On the entropic contribution to the redox energetics of SrFeO3—d

Camilla Haavik,a Tooru Atake,b Hitoshi Kawajib and Svein StÔlen*a

a Department of Chemistry, University of Oslo, Postbox 1033 Blindern, N0315 Oslo, Norway.E-mail : svein.stolen=kjemi.uio.no

b T okyo Institute of T echnology, Materials and Structures L aboratory, 4259 Nagal Suta-cho,Midori-Ku, Y okohama 226-8503, Japan

Received 18th May 2001, Accepted 2nd July 2001First published as an Advance Article on the web 13th August 2001

The entropic contribution to the redox energetics of the grossly disordered high-temperature phase SrFeO3~dis derived from the heat capacities of and determined by adiabaticSrFeO2.500 , SrFeO2.725 SrFeO2.833calorimetry. All three samples are structurally and magnetically ordered at low temperatures and thecalorimetric data allow deconvolution of the total heat capacity and entropy into approximate contributionsof vibrational, magnetic, electronic and conÐgurational origin. Several thermal e†ects that are easily accountedfor in terms of known magnetic and structural transitions are observed and discussed. The conÐgurationalentropy of the disordered high-temperature phase indicates substantial short-range-order on the oxygensub-lattice even at high-temperatures. The standard entropy at 298 K as well as the total non-conÐgurationalentropy of at high-temperatures varies approximately linearly with composition. The entropies ofSrFeO3~dthe following oxidation reactions

SrFeO2.50 (brownmillerite)] 1/6 O2(g)\ SrFeO2.833 (perovskite)

SrFeO2.50 (perovskite) ] 1/6 O2(g)\ SrFeO2.833 (perovskite)

are deduced. The entropy of oxidation is within the uncertainty of measurement, independent of composition.On the other hand, the entropy of oxidation varies signiÐcantly with temperature. In general, the resultssubstantiate the importance of the vibrational characteristics of reactant and product. While it is oftenassumed that the entropy of oxidation is close to [120 J K~1 (mol the present results indicate that theO2)~1,entropic contribution to the redox energetics must be expected to vary to a large degree from one system toanother.

Introduction

(0O d O 0.5) is grossly non-stoichiometric at highSrFeO3~dtemperatures. Three reduced, vacancy-ordered low-symmetryphases are formed on cooling.1 These will here be representedby the ideal stoichiometries (orSrFeO2.875 Sr8Fe8O23),(or and (or TheSrFeO2.75 Sr4Fe4O11) SrFeO2.50 Sr2Fe2O5).phase relations at low temperatures are complex and not wellestablished and and allSrFeO2.75 , SrFeO2.875 SrFeO3appear to have homogeneity ranges. The composition limits ofthe phases can, however, only be vaguely indicated, based oninformation from literature. Oxygen-rich cubic SrFeO3~dseems at room temperature to be stable for2.92O (3[ d)O 3.0.2 For the phase with ideal composition

single-phase materials with a similar structure areSrFeO2.875 ,reported between and A singleSrFeO2.833 SrFeO2.875 .4phase with an orthorhombic superstructure of the basic cubicunit cell has been reported for the composition range from

to However, in the course of theSrFeO2.681 SrFeO2.75 .3present study, small amounts of are observed in aSrFeO2.50sample with the nominal composition Hence, theSrFeO2.725 .compositional range of the orthorhombic phase seems to bemuch narrower than earlier proposed.5 is stoichio-SrFeO2.50metric at low temperatures.1,6

crystallizes in the cubic perovskite structure with allSrFeO3Fe(IV) octahedrally coordinated by oxygen atoms.4 The stoi-chiometric compound is antiferromagnetically ordered below

K.7T N B 130

is structurally ordered below 1120 K and takesSrFeO2.50the brownmillerite structure with half of the Fe(III) on octa-hedrally coordinated sites and half on tetrahedrally coordi-nated sites.1,4,6 is an antiferromagnet withSrFeO2.50 Ne� eltemperature reported as 6738 or 715 K.6

The phase given by the ideal composition isSrFeO2.75structurally ordered below 670 and 598 K for andSrFeO2.753respectively. The low-temperature crystal struc-SrFeO2.731,

ture contains two crystallographically distinct Fe-sites : onesquare-pyramidal, the other octahedral.4 The mean formalvalence of the iron atoms in is ]3.5. The distribu-SrFeO2.75tion of iron-species on the two crystallographic sites is notfully understood. studies indicate two main com-Mo� ssbauerponents with approximately the same isomer shifts and quad-ropole splitting.1,3,9,10 The component with theMo� ssbauermost positive isomer shift is assigned to high-spin Fe(III),whereas the other component is assigned to high-spin Fe(IV).Due to the larger quadrupole interaction expected for theFe(III) component, Takano and co-workers claimed that Fe(III)is Ðve-coordinated.9 On the other hand, the isomer shift ofFe(III) in should be equal to the isomer shift ofSrFeO2.75octahedral Fe(III) observed for thus Gibb con-SrFeO2.50 ,cluded that Fe(III) is octahedrally coordinated.10 The sameconclusion, based on calculation of bond-strength sums, wasreached in a recent crystallographic study.4

