Structural, Mössbauer and Magnetic Study of (Mn0.2Co0.2Ni0.2Cu0.2X0.2)Fe2O4 (X=Fe, Mg) Spinel High-entropy Oxides Fabricated via Reactive Flash Sintering

Journal of the European Ceramic Society 44 (2024) 116686 Available online 26 June 2024 0955-2219/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Structural, M¨ ossbauer and magnetic study of (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 X 0.2 ) Fe 2 O 4 (X=Fe, Mg) spinel high-entropy oxides fabricated via reactive flash sintering A.F. Manch´ on-Gord´ on a , * , G.E. Almanza-Vergara a , S. Molina-Molina a , A. Perej´ on a , b , ** , J.S. Bl´ azquez c , P.E. S´ anchez-Jim´ enez a , b , L.A. P´ erez-Maqueda a a Instituto de Ciencia de Materiales de Sevilla, ICMSE CSIC-Universidad de Sevilla, C. Am´ erico Vespucio 49, Sevilla 41092, Spain b Departamento de Química Inorg´ anica, Facultad de Química, Universidad de Sevilla, Sevilla 41012, Spain c Dpto. Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, Sevilla 41080, Spain ARTICLE INFO Keywords: Reactive flash sintering High entropy oxides M¨ ossbauer spectroscopy Magnetic properties Soft magnetic materials ABSTRACT Herein, it is reported the concomitant synthesis and sintering in a single step of (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 X 0.2 )Fe 2 O 4 (X=Fe, Mg), a spinel-structured high-entropy oxides, by the reactive flash sintering technique. A single phase, identified with a spinel crystal structure Fd3m, was obtained in just 30 min at a furnace temperature of 1173 K. The structural and magnetic properties of the prepared compounds were assessed by the combined use of various techniques, aiming to understand the correlations between functional properties and crystal structure. Characteristic features of the M¨ ossbauer spectra prove the existence of different nonequivalent Fe environments . Both compositions display soft magnetic behavior, characterized by low coercive fields and saturation magnetization reached at low fields. Thus, the substitution of nonmagnetic Mg 2+ for magnetic Fe 2+ results in a decrease in magnetic parameters due to the weakening of the super-exchange interaction among the magnetic moments. 1. Introduction Although the approach of increasing configurational entropy to facilitate the formation of simple, single-phase systems from multiphase precursors was initially proposed for the development of metallic systems, it has been quickly extrapolated to other types of materials [1]. The fundamental concept behind the high-entropy stabilization lies in the combination of a large number of elements in equiatomic proportions within a solid solution. This approach frequently leads to the development of a single-phase structure, thus overcoming the typical enthalpy-driven phase separation that is common in heavily doped systems [2,3]. In this manner, high entropy oxides, HEOs, represent a new class of oxide systems which basically consist of the combination of five or more cations, in equiatomic or near-equiatomic ratios, resulting in the formation of single phases characterized by simple cells. These materials have garnered significant interest since the first HEO compound was synthesized by Rost et al. in 2015 [2]. Since then, several HEOs with diverse structures, microstructures, compositions, and, notably, tailorable properties [4–7], including magnetic properties [8–10], have been developed. The spinel configuration is notable for its exceptional potential as a multicomponent compound [8,10,11]. This is primarily attributed to its large and intricate unit cell, which comprises 32 anion sites surrounded by 24 cations arranged in both octahedral and tetrahedral cages. Spinel-type oxides typically follow the general formula AB 2 O 4 , where ideally, 2+and 3+cations occupy the tetrahedral A-sites and octahedral B-sites, respectively. However, cation inversions are relatively common, where 2+cations occupy the octahedral sites and vice versa. In HEO systems, metal atoms are not directly adjacent within the crystal structure. Consequently, magnetic properties arise from indirect exchange interactions among the participating ions, resulting in nonuniform magnetic interactions due to variations in nearest-neighbour configurations as well as their distribution distances [9]. In this context, the distribution of occupancy (both atomic and in terms of oxidation states, owing to the presence of non-equivalent atomic positions), as well as the atomic distances, play pivotal roles in influencing the magnetic * Corresponding author. ** Correspondence to: Dpto. de Química Inorg´ anica, Facultad de Química, Universidad de Sevilla, Sevilla 41012, Spain. E-mail addresses: [email protected] (A.F. Manch´ on-Gord´ on), [email protected] (A. Perej´ on). Contents lists available at ScienceDirect Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc https://doi.org/10.1016/j.jeurceramsoc.2024.116686 Received 23 January 2024; Received in revised form 7 June 2024; Accepted 20 June 2024 Journal of the European Ceramic Society 44 (2024) 116686 2 properties of HEOs. Therefore, to gain a comprehensive understanding of these magnetic systems, it is essential to combine the examination of the developed microstructure with the specific spectroscopy of the elements within the compounds. This integrated approach allows for the understanding of the diverse magnetic interactions between the atoms in systems with a high level of chemical disorder. Consequently, techniques like 57 Fe M¨ ossbauer spectroscopy are particularly useful for elucidating the nature of HEOs containing