Synthesis and equilibrium oxygen nonstoichiometry of PrBaFe 2 O 5 þ w

A double-cell perovskite PrBaFe 2 O 5 þ w is synthesized and its equilibrium nonstoichiometry investigated after quenching from ﬂ owing gas of varied oxygen partial pressures and temperatures. Whereas w ¼ 0 is reached at 856 (cid:2) C in wet H 2 of p H2O ¼ 0.02 bar yielding p O2 ¼ 4 (cid:3) 10 (cid:4) 21 bar, w ¼ 0.75 obtains at 400 (cid:2) C in O 2 . Below ~1000 (cid:2) C, compositions with w (cid:5) 0.5 order into a Cmmm superstructure that fully converts back upon heating to 1020 (cid:2) C. PrBaFe 2 O 5 of all equivalent Fe 2.5 þ sites orders into Fe 2 þ and Fe 3 þ upon cooling through a ﬁ rst-order transition at 204 K, with a 2 K hysteresis, as investigated by powder X-ray diffraction and differential scanning calorimetry. The valence-mixed and charge-ordered structures are re ﬁ ned from synchrotron X-ray powder diffraction patterns. The nonstoichiometry w is expressed as a function of T and p O2 of the ﬂ owing gas in a formal donor-dopant defect model via least-squares ﬁ t of thermodynamic parameters for point-defect equilibria in the solid.


Introduction
Cubic Ba 0.5 Pr 0.5 FeO 3Àd perovskite synthesized in air is in focus for electrochemical applications, typically in solid solution with similar perovskites of other transition metals [1,2].Its conversion to a tetragonal PrBaFe 2 O 5þw upon testing in reducing atmospheres was recently reported [3].
The mixed-valent [4] double-cell perovskites R III BaFe 2 O 5 [5] are interesting for low-temperature charge ordering [6] in a rarely encountered simple 1:1 ratio of Fe 3þ and Fe 2þ with d xz orbitals ordered and doubly occupied [7].Upon heating, the charges mix in a first-order phase transition into pairs of Fe 2.5þ facing each other, sharing the minority-spin electron of Fe 2þ parentage, and coupling ferromagnetic within an overall antiferromagnetic order [8].
Given that the R ¼ La compound is cubic [9], and considering the redox chemistry of Ce, PrBaFe 2 O 5 is the last unreported lanthanoid member of this series.Among questions asked was the continuation of trends when already the large Nd 3þ is accommodated at the price of an additional distortion of the charge-ordered iron coordinations at low temperatures [10].On the other hand, that large ionic size should make it easiest to accommodate additional oxygen atoms.
PrBaFe 2 O 5þw was therefore synthesized, and the parent structure PrBaFe 2 O 5 investigated as a function of temperature by powder X-ray diffraction (PXD) and differential scanning calorimetry (DSC).The structures of its charge-ordered variant at 100 K and valence-mixed variant at 300 K were refined from synchrotron X-ray powder diffraction (SXPD) patterns.The PrBaFe 2 O 5þw nonstoichiometry was controlled by high-temperature equilibration at controlled partial pressures of oxygen (p O2 ) and characterized in terms of point-defect equilibria in a suitable model.

