Overcoming the strength-ductility trade-off in refractory medium-entropy alloys via controlled B2 ordering

Herein, we showed that controlled additions of Al, which provided a certain degree of B2 ordering, resulted in a ∼ 37%-enhancement of both yield strength and uniform elongation in Alx(NbTiZr)100-x (x = 0; 2.5; 5; 7.5 at.%) refractory medium-entropy alloys. The improvement of properties stemmed from the solid solution and short-range order strengthening, as well as from the alteration in a character of dislocation glide. The B2 ordering caused the formation of multiple dislocation bands and the activation of cross-slip, which improved the macroscopic stability of plastic flow and extended the strengthening stage, thereby postponing necking. GRAPHICAL ABSTRACT IMPACT STATEMENT Controlled Al-induced B2 ordering helps overcome the strength-ductility dilemma in refractory medium-entropy alloys due to solid solution and short-range strengthening coupled with the dislocation motion changing.


Introduction
Chemical ordering in body-centred cubic (bcc) refractory high/medium-entropy alloys (RH/MEAs), designed for high-temperature service [1][2][3][4], has been gained particular attention among the researchers in recent years . Great interest in such a phenomenon is because of its crucial effect on the mechanical properties. Specifically, many Al-containing RH/MEAs, in which Al induced the formation of a B2 (ordered bcc) structure, possessed higher strength at 22-1350°C compared to Al-free counterparts [2,11,30,33,36,38]. Some of these alloys showed yield strength anomaly [24,37], i.e. became stronger with the temperature rise. Meantime, a large part of B2-ordered RH/MEAs had limited plasticity at ambient or intermediate temperatures [7,9,11,19,30,33,37]. CONTACT  To date, several efforts have been made to balance the mechanical performance of B2-ordered RH/MEAs [7,10,19]. However, even a slight increase in the plasticity of B2-ordered RH/MEAs, provided by either chemical (elimination/decrease in the degree of B2 ordering [7,19]) or microstructure (the B2 matrix-to-B2 particles transition [10]) engineering, has resulted in a notable strength degradation. More importantly, the room-temperature tensile ductility, required for potential applications of these alloys as structural materials [41], remained unreported or unachievable.
In the current study, we, for the first time, showed that the enlargement of the degree of B2 ordering in a controllable fashion could overcome the strength-ductility trade-off in RH/MEAs. This counterintuitive strategy was tested on a model bcc NbTiZr RMEA having decent tensile ductility and medium strength [42,43], which was alloyed with various amounts of Al to invoke the B2 ordering. Our results demonstrated that the B2 ordering was a more effective way to improve the overall mechanical performance of the NbTiZr alloy compared to the already reported approaches [44,45].

Materials and methods
The alloys with nominal compositions of NbTiZr, Al 2.5 (NbTiZr) 97.5 , Al 5 (NbTiZr) 95 , and Al 7.5 (NbTiZr) 92.5 (at.%) were produced by the vacuum arc melting of pure metals. The as-cast ingots were cold rolled to a thickness strain of 80%, sealed in vacuumed (10 −2 torr) quartz tubes, annealed at 900°C for 0.5 h, and water quenched. Tensile specimens with the gauge dimensions of 6 × 3 × 1 mm 3 were cut from the annealed sheets. Tensile tests were performed at room temperature in a laboratory air at a constant strain rate of 10 −3 s −1 (Instron 5882). The digital image correlation (DIC) technique was employed to visualise the distribution of local strains produced during the tensile tests. The in-plane Lagrangian strains were measured using a commercial Vic-3D TM system (Correlated Solutions, Inc).
Microstructural investigations were performed using X-ray diffraction (XRD; RIGAKU diffractometer and Cu Kα radiation), electron backscatter diffraction (EBSD; FEI Quanta 600 FEG), and transmission electron microscopy (TEM; JEM JEOL-2100). Selected area diffraction patterns (SADPs) were collected in a < 001 > bcc zone axis at an exposure time of 16 s. Intensity line profiles along the g 200 vector and the threshold segmentation were constructed using an ImageJ software. Dark-field images taken from the aperture positions corresponded to a half-length of the g 200 vector were acquired at an exposure time of 32 s. Figure 1 collects the data on microstructure and phase composition of the Al x (NbTiZr) 100−x alloys. The actual chemical compositions of the alloys are given in Table S1 (Supplementary material). EBSD analysis revealed a fully recrystallised microstructure in all the alloys ( Figures  1(a-d)). Average grain sizes were close to ∼ 20 μm; however, small deviations from this mean value should be noted ( Figure S1, Supplementary material). An initial evaluation by XRD showed that the alloys had a singlephase bcc structure ( Figure S2, Supplementary material). TEM investigation, based on the assessment of SADPs taken in < 001 > bcc zone axes and the intensity line profiles along the g 200 vector (which showed no local maxima at their half-lengths), confirmed the bcc structure in the NbTiZr and Al 2.5 (NbTiZr) 97.5 alloys ( Figures  1(e, f, i, j)). Meanwhile, we detected diffuse and faint 100 B2 superlattice spots in the Al 5 (NbTiZr) 95 alloy (denoted with pink arrows in Figure 1(g)). These B2 superlattice spots were sharper and brighter in the Al 7.5 (NbTiZr) 92.5 alloy (Figure 1(h)). The intensity line profiles along the g 200 vector disclosed approximately four times higher local maxima corresponding to their half-lengths, i.e. the 100 positions, in the Al 7.5 (NbTiZr) 92.5 alloy compared to those in the Al 5 (NbTiZr) 95 alloy (Figures 1(k, l)).

