Enhanced precipitation strengthening of multi-principal element alloys by κ - and B2-phases

improved mechanical properties. The Ni-added MPEA, Al 14.7 C 4.7 Fe 49.9 Mn 26.4 Ni 4.2 , revealed signi ﬁ cant precipita- tionanddispersionhardeningbynanoscale κ -andB2-phasescombinedwithexcellentstrainhardeningcapacity due to slip band re ﬁ nement-induced plasticity (SRIP). A combination of 1 to 1.2 GPa yield strength (21.3 % in- crease) with a total elongation of 20 to 10 % was achieved. The chosen methodology was ef ﬁ cient in the design of a novel MPEA with an improved strength-ductility synergy.

gained much attention in research during the past two decades [1,2]. Instead of relying on one base element, MPEAs are loosely defined as alloys consisting of multiple elements, each with a fraction between 5 and 35 at% [3]. Surprisingly, these alloys often form non-ordered simple crystal structures, such as face-centered cubic (fcc) or body-centered cubic (bcc) [3,4]. The latter is usually explained by high configurational entropy promoting the formation of simple crystal structures at high temperatures, and sluggish diffusion preventing the transformation into more complex phases at low temperatures [5]. As the alloy concept relies on multiple principal elements, MPEAs allow for high degrees of freedom in their chemical and microstructural design. To explore this wide alloy space, several approaches have been employed to screen MPEAs. These were mostly based on CALPHAD-method (CALculation of PHAse Diagrams) [6][7][8] or ab initio [9][10][11][12] calculations combined with conventional [6] or high-throughput [11,13,14] manufacturing methods. However, it was also found that the target properties, often mechanical properties, of MPEAs cannot compete with established alloys in most cases [15]. Hence, advancing from single-phase to multi-phase MPEAs has been a scientific target of the research community recently [16].
The present approach aims to bring together the alloying concepts of MPEAs and highly alloyed steels to design novel alloys with enhanced mechanical properties. Lightweight, κ-carbide strengthened high-manganese steels (HMnS) with high Al, Mn and C contents reveal a unique combination of high strength and ductility. This behavior results from strengthening by coherent, nanoscale precipitates and strong strain hardening due to the activation of slip band refinement-induced plasticity (SRIP) [17][18][19][20][21][22]. The high total elongation of >50 % in these steels allows for further strengthening, since some ductility can be sacrificed for enhanced strength. However, that requires adaption of the chemical composition to promote the formation of additional phases. In both MPEAs [23][24][25] and austenitic steels [26][27][28][29][30][31][32], the incoherent AlNi B2-phase (ordered bcc) was found to act as a suitable phase for efficient precipitation strengthening. Hence, we identified combined κ-carbide and B2-phase strengthening as a promising path to design novel MPEAs with properties that are superior to existing steel concepts.
For computational alloy screening of these types of MPEAs, a custom CALPHAD database was constructed in our previous works [11,33]. The database was compiled from the binary and ternary subsystems of Co-Cr-Fe-Mn-Ni [33] and was extended to Al and C [11]. Even though the database is still in development, it allows for phase prediction and, thus, guided alloy design of Al-C-Co-Cr-Fe-Mn-Ni MPEAs. More specifically, it enables the design of MPEAs based on highly alloyed steels strengthened by κ-carbides and offers new pathways for the efficient computational screening of MPEAs. Based on our previous investigation [34], the alloy Al 14.6 C 4.9 Fe 53.6 Mn 26.9 (at%, converted from X120MnAl30-8), which can be strengthened by precipitation of κ-carbides, was used as the reference state and base alloy. The developed CALPHAD database was employed to reveal suitable alloying elements that promote the concurrent formation of κ-carbides and B2-phase in an fcc-based MPEA. Both Ni and Co were identified as suitable candidates that enable the formation of the B2-phase without suppressing κ-carbides. Hence, Ni-and Co-alloyed Al 14.6 C 4.9 Fe 53.6 Mn 26.9 were produced by ingot casting and postprocessed by thermo-mechanical treatment. The precipitation, deformation and fracture behavior were investigated using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), electron backscatter diffraction (EBSD), electron channeling contrast imaging (ECCI), synchrotron X-ray diffraction (SYXRD), transmission electron microscopy (TEM), and atom probe tomography (APT). The applicability of the proposed methodology for designing MPEAs based on highly alloyed steel concepts and the underlying materials mechanisms are critically discussed.