Fe [12,13]. The investigation of magnetism in HEOs has generated a substantial dataset, allowing for the identification of certain general trends. Thus far, it has been observed that the magnetic properties of HEOs closely resemble those found in structurally similar conventional oxides. For instance, antiferromagnetic properties have been identified in rocksalt structures based on transition metals or orthorhombic perovskites containing combinations of rare earth-transition metal, while ferrimagnetism is observed in spinel structures based on transition metals or hexaferrites [9]. In the case of S-HEOs, their magnetic properties are highly sensitive to the specific cations present in the compound. For example, it has been noted that when nonmagnetic Zn 2+ substitutes for Fe 2+ in (Mg,Co,Ni,Cu,X)Fe 2 O 4 , where X =Zn or Fe, the N´ eel temperature, TN, decreases by approximately 120 K [8]. Additionally, for S-HEOs such as (Cr,Fe,Mn,Co,Ni) 3 O 4 , replacing Zn 2+ with Ni 2+ or Co 2+ leads to a decrease in both magnetic saturation MS and coercive field HC [10]. While the outcomes regarding the single crystallographic structure and composition may seem intuitive and somewhat predictable, the existence of stable long-range magnetic ordering amidst significant chemical disorder is undeniably intriguing. Investigation into the ordering of cation sites is still in its early stages, adding further complexity to the understanding of these systems. HEOs are typically synthesized using traditional solid-state synthesis methods, wherein initial binary oxide powders are blended and then subjected to high-temperature sintering [2,8,14,15]. However, this synthesis approach often requires high temperatures and prolonged dwell times, leading to significant energy consumption. Recently, alternative low-temperature and energy-efficient processing methods have emerged as viable options for synthesizing HEOs. One such method is reactive flash sintering (RFS) [16], a novel technique that has been successfully used to synthesize high-entropy rock salt oxides [17–19] and magnetic systems [20–22] at considerably lower furnace temperatures. RFS is a tailored variation of flash sintering technique, which involves the application of moderate electric fields and temperatures to oxide materials, leading to their rapid densification within a matter of seconds. In a similar vein, RFS enables the concurrent formation and densification of compounds from a blend of precursor oxide powders in their initial green state. This approach is particularly effective for synthesizing complex materials with remarkable efficiency [23]. In a recent study, RFS was utilized to investigate the magnetic properties of spinel zinc ferrite, ZnFe 2 O 4 [24]. The resulting compounds exhibited enhanced saturation magnetization and increased coercivity compared to ferrites sintered using conventional methods. These observed changes were attributed to the generation of non-thermal lattice defects induced by the application of an electric field during processing. Iron-based systems provide an ideal platform for investigating RFS processes and analysing the properties of resulting products [20–22]. The affordability of iron makes it highly desirable across various technological domains. Additionally, the magnetic properties inherent in many iron compounds greatly enhance the depth of information that can be gleaned from these systems. Furthermore, the presence of the M¨ ossbauer isotope, 57 Fe, in significant natural abundance [25] facilitates the exploration of hyperfine interactions within iron-based compounds, contributing to a more comprehensive understanding of these materials. The selection of Mg 2+ , a non-3d metal cation, to induce significant changes in magnetic properties was based on its compatibility with other cations in the system. It is noteworthy that all oxides formed with the selected cations with the +2 valence state share the rock salt crystal structure, with the cations possessing similar ionic radii. In this study, S-HEOs with the composition (Mn 0.2 Co 0.2 Ni 0.2 - Cu 0.2 X 0.2 )Fe 2 O 4 (X=Fe, Mg) have been prepared via RFS. Previous research has shown that conventional pressure-less sintering methods require multiple thermal treatment steps at high temperatures, 1123 K for 10 hours for material formation followed by sintering at 1523 K for another 10 hours [8]. However, our study demonstrates that a pure single-phase material can be achieved using RFS, with just a 30-minute process at 1173 K from a mixture of constituent oxides. Our investigation involved evaluation both the structural and magnetic characteristics of the RFS-prepared compounds. The primary novelty of our research lies in utilizing the RFS technique to produce HEOs with a spinel structure. Additionally, the use of M¨ ossbauer spectroscopy provides valuable insights into the characteristics of these potentially significant oxide systems. 