Antiferromagnetic order is observed below 230 K forHowever, only the Fe(III) ions are reported to beSrFeO2.76 .11

magnetically ordered. The Fe(IV) magnetic spins are proposed

DOI: 10.1039/b104401j Phys. Chem. Chem. Phys., 2001, 3, 3863È3870 3863

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to be subject to conÑicting ferromagnetic super-exchangeinteractions, resulting in either a paramagnetic or a spin-glassstructure.4

Three distinct Fe-sites in a 1 : 2 : 1 abundance are suggestedfor the phase with ideal composition One site isSrFeO2.875 .4square-pyramidal (abundance 1) the others octahedral.

and transform to the disordered high-SrFeO2.86 SrFeO2.83temperature perovskite-structure at 5231 and 570 K.3 Theroom temperature spectrum has two main com-Mo� ssbauerponents with equal intensity.1,3 One is assigned to Fe(IV), theother has an isomer shift between those expected for formalFe(III) and Fe(IV) and is assigned to Fe(]3.5).1,3 Bond-strength sums seem to suggest that Fe(IV) occupies the square-pyramidal and one of the octahedral sites (abundance 1),whereas Fe(]3.5) occupies the remaining octahedral sites.4

Various temperatures are observed ; 80 K has beenNe� elreported for 50 K for Additionally,SrFeO2.84 ,7 SrFeO2.86 .12MacChesney reports several anomalous features in the mag-netic properties of First, the magnetic suscepti-SrFeO2.84 .7bility does not obey the CurieÈWeiss law at K.T N \ T \ 200Second, abrupt changes in the magnetization curve wereobserved both at 50 and at 63 K. Finally, when wasSrFeO2.84cooled in a magnetic Ðeld, a remnant magnetization wasobserved. These features were ascribed to the non-stoichiometric character of the sample and short-range order-ing of vacancies on the oxygen sub-lattice was proposed as apossible reason for the observations.7

The non-stoichiometric high-temperature phase has recent-ly been intensively studied and compositionÈpartial pressureisotherms for have been determined by a number ofSrFeO3~dgroups.13h17 Most studies have focused on the transportproperties of this phase since the system is a model for electro-ceramics that can be used as oxide membranes. Although thedefect equilibria in the system have been given most attention,the models implicitly allow determination of enthalpies andentropies of the redox reactions taking place in the systemwhen the oxygen fugacity is changed. The followingtemperature-independent entropies of oxidation have beenreported [in J K~1 (mol [170,13 [15014 andO2~1)] :[180.17 The former value is extrapolated from results forLa1~x

SrxFeO3~d .13

Since these entropies of oxidation have been determinedfrom the partial derivative of the partial Gibbs energy ofoxygen with respect to temperature and since the partial pres-sure isotherms are determined in a limited temperature rangeonly, a calorimetric study of the entropic contribution to theredox energetics of in particular, and of grosslySrFeO3~dnon-stoichiometric oxides in general, is needed to providebetter understanding. The present report focuses on the ther-mochemistry of the system. Details of the extensive calorimet-ric experiments are presented elsewhere.5,18 A complementarystudy of the enthalpy of oxidation of is reportedSrFeO3~dseparately.19

ExperimentalSample preparation and characterisation

Samples of were prepared from (Merck,SrFeO3~d a-Fe2O3[99%) and (BDH Laboratory Supplies [98.5%).SrCO3Prior to use and were annealed in air at 1073a-Fe2O3 SrCO3K for 40 h and at 673 K for 24 h respectively, in order toobtain constant mass. Stoichiometric amounts of a-Fe2O3and were ground together in a ball-mill and calcinedSrCO3in air at 1250 K for 24 h. After regrinding, the powder waspressed into pellets and annealed in air at about 1500 K for 24h and then slowly cooled. The resulting material (from now oncalled starting material) has composition near andSrFeO2.86takes the tetragonally distorted perovskite structure reportedfor SrFeO2.875 .4

In order to prepare samples with lower oxygen contentseveral approaches may be used. Samples with compositionclose to the ideal were made by quenching theSrFeO2.75starting material from 923 K. The X-ray di†ractograms couldbe indexed in accordance with the structural description of

by Hodges and co-workers.4 However, quenchingSrFeO2.75resulted in broad di†raction peaks. Well-deÐned samples wereobtained by annealing the quenched material in evacuatedsilica-glass tubes some few K below the disordering tem-perature.

Materials annealed at high temperatures (1450È1500 K) andcooled in within the furnace gave samples with oxygenN2(g)content near These samples contained two phases :SrFeO2.54 .brownmillerite-type and minor amounts ofSrFeO2.50In order to prepare samples with the exact stoi-SrFeO2.75 .chiometric composition, either the starting materialSrFeO2.50or the sample with composition was reduced bySrFeO2.54using zirconium as oxygen getter. Zr and the sample to bereduced were contained in separate compartments of an evac-uated and sealed silica tube that was annealed at 873 K. Theoxygen-content and the unit-cell dimensions of the calorimet-ric samples are given in Table 1. The unit-cell dimensionsagree favorably with earlier determinations. Unit cell dimen-sions reported by Hodges et al.4 are given in the table forcomparison.