Results and discussion
Data obtained in the current study confirmed limited applicability of XRD analysis for revealing of the B2 ordering in (R)H/MEAs with low Al contents [17,[46][47][48]. Only by TEM analysis, we discovered the smallest ( > 2.6 at.%) threshold Al concentration for the bcc-to-B2 transition, recorded to date for RH/MEAs [19,22,30], lightweight H/MEAs (LWH/MEAs) [49,50], and beta-Ti alloys [51]. Besides, an examination of SADPs via the intensity profile lines could give us a semi-quantitive appraisal of a degree of ordering in the Al x (NbTiZr) 100−x alloys. Through comparison of the relative intensities of superlattice and fundamental spots [52][53][54][55][56][57], albeit without counting the scattering factors, we established that the Al additions from 5.3-7.7 at.% increased the degree of B2 ordering by about four times.
Here, the term 'degree of B2 ordering' must be clarified. In previous works [7,8,14,19], a multi-component B2 matrix phase in Al-containing RH/MEAs was assumed as a continuous entity with an imperfect lattice containing atoms of constitutive elements, arranged both in random (bcc) and preferential (B2) positions. The occupancy of the B2 sites by a certain sort of atoms, mostly by Al ones, characterised the degree of B2 ordering, which could vary from 0 (disordered) to 1 (ordered), similarly to binary alloys [58]. Meantime, Qiao et al. [30] recently revealed a diffusionless transfer from short-to long-range B2 ordered domains with an increase in the Al content. In that case, the degree of B2 ordering was considered as a dimensional parameter instead of the site occupancy factor.
To gain insight into the B2 ordering phenomenon in the Al x (NbTiZr) 100−x alloys, we performed a more detailed TEM study ( Figure 2). Dark-field imaging of the NbTiZr and  could be distinguished (Figure 2(b)). The threshold segmentation (Figures 2(c, d)) suggested the average size,d, standard deviation, σ , and fraction, f, of these B2 domains as 0.82, 0.33 nm, and ∼ 20%, respectively (Figure 2(e)). The dimensions of < 1 nm allowed identifying these B2 domains as short-range ordered (SRO) entities [54,59,60].
Based on the domain ordering mechanism proposed by Qiao et al. [30], the following scheme of the B2 ordering in the Al x (NbTiZr) 100−x alloys could be suggested.
The Al additions first provoked the bcc-to-B2 transition (between the Al 2.5 (NbTiZr) 97.5 and Al 5 (NbTiZr) 95 alloys), i.e. resulted in the formation of the B2 SRO domains with a very small size, and then increased the degree of B2 ordering (between the Al 5 (NbTiZr) 95 and Al 7.5 (NbTiZr) 92.5 alloys) due to growing of these B2 SRO domains. However, further in-depth investigations are needed to elucidate peculiarities of the B2 ordering more thoroughly, which are beyond the limit of the current paper.     Table 1). According to the engineering stress-strain curves, after yielding, the Al-containing alloys experienced a short strengthening stage followed first by a stress reduction, then continuous yielding, which extended with an increase in the Al content, and finally by a slight strengthening (the Al 2.5 (NbTiZr) 97.5 and Al 5 (NbTiZr) 95 alloys) or a continuous softening (the Al 7.5 (NbTiZr) 92.5 alloy) stage (Figure 3(a)). Similar engineering stress-strain curves with plateau were previously reported in alloys with the bcc (or weakly B2 ordered) structure [46,47,[61][62][63] or in nanolaminates [64]. Although this behaviour should indicate plastic instability and early necking, Wei et al. [63] claimed rather a high value of homogeneous deformation, which they confirmed by DIC analysis. Indeed, our DIC analysis, coupled with the true stress-strain curves, showed that the macroscopic plastic deformation delocalised with the Al additions in the Al x (NbTiZr) 100−x alloys (Figures 3(b, c) and Figure S3, Supplementary material). As a result, the uniform elongation enlarged from ∼ 19% in the NbTiZr alloy to ∼ 26% in the Al 7.5 (NbTiZr) 92.5 alloy (Figure 3(b); Table 1).
