Anisotropic and Nonlinear Thermal and Chemical Expansion of La1

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Anisotropic and Nonlinear Thermal and Chemical Expansion of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) Perovskite Materials Xinzhi Chen and Tor Grande* Department of Materials Science and Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway S Supporting Information *

ABSTRACT: La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) materials were investigated by in situ hightemperature X-ray diffraction in pure O2 and N2. A rhombohedral symmetry was found at ambient temperature for the perovskite materials in agreement with previous reports. The rhombohedral distortion of the perovskite structure (space group R3̅c) from the cubic prototype decreased with increasing temperature, and the materials became cubic perovskites (Pm3m ̅ ) at elevated temperatures. The cubic to rhombohedral phase transition temperature decreased with increasing Sr-substitution level and with decreasing partial pressure of oxygen. The thermal expansion of the materials below the phase transition was strongly anisotropic. The two order parameters of the phase transition, the antiferrodistortive tilting and compression of the FeO6/2 octahedra, were determined by Rietveld refinement of the diffraction patterns. A large chemical expansion of the materials because of thermal reduction of the oxidation state of Fe was observed. The chemical expansion was strongly anisotropic below the rhombohedral to cubic phase transition temperature and strongly nonlinear with respect to the oxygen nonstoichiometry. The microscopic origin of the anisotropic nature of the chemical expansion is discussed as well as the nonlinear dependence of chemical expansion with respect to the concentration of oxygen vacancies.

KEYWORDS: perovskite, LaMO3 (M = Fe, Co, Mn), thermal expansion, chemical expansion, anisotropy, nonlinearity

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INTRODUCTION LaMO3 (M = Fe, Co, Mn) based perovskites, and especially Srdoped La1−xSrxMO3±δ materials, have been widely studied because of their structural, electrical, and magnetic properties.1−7 The substitution of Sr on La sites in these perovskite materials leads to a rich point defect chemistry,6,8 which causes oxygen ionic conductivity due to oxygen vacancies and significant electronic conductivity due to a mixed valence state of the transition metal M.4 The combination of electronic conductivity and oxygen ionic conductivity at elevated temperatures have opened up applications of these materials as cathodes in solid oxide fuel cells (SOFCs), 2,9−11 catalysts,5,12−15 and as mixed ion and electron conducting membranes (MIECs) for oxygen separation or natural gas conversion.16−21 The La1−xSrxMO3±δ materials are permanently exposed to chemical potential gradients in these high temperature electrochemical devices, which also must withstand thermal cycling. The thermo-mechanical properties, including thermal and chemical expansion, are therefore vital for the longterm mechanical stability of these high temperature electrochemical devices. Significant mismatch in thermal expansion between membranes and sealing materials or a cathode and © XXXX American Chemical Society

electrolyte in a SOFC will induce stresses during thermal cycling. Moreover, chemical expansion gives additional stresses when the materials are exposed to a gradient in the chemical potential of oxygen.22 Despite the enormous amount of work on the performances of the these materials in such applications like SOFCs and MIECs, only a limited amount of work has focused on the issues of the thermal expansion,23−29 the chemical expansion due to redox defect chemistry,22,28−31 and mechanical properties of the materials.32−35 The anisotropic nature of the thermal and chemical expansion of La1−xSrxMO3±δ materials is closely related to the deviation from cubic symmetry. The crystal structure, the second order rhombohedral to cubic phase transition and the anisotropic nature of the thermal and chemical expansion of La1−xSrxMnO3+δ and La1−xSrxCoO3−δ materials have recently been studied in the author’s laboratory.36,37 The thermal expansion of the large lattice parameter c is about twice the size of the corresponding thermal expansion of the short unit cell Received: April 4, 2013 Revised: July 19, 2013

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dx.doi.org/10.1021/cm401100c | Chem. Mater. XXXX, XXX, XXX−XXX

Chemistry of Materials

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Table 1. Crystallographic Dataa of Rhombohedral La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) with Space Group at Ambient Temperatureb atomic positions and occupancy

O displ.

x

lattice parameters

atom

x/a

y/b

z/c

occ.

