55 D O I: 1 0. 15 82 6/ ch im te ch .2 01 8. 5. 1. 04 Volkova N. E., Khvostova L. V., Galaida A. P., Gavrilova L. Ya., Cherepanov V. A. Chimica Techno Acta. 2018. Vol. 5, No. 1. P. 55–79. ISSN 2409–5613 N. E. Volkova, L. V. Khvostova, A. P. Galaida, L. Ya. Gavrilova, V. A. Cherepanov Department of Physical and Inorganic Chemistry, Ural Federal University, 19 Mira St., Ekaterinburg, 620002, Russian Federation nadezhda.volkova@urfu.ru Phase equilibria, crystal structure and oxygen nonstoichiometry of the complex oxides in Sm – (Sr, Ba) – (Co, Fe) – O systems Present paper contains available information on the phase equilibria in the Sm – (Sr, Ba) – (Co, Fe) – O systems, including the synthesis routes used, crystal structure, which is often depended on oxygen nonstoichiometry, the data on thermodynamic stability of complex oxides, the obtained results on the homogeneity ranges of solid solutions, formed in the systems, and graphical presentation of phase relations in a form of phase diagrams. Keywords: phase equilibrium; solid solutions; crystal structure; phase diagram Received: 18.01.2018. Accepted: 14.02.2018. Published: 10.05.2018. © Volkova N. E., Khvostova L. V., Galaida A. P., Gavrilova L. Ya., Cherepanov V. A., 2018 Introduction Complex oxides based on sa- marium, alkali earth (Sr, Ba) and 3d tran- sition (Co, Fe) metals have attracted great interest of researchers during the last few decades because of a variety of potential practical applications such as cathodes for the SOFCs [1–6], membranes [7–9], mag- nets [10–12], catalysts [13–16], gas sensors [17–19]. Traditionally, most of the publi- cations devoted to the modern materials focus on their functional properties. At the same time, information concerning the phase equilibria and stability ranges often remains undisclosed or appears fragmen- tary. Systematic studies of phase equilibria are rare. Another important characteristic of these oxides, closely linked with their stability, is the value of oxygen nonstoi- chiometry. Since the overall information con- cerning the crystal structure, phase equi- libria, phase stability, oxygen nonstoichi- ometry and defect structure constitutes the physicochemical basis of the preparation and usage of these materials, it is vitally im- portant. Thus, the present work was aimed to overview the available data concerning the phase equilibria within the Sm – (Sr, Ba) – (Co, Fe) – O system, as well as the crystal structure and oxygen nonstoichi- ometry of the complex oxides formed in these systems. Phase equilibria in Sm – Co – O system A systematic study of phase equilibria in the Sm – Co – O system was performed for the first time by Kropanev et al [20, 21], and later by Kitayama [22]. Samarium 56 cobaltate SmCoO3 was the only phase found to exist in this system. This com- plex oxide was first described by Wold and Ward [23] as perovskite type with the cubic structure (a = 3.75±0.01 Å), although later it was suggested that the ideal perovskite structure is orthorhombically distorted (Table 1) [22, 24–28]. Different techniques have been used for preparation of SmCoO3: a conventional ceramic technique from oxides [20, 21], or from mixture of nitrates dried from their solution [24, 27], or from the mixture of cobalt carbonate and samarium nitrate [23]; via co-precipitation from the nitrates solution by Na2CO3 with following anne- aling in air [22]. The mechanism and kine- tics of solid state SmCoO3 synthesis from oxides has been studied in [29–32]. It was shown that the diffusion stage of synthe- sis occur by transport of Con+ (n  = 2, 3) and O2– ions through the layer of product to the reaction zone that is located on the SmCoO3 – Sm2O3 interphase boundary [29, 30]. The kinetics of synthesis depends on the grain size, oxygen partial pressure and compacting pressure of oxides mixture for both Sm2O3 – CoO and Sm2O3 – Co3O4 systems [30, 31]. Samarium cobaltate SmCoO3 is stable in air up to the incongruent melting point equal to 1344±4 °C [21]. The subsolidus part of the “T – composition” phase dia- gram for the Sm – Co – O system in air is shown in Fig. 1. Thermodynamic properties and sta- bility ranges measured by means of EMF technique in the galvanic cells with solid electrolyte are presented in [20, 21, 33, 34] and those measured by thermogravimetric (TGA) method – in [22]. The equilibrium oxygen partial pressure for the reaction: ½ Sm2O3 + CoO + ¼ O2 = SmCoO3, (1) examined in the galvanic cell with the solid electrolyte (ZrO2 doped by Y2O3) can