The powder X-ray di†raction data were collected with aSiemens D5000, equipped with a primary Ge-monochromatorand a position-sensitive detector, using radiationCu-Ka1(j \ 154.0598 pm) and Si as internal standard (a \ 543.088pm).20 Unit cell dimensions were determined by least-squaresreÐnements using the UNITCELL program.21

The oxygen content of the samples was determined byredox titrations. The sample was dissolved in anSrFeO3~daqueous HCl solution with a known excess amount ofammonium iron(II) sulfate (Mohr salt). Fe(II) from the Fe(II)sulfate reacts with Fe(IV) from and forms Fe(III).SrFeO3~dThe reaction chamber is continuously Ñushed with Ar(g) priorto and during the redox reaction, to prevent oxidation of

Table 1 Oxygen content and unit-cell dimensions of samples used in the calorimetric experiments. The uncertainties in the compositions are thestandard deviations between the titration parallels

(3[ d) inSrFeO3~d a/A� b/A� c/A� Structure

2.501(4) 5.675(1) 15.572(2) 5.530(1) Brownmillerite type (space group Ibm2)2.725(4) 10.974(2) 7.700(2) 5.474(1) Orthorhombic structure (space group Cmmm)2.740(4) 10.976(1) 7.703(1) 5.472(1) Orthorhombic structure (space group Cmmm)2.833(2) 10.929(1) 7.699(1) Tetragonal structure (space group I4/mmm)2.85(1) Unit cell dimensions not determined2.82(1) Unit cell dimensions not determinedLiterature valuesÈHodges et al.42.500 5.672(1) 15.59(2) 5.527(1)2.75 10.974(1) 7.702(1) 5.473(1)2.875 10.929(1) 7.698(1)

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Fe(II) by in air. After completion of the redox reaction,O2(g)the solution was titrated for excess Fe(II) with standard cericammonium sulfate using ferroin (o-phenantroline ferrouscomplex) as an indicator.

Calorimetry

The details regarding the construction of the laboratory-made,stepwise heated, low-temperature calorimeter as well as themeasurement procedures have been described thoroughly else-where.22 Temperatures were measured with a platinum resist-ance thermometer calibrated at the National PhysicalLaboratory, Teddington, U.K., on the basis of ITS-90. Thereproducibility of the heat capacity determinations is approx-imately ^5 ] 10~2% for 100 \ T /K \ 300 and decreaseswith decreasing temperature to B^0.20% at 13 K.22 Samplesmasses of about 20 g were used in the experiments.

The high-temperature adiabatic calorimetric apparatus andthe measuring technique have also been described earlier.23,24Samples of masses of 36È59 g were contained in evacuatedand sealed vitreous silica containers during measurement. Thevolume of the container that Ðts tightly into the calorimeter isabout 40 cm3. A central well in the container holds the heaterand the platinum resistance thermometer. The calorimeter isheated in a step-wise fashion, and electrically heated and elec-tronically controlled adiabatic shields surround the calorime-ter proper. A guard shield system surrounds the adiabaticshield and the whole assembly is placed in a vertical tubefurnace. The calorimeter, shield, and guard are all made ofsilver.

The temperature was measured with an ASL F-18 resist-ance bridge using locally constructed 25 ) platinum resistancethermometers. Temperature calibration is performed accord-ing to the recommendation of ITS-90 to 933.473 K and thetemperatureÈresistance relationship is extrapolated to 1000 K.The accuracy in temperature determination is considered tobe within ^0.02 K to 903 K, and within ^0.10 K above 903K. The temperature resolution is B3 ] 10~5 K.24

Energy was supplied electrically by a constant currentsource. The current through the heater was measured every 10s and the potential drop across the heater every 1 s inbetween. The potential was measured using a 812 digitHewlett-Packard digital voltmeter. The current was deter-mined by measuring the potential drop over a calibratedresistor. The total time, as well as the triggering of the poten-tial and current measurements, were measured or controlledusing a Keithley counter.

The accuracy and precision of the heat capacity determi-nations are approximately ^0.2%.24 In the present case rela-tively low sample masses were used in the calorimetricexperiments and the accuracy is probably somewhat lower,say 0.4%.

