46 D O I: 1 0. 15 82 6/ ch im te ch .2 01 6. 3. 1. 00 4 I. Zvereva1*, T. Pavlova1, V. Pantchuk1, V. Semenov1, Y. Breard2, J. Choisnet2 1 Institute of Chemistry, St. Petersburg State University, 198904 Petrodvorets, Saint Petersburg, Russia 2 Laboratoire CRISMAT, UMR 6508 CNRS ENSI- CAEN and Caen University, 6 bd Maréchal Juin14050 Caen Cedex 4 France *Corresponding author: Tel.: +7 (904) 330-50-19 E-mail: irina.zvereva@spbu.ru The solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5): characterization of Fe (III) – Fe (IV) mixed valences** The results of a magneto chemical and Mössbauer characterization are re- ported for the solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5), the intergrowth of a dou- ble perovskite block and one rock-salt layer type. The charge compensation mechanism induced by the introduction of iron atoms in the matrix of Sr 3 Ti 2 O 7 is sensitive to the conditions of synthesis, namely an oxidation process triggers the formation of mixed Fe(III)–Fe(IV) valences. The crystallographic charac- terization - variation of the cell parameters and structure calculations – brings evidence for the respective occurrence of mixed valences and oxygen vacancies which form in the middle plane of the double perovskite block. Ferromagnetic exchange interactions which are absent in the Fe(III) containing compositions, appear and progressively strengthen depending on the oxidizing treatment. They are ascribed to the presence of an increasing amount of Fe(IV) species. Remarkably, a mixed valence state of iron forms during annealing in air with an increasing contribution of the Fe(IV) species for the larger iron contents, as deduced from Mössbauer data. Keywords: layered oxides; solid solutions; iron; mixed valence; magnetic susceptibility; Mössbauer spec- trometry. **The authors (1) are grateful to The Russian Fund of Basic Research for its financial support (Grant 15-03-05981). © Zvereva I., Pavlova T.,Pantchuk V., Semenov V., Breard Y., Choisnet J., 2016 47 № 1 | 2016 Chimica Techno Acta Introduction Mixed valence states of 3d transition metals such as Ni, Co, Cu and Mn [1–7] can be stabilized in perovskite like oxides when working partial non-isovalent cati- onic substitutions. The fascinating electri- cal and magnetic properties of these oxide materials is strongly connected to the ex- istence of these mixed valence states. Of importance to stabilize unusual oxidation degrees of 3d transition metals is the low- ering of their site symmetry in the perovs- kite layers. In this respect the intergrowths of perovskite (P) layers and rocks-salt (RS) layers are favourable to get mixed valence states of the transition metal, whereas in the high symmetry field of the tridimen- sionnal perovskite structure such unusual oxidation degrees can disproportionate. In the manganites La1+xSr2-xMn2O7 with the P2/RS intergrowth of a double per- ovskite block and one rock-salt layer, the existence of a colossal magnetoresistance (CMR) strongly depends on the mixed valence state of the manganese atoms [5, 6]. As to the oxygen content of these lay- ered perovskite like phases, even if it has no concern to the oxygen stoichiometric LnSr2Mn2O7 phases which contain Mn (III) and Mn (IV) [8], in most cases the oxygen deficiency properties are involved in the existence of the physical properties, as regularly checked in the cuprates and nickelates [1–4]. In the same way, systematic attention has been focused on the rich electrical and magnetic properties of perovskite like in- tergrowth structures of ferrites and their solid solutions [9–14]. As an example the existence of two P2/RS type iron strontium mixed oxide is reported, namely the Fe(IV) one Sr3Fe2O7 [12] and the Fe(III) one Sr3 Fe2O6 [9]. Due to this and in the frame of our previous work on P/RS type chro- mium doped aluminates [15] and P2/RS chromium doped titanates [16], it was de- cided to look for compositions where it is possible to create mixed valence Fe(III) and Fe(IV) state of the iron atoms. In this paper, we report on the partial sub- stitution of iron atoms for titanium