be written as follows [20]: Table 1 The values of unit cell parameter of orthorhombically distorted SmCoO3 (Pbnm space group) a, Å b, Å c, Å Treatment conditions Ref. 5.284±0.006 5.343±0.006 7.506±0.006 Prepared in air, with the excess of CoO [22] 5.283±0.005 5.344±0.005 7.502±0.005 Prepared in air, with the excess of Sm2O3 [22] 5.289 5.354 7.541 Treated in oxygen at 930 °C [24,25] 5.294±0.002 5.352±0.002 7.504±0.003 Prepared at 930 °C and under pressure 60 kbar [26,27] 5.2831(1) 5.3502(1) 7.4962(1) Standard solid state ceramic procedures at 1200 °C in air, with intermediate grindings [28] Fig. 1. The cross-sections of phase diagram for the Sm – Co – O system “T – composition” in air [21] 57 lg , . , P P T K O O 2 2 14800 8 46          = − + (1076 ≤ T, K ≤1474). (2) where is a standard pressure, and standard Gibbs energy corresponding to the reaction (1) is expressed by the equations: Ref. [33]: ∆G J mol T K1 70820 40 47 ( / ) . ( ),= − + × (3) (1076 ≤ T, K ≤1474). Ref. [34]: ∆G J mol T K1 52530 25 0 ( / ) . ( ),= − + × (4) (1080 ≤ T, K ≤1180). The standard Gibbs energy of forma- tion from elements ΔG°f (SmCoO3) was presented in [33] by following equation: ∆G J mol T T f  ( / ) . lg . . = = − − × × +1215600 3 66 270 5 (5) The cross sections of phase diagram for the Sm – Co – O system corresponding to the different fixed parameters are shown in Figs. 2–4. Phase equilibrium in Sm – Fe – O system The detailed study of phase equilibria in the Sm – Fe – O system was performed by Kitayama and Katsura (Fig. 5) [35] and later by Parida et al [36]. Two ternary oxi- des – SmFeO3–δ and Sm3Fe5O12 – exist in the system. Samarium ferrite SmFeO3–δ possesses orthorhombically distorted pe- rovskite structure (space group Pbnm) [24, 35–41], Sm3Fe5O12 crystallizes in the cubic garnet structure (space group Ia3d) [35, 36, 42–45]. It was shown that despite of Sm2O3/ Fe2O3 ratio SmFeO3–δ always appears as the first product in the initial stages of synthesis within the temperature range 700–1300 °C; the reaction rate was greater in the mixtures with the iron oxide excess [46]. This is consistent with the fact that most of the samples with the nominal Fig. 2. The cross sections of phase diagram for the Sm – Co – O system at fixed metal ratio (εSm): a – 0.75; b – 0.5 and c – 0.33. Filled circles – single-phase, half-filled circles – double-phase samples [20]. Dashed lines are SmCoO3 decomposition oxygen partial pressure calculated from [34] 58 composition of Sm3Fe5O12 fired at 700 °C contained SmFeO3–δ as the impurity phase, even if the citrate technique had been used as preparation method [43]. Taking into account these findings, the temperature of final synthesis’ anneals in order to get a single phase samarium ferrite with gar- net structure has to be high enough (≥ 1200 °C). The unit cell parameters for the samarium ferrites SmFeO3–δ and Sm3Fe5O12 are listed in Table 2. A detailed study of crystal struc- ture performed on the single crystal of Sm3Fe5O12 within the range 20 ≤ T, K ≤ 297 reveals the second order phase transi- tion at 68 and 40 K [44]. The coefficients for the temperature dependency of unit cell parameter for Sm3Fe5O12 a T a a a T( ) = + +0 1 2 2 (6) are listed in Table 3. Thermodynamic properties of sama- rium ferrites were reported in [35, 36, 47–49]. At 1200  °C SmFeO3–δ is stable from air down to pO2 = 10 –12.68 atm and Sm3Fe5O12 – down to pO2 = 10 –3.72 atm [35]. Fig. 4. Gibbs triangle of phase equilibria in the Sm – Co – O system at 1273 K [20]. The values of equilibrium oxygen pressure in logarithmic scale are: 1) ≈ 5, 2) ≈1.3, 3) –3.17, 4) –11.8 Fig. 3. The cross sections of phase diagram for the Sm – Co – O system at fixed temperatures: a – 1173 K; b – 1373 K [20]. The composition is represented by molar fraction of metal components 59 Table 2 The values of unit cell parameter of SmFeO3–δ and Sm3Fe5O12 SmFeO3–δ Sm3Fe5O12 (3 – δ) a, Å b, Å c, Å Ref. a, Å Ref. – 5.394 5.592 7.711 [24, 37] 12.519±0.002 [35] 3.0 5.398±0.002 5.598±0.002 7.708±0.002 [35] 12.529±0.001 [42] 2.982 5.398±0.001 5.591±0.001 7.706±0.001 [35] – – – 5.400±0.001 5.597±0.001 7.711±0.001 [38] – – – 5.39853(4) 5.59683(4) 7.70715(5) [39] – – 3.034 5.588(3)* 7.710(6)* 5.392(3)* [40] – – – 5.39 5.58 7.71 [41] – – * Pnma space group Table 3 Polynomial’s coefficients (Eq. 6) for the single crystal Sm3Fe5O12 unit cell parameter [44] Temperature range (K) a0 (Å) a1×10 4 (Å/K) a0×10 6 (Å/K2) 20–297 12.5235 –1.53×10–1 2.21×10–1 20–40 12.5197 2.24 –3.18 40–68 12.5270 –1.407 1.35 