Results and discussion

Heat capacity and thermodynamic properties

The experimental molar heat capacities of SrFeO2.500 ,and at sub-ambient temperatures areSrFeO2.725 SrFeO2.833presented graphically in Fig. 1, whereas corresponding data

for and forSrFeO2.500 , SrFeO2.740 , SrFeO2.82 , SrFeO2.833and for temperatures above ambient are given inSrFeO2.85Fig. 2 and 3.is magnetically ordered below K6,8 andSrFeO2.5 T N B 700

the broad heat capacity shoulder with maximum at around685 K seen in Fig. 2 is due to disordering of the spin orienta-tion. The character of the transition is very similar to the cor-responding transition in at around 735 K.25LaFeO3is reported to have a magnetic orderÈdisorderSrFeO2.75transition at K11 and a heat capacity bump isT N B 220observed in the same temperature region for the SrFeO2.725

Fig. 1 Molar heat capacities of andSrFeO2.50 (È), SrFeO2.725 (…)(6 ) as a function of temperature for temperatures belowSrFeO2.833ambient.

Fig. 2 Molar heat capacity of as a function of tem-SrFeO2.50perature ; low-temperature calorimetry high-temperature calorim-(…),etry The heat capacity of is given as a solid line. The(L). LaFeO325number of moles of atoms are adjusted to be equal to the number ofmoles of atoms in hence (4.5/5) is plotted.SrFeO2.50 , C

p, m(LaFeO3)

Fig. 3 Molar heat capacities of SrFeO2.74 (L), SrFeO2.82 (…),(G) and (J) as a function of temperature forSrFeO2.833 SrFeO2.85temperatures above ambient.

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sample. At 660 K (extrapolated onset) the low-temperaturestructure disorders and the high-temperature perovskite-phaseis formed. The transition temperature compares well withearlier reported transition temperatures ; 670 K for

and 660 K for The transition tem-SrFeO2.753 SrFeO2.74 .26perature reported by Takeda et al.,1 598 K for isSrFeO2.73 ,signiÐcantly lower.

The two temperatures reported in the literature forNe� elare quite di†erent : 80 K for and 50 KSrFeO2.875 SrFeO2.847

for MacChesney et al.7 also report severalSrFeO2.86 .12anomalous features in the magnetic properties of SrFeO2.84for T \ 200 K. The broad heat capacity e†ect observed in thepresent study for in the temperature region fromSrFeO2.83350 to 120 K, is consistent with the earlier observed behaviourthat also took place over an extended temperature range.

The oxygenÈvacancy disordering of the low-temperaturestructure for samples in the compositional range toSrFeO2.82is observed at around 560 K (extrapolated onset) inSrFeO2.85reasonable agreement with the literature values, 5231 and 570K.3

In order to derive the standard entropy of SrFeO2.500 ,and the experimental heat capacitiesSrFeO2.725 SrFeO2.833were Ðtted to polynomials in temperature by the method of

least squares. Below T \ 13 K the heat capacities wereextrapolated as Although the present low-C

p, m\ cT ] bT 3.temperature data do not allow us to derive reliable electronicheat capacity coefficients, the constants obtained allow us toestimate the entropy from zero K. It should be realized thatthe entropy increment from zero to 13 K is small and, hencethe uncertainty in this estimate is negligible for the entropy ofthe disordered phases at high temperatures. The standardentropy at 298 K varies approximately linearly with composi-tion, see Fig. 4. The experimental standard entropies for

are furthermore in good accordance with the stan-SrFeO3~ddard entropy of SrMnO2.60 .27In order to derive the thermodynamic properties of

and at high temperatures we had toSrFeO2.725 SrFeO2.833take into consideration that the samples studied at low andhigh temperatures had slightly di†erent oxygen-contents.Since the e†ect of composition often has a much larger e†ecton the heat capacity and thus on the entropy at low tem-peratures compared to high temperatures, we estimate high-temperature heat capacities for the compositions studied atlow temperatures. For the sample studied at““SrFeO2.875 ÏÏlow temperature had composition whereas theSrFeO2.833 ,three samples used to determine the heat capacity at T [ 300K had compositions andSrFeO2.82 , SrFeO2.833 SrFeO2.85 .We assume that the change in heat capacity with compositionat high temperatures is proportional to the change in the total

Fig. 4 Standard entropy of (Ae \ alkaline earth metal ;AeTmO3~dTm\ transition metal) at 298 K as a function of composition.present study),SrFeO3~d (…, SrMnO3~d (L).27

number of atoms, hence,

Cp, m(SrFeO3~x

) \A5 [ y5 [ x

BC

p, m(SrFeO3~y) (1)

The experimental and adjusted heat capacities for SrFeO2.82and shown in Fig. 5 indicate that the chosenSrFeO2.85approach is reasonable.Samples with di†erent compositions were also used to

determine the heat capacity for ideal SrFeO2.75 ; SrFeO2.725in the low temperature experiments and in theSrFeO2.740high temperature determinations. Analogue corrections as forthe samples were made.SrFeO2.875It should be noted that the overlap between the low- andhigh-temperature determinations for is outside ourSrFeO2.50assumed measurement uncertainty. The high-temperatureresults are about 1% lower than the low temperature resultsat 300 K. The reason for this discrepancy is not known andthe two datasets are given equal weight in the evaluation ofthe thermodynamic properties. The heat capacity used toderive the thermodynamic properties of the compound isgiven by the dotted line in Fig. 2.

