Phase Behavior and Defect Structure of HoBaCo 2 O 6-δ

: The differential scanning calorimetry study showed that the double perovskite HoBaCo 2 O 6-δ (HBC), depending on its oxygen content, undergoes three phase transitions in the temperature range 298–773 K. Their origin was tentatively explained using the relevant literature data. For the single-phase tetragonal HBC, the oxygen nonstoichiometry dependences on the oxygen partial pressure were investigated by thermogravimetric and ﬂow reactor methods in the intermediate-temperature range of 573–773 K. The proposed defect structure of HBC was successfully veriﬁed using the obtained data on its oxygen nonstoichiometry combined with those reported earlier. As a result, the values of the thermodynamic parameters ( ∆ H ◦ i , ∆ S ◦ i ) of the defect reactions proceeding in HBC were determined. The defect structure of HBC was shown to be similar to that of YBaCo 2 O 6-δ (YBC) likely due to similar ionic radii of Ho 3+ and Y 3+ .

Oxygen nonstoichiometry was shown to affect various properties of REBaCo 2 O 6-δ , including magnetic properties [27], temperatures of phase transitions and thermodynamic properties [27,28], and electronic and oxide ion transport [29]. It is of great importance to highlight that the oxygen content of an oxide material, being measured reliably depending on temperature (T) and oxygen partial pressure (pO 2 ), enables validating its defect structure model and, consequently, evaluating the thermodynamics of defect interactions. At the same time, an adequate defect structure model is of key importance for describing and controlling many, if not most, target properties of nonstoichiometric oxides as materials for a variety of applications, including energy storage and conversion [29,30].
Double perovskites REBaCo 2 O 6-δ possess either tetragonal (space group P4/mmm) or orthorhombic structure (space group Pmmm) depending on oxygen content and temperature. Also, upon variation of the size of the RE 3+ -cation and nature of the dopants in the Ba-and Co-sublattices transition to 'simple' cubic perovskite structure (space group Pm-3m) is possible under certain conditions (temperature and oxygen partial pressure) [31].
The Y-containing double perovskite cobaltite, YBC, was shown [28] to undergo two structural transitions upon increasing temperature: the first tetragonal (P4/mmm, 332-type superstructure) phase transforms to an orthorhombic (Pmmm and 122-type superstructure) one and then to a tetragonal phase (P4/mmm, 112-type superstructure). The former transition occurs due to the change of the ordering pattern of oxygen vacancies and the latter because of complete disordering of oxygen vacancies.
HoBaCo 2 O 5.3 , in turn, was shown to possess a tetragonal structure (space group P4/mmm, 112-type superstructure) as a result of holmium and barium atoms ordering along the c-axis [16]. Formation of superstructure with tripled parameters a and b (space group P4/mmm, 332-type superstructure) as a result of oxygen vacancies ordering was reported in [16,32]. However, it was not observed in [27]. Therefore, the fine crystal structure of HBC, including different superstructures, remains a controversial topic.
Oxygen nonstoichiometry of REBaCo 2 O 6-δ was studied for the oxides containing the following rare-earth elements: La [33], Pr [29], Nd [34], Sm [35], Eu [35], and Gd [36]. Several methods were employed in the previous works to measure the oxygen nonstoichiometry of YBC: coulometric titration at high temperatures, 1173-1323 K [37], and thermogravimetry and flow reactor method at moderate temperatures, 573-773 K [28]. The results of the latter were used to make the proposed defect structure model [38] applicable not only in the relatively narrow range of high temperatures (1173-1323 K), but also at lower temperatures, down to 573 K. It was found that the re-evaluated enthalpies and entropies of defect interactions in YBC are close to those for GdBaCo 2 O 6-δ , being distinctively different from those for the other REBaCo 2 O 6-δ with larger rare-earth ions [28]. Unlike YBC, the oxygen nonstoichiometry of HBC was only measured either in a narrow high-temperature range of 1173 to 1323 K at pO 2 between 1 and 10 −5 atm [37], or in a wider temperature range but at pO 2 lower than 10 −4 atm [27]. The oxygen content of HBC, 6-δ, was shown to change under studied conditions in narrow span from 5.02 to 4.98 [37]. It is worth mentioning that a defect structure model evaluated in [37] does not describe the data presented in [27]. Therefore, one can conclude that the oxygen content of HBC needs to be measured reliably in the extended ranges of T and pO 2 and its defect structure remains poorly defined.