0.3

ah = 5.5528(5) ch = 13.4795(8)

0.4

ah = 5.5318(5) ch = 13.4254(9)

0.5

ah = 5.5094(7) ch = 13.4174(9)

La Sr Fe O La Sr Fe O La Sr Fe O

0 0 0 0.1176(8) 0 0 0 0.1215(1) 0 0 0 0.1264(8)

0 0 0 1/3 0 0 0 1/3 0 0 0 1/3

0.25 0.25 0 1/12 0.25 0.25 0 1/12 0.25 0.25 0 1/12

0.7 0.3 1.0 1.0 0.6 0.4 1.0 1.0 0.5 0.5 1.0 1.0

e

Rwp 5.25

0.04898(7) 5.34

0.04515(7) 6.39

0.04018(7)

Lattice parameters ah and ch, atomic positions and the displacement from the cubic position for oxygen ions (e) and goodness of the fit (Rwp). bFor LSF-73 the parameters are collected at 200 °C. a

The materials were dried at 800 °C prior to use to remove humidity. Stoichiometric amounts of the solid state precursors were thoroughly mixed in an agate mortar and fired in air at 1200 °C for 24 h twice with intermediate grindings to ensure chemical homogeneity. The powders were further pressed into pellets and fired at 1200 °C for 12 h. The pellets were crushed, and the powders were finally annealed at 800 °C for 24 h in air and slowly cooled (30 °C/h) to oxidize the materials to obtain a close to stoichiometric oxygen content. High temperature X-ray diffraction (HTXRD) was performed with a θ−θ Bruker D8 ADVANCE diffractometer utilizing Cu Kα radiation and equipped with a VANTEC-1 position sensitive detector. Powders for investigation were contained within an alumina sample holder and heated using a radiant heater mounted within an MRI Physikalische Geräte GmbH high temperature camera. Prior to heating the camera was evacuated and flushed three times with the appropriate sweep gas O2 or N2, and a constant slow flow of gas was maintained for the duration of the experiment. The partial pressure of oxygen in the N2 was estimated to 5 × 10−5 atm. An S-type thermocouple mounted in close proximity to the sample was used for temperature determination. Calibration of the system against an Al2O3 standard gave an estimated temperature error of ±15 °C. Patterns were collected from 100 to 1050 °C (every 25 °C every step), across an angular range 15−75° 2θ, which was the 2θ range possible using a radiant heater. A step size of 0.016° was used. Prior to collecting the pattern, the sample was held for 30 min at the set temperature to establish equilibrium between the material and the atmosphere. Total collection time per scan at one temperature was approximately 70 min, which was sufficient collection time to obtain low signal-to-noise ratio and good accuracy of the diffraction patterns. The heating rate between each temperature was 5 °C/min. Rietveld refinements were carried out with the Topas Academic software version 4.2.47 For La0.6Sr0.4FeO3−δ and La0.5Sr0.5FeO3−δ, the structure of two phases was described using a hexagonal model (R3̅c) at low temperatures and a cubic model (Pm3̅m) at high temperatures as described in a previous study.38 For La0.7Sr0.3FeO3−δ, a mixture of both orthorhombic and rhombohedral phases was observed at ambient temperature and thus Rietveld refinement with the hexagonal setting was started from 200 °C. The peak shapes were described using a Fundamental Parameters model, with broadening described according to a crystallite size type angular dependence. For all temperatures independent variables consisted of five different parameters: Chebychev polynomial background function, lattice parameters, sample displacement, symmetry constrained atomic positions, and isotropic thermal displacement parameters. The atomic positions for the space group R3̅c were (0, 0, 1/4) for La3+/Sr2+, (0, 0, 0) for Fe3+, and (1/6-e, 1/3, 1/12) for O2− where e is the displacement from the ideal cubic position. The oxygen occupancy was fixed to unit at low temperature in line with experiments,8,29 while the oxygen occupancy