68–297 12.5226 –4.9×10–2 1.95×10–1 Fig. 5. Phase equilibria in the Fe – Fe2O3 – Sm2O3 system at 1200 °C (mol%) [35]. Numbers in the figure mean values of –log pO2 at which three crystalline phases are in equilibrium state. Letters R, P, G, and M represent stoichiometric compositions of Sm2O3, SmFeO3, Sm3Fe5O12, and Fe3O4, respectively. M1 is the end member of the magnetite solid solution with chemical composition Fe2.957O4. Pss, Wss, and Mss are the solid solutions of SmFeO3 from P to P1, of FeO from W to W2, and Fe3O4 from M to M1, respectively. W and W2 are the end members of the wustite solid solution with chemical compositions FeO1.049 and FeO1.166, respectively. P1 is nonstoichiometric perovskite phase SmFeO2.982 60 The limits of thermodynamic stability for SmFeO3–δ and Sm3Fe5O12 that can be represented by the reactions (7) and (8) [36] are shown in Fig. 6. 18 SmFeO3 + 4 Fe3O4 + O2 = = 6 Sm3Fe5O12 (7) 2/3 Sm2O3 + 4/3 Fe + O2 = SmFeO3 (8) The temperature dependencies of Gibbs energy that correspond to the processes (7) and (8) are written as follows [36]: ∆μ(O2)/kJ×mol -1 (±0.8) = = –607.3 + 0.2333×(T/K) 1030 ≤ T/K ≤ 1252 (9) ∆μ(O2)/kJ×mol –1 (±0.6) = =–590.7 + 0.1587×(T/K) 1005 ≤ T/K ≤ 1259 (10) The phase diagram for the Sm – Fe – O system in the “log(pO2) – composition” coordinates at 1250 K is shown in Fig 7. The heat capacity anomaly that was detected for SmFeO3 at 673 K and for Sm3Fe5O12 at 560 K was attributed to the second-order magnetic order  disorder transformation [36]. Phase equilibrium in Sm – Sr – Co – O system Two types of solid solutions were found to exist in the Sm – Sr – Co – O system: with the perovskite structure and with the K2NiF4 type structure. The perovskite-type solid solutions Sm1–хSrxCoO3–δ can be prepared by the con- ventional ceramic technique [1, 50–52] or through the solution precursors me thods [53–59] within the temperature range 900–1200 °C in air or in the oxygen flow. It should be noted that using of conventional ceramic technique often yields the samples contaminated by small amounts of impuri- ties, for example, they were detected in the Sm0.5Sr0.5CoO3–δ sample after annealing at 1100 °C in air for 240 h. On the contrary, using the solution precursors routes allow to obtain single-phase samples much faster. Fig.6. Thermodynamic stability of the SmFeO3 and Sm3Fe5O12, constructed from the data in [36] (straight line); circle points are taken from [47], square points are calculated from [48, 49] 61 The synthesis conditions, structure type and unit cell parameters for the various Sm1–хSrхCoO3–δ compositions are listed in Table 4. Sm-enriched Sm1–хSrхCoO3–δ (0 < х < 0.5) obtained at 1200 °C in air possesses the perovskite structure with orthorhom- bic [1, 52] or tetragonal [53] distortions. The increase of strontium content leads to the decrease of orthorhombic distortions [1]. It should be noted that annealing tem- perature not less than 1200 °C is important since the samples Sm1–хSrхCoO3–δ with x ≤ 0.40 annealed at 1100 °C in air for 300 h were double-phase. Depending on the preparation condi- tions, Sr-enriched samples could be ob- tained either with tetragonal (2a×2a×4a) Table 4 The synthesis conditions, structure type and unit cell parameters for the various Sm1–хSrхCoO3–δ compositions Composition Synthesis route Final treatment conditions Crystal structure and unit cell parameters Ref. SmCoO3–δ ceramic route 1200 °C, in air Orthorhombic a = 5.357(1), b = 5.294(1), c = 7.513(2) [1] Sm0.9Sr0.1CoO3–δ Orthorhombic a = 5.363(1), b = 5.298(2), c = 7.518(3) Sm0.8Sr0.2CoO3–δ Orthorhombic a = 5.361(1), b = 5.371(2), c = 7.577(2) Sm0.75Sr0.25CoO3–δ nitrate route 800–1200 °C, in air, finally 1000 °C, 3 days a = 10.877(1), c = 7.716(1) [53] Sm0.7Sr0.3CoO3–δ ceramic route 1200 °C, in air Orthorhombic a = 5.366(1), b = 5.377(2), c = 7.583(1) [1] Sm0.6Sr0.4CoO3–δ Orthorhombic a = 5.369(2), b = 5.389(2), c = 7.588(2) Sm0.5Sr0.5CoO3–δ ceramic route 1200 °C, in air Orthorhombic a = 5.367(2), b = 5.406(1), c = 7.588(2) [1] Fig. 7. The phase diagram for the Sm – Fe – O system at 1250 K [36] 62 Composition Synthesis route Final treatment conditions Crystal structure and unit cell parameters Ref. Sm0.5Sr0.5CoO3–δ nitrate route 1100 °C, in air Orthorhombic a = 5.366(7), b = 5.370(9), c = 7.587(3) [57] EDTA-citrate complexing sol-gel process 900 °C, in air Orthorhombic Pnma a = 5.366, b = 5.398, c = 7.585 [58] ceramic route 1150 °C, in air Cubic a = 3.8086(5) [50] nitrate route 800–1200 °C, in air, finally 1000 °C, 3 days