It should be noticed that HBC, as with YBC [38,39], has a limited thermodynamic stability range. It decomposes into BaCoO 3-δ and HoCoO 3-δ at 1073 K in air atmosphere [40] and becomes stable only at temperatures higher than 1173 K [37]. However, at temperatures lower than 1073 K, HBC is stable because of kinetic factor [37,40]. Therefore, oxygen nonstoichiometry in HBC may be measured reversibly not only at temperatures higher than 1173 K, as it has been conducted in [37], but also at temperatures lower than 1073 K, as in YBC. It is of great interest to model the defect structure of HBC in the extended temperature range and compare modeling results with those for defect structure of other double perovskites studied earlier. Besides, since HBC is regarded, as with other REBaCo 2 O 6-δ oxides, as a promising material for applications at intermediate temperatures, its phase behavior should be studied at temperatures lower than 1073 K. Thereby, this study was aimed at: (i) elucidation of the phase behavior of HBC between room temperature and 773 K; (ii) obtaining experimental pO 2 -T-δ data for this oxide at the low and intermediate temperatures, 573-773 K, using the thermogravimetric and flow reactor methods, suitable for the measurements in these conditions; and (iii) describing the defect chemistry of HBC and thermodynamics of its disordering in the extended temperature range, 573-1323 K.

Experimental
The powder sample of HoBaCo 2 O 6-δ was synthesized using the standard ceramic technique using Ho 2 O 3 , BaCO 3 , and Co 3 O 4 as the precursors. The details of the synthesis procedure were described elsewhere [28]. After the final annealing step at 1373 K for 24 h, to avoid the decomposition of the sample, it was rapidly cooled to 773 K in air, held for 5 h in these conditions, and then cooled to room temperature with a 100 K·h −1 cooling rate. X-ray diffraction (XRD) was used to confirm the phase purity of the synthesized sample. The XRD pattern was obtained using an XRD-7000 diffractometer (Shimadzu, Kyoto, Japan) with Cu Kα radiation. Indexing and Rietveld refinement of the XRD patterns were carried out using the Rietica software package [41].
The chemical composition and morphology of the as-prepared powder sample was examined using a VEGA 3 scanning electron microscope (Tescan, Brno, Czech Republic) equipped with an Ultim Max 40 detector (Oxford Instruments, Abingdon, UK).
Thermogravimetric (TG) measurements were performed with a DynTherm LP-ST (Rubotherm, Bochum, Germany) thermobalance. The absolute oxygen nonstoichiometry in the HoBaCo 2 O 6-δ was determined by the direct reduction in a flow of H 2 /N 2 gas mixture (1:1 by volume, 100 mL·min −1 total gas flow) at 1323 K in the thermobalance. The experimental techniques are described in detail elsewhere [42]. The oxygen content, (6-δ), in the HoBaCo 2 O 6-δ sample slowly (100 K·h −1 ) cooled in air was found to be 5.350 ± 0.005.
Oxygen nonstoichiometry in HoBaCo 2 O 6-δ was also independently measured by the flow reactor method. The original experimental setup used for the flow reactor measurements and step-by-step relaxation procedure were described in detail elsewhere [28].
The MHTC 96 (Setaram, Caluire, France) calorimeter equipped with a differential scanning calorimetry (DSC) sensor was employed for investigating the phase behavior of HoBaCo 2 O 6-δ in different atmospheres. The atmosphere around the sample was controlled by sweeping the calorimetric cell with mixtures of dry air and dry N 2 (pO 2 = 10 −4.3 atm), prepared using RRG-12 (Eltochpribor, Zelenograd, Russia) mass-flow controllers. The exact oxygen content (pO 2 ) in the sweeping gas was measured at the outlet of the calorimeter by an external potentiometric YSZ oxygen sensor. The total gas flow rate was 100 mL·min −1 . The combined thermal and caloric calibration of the DSC setup was carried out using the heats and temperatures of fusion of high-purity standard metals (Ga, In, Sn, Pb, Al).
