Coherent precipitation and stability of cuboidal B2 nanoparticles in a ferritic Fe–Cr–Ni–Al superalloy

The present work developed a new Fe-based superalloy of Fe–10.9Cr–13.9Ni–6.4Al–2.2Mo–0.5W–0.04Zr–0.005B (weight percent, wt. %) with cuboidal B2 nanoparticles coherently precipitated into the body-centred-cubic (BCC) matrix. This alloy possesses excellent microstructural stability at 973 K with a slow particle coarsening rate and the B2 nanoprecipitates still keep cuboidal after 1000 h-aging, which is ascribed to the moderate lattice misfit (ϵ = 0.24–0.67%) between BCC and B2 phases. Also, the current alloy exhibits a prominent mechanical property with a high yield strength of σYS  = 238–258 MPa at 973 K. IMPACT STATEMENT A Fe-based superalloy with cuboidal B2 nanoparticles coherently precipitated into BCC matrix exhibits high microstructural stability and prominent mechanical property at 973 K.


Introduction
Fe-based superalloys (or heat-resistant ferritic stainless steels, FSSs) have been widely applied into hightemperature (HT) fields due to their prominent mechanical property, high thermal conductivity, and low thermal expansion [1][2][3][4]. They are generally strengthened by carbides (Cr 23 C 6 and MC, M = Nb, Ti, V, etc.), Laves phase (Fe 2 M), and Z-CrNbN [1][2][3][4][5]. However, the creep resistance of these alloys would degrade after a long-term operation at HTs (above 923 K) due to the microstructural instability, i.e. the rapid coarsening of precipitates induced by the non-coherency with the bodycentred-cubic (BCC) ferritic matrix [3,4]. Considering that the superiority of Ni-based superalloys at HTs ( > 1073 K) benefits from their unique microstructure of spherical or cuboidal γ '-Ni 3 Al ordered nanoparticles coherently precipitated in face-centred-cubic (FCC)-γ matrix [6][7][8], the coherent precipitation of ordered B2 nanoparticles in the BCC matrix would undoubtedly improve the HT microstructural stability and mechanical properties of Fe-based superalloys. It is demonstrated that in the Fe-10Cr-10Ni-6.5Al-3.4Mo-0.25Zr-0.005B (weight percent, wt. %, designated as FBB8) alloy, the coherent precipitation of spherical B2-NiAl nanoparticles in BCC ferritic matrix indeed exhibits higher microstructural stability than the non-coherent precipitation in traditional FSSs at 973 K [9,10]. Intriguingly, the further addition of 2 wt. % Ti into FBB8 could produce cuboidal B2-NiAl/L2 1 -Ni 2 AlTi hierarchical nanoprecipitates, in which the L2 1 -Ni 2 AlTi is another highly ordered phase of BCC solid solution [11][12][13]. This significantly enhances the tensile yield strength from original 120 MPa up to 280 MPa at 973 K due to the cuboidal nanoprecipitation, which is also much higher than that (160 MPa at 923 K) of Fe-13Cr-4.5Al-2Mo-1Nb (wt. %) FSS strengthened by Fe 2 (Mo,Nb) Laves phase [13,14]. It is known that the formation of spherical or cuboidal nanoprecipitates is closely related to the lattice misfit between BCC and B2 phases [15][16][17][18], in which the particle morphology would change from spherical to cuboidal, and to rod-or needle shape with increasing the . And only a moderate could result in a coherent microstructure with cuboidal B2 nanoprecipitates, as evidenced by the fact that the relatively larger = 0.7% and the smaller = 0.06% correspond to the formation cuboidal B2/L2 1 and spherical B2 nanoprecipitates in FBB8 alloys with and without Ti, respectively [9][10][11]. Unfortunately, the addition of Ti would deteriorate the resistance to oxidation since Ti accelerates the internal oxidation due to its relatively high oxygen permeability at HTs [19]. Therefore, to develop novel Fe-based superalloys or FSSs strengthened by cuboidal B2-NiAl precipitates would be fascinating for HT structural applications.