Cubic a = 3.795(1) [53] glycerin- nitrate route 1100 °C, in air Tetragonal (2a×2a ×4a), I4/mmm a = 7.587(1), c = 15.253(1) [59] Sm0.45Sr0.55CoO3–δ glycerin- nitrate route 1100 °C, in air Tetragonal (2a×2a ×4a), I4/mmm a = 7.593(1), c = 15.333(1) [59] Sm0.4Sr0.6CoO3–δ ceramic route 1150–1200 °C, in air Cubic a = 3.808(2) a = 3.8178(5) [1] [50] glycerin- nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.582(1), c = 15.339(1) [59] Sm0.35Sr0.65CoO3–δ glycerin- nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.596(1), c = 15.328(1) [59] Sm0.33Sr0.67CoO3–δ citrate-nitrate route 1100 °C, oxygen flow Tetragonal (2a×2a×4a), I4/mmm a = 7.6149(4), c = 15.3472(10) [54] Sm0.3Sr0.7CoO3–δ ceramic route 1150–1200 °C, in air Cubic a = 3.823(2) a = 3.8306(1) a =3.830 [1] [50] [51] glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.625(1), c = 15.368(1) [59] Sm0.25Sr0.75CoO3–δ nitrate route 800–1200 °C, in air, finally 1000 °C, 3 days Orthorhombic GdFeO3 type a =5.363(1), b =5.353(1), c =7.592(1) [53] glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.631(1), c = 15.364(1) [59] Sm0.2Sr0.8CoO3–δ citrate nitrate route 1100 °C, oxygen flow Tetragonal (2a×2a×4a), I4/mmm a = 7.6724(4), c = 15.3983(11) [54] ceramic route 1150–1200 °C, in air Cubic a =3.846(2) a = 3.8407(3) [1] [50] glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.669(1), c = 15.405(1) [59] Сontinuation of table 4 63 [54, 59] or cubic [1, 50] structure. One can see that the samples with the tetragonal structure appear in the relatively more oxidizing conditions and the samples with the cubic structures formed in the relatively more reducing conditions (Table 4). Fig. 8 illustrates the XRD pattern for Sr0.8Sm0.2CoO3–δ with the 2ap×2ap×4ap superstructure. Electron diffraction measurements uncovered the formation of 2ap×2ap×4ap superstructure (sp. gr. I4/mmm) within the tetragonal cell, but the intensity of reflec- tions corresponding to the superstructure decreases with the increase of strontium content [54, 55]. The superstructure forms because of the ordering of Sm and Sr cati- ons in the A-site sublattice accompanied by the ordering of oxygen vacancies. For Sr1–xSmxCoO3–δ with x < 0.25, Sm atoms are first incorporated into the A1 position until substitution is complete, while the A2 and A3 sites remain fully occupied by Sr2+. Further increase of samarium content leads to the incorporation of Sm cations into the A3 position, while A1 is fully oc- cupied by Sm3+ and A2 is completely filled with Sr2+. The value of Sm content, x = 0.5, corresponding to the limiting composition of solid solution, represents the situation when half of A3 positions are occupied by Sm3+ and the other half – by Sr2+ [54, 59]. Thermodynamic stability of the Sm1–хSrхCoO3–δ solid solutions has not been studied yet. Usually partial substitution of alkaline-earth elements for rare-earth in the cobaltites with the perovskite structure decreases their thermodynamic stability [60]. The only information concerning the behavior of Sm0.5Sr0.5CoO3–δ under ex- tremely reducing conditions at low tempe- rature is available [61]. It was found that at 250 °C under 4% H2O-96% H2 atmosphere samarium-strontium cobaltite decomposes to SrO, Co(OH)2 and CoO on the surface Composition Synthesis route Final treatment conditions Crystal structure and unit cell parameters Ref. Sm0.15Sr0.85CoO3–δ glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.678(1), c = 15.372(1) [59] Sm0.1Sr0.9CoO3–δ citrate nitrate route 1100 °C, oxygen flow Tetragonal (2a×2a×4a), I4/mmm a = 7.6968(8), c = 15.4672(16) [54] ceramic route 1150–1200 °C, in air Cubic a = 3.848(2) a = 3.8531(4) [1] [50] glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.668(1), c = 15.410(1) [59] Sm0.05Sr0.95CoO3–δ glycerin nitrate route 1100 °C, in air Tetragonal (2a×2a×4a), I4/mmm a = 7.668(1), c = 15.431(1) [59] Fig. 8. XRD pattern for Sr0.8Sm0.2CoO3–δ with the 2ap×2ap×4ap superstructure [59] Сontinuation of table 4 64 of the reduced Sm0.5Sr0.5–αCo1–βO3–γ layer. In the atmosphere of pure H2 at 350  °C Sr0.5Sm0.5CoO3–δ completely decomposes into Sm2O3, SrO and CoO [61]. The solid solutions Sm2–хSrxCoO4 with K2NiF4 type structure (sp. gr. I4/mmm) within the range 0.8 ≤ х ≤ 1.50 were pre- pared either by the conventional ceramic technique at 1200–1300 °C in air [56, 62], or at 1450 K in oxygen flow [63], or by the EDTA-citrate sol-gel method at 1000  °C in oxygen flow [64], or by the glycerin- nitrate technique at 1100  °C in air [59]. The homogeneity range of