An analysis of strain hardening rate, θ , revealed a gradual decrease in θ with the strain increment in the NbTiZr alloy (Figure 3(d)). The Al alloying caused the appearance of a 'hump', i.e. a sharp drop in θ at the onset of plastic deformation and a recovery stage with the evolving strain, terminated at peak values of θ ≈ 1000-1100 MPa. The magnitude of the drop and the extension of the recovery stage increased with the Al additions (Figure 3(d)). Lastly, we found that the Al doping did not change the apparent activation volumes, V * , significantly (Table 1); details on the determination of V * were described in Supplementary material and Refs [42,65]. The values of V * obtained fell in the range of 10-100 b 3 , which meant the thermally activated dislocation glide by overcoming the Peierls-Nabarro barriers was the rate-controlling mechanism of room-temperature plastic deformation in the Al x (NbTiZr) 100−x alloys [42].
Further, we tried to analyse the reasons of a positive impact of the Al additions on the mechanical performance of the Al x (NbTiZr) 100−x alloys. In terms of the strength, the observed increment in YS, YS, induced by the Al alloying was in an agreement with the ones previously reported for Al-containing RHEAs [11,30,66,67] (Figure 4(a)). The strengthening by Al in the studied Al x (NbTiZr) 100−x alloys appeared to be linear with a strengthening rate of ∼ 33 MPa per 1 at.%, which was close to bcc Al x (HfNbTiZr) 100−x ( ∼ 34 MPa/at.%; [67]) and bcc/B2 Al x (Ti 40 Zr 20 Hf 10 V 20 Nb 10 ) 100−x ( ∼ 32 MPa/at.%; [30]) RHEAs, but slightly higher than that of bcc Al x (HfNbTaTiZr) 100−x ( ∼ 25 MPa/at.%; [66]) alloys (Figure 4(a)).
In some alloys, the Al-induced strength increment was ascribed to solid solution strengthening (SSS) [11,66,67]. Given the linear dependence of the YS on the Al content, only the Suzuki model could describe the SSS in Al-containing RH/MEAs [67]. Since Al did not alter the rate-controlling mechanism of plastic deformation in the Al x (NbTiZr) 100−x alloys (Table 1), we suggested that it increased the athermal component of the YS. Thus, the simplified equation, connected the YS and the Al content, could be applied [67]: where α is a material-sensitive parameter; M is the Taylor factor; G is the shear modulus of the NbTiZr alloy; δ is the interaction parameter, included the lattice and shear modulus distortions appeared due to the Al additions; c Al is the Al concentration (  (1) for the Al 2.5 (NbTiZr) 97.5 and Al 5 (NbTiZr) 95 alloys were consistent with the experimental ones (Figure 4(b)); however, a small ( ∼ 10 MPa) deviation should be noted in the Al 5 (NbTiZr) 95 alloy. Meanwhile, Equation (1) underestimated the YS in the Al 7.5 (NbTiZr) 92.5 alloy significantly. Over 50% ( ∼ 130 MPa) of the experimentally observed YS remained unaccounted (Figure 4(b)). This discrepancy could be ascribed to the activation of other strengthening mechanisms. Wang et al. [11] and later Qiao et al. [30] mentioned that the B2 ordering could be responsible for the extra strength increment. Due to similarity of the average grain sizes (Figure 1 and Figure S1, Supplementary material), impurities content (Table S1, Supplementary material), and the absence of secondary phase particles in all the studied alloys, we also assumed that the additional increase in the YS of the Al 7.5 (NbTiZr) 92.5 alloy stemmed from the B2 SRO strengthening. Recently, SRO was stated as the main contributor to the strength of (R)H/MEAs [68][69][70][71] and LWH/MEAs [50,72]. SRO domains usually act as shearable obstacles, increasing the resistance for a dislocation slip due to the creation of diffuse anti-phase boundaries (DAPBs) when being cut [73]. Certainly, the direct evaluation of the SRO strengthening in the Al 7.5 (NbTiZr) 92.5 alloy will be feasible only when the energy of DAPB is available from experimental or, at least, calculated data [54], which are absent to date. Also, in the light of microstructural observations shown next, we can not exclude the possibility of the SRO strengthening in the Al 2.5 (NbTiZr) 97.5 and Al 5 (NbTiZr) 95 alloys. Figure 5 displays fine microstructures formed in the Al x (NbTiZr) 100−x alloys during the tensile tests.