2. Experimental (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 X 0.2 )Fe 2 O 4 (X=Fe, Mg) were synthesized and sintered in a single step by RFS using available oxides with a purity of at least 99 %. The raw materials included α -Fe 2 O 3 (Sigma Aldrich), MgO (Strem Chemicals), NiO (Strem Chemicals), CoO (Thermo Scientific), CuO (IoLiTec Nanomaterials) and MnO 2 (Acros Organics). To remove any moisture, the oxides were dried in a warming oven at 1073 K for 0.5 h and then weighted to stoichiometric proportions. The process began with the preparation of green samples by mixing the precursor powders with a polyvinyl alcohol (PVA) binder solution. These mixtures were then uniaxially pressed into dog-bone shapes, each weighing approximately 0.8 g. The resulting dog-bones were positioned within a tubular furnace using platinum wires attached to their handles. The electrodes of the setup were connected to a 1500 W DC power supply (EA-PSI 9760–06 DT). Subsequently, the dog-bone samples underwent a pre-heating stage, during which the temperature was raised using a heating ramp of 5 K/min up to 723 K. The samples were held at this temperature for 0.5 hours to remove the PVA binder. Following this, the furnace temperature was further increased to 1173 K. During the RFS experiments, the samples were maintained at this temperature while the current intensity was progressively increased at a rate of 10 mA/s until reaching the specified current intensity limit. These conditions were held for different times. Finally, the furnace and power supply were shut down, and the sample was allowed to cool to room temperature, RT, inside the furnace. The material temperature during the flash experiments was monitored using an infrared (IR) camera (PI 1 M, Optris GmbH, Germany). X-ray diffraction (XRD) patterns were obtained using a Rigaku Miniflex diffractometer at RT with Cu-K α radiation. The X-ray analysis software utilized included Bruker DIFFRAC.EVA 4.0 for phase identification and X’Pert HighScore Plus for Rietveld refinement. Scanning electron microscopy (SEM) observations of the specimen surfaces were conducted using a FEI Teneo microscope operating at 20 kV. For characterization of the surface morphology of the cross-sectional fractures, secondary electrons SEM mode was employed with a Hitachi S-4800 microscope (Hitachi, Ltd.). Selected areas were analyzed using energy dispersive spectroscopy (EDS). Detailed microstructure investigation and chemical analysis were carried out using a Talos S200 transmission electron microscope (TEM) operating at 200 kV. The TEM was equipped with an energy dispersive X-ray microanalyser and a high-angle annular dark field detector, enabling high-resolution TEM (HRTEM) imaging and scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy (STEM-EDS). Bulk samples were conveniently thinned for optimal observation in the microscope. The elemental composition of the prepared samples was determined by inductively coupled plasma optical emission spectroscopy (ICP-OES) using a iCAP 7200 ICPOES Duo (ThermoFisher Scientific). The 57 Fe M¨ ossbauer spectroscopy was performed utilizing a transmission geometry setup and a 57 Co(Rh) source. Hyperfine parameters were determined by analyzing the acquired spectra with the NORMOS A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 3 program [26]. Isomer shift values are reported relative to an α -Fe foil at RT. X-ray photoelectron spectroscopy (XPS) measurements were conducted using a Phoibos 100-DLD instrument equipped with a monochromatic Al-K α X-ray source (energy 1486.68 eV) and a hemispherical analyzer. The samples were analyzed in powder form, and the binding energy scale was calibrated using the neutral carbon set at 285 eV. Core-level spectra were processed with CasaXPS software. Magnetic characterization was carried out employing a Quantum Design Physical Property Measurement System (PPMS) with the standard vibrating sample magnetometer option. Temperature-dependent magnetization measurements were conducted following a zero-field cooled (ZFC) protocol, followed by field heating (FH) and field cooled (FC) steps. Initially, the samples were cooled to 5 K in zero magnetic field. Subsequently, a magnetic field of 100 Oe was applied, and the magnetization was measured as the temperature increased (ZFC branch). Magnetization measurements were then performed while applying the magnetic field during both warming (FH branch) and cooling (FC branch). Magnetic field dependence measurements were conducted at RT. Magnetic phase transitions were investigated using thermomagnetic gravimetry (TMG) on a Perkin-Elmer TGA7 instrument (Perkin-Elmer, USA). Instrument calibration was conducted with reference to the Curie temperatures of alumel (436 K), Ni (627 K), and Fe (1053 K) standards. 3. Results and discussion 3.1. Preparation of (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 X 0.2 )Fe 2 O 4 (X=Fe, Mg) by reactive flash sintering The production of the desired compounds via RFS requires meticulous control of the experimental parameters [27]. This is essential to overcome common thermal management issues that can lead to imperfectly homogeneous samples during flash experiments [28]. Such problems include abnormal grain growth, localized melting, and preferential current paths [29], often encountered in conventional flash experiments where temperature is increased while maintaining a constant electric field. To mitigate these challenges and achieve homogeneous systems, a modification of traditional flash experiments has been proposed, involving the use of current ramps [21,30]. It enables a linear increase in the current density through the material, with the applied voltage being automatically adjusted [31]. The furnace temperature is maintained constant in these types of experiments. Here, we employed current density ramps to investigate the synthesis of single-phase spinel (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Fe 0.2 )Fe 2 O 4 (Mg-free compound) and (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Mg 0.2 )Fe 2 O 4 (Mg-containing compound) HEOs via RFS. Fig. 1 illustrates the evolution of electrical parameters during a RFS experiment as a