constant a because of the thermal evolution of the antiferrodistortive rotation of the MO6/2 octahedra in the rhombohedral perovskite. Moreover, the chemical expansion/ contraction is more pronounced along the a-axis for La1−xSrxMnO3+δ, while the chemical expansion along the caxis is larger than along the a-axis in La1−xSrxCoO3−δ. This important difference reflects the influence of oxygen excess (cation deficiency) in the first and oxygen deficiency in the latter material. The phase transitions and the anisotropic nature of the thermal expansion of LaFeO3 have also recently been reinvestigated.38,39 Pure LaFeO3 materials are orthorhombic perovskites with Pbnm space group at ambient temperature and go through a first order phase transition to a rhombohedral perovskite at elevated temperatures.39,40 LaFeO3 transforms to rhombohedral and finally cubic perovskite with increasing Sr substitution,38,41 and the phase transition temperatures from the orthorhombic to rhombohedral and rhombohedral to cubic have been shown to be suppressed by Sr substitution.38 The increasing oxygen non-stoichiometry of La1−xSrxFeO3−δ with decreasing partial pressure of oxygen8 has also been shown to suppress the rhombohedral to cubic phase transition. However, at high level of Sr substitution and oxygen deficiency, ordering of the oxygen vacancies has also been shown to decrease the crystal symmetry because of formation of brownmillerite type of crystal structures.42−46 Here we report on the anisotropic thermal and chemical expansion of materials in the La1−xSrxFeO3−δ series (x = 0.3, 0.4, 0.5) prepared by solid state synthesis. In situ high temperature X-ray diffraction was employed to investigate the anisotropic thermal and chemical expansion of the materials. The strong crystallographic anisotropy of the chemical expansion of La1−xSrxFeO3−δ is reported for the first time as well as the strong nonlinear dependence of the chemical expansion with respect to the oxygen vacancy concentration. Finally, possible microscopic mechanisms for the anisotropic nature of the chemical expansion and the nonlinear relationship between chemical expansion and oxygen deficiency are discussed.

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EXPERIMENTAL SECTION

La1−xSrxFeO3−δ (LSF) powders of compositions x = 0.3, x = 0.4, x = 0.5 were prepared by solid state reaction using La2O3 (VWR, > 99.9%), SrO (Sigma-Aldrich, > 99.9%), and Fe2O3 (VWR, > 99%). B



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was refined at elevated temperatures in the temperature region where thermogravimetry, see below, confirmed the oxygen-non-stoichiometry. Thermogravimetric analysis (TGA) of the annealed La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) was performed using a Netzsch STA 449C TG-DSC in both O2 and N2 atmospheres. The materials were assumed to be stoichiometric with respect to oxygen prior to the analysis. The heating rate was 5 °C/min. Scanning electron microscopy (SEM) was performed using a Hitachi S-3400N instrument.

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RESULTS La0.6Sr0.4FeO3 and La0.5Sr0.5FeO3 were single phase materials at ambient temperature according to X-ray diffraction (XRD). The XRD patterns of La0.7Sr0.3FeO3 below 200 °C could only be refined using a mixture of an orthorhombic and a rhombohedral perovskite phase in line with previous reports,38,48 while from 200 °C and above the diffraction pattern could be indexed to a single rhombohedral perovskite phase. The crystal structure parameters for La0.6Sr0.4FeO3 and La0.5Sr0.5FeO3 at ambient temperature and La0.7Sr0.3FeO3 at 200 °C are summarized in Table 1, and the crystallographic data are in good agreement with the literature.38,41 The particle sizes of the materials were found by SEM to vary between 2 to 9 μm with a relatively narrow particle size distribution (SEM micrographs of the powders are provided in the Supporting Information). The particle size is important for the discussion of the relaxation time to reach equilibrium of the point defect reaction leading to oxygen non-stoichiometry during heating.36 TGA of the three oxide powders were performed, see Figure 1, to confirm that the materials were close to being stoichiometric (δ ≈ 0) after the final annealing step. No weight gain was observed by TGA when the samples were heated in O2 atmosphere, nor was any contraction observed by HTXRD due to oxidation except for La0.5Sr0.5FeO3 (described in detail further below). It was therefore concluded that La0.7Sr0.3FeO3 and La0.6Sr0.4FeO3 powders became essentially stoichiometric with respect to oxygen after cooling slowly from the final annealing step, while a minor oxygen nonstoichiometry (δ) at ambient temperature was inferred for La0.5Sr0.5FeO3−δ. The onset of thermal reduction (δ>0) is shifted downward with increasing Sr substitution and reducing partial pressure of oxygen. The relaxation time during the dynamic TGA measurements is not sufficient to obtain equilibrium, particularly in the case of N2 atmosphere because of the considerable amount of oxygen released from the materials during heating. Attempts to measure the equilibrium oxygen content were not conducted because of the significant body of literature concerning the oxygen deficiency and point defects in the La1−xSrxFeO3−δ system.8,29,49,50 Equilibrium oxygen content in the materials, calculated from a comprehensive model developed by Mizusaki et al. and similar studies,8,29,49,50 is shown for comparison in Figure 1, and this model was used to calculate the oxygen non-stoichiometry for the materials in the following. The models for the three materials are summarized in the Supporting Information. All the diffraction data of La1−xSrxFeO3−δ were refined with the space group R3c̅ or Pm3m ̅ . Generally a good fit (Rwp < 7.0%) was obtained for all the patterns, and a representative Rietveld refinement of the X-ray diffractogram for La0.6Sr0.4FeO3 at 100 °C in O2 is shown in Figure 2. The hexagonal unit cell parameters ah and ch of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) below the second order phase transition temperature are shown as a function of temperature in pure O2 and N2 atmosphere in Figure 3. Above the rhombohedral to