Sm2–хSrxCoO4 solid solutions, estimated by EDX analy- sis, was reported as 0.79 ≤ х ≤ 1.68 [63]. The samples quenched in air from 1100 °C were single-phase within the range 0.7 ≤ x ≤ 1.1 [59]. The unit cell parameters for Sm2–хSrxCoO4 are listed in Table 5. Another representative of the Rud- dlesden-Popper series Sm2SrCo2O7 was reported earlier [64]. It was prepared from Sm2O3, SrCO3 and Co2O3 by solid state synthesis at 1450 K in the flow of oxygen for 3 days [64]. According to the powder X-ray diffraction measurements, it pos- sesses the tetragonal structure with the unit cell parameters: a = 0.3801 nm, c = 1.9562 nm, V = 0.2826 nm3. It was shown that thermal stability of this phase is limited. The X-ray diffraction of the sample after heating at 1550 K for 6 h indicated that the compound decomposes to SmSrCoO4 and SmCoO3 [64]. It worth to mention that Sm2SrCo2O7 formation was not confirmed during the systematic study of phase equi- libria in the ½ Sm2O3 – SrO – CoO system at 1100 °C in air. The projection of isothermal–isobaric phase diagram for the Sm – Sr – Co – O system to the compositional triangle ½ Sm2O3 – SrO – CoO is shown in Fig. 9 [59]. Phase equilibria in Sm – Sr – Fe – O system Three types of solid solutions were re- ported to exist in the Sm-Sr-Fe-O system: Sm1–xSrxFeO3–δ [56, 65–70], Sm2–ySryFeO4±δ [56, 62], and Sr3–zSmzFe2O7–δ [71]. Complex oxides with the overall com- position Sm1–xSrxFeO3–δ may be prepared by solid state [66], glycine nitrate [56, 68, 70], EDTA-citrate sol-gel [7, 67, 69] or co- precipitation [56] methods at 900–1300 °C. All samples of Sm1–xSrxFeO3–δ solid solution range, whether as-prepared in air or treated at high oxygen pressure (100 bar at 600 °C Table 5 The unit cell parameters and unit cell volumes for Sm2–хSrxCoO4 [59, 62, 63] Sample composition a, Å c, Å V, (Å)3 Ref. Sm0.5Sr1.5CoO4–δ 3.761 12.234 173.4 [62] 3.7699(2) 12.4085(6) 176.35(1) [63] Sm0.75Sr1.25CoO4–δ 3.7620(2) 12.3575(8) 174.89(2) [63] Sm0.8Sr1.2CoO4–δ 3.753(1) 12.304(1) 173.36(2) [59] Sm0.9Sr1.1CoO4–δ 3.756(1) 12.266(1) 173.04(2) [59] SmSrCoO4–δ 3.7609(3) 12.2454(9) 173.20(2) [63] 3.752(1) 12.200(1) 171.76(2) [59] Sm1.1Sr0.9CoO4–δ 3.765(1) 12.198(1) 172.95(2) [59] Sm1.2Sr0.8CoO4–δ 3.768(1) 12.171(1) 172.77(2) [59] Sm1.3Sr0.7CoO4–δ 3.777(1) 12.180(1) 173.74(2) [59] 65 [66]), possess orthorhombically distorted perovskite type structure (sp. gr. Pbnm). The unit cell parameters for Sm1–xSrxFeO3–δ are listed in Table 6. Single-phase Sr2–ySmyFeO4±δ samples were synthesized by the glycine nitrate route [56] or by the solid-state technique [62] with the final annealing temperature within the range 1000–1250 °C. The ho- mogeneity range of Sr2–ySmyFeO4±δ solid solution was reported to be equal to 0.5 ≤ y ≤ 1.2 [62]. Sr3–zSmzFe2O7–δ solid solutions were synthesized by the glycine-nitrate method at 1100 °C in air [71]. It was shown that single-phase Sr3–zSmzFe2O7–δ formed in the composition range 0 ≤ z ≤ 0.3 and at z = 1.80. Similarly to the undoped Sr3Fe2O7–δ, partially Sm-substituted Sr3–zSmzFe2O7–δ (z =0–0.3) possesses the tetragonal struc- ture (sp. gr. I4/mmm). Sm-enriched single phase Sr1.2Sm1.8Fe2O7–δ also crystallizes in the tetragonal system, although the space group is different (P42/mnm). All attempts to synthesize Sm-substi- tuted strontium hexaferrite Sr1–zSmzFe12O19 (0.06 ≤ z ≤ 0.5) solid solutions by hydro- thermal [10, 11] or solid state [12] methods failed. It was found that all Sm-containing powders were multiphase; together with SrFe12O19 they contained Fe2O3 and (Sm, Sr)FeO3–δ as the impurity phases. Phase equilibrium in Sm – Ba – Co – O system Relatively large difference in ionic radii between samarium and barium, in com- parison with that between samarium and strontium, results in the formation of so- called “112 type” phase with the formula SmBaCo2O6–δ [72–74] instead of solid so- lution that is typical for the Sr-containing system. The structure of SmBaCo2O6–δ is also called as double perovskite since Sm and Ba atoms are separated to the alter- nating layers along the c axis. Therefore, the value of the c parameter is doubled Fig. 9. The phase diagram of the ½ Sm2O3 – SrO – CoO system at 1100 °C in air: 1 – SmCoO3, CoO, Sr0.5Sm0.5CoO3–δ; 2 – CoO, Sr1–xSmxCoO3–δ (0.05 ≤ x ≤ 0.5); 3 – CoO, Sr0.95Sm0.05CoO3–δ, SrCoO3–δ; 4 – SmCoO3–δ, Sr0.5Sm0.5CoO3, Sr0.7Sm1.3CoO4+δ; 5 – Sr1–xSmxCoO3–δ (0.05 ≤ x ≤ 0.5), Sr2–ySmyCoO4+δ (0.9 ≤ y ≤ 1.3); 6 – Sr1.1Sm0.9CoO4+δ, SrCoO3–δ, Sr0.95Sm0.05CoO3–δ, SrCoO3–δ; 7 – SrCoO3–δ, Sr3Co2O7–δ, Sr1.1Sm0.9CoO4+δ; 