Journal of Alloys and Compounds 966 (2023) 171640 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom Silver-induced γ→ε martensitic transformation in FeMn alloys: An experimental and computational study Aleksandra Bartkowska a, *, Christina E. Lekka b, *, Ludovico Andrea Alberta c, Irena Spasojevic a, Eva Pellicer a, Jordi Sort a, d, ** a Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, E-08193 Cerdanyola del Vallès, Spain b Department of Materials Science and Engineering, University of Ioannina, 45110 Ioannina, Greece c Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden), Helmholtzstr. 20, D-01069 Dresden, Germany d Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, E-08010 Barcelona, Spain A R T I C L E I N F O A B S T R A C T Keywords: Porous FeMn alloys with additions of 0, 1, 3 and 5 wt% of Ag were fabricated using powder metallurgy and Iron-manganese alloys sintering. The microstructure of the fabricated alloys was characterized using X-ray diffraction, transmission Austenite electron microscopy and selected area electron diffraction. While equiatomic FeMn and FeMn-1Ag alloys possess Martensite a fully austenitic structure, a change in the crystallographic structure is observed upon addition of 3 and 5 wt% of Silver Magnetic properties Ag, where a mixture of γ austenite and ε martensite phases is observed. Compression tests reveal that such Phase transformation structural transition causes an increase of the yield stress. The evolution of microstructure with the Ag content can be understood from theoretical calculations which show that Ag atoms prefer the intrinsic stacking fault (ISF) sites, revealing lower energy for the ε atomic plane sequence. This causes local depletion of the electronic charge, therefore weakening the interatomic bonds at the ISF plane and facilitating the phase transition. In addition, the total energy difference between the γ and ε phases decreases upon Ag addition. This enables the coexistence of both phases in the sample with 5 wt% Ag. Both experimental and theoretical data agree that the magnetization value gradually increases upon Ag addition. This is due to the local stress that is introduced by Ag atoms, which expand the Ag-Fe and Ag-Mn first neighbour interatomic bonds compared to FeMn. This stress results in elec­ tronic charge transfer that locally alters the Fe and Mn atomic magnetic moments. These results are appealing for the design of FeMn-based alloys with tuneable phase composition and physical properties for several techno­ logical applications. 1. Introduction associated with the stacking fault energy [8,9]. It has been shown that a low stacking fault energy, below 20 mJ m− 2, facilitates the trans­ Fe-Mn alloys have been studied as versatile materials in widespread formation of fcc γ-austenite into hcp ε-martensite [10]. The stacking applications such as steels for automotive applications [1,2], antiferro­ fault energy can be affected by several factors, such as defects or the magnetic layers in spin valves [3,4], or biodegradable metals for implant addition of elements. For example, additions of Al strongly suppress the applications [5–7], amongst others. The solid solution phases charac­ phase transformation, as they increase the stacking fault energy of teristic of the Fe-Mn system are γ-austenite, α-ferrite, δ-Fe, α-Mn, β-Mn γ-austenite [11]. In contrast, the addition of Si lowers the stacking fault and δ-Mn. Moreover, a metastable hexagonally close-packed (hcp) ε energy, favoring the γ→ε phase transformation [12]. Several ab initio phase can be formed by martensitic transformation in alloys with Mn calculations on Fe reveal that the presence of Mn or C causes a minimum content above 10 wt%. This transformation can occur owing to prior in the stacking fault energy (around − 450 mJ m− 2 for Fe), thus favoring deformation, high applied pressure or fast cooling from the liquid state the ε phase [13–15]. by the movement of Shockley partial dislocations between Fe and Mn on Depending on the crystallographic phase, Fe-Mn alloys can find po­ the (111)γ plane [8]. The γ→ε phase transformation is strongly tential use in different areas of materials science. For instance, * Corresponding authors. ** Corresponding author at: Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, E-08193 Cerdanyola del Vallès, Spain. E-mail addresses: Aleksandra.Bartkowska@uab.cat (A. Bartkowska), chlekka@uoi.gr (C.E. Lekka), jordi.sort@uab.cat (J. Sort). https://doi.org/10.1016/j.jallcom.2023.171640 Received 7 June 2023; Received in revised form 20 July 2023; Accepted 2 August 2023 Available online 4 August 2023 0925-8388/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 γ-Fe50Mn50 alloys are the basis of antiferromagnetic metallic pinning 2. Materials and methods layers used in spin valves or magnetic tunnel junction devices [16]. High-manganese steels, which show mostly austenitic fcc structure, are 2.1. Sample preparation and characterization known for their high strength and ductility, owing to their high strain hardening capacity [17]. These steels, typically comprising high Mn Iron-manganese equiatomic alloys with varying content of Ag (0, 1, 3 contents (> 20 wt%) and additions of C (< 1 wt%), Si (< 3 wt%) and Al and 5 wt%, denoted as FeMn, FeMn-1Ag, FeMn-3Ag and FeMn-5Ag, (< 10 wt%), exhibit various hardening mechanisms, such as respectively) were fabricated using powder metallurgy techniques, twinning-induced plasticity (TWIP) and transformation-induced plas­ namely ball milling of commercial Fe (>99% purity), Mn (>99% purity) ticity (TRIP). The TWIP effect is observed in steels with low stacking and Ag (>99.9% purity) powders in a planetary ball mill for 10 h and fault energy, between 20 and 40 mJ m− 2 [17] and it relies on the subsequent sintering under vacuum at 900 ◦ C, as described in our pre­ transformation of retained austenite into martensite during plastic vious report [7]. X-ray diffraction (XRD) was performed on polished deformation, which enhances both strength and ductility [2]. Further­ surfaces of all tested alloys to assess the phase composition. The ex­ more, in recent years, Fe-based alloys (including Fe-Mn) have emerged periments were performed on a Panalytical X′Pert powder diffractom­ as potential candidates for biodegradable materials applications [5,6, eter with Cu Kα radiation, in the angular range between 20⁰ and 100⁰ and 18]. Biodegradable alloys are a new class of implantable materials that a step size of 0.026⁰ in the Bragg-Brentano geometry. aim to gradually degrade in vivo until their role is fulfilled, without the Thin lamellae of FeMn and FeMn-5Ag samples were prepared for need for an implant removal operation. This is important to limit the transmission electron microscopy (TEM) observations by focused ion cost of medical treatment and to reduce patients’ morbidity. Owing to beam (FIB). The microstructure images and selected-area diffraction the high mechanical strength of iron, these alloys surpass the mechan­ (SAED) patterns were acquired using a Jeol 2011 TEM operating at 200 ical properties of other biodegradable biomaterials, such as polymers, or kV. High-resolution images were also obtained by scanning- Mg- and Zn-based alloys. In the last decade, manganese was established transmission electron microscopy (STEM) utilizing