Thermodynamic Guidelines for the Mechanosynthesis or Solid-State Synthesis of MnFe2O4 at Relatively Low Temperatures

Herein, thermodynamic assessment is proposed to screen suitable precursors for the solid-state synthesis of manganese ferrite, by mechanosynthesis at room temperature or by subsequent calcination at relatively low temperatures, and the main findings are validated by experimental results for the representative precursor mixtures MnO + FeO3, MnO2 + Fe2O3, and MnO2 +2FeCO3. Thermodynamic guidelines are provided for the synthesis of manganese ferrite from (i) oxide and/or metallic precursors; (ii) carbonate + carbonate or carbonate + oxide powder mixtures; (iii) other precursors. It is also shown that synthesis from metallic precursors (Mn + 2Fe) requires a controlled oxygen supply in limited redox conditions, which is hardly achieved by reducing gases H2/H2O or CO/CO2. Oxide mixtures with an overall oxygen balance, such as MnO + Fe2O3, act as self-redox buffers and offer prospects for mechanosynthesis for a sufficient time (>9 h) at room temperature. On the contrary, the fully oxidised oxide mixture MnO2 + Fe2O3 requires partial reduction, which prevents synthesis at room temperature and requires subsequent calcination at temperatures above 1100 °C in air or in nominally inert atmospheres above 750 °C. Oxide + carbonate mixtures, such as MnO2 +2FeCO3, also yield suitable oxygen balance by the decomposition of the carbonate precursor and offer prospects for mechanosynthesis at room temperature, and residual fractions of reactants could be converted by firing at relatively low temperatures (≥650 °C).


Introduction
The Mn − Fe − O system is based on abundant transition metal elements and offers rich redox flexibility in mixed-oxide compounds, such as spinel compositions ( Mn, Fe) 3 O 4 or bixbyite ( Mn, Fe) 2 O 3 .Low-cost precursors combined with affordable processing meth- ods may broaden the applicability of Mn − Fe − O materials from up-to-date applications of ferrites in nanotechnologies to mass production processes such as the chemical looping gasification of biomass [1], oxygen storage materials for chemical looping combustion [2], pigments [3], etc., while also extending the applicability of corresponding single-oxide Fe − O and Mn − O systems [4].Available low-grade Fe-and Mn-rich ores also contribute to the feasibility of some of these applications of manganese ferrite [3].In this case, one should also consider the role of gangue components of the natural precursor, which might affect relevant properties and/or may segregate as secondary crystalline phases or in the amorphous fraction after high-temperature firing.
Phase equilibria in the Mn − Fe − O system depend on the Mn : Fe ratio and thermochemical conditions of processing, i.e., redox conditions and temperature, as described by phase diagrams [5] and thermodynamic modelling [6].Thus, prospects to obtain singlephase MnFe 2 O 4 depend on firing schedules and specific atmospheres such as CO 2 /CO [7], which may induce unusual microstructures and potential impacts on the magnetic and dielectric properties of ferrites.The effective phases obtained by solid-state reactions may also depend on starting precursors [8].
Conditions of processing, combined with subsequent heat treatments [9][10][11], also determine the crystallite size, changes in oxidation states, and cation occupancy in tetrahedral and octahedral positions of Mn x Fe 3−x O 4 spinels, with corresponding effects on relevant properties and prospective applications [12].In addition, thermochemical treatments may cause the selective segregation of iron oxides or manganese oxides [13] and corresponding changes in the Mn : Fe ratio of nonstoichiometric spinels Mn x Fe 3−x O 4 .
Thus, it is important to develop flexible methods allowing the synthesis of ferrites in wide ranges of mechanochemical and/or thermochemical conditions, including processing at room temperature by direct mechanosynthesis from solid precursor mixtures, to avoid undue changes promoted at higher temperatures, depending on suitable precursors [14].Mechanochemical treatments may also induce nanostructuring and changes in site occupancy [15], including the nanostructuring of MnFe 2 O 4 after previous firing at high temperature [16].
The high density and hardness of steel milling vials and balls are most suitable for high-energy milling to overcome the kinetic limitations of room-temperature solid-state kinetics.However, these milling media may induce contamination with metallic Fe, changing the intended Fe : Mn stoichiometry, or causing the onset of secondary mixed-oxide phases, such as (Fe, Mn)O [17].The onset of metallic Fe was also reported after the mechanosynthe- sis of a 0.5Mn 2 O 3 + Fe 2 O 3 powder mixture, in spite of its stoichiometric ratio (Mn:Fe = 1:2) and oxygen excess relative to the spinel structure, i.e., O:(Mn + Fe) > 4:3 [18].Differently, MnO + Fe 2 O 3 or 1/3Mn 3 O 4 + Fe 2 O 3 powder mixtures did not react under mild mechanical activation, and conversion to manganese ferrite required calcination at about 900 • C in an inert atmosphere [19].Metallic Fe + Mn precursors were used as precursors for the mechanosynthesis of MnFe 2 O 4 by wet milling [20], and metal + oxide precursor mixtures were also proposed, such as 2Fe + MnO 2 [9] or Mn + Mn 2 O 3 + 3Fe 2 O 3 [21].On the contrary, the mechanical activation of fully oxidised precursors (MnO 2 + Fe 2 O 3 ) only induced amorphisation, even after 40 h, and conversion to MnFe 2 O 4 required subsequent calcination at high temperatures in the order of 1200 • C [22], except possibly in relatively reducing conditions [7] or a vacuum [21].
Non-oxide precursors have also been proposed such as mixtures of Mn(OH) 2 + Fe 2 O 3 or Mn(OH) 2 + Fe(OH) 3 .Both mixtures converted to MnFe 2 O 4 after mechanosynthesis in a steel vial and with steel balls for 25 h [23].The onset of intermediate phases after a shorter milling time shows that the stable oxyhydroxide phase FeOOH forms readily under mechanical activation by the decomposition of Fe(OH) 3 or partial hydration of Fe 2 O 3 in contact with Mn(OH) 2 .
Mixed carbonate + oxide precursor mixtures were also proposed, namely MnCO 3 + Fe 2 O 3 , which were milled at 450 rpm in toluene, for as long as 90 h, and required subsequent calcining at 750 • C [24] or other combinations of mechanical activation and calcination [25], for conversion to MnFe 2 O 4 .The 2FeCO 3 + MnO 2 powder mixture was found more successful in reaching conversion to the spinel phase at room temperature, within the detection limits of X-ray diffraction, by direct mechanosynthesis at a sufficiently high milling rate, even without subsequent calcination [26].
Thus, the main objective of this work was to propose guidelines for the room-temperature mechanosynthesis of MnFe 2 O 4 from different combinations of precursor mixtures or by mechanical activation and subsequent calcination at intermediate temperatures, avoiding tedious trial and error tests and minimizing undue experimental work.This was guided by thermodynamic predictions and demonstrated by experimental evidence using representative mixtures of precursors.