Figure 1. Oxygen stoichiometry versus temperature of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) in O2 and N2 atmospheres. The equilibrium oxygen content calculated by a model provided by Mizusaki et al.8,29,49,50 is shown for comparison.

Figure 2. Typical Rietveld fit of an X-ray diffraction pattern of La0.6Sr0.4FeO3−δ collected at 100 °C in O2 atmosphere, Rwp = 5.45.

cubic phase transition temperature the cubic unit cell parameters are displayed in Figure 3 as well. The lattice parameters and the atomic position of oxygen are summarized for each temperature and atmosphere in the Supporting Information. The thermal expansion of the lattice parameters of La0.7Sr0.3FeO3−δ below ∼400 °C was not dependent on the oxygen partial pressure, see Figure 3a. The thermal expansion C



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although it is also clearly evident in this case, particularly for ch at the highest temperatures. The thermal evolution of the hexagonal unit cell parameters for La0.6Sr0.4FeO3−δ, shown in Figure 3b, was qualitatively similar to La0.7Sr0.3FeO3−δ. The unit cell parameters of La0.5Sr0.5FeO3−δ demonstrated a slightly different behavior in pure O2 (Figure 3c). The thermal expansion of ch is weakly suppressed from about 350 to about 500 °C, indicating that an oxidation of the material occurred in this temperature region in O2. The onset temperature of chemical expansion due to oxygen loss is clearly decreasing with increasing Sr content, as can also be seen in Figure 1. The thermal evolution of ah and ch are qualitatively dissimilar, which is due to the overlapping occurrence of the second order phase transition and the onset of chemical expansion as discussed in the following. The thermal expansion of the cubic cell parameter ac for the three materials displays a strong dependence of the partial pressure of oxygen with significant higher lattice constants in N2 relative to O2. This is in line with the significant chemical expansion reported for LSF.38 The linear thermal expansion coefficients (TECs) of the two unit cell lattice parameters, found by a linear fit to the data in given temperature intervals, are summarized in Table 2 for all three materials. They are in good agreement with a previous XRD study.38 The isotropic thermal expansion calculated from the unit cell volume is in reasonable agreement with those reported by dilatometry,38 also given in Table 2 for comparison. Significant anisotropy in the thermal expansion of ah and ch is observed. The TEC of ch is almost two times higher than the TEC of ah. Chemical expansion contributes significantly to the TEC, particularly in N2 atmosphere. To illustrate the unit cell distortion and anisotropy of the thermal and chemical expansion, the normalized pseudocubic lattice parameters apc=ah/21/2 and cpc=ch/121/2 for the three compositions are shown in Figure 4. The distortion mainly due to the antiferrodistortive tilting of the FeO6/2 octahedra, evidenced by the difference between pseudocubic lattice parameters apc and cpc, is clearly decreasing with increasing temperature. The pseudocubic lattice parameters apc and cpc for the three materials become equal at the rhombohedral to cubic phase transition temperature. The thermal evolution of the normalized lattice parameters reveals that the partial pressure of oxygen dependence of ch is significantly more pronounced than for ah, which is in a good accord with a recent study of La1−xSrxCoO3‑δ.37 The strong depression of the phase transition with decreasing partial pressure of O2 is strongly coupled to an elongation of the c-axis.