The enthalpy and entropy of the structural orderÈdisordertransitions observed for and at 660SrFeO2.740 SrFeO2.833and 560 K are determined by integration of the observed heatcapacities in the transitional region. The enthalpy and entropyof the transitions are J mol~1 and*structHm \ 5328

J K~1 mol~1 for and*structSm\ 7.76 SrFeO2.740 *structHm \J mol~1 and J K~1 mol~1 for2071 *structSm \ 3.67

SrFeO2.833 .Smoothed values of the molar heat capacities and derived

values of the molar enthalpies and entropies for SrFeO2.500 ,and at selected temperatures are givenSrFeO2.725 SrFeO2.833in Tables 2È4.

The molar entropies of andSrFeO2.500 , SrFeO2.725given in Tables 2È4 are deduced from experimen-SrFeO2.833tal data. These entropies include all entropy contributions dueto vibrations as well as due to the disordering that take placein the temperature range covered experimentally. Hence,neglecting zero-point or residual entropy, the entropies shouldinclude the entropy due to randomization of the spins on theiron atoms, due to distribution of di†erent species on the dif-ferent sub-lattices as well as the vibrational and electroniccontributions.

In order to deduce entropies at the temperatures wherecompositionÈpartial pressure isotherms have been determinedby equilibration techniques, the experimental heat capacitiesmust be extrapolated to higher temperatures. The extrapo-

Fig. 5 Molar heat capacities of andSrFeO2.82 (K), SrFeO2.833 (L)as a function of temperature. Heat capacities ofSrFeO2.85 (È)

and adjusted to correspond to the compositionSrFeO2.82 SrFeO2.85of the sample used in the low-temperature experiments, SrFeO2.833 ,are given by and(=) (@).

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Table 2 Molar heat capacities molar enthalpies andCp, m , *0THmmolar entropies at selected temperatures for*0TSm SrFeO2.500g mol~1NMM(SrFeO2.50)\ 183.4635

Cp, m/ *0THm/ *0TSm/

T /K J K~1 mol~1 J mol~1 J K~1 mol~1

15 0.779 3.075 0.28620 1.803 9.304 0.63725 3.338 21.960 1.19630 5.305 43.408 1.97235 7.613 75.582 2.96040 10.168 119.95 4.14145 12.886 177.53 5.49450 15.696 248.96 6.99760 21.406 434.45 10.3670 27.068 676.90 14.0980 32.668 975.06 18.0690 38.016 1328.8 22.22

100 43.025 1734.2 26.49120 52.229 2688.5 35.16140 60.494 3817.2 43.85160 67.897 5102.5 52.42180 74.470 6527.5 60.80200 80.242 8075.9 68.95220 85.245 9732.1 76.84240 89.522 11 480 84.45260 93.129 13 308 91.76280 96.133 15 202 98.77298.15 98.02 16 968 104.89300 98.21 17 149 105.49350 102.97 22 180 120.99400 107.60 27 445 135.05450 111.95 32 936 147.98500 115.48 38 625 159.96550 118.07 44 467 171.10600 120.51 50 429 181.47650 124.89 56 550 191.27683.86 130.82 60 869 197.74694.21 122.16 62 177 199.64700 121.52 62 883 200.65750 118.01 68 857 208.90800 117.90 74 739 216.49

lation is based on using the sum of the heat capacities ofSrO28 and the (““non-magnetic ÏÏ) heat capacity of (0.5) a-

to Ðx the shape of the vs. T curve. ForFe2O329 Cp, mand for the heat capacity above theSrFeO2.500 SrFeO2.740magnetic and structural orderÈdisorder temperatures, respec-

tively, were used to Ðx the absolute values of the heat capac-ity. For the heat capacity was not measured aboveSrFeO2.833the structural orderÈdisorder transition and was insteadassumed to be proportional [eqn. (1)] to the heat capacity of

for The extrapolated entropies areSrFeO2.740 T [Tstruct .given as a function of temperature in Fig. 6. The discontinuityfor at 1120 K is due to the structural orderÈSrFeO2.50disorder transition. The enthalpy and entropy of transitionwere determined by di†erential thermal analysis, (DTA) (seeref. 5 for details). Four determinations were made, resulting in

K (extrapolated onset), kJTstruct\ 1120(5) *structHm \ 8.5(1.2)mol~1 and J K~1 mol~1. The transition*structSm \ 7.6(1.2)temperature compares well with earlier reported values ;1103,1 1123 K.6

The entropy increments from 800 to 1200 K are to someextent determined by the chosen extrapolation of the heatcapacity at temperatures above the maximum temperature ofthe experiments. Other extrapolation schemes may be pro-posed. The present scheme is, however, in our opinion themost reasonable since it is based on the use of the heat capac-ity of the binary oxides as a starting point to determine theshape of the vs. T curve at high temperatures. Addi-C

p, mtionally, the absolute value is Ðxed by the experimental lower-temperature data. The latter choice is the more importantfactor for the deduced entropy increments.