function of time when a current density ramp is applied. The data correspond to the RFS experiment carried out in the Mg-free compound at a furnace temperature of 1173 K and a maximum current density limit of 450 mA mm −2 . Initially, the electric field steadily increases automatically until the flash is triggered, and the electrical conductivity becomes high enough to initiate the prescribed current density ramp. Subsequently, the electric field diminishes and stabilizes at a constant value when the predetermined maximum current density is achieved and maintained. This reduction in the electric field is linked to the increase in the temperature of the sample, leading to a decrease in its resistance. A similar trend is observed for the dissipated power density, determined by the product of the current density through the sample, J, and the applied electric field, E, resulting in P=JE. IR thermographic images reveal a substantial temperature rise across the sample surface during the flash experiment, reaching differences of approximately 350 K between t=0 and t=15 min. Temperature gradients have not been observed within the specimen, as it is shown in the inset of Fig. 1. Several experiments were conducted, exploring various combinations of parameters to identify the optimal conditions for the production of pure S-HEOs. The results for the production of Mg-free HEO are summarized in Table 1. From Table 1, it is evident that monophasic samples require a minimum J threshold of 450 mA mm −2 and a flash treatment lasting 30 minutes at a furnace temperature of 1173 K, as detailed in the next section. Under all other examined conditions, the reaction remained incomplete. It is notable that the RFS technique allows for the attainment of a single-phase HEO at a furnace temperature ∼300 K lower than conventional processing method [8]. This observation is consistent with findings across various HEOs when comparing the conditions required for RFS and solid-state reaction, SSR, techniques [17–19,32,33,34]. In this regard, it has been speculated that the applied electric field may induce a non-equilibrium thermodynamic state, facilitating reactions at lower temperatures [18]. However, our results indicate that the 0 5 10 15 0 5 10 15 20 t=0 min t=15 min 1173 K 1523 K E (V/cm) t (min) 0 200 400 600 J (mA mm -2 ) 0 100 200 300 400 500 P (mW mm -3 ) Fig. 1. Evolution of electrical parameters (electric field, current density and power density dissipation) as a function of time during a reaction flash experiment (current ramp of 10 mA s −1 , furnace temperature 1173 K and current density limit of 450 mA mm −2 ) in the Mg-free compound. Inset displays infrared thermographic images of the specimen at t=0 min and t=15 min during the flash. A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 4 temperature required for HEO formation is comparable to that required for its production by SSR. In this context, recent studies have demonstrated that the RFS technique enhances the solid-state diffusion phenomenon [35], potentially explaining the significant reduction in time and temperature requirements. On the other hand, the current density values required for generating Mg-free HEO are slightly higher compared to those for simpler systems. Nevertheless, these values align with the observed current density employed for other HEOs synthesized via RFS [18]. Once the minimum power density necessary for forming the single-phase Mg-free HEO was determined, identical experimental conditions were applied to successfully produce the Mg-containing composition, as shown in the following section. Despite significant efforts in the pursuit of new high-entropy materials, our understanding of these systems remains nascent, and numerous challenges persist. A widely accepted definition of "high-en- tropy materials" is those where the configurational entropy, Sconf , exceeds 1.5 R [36]. This criterion is accepted due to the emergence of new properties observed when entropy surpasses this threshold [37]. However, substantial and positive entropy values are necessary only if the enthalpy of mixing is also significant and positive, characteristic of "entropy-stabilized materials”. It is noteworthy that in several instances, the enthalpy of mixing is negative, where high entropy does not dominate the Gibbs free energy landscape. These materials labelled as "high-entropy materials" are evidently not entropy-stabilized. In the context of the spinel structure, its robustness enables it to accommodate various bivalent and trivalent cations without compromising stability or triggering decomposition processes. Consequently, phenomena characteristic of entropy stabilization, such as alterations in phase stability due to temperature variations or an increase in the number of components, have not yet been documented in this material class [38]. 