Figure 3. Hexagonal lattice parameters ah and ch below the phase transition temperature and cubic lattice parameter ac above the transition as a function of temperature in pure O2 and N2 atmospheres for La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5). The black and red dotted lines are guides to recognize the onset of phase transition in N2 and O2 atmospheres.

of ah and ch demonstrated a strong dependence on the oxygen partial pressure above ∼400 °C, which is a clear signature of the onset of chemical expansion due to evolving oxygen nonstoichiometry. Both ah and ch deviates significantly from a linear behavior in N2, while the nonlinearity is less pronounced in O2

Table 2. TECs for the Rhombohedral and Cubic Phases in the La1−xSrxFeO3−δ System in Pure O2a Sr content (×)

αah (×106 K−1)

αch (×106 K−1)

αiso (×106 K−1)

0.3

10.4 ± 0.3 (11.6 ± 1.1) 14.7 ± 0.3 10.6 ± 0.3 (14.8 ± 0.2) 12.9 ± 0.3

19.3 ± 0.3

0.4

αac (×106 K−1)

αdil (×106 K−1)

temperature range (°C)

13.5 ± 0.3

14.0 ± 0.2

200−750

27.2 ± 0.3 20.5 ± 0.3

18.1 ± 0.3 14.1 ± 0.3

13.4 ± 0.4

850−1050 30−700

26.3 ± 0.3

19.2 ± 0.3 14.0 ± 0.4

700−900 900−1050 30−600

20.6 ± 0.3 0.5

12.3 ± 0.3 (10.0 ± 2.0)

21.4 ± 0.3

15.3 ± 0.3 24.6 ± 0.3

a

21.3 ± 0.3

625−900

TEC (numbers in parentheses) by previous XRD and dilatometry38 are given for comparison. D



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Figure 5. Rhombohedral angle of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) as a function of temperature in pure O2 and N2 atmospheres.

ature up to the phase transition temperature in O2. In contrast to the measurements in O2 the rhombohedral angle deviates from the linear behavior from about 400 °C for La0.7Sr0.3FeO3−δ in N2 and decreases more rapidly with increasing temperature because of the chemical expansion caused by thermal reduction of Fe. A similar behavior can also be observed for La0.6Sr0.4FeO3−δ and La0.5Sr0.5FeO3−δ. The thermal evolution of the unit cell volume of the three materials as a function of temperature and atmosphere is shown in Figure 6. The unit cell volume is continuous through the

Figure 4. Normalized lattice parameters apc = ah/21/2 and cpc = ch/121/2 and the cubic lattice parameter ac as a function of temperature in pure O2 and N2 atmospheres for La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5).

The rhombohedral to cubic phase transition temperature determined from the refinement of the HTXRD diffraction data for the three materials are summarized in Table 3. The phase Table 3. Second Order Phase Transition Temperature from Rhombohedral to Cubic Crystal Structure Observed for LSF73, LSF-64, and LSF-55 composition

phase transition

in O2 (°C)

in N2 (°C)

LSF-73 LSF-64 LSF-55

R→C R→C R→C

1150 ± 25 900 ± 25 625 ± 25

950 ± 25 700 ± 25 450 ± 25

Figure 6. Unit cell volume of the pseudocubic unit cell of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) as a function of temperature in pure O2 and N2.