Table 3 Molar heat capacities molar enthalpies andCp, m , *0THmmolar entropies at selected temperatures*0TSm SrFeO2.725g mol~1NMM(SrFeO2.725)\ 187.0634

Cp, m/ *0THm/ *0TSm/

T /K J K~1 mol~1 J mol~1 J K~1 mol~1

15 0.408 1.396 0.12220 1.177 5.098 0.33025 2.602 14.274 0.73330 4.627 32.118 1.37835 7.126 61.330 2.27440 9.970 103.95 3.40845 13.045 161.42 4.75850 16.263 234.64 6.29860 22.878 430.26 9.84670 29.457 692.00 13.8780 35.787 1018.5 18.2290 41.772 1406.6 22.78

100 47.405 1852.8 27.48120 57.668 2905.7 37.05140 66.667 4151.1 46.63160 74.500 5564.5 56.06180 81.413 7124.9 65.24200 87.789 8817.5 74.15220 93.702 10 634 82.80240 95.531 12 538 91.08260 98.462 14 478 98.84280 101.206 16 475 106.24298.15 103.79 18 334 112.67300 104.03 18 526 113.32350 109.46 23 870 129.78400 113.43 29 448 144.67450 116.35 35 196 158.21500 118.71 41 073 170.59550 121.11 47 067 182.02600 124.28 53 197 192.68640 127.95 58 237 200.81OrderÈdisorder transition710 128.73 72 451 221.74750 129.37 77 613 228.82800 130.25 84 101 237.19

From redox energetics to composition–partial pressureisotherms

Single phase is stable over the whole compositionalSrFeO3~dregion, 0\ d \ 0.5, at temperatures above 1120 K, the tem-perature at which brownmillerite type transformsSrFeO2.50into the perovskite-type structure. Below this temperaturebrownmillerite type precipitates when isSrFeO2.50 SrFeO3~dreduced below a certain limit. The main aim of the presentstudy is to deduce the entropic contribution to the energeticsof the perovskite-type phase with respect to oxidation/reduction. In order to compare the present calorimetric datawith earlier compositionÈpartial pressure isotherms, a model

Fig. 6 Extrapolated molar entropies of (ÈÈ),SrFeO2.50(È È È) and (É É É) as a function of temperatureSrFeO2.725 SrFeO2.833above 800 K.

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Table 4 Molar heat capacities molar enthalpies andCp, m , *0THmmolar entropies at selected temperatures for*0TSm SrFeO2.833g mol~1NMM(SrFeO2.833)\ 188.7913

Cp, m/ *0THm/ *0TSm/

T /K J K~1 mol~1 J mol~1 J K~1 mol~1

15 0.595 2.527 0.24420 1.377 7.217 0.50825 2.771 17.314 0.95330 4.814 36.018 1.63035 7.393 66.345 2.56040 10.371 110.60 3.73745 13.748 170.71 5.14950 17.508 248.91 6.79460 24.896 461.08 10.6470 31.672 745.92 15.0280 37.957 1093.5 19.6590 44.642 1506.6 24.51

100 50.909 1984.9 29.54120 61.221 3112.1 39.79140 69.025 4413.2 49.80160 76.544 5870.4 59.52180 83.204 7469.2 68.93200 89.039 9193.0 78.00220 94.038 11 025 86.73240 97.540 12 944 95.08260 100.934 14 929 103.02280 103.968 16 978 110.61298.15 106.05 18 887 117.22300 106.26 19 083 117.87350 111.41 24 529 134.65400 115.86 30 212 149.82450 120.13 36 112 163.71500 124.98 42 235 176.61540 129.90 47 328 186.41OrderÈdisorder transition600 127.10 56 646 202.76

describing the variation of the oxygen partial pressure withcomposition is needed.

The redox process involves a simultaneous change inoxygen non-stoichiometry and in the formal valence state ofthe transition metal. In the simplest model the non-stoichiometric oxide is seen as an ideal solid solution of twolimiting compositions with di†erent formal valence state i.e.

and where Ae\ alkaline earthAeTmO3 AeTmO2.5 ,30,31metal and Tm \ transition metal. Let us for simplicity assumethat Tm(III) and Tm(IV) are mixed randomly on the iron sub-lattice while O2~ and are distributed randomly on theVO2~oxygen sub-lattice. The ideal solution assumption implies thatthe Gibbs energy of the redox reaction is independent of com-position. The relationship between the partial pressure ofoxygen and stoichiometry of the phase is then given through

log P(O2)\4

RT ln 10[*fG0(SrFeO3)[*fG0(SrFeO2.5)]

] 4[log(1[ 2d)[ log(2d)][ 2 logA d3 [ d

B(2)

The Ðrst term on right is in this ideal solution approach theGibbs energy of oxidation

*fG0(SrFeO3)[ *fG0(SrFeO2.5)4 *ox G\ *ox H [ T *ox S

(3)

that corresponds to the reaction

SrFeO2.5 (perovskite) ] 14O2 ] SrFeO3.00 (perovskite) (4)

In the ideal solid solution model used the enthalpy andentropy of oxidation are independent of composition. Non-ideal terms can easily be incorporated into the model. Thiswill enable us to take compositional e†ects on the entropy ofoxidation into consideration and the Gibbs energy of oxida-tion will no longer be directly related to eqn. (4).