Phase diagram calculations
The modified custom CALPHAD database [33] was used for thermodynamic screening. Based on the steel composition of Al 14.6 C 4.9 Fe 53.6 Mn 26.9 (at%) [34,35], additions of Ni and Co were considered, which together with Al promote the formation of the B2-phase. In the thermodynamic calculations, Fe was replaced with up to 8 at% Ni or Co and the results were then compared to calculations without the additions. The ideal B2-phase consists of equal mole fractions of AlNi or CoAl, but experimentally it is usually very far from this composition and may contain Fe and Mn. The design goal was the identification of compositions that are mostly fcc in a relatively wide temperature range above 800°C with about equal amounts of κand B2-phase below 800°C. Compositions reasonably fulfilling these conditions were found in Al 14

Thermodynamic screening
The calculated phase compositions of the alloys are shown in Fig. 1. The BASE alloy is single-phase fcc from about 800°C up to its solidus temperature at about 1300°C. Below about 800°C, the κ-phase is expected to form, but not the B2-phase. Below 500°C the fcc phase would completely decompose to bcc, β-Mn, κ-phase and M 23 C 6 . However, the diffusion rate of all elements except C is too low to enable this complete transformation and the decomposition of the fcc-phase beyond the formation of κ-phase has not yet been reported. All three alloys solidify peritectically, forming up to 40 % bcc before the solidification changes to fcc. Such solidification can lead to non-obvious inhomogeneous distributions of the alloying elements since the partitioning to the bcc and fcc phases is different. According to the calculation, the BASE Ni alloy is single-phase between 1150 and 1300°C. Below 800°C, the precipitation of both κand B2-phase is expected and below 550°C the B2-precipitation is increasingly replaced by L12 with an ideal composition of Ni 3 Al. In the BASE Co alloy, about equal amounts of κand B2-phase are expected to precipitate between 500 and 800°C. Below 500°C, the disordered fcc phase is no longer stable, but its decomposition is expected to be too slow to be observed. Above about 950°C, the alloy is expected to be single-phase fcc up to its solidus just below 1300°C. The annealing temperatures were based on the expected precipitation of B2-, B2/κ -or B2/κ/ L1 2 -phases in fcc, as indicated in Fig. 1.

Material and processing
Both BASE Ni and BASE Co alloys were prepared by vacuum induction melting with input materials containing >99.8 % purity. Water jet cutting was used to produce~12 mm sheets, which were then subjected to the processing route schematically shown in Fig. 2. Thus, they were hot rolled at 1150°C to 4 mm thickness and subsequently homogenized for 5 h (state HM). After air cooling, cold rolling was performed with a reduction of 50 % down to 2 mm (state CR). Further heat treatments were performed according to the thermodynamic calculations. First, the sheet was recrystallized in the single-phase fcc region at 1200°C for 3 min followed by water quenching to obtain a fully austenitic microstructure (state RX). Aging was then performed at the temperatures indicated in Fig. 1 with aging times ranging from 15 min to 16 h followed by water quenching (state aged), and will be referred to as Alloy ([temperature]/[time]). The chemical compositions obtained by wet-chemical analysis after processing of the investigated alloys are given in Table 1.