Thermodynamic Modelling
Quasi-planar chemical potential diagrams for mixed metal-oxide systems were derived analogously to the method that was proposed by Yokokawa and co-authors [29,30], previously applied to assess the phase stability in a variety of systems in solid-state electrochemical applications [31], and to assess their contamination [30,32] or degradation by interaction with reactive gases [33].Other recent references address relevant issues of materials proposed for catalytic applications in different systems such as Ni − Al − O [34], Fe − Ti − O [35], CaO − SiO − CO 2 [36], etc., or the synthesis of catalytic materials in the systems Fe − Si − O [37], Ca − Fe − O [38], or Ce − Al − O [39], and guidelines for the processing of SrTiO 3 by mechanosynthesis [40].
Similar methods were applied here as guidelines for the mechanosynthesis of MnFe 2 O 4 from different combinations of precursors in the systems Mn − Fe − O or Mn − Fe − O − C. Chemical potential diagrams were derived from 2-phase equilibria, which establish relations between the chemical potentials of the transition elements, the chemical potentials of O 2 and/or CO 2 , and the free energy of the corresponding reactions.One may refer to the MnCO 3 /MnFe 2 O 4 equilibrium as a representative example: (1) These are expressed per unit of Mn and unit of Fe to obtain a ready relation between their activity ratio and the free energy of the reaction.In this case, we obtained planar diagrams for the dependence of the chemical potentials of transition elements RTln(a Mn /a Fe ) vs. the chemical potential of oxygen RTln(pO 2 ), for a specified partial pressure of CO 2 .Thermody- namic data required for the calculations of free energy were retrieved from the database of the FACTSAGE v.5.5 software package [41].
These chemical potential diagrams can be a suitable guideline for the solid-state kinetics of the formation of generic spinels AB 2 O 4 , which has been related to the chemical potential gradient of the controlling species across the reaction product, namely ∆µ A , for conditions when the controlling species is A n+ (Figure 1a,b) or −∆µ B for B m+ (Figure 1c,d) [42].In fact, the controlling cationic species may also depend on the redox conditions and tetrahedral or octahedral site occupancy, with variable degrees of inversion, and possibly also deviations from the nominal trivalent/divalent ratio, 1 [43]; this may be compensated by cation vacancies Fe, Mn) 3−δ O 4 [44].High-energy milling or subsequent firing may also induce variable degrees of vacancy ordering [45], with an impact on diffusivity.
Thus, one must consider the combined differences ∆µ A − ∆µ B to account for both cases of controlling cationic species or their combination, assuming that charge neutrality is readily sustained by electronic conductivity, relying on the hopping of polarons [46].In addition, porous samples are expected to allow ready oxygen transport, minimising local gradients of the chemical potential of oxygen ( ∆µ O 2 ≈ 0 .Otherwise, one should consider the co-diffusion of cationic and anionic species, which also depends on ∆µ O 2 (Figure 1b,d).In fact, the diffusivities of different cationic species in spinels [47] are expected to exceed the diffusivity of oxygen ions [48], at least at high temperatures (≥1200

Experimental Methods
The MnO + Fe O (Sigma Aldrich, St. Louis, MO, USA, 99%) powder mixtur used as a case study to demonstrate the mechanosynthesis of MnFe O at room tem ture from precursor mixtures with oxygen balance.MnO was obtained by the redu of MnO (Alfa Aesar, Ward Hill, MA, USA, 99%) in flowing 10% H -90% N2 at 850 ° 5 h.Mechanosynthesis was performed in air, in a PM100 Retsch planetary ball mill, a TZP vial (Retsch, Haan, Germany, 125 cm 3 ) and TZP balls (TOSOH Co., Tokyo, J of diameters 10 mm and 15 mm at a ratio of 2: 1, with a balls/powder weight ratio of at a rotational speed of 500 rpm, and for 3 or 9 h of cumulative milling time.Millin performed for periods of 10 min with a subsequent pause of 5 min to prevent overhe by attrition.Powder X-ray diffraction (XRD) was performed for the phase identific of precursors and reacted mixtures after mechanosynthesis, using a Rigaku SmartL diffractometer (Rigaku, Tokyo, Japan , in the X-ray fluorescence reduction mode of detector with a CuKα radiation source (40 kV, 30 mA), in the 2θ range 10−90°, with size = 0.02°, and with a speed of 3 °/min.Nickel powder (Alfa Aesar, 99.9%) was add an internal reference to quantify phase contents.
The fully oxidised oxide mixture MnO + Fe O was selected as a case study o cursors which require a combination of mechanical activation and subsequent the chemical treatment.In this case, mechanical activation was performed in a TZP vial TZP zirconia balls of diameter 10 mm and with a balls/powder weight ratio of 10 350 or 450 rpm, for 10 h of cumulative milling time, with periods of 5 min milling foll by a 5 min pause.Subsequent thermal treatments of activated powders were perfo