Experimental
Synthesis of the master sample.PrBaFe 2 O 5þw was synthesized from amorphous precursors obtained by liquid mixing in melted citric acid [11,12]: In advance, Pr 2 O 3 was prepared by reduction of Pr 6 O 11 (99.9%,Metal Rare Earth Limited, Shenzhen, China) in flowing gas of 10% H 2 in Ar (4N, AGA) at 800 C and an iron stick was sintered from iron powder (Fe p.a., Riedel de H€ aen) in the same atmosphere at 650 C, both in a dedicated corundum boat.The synthesis started by dissolving a magnetically stirred iron piece of 8.7111 g in 50 mL water with gradually added 80 mL of 65% HNO 3 .Simultaneously, 12.8525 g of Pr 2 O 3 was dry-mixed by magnetic stirring rod in a covered 2.5 L beaker with 280 g of high-purity citric acid monohydrate (Fluka, <0.02% sulfate ash).This mixture was melted on a hot plate after adding about 20 mL of water at the bottom of the beaker, below the powder.Once Pr 2 O 3 dissolved in the stirred melt, the iron nitrate solution was added gradually by having each dose of it react fully until the evolution of nitrous gases ceased.The eventually formed clear melt of reddish color was then cooled below 100 C to densify; some 50 mL of water was added on top of it when washing hot viscous melt was poured into a hot 2 L porcelain bowl at 180 C inside a drying oven.At this temperature, brittle foam of a dark brown organic precursor forms overnight.Its powder was incinerated into an inorganic precursor in a lid-covered porcelain crucible kept at 390 C in a bench-top one-crucible oven for 23 days.This X-ray amorphous precursor powder was calcined at 880 C in a tube furnace under flowing H 2 and Ar gas mixture of fixed humidity and p O2 (Table 1).The product milled in a vibration mill was then cold pressed at 150 kg/cm 2 into cylinders of 8 mm in diameter that were sintered at conditions listed in Table 1 into a phase-pure PrBaFe 2 O 5.2 master sample.
Oxygen nonstoichiometry control.The oxygen content in PrBaFe 2 O 5þw was fixed by equilibration in the open system [13] of flowing humidified gas of O 2 or H 2 mixed with Ar.The master sample was hanging on a 0.2 mm thin Pt wire in a glass-mullite-glass tube (inside a vertical tube furnace), connected on top via a glass elbow with ground joints to a long horizontal glass tube that fed the input gas and had a magnet-operated hook holding the sample wire.The ground joint on the furnace-tube bottom end was connected to a short glass tube fastened with an O-ring flange to a brass container with a bottom inflow of high-purity argon (99.999%) from P 2 O 5 dryer.The gas outlet of the system was in that short glass tube right above the metal container.The equilibration gas was obtained by mixing 99.999% argon with H 2 or O 2 or a commercial high-purity mixture of H 2 in Ar of certified composition around 10% of hydrogen.The mixing ratio of the up to two-step gas mixing was calculated from laboratory-flowmeter (Brooks Instrument) values calibrated on the actual component gasses.The p O2 at equilibration temperatures between 400 and 1042 C was controlled by a two-step humidification of the gas in distilled water at 17.3(1) C and calculated from the Ar þ O 2 or Ar þ H 2 mixing ratio and thermodynamics of water formation [14,15].The sintered silvery-black pellets of about 1 g mass were quenched by free fall onto the brass bottom with the dry-argon inlet.Three days of equilibration were adopted at 1042 or 1000 C and gradually increased up to 11 days along the sequence 924, 856, 796, 742, 693, 648, 608, 570, 536, 505, 476 and 400 C).The kinetics at lowest temperatures was tested by equilibrating two samples; one more and one less oxidized than the final equilibrium product.The quenched PrBaFe 2 O 5þw samples were characterized by chemical analysis and PXD and stored under argon.
Specific important samples: Three cylinders of PrBaFe 2 O 5.001(4) were quenched after 50 h equilibration at 825 C in flowing H 2 humidified to p H2O ¼ 0.0222 bar and were characterized by low-temperature PXD and DSC.For SXPD, two of them were a year later homogenized in the closed system [13] of an evacuated silica-glass ampoule by a three-months equilibration at 450 C with an iron-foil wrap (99.5%, Goodfellow, thickness 25 μm), yielding PrBaFe 2 O 5.011 (1) .
Nonstoichiometry analysis.The w in PrBaFe 2 O 5þw was determined by cerimetric titration [13] of Fe 2þ present after digestion in 5M-6M hydrochloric acid: About 0.15 g of finely powdered PrBaFe 2 O 5þw with w < 0.5 is weighed into a 10 mL borosilicate glass ampoule ("Gold-Band" was used).The ampoule is then one-third filled with H 2 O and flushed with high purity Ar prior filling the rest of its cylindrical space with concentrated hydrochloric acid and sealing it close to the top (not at its neck) in a sharp flame of a propane-butane burner.This dilution yields HCl concentration of 17.3 wt %, well below the azeotrope of 20.2% that boils at 108 C. The dissolution of the powder is assisted by a very short heating in a soft flame and having the sealed ampoules stand on a 100 C laboratory heating plate with intermittent stirring in ultrasound bath.The cooled-down ampoule is then opened at its neck and emptied into a titration flask flushed in advance with Ar.The flask walls are washed with concentrated hydrochloric acid, and 20 mL of 50% H 3 PO 4 added to mask the Fe 3þ color.Direct titration on ferroin redox indicator (Merck), with a Titripur 0.1 M cerium(IV)sulfate (Merck) in a 10 mL automatic burette yields best results when the residue in the ampoule is left to be flushed by water into the titration flask after the equivalence point is crossed.After the glass walls are washed once again with hydrochloric acid, the final equivalent point is reached with a drop or its fraction.The w ≳ 0.5 nonstoichiometry of PrBaFe 2 O 5þw was determined likewise, after a corresponding small amount (about 0.1 g) of (NH 4 ) 2 Fe(SO 4 ) 2  •7H 2 O (99þ, AlfaAesar) was weighed into the ampoule to reduce the sample's iron(>III) upon its subsequent dissolution, to be followed by back titration.With the highest oxidized samples, one has to give the dissolution a time, not to heat the ampoule much, in order to prevent O 2 formation (bobbles).Prior use, both Fe II standards were titrated with the same Ce 4þ solution; the former in a well acidified environment to prevent cerium precipitation.
Powder diffraction.PXD patterns were collected with monochromatized CuK α1 radiation (40 kV, 30 mA) between 6 and 100 2θ in the G670 Huber transmission diffractometer (with Guinier camera and imaging plate) calibrated on the NIST standard silicon (low-temperature setup) or with this Si as an internal standard of a ¼ 5.430825 Å (roomtemperature setup).Low-temperature patterns of PrBaFe 2 O 5.001(4) were collected for 30 min every 10 between 50 and 300 K. Patterns of the two-phase system across the charge-ordering transition were collected between 200 and 218 K with 3 K interval, each pattern 4 h.Rietveld refinements were done with the GSAS software suite [16] between 10 and 98 2θ on patterns with scan step of 0.005 2θ.
Synchrotron X-ray powder diffraction.SXPD was performed on PrBa-Fe 2 O 5.011(1) at the high-resolution diffractometer ID22 of ESRF Grenoble.Data for the charge-ordered phase were collected at 100 K over 3 h in steps of 0.0005 2θ (binned to 1, 2, and 3 steps), with wavelength λ ¼ 0.40007 Å over redundant angular ranges to ensure good contribution from all 9 parallel detectors into the diffraction pattern from 2.5 to 43 2θ.The powder sample, sealed in a glass capillary of 0.3 mm in diameter, was rotated at 60 s À1 in the beam of a 1.5 Â 2 mm area.The sample temperature was controlled by the N 2 gas flow from a 700-series Oxford Cryostream Plus.Data for the valence-mixed phase were collected at 300 K for 15 min with λ ¼ 0.42749 Å and binned into a diffraction pattern used between 3 and 43 2θ.Rietveld refinements were done with GSAS [16], using lorentzian profiles with Stephens' [17] micro-strain broadening coefficients S 400,040,004 and S 220,202,022 to model the peak asymmetry due to residual distribution [12] of the oxygen nonstoichiometry across the sample.The 100 K refinement of the charge-ordered structure was started on the 3-step binned pattern, released for heavy atoms first, then gradually for oxygens, with the square-pyramidal oxygen-apex x coordinate as the last one, right after 0.2% of Fe impurity (not detected by the in-house diffractometer) was refined.The result was then verified and concluded by a straightforward refinement on the denser 1-step binned pattern.
Differential scanning calorimetry (DSC).To obtain the phase-transition entropy and enthalpy, Perkin-Elmer Pyris 1 instrument with liquidnitrogen heat sink was used to register the heat flux into the sample upon a 20 K/min warming of 0.1-0.2g of coarsely pulverized samples in a sealed aluminum pan.Calibration and data evaluation were performed as described previously [12].The transition hysteresis was evaluated by measuring three cyclic scans of heating and cooling across the transition at 40, 20 and 10 K/min, with subsequent extrapolation of the peak temperatures to 0 K/min.a The sintered pellets of the last synthesis batch were taken and sintered further to suit better the quenching experiments (the results of which nevertheless did not deviate from those for pellets not "densified").