atoms in the P2/RS type strontium titanate Sr- 3Ti2O7 [17] (Fig. 1) in terms of a struc- tural analysis (XRPD) and a magnetic and Mössbauer characterization of iron low compositions of the solid solution Sr3Ti2-xFexO7-δ (x ≤ 0.5). The entire solid solution exists but up to now the reported results have a concern with iron richer compositions (2 ≥ x ≥ 0.5) [18, 19]. Even more iron diluted compositions (x ≤ 0.2) were never considered for crystal chemi- cal and physical studies, as well. Con- sequently, the main goal of the present work consisted in clearing up the crystal chemical mechanism of charge compen- sation induced by the introduction of iron atoms in the matrix of Sr3Ti2O7: formation of the Fe (III) and Fe (IV) mixed valences together with the creation of oxygen va- cancies. Experimental Eight compositions Sr3Ti2-xFexO7-δ (0 ≤ x ≤ 0.5) were synthesized from solid state reaction of the mixtures of precursor oxides TiO2, Fe2O3 and carbonate SrCO3 (Johnson Matthey, purity ≥ 99.95 %). According to the ceramics methods, the samples were pelletized and calcined in air at 1200 °C and then at 1350 °C for 40 h each. The solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5): characterization of Fe (III) – Fe (IV) mixed valences 48 № 1 | 2016 Chimica Techno Acta The compositions x ≥ 0.2 were con- sidered for X-ray structural analysis from cell parameters to structure calculations. The diluted compositions 0 < x ≤ 0.2 were retained for the magnetic and the Möss- bauer study. In order to receive relevant information regarding the oxygen stoi- chiometry, different heating conditions were worked for some compositions as- prepared in air: – an oxidizing treatment: 850 °C for 10 h and 150 bars oxygen pressure (x = 0.2 and x = 0.5) – a reducing treatment: a DTA Seta- ram device used with an hydrogen-argon atmosphere from room temperature up to 850 °C for 8 h. This was applied specifi- cally to the richest iron composition x = 0.5. The iron content of the as-prepared samples was determined from atomic emission spectrometry. The maximum deviation between the theoretical and the experimental value of the iron content of a given sample does not exceed 5 %. XRPD diffractograms were recorded with a Philips PW3020 diffractometer using the Cu Kα radiation in the 2q angular range 5–110 °, step size 0.04 ° and counting time 12s. Structure calculations were car- ried out with the FullProf code [20]. The magnetic susceptibility was measu- red according to the Faraday method in the temperature range 77–400 K. The precision is better than 2 %. Mössbauer spectra were recorded at room tempera- ture by using spectrometer Wissel (57Fe in a rhodium matrix), the isomeric shifts being calculated with respect to α Fe. In order to evaluate the part of paramagnetic species, the intensity of the signals was determined precisely up to the resonance factor. XRPD results: cell constants and structure calculations XRPD phase analysis ensured the ex- istence of iron containing mixed oxide isotypic of Sr3Ti2O7 (Fig.  1) which forms within the whole range of compositions (0 ≤ x ≤ 0.5). When the iron content of the Sr3Ti2-xFexO7-δ compositions does not exceed the value x = 0.3 no extra phase is observed. In the range of compositions 0.3 < x ≤ 0.5 some faint amount of a Sr4 Ti3O10 type phase i.e. a P3/RS intergrowth phase accompanies the major P2/RS phase. The values of the tetragonal unit cell constants - a, c and volume V for x = 0.2 air prepared and after oxidation, x = 0.3 air prepared and x = 0.5 (air prepared, after oxidation and after reduction) are reported in Table 1. The corresponding variation versus x is shown in Fig.  2. In order to better understand the meaning of such a variation in terms of the cru- Fig. 1: (a) P2/RS intergrowth structure of Sr3Ti2O7: P - perovskite block; RS - rock-salt layer. (b) Connection of octahedra and MO9 and MO12 polyhedra Zvereva I., Pavlova T.,Pantchuk V., Semenov V., Breard Y., Choisnet J. 49 № 1 | 2016 Chimica Techno Acta cial problem of the mixed valences of Fe atoms, it was decided to include the vari- ation which can be modelled