It is difficult to tailor the BCC/B2 lattice misfit to a moderate value moderately for cuboidal nanoprecipitation since there exists a relatively larger composition difference between them, which is different from that in Ni-based superalloys [6][7][8]. Generally, a large composition difference between BCC/B2 would result in a large lattice misfit to form a typical weave-like microstructure [20,21]. So it is challenging to develop the Fe-based superalloys with cuboidal B2 nanoprecipitates in BCC ferritic matrix due to a much larger composition difference between them, in which the BCC/B2 would like to exhibit a weave-like microstructure [20,21]. In previous works, we have developed a series of multi-component alloys with cuboidal B2 nanoprecipitates in the BCC matrix using in light of the cluster composition formula of Al 2 M 14 (M represents different combinations of Fe, Co, Ni, and Cr), which exhibit high microstructural stability at HTs and prominent mechanical properties showing a coherent microstructure with cuboidal B2 nanoprecipitates in the BCC matrix [15][16][17]. Here, by setting the M as M 14 = Fe 10 Ni 2 Cr 2 , we can obtain the composition of Al 2 (Fe 10 Ni 2 Cr 2 ) ( = Fe-12.5Cr-14.1Ni-6.5Al, wt. %), which is a Fe-based superalloy according to the Cr-and Ni-equivalence in stainless steels [22]. In addition, the addition of Mo could increase the lattice constant of BCC matrix, leading to a favourable reduction in the BCC/B2 lattice misfit [23,24]. As slow diffusing elements, both Mo and W could inhibit the coarsening of B2 particles since they would like to segregate on the BCC/B2 interfaces [10]. Thus a minor amount of Mo and W is substituted for Cr in the above composition with a specific ratio of Cr to (Mo + W) = 8/1 (in molar fraction). A trace amount of Zr and B should also be added to improve the ductility of high-strength steels through enhancing grain-boundary cohesion for the prevention of intergranular fracture [25,26]. Therefore, the optimal composition is finally determined as Fe-10.9Cr-13.9Ni-6.4Al-2.2Mo-0.5W-0.04Zr-0.005B (wt. %) to achieve the BCC/B2 coherent microstructure with cuboidal B2 nanoprecipitates. Then, the BCC/B2 microstructural evolution with the aging time at 973 K will be investigated, in which the coarsening behaviour of cuboidal B2 nanoparticles will be discussed. Moreover, the mechanical property of this alloy at both room temperature and 973 K will be studied, where the strengthening mechanisms are also elucidated.

Experimental
The current alloy ingots were prepared by arc melting and suction cast into a 6-mm-diameter cylindrical copper mould under an argon atmosphere. The purities of raw metals are 99.999 wt. % for Al, 99.99 wt. % for Fe, Ni, Zr, and B, and 99.9 wt. % for Cr, Mo, and W, respectively. These ingots were remelted at least five times to ensure composition uniformity. Both cast ingots and rods were solid-solutionized (ST) at 1473 K for 2 h in a muffle furnace. Then, these ST specimens were aged at 973 K for different times up to 1000 h. Each heat treatment was followed by water quenching. The crystalline structures of alloy specimens at different treatments were identified, using a Bruker D8 X-ray diffractometer (XRD) with the Cu K α radiation (λ = 0.15406 nm). The microstructure was examined using Olympus optical microscopy (OM), Zeiss Supra 55 scanning electron microscopy (SEM), and JEM2100F FEG scanning transmission electron microscopy (STEM). The etching solution for OM and SEM observation was composed of 5 g FeCl 3 ·6H 2 O + 25 ml HCl + 25 ml C 2 H 5 OH, and the TEM specimens were prepared by twin-jet electron-polishing in a solution of 10% HClO 4 + 90% C 2 H 5 OH (volume fraction) at a cryogenic temperature of 243 K. Elemental distribution of the aged alloy was analysed, using an FEI Helios NanaLab 600 Dual-Beam focused ion beam (DB-FIB) instrument equipped with the energy-dispersive spectrometer (EDS). The chemical composition was analysed using SHIMADZU electronic probe micro-analyser (EPMA) with a Super-X energy dispersive. The melting temperature of this alloy was measured by NETZSCH STA 449F3 Differential Scanning Calorimetry (DSC) with a heating rate of 10 K/min. The statistical analysis of the volume fraction and size of precipitated particles and the grain sizes at different heat-treated states were measured from the SEM/OM morphology images (at least 6 images) employing the ImageJ software [27]. The mean radius (r) of precipitates is calculated from the traced areas using a circular-equivalent, i.e. r = √ (area/π ) . Microhardness of different heat-treated samples was tested with an HVS-1000 Vickers hardness tester under a load of 500 g for 15 s, in which at least 10 indents were taken to obtain an average value. Uniaxial tensile tests at 973 K were conducted on a UTM5504 Material Test System (MTS) with a heating furnace and with a nominal strain rate of 1 × 10 −3 s −1 . The gauge dimension of tensile samples is 3 mm in diameter and 25 mm in length, and three samples for each heat treatment were tested.