a Teknai Fei instru­ as suitable alloying element in Fe-based biodegradable alloys, since a ment operating at 200 kV. The SAED patterns were indexed by the Gatan high content of Mn stabilizes the austenite phase which exhibits anti­ Digital Micrograph software, which was also employed to analyze the ferromagnetic properties, thus making this material compatible with high-resolution images and the corresponding fast Fourier transform magnetic resonance imaging (MRI) [7,18–23]. In addition, alloys with (FFT) images. From the SAED patterns and the FFT, the interplanar various amounts of Mn demonstrate good mechanical properties, a distances were obtained as well as the lattice constants. degradation rate higher than in pure Fe, and good cytocompatibility [18, The mechanical properties of the alloys were assessed through 19,23,24]. compression testing. Specimens of cylindrical shape were prepared ac­ Due to the extensive use of artificial implant materials, implant- cording to DIN 50106:2016–11 with a height (4 mm) to diameter (2 mm) associated bacterial infections have become increasingly common ratio of 2. Loading surfaces were ground with silicon carbide papers to because of biofilm formation, adhesion, and colonization of bacteria on become plane parallel. Uniaxial compression tests were performed at the implant surface [25,26]. Therefore, there is a need to develop ma­ room temperature using an Instron 8562 device at a constant strain rate terials with antibiofilm and antibacterial properties. Among other stra­ of 1 × 10− 3 s− 1 and at least three specimens per composition were tegies, addition of Ag has been extensively tested and proven efficient in tested. The tests were halted at fracture. The following mechanical promoting antibacterial properties [27,28]. Besides preventing the properties were determined from the engineering stress-strain biofilm formation on the material surface [7], the addition of Ag to the compression curves: compressive yield strength (proof offset 0.2%, Fe-Mn system has several advantages such as accelerating short-term R0.2), compressive ultimate strength (Rm) and compressive strain (A). corrosion [29] or increasing the strength [30]. In fact, the solubility of To assess magnetic properties, hysteresis loops were recorded at Ag in γ-austenite is below 0.4 at% [31], therefore the formation of room temperature using a vibrating sample magnetometer (VSM, Ag-rich precipitates is expected. These precipitates can act as micro­ MicroSense). The maximum applied magnetic field was 20 kOe. The galvanic cells [29], which help increase the corrosion rate of Fe-based saturation magnetization values were determined from the hysteresis alloys. loops. Additional magnetic force microscopy (MFM) measurements Interestingly, reports on FeMn-Ag alloys have shown that additions were performed using Asylum Research Atomic Force Microscope to of Ag favor the formation of the martensitic phase, although so far this map the magnetic field distribution of FeMn-3Ag and FeMn-5Ag sam­ effect has not been understood or described in detail. For example, in the ples. MFM measurements were performed in two pass mode; in the first Fe30Mn-Ag alloys reported by Liu et al. [32], the content of the ε phase pass topography of the sample surface was obtained, while in the second increased upon the addition of Ag. In another study by Babacan et al. pass magnetic forces between previously magnetized tip and the sample [33], Ag-bearing alloys showed a higher content of martensite than al­ were sensed at the lift height of 30 nm. All the measurements were loys without Ag. Similar observations were described by performed at remanence state of the as-grown samples. Dehghan-Manshadi et al. [34], where additions of Ag increased the in­ tensity of the ε-martensite peaks in diffraction measurements. Hence, 2.2. Computational details besides providing antibacterial properties, addition of Ag to Fe-Mn can lead to microstructural changes that improve the compressive yield In this work, the Vienna ab initio simulation package (VASP) density strength of the alloy. However, the effect of added Ag on the structure functional theory (DFT) based on the projector augmented wave method and the mechanical and magnetic properties of Fe-Mn alloys has been formulated to treat collinear and noncollinear magnetic structures is largely overlooked. applied [35–37]. The exchange correlation effect is tuned with the In this work, we investigate the phase transformation from austenite generalized gradient approximation (GGA) by Perdew-Burke-Enzerhof to martensite induced in Fe-Mn alloys by the addition of 1 – 5 wt% Ag. (PBE) [38]. A minimal basis set is adopted, which includes 3d, 4 s and We also correlate the changes in microstructure with the mechanical and 4p orbitals having a cutoff of 300 eV. magnetic properties of the resulting alloys. Moreover, a theoretical The ordered γ-FeMn austenite is treated using the primitive CuAu-I- study is conducted to understand the phase transformation and the al­ unit cell [37,39] and a 2 × 2 × 2 supercell using (4 × 4 × 4) and (8 × 8 × terations of the magnetic properties of FeMn due to the presence of Ag, 8) k-points meshed to sample the Brillouin zone. The antiferromagnetic mainly associated to a charge transfer and alterations in the first (AFM) spin configurations are notated by 1Q (collinear) and 2Q or 3Q neighbor’s atomic magnetic moments. (non-collinear) including several Fe and Mn moments directions in line with previous reports [35,39]. In particular, in 1Q there are several combinations of the atomic moments’ alignment in the unit cell e.g., 2 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 antiparallel Fe-Fe (↑↓) and Мn-Mn (↑↓) moments or parallel Fe-Fe (↑↑) and Мn-Mn (↓↓) moments [35]. In 2Q the moments in the four-atom CuAu-I unit cell can be along [100], [100], [010], [010] or along [110], [110], [110], [110] etc. while in 3Q spins can point to the cell center or have any directions in the three axes [35,39]. In addition, in ab initio calculations the atomic percent is used, therefore γ-FeMn repre­ sents the γ-Fe50Mn50 (at%) or γ-Fe49.59Mn50.41 (wt%) in atomic or weight percent, respectively. The calculations started at the experi­ mental lattice constant of γ-FeMn at zero temperature (a = 3.60 Å) choosing the same spin states with the available theoretical data [37, 39–41] for comparison reasons while cell and atomic relaxation were also employed in several ordered, disordered and Fe- or Mn- rich first neighborhood Ag environments having 16 or 32 atoms, offering in total 58 different configurations. In particular, in the 32 atoms supercell, 1 Fe was replaced by Ag in order to mimic the different Fe-Mn neighborhoods of Ag resulting in system of γ-Fe46.875Mn50Ag3.125 (at%) or γ-Fe45.91M­ n48.18Ag5.91 (wt%) having 15 Fe, 16 Mn and 1 Ag atoms. When replacing 1 Mn, the γ-Fe50Mn46.875Ag3.125 (at%) or γ-Fe48.915Mn45.14Ag5.91 (wt%) crystal have 16 Fe, 15 Mn and 1 Ag atoms. Moreover, the cases of replacing 1 Fe and 1 Mn atoms by Ag atoms were considered, in order to Fig. 1. XRD patterns of FeMn, FeMn-1Ag, FeMn-3Ag and FeMn-5Ag sintered alloys. The symbol γ corresponds to fcc austenite, while ε denotes the peaks mimic the cases with Ag first neighbors, resulting in γ-Fe46.875M­ from hcp martensite