in the cases of a Fe (III) and a Fe (IV) solid solution i.e. the lines which connect the oxides Sr3Ti2O7 – Sr3Fe2O7 and Sr3Ti2O7 – Sr3Fe2O6, respectively. At first it should be stated that the nearly perfectly linear variation of Vair the unit cell volume of the as-prepared com- positions (Fig. 2a) brings evidence for the existence of a solid solution in the entire range of compositions 0 ≤ x ≤ 0.5. Moreo- ver the variation of V strongly depends on the heating conditions: the oxidized compositions – Fe (IV) – exhibit a value of Vox smaller than the reduced one Vred – Fe (III) whereas Vair takes intermediate valu- es. More precisely, the latter result is the combination of two different trends in the crystal chemical evolution of the solid so- lution Sr3Ti2-xFexO7-δ herein investigated: – in the oxidized compositions, the substitution of the smaller Fe4+ cations (rCNVI = 0.585 Å) [21] for the Ti 4+ one (rCNVI = 0.605 Å) results in a decrease of V. – in the reduced compositions, the creation of oxygen vacancies cancels the effect of the substitution of bigger Fe3+ cat- ions (rCNVI = 0.645 Å) for the Ti 4+ one, re- sulting in an overall decrease of V whose slope is weaker than in the oxidized com- positions. The precise contribution of a (Fig. 2b) and c (Fig. 2c) parameters to the varia- tion of the unit cell volume is rather dif- ficult to ensure. At least one can assume the parameter a to be more sensitive to the decrease of size of the cations sitting in the octahedral sites. This result fully agrees with that is reported in the study of the compositions x ≥ 0.5 i.e. annealing at high oxygen pressure triggers a decrease Table 1 Unit cell parameters (Å) and volume (Å3) in the solid solution Sr3Ti2-xFexO7-δ x 0 [15 ] 0.2 air 0.2 oxid. 0.3 air 0.5 air 0.5 oxid. 0.5 red. *1oxid. *1red. a 3.902 3.8988(3) 3.8956(4) 3.8968(2) 3.8941(2) 3.8910(4) 3.8974(4) 3.877 3.898 c 20.371 20.334(4) 20.310(5) 20.323(2) 20.306(1) 20.272(5) 20.305(2) 20.26 20.20 V 310.2 309.1 308.2 308.6 307.9 306.9 308.4 304.5 307.0 *1: calculated values as the average of Sr3Ti2O7 and Sr3Fe2O7 (oxid.) [12] and Sr3Fe2O6 (red.) [9]. Fig. 2: Variation of the cell volume (Å3) and cell parameters (Å) in the solid solution Sr3Ti2-xFexO7-δ The solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5): characterization of Fe (III) – Fe (IV) mixed valences 50 № 1 | 2016 Chimica Techno Acta of the parameter a [19]. On the contrary, the existence of a large amount of oxygen vacancies induces a pronounced lowering of the value of the parameter c. As a main result of the observed variation of the unit cell volume, it must be stated that the solid solution Sr3Ti2-xFexO7-δ which forms by heating in air contains a mixed valence state of the iron atoms. In order to learn about some modifications which are expected in the P2/RS intergrowth of the iron contain- ing solid solution, it was decided to carry out a profile analysis of the XRPD di- fractograms of the compositions x ≥ 0.2. For x = 0.5 three cases were considered: as-prepared in air, oxidized and reduced samples and for x = 0.2 the as-prepared and the oxidized sample. The structure of Sr3Ti2O7 [17] was retained: S.G. I4/mmm. Concerning the oxygen non-stoichiome- try, XRPD is rather unsensitive to a small variation of the oxygen content. Conse- quently, only in a final step of the calcu- lations of the air prepared compositions, a value of δ the oxygen deficiency arbi- trarily fixed to the half of the maximum value corresponding to a full reduction was considered (δ = x/4). The results of the Mössbauer characterization here af- ter reported ensured a value of δ close or lower than the half of a full reduction. As it was previously performed in the chro- mium containing solid solution Sr3Ti2-x CrxO7-δ [16] we did an attempt to find the likely location of the oxygen vacancies in one of the three possible sites, namely the inner apical O1, the equatorial O2 and the outer apical O3 (Fig. 1b). In this respect, the main results to be received from the structural analysis are as follows: – the oxygen deficiency of the air prepared and