Microstructure characterization techniques
Microstructure specimens with dimensions of 12×10×2 mm 3 (rolling direction (RD) × transverse direction (TD) × normal direction (ND)) were cut by electrical discharge machining. Specimens for analysis of the deformed microstructure were taken close to the fracture surface of the tensile samples in the RD×ND plane. For SEM and EBSD analysis, the samples were first ground with up to 1200 SiC grit paper followed by mechanical polishing using 6 and 1 μm diamond suspensions. Finally, they were electrolytically polished at 20 (BASE Ni ) or 24 (BASE Co ) for 15 s in Struers A2 electrolyte. For ECCI and TEM analysis, samples were ground with 400 to 2500 SiC grit paper and mechanically polished using 3 and 1 μm diamond suspensions. Subsequently, the samples were fine-polished in an oxide polishing suspension (OPS) containing 50 nm silica particles for 30 min. The sample surfaces were cleaned with soap and water to remove the residual nano-silica particles.
Various SEM methods including secondary electron (SE) imaging, EBSD and EDS were performed on a Zeiss Sigma field emission gun (FEG) SEM with EBSD and EDS detectors by Oxford. For EBSD analysis, a voltage of 20 kV was chosen with a working distance between 16 and 18 mm and a step size of 1 μm. Analysis and noise reduction of the EBSD data was carried out with the MATLAB® based MTEX toolbox [36,37]. The grain size was determined by merging grains along annealing twins and calculating the mean equivalent diameter of the grain area as a circle. SE micrographs and EDS were recorded at a voltage of 15 kV with a working distance between 8 and 9 mm for the microstructure and between 10 and 15 mm for the fracture surfaces. ECCI was conducted in a Zeiss-Merlin instrument using a voltage of 30 kV and a current of 2 to 4 nA.
SYXRD was performed on the P02.1 powder diffraction beamline at DESY, Hamburg, with a wavelength of 0.20682 Å for recording diffraction patterns on a PerkinElmer XRD1621 fast area detector. The data were integrated into 1D diffractograms using Fit2D [38,39]. Complete rings were analyzed within a range of 2Θ from 2.85°to 11.35°. Subsequent analysis of the phase fractions was performed with a Rietveld analysis using the open-source software Material Analysis Using Diffraction (MAUD) [40].
TEM analysis was conducted using an image-corrected FEI Titan Themis 80-300 operated at 300 kV. A site-specific focused ion beam (FIB) lift-out procedure was adapted using a dual-beam FEI Helios Nanolab 600i FIB instrument. Selected area electron diffraction (SAED) patterns were simulated using the open-source software Phase Transformation Crystallography Lab (PTCLab) [41].
A LEAP 5000 XR from Cameca Instruments Inc. operated in voltagepulsing mode was used for atom probe tomography (APT). A pulse repetition rate of 200 kHz was used and the specimen was kept at a base temperature of 60 K. The detection rate was kept at a frequency of 0.5 ions per 100 pulses on average and a pulse fraction of 15 %. The APT data were analyzed with the IVAS software 3.8.4.  [34], (b) BASE Ni and (c) BASE Co calculated with the CALPHAD-method using the custom database. In BASE, the highest fraction of the κ-phase in the fcc-matrix was obtained by annealing at 550°C [34]. The annealing temperatures for BASE Ni and BASE Co are also shown and were based on the expected precipitation of B2-, B2/κ-or B2/κ/L1 2 -phases in the fcc-matrix.

Fig. 2.
Thermo-mechanical processing route applied in the present study. Samples were investigated in the homogenized (HM), cold rolled (CR), recrystallized (RX) and aged states. Table 1 Chemical composition of the investigated alloys. The composition of BASE was taken from Ref. [34]. Measurements were taken in wt% and converted to at%.

Mechanical characterization techniques
The Vickers hardness was determined on a Wolpert Instron TESTOR 930 with a force of 294.2 N (HV30) on the polished RD-ND plane of the microstructure samples. The mean value from three measurements was taken for each sample. Dog bone-shaped specimens with a cross-section of 2×2 mm 2 (TD×ND) and a gauge length of 13 mm (RD) were prepared from the sheets via electrical discharge machining. Quasi-static uniaxial tensile tests were then performed on a Z4204 Zwick/Roell device at room temperature with a strain rate of 2.5 × 10 −4 s −1 .

Initial microstructure
In Fig. 3, the microstructures from EBSD analyses are shown in HM, CR and RX condition for the BASE Ni and BASE Co alloys. A single-phase fcc microstructure was measured in each state. After HM (1150°C/ 5 h) and RX (1200°C/3 min) annealing, a fully recrystallized microstructure with annealing twins was obtained. Compared to the HM state, the grain size in RX was reduced from 212 to 155 μm in BASE Ni and from 183 to 119 μm in BASE Co .