Experimental Methods
The MnO + Fe 2 O 3 (Sigma Aldrich, St. Louis, MO, USA, 99%) powder mixture was used as a case study to demonstrate the mechanosynthesis of MnFe 2 O 4 at room temperature from precursor mixtures with oxygen balance.MnO was obtained by the reduction of MnO 2 (Alfa Aesar, Ward Hill, MA, USA, 99%) in flowing 10% H 2 -90% N 2 at 850 • C for 5 h.Mechanosynthesis was performed in air, in a PM100 Retsch planetary ball mill, using a TZP vial (Retsch, Haan, Germany, 125 cm 3 ) and TZP balls (TOSOH Co., Tokyo, Japan) of diameters 10 mm and 15 mm at a ratio of 2:1, with a balls/powder weight ratio of 14:1, at a rotational speed of 500 rpm, and for 3 or 9 h of cumulative milling time.Milling was performed for periods of 10 min with a subsequent pause of 5 min to prevent overheating by attrition.Powder X-ray diffraction (XRD) was performed for the phase identification of precursors and reacted mixtures after mechanosynthesis, using a Rigaku SmartLab SE diffractometer (Rigaku, Tokyo, Japan , in the X-ray fluorescence reduction mode of a 2D detector with a CuK α radiation source (40 kV, 30 mA), in the 2θ range 10−90 • , with a step size = 0.02 • , and with a speed of 3 • /min.Nickel powder (Alfa Aesar, 99.9%) was added as an internal reference to quantify phase contents.
The fully oxidised oxide mixture MnO 2 + Fe 2 O 3 was selected as a case study of precursors which require a combination of mechanical activation and subsequent thermochemical treatment.In this case, mechanical activation was performed in a TZP vial, with TZP zirconia balls of diameter 10 mm and with a balls/powder weight ratio of 10:1, at 350 or 450 rpm, for 10 h of cumulative milling time, with periods of 5 min milling followed by a 5 min pause.Subsequent thermal treatments of activated powders were performed in air and in argon atmospheres in the temperature range of 750 to 1000 • C. XRD was used for phase identification in as-milled precursors and after thermal treatments.
A mixture of MnO 2 + FeCO 3 -based natural siderite was used as a case study of mechanosynthesis from an oxide + carbonate precursor mixture, under different milling conditions, as shown in Table 1.Several samples which were mechanically activated at 450 rpm, were subsequently treated at temperatures from 550 • C to 900 • C for times ranging from 2 h to 8 h in an Ar atmosphere.The cation composition of the natural siderite was assessed by inductively coupled plasma optical emission spectroscopy (ICP-OES) (Jobin Yvon Activa M, Horiba, Kyoto, Japan), yielding: 70.5% Fe, 18.6% Mg, 5.6% Ca, 3.4% Si, and 1.9% Al.

Synthesis from Oxide and/or Metallic Precursors
Figure 2 shows the chemical potential diagram for metal-oxide phases in the Mn − Fe − O system at room temperature, including the driving forces for the solid-state reaction from the stoichiometric MnO + Fe 2 O 3 mixture; this confirms the prospects of room-temperature mechanosynthesis.The driving force is expected to converge to ∆µ Mn − ∆µ Fe ≈ 35 kJ/mol, which corresponds to the chemical potential differences between the three-phase contacts MnO/Mn Oxygen balance is also expected for the synthesis of MnFe O from mixtures of Mn O and Fe O : with the free energy of the reaction ∆ = −24 kJ/mol.In fact, the 1/3Mn O +2/3Fe O precursor mixture may even provide better kinetic conditions for the mechanosynthesis In addition, the MnO + Fe 2 O 3 powder mixture yields a precise oxygen balance in contact with O 2 -lean atmospheres: ( The free energy ∆G R = −25 kJ/mol shows that this reaction is spontaneous, assuming self-controlled redox conditions, as expected in sealed or inert atmospheres or under moderate vacuum [17].In fact, the redox pairs MnO/Mn In this case, the free energy of this reaction ∆G R = +67 kJ/mol shows that the inert atmosphere (Ar) does not meet this requirement at room or intermediate temperature (Figure 3a) since the redox conditions of Ar only reach the stability window of MnFe 2 O 4 at temperatures above about 800 • C (Figure 3b).Firing in air would require even higher temperatures, namely above 1100 • C (Figure 3c); this suggests an apparent contradiction between the actual thermodynamic predictions and the reported experimental results obtained in Ar or air at a relatively low temperature [21].In this case, one may assume that the oxygen balance was reached by the incorporation of a fraction of metallic Fe from the milling balls and vial, as mentioned by others [18], i.e.: 1/3Fe + 4/9Mn 2 O 3 + 8/9Fe 2 O 3 → Mn 8/9 Fe 19/9 O 4 . (7) A similar compensation to reach the oxygen balance may be provided by a fraction of Mn, as reported also by Ding et al. [21]: The free energy of this reaction ∆ = −95 kJ/mol also shows that this should be spontaneous, except for difficulties raised by the high instability of the metallic precursor.
In this case, the free energy ∆ = +108 kJ/mol shows that reactivity should require highly reducing conditions or the synthesis of MnFe O in air at high temperatures, i.e., 1100 °C [49] or higher temperatures [8].Inert atmospheres or a vacuum may allow syn- A similar compensation to reach the oxygen balance may be provided by a fraction of Mn, as reported also by Ding et al. [21]: The free energy of this reaction ∆G R = −95 kJ/mol also shows that this should be spontaneous, except for difficulties raised by the high instability of the metallic precursor.Figure 3 also shows that even higher firing temperatures should be required for the synthesis of manganese ferrite from the most stable oxide mixture (MnO 2 + Fe 2 O 3 ): In this case, the free energy ∆G R = +108 kJ/mol shows that reactivity should require highly reducing conditions or the synthesis of MnFe 2 O 4 in air at high temperatures, i.e., 1100 • C [49] or higher temperatures [8].Inert atmospheres or a vacuum may allow synthesis at somewhat lower temperatures but still in the order of 800  [20], as follows: Mn Note that this reaction should be highly spontaneous in a wet hydrogen atmosphere (∆G R = −204 kJ/mol).A fraction of metallic precursor added to mixtures of MnO 2 and Fe 2 O 3 may also allow oxygen balance by the partial substitution of hematite: (∆G R = −171 kJ/mol) or by changing the Mn : Fe ratio in the manganese ferrite: This metallic fraction may be introduced by the erosion of steel milling media [17,18].