reduced compositions oc- curs in the inner apical O1 positions i.e. in the middle plane of the double perovskite block. This meets the different data ob- tained in the P2/RS cuprates [22] and the solid solution Sr3Ti2-xCrxO7-δ [16]. – the equatorial M-O2 distances (Ta- ble 2), within the precision of the calcula- tion procedure are unsensitive to the sub- stitution of iron atoms for titanium. – as regularly observed in the inter- growth structures, there is an apical dis- torsion of the octahedra, as visible from the obtained values of the correspond- ing inner apical M-O1 and outer apical M-O3 distances (Table 2). The main data observed in Sr3Ti2O7 i.e. the coupling of a longer inner M-O1 distance with a smaller outer M-O3 one is saved for the whole se- ries of compositions. Magneto chemical and mossbauer results The temperature dependence of the molar magnetic susceptibility in four air prepared compositions (x = 0.02; 0.08; 0.12; 0.18) of the solid solution Table 2 Metal oxygen distances (Å) in the (Ti, Fe)O6 octahedra in the solid solution Sr3Ti2-xFexO7-δ M-O dist. M = Ti, Fe Sr3Ti2O7 Air prep.[17] x = 0.2 Oxidized x = 0.2 Air prep. x = 0.3 Air prep. x = 0.5 Oxidized x = 0.5 Air prep. x = 0.5 Red. M-O1 x1 1.995 2.02(1) 2.02(1) 2.00(1) 2.03(1) 2.00(1) 2.02(1) M-O2 x4 1.949 1.95(1) 1.95(1) 1.95(1) 1.95(1) 1.95(1) 1.95(1) M-O3 x1 1.887 1.91(2) 1.92(2) 1.94(2) 1.91(2) 1.91(2) 1.96(2) Zvereva I., Pavlova T.,Pantchuk V., Semenov V., Breard Y., Choisnet J. 51 № 1 | 2016 Chimica Techno Acta Sr3Ti2-xFexO7-δ is shown in Fig.3. Within the temperature range 77–400 K there is a monotonic decrease of χ versus T and for given temperature the observed value of χ systematically increases when x, the iron content, gets larger. The experimen- tal data of the molar magnetic susceptibil- ity have been used for calculating a para- magnetic value per one mole of iron, by subtracting the diamagnetic contribution of Sr3Ti2O7 and iron atoms. The thermal variation of the paramagnetic susceptibil- ity is described by a Curie-Weiss law χ = C/(T-q) over the whole temperature range under consideration. Curie constant C takes a value close to 4 emu.K, where as Weiss temperature q, slightly increases versus x (Table 3). Table 3 Curie constant C and Weiss temperature q in the air prepared) Sr3Ti2-xFexO7-δ x C, emu. q, K 0.02 4.07 -18 0.08 4.00 -1.1 0.12 4.04 2.8 0.18 4.01 7.8 The calculated effective magnetic mo- ment meff shows a complex dependence on both temperature and iron content, as visible in Fig. 4 for the air prepared com- positions x = 0.02, 0.08; 0.12; 0.18. Such behaviour cannot be explained on the basis of one paramagnetic species and consequently, a mixed valence state of the iron cations which are introduced in the diamagnetic matrix of Sr3Ti2O7 is likely to occur in the solid solution. Concerning the magnetic interactions, it can be rea- sonably assumed that they progressively change from an antiferromagnetic prop- erty to a ferromagnetic one, depending on an increasing of iron content. The concentration dependence of meff in the temperature range 298–400 K can be modelled in the following way: 298К 400К µ µ = + = + 5 44 2 11 5 47 1 82 , , , , x x (1) By extrapolating these equations at zero concentration of iron, the value of the effective magnetic moment mx→0 of a single iron cation in the solid solution above the room temperature (RT) can be estimated as nearly constant and equal to 5.45 MB. The theoretical values of meff of a sin- gle iron cation are 5.92 MB and 4.9 MB, for Fe3+ (s = 5/2) and Fe4+ (s = 2), respec- tively. Clearly, the observed value 5.45 MB gives evidence for the presence of iron cations with a number of unpaired elec- trons smaller than 5, very likely 4 as in the Fe4+ species. If the exchange interactions between the paramagnetic iron species above RT are assumed to be weak enough not to induce a deviation of the effective magnetic moment with respect to the value of meff for a single paramagnetic iron Fig. 3. Temperature dependence of cM the molar magnetic susceptibility for the air prepared solid solution Sr3Ti2- xFexO7-δ. 