Results and discussion
3.1.Charge-ordered and valence-mixed PrBaFe 2 O 5 While at 100 K PrBaFe 2 O 5 is charge ordered with two unequal squarepyramidal coordinations of iron, at 300 K it is valence mixed with all iron polyhedra equivalent (Fig. 1).The refined structure parameters of PrBaFe 2 O 5 as charge ordered are in Table 2, as valence mixed in Table 4.
The Fe 2þ square pyramid is larger and has the O(1) apex somewhat tilted from the ideal right angle towards the "square" base.To verify the tilt location, the x ¼ 0.2341 coordinate of the vertex oxygen O(1) was inverted about ¼ so that the Fe 3þ pyramid became tilted instead, and everything was refined.The long but convergent refinement ended back with the tilted apex at the Fe 2þ square pyramid.The base of this pyramid is expanded along a, making the 2.058( 29 Bond-valence parameters [18] were used to obtain bond valences (bond orders) of metal-oxygen bonds from interatomic distances.Summing at each atom yields the so called bond-valence sum that typically is close to the absolute value of the atom's oxidation state.The result in Table 3 illustrates this on Ba and Pr (obtained with data in Table 2, it includes the slight thermal contraction upon cooling to 100 K in Fig. 2).The degree of the Fe 3þ and Fe 2þ ordering is 2.63À2.32¼ 0.31, whereas 2.78À2.32¼ 0.55 for NdBaFe 2 O 5 [19] and 3.00À2.18¼ 0.82 for DyBaFe 2 O 5 [9].This is also illustrated by DSC, vide infra.
The variation of the PrBaFe 2 O 5.001(4) cell parameters as a function of temperature is plotted in Fig. 2 per single-perovskite (sp) cell so that the two phases in Fig. 1 are comparable.The phase coexistence (detailed in Fig. 3) and the discontinuous volume contraction confirm the first order [21] of the phase transition and its localized-to-itinerant character [22]; as in the other RBaFe 2 O 5 compounds [9].The orthorhombic distortion a sp Àb sp ¼ 0.077 at 100 K (in Fig. 2 middle) reflects the combined action of the d xz orbital ordering and magnetostriction [10].As the value is less than 0.089 for NdBaFe 2 O 5.001(1) at the same temperature [19], it suggests lower degree of charge and orbital ordering in PrBaFe 2 O 5.001 (4) .Above the valence-mixing transition, only the magnetostriction contributes to the orthorhombic distortion.
DSC records directly the latent heat (Fig. 4) that feeds the mixing entropy of the two distinguishable iron sites becoming indistinguishable, ideally 2Rln(2) JK À1 mol À1 of PrBaFe 2 O 5 .As in the other RBaFe 2 O 5 phases [8,9], complete formation of the valence-mixed phase is achieved only after a temperature interval, here of about 50 K, above the main transition.A very weak checkerboard charge ordering has been reported [23] in this interval, not refinable reliably from diffraction data of the other RBaFe 2 O 5 phases.The DSC temperature scan in Fig. 4 shows that this intermittent range of residual charge order or separation ends upon heating through the broad weak peak topping at about 260 K.
The T c at zero-rate cooling and heating (Fig. 5) and other thermal parameters of these two valence-mixing transitions in PrBaFe 2 O 5.001(4) are listed in Table 5 and    a Standard deviations follow from variance-covariance matrix treatment of error propagation [20] from the refined atomic parameters to bond lengths, bond valences and bond-valence sums.
a degree of charge separation agrees well with 0.31 for the degree of longrange charge ordering according to PXD (vide supra), see also Ref. [24].While Table 5 refers to stoichiometric PrBaFe 2 O 5.001(4) , already a small increase in w suppresses the stability of charge ordering.The DSCmeasured enthalpy and entropy of the transition for this and two other PrBaFe 2 O 5þw samples, with w ¼ 0.011(1) and 0.0345 (5), are plotted in Fig. 6 and evaluated by fit with a model of suppression of the ordering or "freezing" point of the PrBaFe 2 O 5 solvent due to increased concentration of the solute w, applied to this first-order transition as described in Ref. [9].Given that the thermodynamic transition temperature T c ¼ ΔH/ΔS, the result suggests loss of any charge ordering above the PrBa-Fe 2 O 5.082 nonstoichiometry level, with last T c of about 173 K referring to the DSC-peak gravity-center temperature that zeroes the driving force of this discontinuous order-disorder transition.This result in Fig. 6 follows well the trend evaluated in Ref. [9] for other RBaFe 2 O 5 phases.