The last two terms in eqn. (2) represent the partial conÐgu-rational entropy of oxygen and the entropic contribution tothe redox energetics, and should not include the struc-*oxS,tural conÐgurational contribution. This term is includedexplicitly in the conÐgurational part of the equation. Hence,the experimental conÐgurational entropy should be subtractedfrom the total experimental entropy where appropriate.

Entropic contribution to the redox energetics of SrFeO3—d

The entropy increments of the structural orderÈdisorder tran-sitions have three main contributions. The Ðrst is due to thedi†erence in the vibrational properties of the low-temperaturephase that is more or less ordered and the disordered high-temperature phase. The second is the di†erence in electronicentropy, while the last is the conÐgurational entropy due to adistribution of oxygen vacancies and oxygen atoms on theoxygen lattice sites and di†erent iron cations on the Fe sub-lattice at high temperatures. At low temperatures the inter-action between the defects leads to the formation of orderedsuperstructures. As a Ðrst approximation we will assume thatthe changes in both the vibrational and the electronic entropyon disordering are negligible. We will also assume that thelow-temperature structures are completely ordered. Theexperimental entropy of transition is then identical to the con-Ðgurational entropy of the disordered perovskite phase. Still,the homogeneity regions of and indi-SrFeO2.75 SrFeO2.875cate that this is a Ðrst approximation only, at least for thesecompositions, since the Ðnite homogeneity-regions indicatethat the material cannot be completely ordered at 0 K.

The experimental conÐgurational entropies may be com-pared with simple estimates assuming random distributions ofthe di†erent species at the di†erent sub-lattices. The total con-Ðgurational entropy is given by :

*config S \ R[(1 [ 2d) ln (1 [ 2d) ] (2d) ln (2d)]

] RCd ln

Ad3

B] (3 [ d) ln

A1 [

d3

BD(5)

where the Ðrst term on the right hand side corresponds to arandom distribution of Fe(III) and Fe(IV) on the iron sub-lattice. The last term is the contribution from a random dis-tribution of oxygen ions and oxygen vacancies on the oxygensub-lattice. The dotted line in Fig. 7 gives the total conÐgu-rational entropy as a function of (3 [ d). The experimentalconÐgurational entropies are much lower. For theSrFeO2.50

Fig. 7 Comparison of the presently determined conÐgurationalentropies of disordered and withSrFeO2.500 , SrFeO2.740 SrFeO2.833ideal solution estimates. The solid line represents the conÐgurationalentropy corresponding to a random distribution of oxygen ions andoxygen vacancies on the oxygen sub-lattice. The dashed line rep-resents a random distribution of Fe(III) and Fe(IV) on the iron sub-lattice ; while the dotted line is the sum of these two contributions.

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di†erence between the theoretical and experimental conÐgu-rational entropy may only be due to some degree of order onthe oxygen sub-lattice above Hence, signiÐcant short-Tstruct .range order is present in the high-temperature phase. Entropymodels that include short-range order in the high-temperaturephase are not easily derived since the main structural buildingblock is corner-sharing Such considerationsTmO6-octahedra.are outside the scope of the present paper.

The total entropy and the total non-conÐgurational entropyof are given as a function of composition at selectedSrFeO3~dtemperatures in Fig. 8. The entropy of needed toSrFeO3determine is obtained by the linear extrapolation indi-*oxScated by the solid lines. We have here assumed all phases tobe perfectly ordered at zero K. It has been suggested that theFe(IV) ions in are magnetically disordered at 4 K.SrFeO2.75This would imply that the magnetic disordering entropy ofFe(IV) in is not included in our experimentallySrFeO2.75determined entropy for Adding a theoretical spin-SrFeO2.75 .only entropy, J K~1 mol~1 would, however,*spinvonlyS \ 6.0lead to an unexpected maximum in entropy vs. composition.

The entropies of the following two reactions

SrFeO2.50 (brownmillerite)] 1/6 O2(g)

\ SrFeO2.8333 (perovskite) (6)

SrFeO2.50 (perovskite) ] 1/6 O2(g)

\ SrFeO2.8333 (perovskite) (7)

are given as a function of temperature in Fig. 9. Theseentropies are related through the entropy of the orderÈdisorder transition in SrFeO2.50

SrFeO2.50 (brownmillerite)\ SrFeO2.50 (perovskite) (8)

Entropies of oxidation deduced from equilibrationstudies13,14,17 are also included in the Ðgure. The temperatureof measurement used in the Ðgure is in each case the mediantemperature of the experiments. The entropies of oxidation inthese studies are deduced from point-defect equilibrium treat-ment of the main defect reaction that takes place in SrFeO3~d(0\ d \ 0.5)

2OOx ] 4FeFex \ 2V 0~~ ] 4FeFe@ ] O2(g) (9)

It can be shown that this treatment leads to an equation thatcorrespond to the present eqn. (2)31 and, hence, that theentropy of oxidation deduced from this kind of Kro� gerÈVinktreatment corresponds to the entropy of reaction (6).