transition temperature of La0.7Sr0.3FeO3−δ in O2 was obtained by extrapolating the ratio of apc/cpc to unity.36,51−55 The rhombohedral to cubic phase transition temperature was clearly dependent on the partial pressure of O2 and the Sr content, and the phase transition temperature decreases with increasing Sr substitution and decreasing partial pressure of oxygen. The evolution of the rhombohedral angle as a function of temperature, partial pressure of oxygen, and Sr substitution is illustrated in Figure 5. In line with previous investigations,38 the rhombohedral angle is almost decreasing linearly with temper-

phase transition region, which provides clear evidence for the second order nature of the phase transition. Surprisingly, the unit cell volume is strongly dependent on the Sr-constant at low temperature, while at high temperature the difference in unit cell volume of the materials becomes less dependent on the Sr-substitution level and becomes nearly equal for the three compositions in both O2 and N2 atmospheres. A slight contraction of the unit cell volume is found for La0.5Sr0.5FeO3−δ in the temperature region from around 350 to 500 °C which is in a good agreement with the findings in Figure 4 and Figure 5. E



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DISCUSSION Oxygen Non-stoichiometry and Point Defect Chemistry. The TGA and HTXRD measurements confirmed that the materials were essentially stoichiometric with respect to oxygen at ambient temperature in line with previous reports.8,29,49,50 At elevated temperature the oxidation state of Fe was reduced, and the point defect chemistry is important for the interpretation of the crystallographic data. According to Mizusaki et al. and others8,29,49,50 the major defect species in La1−xSrxFeO3−δ solid solutions are oxygen vacancies, Sr on La ’ ’ • site and Fe2+ and Fe4+, which is denoted as V•• O ,SrLa,FeFe,FeFe by 56 Kröger−Vink notation. To accommodate the electronic neutrality the concentration of these defect species must meet the following equations.8,29,49,50 First the principle of electroneutrality yields , , • [Sr La ] + [FeFe ] = 2[V •• O ] + [Fe Fe]

(1)

Figure 7. Calculated oxidation state of Fe as a function of temperature in pure O2 and N2 atmospheres using the defect model reported by Mizusaki et al.8,47 The inset shows the oxygen vacancy concentration as a function of temperature.

where [ ] indicates the concentration of each point defect species. The oxygen incorporation with La1−xSrxFeO3−δ can be described by the following point defect equilibrium: 1 × × • O2 (g ) + V •• O + 2Fe Fe = OO + 2Fe Fe 2

temperature, while at high temperature the oxidation state of Fe is mainly determined by the partial pressure of oxygen. According to Shannon57 La3+ and Sr2+ have relatively equal ionic radii, and the contraction of the unit cell volume (Figure 6) with increasing Sr content at low temperature is due to the oxidation of Fe from Fe3+ to Fe4+. At elevated temperature the volume become less dependent on the Sr content (Figure 6) since the average oxidation state of Fe become independent of the Sr content (Figure 7). It can be concluded that the oxidation state of Fe dominates the observed expansion/ contraction of the unit cell volume of the LSF solid solutions. Anisotropic and Nonlinear Thermal and Chemical Expansion. The TECs of LSF in O2, summarized in Table 2, are in good agreement with previous reports.29,38 The average isotropic TECs, calculated from the XRD data, are in reasonable agreement with dilatometric data.38 The isotropic thermal expansion of LSF increases slightly with increasing Sr content and temperature. The crystal structure is compressed along the ch-axis because of the antiferrodistortive rotation of the FeO6/2 octahedra. Because of the rectification of the antiferrodistortive rotation of the FeO6/2 octahedra with increasing temperature, the thermal expansion along ch-axis is more pronounced than the thermal expansion of the ah-axis. The data in Table 2 show that the thermal expansion along the ch-axis is about twice the magnitude of the thermal expansion along the ah-axis. Similar, highly anisotropic thermal expansion has also been reported for isostructural perovskites such as LaAlO 3 , 51−53 La 1−x A x CoO 3−δ (A = Sr, Ca), 54,55 and La1−xSrxMO3±δ (M = Co, Mn).36,37 The anisotropic chemical expansion could only be measured at the intermediate temperature interval between the onset of thermal reduction, To, and the rhombohedral to cubic phase transition, Tc.36 Thus to determine the anisotropic chemical expansion, the relative change in the lattice parameters ah and ch due to a change in the partial pressure of oxygen needs to be calculated. The expansion εa and εc changing from O2 to N2 atmosphere as a function of temperature below the phase transition are shown in Figure 8. For simplification it is assumed that both the thermal and the chemical expansion vary linearly with temperature and oxygen non-stoichiometry. Thus, for anisotropic materials in the absence of external mechanical stress, the anisotropic expansion can be defined as