3.2. Structural characterization The crystal structure of the prepared pellets was examined through XRD at RT. Fig. 2a displays the XRD patterns of Mg-free HEO specimens synthesized via RFS at a furnace temperature of 1173 K, with different current density limits (as indicated in the figure). As mentioned earlier, a minimum current density limit of 450 mA/mm 2 was necessary to achieve complete reaction and obtain a single-phase cubic spinel structure with the Fd3m space group. For any other conditions, additional peaks corresponding to the Fe 2 O 3 starting powder (the major raw phase) are present. This underscores the significant difference between producing these HEOs by RFS or SSR, where in the latter technique higher temperatures and extended dwell times are required [8]. Conversely, in RFS, 1173 K for 30 min is enough to produce the entropy-stabilized spinel phase. Fig. 2b illustrates the XRD patterns of both studied HEO compositions. Both samples exhibit a monophasic cubic spinel structure. Satisfactory Rietveld refinement of the XRD patterns at RT corresponding to the single-phase samples was obtained (see Figure S1). From the refinements, cell parameters a=8.3805(2) and 8.3914(3) Å were determined for the Mg-free and Mg-containing HEOs, respectively. These values are in line with those previously reported for the same compositions [8]. SEM micrographs of the fracture of the prepared materials are shown in Fig. 3. The microstructure of the compounds aligns with well-sintered materials characterized by a relatively uniform distribution of grain sizes, all measuring less than 5 μ m. It has been previously noted that an increase in current density results in larger grain sizes [39]. While the grain sizes observed in our samples are relatively large compared to those achieved with other compounds prepared by RFS, it is important to note that, in that case, they are achieved with significantly lower current density values [22]. This parameter determines the temperature reached by the flashed sample. Fig. 3 illustrates that both compositions exhibit an octahedral morphology with slight variations in orientation, Table 1 Experimental conditions tested in the reactive flash process of Mg free HEO, in terms of furnace temperature, current density limit and flash holding time. The mean surface temperature of the specimens at the maximum current density measured by the IR camera is also provided. Furnace temperature (K) Current density (mA/mm 2 ) Time (min) Obtained pellet Surface temperature (K) 1173 100 10 Incomplete 1300 1173 200 15 Incomplete 1310 1173 250 20 Incomplete 1350 1173 300 25 Incomplete 1380 1173 350 30 Incomplete 1440 1173 400 30 Incomplete 1490 1173 450 30 Complete 1510 30 40 50 60 450 400 350 250 150 Intensity (a.u.) 2 θ (degrees) 220 311 222 400 422 511 440 a) 100 30 40 50 60 Intensity (a.u.) 2 θ (degrees) Mg free HEOs Mg containing HEOs b) 220 311 222 400 422 511 440 Fig. 2. XRD patterns at room temperature of a) Mg free HEOs at 1173 K at the indicated current density limits (units: mA mm −2 ) and b) the single-phase HEOs studied compositions prepared by RFS. The main reflection peaks of hematite ( α -Fe 2 O 3 ) are indicated in the upper panel (squares symbols). The indexed peaks correspond to the main diffraction peaks of the iron based MnFe 2 O 4 reference patterns (ICSD 155275) showing single-phase spinel (space group Fd3m). A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 5 which is related to their preferred crystal growth orientation. In the case of a cubic spinel, when the growth rate of the {200} faces is the highest, the crystallite shape is governed by the {111} faces, resulting in an octahedron with four-sided pyramids. Conversely, when the preferred orientation is <111>, the grain shape changes from an octahedron to a truncated pyramid, resembling a triangular plane [40]. This latter configuration seems to be the case for the studied compounds, especially in the case of the Mg-free compound. To assess the elemental distribution in the synthesized S-HEOs, crosssection SEM imaging coupled with EDS measurements were conducted. The EDS mapping images depicted in Figure S2 reveal the even distribution of all elements in both compounds. No signs of segregation or clustering can be observed, confirming the chemical and microstructural homogeneity of the materials and validating their compositional consistency on the microscale. For a deeper insight into the morphology and microstructure of the HEOs, the bulk structure was further examined using TEM at boundary junctions (Figs. 4a and 4b). High-resolution TEM (HRTEM) images of the bulk specimens are presented in Figs. 4c and 4d. The lattice spacing, d, was measured to be approximately 3.0 and 2.6 Å, corresponding to the (220) and (311) lattice planes in the spinel structure (PDF#54–0964) for the Mg-free HEO. In the case of the Mg-containing HEO, a lattice spacing of approximately 4.9 Å, attributed to the (111) diffraction plane, was observed. These measurements confirm the high crystallinity of the synthesized HEOs compounds. The selected electron diffraction patterns (Figs. 4e and 4f) were indexed to match the Fd3m spinel structure. Fig. 3. SEM images of the studied HEOs prepared by RFS corresponding to the a) Mg-free and b) Mg-containing HEOs. Fig. 4. TEM (a and b), HRTEM (c and d) and SAED (e and f) images of the studied HEOs prepared by RFS. First and second rows correspond to the Mg-free and Mgcontaining HEOs, respectively. A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 6 In the context of cubic crystals, Bragg’s law can be specifically applied to determine the lattice parameter a of the spinel phase as a = dhkl  h2+k2+l2 √, where dhkl represents the interplanar distance of the plane with Miller indices hkl. Using the obtained values of d along with their corresponding indices, the lattice parameter was estimated to be 8.5 and 8.6 Å from Fig. 4c for the Mg-free HEO, while the Mg-containing compound had an estimated lattice parameter of 8.50 Å. Additionally, the reciprocal lattice vector Ghkl →can be linked to the dhkl parameter, and once the selected-area electron diffraction (SAED) pattern is indexed, the lattice parameter can also be estimated using Bragg’s law. For example, by using d111 for the