In all the alloys, plastic deformation was dominated by a/2 < 111 > screw dislocations ( Figure S5, Supplementary material) but with a significant difference in their spatial distribution ( Figure 5). In the NbTiZr alloy, dislocations were distributed homogeneously ( Figure 5(a)). Starting from the Al 2.5 (NbTiZr) 97.5 alloy, dislocation motion tended to localise in dislocation bands (DBs; denoted with white dashed lines in Figure 5(b)). Further Al additions intensified this process; however, DBs were mutually intersected, suggesting a developed crossslip ( Figures 5(c, d)). In-between these intersected DBs, we found relatively large cells with a reduced dislocation density.
The localisation of plastic deformation in DBs was previously observed in face-centred cubic (fcc) alloys [ 74,75], beta-Ti alloys, Ti-Al-Nb, Ti-rich HEAs, and RHEAs [40,46,47,[76][77][78]. Recent study by Li et al. [75] showed that, in an fcc FeCoCrNiMn alloy, this process could be attributed to heterogeneous lattice strains. Meanwhile, Gerold and Karnthaler [74] demonstrated that localised planar slip in fcc alloys originated from SRO. Zhang et al. [54] further experimentally confirmed a decisive role of SRO domains on the localisation of plastic deformation in the Ti-6Al alloy. Li et al. [76] also connected the formation of DBs in beta-Ti alloys with the presence of SRO domains. Loretto et al. [48] claimed that the emergence of DBs in these alloys was a more solid confirmation of the B2 ordering in alloys with low Al contents compared to SADPs (Figures 1(il)). This could mean that even the Al 2.5 (NbTiZr) 97.5 alloy had the B2 structure, but the degree of B2 ordering, i.e. the size of B2 SRO domains, was negligible compared to the Al 5 (NbTiZr) 95 and Al 7.5 (NbTiZr) 92.5 (Figures 2(be)) counterparts.
In terms of the ductility, the localisation of plastic deformation in DBs is considered to be harmful for bcc alloys due to the accumulation of high pile-up stresses, leading to premature fracture [51,69]. Contrastingly, our findings showed that the DBs-proned Al 7.5 (NbTiZr) 92.5 alloy achieved a ∼ 37% higher uniform elongation than the NbTiZr alloy with the homogeneous distribution of dislocations ( Figure 3; Table 1). It could be connected with changing of strain hardening behaviour. At the onset of plastic deformation, dislocations in the Al-containing alloys experience higher stresses to motion than in the NbTiZr counterpart due to the presence of the B2 SRO domains. To proceed plastic deformation, dislocations should shear these SRO domains. When it happens, the first dislocations decrease the slip resistance for the following dislocations, resulting in the DBs formation. The latter process is accompanied by the stress reduction and the steep drop of strain hardening rate (Figures 3(a, d); so-called 'glide plane softening' phenomena [74,77]). In turn, plastic deformation within DBs does not eliminate the B2 ordering and only reduces its degree (Figures 5(eh)), that is, a certain, albeit much reduced, amount of SRO domains persists, similar to results by Zhang et al. [54]. These survived B2 SRO domains seem to create additional (back) stresses, along with the arising contribution of forest hardening [63], for the glide of new dislocations within DBs, thereby leading to the recovery of strain hardening rate (Figure 3(d)). Meantime, the activation of cross-slip results in the formation of new DBs, which help relieve extra pile-up stresses and extend the strengthening stage, thus, delaying necking.
In general, the relative improvement of the mechanical performance of the NbTiZr alloy due to the Al-induced B2 ordering appeared to be more uniform (+ 37% in strength and + 37% in ductility (Table 1)) and, thus, more effective than those of boron (+ 19% in strength and 49% in ductility; [44]) or Mo and Ta (+ 35% in strength and + 16% in ductility; [45]) additions. Naturally, there must be a limit for the Al content, when the B2 ordering deteriorates the mechanical properties of the NbTiZr alloy. We produced an Al 15 (NbTiZr) 85 alloy, which was brittle; multiple cracks appeared at early stages of cold rolling ( Figure S6, Supplementary material). However, the interval between the Al 7.5 (NbTiZr) 92.5 and Al 15 (NbTiZr) 85 alloys should be further examined. Also, high-temperature properties and peculiarities of plastic deformation are needed to be investigated. These are goals for future studies.

Conclusions
In summary, we proposed a new strategy to solve the strength-ductility dilemma in RH/MEAs. By invoking of the B2 ordering and a further controlled increment of its degree during Al alloying, one could enhance the yield strength and uniform elongation from 680 MPa and ∼ 19% in the NbTiZr alloy to 930 MPa and ∼ 26% in the Al 7.5 (NbTiZr) 92.5 alloy. The resulted properties originated from the solid solution and SRO strengthening, as well as from changes in the dislocation glide character. The B2 ordering led to the formation of multiple dislocation bands and the activation of cross-slip, which prolonged the strengthening stage and prevented early necking.

Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.