Mechanical properties
The hardness evolution during the annealing treatments (see Fig. 1) is shown in Fig. 4. Annealing in the fcc+B2 region barely influenced the hardness in either investigated alloy. In the BASE Ni alloy (Fig. 4a) annealed in the fcc+B2+κ region, the hardness increased moderately up to 4 h, after which it increased more strongly as indicated in a slope transition. In contrast, specimens annealed in the fcc+B2+κ+L1 2 region were characterized by an overall lower hardness without a slope transition. In the BASE Co alloy (Fig. 4b) annealed in the fcc+B2+κ   Fig. 1). Annealing for B2-phase in fcc (at 850°C in BASE Ni and 800°C in BASE Co ) did hardly affect the hardness evolution.   6. SYXRD (a to d) 2D patterns displayed with logarithmic intensity, which were integrated into (e) 1D diffractograms using Fit2D [38,39]. The phase fractions of the κand B2-phases were determined by a Rietvelt analysis using MAUD [40], where the superlattice reflection for the κand B2-phases were carefully fitted for the determination of the lattice constants. The ideal, calculated 1D diffractograms without background radiation are overlaid in each measurement to show the (hkl) peak locations. In the BASE Ni samples, the fraction of κ-phase decreased from 4 to 16 h, while the fraction of B2-phase increased. In the BASE Co (600°C/4 h) alloy, 23.5 % κ-phase and only trace amounts of B2-phase were calculated. (d) The SAED pattern was simulated using these phases, the lattice parameter in Fig. 6 and a 45°rotation of the B2-phase around the ϕ 1 -axis. (e) Dark field (DF) image for the κ-phase using the respective superlattice diffraction spots showing a cuboidal precipitate morphology.  region, only a minor increase in hardness was observed with increasing time. Based on the highest hardness after annealing at 600°C (see Fig. 4), the mechanical properties of these specimens were investigated in more detail by tensile testing (Fig. 5). In the BASE Ni alloy (Fig. 5a), annealing up to 8 h resulted in higher yield strength (R p0.2 , 428 to 1067 MPa) and ultimate tensile strength (R m , 811 to 1186 MPa), while the uniform elongation (A g ) decreased from 66.3 to 6.7 %. After annealing for 16 h, brittle failure occurred within the elastic region. Annealing of the BASE Co alloy (Fig. 5b)

Precipitate analysis
The results of the SYXRD phase analysis are shown in Fig. 6. Based on the slope transition in the hardness curves (see Fig. 4a), the BASE Ni samples annealed at 600°C for 4 to 16 h were investigated. The 2D patterns did not manifest in continuous rings due to the coarse grain size (see Fig. 3). κand B2-phase superlattice reflections were clearly detected and both phases were present in the samples. With increasing annealing time, the fractions of κ-phase decreased from 19.3 to 13.7 vol%, while the fraction of B2-phase increased from 1.0 to 6.8 vol%. Furthermore, the lattice parameters for the κand B2-phases increased with extended annealing from 3.726 to 3.772 Å and from 2.821 to 2.847 Å, respectively, while the fcc lattice parameter remained unaffected at 3.671 Å. For the BASE Co alloy, the state annealed at 600°C for 4 h was analyzed. A fraction of 23.5 vol% κ-phase was detected with trace amounts of B2-phase. Furthermore, the narrower peak corresponding to the κ-phase indicated coarser precipitates in BASE Co compared to the BASE Ni alloys.
As a preliminary database was used, the thermodynamic calculations can lead to imprecise results. This was the case with the BASE Co alloy, where the formation of the B2-phase and its strengthening effect was not observed. The accuracy of the custom database for MPEAs are part of a separate investigation. Therefore, more detailed characterizations of the microstructural development were limited to the BASE Ni alloy annealed at 600°C. Specifically, a second hardening stage appeared after annealing for 4 (Fig. 4a). Precipitate formation within the fcc matrix of the BASE Ni (600°C/ 4 h) alloy was analyzed by ECCI and TEM (Fig. 7). The precipitates manifested in a basketweave type structure (Fig. 7a). Further analysis of the corresponding SAED patterns (Fig. 7b and c) revealed fcc spots and superlattice reflections for the E2 1 κ-phase as well as satellite spots around the fcc peaks. The simulation of the pattern (Fig. 7d) revealed the B2-phase rotated by 45°around the ϕ 1 -axis as the phase being responsible for the satellite spots according to the lattice parameters of the constituting phases. It should be mentioned that the detected superlattice reflections of 〈110〉 cannot be definitively assigned to the κor B2-phase because of overlapping patterns and generally low intensities. The dark field (DF) image (Fig. 7e) showed a cuboidal morphology of the κ-phase with a precipitate size of 10 nm.
The matrix precipitates were further analyzed by STEM EDS (Fig. 8), where the basketweave precipitate structure was visible as dark areas in Fig. 8a. The basketweaves had a width of~10 nm and were depleted in Fe (Fig. 8b). Additionally, high-intensity spots of Ni (Fig. 8e) were observed within the precipitate structure.
The APT analysis in the BASE Ni (600°C/4 h) alloy is shown in Fig. 9. The B2-precipitates were found to be adjacent to the κ-carbide (Fig. 9a) and were characterized by a small size of about 4.4 nm (Fig. 9f). In contrast to the (Fe,Mn) 3 AlC x κ-carbides, the B2-phase was enriched in Ni and Al and depleted in C, Mn and Fe ( Fig. 9d and e).