The wide nonstoichiometry of PrBaFe 2 O 5þw
The nonstoichiometric oxygen w is accommodated in the Pr layer, in the empty ½ ½ ½ site of the valence-mixed PrBaFe 2 O 5 cell in Fig. 1 6.The structure type is the same as for R ¼ Sm and Nd refined [5] in Pnma of lower symmetry.Further equilibrium oxidation can be achieved in O 2 at lower temperatures, such as PrBaFe 2 O 5.75 at 400 C. The largest Pr 3þ cation introduces the widest oxygen nonstoichiometry range of RBaFe 2 O 5þw .
To describe nonstoichiometry, one needs to identify the point defects causing it.That means to choose the defect model for PrBaFe 2 O 5þw .An extended structure typically has intrinsic electronic defect pairs due to thermal excitation across the band gap.In metal U iso (in Å 2 ) were constrained equal for all oxygens.oxides, these electrons and holes reside at the respective reduced and oxidized metal-ion defects, the reduced close to the conduction band and the oxidized close to the valence band [26].The defect model then depends on the identity of the intrinsic ionic-defect pair.Of the four choices available for that pair, see for example Fig. 4 in Ref. [13], the crystal structure in Fig. 1 suggests the anion-Frenkel pair composed of      U iso (in Å 2 ) were constrained equal for all atoms.Coordinate x was constrained equal for O(1) and O(2) to achieve convergence.
oxygen interstitials and oxygen vacancies.In a pure binary oxide of narrow nonstoichometry, their concentration would rise from the nominally stoichiometric composition; the oxygen interstitials upon oxidation, the vacancies upon reduction, as if they grew from the stoichiometric plateau as a function of changing oxygen partial pressure.However, plotting the actual nonstoichiometry w versus log(p O2 ) data for RBaFe 2 O 5þw , tabulated for example in Refs.[12,24,25], suggests not one plateau but two: One at w ¼ 0 (the integer structure in Fig. 1), the other at w ¼ 0.5 (the integer oxidation state Fe III ).Such a wide nonstoichiometry between two plateaus as a function of log(p O2 ) can be modeled as an intrinsic doping [13].In this case, as if hypothetical Ba 2 Fe III 2 O 5 were doped by one Pr donor atom per formula, substituting for one Ba.The stoichiometric composition PrBaFe 2 O 5 of the integer structure (Fig. 1) is reached in reducing atmospheres, the integer-oxidation-state PrBaFe 2 O 5.5 in more oxidizing atmospheres.
Kr€ oger-Vink notation [27] is used to write formation reactions and equilibrium constants for the two intrinsic defect pairs in the stoichiometric oxide as if in solution, with concentrations (in square brackets) per regular sites or per formula of the solid "solvent": The equilibrium with «nil» means having a solid on both sides of the reaction equation (solid Oxidation and reduction of this stoichiometric oxide proceeds as: These four equations are related via the electroneutrality condition; negative and positive defect charges must compensate.For donor doping of Pr at Ba site, it has the following form (as the charge concentration due to a doubly-charged defect is twice the defect's concentration): The electroneutrality equation ( 5) and any three of equations ( 1)-( 4) are needed to calculate the equilibrium concentrations of the defects as a function of the partial pressure of oxygen during the high-temperature equilibria in PrBaFe 2 O 5þw .
], the isothermal oxygen-defect concentrations versus p O2 were expressed with equilibrium constants of equations ( 1 ]) ¼ 0 of fractional powers.In lack of good analytical solutions, these concentrations were solved numerically by the bisection method that finds the unknown concentration by halving the interval that is closer to zeroing the function.The least-squares fit compared this ] quantity with the experimental w for the given p O2 , using the three equilibrium constants as fit parameters.Likewise for remaining experimental w versus p O2 points (Fig. 9 top).The refined equilibrium constants were then plugged into the f(  7).
A more nuanced analysis of the nonstoichiometry includes varied temperature.Such least-squares fits require reaction entropies and enthalpies instead of equilibrium constants of the isothermal fit.The reaction Gibbs energy relates to the equilibrium constant as Δ r G ¼ ÀRTln(K) and equals Δ r G ¼ Δ r H À TΔ r S. That makes six fit parameters for the three defect reactions chosen to enter the oxygennonstoichiometry equation set; Equations ( 1 ] versus log(p O2 /bar), compared with data points ( ) for GdBaFe 2 O 5þw of Ref. [12].Bottom: Ionic and electronic defect concentrations per formula unit with obtained fit parameters K i ¼ 10 À4.66 (12) and K aF ¼ 10 À1.06(30) (note their relation to defect-pair concentration cross-points in the plot) and K ox ¼ 10 À3.1 (4) .U iso (in Å 2 ) were constrained equal for all oxygens.
decreasing the entropy of the reaction system, and Δ ox S should be negative.The reaction might also be exothermic, hence Δ ox H negative (and the more so the more electropositive the R atom is in RBaFe 2 O 5 ).If the band gap of our black-colored solids does not depend on temperature, it is close to the enthalpy of the intrinsic ionization in Equation ( 1) [28].
All three pairs of ΔS and ΔH should at 1000 C correspond to the isothermal fit in Fig. 9.The result is in Fig. 10.The fit-parameter overview in Table 8 illustrates that the temperature dependent fit maintains reasonably well the 1000 C values of the three equilibrium constants sufficient to fit the single isotherm.Fig. 10 shows how the nonstoichiometry plateau at the integer structure of w ¼ 0 starts to appear well below 1000 C as the curves move in the vicinity of w ¼ 0 somewhat to the left.This is visualized by the three points obtained in not wetted H 2 (ppm humidity measured in the output gas), which would have been off the straight lines generated by the pure-oxide "undoped" PrBaFe 2 O 5.5 model.