Because the stability issues and the phase behavior were expected to be quite similar for two double perovskites RBaCo 2 O 6-δ (R = Ho, Y), for the DSC measurements performed for HoBaCo 2 O 6-δ in the present work we followed the same procedure as was used for YBaCo 2 O 6-δ in our previous study [28]. This also facilitates a direct comparison between the DSC curves obtained for these two oxides.

Sample Characterization and Phase Behavior
The XRD pattern of the as-prepared sample of HoBaCo 2 O 5.35 is shown in Figure 1. It was indexed using P4/mmm space group employed earlier for YBaCo 2 O 5.33 [28]. The results of the Le Bail fitting (χ 2 = 1.4) are also shown in Figure 1. The refined lattice constants, a = b = 11.629(1) Å and c = 7.498(1) Å, were found to be in good agreement with ones reported previously [16,37].
The SEM-EDX micrographs of the HoBaCo 2 O 5.35 sample are shown in Figure 2. As seen, the powder possesses micron-size particles with uniform distribution of elements. The measured and nominal compositions of the sample were found to be in good agreement with each other.
The results of the DSC studies of the phase behavior of HBC in the atmospheres with different pO 2 are given in Figures 3 and 4. Figure 3 indicates that the number of phase transitions and the shape of the DSC curves strongly depend on the oxygen content in the sample as evidenced, for example, by the comparison of the curves recorded at log(pO 2 /atm) = −0.68, −1.0 and −1.5. As seen, even the change of the oxygen content as small as 0.02 significantly affects the shape of the DSC curve. As a result, depending on the oxygen content, 6-δ, HBC exhibits 1 to 3 phase transitions at temperatures T 1 , T 2 , and T 3 , respectively, upon heating in the range of 298 to 573 K. At higher temperatures, the onset of the large endothermic peak is obviously seen on the DSC curves recorded for all HBC samples except that with the lowest oxygen content (5.00). This peak corresponds to oxygen release from HBC lattice.    The results of the DSC studies of the phase behavior of HBC in the atmosphe different pO2 are given in Figures 3 and 4. Figure 3 indicates that the number transitions and the shape of the DSC curves strongly depend on the oxygen conte sample as evidenced, for example, by the comparison of the curves reco sponding DSC-peaks) depend to some extent on the oxygen content in HBC. increases strongly with oxygen content whereas its variation induces only sma at T1 and T2. Similar phase behavior was found earlier for YBC [28]. For the sa parison, variation of the phase transition temperatures with oxygen content shown in the insert of Figure 4.   sponding DSC-peaks) depend to some extent on the oxygen content in HBC. increases strongly with oxygen content whereas its variation induces only sm at T1 and T2. Similar phase behavior was found earlier for YBC [28]. For the sa parison, variation of the phase transition temperatures with oxygen conten shown in the insert of Figure 4.    Figure 4 shows that the transition temperatures (determined as maxima of the corresponding DSC-peaks) depend to some extent on the oxygen content in HBC. As seen, T 3 increases strongly with oxygen content whereas its variation induces only small changes at T 1 and T 2 . Similar phase behavior was found earlier for YBC [28]. For the sake of comparison, variation of the phase transition temperatures with oxygen content in YBC is shown in the insert of Figure 4.
Such similarity in the observed phase behavior of the double perovskites containing Ho and Y can be explained by the almost equal radii of these cations [43]. This allows us to interpret the origin of the phase transitions in HBC in the same way as in the Y-containing analog. The transition observed at the lowest temperature, T 1 , is, most probably, of magnetic origin [28]. Suard and Fauth also found magnetic phase transition for HoBaCo 2 O 5 at T = 340 K [44,45] i.e., close to temperature of phase transition detected in the present work. The middle-temperature phase transition, occurring at T 2 , may be identified with the transition of the tetragonal phase with s.g. P4/mmm and 332-type superstructure to the orthorhombic phase with s.g. Pmmm and 122-type superstructure, associated with the change in the ordering pattern of oxygen vacancies [28]. Finally, the phase transition at the high temperature, T 3 , seems to be the result of complete disordering of oxygen vacancies and formation of tetragonal phase, which is characterized by s.g. P4/mmm and 112-superstructure [28]. Thus, at temperatures higher than 573 K, HBC possesses P4/mmm tetragonal crystal structure and all the results of the oxygen content determination and defect structure analysis presented and discussed further correspond to this particular phase state of HBC.