Mg-free compound, it is possible to estimate a value of a=8.45 Å.It is important to note that the obtained results are just estimations. Results from XRD are more reliable and with smaller error. The STEM-EDS elemental mappings of the RFS-prepared samples are displayed in Fig. 5. These mappings capture the signals of Co, Cu, Fe, Mg, Mn, and Ni elements. Notably, all these elements are evenly distributed within the particles, with no evident of element segregation. However, the concentration of Mg appears to be notably lower compared to other elements. This observation has been noted previously in Mg-containing S-HEOs, such as in the same composition synthesized via SSR [8] or (Cr, Fe,Mn,Mg,Ni) 3 O 4 compound [41]. In any case, EDS images provide strong confirmation of the nano-level chemical homogeneity of the different elements within the samples. The chemical compositions of the samples were quantitatively determined via ICP-OES. The atomic ratio of Fe:Mn:Co:Ni:Cu:Mg in Mg-free and Mg-containing samples are 1.00:0.09:0.09:0.09:0.11:0.0 and 1.00:0.11:0.10:0.11:0.11:0.05, respectively (see Supplementary Table S1). Obtained results are very close to the stoichiometric ratio in the chemical formula in the case of the Mg-free compound, and confirm the lower concentration of Mg in the Mg-containing sample suggested by EDS. Therefore, the comprehensive analysis carried out in this work, which combines XRD patterns, EDS mapping, and STEM images with corresponding EDS mapping, confirms the successful formation of high-entropy systems prepared by RFS. 3.3. Study of the spinel inversion The spinel structure is characterized by the presence of two distinct Fig. 5. HAADF-BF-EDS elemental mapping for the HEOs a) Mg-free and b) Mg-containing prepared by RFS. A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 7 cation positions. In the case of spinel ferrites, it is common for some Fe 3+ ions, which should typically occupy the [FeO 6 ] octahedral sites, to be found instead in the tetrahedral positions, while divalent cations M 2+ take up the vacant octahedral sites. For spinel ferrites MFe 2 O 4 , the distribution of cations between these tetrahedral (A) and octahedral (B) sites is often represented as (M2+ 1−λFe3+ λ) A [M2+ λFe3+ 2−λ] B O 4 . Here, λ is the degree of cation inversion within the structure and is related to the proportions of M 2+ and Fe 3+ ions in the (A) and [B] sites [42,43]. For λ=0, it indicates a normal spinel, where 2+cations occupy the tetrahedral (A) site and 3+cations occupy the octahedral [B] sites. λ =1 indicates an inverse spinel, where the cation distribution is the opposite of the normal spinel. Finally, partially inverse spinels can be found with values of λ between 0 and 1, indicating a mixture of 2+and 3+cations in both (A) and [B] sites. Analyzing the distribution of elements and their oxidation states in high entropy systems can be challenging, but some insights can be provided based on the preferences of different 3d elements. These preferences are often established based on the crystal-field stabilization energy. Among the elements considered, Mg is the only non-3d element. In the majority of spinels, Mg 2+ is primarily found in the tetrahedral sites. For Mn 2+ ions, the crystal-field stabilization energy is zero for both tetrahedral and octahedral coordination, while Mn 3+ ions strongly prefer octahedral sites. Co 2+ ions, however, do not exhibit a distinct preference for any sites. When Fe is in its divalent Fe 2+ state, it shows minimal affinity for octahedral sites. Conversely, divalent Ni 2+ ions demonstrate a pronounced preference for octahedral sites among 3d ions, often resulting in inverse spinels for many Ni-containing compositions. It is common for some Fe 3+ ions, which would typically occupy octahedral positions, to reside in tetrahedral sites [41]. Given these trends, the synthesized compounds are expected to adopt an inverse spinel structure, primarily attributed to the presence of trivalent iron cations. Taking these considerations into account, the existence of this phenomenon in the prepared HEOs was investigated through XPS. In Fig. 6a, the complete XPS survey spectra for both compositions are shown. These spectra indicate the presence of Mg, Mn, Co, Fe, Cu, and Ni in the synthesized compounds and confirm the absence of any foreign elements on the sample surface. Upon closer inspection, both materials exhibit similar XPS spectra for Mn 2p, Co 2p, Fe 2p, Cu 2p, and Ni 2p. Additionally, Mg 1 s is observed in the case of the Mg-containing sample. The XPS results for the Fe element in both compounds are displayed in Figs. 6b and 6c, corresponding to the Mg-free and Mg-containing compounds, respectively. The Fe 2p spectrum is broad, and its deconvolution into constituents may not lead to accurate estimation of the cation distribution. However, it suggests the existence of a peak related to Fe 2+ at 709.8 eV, which could indicate the existence of Fe 2+ ions located in the octahedral sites. Moreover, the Fe 3+ ions occupying the octahedral and tetrahedral sites are represented by distinct peaks at around 711 and 713 eV, respectively [44]. The results confirm the presence of an inversion phenomenon in the studied compounds. The area ratios of Fe 3+ (tet):Fe 3+ (oct) for the Mg-free and Mg-containing HEOs are 1:2.4 and 1:1.5, respectively. These values differ from those of normal spinel structure ferrites [45], but are consistent with those reported for other (5 M)Fe 2 O 4 high-entropy ferrites [40]. XPS was also used to explore potential element reductions