Synthesis from Carbonate + Carbonate or Carbonate + Oxide Precursor Mixtures
Figure 4 shows the stability ranges of iron carbonate and manganese carbonate and their equilibrium with the oxide phase or metallic Fe.This emphasises that the high-energy milling of carbonate mixtures is unlikely to yield manganese ferrite at room temperature due to the wide stability range of manganese carbonate, even when the partial pressure of CO 2 remains low (Figure 4a).An onset of manganese ferrite from carbonate precursors and under a CO 2 -rich atmosphere is only expected upon heating to temperatures above 560 K, as also shown in Figure 4c, or somewhat lower temperatures in a CO 2 -lean atmosphere, such as above 473 K with pCO 2 ≈ 0.01 atm, after previous decomposition of iron carbonate.In fact, the redox range of FeCO 3 stability in Figure 4 narrows rapidly upon approaching this temperature (Figure 4b), in close agreement with experimental evidence that the decomposition of FeCO 3 occurs likely upon heating above about 200 • C for synthetic FeCO 3 or at higher temperatures for low-grade natural siderite minerals [50].In this case, the decomposition of siderite only retains the divalent state of iron as a thermodynamically unstable phase at intermediate temperatures, evolving to Fe 3 O 4 + Fe in an inert atmosphere, and progressing by extinction of the fraction of metallic Fe and subsequent oxidation to magnetite or hematite in sufficiently oxidising atmospheres.
The stability ranges of manganese carbonate [51] and iron carbonate [52] and their decomposition temperatures also depend on operating atmospheres and may be delayed by kinetic limitations.For example, the decomposition of MnCO in atmospheres with a moderate partial pressure of CO (≈20 kPa) and upon heating at 6 K/min reached a peak at ≈ 685 K, and the corresponding activation energy was about 270 kJ/mol [51].From these parameters, one may predict a decomposition peak at ≈ 607 K upon heating at a very low rate (0.1 K/min); this is close to thermodynamic predictions for the decomposition of manganese carbonate (MnCO → MnO + CO ) at  > 607 K under CO ≈ 0.2 atm.Thus, one may expect the conversion of both carbonate precursors on heating to intermediate temperatures, and the stability diagram should converge to the corresponding oxide phases (Figure 3).  Figure 4 also shows that the synthesis of manganese ferrite by the mechanical activation of MnCO + Fe O powder mixtures should require subsequent heating to intermediate temperatures at the onset of a stability window for MnFe O .In fact, synthesis has been reported after the mechanical activation of MnCO + Fe O precursors and then calcining at 673 K [25], which is somewhat higher than the decomposition temperature predicted for MnCO → MnO + CO in a CO atmosphere (≈ 649 K).Thus, one cannot exclude the possibility of the onset of MnO formed as an intermediate phase before the conversion of the resulting oxide mixture to MnFe O , as described by Equation (3).
Room-temperature mechanosynthesis of MnFe O from manganese dioxide and iron carbonate was demonstrated recently [26]; this may seem to contradict the thermodynamic equilibrium predictions at room temperature in a CO -rich atmosphere (Figure 5a), which suggests thermodynamic feasibility for the onset of MnCO by the partial reduction of MnO , combined with the oxidative decomposition of FeCO : with ∆ = −58 kJ/mol.However, the carbonation of manganese oxides may be hindered The stability ranges of manganese carbonate [51] and iron carbonate [52] and their decomposition temperatures also depend on operating atmospheres and may be delayed by kinetic limitations.For example, the decomposition of MnCO 3 in atmospheres with a moderate partial pressure of CO 2 (≈20 kPa) and upon heating at 6 K/min reached a peak at ≈ 685 K, and the corresponding activation energy was about 270 kJ/mol [51].From these parameters, one may predict a decomposition peak at ≈ 607 K upon heating at a very low rate (0.1 K/min); this is close to thermodynamic predictions for the decomposition of manganese carbonate ( MnCO 3 → MnO + CO 2 ) at T > 607 K under pCO 2 ≈ 0.2 atm.Thus, one may expect the conversion of both carbonate precursors on heating to intermediate temperatures, and the stability diagram should converge to the corresponding oxide phases (Figure 3).
Figure 4 also shows that the synthesis of manganese ferrite by the mechanical activation of MnCO 3 + Fe 2 O 3 powder mixtures should require subsequent heating to intermediate temperatures at the onset of a stability window for MnFe 2 O 4 .In fact, synthesis has been reported after the mechanical activation of MnCO 3 + Fe 2 O 3 precursors and then calcining at 673 K [25], which is somewhat higher than the decomposition temperature predicted for MnCO 3 → MnO + CO 2 in a CO 2 atmosphere (≈ 649 K).Thus, one cannot exclude the possibility of the onset of MnO formed as an intermediate phase before the conversion of the resulting oxide mixture to MnFe 2 O 4 , as described by Equation (3).
Room-temperature mechanosynthesis of MnFe 2 O 4 from manganese dioxide and iron carbonate was demonstrated recently [26]; this may seem to contradict the thermodynamic equilibrium predictions at room temperature in a CO 2 -rich atmosphere (Figure 5a), which suggests thermodynamic feasibility for the onset of MnCO 3 by the partial reduction of MnO 2 , combined with the oxidative decomposition of FeCO 3 : with ∆G R = −58 kJ/mol.However, the carbonation of manganese oxides may be hindered by kinetic limitations, except for the ready carbonation of MnO [53], requiring sufficiently reducing conditions to reach the redox range of MnO, i.e., RTln(pO 2 ) < −387 kJ/mol at room temperature.In the reported conditions of mechanical activation of the FeCO 3 + MnO 2 reactants [26], the reducing conditions should be established by the FeCO 3 /Fe 2 O 3 redox pair, reaching only RTln(pO 2 ) ≈ −322 kJ/mol in a CO 2 atmosphere (Figure 5).Thus, we devised an alternative metastable diagram (dashed lines in Figure 5), which is based on metastable two-phase boundaries in the absence of manganese carbonate; this includes the FeCO 3 /Fe 2 O 3 boundary, combined with metastable two-phase boundaries FeCO 3 /Mn 3 O 4 and FeCO 3 /MnFe 2 O 4 , and the oxide/oxide boundaries expected for the Mn − Fe − O system in the moderate-to-oxidising range.This metastable diagram provides a plausible explanation for the onset of MnFe 2 O 4 at room temperature, assuming that the conditions of high-energy milling are sufficient to overcome kinetic restrictions.Note also that the metastable window of MnFe 2 O 4 may even be enlarged by slight overheating (Figure 5b), which may be caused by attrition during mechanical activation.