Deformation and fracture behavior
The microstructure close to the fracture surface of the BASE Ni (600°C/4 h) sample is shown in Fig. 10. In the deformed microstructure, two exclusive non-coplanar slip planes were detected to which the dislocation movement was confined. The basketweave-shaped precipitates can be found between and inside the slip bands.
The tensile fracture surfaces for the BASE Ni alloys annealed at 600°C are shown in Fig. 11. Increasing annealing times first led to fully ductile (30 min, Fig. 11a), small amounts of intergranular (4 h, Fig. 11b), predominantly intergranular (8 h, Fig. 11c) and finally intragranular fracture (16 h, Fig. 11d).  Even though a thin grain boundary phase was detected in the BASE Ni (600°C/4 h) alloy (Fig. 7a), intergranular fracture was most prominent in the BASE Ni (600°C/8 h) alloy (Fig. 11c). One representative grain boundary phase is shown in Fig. 12 and was investigated in more detail by EBSD and EDS. Two phases, a bright and a dark one, were observed in the BSE micrograph (Fig. 12a) and were found to be fcc, as shown in the EBSD map in Fig. 12b. Additionally, a small fraction of bcc phase was detected (Fig. 12c). The EDS line scan inside the two-phase structure (Fig. 12d) revealed the dark phase to be enriched in Mn and Al, while the bright phase had a similar composition to the matrix. Spots inside the phase showed high intensities of Ni, which may be caused by an AlNi B2-phase. While the grain boundary phase coarsened from 4 to 16 h annealing, the composition was similar between the different states.

Discussion
A custom CALPHAD database was used for thermodynamics-based screening of Al-C-Fe-Mn-Ni/Co MPEAs, aiming at an fcc-based MPEA with κand B2-strengthening. 4.2 at% Ni or Co were added to the Al 14.6 C 4.9 Fe 53.6 Mn 26.9 (at%) BASE alloy to promote the formation of B2-precipitates in addition to κ-carbides. The BASE Co MPEA did neither reveal significant precipitation of the B2-phase nor strength enhancements compared to the BASE alloy. In contrast, the BASE Ni MPEA showed strongly increased strength as a result of B2-phase formation. For the latter alloy, the strength increase was most pronounced following annealing at 600°C (see Fig. 4a and Fig. 5a) due to the combined formation of the B2-and κ-phase. The strength evolution during annealing can be subdivided into two regimes that are predominantly caused by either the formation of κ-carbides (<4 h) or the B2-phase (≥4 h).

Formation of κ-carbides in the BASE Ni alloy
In the first strengthening regime (600°C/<4 h), only small amounts (<1.0 vol%) of B2-phase and predominantly κ-carbides were formed (see Fig. 6). The SYXRD, TEM and APT analyses (Figs. 6, 7 and 9) confirmed the presence of the coherent (Fe,Mn) 3 AlC x κ-carbides with an E2 1 Preovskite structure [42] by their superlattice reflections. After 4 h annealing, coherent and cubic κ-precipitates with a size of~10 nm and a fraction of 19.3 vol% were formed within the fcc matrix (Fig. 7e). The amount is similar to the fractions predicted by CALPHAD (Fig. 1b) and also coincides with the amount of κ-phase detected in similarly annealed BASE samples [35]. Additionally, the cubic κ-phase was arranged in a basketweave pattern resulting from spinodal decomposition, which agrees with the formation process in the BASE alloy [34,43] and other κ-carbide strengthened HMnS [17,[44][45][46][47][48][49]. Extended annealing resulted in a lattice parameter increase from 3.726 to 3.772 Å due to the enrichment of C in the κ-phase [50,51]. Consequently, the modification performed in the BASE alloy by 5 wt% Ni addition had a negligible influence on the precipitation of κ-carbides until 4 annealing at 600°C.
After annealing at 600°C between 4 and 16 h, the fraction of κcarbides decreased from 19.3 to 13.7 vol%. This effect coincided with the formation of the Al-and Ni-rich B2-phase after the incubation period of 4 h (see Sec. 4.2). At shorter annealing times, the added Ni to the BASE alloy had a negligible influence on the formation behavior and volume fraction of the κ -carbides. However, the beginning of the B2-phase formation at 4 h did not only promote the depletion of Al in the matrix, but also the partial dissolution of Al from adjacent κ-carbides, which lowered their thermodynamic stability [17,42,52]. According to the CALPHAD calculation, 14.1 % κand 11.2 % B2-phase are predicted at 600°C. The result matches the fraction of the κ -phase after 16 h (see Fig. 6c) well. To reveal the phase formation before the formation of the B2phase, an additional calculation was made that excluded the B2-phase from the equilibrium, i.e. only fcc and κ-phase were allowed to form. Accordingly, the calculated amount of κ-phase was 18.4 %, which corresponds well with the amount of κ-carbides found after 4 h annealing (see Fig. 6a). Hence, the formation of κ-carbides was completed before the nucleation of the B2-phase was initiated. The performed CALPHAD calculations can be found in the Supplementary Data.