occurring during the formation of the studied compounds. Supplementary Figure S3 presents HR-XPS spectra for cations with variable valence, specifically Cu, Co, and Mn. The results suggest that the Cu [46,47] and Mn [48–50] are in the divalent states, while the Co cations exhibit mixed divalent/trivalent states. The HR-XPS spectrum of Co consist on peaks at around 776.0 eV (Co 2p 3/2 ) and 794.8 eV (Co 2p 1/2 ), representing the Co 3+ state [51]. Additionally, peaks around 780.1 eV (Co 2p 3/2 ) and 796.7 eV (Co 2p 1/2 ) correspond to Co 2+ state. Furthermore, two satellite peaks for Co 2p 3/2 (782.8 and 786.1 eV) and for Co 2p 1/2 (799.7 and 0 200 400 600 800 1000 1200 1400 Intensity (a.u.) Binding Energy (eV) Mg containing HEO Mg free HEO Ni 2p Co 2p Fe 2p O 1s C 1s Mn 2p Cu 2p Mg 1s a) 700 710 720 730 740 Intensity (a.u.) Binding Energy (eV) b) (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Fe 0.2 )Fe 2 O 4 Fe 2+ (oct) Fe 3+ (oct) Fe 2p Fe 3+ (tet) Fe 2+ (sat) Fe 3+ (sat) 700 710 720 730 740 Intensity (a.u.) Binding Energy (eV) Fe 3+ (oct) (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Mg 0.2 )Fe 2 O 4 c) Fe 3+ (tet) Fe 2p Fig. 6. a) XPS survey and Fe 2p XPS results corresponding to the b) Mg-free and c) Mg-containing studied compounds. A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 8 802.6 eV) confirm the presence of both Co 2+ and Co 3+ states [47,51,52]. Fig. 7 presents the M¨ ossbauer spectra of the studied compounds, which were measured at RT with high velocity resolution. The parameters obtained from the spectral fittings are summarized in Table 2. The spectra exhibit non-symmetrical six-line patterns and broad lines, which suggest the presence of a superposition of multiple magnetic sextets due to the presence of iron in different environments. In M¨ ossbauer measurements, the inversion of the spinel structure should be reflected by the presence of two sub-spectra with different values of hyperfine field and isomer shift, which can be observed in all obtained spectra. The two contributions with low isomer shift δ confirm the existence of two different environments for the Fe +3 cation. Furthermore, an additional sextet is observed in the case of the Mg-free compounds, which could indicate the presence of Fe 2+ ions, characterized by a high isomer shift (typical values of δ for the 2+state are generally found in the range from 0.8 to 1.5 mm/s [53]), in agreement with XPS results. The hyperfine values obtained for the sextets attributed to the presence of Fe +3 cations in the compounds can be compared to previously reported values reported for MgFe 2 O 4 samples prepared by various methods [42,54–56]. While the literature values are similar, the values obtained in this study are slightly smaller. It is important to note that the influence of different metal ions (M) on the hyperfine field of iron in spinel structures, M x Fe 3-x O 4 , has been extensively studied. Research has shown that nickel, cobalt, and copper slightly increase the hyperfine field of iron [57], while the effect of manganese depend on the sample preparation [57,58]. The observed influence of the iron neighborhood in the studied samples does not precisely match the behavior in binary iron oxides. However, it is worth noting that M¨ ossbauer spectra are often analyzed using the additive model, where the influence of each atom in the immediate vicinity of the Fe atom is considered independently. This analysis is typically applied to each sub-spectrum separately. Nevertheless, the intrinsic disorder in multicomponent systems like HEOs makes it challenging to use this kind of analysis, as the additivity of the influence of the neighbors cannot be assumed due to the complex interactions between the different elements. The quantity of Fe 3+ cations present in both octahedral [B] and tetrahedral (A) sites of the spinel structure depends on the degree of cation inversion, which is represented by the parameter λ [59]. λ can be determined from the subspectral areas, which are estimated through parameters obtained from fitting the M¨ ossbauer spectra. The calculation of λ is as follows: I(A)/I[B]=f(A) f[B] λ 2−λ(1) where I(A)and I[B]represent the subespectral areas of the sextets and f(A) and f[B], which are the recoil-free fraction corresponding to tetrahedral and octahedral sites. The ratio f(A)/f[B]is assumed to be 0.94 at RT [56]. The obtained values for λ (see Table 2) are close to 0.66, which indicates a totally random distribution of Fe atoms in both tetrahedral and octahedral positions. This observation aligns with the preparation method of the studied samples through RFS, a non-equilibrium technique that facilitates the random positioning of the different chemical species. The inclusion of Mg 2+ ions results in a λ value nearing 0.66, facilitating a higher degree of inversion within the spinel structure. On the other hand, the absence of Mg 2+ cations increases the number of Fe 3+ ions occupying the (A) sublattices, resulting in higher values of Bhf (and a higher net magnetization as will be seen later) and λ. The degree of cation inversion in ferrites has a significant impact on their magnetic, electrical and optical properties [60,61]. The Jahn-Teller effect, caused by the ions with a 3+valence in the octahedral sites, is another behavior associated to cation inversion [62]. It should be taken into account that an in-field M¨ ossbauer spectrum could provide more accurate information regarding inversion and ionic distribution [54]. 