And the melting temperature of this alloy measured by DSC is about 1679 K ( Figure S1, in Supplementary Material), which is comparable to those (1671-1727 K) of existing commercial stainless steels containing a certain amount of Cr and Ni [28]. The XRD results in Figure  S2 show that all the alloy specimens in different heattreated states consist of primary BCC solid solution plus a B2 phase (characterized by a weak (100) diffraction peak). The lattice constants of these two phases were then calculated, being a BCC = 0.2877 ± 0.0042 nm and a B2 = 0.2887 ± 0.0047 nm, respectively. Moreover, the lattice misfit calculated with the equation of = 2 × (a B2 -a BCC )/(a B2 + a BCC ) [29] could increase from = 0.24% in 0.5 h-aged sample to = 0.67% in 1000 h-aged sample with prolonging aging time, in which the average value is about ∼ 0.35%.
The OM image ( Figure S3a) of the solid-solutionized alloy indicates that the alloy matrix consists of coarse ferritic grains with a size of 300-500 μm, where no second phase particles appear on grain boundaries. The precipitation of B2 nanoparticles in different heat-treated states was observed by SEM, as presented in Figure 1 and Figure S3. In the solid-solutionized state, the cuboidal B2 nanoparticles with a radius of r ∼ 30 nm are uniformly distributed in the ferritic matrix (Figure 1a). Moreover, there also exist ultra-fine ( < 5 nm) spherical nanoparticles, which might be caused by the secondary precipitation during water quenching [30]. After aging at 973 K, these cuboidal nanoparticles are regularized gradually with prolonging the aging time, and the ultra-fine nanoparticles disappear. In particular, the radius of these cuboidal B2 nanoprecipitates increases gradually from r ∼ 37 nm for 0.5 h-aging to r ∼ 78 nm for 100 haging (Figure 1b and c and Figure S3b-e). With further increasing the aging time, the particle size would increase more slowly from r ∼ 88 nm for 200 h-aging to r ∼ 114 nm for 500 h-aging, then to r ∼ 136 nm for 1000 h-aging, as seen in Figure 1(d-f). It is noted that no other second phases appear on the grain boundaries even after 1000 h-aging, as presented in the inset of Figure 1(f). In addition, the volume fraction of cuboidal B2 precipitates increases slightly from f ∼ 20.4% in 0.5 h-aged state to f ∼ 24.8% in 48 h-aged state, and then does not vary with the aging time. Coherent precipitates in ferritic alloys were generally coarsened by the agglomeration of particles during aging, leading to an almost-constant volume fraction [31]. To investigate the variation of B2 particles at a much higher temperature, the solid-solutionized alloy was further aged at 1073 K for up to 100 h, in which the B2 nanoparticles still maintain cuboidal, similar to that in 973 K-aged state. However, the B2 nanoparticles in 1073 K-aged state are coarsened, as evidenced by the particle size increasing from r ∼ 141 nm for 24 h-aging to r ∼ 158 nm for 48 h-aging, then to r ∼ 175 nm for 100 h-aging ( Figure S4), which is much faster than that in 973 K-aged state.