Synthesis from Hydroxide + Oxide or Hydroxide + Oxyhydroxide Precursor Mixtures
The mechanosynthesis of manganese ferrite from hydroxide Mn(OH) + 2Fe(OH) mixtures or hydroxide + oxide Mn(OH) + Fe O mixtures was also clearly demonstrated [23].However, the chemical potential diagrams (Figure 6a) show that the stable phases in contact with manganese ferrite should be Mn(OH) and FeOOH , because the Fe(OH)

Synthesis from Hydroxide + Oxide or Hydroxide + Oxyhydroxide Precursor Mixtures
The mechanosynthesis of manganese ferrite from hydroxide Mn(OH) 2 + 2Fe(OH) 3 mixtures or hydroxide + oxide Mn(OH) 2 + Fe 2 O 3 mixtures was also clearly demonstrated [23].However, the chemical potential diagrams (Figure 6a) show that the stable phases in contact with manganese ferrite should be Mn(OH) 2 and FeOOH, because the Fe(OH) 3 phase is unstable and transforms readily to goethite FeOOH during the high-energy milling of hydroxide mixtures:

Synthesis from Oxide Mixtures
Figure 7 shows the feasibility of the mechanosynthesis of MnFe O (JCPDS 01-074-2403) from stoichiometric powder mixtures of MnO (JCPDS 01-075-1090) + Fe O (JCPDS 01-087-1166) at a moderate milling rate of 500 rpm for 3 h to 9 h.Though large fractions of reactants are still present after milling for a relatively short milling time, one already observes significant intensity in the main reflections of the spinel phase after 3 h, using Ni (JCPDS 01-087-0712) as reference.The intensities of precursor phases then drop markedly after milling for 9 h, and the spinel phase becomes prevailing, co-existing with residual contents of reactants (Fe O and MnO) and the onset of magnetite  The stability of the goethite phase may also explain its onset as an intermediate phase, combined with MnO [23], by the mechanical activation of mixtures of manganese hydroxide + hematite: Nevertheless, the stability range of MnFe 2 O 4 in equilibrium with the hydroxide + oxyhydroxide mixture was still very narrow at room temperature (Figure 6a), even in fairly dry conditions and only up to about pH 2 O ≈ 0.03 atm, when the chemical potential driving force ∆µ Mn − ∆µ Fe vanished.Thus, one may be surprised by the evidence that MnFe 2 O 4 still formed after a sufficiently long time (25 h) in air.A plausible explanation for this experimental evidence may be based on slight overheating under high-energy milling, taking into account that the stability range of MnFe 2 O 4 increases significantly with slight heating (Figure 6b).Note that the authors of ref. [23] did not mention if milling was stopped at regular intervals to prevent overheating by attrition.

Synthesis from Oxide Mixtures
Figure 7 shows the feasibility of the mechanosynthesis of MnFe 2 O 4 (JCPDS 01-074-2403) from stoichiometric powder mixtures of MnO (JCPDS 01-075-1090) +Fe 2 O 3 (JCPDS 01-087-1166) at a moderate milling rate of 500 rpm for 3 h to 9 h.Though large fractions of reactants are still present after milling for a relatively short milling time, one already observes significant intensity in the main reflections of the spinel phase after 3 h, using Ni (JCPDS 01-087-0712) as reference.The intensities of precursor phases then drop markedly after milling for 9 h, and the spinel phase becomes prevailing, co-existing with residual contents of reactants (Fe 2 O 3 and MnO) and the onset of magnetite Fe 3 O 4 e (JCPDS 01-079-0418).This confirms the three-phase contact MnFe 2 O 4 /Fe 2 O 3 /Fe 3 O 4 , as indicated in Figure 2. On the contrary, one did not detect Mn 3 O 4 (JCPDS 01-080-0382) and could not confirm the three-phase contact MnFe 2 O 4 /MnO/Mn 3 O 4 in Figure 2. Still, one may assume that the redox condition remains reducing and is nearly controlled by the Fe 2 O 3 /Fe 3 O 4 redox pair; this retains conditions for reactivity at room temperature, and the kinetics are mainly determined by the chemical potential gradients of the transition metal elements (∆µ Mn −∆µ Fe ) shown in Figure 2. The gradual conversion of precursors was also assessed by the reference intensity ratio (RIR) [54] based on the integrated intensities (Figure 7) of the main reflections of Fe O ( ( ) ) and MnO ( ( ) ), taking the main reflection of Ni ( ( ) ) as a reference.The Ni standard was added as 20 wt.% of the reactants' contents in the stoichiometric mixture of MnO + Fe O .The composition of this three-phase mixture (26.6 .% MnO + 57.7 .% Fe O + 16.7 .% Ni) was then combined with their intensity ratios to obtain the calibration factors, and these were used to assess the contents of residual reactants after 3 h and after 9 h, as shown in Table 2.The gradual conversion of precursors was also assessed by the reference intensity ratio (RIR) [54] based on the integrated intensities (Figure 7) of the main reflections of  (26.6 wt.%MnO + 57.7 wt.%Fe 2 O 3 + 16.7 wt.%Ni) was then combined with their intensity ratios to obtain the calibration factors, and these were used to assess the contents of residual reactants after 3 h and after 9 h, as shown in Table 2.
Mechanical activation was performed at 350 rpm or 450 rpm for 10 h, and changes in milling conditions only yielded a decrease in the intensity of reactant reflections.The synthesis of MnFe 2 O 4 required subsequent thermochemical treatment at sufficiently high temperatures to overcome the redox gap, such as heating to about 1000 • C in air, as indicated by the thermodynamic predictions (Figure 2), and firing at lower temperatures converted the MnO 2 precursor to a bixbyite phase, which may contain significant contents of Fe, i.e., ( Mn, Fe) 2 O 3 , in close agreement with thermodynamic modelling [5].Otherwise, Figure 3 suggests that firing in an inert (Ar) atmosphere may allow the onset of MnFe 2 O 4 at ≈800 • C. In fact, deviations from stoichiometry may explain the results obtained by firing at 750 • C in Ar, which already showed the onset of a spinel phase, co-existing with Fe 2 O 3 and traces of Mn 2 O 3 (JCPDS 01-076-0150).The corresponding thermodynamic predictions suggest that MnFe 2 O 4 should co-exist with Fe 2 O 3 and Mn 3 O 4 rather than Mn 2 O 3 .A fraction of residual Fe 2 O 3 was still present after firing at 900 • C (Figure 8), indicating kinetic limitations and suggesting that the composition of the spinel phase still deviates from equilibrium, i.e., Mn 1+δ Fe 2−δ O 4 .2), and firing at lower temperatures converted the MnO precursor to a bixbyite phase, which may contain significant contents of Fe, i.e., (Mn, Fe) O , in close agreement with thermodynamic modelling [5].
Otherwise, Figure 3 suggests that firing in an inert (Ar) atmosphere may allow the onset of MnFe O at ≈800 °C.In fact, deviations from stoichiometry may explain the results obtained by firing at 750 °C in Ar, which already showed the onset of a spinel phase, coexisting with Fe O and traces of Mn O (JCPDS 01-076-0150).The corresponding thermodynamic predictions suggest that MnFe O should co-exist with Fe O and Mn O rather than Mn O .A fraction of residual Fe O was still present after firing at 900 °C (Figure 8), indicating kinetic limitations and suggesting that the composition of the spinel phase still deviates from equilibrium, i.e., Mn  Fe  O .