Oxygen Nonstoichiometry and Defect Structure of HoBaCo 2 O 6-δ
In previous studies, the oxygen nonstoichiometry of HBC was measured only in the high-temperature range of 1173 to 1373 K [37]. At temperatures lower than 1123 K, this oxide is thermodynamically metastable in air [40]. However, the XRD pattern of the HBC sample annealed at 773 K for 100 h did not reveal any evidence of HBC decomposition [40]. This means that below 773 K, a rate of the solid-state reaction of HBC decomposition becomes so low that this oxide can be regarded as kinetically stable. For this reason, the temperature of 773 K was selected as the upper limit of the temperature range, in which the oxygen nonstoichiometry, δ, of HoBaCo 2 O 6-δ was measured in the present work. In turn, at a temperature as low as 573 K, HBC still exhibits relatively fast oxygen exchange with the ambient atmosphere, simultaneously retaining, as mentioned above, the same tetragonal crystal structure. Figure 5 shows the experimental data on the oxygen nonstoichiometry, δ, in HoBaCo 2 O 6-δ , measured using different techniques as a function of T and pO 2 . The results of high temperature coulometric titration measurements reported in [37] are also given in Figure 5 for comparison. As seen in Figure 5, the results obtained by TG and flow reactor methods are in good agreement with each other. Furthermore, oxygen nonstoichiometry at lower temperatures varies in the wide range from 0.600 to 0.929, whereas at high temperatures it is close to 1 and changes with pO 2 only slightly. Similar observations were also reported earlier for YBC [28]. It is worth mentioning that the oxygen content in HoBaCo 2 O 6-δ and YBaCo 2 O 6-δ is about the same as shown in Figure 6, where that is given as a function of temperature in air for both double perovskites.
The combined dataset shown in Figure 5, including both the oxygen nonstoichiometry measured in the present work and that reported elsewhere [37], was used for verification of the HBC defect structure model reported by us in an earlier study [28,29,[34][35][36]. The defect reactions considered within the framework of this model are shown in Table 1.

No.
Reaction ·· + 2Co Co 70.2 ± 1.5 a 66.5 ± 1.5 a a The values following the «±» symbol correspond to expanded standard uncertainty calculated based on the Levenberg-Marquardt fitting procedure at the level of confidence ≈ 95%. b The value was fixed as 0 during the fitting procedure [28,29,[34][35][36].    •-data obtained by thermogravimetric analysis, -data obtained by flow reactor method, -data obtained by coulometric titration in [37].   The values following the «±» symbol correspond to expanded standard uncertainty calculated based on the Levenberg-Marquardt fitting procedure at the level of confidence ≈ 95%. b The value was fixed as 0 during the fitting procedure [28,29,[34][35][36]. A set of nonlinear equations, comprising the equilibrium constants of the defect reactions (see Table 1), the charge neutrality, and the mass balance conditions, was solved analytically with respect to the concentrations of all the defect species involved. As a result, the model equation i are standard enthalpies and entropies of the quasi-chemical reactions, respectively (see Table 1). This equation was fitted to the combined pO 2 -T-δ data set. The results of fitting are summarized in Table 1 and Figure 7. As seen, the experimental values and those calculated using the model proposed coincide with each other well. It is interesting to mention that correct determination of the reaction (2) enthalpy requires the use of high-temperature data on HoBaCo 2 O 6-δ oxygen nonstoichiometry. The reason is low concentration of nonclustered oxygen vacancies at δ < 1. As a result, the data in the temperature range T = 573-773 K can be, in principle, described using the simplified defect structure model, which does not account for the reaction (2). However, the analysis of the whole dataset requires all the defect reactions listed in the Table 1. ard enthalpies and entropies of the quasi-chemical reactions, respectively (see Table 1). This equation was fitted to the combined pO2-T-δ data set. The results of fitting are summarized in Table 1 and Figure 7. As seen, the experimental values and those calculated using the model proposed coincide with each other well. It is interesting to mention that correct determination of the reaction (2) enthalpy requires the use of high-temperature data on HoBaCo2O6-δ oxygen nonstoichiometry. The reason is low concentration of nonclustered oxygen vacancies at δ < 1. As a result, the data in the temperature