8 – Sm2O3, SmCoO3–δ, Sr0.7Sm1.3CoO4+δ; 9 – Sr2–ySmyCoO4+δ (0.9 ≤ y ≤ 1.3), Sm2O3; 10 – Sm2O3, Sm2SrO4–δ, Sr1.1Sm0.9CoO4+δ; 11 – SrO, Sm2SrO4–δ, Sr1.1Sm0.9CoO4+δ; 12 – SrO, Sr3Co2O7–δ, Sr1.1Sm0.9CoO4+δ [59] Table 6 The unit cell parameters for the Sr1–xSmxFeO3–δ solid solution x Structure a, Å b, Å c, Å Ref. 0.5 Orthorhombic sp. gr. Pbnm 5.4622(1) 5.4627(4) 7.7249(1) [70] 0.667 5.4728(2) 5.4454(2) 7.6973(2) [66] 0.8 5.396 5.562 7.711 [69] 66 relatively to the ordinary perovskite struc- ture, and the unit cell can be represented as ap×ap×2ap. Another specific feature of this structure that is caused by the cati- on separation is the location of oxygen vacancies. It is generally acknowledged that oxygen vacancies are not distributed randomly in the lattice while the oxy- gen content changes within the range 5 < (6–δ) < 6, but are concentrated in the particular planes. According to the most widespread point of view, oxygen vacan- cies are located in the SmOδ planes while BaO planes remain completed [74–76], however, alternatively the opposite model was suggested in [77]. Such accumulation of oxygen vacancies in the specific planes (doesn’t matter what they are – either SmOδ or BaOδ) results in the ordering of oxygen vacancies when the value of (6–δ) is equal approximately to 5.5, leading to the doubling of b-parameter and forma- tion of the ap×2ap×2ap supercell. SmBaCo2O6–δ can be prepared by a conventional ceramic technique [3, 74, 78–81] and via solution methods using different precursors [82–84]. It possesses the orthorhombic structure (space group Pmmm) with the ap×2ap×2ap supercell. The value of oxygen content at room tem- perature in the sample slowly cooled in air was found to be 5.61 [81]. This value corresponds to the orthorhombic structure. The X-ray diffraction pattern for SmBa- Co2O5.61 refined by the Rietveld analysis is shown in Fig. 10 and the structural para- meters are listed in Table 7. The samples within the composi- tional range Sm1–xBaxCoO3–δ with x < 0.5 annealed at 1100  °C in air were double- phase and consisted of SmBaCo2O5.61 and SmCoO3–δ, while the samples with x > 0.5 were the mixtures of SmBaCo2O5.61 and BaCoO3–δ [72, 73]. High temperature in situ XRD mea- surements reveals the structural transfor- Table 7 The unit cell parameters and atomic coordinates for SmBaCo2O5.61 [81] Space group Pmmm atom x y z Sm 0.5 0.229(3) 0.5 Ba 0.5 0.250(1) 0 Co1 0 0.5 0.255(2) Co2 0 0 0.254(2) O1 0 0 0 O2 0 0.5 0 O3 0 0.5 0.5 O4 0 0 0.5 O5 0.5 0 0.239(3) O6 0.5 0.5 0.247(3) O7 0 0.244(2) 0.238(2) a = 3.886(1) Å; b = 7.833(1) Å; c = 7.560(1) Å; V = 230.22(2) (Å)3; RBr = 10.7%; Rp = 7.73%; Rexp = 4.46% 67 mation from orthorhombic to tetragonal cell between 450 and 550 °C (Fig. 11) that is in good agreement with the value of oxygen content in SmBaCo2O6–δ within this tem- perature range. Temperature dependence of unit cell parameters for SmBaCo2O6–δ is shown in Fig. 12. Although the radius of samarium is significantly larger than radius of cobalt ions, it was found that the solid solutions represented by the formula BaCo1–zSmzO3–δ can be prepared by citrate-nitrate method at 1100 °C in air within the range 0.1≤ z ≤0.2. Partial substitution of Sm for Co stabilized the cubic structure similarly to BaCo1–zYzO3–δ [85]. Fig. 13 illustrates XRD pattern for the single-phase cubic solid so- lution BaCo0.85Sm0.15O3–δ as an example. The unit cell parameters refined by the Rietveld method are listed in Table 8. The sample with nominal composition z = 0.05 con- sisted of cubic BaCo0.9Sm0.1O3–δ and hexa- gonal BaCoO3–δ. One more complex oxide with the formula Sm2BaCo2O7 representing the Ruddlesden-Popper (RP) (n=2) phase was reported to exist in the Sm – Ba – Co – O system [63, 86]. It was obtained by solid- state reaction from Sm2O3, BaCO3 and Co2O3 at 1300 K in the flow of oxygen for 2 weeks. The crystal structure was described by the orthorhombic cell with the parame- ters a = 3.821 Å, b = 3.776 Å and c = 19.426 Å [85]. However, Gillie et al. [87] using same preparation method with prolonged annealing in flowing oxygen at 1100 °C did not obtain the single phase but the mixture composed of two distinct phases: an oxy- Fig. 11. High-temperature in situ diffraction data for SmBaCo2O6–δ [84] Fig. 12. Temperature dependencies of the unit cell parameters and unit cell volume for SmBaCo2O6–δ in air [84] Fig. 10. The X-ray diffraction pattern for SmBaCo2O5.61, refined by the Rietveld method [72] Fig. 13. XRD pattern for the cubic solid