Synthesis from Carbonate + Oxide Mixtures
Figure 9 shows the results of the mechanical activation or mechanosynthesis of mixtures of MnO + FeCO -based siderite achieved under the different conditions detailed in Table 1.We found significant effects of the milling rate, which caused a decrease in the

Synthesis from Carbonate + Oxide Mixtures
Figure 9 shows the results of the mechanical activation or mechanosynthesis of mixtures of MnO 2 + FeCO 3 -based siderite achieved under the different conditions detailed in Table 1.We found significant effects of the milling rate, which caused a decrease in the reflections of both precursors and showed an onset of the main reflections of the spinel phase upon changing from 350 rpm to 450 rpm.The milling media also played a key role in the structural changes since the use of mild nylon vial hinders conversion to the spinel phase and may even enhance the crystallinity of the carbonate phase.On the contrary, the use of the TZP vial and more severe milling conditions allowed a complete extinction of the XRD reflections of both precursors.In fact, the free energy ∆G R = −80 kJ/mol suggests prospects for complete conversion to the spinel: Thus, mechanosynthesis can be attained by sufficiently high-energy milling, achieved with a high balls/powder ratio, a fraction of heavier balls, or a combination of higher rotation speed and longer time [26].
Still, the reflections of the spinel phase are located between the corresponding reflections of MnFe 2 O 4 (dashed lines) and Fe 3 O 4 (dotted lines), suggesting partial Mn-deficiency, i.e., Mn 1−x Fe 2+x O 4 .Note that magnetite and manganese ferrite possess identical structures.In addition, a fraction of the initial precursors may be incorporated in a significant amorphous phase [26], possibly combined with the gangue components from the natural siderite precursor, which contains relatively large fractions of Mg and Ca.These impurities may exert significant effects on the structural features and properties of manganese ferrite [55,56].
Subsequent heat treatments at intermediate temperatures were planned to confirm that the conversion of MnO 2 + FeCO 3 -based siderite to MnFe 2 O 4 is hindered mainly by kinetics.The prevailing conversion to the spinel only occurred at temperatures ≥ 900 • C, whereas intermediate temperatures yielded mainly intermediate phases:.
In fact, we expected a ready decomposition of both precursors upon heating [50,51] before reaching the lowest firing temperature in Figure 10 (550 • C).Heat treatments at higher temperatures may be controlled by a gradual conversion of the intermediate oxide phase to the spinel phase, as emphasised by the results obtained by firing at 650 • C for different times (Equation ( 4)).
In this case, one may assume that the driving force for the synthesis of MnFe 2 O 4 corresponds to the chemical potential differences between the two-phase lines Fe 3 O 4 /MnFe 2 O 4 and Mn 3 O 4 → MnFe 2 O 4 , as shown in Figure 2. tions of MnFe O (dashed lines) and Fe O (dotted lines), suggesting partial Mn-deficiency, i.e., Mn Fe O .Note that magnetite and manganese ferrite possess identical structures.In addition, a fraction of the initial precursors may be incorporated in a significant amorphous phase [26], possibly combined with the gangue components from the natural siderite precursor, which contains relatively large fractions of Mg and Ca.These impurities may exert significant effects on the structural features and properties of manganese ferrite [55,56].
In fact, we expected a ready decomposition of both precursors upon heating [50,51] before reaching the lowest firing temperature in Figure 10 (550 °C).Heat treatments at higher temperatures may be controlled by a gradual conversion of the intermediate oxide phase to the spinel phase, as emphasised by the results obtained by firing at 650 °C for different times (Equation ( 4)).
In this case, one may assume that the driving force for the synthesis of MnFe O corresponds to the chemical potential differences between the two-phase lines Fe O / MnFe O and Mn O → MnFe O , as shown in Figure 2.

Conclusions
Thermodynamic predictions in the form of chemical potential diagrams provide sound guidelines to assess the feasibility of the solid-state synthesis of manganese ferrite

Conclusions
Thermodynamic predictions in the form of chemical potential diagrams provide sound guidelines to assess the feasibility of the solid-state synthesis of manganese ferrite from different precursors, including oxides, metals, carbonates, hydroxides or oxy-hydroxides, and their combinations; this is useful to avoid undue experimental work with unsuitable precursor mixtures and provides suitable recommendations for subsequent heat treatments in air or controlled atmospheres for conditions where mechanical activation alone is ill suited to induce the conversion of reactants.Direct mechanosynthesis was predicted for representative combinations of oxide + oxide or oxide + metal precursor mixtures with oxygen balance, and the experimental results confirm the thermodynamic guidelines for the reactant mixture of MnO + Fe 2 O 3 .In this case, mechanosynthesis at room temperature yielded a slightly nonstoichiometric ferrite and residual fractions of reactants (≈16% Fe 2 O 3 and ≈2% MnO) after 9 h.On the contrary, precursors without oxygen balance require a combination of mechanical activation and subsequent calcining under controlled thermochemical conditions, as confirmed experimentally for MnO 2 + Fe 2 O 3 .In this case, this may still be obtained by subsequent thermal treatments in a neutral atmosphere at T ≥ 750 • C, as indicated by the thermodynamic predictions and confirmed experimentally.The formation of MnFe 2 O 4 from the oxide + carbonate mixture was predicted by metastable diagrams in contact with CO 2 -based atmospheres and was also confirmed by the experimental results.In this case, kinetic restrictions may hinder the conversion of reactants under mild mechanical activation, but the ferrite phase still forms when increasing the balls/powder ratio and using a fraction of heavier balls.Otherwise, the full conversion of reactants to MnFe 2 O 4 may still require subsequent calcination at ≥650 • C.

Figure 1 .
Figure 1.Schematic representation of mechanisms of solid-state synthesis of AB2O4 spinels fro and B O precursors under the corresponding gradients of chemical potentials, controlled transport of a cationic species A (a,b) or B (c,d), with ready gas phase transport in a p reacting medium (a,c), or under additional limitations of gas phase transport and transport of ions (b,d).

Figure 1 .
Figure 1.Schematic representation of mechanisms of solid-state synthesis of AB 2 O 4 spinels from AO and B 2 O 3 precursors under the corresponding gradients of chemical potentials, controlled by the transport of a cationic species A n+ (a,b) or B m+ (c,d), with ready gas phase transport in a porous reacting medium (a,c), or under additional limitations of gas phase transport and transport of oxide ions (b,d).