range T = 573-773 K can be, in principle, described using the simplified defect structure model, which does not account for the reaction (2). However, the analysis of the whole dataset requires all the defect reactions listed in the Table 1. The values of the thermodynamic functions of the defect reactions determined in the present work for HBC and those estimated earlier for other REBaCo2O6-δ [28,[33][34][35][36] are given simultaneously in Figure 8 as a function of RE 3+ -cation radius (CN = 9 radii were employed since they are available in [43] for all the RE 3+ -cations). As seen the enthalpy of the cobalt disproportionation reaction (1) (see Table 1), being on average around 30 kJ·mol −1 is somewhat decreasing from RE = La to Y(Ho) with decreasing RE 3+ radius. The oxygen exchange reaction (3) (see Table 1) becomes more endothermic and the pseudocluster formation reaction (2), and becomes less exothermic with increasing RE 3+ size, indicating the decreasing energy gain from oxygen vacancies preferential formation in RE 3+ containing layers. The estimated values of the thermodynamic functions of corresponding defect reactions (1)-(3) (see Table 1) for HBC can be compared with those obtained earlier for YBC [28]. Since, as noted above, the values of the oxygen nonstoichiometry of both oxides are very close to each other, it is not surprising that enthalpies and entropies of the appropriate defect reactions (see Figure 8) are nearly equal within the uncertainty limits. The values of the thermodynamic functions of the defect reactions determined in the present work for HBC and those estimated earlier for other REBaCo 2 O 6-δ [28,[33][34][35][36] are given simultaneously in Figure 8 as a function of RE 3+ -cation radius (CN = 9 radii were employed since they are available in [43] for all the RE 3+ -cations). As seen the enthalpy of the cobalt disproportionation reaction (1) (see Table 1), being on average around 30 kJ·mol −1 is somewhat decreasing from RE = La to Y(Ho) with decreasing RE 3+ radius. The oxygen exchange reaction (3) (see Table 1) becomes more endothermic and the pseudocluster formation reaction (2), and becomes less exothermic with increasing RE 3+ size, indicating the decreasing energy gain from oxygen vacancies preferential formation in RE 3+ containing layers. The estimated values of the thermodynamic functions of corresponding defect reactions (1)-(3) (see Table 1) for HBC can be compared with those obtained earlier for YBC [28]. Since, as noted above, the values of the oxygen nonstoichiometry of both oxides are very close to each other, it is not surprising that enthalpies and entropies of the appropriate defect reactions (see Figure 8) are nearly equal within the uncertainty limits.
Interestingly, it seems some irregularities in the variation of thermodynamic parameters in the case of the cobaltites containing rare-earth cations possessing stable electron configurations, such as La 3+ ([Xe]), Gd 3+ ([Xe]4f 7 ) and Y 3+ ([Kr]), can be observed in Figure 8. The double perovskites REBaCo 2 O 6-δ containing these three cations clearly deviate, albite to a different extent, from the smoothed lines draw through the points belonging to the rest of the compounds. The largest deviation is exhibited by the standard enthalpy and entropy of the quasichemical reaction (3), describing oxygen release from the oxide lattice accompanied by the formation of oxygen vacancies in the RE 3+ -layers i.e., in the case of the oxidation reaction. Intuitively, this seems quite logical in a sense that the redox reactions are highly dependent on the electronic structure of participating chemical species especially considering that point defects as quasiparticles, being the components of the same crystal lattice, are not completely independent of each other, contrary to chemical reagents of the real chemical reactions. However, the detailed understanding of the origin of these observations is lacking at present. As far as we know, this is the first experimental observation of the role played by the rare-earth cations in governing the redox properties of perovskites. Such data and such observations are very rare. Typically, it is believed that the 3d-metal-oxygen sublattice plays the major role in the redox properties of perovskite oxides. Although this is largely true, the influence of the rare-earth cations, as shown here, can, in some cases, be quite sensible and should not be completely ruled out. The origin of this effect should be thoroughly studied, including detailed electronic structure calculations for the REBaCo 2 O 6-δ cobaltites.