1. x = 0.02; 2. x = 0.08; 3. x = 0.12;4. x = 0.18 The solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5): characterization of Fe (III) – Fe (IV) mixed valences 52 № 1 | 2016 Chimica Techno Acta cation, the existence of a Fe(III)-Fe(IV) mixed valence state of the iron atoms in the solid solution is ensured. The observed effective magnetic mo- ment in the solid solution with a zero concentration of iron can be modelled in terms on the only Fe3+ and Fe4+ cations, according to the following formula: x Fe Fe Fe Fe Fe Fe → = + + = + + + + + + 0 2 2 2 3 3 4 4 3 4 1 µ µ µ0 a a a (2) where mi and ai are the magnetic moment and the concentration of a given iron cation. Introducing into this equation the calculated value of mx→0 = 5.45 MB allows to calculate the concentration of Fe4+ as equal to 0.48(4). The presence of the two species Fe3+ and Fe4+ in the diluted solid solution looks unambiguous. Considering the temperature depend- ence of the effective magnetic moment al- lows to point to the following statements: – for the lowest iron concentrations (x ≤ 0.08) the magnetic properties, up to a large extent, correspond to what is ex- pected from antiferromagnetic exchange interactions. – for larger iron concentrations (x > 0.08) ferromagnetic exchange interactions take an increasing part depending on an increasing iron concentration (Fig. 4). The Fe(III) – Fe(IV) mixed valence state of the iron atoms in the solid solu- tion triggers three kinds of magnetic ex- change interactions, namely Fe3-O-Fe3+, Fe3+-O-Fe4+ et Fe4-O-Fe4+. Exchange inter- actions between Fe3+ cations in the layered perovskite like phases are antiferromag- netic [23, 24]. When atoms with different electronic configuration are concerned, the exchange interactions are always fer- romagnetic. As regards the Fe4+-O-Fe4+ exchange interactions, they are either antiferromagnetic or ferromagnetic de- pending on the site symmetry of the iron atoms. In order to learn about the cha- racter of the exchange interactions in the Fe4+-O-Fe4+ clusters, an analysis of the in- fluence of the experimental heating con- ditions on the magnetic properties was carried out in the limiting composition x = 0.5 of the solid solution. The tempera- Fig. 4. Variation of the effective magnetic moment versus temperature in the air prepared solid solution Sr3Ti2-xFexO7-δ. 1. x = 0.02; 2. x = 0.08; 3. x = 0.12; 4. x = 0.18 Fig. 5: Variation of the effective magnetic moment versus temperature in the composition x = 0.5. 1. oxidizing treatment; 2. air prepared; 3. reducing treatment; ––: single Fe3+ cation Zvereva I., Pavlova T.,Pantchuk V., Semenov V., Breard Y., Choisnet J. 53 № 1 | 2016 Chimica Techno Acta ture dependence of the effective magnetic moment observed in Sr3Ti1.5Fe0.5O7-δ as prepared in air and heated in oxidizing or reducing conditions, is shown in Fig. 5. In the latter case, the sample contains only Fe3+ species, as checked by thermal ana- lysis, and the exchange interactions are antiferromagnetic. Above RT (Fig.  6) meff in the reduced sample takes a value very similar to that of the Fe3+ cation 5.92 MB. In the air prepared sample the value of meff is intermediate between the reducing and the oxidizing cases, which result ensures the existence of two different exchange interactions. Finally, in the oxidized sample the Fe4+ species are responsible of the strong ferromagnetic character of the exchange interactions, in agreement with the results reported for the ferrate Sr3Fe2O7 [12]. At this stage, one result remains not immediately understandable in a simple way: the value of meff even at temperatures higher than RT (Fig. 5) largely exceeds the value of single Fe4+ cations: approximately 7 MB to be compared with 4.9 MB. One must take into account that for such iron concentration in the solid solution (25 %) the tendency of the paramagnetic species to aggregate will be important. It was pre- viously observed and modelled in the P/ RS intergrowth structure of the solid so- lution YCaAl1-xCrxO4 [25]. Consequently, the actual value of the magnetic moment will be due not only to the single