Conclusions
Synthesis from amorphous oxide-or carbonate precursors in flowing wet mixtures of H 2 and Ar at !880 C yields a double-cell perovskite PrBaFe 2 O 5þw with Ba and Pr ordered and a wide oxygen nonstoichiometry range.The bottom of the range is around w ¼ À0.016 reached in equilibrium with wet H 2 of p H2O ¼ 0.02 bar at ~856 C. Lower oxygen contents may be obtained, but they are due to partial reduction to metallic iron manifested already with a neodymium magnet.At 400 C, equilibrium nonstoichiometry w ¼ 0.75 is reached in oxygen.The nonstoichiometric oxygen w is disordered in the double-cell perovskite structure.Upon equilibration at or below 980 C of PrBaFe 2 O 5þw with w !0.5, ordered Cmmm superstructure obtains, stable up to a two-phase mixture around 1000 C, with full disorder at 1020 C.
Of all RBaFe 2 O 5 variants, PrBaFe 2 O 5 has the lowest degree of charge ordering to Fe 2þ and Fe 3þ in its low-temperature structure.Calculated as a difference of the two iron bond-valence sums derived from crystalstructure data, the degree of long-range charge ordering is 0.31.The DSC entropy of mixing gives 0.41 for the degree of charge separation.The R ¼ Pr variant has the lowest T c ¼ 204 K of the main charge-ordering transition.It exhibits a 2 K wide hysteresis at zero heating/cooling rate.Taking the nonstoichiometric oxygen as a solute that depresses the ordering/"freezing" temperature T V , the transition enthalpy and entropy as a function of w extrapolate to the narrowest nonstoichiometry range (of all lanthanoid R versions) that allows the low-temperature charge separation/ordering: 0 w 0.082 (DyBaFe 2 O 5 separates charges up to w ¼ 0.25 [9]).
The wide nonstoichiometry in PrBaFe 2 O 5þw can be modeled with anion-Frenkel intrinsic defects as if it were a donor-doped Ba 2 Fe III  2 O 5 where one Pr replaces one Ba.This allows fitting two nonstoichiometry plateaus seen as a function of p O2 ; one at w ¼ 0, one at Fe III .Since the Pr ionic size is closest to Ba in the RBaFe 2 O 5þw series of double-cell perovskites, the donor-doped model at the highest tested temperature 1000 C becomes close to the model of stoichiometric undoped oxide of one nonstoichiometry Fe III plateau from which the w isotherm goes straight down through the w ¼ 0 composition.However, at lower temperatures, the donor-doped model is needed to fit experimental points indicating a small curvature of the isotherm at w ¼ 0.