phase. n46.875Ag6.25 (at%) or γ-Fe44.62Mn43.89Ag11.49 (wt%). It should be noted that although the theoretical atomic percentages are not exactly the ones of the experimental weight percentages, they offer a good description of samples consist of a mixture of phases, namely fcc γ-austenite and the behaviour of γ-FeMn upon Ag addition. The ab initio calculations hexagonal close-packed (hcp) ε-martensite phases. This is a rather sur­ were performed at FeMn-6Ag (wt%) which is close to FeMn-5Ag (wt%), prising result given the small amount of added Ag. In fact, the where the experiments already revealed the appearance of the martensitic phase in FeMn alloys is typical for lower Mn contents, of 15 martensite phase and a slight increase of magnetization. The higher Ag − 30 wt% [18,44]. It has been reported that the driving force for the content of γ-Fe44.62Mn43.89Ag11.49 (wt%), named FeMn-12Ag (wt%), ε-martensite phase is the low stacking fault energy upon the addition of was also considered to study the cases of having two Ag as first neigh­ manganese and other elements to Fe [8]. Our results reveal that the bors and to investigate the trends of the structural and magnetic prop­ addition of small amounts of Ag may significantly contribute to the γ to ε erties upon further increase of the Ag percentage. phase transformation. Fig. 1 also reveals small amounts of Similarly, the ε-FeMn martensite primitive unit cell and 16 or 32 iron-manganese oxides formed during the sintering process. The weight atoms’ supercells were used along with a (8 × 8 × 8) k-point mesh in the percentage of phases was calculated using X′Pert HighScore Plus soft­ suggested collinear AFM spin state having pure Fe or Mn atomic [0001] ware and the results have shown that the percentage of martensite layers (named herein pure[0001]) [42] and a system with mix Fe-Mn content increases from 0 wt% in FeMn to 71.5% and 77 wt% in [0001] layers, as expected due to the geometry of ordered γ-FeMn FeMn-3Ag and FeMn-5Ag, respectively. Accordingly, the percentage of (111) austenite structure, resulting in 26 configurations (named herein austenite decreases from 100% in FeMn to 26.5% and 23 wt% for FeMn [0001]). In addition, ε-FeMn represents the ε-Fe50Mn50 (at%) and FeMn-3Ag and FeMn-5Ag, respectively. ε-Fe49.59Mn50.41 (wt%) in atomic and weight percent, respectively. The Figs. 2 and 3 show the bright-field TEM images of the FeMn and Ag substitution in ε-FeMn was accounted in a similar way as for γ-FeMn, FeMn-5Ag samples, respectively, together with their selected area resulting in ε-Fe45.91Mn48.18Ag5.91 (wt%) or ε-Fe48.915Mn45.14Ag5.91 (wt electron diffraction (SAED) patterns. The samples were cut from a dense %) for the different first neighbor environments (when replacing Fe or area to avoid the occurrence of pores. These figures clearly demonstrate Mn by Ag) named therefore ε-FeMn-6Ag. The case of both Fe and Mn the distinct features of the two samples. In Fig. 2(a,b), the FeMn alloy atoms’ substitution results in ε-Fe44.62Mn43.89Ag11.49 (wt%) and named (with no Ag) shows the presence of elongated grains, with a thickness of ε-FeMn-12Ag in wt% for an easier comparison with the experimental approximately 20 nm. The microstructure contains a large number of data. defects, and it is difficult to clearly define the grain boundaries. The The atomic relaxations were continued until the Helmann-Feynman SAED pattern, shown in Fig. 2(c), confirms the presence of γ-austenite, forces acting on the atoms were less than 0.01 eV/Å and the total energy where (111), (200), (220) and (311) planes were identified, with a lat­ changes were less than 10− 6 eV. All the calculations were carried out in tice constant of 3.56 ± 0.03 Å. This value is in accordance with the spin-polarized mode. lattice constant of the γ-austenite phase in Fe-40Mn alloy as described in the literature [45]. In Fig. 2(a) we can observe some bright, rounded 3. Results and discussion particles, with a diameter of approximately 200 nm, which can be attributed to iron-manganese oxide, as also detected in the corre­ 3.1. Effect of Ag addition on microstructure of FeMn alloys sponding XRD pattern (Fig. 1). In the FeMn-5Ag sample presented in Fig. 3, the grains are more The SEM images of the synthesised porous alloys are shown in equiaxed and larger, with a size of approximately 400 nm. The grain Supplementary Fig. S1. The alloys show a similar porous microstructure, boundaries are very well defined. Apart from austenitic grains, the ε with macropores of around 20 µm for all the investigated compositions. phase is also present, as shown in Fig. 3(a) (orange) and confirmed by The percentage of macroporosity, calculated from the SEM images, was SAED (Fig. 3b). Specifically, the reflections from (111)γ, (200)γ and between 18% and 22% and increased slightly with Ag content. Fig. 1 (100)ε were identified in Fig. 3(b). Meanwhile, spots attributed to γ shows the XRD patterns of the four studied alloys. Equiatomic FeMn and austenite are present in Fig. 3(c). The lattice constant of the γ phase was FeMn-1Ag samples mainly possess the face-centered cubic (fcc) 3.56 ± 0.04 Å. The a lattice constant of the ε martensite, calculated γ-austenite phase, which is in accordance with the Fe-Mn phase diagram based on the (100) interplanar distance, was 2.53 ± 0.03 Å, which for this composition [43]. Meanwhile, the FeMn-3Ag and FeMn-5Ag agrees with values reported in literature [46]. The high-resolution image in Fig. 3d together with the FFT analysis performed in the region 3 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 Fig. 2. TEM images of FeMn alloy: (a) low magnification image, (b) magnified detail of the area enclosed within the yellow square in panel a), (c) STEM image together with SAED pattern. Fig. 3. TEM images of FeMn-5Ag alloy (a) low magnification image with red arrows pointing to Ag particles. The inset shows the corresponding, indexed SAED pattern where blue lines correspond to ε phase and yellow lines to γ phase. (b) SAED pattern of the region enclosed in the orange circle in panel a) and (c) SAED pattern of the region enclosed in the green circle in panel a), (d) high-resolution STEM image with the FFT performed on the highlighted area in red, indicating the occurrence of ε phase. highlighted in red shows the presence of the ε-martensite (101) plane. 