3.4. Magnetic characterization Hysteresis loops were conducted at RT (300 K) and measured under a magnetic field of up to 10 kOe. The results are presented in Fig. 8, with the corresponding magnetic parameters (coercivity, HC, and saturation magnetization, σ S) compiled in Table 3. The loops of both specimens exhibit similar behavior, characterized by low coercive fields and saturation at magnetic fields greater than 5 kOe. These results confirm that both studied compounds qualify as soft magnetic materials. The data presented in Table 3 indicate that the coercivity HC and saturation magnetization σ s of the Mg-free HEOs surpass those of the Mg-containing HEOs. Same behaviour is reported for the N´ eel temperature, TN, value, which was determined using the TMG signal (see -10 -5 0 5 10 Intensity (a.u.) -10 -5 0 5 10 velocity (mm/s)velocity (mm/s) Intensity (a.u.) a) b) Experimental data Total fitting Site Fe +3 B Site Fe +3 A Site Fe +2 Fig. 7. Experimental (open symbols) and fitting of the M¨ ossbauer spectra (continuous lines) taken at 300 K of a) Mg free and b) Mg containing HEOs. Table 2 Hyperfine parameters obtained from M¨ ossbauer spectra at room temperature of the studied samples. Bhf is the magnetic hyperfine field, QS is the quadrupolar splitting, δ the isomer shift relative to α -Fe and A the Fe atomic fraction of each contribution. (Estimated errors in Bhf , δ, Q, and A are ±0.2 T, 0.03 mm s −1 , 0.1 mm s −1 and 0.5 respectively). λ is the degree of inversion. Sample Component Bhf (T) Q(mm/ s) δ(mm/ s) A(%) λ Mg Free Site Fe+3 B 49.5 0.0 0.43 60.3 0.78 Site Fe+3 A 49.3 -0.1 0.10 34.1 Site Fe+2 49.5 0.0 0.88 5.6 Mg containing Site Fe+3 B 49.1 0.00 0.46 66.2 0.70 Site Fe+3 A 48.9 0.0 0.02 33.5 A.F. Manch´ on-Gord´ on et al. Journal of the European Ceramic Society 44 (2024) 116686 9 Figure S4), coinciding with a substantial decrease in the magnetization. The measured TN values align with those reported by Music´ o et al. [8] for the same compositions obtained by SSR. The magnetic properties of the studied compounds are a consequence of super-exchange interactions occurring between the Fe group ions in both the tetrahedral and octahedral sites. Following Hund’s first rule, the 3d electrons within ions such as Mn 2+ , Fe 2+ , Fe 3+ , Co 2+ , Ni 2+ and other Fe group elements are distributed across various orbitals to maximize their electron spin magnetic moment, thereby exhibiting stronger magnetism [64]. Given that the Mg-free HEO comprises most of these ions, it displays a higher saturation magnetization. Conversely, the introduction of non-magnetic Mg 2+ ions in the Mg-containing HEO weakens the super-exchange interaction between magnetic moments, leading to a reduction in the overall magnetic moment. This observation is consistent with the MS results. For comparison purposes, Table 3 incorporates previously reported data for other S-HEOs samples. The saturation magnetization values for the same compositions obtained by Music´ o et al. by SSR [8] align with those in this study. Nevertheless, it is worth noting that Music´ o et al. do not report coercivity values. This parameter is significantly influenced by grain size, which is expected to be smaller in the samples produced in this by the RFS technique compared to those of SSR. The compositional variation within S-HEOs has a profound impact on site occupations, and consequently influencing their magnetic properties. For instance, Cr-rich systems, where Cr primarily occupies octahedral sites, exhibit magnetic order at low temperatures (<50 K). On the other hand, Fe-rich -10000 0 10000 -80 -60 -40 -20 0 20 40 60 80 σ (emu/g) Mg free Mg containing Magnetic Field (Oe) -100 0 100 -5 0 5 σ (emu/g) Magnetic Field (Oe) Fig. 8. Magnetic hysteresis loops taken at 300 K of the studied HEOs prepared by RFS. Inset shows the low field regions of the hysteresis loops. Table 3 Transition temperatures from the TMG experiments and magnetic parameters measured at room temperature of coercivity, HC, and the saturation magnetization, σ S, of the studied samples. Experimental values for other HEOs spinel compositions from the literature at room temperature have been included for comparison. Sample Technique Tt (K) HC (Oe) σ s(emu/g) Reference (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Fe 0.2 )Fe 2 O 4 RFS 764 56 63 This work (Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 Mg 0.2 )Fe 2 O 4 737 20 57 (Mg 0.2 Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 )Fe 2 O 4 SSR 74.1 56.1 [40] (Mg 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Fe 2 O 4 204.5 44.3 (Mg 0.2 Fe 0.2 Co 0.2 Ni 0.2 Zn 0.2 )Fe 2 O 4 48.4 22.7 (Mg 0.2 Co 0.2 Ni 0.2 Cu 0.2 Zn 0.2 )Fe 2 O 4 SSR 648 65 [8] (Mg 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Fe 2 O 4 774 46 (Mg 0.2 Mn 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Fe 2 O 4 735 50 (Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Fe 2 O 4 715 46 (Cr 0.2 Fe 0.2 Mn 0.2 Co 0.2 Ni 0.2 )O 3 Solid combustion 183 9.9 [10] (Cr 0.2 Fe 0.2 Mn 0.2 Co 0.2 Ni 0.2 )O 3 64 8.1 (Cr 0.2 Fe 0.2 Mn 0.2 Ni 0.2 Zn 0.2 )O 3 91 5.6 (Co,Cr,Fe,Mn,Ni,Al) 3 O 4 Solid combustion 436 4.2 [63] (Al,Cr,Fe,Mn,Ni) 3 O 4 530 1.6 (Co,Cr,Fe,Al,Ni) 3 O 4 750 11.4 (Co,Cr,Fe,Mn,Al) 3 O 4 749 10.6 (Co 0.2 Cu 0.2 Mg 0.2 Ni 0.2 Zn 0.2 )Cr 2 O 4 SSR 36 [8] (Co 0.2 Cu 0.2 Fe 0.2 Mg 0.2 Ni 0.2 )Cr 2 O 4 23 (Co 0.2 Cu 0.2 Mg 0.2 Mn 0.2 Ni 0.2 )Cr 2 O 4 30 (Co 0.2 Cr 0.2 Fe 0.2 Mn 0.2 Ni 0.2 ) 3 O 4 425 (Mg 0.2 Co 0.2 Ni 0.2 Cu 0.2 Zn 0.2 )Fe 2 O 4 648 (Al 0.2 Co 0.2 Fe 0.2 Mn 0.2 Ni 0.2 ) 3 O 4 Microwave assisted co-precipitation technique 538 25.4 14.3 [52] A.F. Manch´ on-Gord´ on et al.