The 48 h-aged alloy samples were further analysed by the TEM to verify the crystalline structure of precipitates, as shown in Figure 2. It is the cuboidal B2 nanoprecipitates embedded into the BCC matrix, as demonstrated by the selected area electron diffraction (SAED) pattern along the [110] BCC direction in both bright-field (BF) and dark-field (DF) images (Figure 2a and b). The high-resolution TEM (HRTEM) image and fast Fourier transform (FFT) patterns presented in Figure 2(c, c-1, c-2) indicate that the interface between B2 particle and BCC matrix is coherent, where the schematic crystalline structures of BCC and B2 phases are also inserted in Figure 2(c). The elemental distribution in the 48 h-aged alloy was also analysed with the EDS equipped in DB-FIB, as shown in Figure 3. It is found that Ni and Al elements are enriched in B2 nanoparticles, and Fe, Cr, Mo, and W are mainly segregated in the BCC matrix.
Since the volume fraction of B2 nanoprecipitates remains almost unchanged with the aging time prolonging in the current alloy, the classic Ostwald ripening theory proposed by Philippe and Voorhees (i.e. the PV theory) could be applied to study the coarsening behaviour of B2 nanoparticles, which has been extensively used in multicomponent alloys [32,33]. Such a time-dependent coarsening process could be described with the following Equation (1): where r(t) is the mean radius of precipitates at the aging time t; t 0 = 0 h represents the solid-solutionized state; and k is the coarsening rate constant. Figure 4(a) gives the variation of particle size r 3 of B2 nanoprecipitates with the aging time, which could be well fitted by the PV theory. Thus the coarsening rate constant is obtained as k = 6.9 × 10 −28 m 3 ·s −1 . For comparison, we also plotted the variation of r 3 of particles with the aging time at 973 K in existing FBB8 and Ti-modified FBB8 alloys, from which the coarsening rate constants are 4.9 × 10 −28 m 3 ·s −1 and 5.9 × 10 −28 m 3 ·s −1 , respectively, comparable to that of the current alloy. The coarsening rate constant of coherent particles in BCC steels is much lower than that ( ∼ 1.7 × 10 −26 m 3 ·s −1 at 873 K) of Cr 23 C 6 carbides in Fe-9Cr-1Mo-0.2V-0.1C-0.08Nb-0.05N (wt. %, T91)  steel [34], showing a much slower coarsening behaviour and a higher microstructural stability. It is known that the equilibrium morphology of precipitates is strongly dependent on both the elastic strain energy and the interfacial energy at the precipitate/matrix interface, which could be described by the characteristic parameter, L = 2 C 44 r/σ , being proportional to the lattice misfit and the mean radius r of particles since the elastic strain energy is related to [35][36][37]. Then we calculated the L value of B2 nanoparticles in the current alloy, being L = 0. 16-4.72, where the elastic constant of the BCC matrix is taken as C 44 = 116 GPa [38], = 0.24-0.67% and r = 30-136 nm for the current alloy, and the interfacial energy is σ = 0.15 J·m −2 [39]. Although the L value increases gradually from 0.16 after 0.5 h-aging to 4.72 after 1000 h-aging with prolonging aging time, it is still less than the critical value of L * = 5.6, above which the particle morphology would change from cuboid to plate-like or needle-like shape [37]. Therefore, this moderate lattice misfit ( = 0.24-0.67%) contributes to the formation of cuboidal B2 nanoprecipitates in the current alloy.
Microhardness (HV) measurements were initially conducted to evaluate the age-hardening response of the current alloy. The variation of HV with the aging time at 973 K is presented in Figure 4(b), in which the tendency of the radius of the B2 particles is also shown. It is found that the HV decreases rapidly from ∼ 467 HV in the solid-solutionized state to ∼ 419 HV after 0.5 haging, which might result from the dissolution of ultrafine spherical B2 nanoparticles into the BCC matrix since the particle size (60-70 nm) of cuboidal B2 nanoparticles in both states are comparable (Figure 2a and b). Then, it keeps almost constant till 24 h-aging, followed by a slight decrease to ∼ 344 HV (48 h-aged), to ∼ 304 HV (300 haged), and lastly to ∼ 284 HV after 1000 h-aging. The slow decrease of HV in the late-period aging is ascribed to the relatively high thermal stability of B2 nanoparticles. Moreover, the precipitation of cuboidal B2 particles in the current alloy could achieve the maximum strengthening effect (see the details in Supplementary Material).