mono- meric iron species but it will include the contribution of the various clusters, at least up to tetramers which likely have a concern to the observed magnetic mo- ment. As deduced from the temperature dependence of the effective magnetic moment, the ferromagnetism of the ex- change interactions undoubtedly in- creases versus the increasing amount of iron in the solid solution. More precisely, this data gives evidence for the increas- ing part of the Fe4+ species. In order to receive another evidence for the presence of Fe4+ and even more to calculate its con- centration, the solid solution was studied by Mössbauer spectrometry. Fig. 6 shows Mössbauer spectra of three compositions a b c Fig. 6. Mössbauer spectra of air prepared compositions of the solid solution Sr3Ti2-xFexO7-δ: a – 0.12; b – 0.16; c – 0.2 The solid solution Sr 3 Ti 2–x Fe x O 7–δ (x ≤ 0.5): characterization of Fe (III) – Fe (IV) mixed valences 54 № 1 | 2016 Chimica Techno Acta x = 0.12; 0.16; 0.20 prepared in air. In any case there is the superposition of two sig- nals with very different isomeric shifts d1 = 0.431 mm/s and d2 = –0.08 mm/s – corresponding to the cations Fe3+ and Fe4+, respectively [26–28]. The observed value of the quadrupolar splitting for Fe3+ DЕ1 = 0.29 mm/s - is consistent with a lower site symmetry for Fe3+ than for Fe4+ DЕ2 = 0.22 mm/s. On the basis of the Jahn-Teller effect of the 3d4 Fe4+ cations, a supplementary distortion of the corre- sponding (Fe4+O6) octahedra is expected. In fact, the existence of oxygen vacancies in the inner apical positions of the dou- ble perovskite block, as ensured from the structure calculations, triggers a lowering of the site symmetry of the Fe3+ cations. For comparison, the solid solution Sr3-xLaxTi2-xFexO7 was considered. In such case the fully charge compensated dou- ble substitution of the cationic couple x (La3+ + Fe3+) for x (Sr2+ + Ti4+) allows to maintain the oxygen stoichiometry i.e. there are no oxygen vacancies. The Möss- bauer data observed for the composition x = 1 namely Sr2.9La0.1Ti1.9Fe0.1O7 reveal the existence of one signal with an isomeric shift d = 0.32 mm/s which corresponds to an iron cation Fe3+ in a high symmetry local field. Clearly, this is another proof that the Mössbauer spectrometry ensures the presence of the two species Fe3+ and Fe4+ in the air prepared solid solution Sr3Ti2-xFexO7-δ. The analysis of the iron concentra- tion dependence of the intensity of the two Mössbauer signals brings the oppor- tunity to evaluate the respective parts of Fe3+ and Fe4+. In Table 4 we report for the three compositions x = 0.12; 0.16; 0.20 the estimated values of the Fe3+ and Fe4+ concentration (%) and the corresponding values of y the (Fe4+) composition and δ the oxygen deficiency. Table 4 Fe4+ and Fe3+ concentration (%), y (Fe4+) composition and estimated value of δ the oxygen deficiency in the solid solution Sr3Ti2-xFexO7-δ (air prepared) x Fe4+(%) Fe3+(%) y (Fe4+) δ 0.12 41.5 58.5 0.05 0.035 0.16 46.7 53.3 0.07 0.045 0.20 66.5 33.5 0.13 0.035 We receive the confirmation that the amount of Fe4+ increases versus x the iron composition i.e. when the iron concentra- tion in the solid solution is large enough - x ≥ 0.16 - the air prepared samples contain the Fe4+ cations as main species. These re- sults are in good agreement with the main information obtained from the magnetic properties. Finally an estimation of δ the oxygen deficiency in the solid solution Sr3Ti2-xFexO7-δ allows to ensure the oxygen non-stoichiometry property which is not large enough (δ < x/4) to be determined from XRPD calculations. Conclusion The solid solution Sr3Ti2-xFexO7-δ with- in its homogeneity range shows a remark- able ability to promote an oxidation of Fe(III) to Fe(IV) even annealed in air. The existence of a mixed valence state of the iron atoms with a major contribution of the Fe(IV) species is well established. In this respect, these new data well compare with those previously obtained in the case of chromium atoms in the solid solution Sr3Ti2-xCrxO7-δ [16]. 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