Even though EXAFS may predict only a preference to 4d or 5d elements based on the X-ray scattering contrast, theory predictions and the present experimental work may be discussed together.By combining information from the here pursued EXAFS experiments and results reported e.g. by Zhou et al. [35], He et al. [36] and/or Widom et al. [30], at the 1 st shell only, the following can be deduced: • Nb has no preference for 4d or 5d elements as its neighbors, i.e. it is surrounded by Mo and W equally. • Mo has slight preferences for 4d elements over 5d elements, i.e. it prefers Nb over Ta, favoring Mo-Nb over the Mo-Ta pair.• W has a clear preference for 4d over 5d elements, i.e. it prefers Nb over Ta, assumed valid for the Nb-W pair in the 2 nd shell as well from both Nb and W sides.
Overall, SRO is low but non-negligible in the investigated heat-treated MoNbTaW, revealing a spatial coherence length of at least a few Å.Even though no ordered phase formation was found in this study, bonding preferences show that the modeling employed in the literature by He et al. [36] seems to predict ordering more accurately, contrarily to the smaller differences shown by Widom et al. [30].The existence of SRO at 2273 K indicates that the mixing enthalpic energy contribution, stemming from the differences in the interatomic bond energies, is relatively strong, overcoming the entropic contribution to some extent, even at such high temperature.These results imply that an influence of the SRO on the dislocation mobility at high-temperatures might be quite different than what was reported in Yin et al. [41].In addition, such local ordering in the alloy may act as a precursor for formation of extended ordering predicted at lower temperatures [30,33,35,36,49].That phase formations from chemical SRO in the MoNbTaW bcc solid solution can be 'predicted' from a high-temperature structure, supports results obtained in previous studies on an fcc solid solution [39], raising the question if this is generally true.Even though this correlation is not clearly demonstrated in literature, and the present bcc-based with the previous fcc-based [39,53] studies suggest that holds true, the temperature difference in the phase diagram between measurements and lower temperature domains of second phases do play a critical role to substantiate this conclusion, and will be a matter of future investigations.

Conclusion
A partially homogenized, single-phase bcc MoNbTaW medium entropy alloy was investigated by EXAFS to determine its short-range ordering and compare it to modeling-derived phase predictions.Despite the unprecedented heat-treatment conditions used, a nonnegligible amount of short-range ordering was revealed.Specifically, W shows the strongest preferential bonding behavior, i.e. it prefers 4d elements Nb and Mo over Ta in the 1 st shell.Mo has a slight preference for Nb as its nearest neighbor while Nb is indifferent, and Ta's preferences could not be determined due to its L edges being too close to the W L edge.Despite the approximate temperature gap of 700 K between the annealing condition at T = 2273 K, and the predicted lowtemperature B2(Mo,W;Ta,Nb) and B32(Nb, W) ordered phases, bonding preferences from the high 2273 K anneal (such as Nb-W) are in agreement with the expected lowtemperature ordering and prove that the spatial coherence length of chemical short-range order reaches at least the 2 nd shell, i.e. 3.2 Å.These results align well with earlier fcc high-temperature short-range ordering, suggesting that high-temperature SRO can foreshadows low-temperature ordering and phase formation.

Figure 1 .
Figure 1.SEM overview and the corresponding EDS linescans with frequency histograms of (a) the as-cast MoNbTaW alloy and (b) the specimen heat treated at 2273 K, 24 h.Linescans were smoothed by Savitzky-Golay 20 p (as-cast) and 10 p (heat-treated), and frequency histograms were fitted through a normal distribution indicating the resulting standard deviation σ (in at.%), with the associated uncertainty in brackets.

Figure 2 .
Figure 2. Observed X-ray diffraction pattern (black) of as-cast (AC) and heat-treated (2273 K-24 h, HT) together with the corresponding fit (red) and the difference of the two (green).Ticks identify the Im 3m phase.

Figure 3 .
Figure 3.Comparison between XRD results (full averaged structure, lines) and EXAFS (local structure, markers), with 1 st and 2 nd shell distances to 4d (full markers) and 5d (empty markers), and calculations of 1 st and 2 nd shell distances according to Vegard's law (dashed lines).

Figure 4 .
Figure 4. 1 st and 2 nd shells nearest neighbor (NN) preference (in %) per each absorber Nb, Mo and W, where 0.5 corresponds to a completely disordered environment.