(2)

The corresponding equilibrium constant for eq 2 can be described as K OX =

× [OO ][Fe•Fe]2 1/2 •• PO2 [V O ][Fe×Fe]2 ’ FeFe and

=

The point defects disproportionation reaction of

(3 − δ)[Fe•Fe]2 1/2 PO2 δ[Fe×Fe]2

• FeFe FeFe×

(3)

can be related by the

, 2Fe×Fe = FeFe + Fe•Fe

(4)

The corresponding equilibrium constant for eq 4 is given by Ki =

, [Fe•Fe][FeFe ]

[Fe×Fe]2

(5)

The concentration of the iron species in La1−xSrxFeO3−δ must obey the mass balance of Fe given by , [Fe×Fe] + [FeFe ] + [Fe•Fe] = 1

(6)

Combination of eqs 1, 3, 5, and 6 enable the calculation of the oxygen non-stoichiometry, (3 − δ), as a function of temperature and Sr substitution, which is shown in Figure 1. In these calculations the thermodynamic data for the defect equilibria, reported by Mizusaki et al.,8,49 are summarized in the Supporting Information. As the temperature increases the oxygen deficiency increases, the onset temperature of the reduction is lowered by increasing the Sr substitution and by decreasing the partial pressure of oxygen. For simplification the valence of Fe in LSF solid solution is assumed as a mixed valence between +3 and +4 and the shift in the oxygen nonstoichiometry can be described by the equation +3 La1 − xSrxFe+y 4Fe1/ yO3 − δ Δ

+3 → La1 − xSrxFe+y ′4Fe1/ y ′O3 − δ ′ +

δ′ − δ O2 (g ) 2

(7)

Thus the average oxidation state of Fe in the materials in N2 and O2 atmosphere can be calculated according to the point defect equilibria, and this is shown in Figure 7. The oxidation state of Fe is controlled by the Sr-substitution level at low F



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possible to determine the anisotropic chemical expansivity (αac and αac) by measurement of the lattice expansion as a function of the change in the oxygen non-stoichiometry (Δδ) at constant temperature. The calculated isothermal chemical expansion of the three LSF materials as a function of the change in oxygen non-stoichiometry (Δδ) is shown in Figure 9. The chemical expansion displays strong anisotropy and is significantly lower along the ah-axis relative to the ch-axis.

Figure 8. Relative expansion of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) as a function of temperature in pure O2 and N2 atmospheres. The dotted lines are linear fits to the data for the thermal expansion in the temperature interval from ambient temperature to the phase transition temperature in N2.

Δεa(T , δ) =

ahi − ah0 = αaTΔT + αacΔδ ah0

c − ch 0 Δεc(T , δ) = hi = αc TΔT + αccΔδ cho

(8)

Figure 9. Anisotropic and nonlinear chemical expansion for La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) as a function of Δδ at constant temperature, the red symbols denote the chemical expansion along caxis, the dark symbols denote the chemical expansion along a-axis. Red and black dotted lines are fitted lines based on eqs 12 and 13, and the blue dotted lines are guides to the eye.

(9)

where αaT, αcT and αac, αcc are thermal and chemical expansivity along ah and ch axes, respectively. Δεa and Δεc are the expansion relative to the lattice parameters measured at ambient temperature. The reference lattice parameters for La0.7Sr0.3FeO3−δ are at 200 °C, while ambient temperature is used for the two other compositions. If ΔT = 0, only chemical expansion contributes to the total expansion; then eqs 8 and 9 can be simplified by Δεac = αacΔδ

(10)

Δεcc = αccΔδ

(11)