High-temperature tensile tests at 973 K of the aged alloy specimens for 24, 48, and 100 h were subsequently performed, and the engineering stress-strain curves are shown in Figure 4(c), from which the yield strength (σ YS ) and elongation to fracture (δ) are measured. It is found that the mechanical properties of these aged samples are comparable, with a yield strength of σ YS = 238-258 MPa and a ductility of δ = 50-56% at 973 K. Obviously, the σ YS of this alloy is much higher than that (σ YS = 120 MPa at 973 K) of FBB8 alloy containing spherical B2 precipitates ( ∼ 53 nm) [10,13], and is slightly lower than that (σ YS = 280 MPa at 973 K) of Ti-modified FBB8 alloy containing cuboidal B2/L2 1 precipitates ( ∼ 57 nm) [11,13]. It is mainly ascribed to the lattice misfit between BCC and B2/L2 1 phases, in which a larger would induce a stronger elastic strain field to hinder dislocation motion [40]. Indeed, it has been demonstrated that the dominant creep mechanism of FBB8 alloy at 973 K is the dislocation climb bypassing of B2 nanoprecipitates with repulsive elastic interaction strain field induced by the lattice misfit [24,40]. Thus the threshold strength (σ th ) for dislocations to bypass particles is strongly affected by the lattice misfit between BCC and B2 phases. Generally, the magnitude of threshold strength (σ th ) is about 0.4-0.5 times of the strength increment from the Orowan mechanism ( σ orowan ) [24,40]. The threshold strength of the current alloy is then roughly estimated to be σ th = 148-185 MPa with the Eq. (S1-c), in which G = 57 GPa at 973 K [41], f = 24.8% and r = 78 nm for the 100 h-aged alloy were taken. It is found that this value is much greater than that (σ th = 69 MPa) of FBB8 alloy, and comparable to that (σ th = 172 MPa) of Ti-modified FBB8 [13,24,42]. It is mainly ascribed to the relatively-large lattice misfit ( = 0.24-0.67% for the current alloy and = 0.7% for Ti-modified FBB8 alloy) that generates a strong elastic strain field to impede the dislocation climbing, compared to the FBB8 alloy ( = 0.06%) [10,11,42,43]. However, an excessive lattice misfit would reduce the threshold strength due to the fading coherency, as evidenced by the fact that the threshold strength of the FBB8 alloy modified by 4 wt. % Ti decreases down to σ th = 143 MPa due to the ∼ 1.3% [30,42,44,45]. Therefore, a moderate lattice misfit ( = 0.2-0.7%) is necessary to both the formation of cuboidal B2 nanoprecipitates and the high microstructural stability at HTs, which finally contributes to the achievement of an optimal mechanical property.

Conclusion
In conclusion, we obtained a new Fe-based superalloy of Fe-10.9Cr-13.9Ni-6.4Al-2.2Mo-0.5W-0.04Zr-0.005B (wt. %) containing a special coherent microstructure of cuboidal B2-NiAl nanoparticles precipitated into BCC matrix. Even after long-term aging at 973 K for 1000 h, these B2 particles still keep cuboidal with a relatively low coarsening rate constant, as evidenced by the particle size being changed from r ∼ 60 nm in solid-solutionized state to r ∼ 136 nm in 1000 h-aged state. It is mainly ascribed to the moderate lattice misfit ( = 0.24-0.67%) between BCC and B2 phases. Moreover, it is the cuboidal B2 nanoprecipitation in the BCC matrix that renders the alloy with high microstructural stability and high mechanical strength (σ YS = 238-258 MPa) at 973 K.