3 O 4 / 19 Figure 2 .
Figure2shows the chemical potential diagram for metal-oxide phases in the Mn − Fe − O system at room temperature, including the driving forces for the solid-state reaction from the stoichiometric MnO + Fe 2 O 3 mixture; this confirms the prospects of room-temperature mechanosynthesis.The driving force is expected to converge to ∆µ Mn − ∆µ Fe ≈ 35 kJ/mol, which corresponds to the chemical potential differences between the three-phase contacts MnO/Mn 3 O 4 /MnFe 2 O 4 and Fe 3 O 4 /Fe 2 O 3 /MnFe 2 O 4 , as shown in Figure 2, for sufficiently porous samples with the ready transport of O 2 and minimum gradients of the chemical potential of oxygen ∆µ O 2 .Materials 2024, 17, x FOR PEER REVIEW 6 of 19

Figure 2 .
Figure 2. Chemical potential diagrams for the Mn − Fe − O system at room temperature.

Figure 3 .
Figure 3.Chemical potential diagrams for the reactivity of different combinations of oxide and/or metallic precursors at 773 K (a), 1073 K (b), and 1373 K (c).The shaded green area shows the stability range of manganese ferrite, and the shaded red area is the redox range which may be adjusted with the H /H O redox pair, from H -rich conditions H : H O = 100 to H -lean conditions H : H O = 0.01.

Figure 3
Figure 3 also shows that even higher firing temperatures should be required for the synthesis of manganese ferrite from the most stable oxide mixture (MnO + Fe O ):

FeFigure 3 .
Figure 3.Chemical potential diagrams for the reactivity of different combinations of oxide and/or metallic precursors at 773 K (a), 1073 K (b), and 1373 K (c).The shaded green area shows the stability range of manganese ferrite, and the shaded red area is the redox range which may be adjusted with the H 2 /H 2 O redox pair, from H 2 -rich conditions H 2 :H 2 O = 100 to H 2 -lean conditions H 2 :H 2 O = 0.01.

Figure 4 .
Figure 4.Chemical potential diagrams for the stability of iron and manganese carbonates and their equilibrium with corresponding oxides at 298 K with CO = 0.0004 atm (a) and at 453 K (b), 560 K (c), and 643 K (d) with CO = 1.0 atm.

Figure 4 .
Figure 4.Chemical potential diagrams for the stability of iron and manganese carbonates and their equilibrium with corresponding oxides at 298 K with pCO 2 = 0.0004 atm (a) and at 453 K (b), 560 K (c), and 643 K (d) with pCO 2 = 1.0 atm.

Materials 2024, 17 ,Figure 5 .
Figure 5.Chemical potential diagram for the Mn − Fe − O − C system at CO = 0.5 atm at room temperature (a) and at 373 K (b).The solid lines show equilibrium diagrams, and the dashed lines show metastable predictions for reactivity between FeCO and MnO , assuming that the carbonation of manganese oxide is hindered.

Figure 5 .
Figure 5.Chemical potential diagram for the Mn − Fe − O − C system at pCO 2 = 0.5 atm at room temperature (a) and at 373 K (b).The solid lines show equilibrium diagrams, and the dashed lines show metastable predictions for reactivity between FeCO 3 and MnO 2 , assuming that the carbonation of manganese oxide is hindered.

Materials 2024, 17 ,Figure 6 .
Figure 6.Chemical potential diagram for the Mn − Fe − O − H system at 298 K with H O = 0.03 atm () and 343 K with H O = 0.10 atm (b).

4 ⁄
Figure7shows the feasibility of the mechanosynthesis of MnFe O (JCPDS 01-074-2403) from stoichiometric powder mixtures of MnO (JCPDS 01-075-1090) + Fe O (JCPDS 01-087-1166) at a moderate milling rate of 500 rpm for 3 h to 9 h.Though large fractions of reactants are still present after milling for a relatively short milling time, one already observes significant intensity in the main reflections of the spinel phase after 3 h, using Ni (JCPDS 01-087-0712) as reference.The intensities of precursor phases then drop markedly after milling for 9 h, and the spinel phase becomes prevailing, co-existing with residual contents of reactants (Fe O and MnO) and the onset of magnetite Fe O e (JCPDS 01-079-0418).This confirms the three-phase contact MnFe O Fe O Fe O ⁄ ⁄ , as indicated in Figure 2. On the contrary, one did not detect Mn O (JCPDS 01-080-0382) and could not confirm the three-phase contact MnFe O MnO Mn O ⁄ ⁄ in Figure 2. Still, one may assume that the redox condition remains reducing and is nearly controlled by the Fe 2 O 3 Fe 3 O 4 ⁄ redox pair; this retains conditions for reactivity at room temperature, and the kinetics are mainly determined by the chemical potential gradients of the transition metal elements (∆ − ∆ ) shown in Figure 2.

Figure 6 .
Figure 6.Chemical potential diagram for the Mn − Fe − O − H system at 298 K with pH 2 O = 0.03 atm (a) and 343 K with pH 2 O = 0.10 atm (b).

Materials 2024 , 19 Figure 7 .
Figure 7. X-ray diffractograms of samples obtained by mechanosynthesis of MnO + Fe O powder mixtures milled at 500 rpm for 3 h and 9 h.Ni powder was used as an internal standard as a guideline for differences in relative intensities of residual precursor fractions and onset of reaction products.The markers identify reflections ascribed to MnO (), Fe O (), MnFe O (), Fe O () and Ni ().The relative areas under the main reflection of Fe O (104), MnO (200), and Ni (111), are shown in black, green, and red, respectively.

Figure 7 .
Figure 7. X-ray diffractograms of samples obtained by mechanosynthesis of MnO + Fe 2 O 3 powder mixtures milled at 500 rpm for 3 h and 9 h.Ni powder was used as an internal standard as a guideline for differences in relative intensities of residual precursor fractions and onset of reaction products.The markers identify reflections ascribed to MnO (  Fe 2 O 3 (I Fe 2 O 3 (104) ) and MnO (I MnO(200) ), taking the main reflection of Ni (I Ni(111) ) as a reference.The Ni standard was added as 20 wt.% of the reactants' contents in the stoichiometric mixture of MnO + Fe 2 O 3 .The composition of this three-phase mixture

Figure 8 .
Figure 8. X-ray diffractograms of samples obtained by mechanical activation of MnO + Fe O powder mixtures milled at 350 rpm or 450 rpm for 10 h and then fired in air or Ar at different temperatures for 2 h.The markers identify reflections ascribed to MnO (), Fe O (), MnFe O (), and Mn O ().