3.2. Effect of Ag on atomic structure and spin configurations Moreover, apart from the austenite and martensite phases, Ag-rich particles were identified and highlighted in Fig. 3(a) with red arrows Aiming to understand the influence of Ag in the structural properties and confirmed by high-angle annular dark field (HAADF) and EDS of FeMn-Ag alloys, DFT calculations were performed for several atomic analysis, presented in Supplementary Fig. S2. These particles had a rearrangements in γ-FeMn and ε-FeMn and spin states. The starting diameter of 150–300 nm. As expected, Ag is lowly soluble in the FeMn points were the AFM collinear (1Q) and non-collinear (2Q or 3Q) spin matrix, and therefore Ag precipitates also form. states for the γ-FeMn primitive unit cell available in the literature [37, A similar morphology of the ε phase has been observed in the liter­ 39,42] along with the AFM collinear ε-FeMn phases [42], as shown in ature [47–49]. This platelet structure of ε martensite, as shown in Fig. 3 Fig. 4(a,b). These DFT studies on γ-FeMn alloys with collinear or (a), subdivides γ grains by moving from one-grain boundary to the other non-collinear spin states found for the γ-Fe50Mn50 an energy preference on the opposite side, which was identified as Type II ε-martensite [49]. towards the 2Q and 3Q states along with an underestimation of the The subdivision of γ grains leads to a dynamic grain refinement, which experimental lattice constant (3.54 Å with GGA and 3.42 Å with local in turn may lead to an improvement in the mechanical properties of the density approximation (LDA) [37,39,42]) except from the introduced Ag-containing alloys. The type of martensite formed depends on the frozen core approximation in the exact muffin-tin orbital (EMTO-DFT) initial size of the γ grains and it has been shown that an extensive grain method [39]. To this end, most of the previous theoretical studies on refinement suppresses the γ to ε transformation [49]. This may be the γ-Fe50Mn50 were performed at the experimental lattice constant reason why the martensite phase is observed only in the big grains of the (3.63 Å) or its extrapolation at zero temperature (3.60 Å) [37,39] since γ phase. it was really interesting to understand the existence of different AFM (1Q, 2Q, 3Q) spin states and verify the related lack of experimental 4 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 Fig. 4. FeMn-Ag alloys’ selective atomic structures for (a) austenite and (b) martensite phases along with the main AFM collinear (1Q) and non-collinear (2Q and 3Q) spin states. Fe, Mn and Ag atoms are depicted by gold, magenta and grey spheres. (c) Total energy difference ΔЕ of AFM collinear and non collinear spin states for different atomic rearrangements and crystal structures. ΔЕ’s negative values denote alloy stability against their corresponding pure element phases. Open and filled symbols represent the DFT results on the theoretical and the experimental lattice constants while γ-Collinear (γ-C in green circles), γ-Non-Collinear (γ-NC in blue squares) and ε-Collinear (ε in red diamonds) stand for spin states. As a guide to the eye, dashed lines correspond to the average ΔE values of all under-study stable (ΔЕ < 0) configurations for each structure γ-C (green line), γ-NC (blue line) and ε (red line) that might coexist in the experimental conditions. The difference between the γ and ε phases’ energetically favoured ΔЕ values is denoted by a black vertical arrow while the corresponding deviation between the average values is shown with dashed vertical arrows. The compositions FeMn-6Ag (wt%) describe the γ-Fe45.91Mn48.18Ag5.91 (wt%) and γ-Fe48.915Mn45.14Ag5.91 (wt%) cases while FeMn-12Ag (wt %) refers to Fe45.75Mn46.51Ag11.49 (wt%). consensus concerning the favoured spin configurations. In line with (↑↓) and Мn-Mn(↑↓) moments as the most energetically favored [37,39]. these previous calculations, the current DFT results also underestimate Nevertheless, the non-collinear 2Q (having the spins pointing along the the γ-FeMn lattice constant (3.53 Å and 3.54 Å for the collinear and [110], [110], [110], [110] as in [39]) and 3Q (with spins towards the non-collinear primitive unit cells) compared with the projected center of the unit cell, similar to [35,39]) are energetically favored augmented wave (PAW) method (3.53 Å) and simple EMTO (3.54 Å) against all collinear configurations, in line with previous studies [37, [39] and the experimental results of this work, presented in Fig. 1. 39]. It should be noted that the non-collinear energetically favored Therefore, in Fig. 4(c) the current DFT results are presented for both γ-FeMn of this work has the Fe moments parallel to each other and the cases: i) at the experimental lattice constant (filled symbols) and ii) for Mn moments creating a global anti-parallel magnetization as expected the totally relaxed (unit cell and atomic positions) configurations (open from the approach we have used [37]. The γ-FeMn disorder relaxed symbols). The total energy difference (ΔЕ) was estimated for all cases supercell also shows a preference towards the non-collinear state using the EFeMn-Ag total energy corresponding to all studied spin states, (− 2.09 eV) compared to the collinear state (− 0.96 eV) while the compositions and atomic environments in order to reveal the energeti­ collinear γ-FeMn unit cell of the (111) face (− 0.22 eV) has almost the cally favoured structure using the expression (Eq. 1): same energy with all collinear γ-FeMn primitive unit cells (oriented along (001)) as expected. Concerning the martensite ε-FeMn, the ΔE = EFeMnAg − (NFeEFe + NMnEMn + NAgEAg) (1) experimentally suggested structure having pure [0001] Fe or Mn atomic where EFe, EMn and EAg stand for the corresponding austenite or layer sequence [42] was considered and found to be unfavored martensite single elements’ structure and NFe, NMn and NAg are the (− 0.88 eV) compared to mixed FeMn [0001] atomic layers which are related number of atoms. ΔE was calculated in order to be able to related to the γ-FeMn (111) face geometry (− 1.75 eV), both calculated compare different phases, Ag contents and cells’ sizes. It should be noted at the experimental lattice constants a = 2.53 Å and c = 4.079 Å of that although several units and supercells (ordered or even disorder- ε-Fe80Mn20 [50], Fig. 4(b). Similar ε-FeMn mixed structure preference like) are chosen in this work, in total 84 configurations, they cannot was found when using the present work’s ε-Fe50Mn50 lattice constants a be directly compared to the experimentally observed solid solution = 2.47 Å and c = 3.93 Å having only a ΔЕ underestimation (the FeMn austenite and martensite phases, which sometimes even co-exist. [0001] shows − 0.66 eV against pure [0001] ε-FeMn − 0.07 eV). It Nevertheless, they might provide an estimation of the FeMn behaviour should be noted that the AFM collinear and non-collinear ε-FeMn states upon Ag addition. reveal equivalent ΔE (the difference might be 0.01 eV) and therefore are Starting with the binary alloy, for the γ-FeMn collinear states (1Q) presented in Fig. 4(c) with the same symbol (diamond). different AFM spin moment combinations on the 4-unit cell’s atoms (up Turning on the ternary FeMn-Ag system, the same austenite and or down) have been considered following the spin configurations martensite binary supercells were used to reveal the effect of Ag sub­ depicted in [37] and presented in Fig. 4(c) with filled green spheres. stitution, as shown in Fig. 4(a,b). In the ordered γ-FeMn-6Ag (wt%), the Although the energy difference between the several collinear AFM spin two available cases of Fe (γ-Fe46.875Mn50Ag3.125 (at%) or γ-Fe45.91M­ states is small (up to 0.05 eV/atom) in line with [37], the results of this n48.18Ag5.91 (wt%)) or Mn (γ-Fe50Mn46.875Ag3.125 (at%) or γ-Fe48.915M­ work reveal the AFM collinear 1Q of Fig. 4(a) that has antiparallel Fe-Fe n45.14Ag5.91 (wt%)) substitution by Ag atoms were considered. In Fig. 4 5 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 (a), the energetically favored γ-FeMn-6Ag (γ-Fe46.875Mn50Ag3.125 (at%) ABCACBA, b) the intrinsic stacking fault (ISF) that has a “missing” plane or γ-Fe45.91Mn48.18Ag5.91 (wt%)) atomic and spin configurations are due to shear and a sequence ABCABCA|CABC while c) the