Formation of B2-phase in the BASE Ni alloy
Annealing at 600°C for 4 h resulted in the formation of the B2-phase besides κ-carbides. With the measured and simulated SAED patterns of the matrix (see Fig. 7b-d), the formation of the B2-phase with a rotation of 45°around the ϕ 1 -axis of the fcc matrix was revealed. This confirms the orientation relationship of 111 B2 ∥ 200 ð Þ fcc and 001 ½ B2 ∥ 001 ½ fcc for B2-phase containing fcc MPEAs [53]. This B2-phase is Al-and Nirich and forms within the basketweave precipitate structure, which can be seen in the APT measurement ( Fig. 9) and the analysis of the EDS STEM data in Fig. 13. The precipitate structure contains the κcarbides formed at shorter annealing times by spinodal decomposition (see Sec. 4.1, Fig. 9b, Fig. 13b and c). Since the B2-phase was detected adjacent to the κ-carbides (see Fig. 9a, Fig. 13f), nucleation occurred preferably at coherent κ/matrix-interfaces. Furthermore, both the size distribution of the B2-phase from APT (see Fig. 9f) and the highintensity spots of the B2-phase (see Fig. 13e) revealed a spherical shape with a diameter of <5 nm, roughly half that of the κ-carbides (see Fig. 7). The observed spherical shape conforms with previous studies on B2-phase containing austenitic steels [26,54]. In contrast to the κ-phase, the incoherent B2-phase [26,30,54] formed by nucleation and growth mechanisms, as substantiated by the incubation period of about 4 h. As stated above, large amounts of nucleation sites were available in the form of coherent phase boundaries between the fcc-matrix and the κ-phase. Consequently, numerous finely dispersed and nano-sized B2-precipitates form inside the fcc matrix. It should be noted that the small B2-phase size also makes detection by SYXRD challenging, as considerable peak broadening can occur within the detected size range of <10 nm [55]. Therefore, the (100) and (110) B2-phase peaks appear very shallow in the diffraction patterns (see Fig. 6), which leads to faint superlattice reflections and considerable peak overlapping. As the broadening effect does not disappear after 8 and 16 h, nano-sized B2-precipitates were retained during extensive annealing. Furthermore, negligible amounts of B2phase were found at the grain boundaries (Fig. 12) and the detected B2-phase fraction is predominantly located in the matrix. Extended annealing times of 4, 8 and 16 h resulted in an increased volume fraction of 1.0, 2.3 and 6.8 vol% B2-phase, respectively (see Fig. 6).