All values from the equilibration studies are more negativethan the value reported here. Since, these entropies of oxida-tion have been determined from the partial derivative of thepartial Gibbs energy of oxygen with respect to temperatureand since the partial pressure isotherms are determined in a

Fig. 8 Molar entropy (Ðlled symbols) and molar non-conÐgurationalentropy (open symbols) of disordered at 800 1000SrFeO3~d (=, K),

and 1200 K.(…, L) (>, |)

Fig. 9 Entropies of reaction (6) (G) and (7) (H) as a function of tem-perature. Literature values13,14,17 corresponding to reaction (6) arealso included.

limited temperature range only, we believe the present calori-metric results to be more accurate. It should be noted that thevibrational entropy is much larger than the conÐgurationalentropy. Hence, although the conÐgurational entropy deducedin the present study have a signiÐcant uncertainty (of theorder of 2 J K~1 mol~1) this does not represent a large uncer-tainty in the entropy of oxidation.

The variation of the entropy of oxidation with temperatureis to some extent given by the chosen extrapolation of the heatcapacities to high temperatures. However, the most importantpart of the estimate, the absolute value of the heat capacity, isdetermined by the experimental heat capacities above thestructural orderÈdisorder temperature for two of the samples.The shape of the heat capacity curves at high temperatures isless important for the entropy estimate. Hence, we are con-Ðdent that the extrapolated temperature dependence is rea-sonable. This is substantiated by the fact that the observedtemperature dependence is within the range observed forredox reactions that involve binary transition metal oxides,see Fig. 10. A temperature dependence of the entropy of oxi-dation of the order presently observed, hence, seems to bewithin the uncertainty of the entropy of oxidation deducedfrom the equilibration studies. Finally it should be noted that

Fig. 10 Entropy of oxidation per mol as a function of tem-O2perature. The present data for are compared with valuesSrFeO3~dfor pairs of binary transition metal oxides (the thermochemical dataare taken from Barin32). Example : Mn(2,3) represents the reaction4MnO (s). Entropies of reaction (6) and(s)] O2 (g)\ 2Mn2O3 (…)(7) are also given (per mol(L) O2).

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Fig. 11 Deconvolution of the non-conÐgurational entropy ofand of at 1000 K into contributions of vibrational,SrFeO2.5 SrFeO3magnetic and electronic origin.

if the entropic contribution to the redox energetics varies withtemperature, the enthalpy of oxidation must also vary withtemperature.19

The present entropy of oxidation is low compared to theentropy of redox reactions between pairs of binary transitionmetal oxides, see Fig. 10. This di†erence is interesting andneeds further consideration. The entropy of oxidation, givenby the di†erence in entropy between andSrFeO2.50 SrFeO3.0 ,can be deconvoluted into approximate vibrational, electronicand magnetic contributions. If we use T \ 1000 K as anexample, is structurally ordered while magneticallySrFeO2.50disordered. Using an estimated magnetic entropy based on thespin-only approximation were is given by Rln(2S ] 1),*magnSthe total harmonic ] anharmonic vibrational entropy isdeduced, see Fig. 11. The electronic contribution is negligiblysmall for semi-conducting on the otherSrFeO2.50 . SrFeO3 ,hand, is reported to have metallic conductivity7 and a signiÐ-cant electronic heat capacity coefficient must be expected. Letus assume an electronic heat capacity coefficient of the orderobserved for metals, 5 mJ K~1 mol~1. Using the spin-onlymagnetic entropy the total vibrational entropy is obtained.Although this deconvolution scheme is uncertain, a main con-clusion is evident ; the entropic contribution to the redox ener-getics is to a large extent given by the vibrational entropies ofthe limiting compounds, in this case andSrFeO2.50It follows that the entropic contribution to theSrFeO3.00 .redox energetics of non-stoichiometric oxides must beexpected to vary considerably from case to case. This isevident from Fig. 10 that shows that the entropy of the binaryredox pairs also varies considerably from case to case. Themain reason for the large spread in behaviour is related to thevibrational properties of the oxides. While the absolute valuesof the entropy of the binary iron oxides FeO and areFe2O3approximately equal per mol iron, the entropy of SrFeO3~dshows a much stronger dependence on composition. A maindi†erence is that whereas e.g. FeO and take di†erentFe2O3structures, the changes in structure on going from SrFeO2.50to is much smaller. Hence, to a Ðrst approximationSrFeO3

the entropy depends on the total number of atoms present inthe compound. New atoms that are incorporated into thestructure do not alter the vibrational characteristics of thephase signiÐcantly but contribute with six degrees of freedomper atom, hence by a 3k contribution to the heat capacity athigh temperatures.

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