extrinsic presented where Ag prefers to have as many as possible Mn atoms in the stacking fault ABCACBABC that has an extra plane. This description first neighborhood. In particular, the collinear 1Q AFM γ-Fe45.91M­ becomes more complicated in the case of alloys like γ-TiAl or γ-FeMn n48.18Ag5.91 (wt%) (− 2.06 eV) of Fig. 4(a) is favored against the where the local chemical neighborhood or magnetism are also involved. collinear 1Q AFM γ-Fe48.915Mn45.14Ag5.91 (wt%) (− 1.48 eV) with more In this work the intrinsic stacking fault was considered since it is directly Fe atoms as seen in Fig. 4(b). Interestingly, all γ-FeMn-6Ag (wt%) non- related to the generalized stacking fault energy or γ surface that is collinear states are less preferred compared to the binary FeMn cases defined by shearing two parts of the crystal with respect to each other while the average ΔE (dashed lines) shows equivalent values between along a certain plane (here in the (111) plane). The intrinsic stacking γ-NC and γ-C. Furthermore, Ag prefers the FeMn [0001] martensite fault corresponds to a particular shear point (→ u /3 along the [121]) ε-FeMn-6Ag (wt%) configuration by 1 eV against the pure [0001] as where the existence of a minimum on the γ surface suggests that the well as the Fe atomic position (− 1.53 eV in Fe site, ε-Fe45.91M­ transition is favoured [13,14,51–53]. n48.18Ag5.91 (wt%), and − 1.39 eV in Mn site, ε-Fe48.915Mn45.14Ag5.91 The pure Fe and FeMn supercells having 6 fcc(111) unit cells along (wt%). Fig. 4(c)). Similar preference was observed for the austenite the [111] axis and periodic boundary conditions in the in-plane meshed phase, revealing the Ag preference towards a ‘rich in Mn’ 1st neigh­ by 2 × 4 × 1 k-points were firstly considered following Bleskov [13] and borhood environment. Gholizadeh et al. [14]. In Fig. 5(a) the case of FeMn is presented in the Upon Ag enrichment, in Fe45.75Mn46.51Ag11.49 (wt%) or FeMn-12Ag perfect austenite γ-phase (oriented along fcc(111) having the stacking (wt%), where two Ag atoms might become first neighbours, the sequence of ABCABC) as well as the ISF which stands for shear of the austenite collinear states are favored compared to the non-collinear ones while including the martensite cases all ΔЕ values decrease, as shown in γ-phase by → u /3 along the [121] resulting the intrinsic stacking fault Fig. 4(c). Moreover, at much higher Ag compositions, e.g. the FeMn- plane (…ABCABCA|CABC…) presented with a dashed black line. In 39Ag (wt%) which describes the four atom primitive γ and ε unit cells Fig. 5(a) the γ-FeMn 36 atoms’ supercell represents the γ-Fe50Mn50 (at with compositions γ-Fe40.16Mn20.41Ag39.43 (wt%) and γ-Fe20.01M­ %) or γ-Fe49.59Mn50.41 (wt%) in atomic or weight percent, respectively n40.69Ag39.30 (wt%) (not included in this figure), the ΔЕ values become while in (b) the refers to γ-Fe47.2Mn50Ag2.77 (at%) or γ-Fe46.41M­ positive revealing this system’s instability. Concerning the spin states, n48.34Ag5.26 (wt%) having 17 Fe, 18 Mn and 1 Ag atoms named for the γ-Fe45.75Mn46.51Ag11.49 (wt%) or γ-FeMn-12Ag (wt%) AFM 1Q simplicity FeMn-5Ag and in (c) the γ-Fe47.22Mn47.22Ag5.55 (at%) or (− 1.51 eV) state and the ε- Fe45.75Mn46.51Ag11.49 (wt%) or ε-FeMn-12Ag γ-Fe45.23Mn44.50Ag10.27 (wt%) having 17 Fe, 17 Mn and 2 Ag atoms (wt%) in the mix FeMn [0001] (− 1.23 eV) configuration seem to be the named for simplicity FeMn-10Ag. In Fig. 5(b,c) the FeMn-Ag cases were preferred ones (Fig. 4(b, c)). named FeMn-5Ag (wt%) FeMn-10Ag (wt%) for easier comparison with Overall, the results shown in Fig. 4(c) indicate that the energy dif­ our experimental data. ference between the austenite and martensite phase progressively de­ The intrinsic stacking fault energy (γ ISF ) excess due to the defect creases with the increase of Ag content as denoted by continuous black formation is given by Eq. (3): / vertical arrows in Fig. 4(c) between the energetically favored structures γ ISF = (Gdef − Gideal ) S (3) or with a dashed black vertical arrow between the average ΔЕ values of all stable understudy (dashed blue, green and red lines stand for γ-NC, where Gdef is the energy of the supercell with defects (the ε-like phase γ-C and ε configurations). In particular, for FeMn the energy difference herein), Gideal is the energy of the ideal fcc(111) (the γ- phase herein) and between the favored γ-NC (ΔЕ = − 2.66 eV) and ε (ΔЕ = − 1.75 eV) is S is the interface area over which the defect is extended [13,14]. The γ ISF 0.9 eV, while for γ-Fe45.91Mn48.18Ag5.91 (wt%) or γ-FeMn-6Ag (wt%) the of non-magnetic Fe, − 424 mJ m− 2 for the optimized 3.45 Å lattice γ-C (ΔЕ = − 2.06 eV) becomes favored against γ-NC and differs to ε (ΔЕ constant, is in line with the previous reports on ab initio calculations for = − 1.53 eV) by 0.5 eV and is further reduced to 0.3 eV at Fe45.75M­ this material, i.e., − 422 mJ m− 2 and − 451 mJ m− 2 [13], n46.51Ag11.49 (wt%) or FeMn-12Ag (wt%). Similarly, the difference be­ − 464 mJ m− 2 [15] and − 450 mJ m− 2 [14]. tween the average ΔЕ austenite and martensite values decreases from Similar ISF values were predicted for FeMn (− 501 mJ m− 2), as 0.9 eV (FeMn, γ-NC and ε) to 0.3 eV (Fe45.91Mn48.18Ag5.91 (wt%) or shown in Fig. 5(a), compared to non-magnetic disordered fcc Fe-Mn FeMn-6Ag(wt%), γ-C and ε) and 0.2 eV (Fe45.75Mn46.51Ag11.49 (wt%) or 22.5 at% (− 450 mJ m− 2) alloys and paramagnetic Fe-Mn40at% FeMn-12Ag(wt%), γ-C and ε). The small energy difference (0.3 eV on (− 325 mJ m− 2) [51] as well as − 510 mJ m− 2 for Fe23Mn1 [52]. It average or 0.5 eV in favoured cases) between these austenite and should be noted that although the ab initio values are really far from the martensite states in Fe45.91Mn48.18Ag5.91 (wt%) or FeMn-6Ag(wt%) ex­ experimental values of 15–33 mJ m− 2 for Fe-Mn alloys [53] due to the plains the experimental results of this work, which found a co-existence tiny and perfect (using periodic boundary conditions) supercell, they of both phases at FeMn-5 wt% Ag (Fig. 1). already reveal that the ISF structure is favored over the ideal fcc perfect structure. The next step was to substitute Fe or Mn atoms by Ag starting from 3.3. Intrinsic stacking fault energy considerations the Fe position since Ag prefers the Mn first neighbor atoms, as described in Section 3.2 and observed in Fig. 4. Aiming to further understand the influence of Ag addition on the In Fig. 5(b) the Fe46.41Mn48.34Ag5.26 (wt%) or FeMn-5Ag (wt%) case FeMn austenite-to-martensite phase transformation, the intrinsic stack­ is presented in two atomic AFM configurations having the Ag atom in ing fault energy was evaluated. The pure Fe and FeMn cases were the stacking fault plane (ΔЕ = − 0.87 eV) in a Fe position that is less considered first due to the absence of FeMn-xAg stacking fault energy favored compared to a possible Fe (ΔЕ = − 1.04 eV, Fe46.41Mn48.34Ag5.26 calculations. Concerning the non-magnetic pure Fe at 0 K, previous ab (wt%)) or Mn (ΔЕ = − 1.13 eV, Fe49.11Mn47.22Ag5.26 (wt%)) site further initio calculations revealed that the hexagonal close packed stacking is from the stacking fault plane. These results suggest that atomic Ag could energetically favored with respect to the fcc stacking [13–15]. There­ exist in several positions (close or not to the stacking fault plane) since fore, the fcc(111) structure