Declaration of competing interest
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
) Å bond Fe(1)-O(3a) and the 2.062(27) Å bond Fe(1)-O(3b) longer than the 2.001(1) Å bonds to the other two base oxygens.That distortion accomplishes several goals: It facilitates double occupancy as well as ordering of d xz orbitals of Fe 2þ , and it avoids a too high repulsion of the tilted apex from the base oxygens.The d 5 high-spin Fe 3þ pyramid is regular and smaller.
right.Unit-cell parameters of samples quenched from temperatures high enough (Fig. 7) to keep the nonstoichiometric oxygen disordered in this cell are plotted in Fig. 8. Below the N eel temperature of about 430 K (Fig. 4), PrBaFe 2 O 5 and other RBaFe 2 O 5 phases develop a magnetostrictive orthorhombic distortion [25] of the space-group symmetry Pmmm.Increasing the nonstoichiometry w quickly removes that distortion, and tetragonal (P4/mmm) PrBaFe 2 O 5þw forms at 1000 C all the way up to PrBaFe 2 O 5.48 .Tetragonal PrBaFe 2 O 5.50 requires 1020 C since below 980 C it fully orders into Pr 2 Ba 2 Fe 4 O 11 of the Cmmm space group, with two phases at 1000 C. Rietveld refinement of the Cmmm Pr 2 Ba 2- Fe 4 O 11 fits all observed PXD reflections, and the obtained parameters are listed in Table