Tensile test behavior of the new BASE Ni MPEA
A comparison of the tensile properties of the alloys BASE Ni with BASE is given in Fig. 14. The progression of the strain hardening curves in the BASE Ni RX and (600°C/30 min) annealed states (Fig. 14b) showed the formation of another hardening stage at the beginning of plastic deformation, where the strain hardening rate increased again. This is Fig. 13. Precipitate analysis in the BASE Ni alloy (600°C/4 h) using the STEM EDS data from Fig. 8 with modified intensity scaling. The (Fe,Mn) 3 AlC x κ-carbides contain fewer Fe than the matrix (see Sec. 4.1), which can be distinguished in (a). By thresholding the values in (b), the location of the κ-carbides was derived, which is confirmed by the similar dimensions to the κcarbides detected in the (c) DF image (Fig. 7). (d) The AlNi-rich B2-phase can be distinguished by the correspondingly combined element map. (e) Subsequent thresholding revealed the location of the B2-phase in the maps. In (f), both the κand B2-phase are marked in the HAADF image, where the B2-phase was found close to the κ-carbides. Note: In (b, e), clusters containing fewer than 15 pixels after thresholding were discarded due to a high probability of originating from noise. correlated with the activation of shear band refinement-induced plasticity (SRIP) [17,43,45,46,49,56,57]. In these alloys, the medium stacking-fault energy (SFE) between 80 and 120 mJm −2 results in deformation accommodated by undissociated dislocation glide [58][59][60][61]. Nevertheless, dislocations are confined to planar glide in the fcc matrix, regardless of the κ-precipitation state. Currently, this phenomenon is not fully understood, but closely linked to interactions of dislocations with short-or long-range ordered regions and related glide plane softening [34,35,62,63]. As a consequence, pronounced planar glide of dislocations results in high strain hardening capacity from the formation of slip bands during deformation and related dynamic grain refinement [34,42,56], i.e. the SRIP mechanism. This deformation mechanism was confirmed in BASE Ni (see Fig. 10) and was also observed in C-alloyed MPEAs with high Mn and Al contents [64,65]. After the precipitation of κ-carbides in the 30 min annealed state, increased amounts of κphase are sheared during deformation, which decreases the activity for slip band formation [66] and therefore decreased the strain hardening rate. The same strain hardening progression was observed in the BASE alloy, which supports the finding of the predominant κ-carbide formation below 4 h.
Strengthening in the BASE Ni by a finer grain size can be excluded due to a similar grain size to the BASE alloy [34], so can be the effect of grain boundary phase formation, which also occurred in other κ-carbide strengthened steels after long annealing times [17,35,44,45]. In the BASE Ni alloy, the formation of B2-phase started to occur at 600°C annealing after 4 h (see Sec. 4.2). According to [26,30,54], these B2particles share incoherent interfaces with the fcc matrix and thus cannot be sheared during deformation, resulting in dispersion hardening. According to [26,54], dislocations bow out at B2/matrix interfaces and bypass the B2-phase particles, leaving behind a dislocation loop that induces back stresses on the following dislocations and results in higher flow stresses, i.e. the Orowan mechanism. Therefore, higher R p0.2 of 54 and 187 MPa (or a 6.1 and 21.3 % increase) were obtained compared to the BASE alloy (Fig. 14a) at 4 and 8 h annealing due to 1.0 and 2.3 vol% of B2-phase, averaging to about 68 MPa vol% −1 . Dispersion strengthening is frequently used in oxide dispersion-strengthened (ODS) alloys [67][68][69]. The exact amount of strengthening at room temperature obtained by ODS varies depending on particle size, fraction and alloy. For instance, ODS CoCrFeMnNi alloy containing 0.3 wt% with about 10 to 15 nm in size revealed an increased tensile yield strength of 298 MPa [70].
However, the dispersion hardening also affected the activation of SRIP to some extent. The BASE Ni (600°C/4 h) alloy showed a reduced strain hardening rate compared to the BASE (550°C/16 h) alloy, which is an indication for decreased slip band activity [66]. The amount of κ-phase was similar in both states [34], and therefore the back stresses induced on the dislocations by the Orowan mechanism on the finely dispersed B2-particles [26,54] impeded slip band formation in BASE Ni . Since the activation of SRIP in the κand B2-phases containing alloy was confirmed by microstructure analysis (see Fig. 10), the SRIP effect must have been retained, albeit with reduced activity.
Even though slip band activity was reduced by the B2-phase, an improved mechanical property profile can be achieved by Ni addition to the BASE alloy, especially with respect to the alloy's strength. With a comparable total elongation in the BASE (550°C/16 h) and BASE Ni (600°C/4 h) alloys, R p0.2 and R m were increased in BASE Ni by 54 and 37 MPa, respectively. Furthermore, higher fractions of B2-phase in the BASE Ni (600°C/8 h) alloy lead to R p0.2 and R m of 1067 and 1186 MPa with a reasonable A g of 6.7%, which is not achievable using the BASE concept. As the desired B2-phase dispersion hardening was achieved as a result of the initial alloy screening, the introduced methodology can be used as a productive tool for MPEA design. Apart from that, the strengthening effect related to grain refinement [22,57] was beyond the scope of the present study (see Fig. 3). Further tailoring of the microstructure by thermo-mechanical treatments will be investigated separately, which will presumably further improve the mechanical properties.
The precipitation of the B2-phase also had a strong influence on the fracture behavior of the tensile samples (see Fig. 11). Short-time annealing up to the BASE Ni (600°C/4 h) alloy resulted mainly in the formation of κ-carbides and predominantly ductile fracture behavior. At 4 h, small amounts of intergranular fracture were caused by a thin grain boundary phase (see Fig. 7a). At 8 h, however, intergranular fracture was observed due to much coarser precipitations at grain boundaries (see Fig. 12). According to the composition of the different phases, the formation of fcc and κ-carbides was identified [46,48]. The morphology of the grain boundary phase resembled that of overaged κ-strengthened HMnS [17,44,45], which additionally contained small amounts of the B2- phase and led to intergranular fracture. In the BASE Ni (600°C/16 h) alloy, high amounts of 6.8 vol% B2-phase in the fcc matrix (see Fig. 6c) caused embrittlement and premature intragranular fracture.