with an intrinsic stacking fault plane (… the difference in ΔЕ between different sites is 0.1–0.2 eV. Similar en­ ABCABCA|CABC…) that locally mimics the hcp stacking plane is more ergies are expected in lower Ag compositions, like FeMn-1Ag (wt%) and stable than the perfect fcc phase [13–15]. It should be noted that in the FeMn-3Ag (wt%), where the probability of Ag atoms having Fe and Mn fcc phase there might be several stacking faults irregularities in the three neighbor atoms is enhanced compared to Ag-Ag first neighbors. ABC (111) atomic planes’ sequence. The perfect ABCABCABC stacking Nevertheless, using the present supercells, higher Ag compositions sequence could change to: a) twin boundary that has a twin mirror plane 6 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 Fig. 5. FeMn-xAg(111), x = 0, 5, 10 wt% atomic representation of the intrinsic stacking fault structures for characteristic cases. Fe, Mn and Ag atoms are presented by gold, magenta and grey spheres. Dashed line denotes the stacking fault plane. The compositions FeMn-5Ag (wt%) describe the Fe46.41Mn48.34Ag5.26 (wt%) and Fe49.11Mn47.22Ag5.26 (wt%) cases while FeMn-10Ag (wt%) refers to Fe45.23Mn44.50Ag10.27 (wt%). In Fig. 5(c) the electron charge density difference is also plotted along with atoms where the light blue semicircles denotes depletion of the electron charge that is enhanced close to the stacking plane. can be achieved where two Ag atoms might be first, second or third 3.4. Effect of Ag on mechanical and magnetic properties of FeMn alloys neighbors. In Fig. 5(c) for Fe45.23Mn44.50Ag10.27 (wt%) or FeMn-10Ag (wt%) the cases of Ag-Ag atoms being third (ΔЕ = +0.04 eV) neigh­ The mechanical and magnetic properties of the samples under study bors (one Ag atom is at the stacking plane and another one two layers were experimentally determined to assess the impact of the Ag content further) is unstable while the case where both Ag atoms are neighbors on these properties. The compressive stress-strain curves of the studied and fully occupy the stacking fault plane (ΔЕ = − 1.22 eV) is favored FeMn-xAg samples are presented in Fig. 6. The average values of the occupying. The FeMn-10Ag (wt%) where both Ag atoms are first compressive yield strength (R0.2), compressive ultimate strength (Rm) neighbors but lay two atomic layers further from the stacking fault plane (ΔЕ = − 0.45 eV) is less favored. Nevertheless, the preference of having in the system Ag-Ag first neighbors with stable configuration (ΔЕ < 0) is in line with the existence of Ag particles in FeMn-5Ag(wt%) (see Fig. 4). Although, there are several atomic configurations and rearrangements that someone could take into account, the ones presented in Fig. 5(b,c) and described in this paragraph are characteristics and could interpret the Ag behaviour close to the stacking fault plane. The FeMn-5Ag(wt%) intrinsic stacking fault energies with Ag atom occupying a Fe site at the SF plane (ISF = − 424 mJ m− 2) or two layers further from it (ISF = − 457 mJ m− 2) increase compared to FeMn (ISF − 501 mJ m− 2) but remain negative denoting the possible existence of both phases in the crystal. Upon full occupation of the stacking fault plane by Ag in FeMn-10Ag (wt%) ISF decreases to ISF − 440 mJ m− 2 while a smaller reduction is found for the partial Ag occupation of the stacking plane ISF = − 413 mJ m− 2, thus showing the tendency of the system towards the martensite structure in both configurations. In Fig. 5(c), the electron charge density difference is presented where depletion of the electron charge (light blue area) close to the stacking plane and the nearest neighboring atomic layers thus weakening the interatomic bonds and allowing therefore an easier slip of atoms and therefore a phase transi­ Fig. 6. Compression stress-strain curves for FeMn, FeMn-1Ag, FeMn-3Ag and tion from the austenite towards martensite structure. FeMn-5Ag samples. Tests were performed at a strain rate of 10− 3 s− 1 and halted at fracture. 7 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 and compressive strain (A) are presented in Table 1. The shape of the curves indicates the high ductility of the sample, especially considering its high porosity. All tested samples possess a high 0.2% compressive offset yield strength (R0.2), above 181 MPa. Among all tested samples, FeMn-3Ag and FeMn-5Ag show the highest compressive strength (430 and 398 MPa, respectively) compared to FeMn and FeMn-1Ag, as pre­ sented in Fig. 6. The highest values of R0.2 were obtained for the FeMn- 5Ag sample (254 MPa), whereas FeMn-3Ag possesses the highest compressive strength (430 MPa). FeMn-5Ag and FeMn-3Ag alloys exhibit better mechanical properties at compression than FeMn and FeMn-1Ag alloys, with the maximum 40% increase in R0.2 and 28% increase in Rm. This increase in me­ chanical strength is mainly attributed to the different phase composi­ tions of the Ag-containing samples as well as to Ag precipitation at the grain boundaries, which leads to precipitation strengthening. The martensite platelets and Ag precipitates act as planar obstacles and can reduce the mean free path of the dislocation movement, thereby strengthening the material [9,54]. A similar increase in the mechanical properties of Ag-containing FeMn alloys was previously observed by Liu et al. [55], where the addition of 0.8 wt% Ag resulted in an increase in Fig. 7. Magnetization loops of the FeMn, FeMn-1Ag, FeMn-3Ag and FeMn-5Ag yield strength from 94 to 130 MPa, which was mainly attributed to samples. Inset shows magnified region between − 2.5 kOe and 2.5 kOe. Ag-rich particles on the grain boundaries. Even a small addition of 1 wt % Ag leads to an improvement in the mechanical properties when it will be shown below. On the other hand, the fact that MS is rather low compared to the FeMn alloy. Moreover, the addition of Ag does not in all investigated material, makes them compatible with MRI scans. cause changes in the compressive strain and the values oscillate between 7.7% and 8.8%. 3.4.1. Ag influences the FeMn magnetization and crystal’s magnetic In Table 1, the literature values of R0.2, Rm and A are presented for moment various porous FeMn alloys. The samples presented in this study show When adding a non-magnetic material like Ag to FeMn, which is well results comparable to the porous, selective-laser-melted (SLM)-fabri­ known for its antiferromagnetic properties [59,60], it is not easy to cated Fe-Mn alloy. At the same time, their strength is higher than that of explain the observed increasing magnetization trend of Fig. 7. To this most other porous alloys formed by sintering of powders. Compared to end, the first step is to deeply understand the AFM properties of FeMn. dense FeMn alloys with similar composition, our materials exhibit lower The literature survey reveals many experimental data on FexMn1− x al­ compression strength because the macropores present in the material act loys which do not agree on the type of AFM spin states [42,53,59–64]. as stress concentration points during deformation. For example, neutron diffraction experiments found AFM long-range The magnetic hysteresis loops of the FeMn− xAg alloys, measured by order in chemically disorder bulk γ-Fe0.75Mn0.25 [42,59], similar to VSM at room temperature, are shown in Fig. 7. The results