Figure 8 .
Figure 8. X-ray diffractograms of samples obtained by mechanical activation of MnO 2 +Fe 2 O 3 powder mixtures milled at 350 rpm or 450 rpm for 10 h and then fired in air or Ar at different temperatures for 2 h.The markers identify reflections ascribed to MnO 2 (

Figure 9 .Figure 9 .
Figure9.X-ray diffractograms of samples processed from MnO + FeCO -based siderite milled under the conditions listed in Table1.The vertical lines show expected reflections of the most relevant phases as a guideline for conversion to the spinel phase.The markers identify reflections ascribed to MnO (), FeCO () and SiO ().Subsequent heat treatments at intermediate temperatures were planned to confirm that the conversion of MnO + FeCO -based siderite to MnFe O is hindered mainly by kinetics.The prevailing conversion to the spinel only occurred at temperatures ≥900 °C, whereas intermediate temperatures yielded mainly intermediate phases:

3 Figure 10 .
Figure 10.X-ray diffractograms of samples processed from MnO 2 + FeCO 3 -based siderite milled at 450 rpm and then fired at different temperatures for 2 h or 8 h in Ar atmosphere.The markers identify reflections ascribed to MnO 2 (

Table 1 .
Conditions of mechanical activation or mechanosynthesis of MnO 2 + siderite powder mixtures.
3 O 4 and Fe 3 O 4 /Fe 2 O 3 provide nearly stable redox conditions, at nearly identical chemical potentials of O 2 , and may act as temporary redox buffers in nominally inert atmospheres (e.g., Ar) or even in air.In these conditions, one may assume that the MnO/MnFe 2 O 4 equilibrium converges towards the MnO − MnFe 2 O 4 − Mn 3 O 4 triple point, and Fe 2 O 3 /MnFe 2 O 4 equilibrium converges towards the Fe 2 O 3 − MnFe 2 O 4 − Fe 3 O 4 triple point.Oxygen balance is also expected for the synthesis of MnFe 2 O 4 from mixtures of Mn 3 O 4 and Fe 3 O 4 : 1/3Mn 3 O 4 + 2/3Fe 3 O 4 → MnFe 2 O 4 ; (4) with the free energy of the reaction ∆G R = −24 kJ/mol.In fact, the 1/3Mn 3 O 4 +2/3Fe 3 O 4 precursor mixture may even provide better kinetic conditions for the mechanosynthesis of MnFe 2 O 4 as compared to the MnO + Fe 2 O 3 mixture, based on the structural similarity of Fe 3 O 4 and MnFe 2 O 4 (space group Fd3m).Thus, one expects gradual concentration profiles across a diffuse interface Fe 3 O 4 /MnFe 2 O Mn 2 O 3 and Mn 3 O 4 ) and, eventually, down to the Mn 3 O 4 /MnFe 2 O 4 interface in Figure 2. In fact, the two-phase Fe 3 O 4 /Fe 2 O 3 redox pair is strongly reducing relative to the redox pairs MnO 2 /Mn 2 O 3 and Mn 3 O 4 /Mn 2 O 3 and less reducing relative to the redox conditions of the three-phase contact Mn 3 O 4 /Fe 2 O 3 /MnFe 2 O 4 .Other oxide mixtures require different approaches to meet the oxygen balance.Ding et al. [21] reported the synthesis of a MnFe 2 O 4 -based spinel by the mechanical activation of Mn 2 O 3 + Fe 2 O 3 powder mixtures in Ar atmosphere: 4boundary, which is represented by a dotted line in Figure2.In addition, the Mn : Fe ratio in manganese ferrite may deviate from the nominal stoichiometry, i.e., Mn 1+x Fe 2+x O 4 .A clear boundary with a sharp concentration change is only expected at the MnFe 2 O 4 /Mn 3 O 4 interface, taking into account the structural differences between the cubic structure of MnFe 2 O 4 (space group Fd3m) and the tetragonal structure of Mn 3 O 4 (space group I4 1 /amd).The MnO 2 + 2Fe 2 O powder mixture also allows oxygen balance:MnO 2 + 2FeO → MnFe 2 O 4 (5)and the free energy of this reaction ∆G R = −167 kJ/mol indicates that this should be even more spontaneous than Equations (3) or (4).However, the mechanisms of this reaction may be complex since FeO is a very unstable phase and may oxidise readily to Fe 3 O 4 in contact with the strongly oxidising phase MnO 2 , which may also undergo gradual reduction through intermediate phases ( • C. Figure 3 also emphasises the limited temperature range when the redox pair H 2 /H 2 O may be used to adjust the thermochemical conditions of MnFe 2 O 4 .This shows that H 2based gases only provide feasible oxygen balance for synthesis from Mn 2 O 3 + Fe 2 O 3 or MnO 2 + Fe 2 O 3 from room temperature to about 773 K, depending on the H 2 : H 2 O ratio, and from H 2 -rich conditions (e.g., H 2 : H 2 O = 100) to H 2 -lean conditions (H 2 : H 2 O = 0.01).Thus, the H 2 /H 2 O pair also fails as a redox buffer at intermediate temperatures in the range of 500 • C−800 • C. Still, the H 2 : H 2 O redox buffer may explain the feasibility of the direct mechanosynthesis of MnFe 2 O 4 from metallic precursors in wet conditions

Table 2 .
Approximate contents of reactants and other phases (mainly the MnFe O -based spinel) after milling the MnO + Fe O mixture.
Materials 2024, 17, x FOR PEER REVIEW 14 of 19 of the reacting MnO + Fe O mixture and the stability range of MnFe O ( ∆ ≥ 134 kJ/mol).Mechanical activation was performed at 350 rpm or 450 rpm for 10 h, and changes in milling conditions only yielded a decrease in the intensity of reactant reflections.The synthesis of MnFe O required subsequent thermochemical treatment at sufficiently high temperatures to overcome the redox gap, such as heating to about 1000 °C in air, as indicated by the thermodynamic predictions (Figure

Table 2 .
Approximate contents of reactants and other phases (mainly the MnFe 2 O 4 -based spinel) after milling the MnO + Fe 2 O 3 mixture.