the rest of the compounds. The largest deviation is exhibited by the standard enthalpy and entropy of the quasichemical reaction (3), describing oxygen release from the oxide lattice accompanied by the formation of oxygen vacancies in the RE 3+ -layers i.e., in the case of the oxidation reaction. Intuitively, this seems quite logical in a sense that the redox reactions are highly dependent on the electronic structure of participating chemical species especially considering that point defects as quasiparticles, being the components of the same crystal lattice, are not completely independent of each other, contrary to chemical reagents of the real chemical reactions. However, the detailed understanding of the origin of these observations is lacking at present. As far as we know, this is the first experimental observation of the role played by the rare-earth cations in governing the redox properties of perovskites. Such data and such observations are very rare. Typically, it is believed that the 3d-metal-oxygen sublattice plays the major role in the redox properties of perovskite oxides. Although this is largely true, the influence of the rare-earth cations, as shown here, can, in some cases, be quite sensible and should not be completely ruled out. The origin of this effect should be thoroughly studied, including detailed electronic structure calculations for the REBaCo2O6-δ cobaltites.

Conclusions
The HoBaCo2O6-δ double perovskite samples were synthesized via the standard ceramic technique and were studied by DSC in the temperature range 298-773 K at different pO2 between 0.21 and 5·10 −5 atm. DSC revealed a large endothermic effect above ca. 640 K, corresponding to oxygen release from the oxide lattice. At lower temperatures, depending on the pO2, which defines the actual oxygen content, 6-δ, in HBC, there were up to three smaller endothermic effects corresponding to phase transitions. The lower-temperature phase transition (1), exhibited by HBC samples with oxygen content spanning from 5.00 to 5.33, was identified as having magnetic origin. The endothermic effects on the DSC curves at higher temperatures were referred to the tetragonal (s.g. P4/mmm, 332-type superstructure) to orthorhombic (s.g. Pmmm and 122-type superstructure) to tetragonal (s,g, Figure 8. Dependences of ∆H • i (i = 1-3) (a) and ∆S • 3 (b) on RE 3+ radius (crystal radii of 9-coordinated RE 3+ [36]) for REBaCo 2 O 6-δ : RE = Ho-the present work, RE = La [33], Pr [29], Nd [34], Sm [35], Eu [35], Gd [36], and Y [28]. The lines are to guide the eye only.

Conclusions
The HoBaCo 2 O 6-δ double perovskite samples were synthesized via the standard ceramic technique and were studied by DSC in the temperature range 298-773 K at different pO 2 between 0.21 and 5·10 −5 atm. DSC revealed a large endothermic effect above ca. 640 K, corresponding to oxygen release from the oxide lattice. At lower temperatures, depending on the pO 2 , which defines the actual oxygen content, 6-δ, in HBC, there were up to three smaller endothermic effects corresponding to phase transitions. The lower-temperature phase transition (1), exhibited by HBC samples with oxygen content spanning from 5.00 to 5.33, was identified as having magnetic origin. The endothermic effects on the DSC curves at higher temperatures were referred to the tetragonal (s.g. P4/mmm, 332-type superstructure) to orthorhombic (s.g. Pmmm and 122-type superstructure) to tetragonal (s,g, P4/mmm, 112-type superstructure) phase transitions due to step by step disordering of oxygen vacancies.
The oxygen content in the single-phase tetragonal HBC was determined at T = 573-773 K and pO 2 = 0.21-10 −2.12 atm using TG and the flow reactor method. The data obtained in this way were used to extend the applicability range of the defect structure model proposed earlier [37] from the narrow high-temperature range of 1173-1323 K down to as low as 573 K.
The defect structure of HBC was found to be similar to that of YBC. Thermodynamic functions of defect reactions estimated for HBC were compared with those determined earlier for other REBaCo 2 O 6-δ . It was shown that the enthalpies of all the quasichemical reactions increase more or less gradually with increasing RE 3+ cation radius in the row Ho(Y)-La whilst entropy of oxygen exchange reaction gradually decreases from Pr to Ho. The cobaltites containing rare-earth cations possessing stable electron configurations such as La 3+ ([Xe]), Gd 3+ ([Xe]4f 7 ) and Y 3+ ([Kr]) deviate from these dependencies. This observation shows that the role played by the rare-earth cations in governing the redox properties and defect chemistry of perovskites is not well understood at present and needs further thorough study. Data Availability Statement: The reported data are available by a reasonable request from the corresponding author.