reveal that the 1Q spin state in Fig. 4(a), while Mössbauer neutron diffraction the saturation magnetization increases with the Ag content. Among all measurements revealed three AFM states depending on the Mn tested alloys, the highest magnetization value was obtained for the composition named 1Q (the collinear structure for Mn -rich and Fe-rich FeMn-5Ag alloy (1.075 emu g− 1), whereas the lowest value was ob­ contents) and 2Q or 3Q (the non-collinear ones for γ-FexMn1− x, 0.3 < tained for the FeMn alloy without the addition of Ag (0.045 emu g− 1). x < 0.8 alloys) [59–61]. Moreover, the addition of Mn drastically re­ MFM analyses were performed to further study the magnetic behaviour duces the magnetic susceptibility of Fe-based alloys [55] while for of the samples. The results (see Supplementary Fig. S3) reveal that FexMn1− x, 0.3 < x < 0.8 alloys, experiments suggested the 1Q state for FeMn-5Ag shows a more pronounced ferromagnetic signal than the Fe0.66Mn0.34 [62], the 3Q (partially the 2Q) state for Fe0.5Mn0.5 [63] and FeMn-3Ag sample (for which virtually no magnetic contrast is detected). the 3Q for Fe0.54Mn0.46 [64], resulting in a lack of experimental The magnetic contrast observed for the FeMn-5Ag sample indicates a consensus. This behaviour could be attributed to bcc Mn which not only weakly ferromagnetic response, in agreement with the low saturation undergoes a first-order transition from a low spin state to high spin state magnetization observed in the corresponding hysteresis loop (Fig. 7), in both ferromagnetic (FM) and AFM states, but it is also sensitive to which is equivalent to approximately 0.5% the value of MS of pure Fe compression or expansion [65]. To this end, earlier calculations revealed (MS,Fe = 220 emu g− 1). Since this was a counterintuitive result, DFT a narrow double moment region where low and high spin states co-exist, simulations were also run, aiming at finding a plausible explanation, as giving rise to dissimilar lattice constants [66]. Therefore, the introduc­ tion of a third element in the system, like Ag, could introduce local stress Table 1 (compression or expansion in the interatomic distances) which might Selected parameters calculated from the compression tests: yield strength (R0.2), lead to different behaviour in the magnetic properties, in line with C compressive strength (Rm) and compressive strain (A) together with literature addition in Fe-Mn-C, which may give raise to spin-glass-like regions values on porous and dense Fe-Mn alloys. [67]. It is worth reminding here the Ag preference towards Mn’s first Material R0.2 (MPa) Rm (MPa) A [%] Reference neighbour atoms as depicted in Fig. 4 (Section 3.2), which means that FeMn 181 ± 6 336 ± 8 8.5 ± 0.50 This study the electronic and magnetic properties of Mn atoms are mainly affected FeMn-1Ag 205 ± 26 352 ± 14 8.3 ± 0.3 This study by Ag atoms. Furthermore, in previous reports describing Fe-30Mn-xAg FeMn-3Ag 234 ± 16 430 ± 7 8.8 ± 0.5 This study alloys, the authors found a tendency to decrease the magnetization upon FeMn-5Ag 254 ± 10 398 ± 10 7.7 ± 0.3 This study SLM Fe-35Mn scaffold 89.2 304.0 - [56] the addition of Ag [30]. For example, in the reports by Liu et al. [30,55], ± 1.9 ± 7.4 the addition of up to 5 wt% Ag led to a slight decrease in magnetic Porous PM Fe-35Mn 64 567 - [24] susceptibility. In our case, the FeMn-xAg, as shown in Fig. 8(a), reveals a 10 wt%HA+Fe30Mn - 186 ± 12 - [57] small increase in magnetization upon Ag addition which can be a result Porous Fe-44Mn 10 ± 1 - - [58] Dense Fe-30Mn-6Si- 353 ± 34 1849 ± 39 - [33] of the higher Mn amount (~50 wt%) along with the observed phase 1.2Ag transformation and the corresponding co-existence of γ and ε phases that 8 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 Fig. 8. Magnetization of FeMn-xAg by experimental (a) and theoretical (b) data. In (a) the magnetic moment in μB/atom is derived from the Magnetization Ms. The compositions FeMn-6Ag (wt%) describe the γ-Fe45.91Mn48.18Ag5.91 (wt%) and γ-Fe48.915Mn45.14Ag5.91 (wt%) cases while FeMn-12Ag (wt%) refers to Fe45.75M­ n46.51Ag11.49 (wt%). In (b) open and filled symbols represent the DFT results on the theoretical and the experimental lattice constants while γ-Collinear (γ-C in green circles), γ-Non-Collinear (γ-NC in blue squares) and ε-Collinear (ε in red diamonds) stand for spin states in line with Fig. 4. As a guide to the eye, the average values of all under-study for each structure γ-C (green line), γ-NC (blue line) and ε (red line) that might coexist in the experimental conditions are also shown. The energetically favoured γ-NC, γ-C and ε cases are highlighted by magenta squares. Note that the experimental values of MS are a bit lower than the theoretical ones. This can be due, at least in part, to the formation of Ag precipitates (i.e., a fraction of the Ag added to the system does not get introduced into the FeMn crystallographic structures but, instead, remains in the form of Ag precipitates). Also, bear in mind that the calculations were performed at tiny periodic unit cells and 0 K whereas the magnetic measurements are performed at room temperature. possess different magnetic properties. magnetic moment of Mn is always higher than the Fe ones. The average Firstly, the total crystal magnetic moment was calculated in order to magnetic moment of γ-FeMn is zero for the AFM collinear 1d spin states compare it with the experimental data of this work. In Fig. 8(a, b) both due to the Fe-Fe and Mn-Mn nearest neighbor antiferromagnetic in­ experimental magnetization, MS, and DFT crystal magnetic moment are teractions and 0.008 μВ atom− 1 for the noncollinear 3Q configuration enhanced with Ag content. In Fig. 8(a) the magnetic moment (μB/atom) while non-zero but relatively small (less than 0.06 μВ atom− 1) values are is also calculated from the experimental magnetization Ms (emu g− 1) found for the other austenite spin states. The Fe and Mn atomic magnetic and the weighted g mol− 1 percentage for FeMn – x Ag (x = 0, 1, 3, 5) %. moments in ε-FeMn are reduced compared to the γ-FeMn while the mMn In Fig. 8(b), the γ-FeMn crystal magnetic moment of the favored non- values might be similar or even smaller than mFe. In particular, the collinear γ-NC is zero (denoted by blue square), in agreement with favored FeMn [0001] AFM spin state has mFe = 1.42 μВ and mMn previous theoretical and experimental data [35,39]. Nevertheless, the = − 1.15 μВ at the ε-Fe50Mn50 and might be lowered to mFe = 0.65 μВ average crystal magnetic moment values of all the under-study cases in and mMn = − 0.42 μВ in the relaxed DFT ε-Fe50Mn50 lattice. It should be Fig. 4 are almost zero. In particular, the energetically favored ε-FeMn noted that all ε-FeMn cases prefer the AFM spin states against the FM shows an average crystal magnetic moment of 0.065 μВ atom− 1 (from ones in line with [42]. These DFT results are in agreement with the 0 up to 0.13 μВ atom− 1) for several configurations and spin states which experimentally observed magnetic moment reduction due to increase of might coexist in the experimental conditions. Mn content [60] especially when co-existence of both γ and ε phases Concerning the FeMn-6Ag wt% and FeMn-12Ag wt% alloys, the holds. average crystal magnetic moment also depends on the spin states and Concerning the γ-FeMn-6Ag