solution BaCo0.85Sm0.15O3–δ, refined by the Rietveld method [72] 68 genated 112-type phase SmBaCo2O5+x (x ≈ 0.5), and double-layered RP target com- pound. From a set of obtained results it was concluded that the composition of RP phase is probably close to Sm2.1Ba0.8Co2.1O7-δ (where δ ≈ 1). The unit cell parameters re- fined within the Pnnm space group were equal to a = 5.4371(4) Å, b = 5.4405(4) Å, and c = 19.8629(6) Å [87]. The only one complex oxide Sm2BaO4±δ was described in the Sm – Ba – O system [73, 88, 89]. It can be prepared as a single phase by a conventional ceramic tech- nique at 1500 °C in air for about 24 h [88]. Sm2BaO4±δ demonstrates low stability at room temperature due to high hygrosco- picity and reactivity with CO2 [88, 89]. However, DTA curves in the temperature range 950–1400  °C in air indicated no phase transitions occurred. The presumed space group is Pbna with the lattice pa- rameters a = 12.313 Å, b = 10.535 Å, c = 3.564 Å [88]. The standard Gibbs energy of Sm2BaO4 formation from the binary oxides Sm2O3 and BaO, determined by the high- temperature CaF2-based EMF method, was evaluated as –110 kJ/mol at 1100 K [89]. According to the XR results, partial dis- solution of BaO in Sm2O3 at 1100  °C in air was about 15 mol% [72]. The unit cell parameters for the Sm2–xBaxO3 solid solu- tions are listed in Table 9. The phase diagram for the Sm – Ba – Co – O system at 1100  °C in air [72] is shown in Fig. 14. According to the ob- tained results, it could be assumed that RP phase is thermodynamically unstable at 1100 °C in air but could be synthesized in more oxidizing conditions. Phase equilibria in Sm – Ba – Fe – O system In contrast with SmBaCo2O6–δ, simi- lar samarium-barium ferrite SmBaFe2O6–δ with the double perovskite structure can be obtained only under reduction con- ditions. Karen et al. [90, 91] synthesized SmBaFe2O6–δ at 985–1020 °C in atmosphere with oxygen partial pressure pO2 about 10–14.88–10–15.5 bar that was achieved by Table 8 The unit cell parameters for BaCo1–zSmzO3–δ, refined by the Rietveld method [72] z a, Å V, (Å)3 RBr,% Rf ,% Rp,% 0.1 4.108(1) 69.33(1) 2.04 1.72 13.4 0.15 4.131(1) 70.51(1) 1.59 1.50 9.76 0.2 4.143(1) 71.13(2) 1.30 1.09 16.4 Table 9 The unit cell parameters for the Sm2–xBaxO3 solid solutions Sm2–xBaxO3 Space group C2/m x a, Å b, Å c, Å V, (Å)3 RBr,% Rf ,% Rp,% 0.05 14.191(1) 3.628(1) 8.860(1) 449.22(2) 1.27 1.15 10.2 0.1 14.180(1) 3.626(1) 8.855(1) 448.39(1) 3.20 2.45 13.9 0.2 14.177(1) 3.625(1) 8.853(1) 448.08(1) 2.40 2.21 13.7 0.3 14.175(1) 3.625(1) 8.851(1) 447.92(2) 1.82 2.01 13.3 69 mixing of hydrogen, argon or oxygen and water vapor. Moritomo et al. [92] prepared SmBaFe2O6–δ at 985 °C for 40 h in an evacu- ated fused-silica tube with Fe metal grains put inside the tube, which served as a get- ter mixture (Fe/FeO) and provided the oxygen partial pressure of about 7.6×10–16 atm. Although it is impossible to prepare SmBaFe2O6–δ in air, it remains single-phase after annealing at 900 °C in air [93] or even at 985ºC in pure oxygen [91]. The crystal structure of SmBaFe2O6–δ is well described within the tetragonal or the orthorhombic unit cell (ap×ap×2ap), depending on the oxygen content [90–93]. Similarly to the Co-containing double per- ovskite, the appearance of the (ap×2ap×2ap) supercell takes place in the vicinity of oxy- gen content equal to 5.5. The values of unit cell parameters and synthesis conditions for SmBaFe2O6–δ are listed in Table 10. The complex oxide SmBa2Fe3O8+δ can be obtained at 500 °C in oxygen flow [93] or at 1100 °C for 200 h [94]. The structural refinements were performed by the Riet- veld method within the ideal perovskite cubic structure (space group Pm3m). The on ly sing le-phas e s ample Sm0.375Ba0.625FeO3–δ was prepared at 1100 °C in air [95, 96] and described within a cu- bic unit cell (space group Pm3m) with a = 3.934(1) Å. However, transmission electron microscopy revealed that Sm0.375Ba0.625FeO3–δ possesses tetragonal structure with 5-fold c para meter ap×ap×5ap. Such complex struc- ture is formed by alternation of the lay- ers contai ning exclusively samarium and barium with the mixed layers, as follows: Sm–Ba– (Sm, Ba)–(Sm, Ba)–Ba–Sm [95, 96] (Fig. 15). Table 10 The values of unit cell parameters and synthesis conditions for SmBaFe2O6–δ [90] 6–δ a, Å b, Å c, Å structure Ar/H2 log(pH2O) log(pO2) T, °C 4.980 3.963 3.946 7.609 orthorhombic ap×ap×2a (sp.gr. Pmmm) 8.78 –4.1 –27.6 670 4.999 3.963 3.945 7.612 8.65 –4.4 –29.3 630 5.002 3.962 3.945 7.611 8.65 –4.2 –28.6 640 5.007 3.962 3.944 7.611 8.65 –4.3 –29.4 620 5.014 3.962 3.946 7.612 8.78 –4.1 –27.9 660 5.016 3.963 3.946 7.612 8.78 –4.1 –28.2 650 5.022 3.962 3.944 7.617 8.78 –4.1 –28.5 640 5.030 3.959 3.948 7.621 16.3 –1.68 –15.31 1000 5.064 3.953 7.628 tetragonal (sp.gr P4/ mmm) ap×2ap×2a 24.9 –1.67 –14.93 1000 5.095 3.952 7.636 41.3 –1.68 –14.53 1000 5.137 3.949 7.649 74.2 –1.68 –14.03 1000 5.142 3.950 7.654 83.2 –1.64 –13.85 1000 5.182 3.949 7.664 101 –1.68 –13.76 1000 5.202 3.947 7.671 137 –1.69 –13.51 1000 5.249 3.946 7.686 238 –1.66 –12.96 1000 5.320 3.943 7.705 398 –1.62 –12.44 1000 5.346 3.943 7.714 341 –1.65 –12.64 1000 70 Phase equilibrium in Sm – Co – Fe – O system The solid solutions between sama- rium ferrite and samarium cobaltite Sm- Fe1–xCoxO3–δ were extensively studied [52, 97–102] because of their possible applica- tion as gas sensors. Polycrystalline samples of SmFe1–xCoxO3–δ can be prepared by the pyrolysis of cyanide complexes [97, 99], sol–gel method [98, 100, 102] or conven- tional solid-state technique [52] at 800– 1100 °C. It was shown that the homogene- ity range of SmFe1–xCoxO3–δ solid solutions extended to the entire range of composi- tions (0 ≤ x ≤ 1). Similarly to the undoped parent oxides SmFeO3–δ and SmCoO3–δ, the structure of all SmFe1–xCoxO3–δ solid solu- tions was identified as orthorhombic. The unit cell parameters and unit cell volume values are listed in Table 11 [98, 102]. Another solid solution in the Sm – Fe – Co – O system was obtained by partial sub- stitution of Sm for Fe in the cobalt ferrite CoFe2O4 with spinel structure [103–107]. The solid oxides with overall composi- tion CoFe2–ySmyO4 were prepared at 400– 1000 °C by co-precipitation [103–105] or sol-gel decomposition [105, 107] me thods. Single-phase samples CoFe2–ySmyO4 were obtained at temperatures 400–700  °C within the ranges 0 ≤ y ≤ 0.2 [105] and 0 ≤ y ≤ 0.4 [107] by sol-gel technology or Fig. 14. A projection of isobaric-isothermal phase diagram of the Sm–Ba–Co–O system to the metallic components triangle (T = 1100 °C, pO2 = 0.21 atm): 1 – SmCoO3–δ, CoO and SmBaCo2O6–δ; 2 – CoO, SmBaCo2O6–δ and BaCoO3–δ; 3 – melt; 4 – Sm2O3, SmCoO3–δ and SmBaCo2O6–δ; 5 – SmBaCo2O6–δ and Sm2–xBaxO3–δ (0 ≤ x ≤ 0.3); 6 – SmBaCo2O6–δ, BaCoO3–δ and BaCo0.9Sm0.1O3–δ; 7 – SmBaCo2O6–δ, BaCo0.9Sm0.1O3–δ and Sm1.7Ba0.3O3–δ; 8 – Sm1.7Ba0.3O3–δ and BaCo1–zSmzO3–δ (0.1 ≤ z ≤ 0.2); 9 – Sm1.7Ba0.3O3–δ, Sm2BaO4 and BaCo0.8Sm0.2O3–δ; 10 – BaCoO3–δ, Ba2CoO4 and BaCo0.9Sm0.1O3–δ; 11 – Ba2CoO4 and BaCo1–zSmzO3–δ (0.1 ≤ z ≤ 0.2); 12 – Sm2BaO4, Ba2CoO4 and BaCo0.8Sm0.2O3–δ; 13 – Sm2BaO4, Ba2CoO4 and BaO [72] Fig. 15. Crystal structure of five-layered ordered perovskite Sm1.875Ba3.125Fe5O15–δ [95, 96] 71 Table 11 The unit cell parameters and unit cell volume of the SmFe1–xCoxO3–δ solid solutions [98, 102] x a, Å b, Å c, Å V, Å 3 Ref. 0 5.5871 7.6977 5.3852 231.61 [98] 5.400 5.593 7.708 232.83 [102] 0.1 5.8551 7.5196 5.0739 223.40 [98] 5.390 5.557 7.691 231.19 [102] 0.2 5.8421 7.4964 5.0670 221.91 [98] 5.378 5.554 7.668 229.01 [102] 0.3 5.7916 7.4653 5.0618 218.85 [98] 5.364 5.520 7.634 226.03 [102] 0.4 5.7812 7.4689 5.0533 218.20 [98] 5.363 5.448 7.620 224.26 [102] 0.5 5.7189 7.4671 5.0649 216.29 [98] 5.340 5.453 7.584 220.83 [102] 0.6 5.324 5.422 7.554 218.09 [102] 0.7 5.316 5.412 5.548 217.17 [102] 0.8 5.6564 7.3754 4.9933 208.31 [98] 5.308 5.394 7.536 215.76 [102] 0.9 5.297 5.371 5.518 213.91 [102] 1.0 5.5148 7.2953 4.9582 199.48 [98] 5.286 5.353 7.499 212.18 [102] Fig. 16. A projection of isobaric-isothermal phase diagram for the Sm–Fe–Co–O system to the compositional triangle (T = 1100 °C, pO2 = 0.21 atm): 1 – Sm2O3, SmFe1–xCoxO3–δ (0 ≤ x ≤ 1.0); 2 – Co1–uFeuO (0 ≤ u ≤ 0.13), SmFe1–xCoxO3–δ (0.2 ≤ x ≤ 1.0); 3 – Co0.87Fe0.13O, Co1.35Fe1.65O4, SmFe0.8Co0.2O3–δ; 4 – SmFe1–xCoxO3–δ (0 ≤ x ≤ 0.2), Co1+vFe2–vO4 (–0.1 ≤ v ≤ 0.35); 5 – SmFeO3, Sm3Fe5O12, Co0.9Fe2.1O4; 6 – Sm3Fe5O12, Co0.9Fe2.1O4, Fe1.985Co0.015O3; 7 – Sm3Fe5O12, Fe2–wCowO3 (0 ≤ w ≤ 0.03) [102] 72 within the range 0 ≤ y ≤ 0.5 [106] by co- precipitation by sodium hydroxide with following annealing at 800 °C. However, further increase of temperature (> 800 °C) led to the decomposition of CoFe2–ySmyO4 (y > 0.1 [105, 107] or y ≥ 0.3 [106]) with a decrease in Sm content and formation of SmFeO3 as a secondary phase. The increase of calcination temperature up to 1000 °C resulted in the complete decomposition of the CoFe2–ySmyO4 solid solution even with y = 0.1 [107]. 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