Conclusion
A custom CALPHAD database of the Al-C-Co-Fe-Mn-Ni system was developed and applied for theoretical, thermodynamics-based screening of Ni-and Co-added Al 14.6 C 4.9 Fe 53.6 Mn 26.9 (at%) alloys. Based on the thermodynamic calculations, novel precipitation strengthened Al-C-Fe-Mn-Ni/Co MPEAs were designed. The alloys were derived from highly alloyed steel concepts and revealed the κand B2-phase strengthened Al 14.7 C 4.7 Fe 49.9 Mn 26.4 Ni 4.2 as the most promising MPEA of this study. The addition of Ni was found to be efficient for promoting the precipitation of B2-particles, whereas the Co-added alloy revealed no strength improvement from the B2-phase. Detailed microstructural and mechanical characterization was carried out to reveal the underlying mechanisms active during annealing and deformation in the newly developed alloys. The following conclusions can be drawn: • A preliminary CALPHAD-database for thermodynamics-based phasestability calculations in the Co-Cr-Fe-Mn-Ni system with incomplete extensions to Al and C was developed. The database was successfully applied for the identification of κand B2-phase strengthened fccbased MPEAs, both for its chemical compositions and related heat treatments. • Annealing of Al 14.7 C 4.7 Fe 49.9 Mn 26.4 Ni 4.2 at 600°C for <4 h resulted in the formation of spinodally decomposed κ-carbides with a size of 10 nm, similar to the related steel concept. After prolonged annealing for ≥4 h, AlNi B2-precipitates formed on the numerously available coherent fcc/κ-carbide interfaces, resulting in finely dispersed nanoscale (<5 nm) B2-particles. Concurrently, the fraction of the κ-phase decreased with increasing B2-phase fraction due to a partial dissolution of Al from adjacent κ-carbides.
• During plastic deformation, the slip band refinement-induced plasticity (SRIP) effect enabled pronounced strain hardening in the investigated MPEAs. The introduction of non-shearable B2-precipitates lowered the slip band activity, resulting in a smaller contribution of SRIP to the accommodation of plastic deformation. • In the Al 14.7 C 4.7 Fe 49.9 Mn 26.4 Ni 4.2 alloy, the careful balance of precipitation hardening by the κ-phase (≥ 18.4 vol%), dispersion hardening by the B2-phase (≤2.3 vol%), and the SRIP effect ultimately improved the mechanical performance compared to the initial steel concept, resulting in an optimized strength-ductility combination. An up to 21.3 % yield strength increase was achieved to 1 to 1.2 GPa combined with a total elongation of 20 to 10 %. • Overaging of Al 14.7 C 4.7 Fe 49.9 Mn 26.4 Ni 4.2 resulted in the formation of a grain boundary κ-phase, which caused reduced ductility due to intergranular fracture for moderate annealing times (8 h). While the B2precipitates caused a high strengthening effect, high fractions of 6.3 vol% inside the matrix after extended annealing (16 h) led to brittle intragranular and premature fracture.

Data availability
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Declaration of Competing Interest
The authors confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support beside the stated ones for this work that could have influenced its outcome.