wt%, the collinear AFM spin state be­ structural configuration along with compositions showing, nevertheless, comes favoured along with the Ag preference in Mn-rich 1st neighbour a small MS increase behaviour upon Ag substitution. Namely, the environment shown in Fig. 9. Although the Ag atomic moment is average crystal magnetic moment of γ-NC and γ-C tends to increase upon virtually zero, the presence of Ag atom alters the 1Q collinear spin Ag substitution, similar to the experimental magnetization, while the ε symmetry of the γ-FeMn system influencing the atomic magnetic magnetic moment is also enhanced in ε-FeMn-6Ag. The calculated moment of the Fe and Mn neighbouring atoms compared to the γ-FeMn magnetic moment of the energetically favored configurations is pre­ (mFe = ± 1.56 μВ and mMn = ± 2.20 μВ), resulting in a range from 0.25 sented in Fig. 8(b) showing the enhanced μВ upon Ag substitution. to – 1.72 μВ for mFe and from 2.08 to 2.62 μВ for mMn which depends on Although there is an agreement between the present experimental data the neighbor distance and the spin direction. In particular, Ag has 12 and the theoretical calculations, one should bear in mind that the DFT first neighbors consisting of four Fe and eight Mn atoms. The Fe first unit cells are tiny and cannot include dislocations or grain boundaries neighbors are located in the same (001) plane with Ag and show which might also influence the spin states and the concomitant magnetic − 1.72μВ while upon Ag introduction they lose − 0.02 e- per atom. In moments. The increase of the Fe magnetic moment upon a non-magnetic addition, due to atomic relaxation, the Ag-Fe first neighbor distance √̅̅ element like Cu was also observed in the nanocluster cases [68]. increases to 2.624 Å compared to 2.546 Å (stand for a 22, a = 3.6 Å experimental value used in the simulation cell) resulting in 3.1% local 3.4.2. Ag alters the Fe and Mn atomic magnetic moment expansion of the Ag-Fe bonds and therefore local stress. In the third The Fe and Mn atomic magnetic moment of austenite and martensite column of Fig. 9(a) the electron charge density difference is depicted structures were evaluated with and without Ag atoms. Starting with the along with the Ag, Fe and Mn atomic balls. The blue sphere around Ag γ-FeMn, the atomic magnetic moments stand in the range of 1.3–1.8 μВ particle denotes the Ag’s spherical 5 s electron charge depletion (− 0.024 for the Fe (mFe) and within 1.83–2.4μВ for the Mn (mMn) atoms, in line e- per atom) which also affects its first and second neighbourhood. In with previous GGA-DFT calculations [37,39]. In particular, the ener­ particular, the second Ag-Fe neighbors retain the 3.6 Å distance but they getically favored 1Q collinear configuration of Fig. 4(a) has gain charge + 0.03 e- per atom which is presented by green hemispheres mFe= ± 1.56 μВ and mMn = ± 2.20 μВ compared to ± 1.54 μВ and in the third column. The rest of Fe neighboring atoms’ distances are not ± 2.08 μВ, respectively, of Ref. 35 while the 3Q non-collinear spin state affected by the Ag presence although they gain charge similar to the mFe (1.87 μВ) and mMn (2.17 μВ) are in line with the corresponding mFe second neighbors. The Mn-Ag first neighbor distance is expanded by (1.85 μВ) and mMn (2.12 μВ) [37]. It should be noted that, like in pre­ 3.4%, the atomic magnetic moment is increased to 2.62 μВ or − 2.95 μВ vious DFT studies, for all under-study cases of γ-FeMn, the atomic 9 A. Bartkowska et al. Journal of Alloys and Compounds 966 (2023) 171640 Fig. 9. FeMn-Ag atomic representation and spin state, atomic magnetic moment and electronic charge density difference: (a) γ-FeMn-6Ag wt%, (b) γ-FeMn-12Ag wt % and (c) ε-FeMn-12Ag wt%. Fe, Mn and Ag atoms are presented by gold, magenta and grey spheres. Dashed lines denote the Fe (gold) and Mn (magenta) atomic magnetic moment of γ-FeMn (in a, b) or ε-FeMn (in c). In the third column the electron charge density difference revealing charge transfer is shown along with the atomic representation, as blue spheres around Ag atoms and blue/green hemispheres with isovalue + 0.1 (for charge gain e-/Bohr3 in green) and − 0.1e-/Bohr3 (for charge lose in blue). compared to mMn = ± 2.20 μВ of the pure γ-FeMn, as shown in Fig. 9 observed in the electronic charge density difference from the Ag atoms (second column). In line with Fe, the Mn first neighbor atoms of Ag lose and its first neighbors (blue area indicated charge loss) towards the charge − 0.02 e-/atom (average value on the 8 atoms presented with second and third neighbors (green hemispheres show charge gain and blue hemispheres in the third column) while the following neighbors blue hemispheres charge loss along the Ag-neighbor atoms directions.). gain charge (green hemispheres). This charge loss or gain is also illus­ This Ag charge loss (0.02 e- per atom), although small, is due to Ag’s trated in the electron charge density difference Δρ of the third column in unpair 5 s electron resulting in a positively charged Ag ion in the FeMn Fig. 9 where the blue spherical area around the Ag atom denotes that the matrix, revealing the will of Ag to offer electrons to the system. This in 5 s orbital main loss (− 0.024 e- per atom) also affects the neighbouring turn might be related to its antibacterial properties and its ability to atoms. In particular, the electronic charge transfer on the Ag’s neigh­ induce generation of reactive oxygen species [69,70]. Charge transfer borhood atoms, caused by Ag, reveals electric dipole moment features between Ag and Al has been also found in the case of Ag in AlN matrix on the Fe or Mn atoms having charge loss close to Ag (blue hemisphere) affecting the electronic properties and bonding characteristics [71]. and charge gain away from Ag (green hemisphere) in the bond direction between Ag and all neighboring atoms. 4. Conclusions Similar behaviour is also depicted in the case of γ-FeMn–12Ag wt% and ε-FeMn-12Ag wt%, now influencing a higher number of Ag atoms’ The present study was devised to determine the effect of Ag on the neighbors. In the case of ε-FeMn-12Ag wt%, the Fe (from 1.10μВ up to phase composition and physical properties (mechanical and magnetic) 1.9μВ) and Mn (− 2.30μВ) first neighbor atomic magnetic moments in­ of FeMn alloys. The study consisted of a variety of experimental tech­ crease compared to the pure ε-FeMn (+1.37μВ for Fe and − 1.11μВ for niques and was supported by theoretical calculations. The basic struc­ Mn) while the Fe next-next nearest neighbors reveal smaller atomic tural and magnetic properties of FeMn were reproduced in line with magnetic moment (from 0.2μВ up to 0.9μB) and slowly converge towards previous data. the ε-FeMn far from Ag atoms. The Ag-Fe first neighbor bonds are This study has experimentally identified the co-existence of γ-FeMn expanded from 1% up to 4% along with the Ag-Mn bonds (2%) showing and ε-FeMn upon Ag addition to equiatomic FeMn alloys, which is the local stress introduction by Ag that might be responsible for the related to the decrease of the ISF energy along with the decrease in the changes of spin states, in line with bcc Mn spin alterations due to ΔE between the two phases. The Ag atoms prefer the ISF sites, thus expansion or contraction [65,66]. 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