Fig. 2 .
Fig. 2. Temperature dependence of PrBaFe 2 O 5.001(4) volume, orthorhombic distortion and cell parameters per hypothetical single-perovskite cell (subscript sp) to illustrate changes at the phase transition.

Fig. 3 .
Fig. 3. Phase coexistence across the middle range of the valence-mixing transition upon heating the P2 1 ma PrBaFe 2 O 5.001(4) from 40 K to Pmmm at 300 K.

Fig. 4 .
Fig. 4. DSC endothermic effects upon warming 0.2297 g of PrBaFe 2 O 5.011(1) : Loss of charge-and d xz -orbital order around 205 K, loss of weak charge order or separation around 260 K, loss of antiferromagnetic order at T N .

Fig. 5 .
Fig. 5. DSC cycle on 0.10575 g of PrBaFe 2 O 5.001(4) to evaluate the hysteresis of the first-order transition by extrapolating the peak temperatures to zero heating and cooling rate.

Fig. 6 .
Fig. 6.Effect of PrBaFe 2 O 5þw nonstoichiometry on ΔS and ΔH of the main charge-ordering transition.Fit by model of depression of the ordering/ "freezing" temperature by the solute/nonstoichiometry, as in Ref. [9].

Fig. 7 .
Fig. 7. PrBaFe 2 O 5þw double-cell perovskite (P4/mmm) with w disordered and occurrence of the Cmmm superstructure ordered when w !0.5 Their twophase equilibrium range upon cooling and heating is marked by the turquoise bar.
)-(3) as polynomial equations f([O i 00 ]) ¼ 0 and f([v O polynomials that were solved numerically into the evolution of all four defect concentrations along the p O2 range (Fig.9bottom).Defect concentrations in Fig.9bottom concern the donor-doping model of the wide nonstoichiometry.The PrBaFe 2 O 5.0 integer structure is reached at the low p O2 needed to reduce iron to the point where all oxygen brought in by the donor is removed.The integer Fe III state occurs at a higher p O2 , in PrBaFe 2 O 5.5 of structure far from being integer.The w ¼ 0 plateau at the integer-structure PrBaFe 2 O 5.0 is indistinct at this temperature of 1000 C. In contrast, GdBaFe 2 O 5þw of smaller Gd 3þ has a distinct plateau at its O 5 composition.Accordingly, this is due to increased K aF of oxygen defects in the R ¼ Pr version, as well as increased K ox to reach high oxygen contents in oxygen-rich atmospheres.At 1000 C, the √K aF yields[O i 00 ]¼[v O ] ¼ 0.3 at the zero-nonstoichiometry point in Fig. 9.Such a high concentration of v O and O i 00 cannot remain in the ambient structure of PrBaFe 2 O 5 .Indeed, refinement of oxygen-site occupancies from SXPD data does not give any substantial improvement of the fit (Table

Table 1
Synthesis conditions of the PrBaFe 2 O 5.2 master samples used for oxygen-content control across the non-stoichiometry range.

Table 2
(1)stal structure parameters of charge-ordered PrBaFe 2 O 5.011(1)at 100 K refined from SXPD data.U iso (in Å 2 ) were constrained equal for Ba and Pr, all Fe, all O.The z coordinates of O(2a) and O(2b) were constrained equal to keep the pyramidal bases flat and prevent refinement oscillation.All site occupancies ¼ 1.Including the nonstoichiometric O at ¼ ½ ½ or refining its negligible occupancy does not improve the fit.

Table 6
Crystal structure parameters for Pr 2 Ba 2 Fe 4 O 11 quenched from Ar at 856 C as refined from room-temperature PXD data.

Table 7
SXPD pattern refinement results when oxygen occupancies are released in PrBaFe 2 O 5.011(1) at 300 K.