The chemical expansion rapidly reduces the compression along the ch-axis leading to a pronounced increase in cpc approaching apc (Figure 4). This demonstrates the strong effect of rectification of the antiferrodistortive tilting of the FeO6/2-octahedra with increasing oxygen vacancy concentration. Moreover, this effect is also evident from the strong depression of the ferroelastic to paraelastic phase transition temperature with decreasing partial pressure of oxygen (Table 3). The chemical expansion is clearly nonlinear with respect to the oxygen non-stoichiometry (see Figure 9). Therefore, the

where Δεac and Δεcc are chemical expansion along ah and ch axis, respectively, at constant temperature. It is therefore G



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chemical expansion along the ch-axis and ah-axis were fitted to a third-order and second-order polynomial expressions, respectively. Δεcc = a0Δδ + a1Δδ 2 + a 2Δδ 3

Δεac = a0Δδ + a1Δδ

larger for the unit cell parameter ch than ah, while for cation deficient LSM the chemical expansion is larger for ah than ch. The anisotropic chemical expansion of respectively cation deficient and oxygen deficient perovskite oxides are therefore different. This shows that oxygen vacancies and cation vacancies have a different effect on the tilting (or compression) of the octahedra. Structural Properties, Order Parameters, and Phase Diagram. The unit cell distortion gradually decreases with increasing Sr substitution in the rhombohedral R3̅c phase, as seen from the difference in normalized lattice parameters αPc and cPc in Figure 4. The normalized lattice parameters αPc and cPc become equal when approaching the second order phase transition temperature where the perovskite structure transforms to the highly symmetric cubic phase (Pm3̅m). The rhombohedral angle of the cubic phase, shown in Figure 5 is equal to 60°. Because of the distortion of FeO6/2 octahedra, the rhombohedral angle is larger than 60°, and with increasing Sr content the structural distortion and the rhombohedral angle decreases. The two order parameters for the phase transition, the antiferrodistortive tilting (major) and compression (minor) of the FeO6/2-octahedra, calculated from the atomic position of oxygen in the rhombohedral unit cell58,59 are shown in Figure 10. The rotation angle is calculated by the expression φ = arctan 2e√3, where e is defined in Table 1, while the compression of the octahedra is calculated by η = ((ch cos φ)/ (ah(6)1/2)). Even though oxygen has a low scattering power

(12)

2

(13)

The parameters found by a regression analysis are given in Table 4. The linear term in the polynomial expression for Table 4. Parameters Obtained from Third-Order and Second-Order Polynomial Fit of the Chemical Expansion Using Equations 12 and 13, Respectively x = 0.3

α0 α1 α2

x = 0.4

x = 0.5

along chaxis

along ahaxis

along chaxis

along ahaxis

along chaxis

along ahaxis

0.0418 −0.598 6.10

0.00602 0.1527

0.0366 −0.526 3.99

0.00694 0.0639

0.0325 −0.4113 3.93

0.00675 0.01942

chemical expansion along the ah-axis are nearly the same for all three compositions, while the linear term for the ch-axis polynomial slightly decreases with increasing Sr content. The higher order polynomial terms are significantly different for the chemical expansion along two principal axes in the hexagonal unit cell. The experimental data show that at low Δδ the linear terms dominate the chemical expansion and that the chemical expansion along ah-axis is nearly independent of the Sr content, while chemical expansion along the ch-axis decreases slightly with increasing Sr content. As Δδ becomes larger a strong nonlinearity of the chemical expansion is evident, particularly along the ch-axis. The close to linear chemical expansion in the low Δδ region can be rationalized by a simplified function of the ionic radii of Fe4+ and Fe3+,57 corresponding to αac ≈ (12(rFe3+ − rFe4+)/a0).60 The estimated value is about 0.18, which is considerably larger than the experimental value in line with previous findings for La1−xSrxCoO3−δ.60,37 The present data show clearly that the anisotropic chemical expansion is strongly nonlinear with respect to the oxygen vacancy concentration, which has previously been found for La1−xSrxCoO3−δ by both X-ray diffraction37 and dilatometry.60,61 There are no apparent simple physical explanations of the strong nonlinearity of the chemical expansion as discussed in previous works.37,60,61 At high oxygen vacancy concentrations the tendency for oxygen ordering similar to the brownmillerite type of crystal structure has also been observed in the LSF system at high Sr content.38,42−46 Any signature of oxygen vacancy ordering in this study was not observed, but vacancy ordering may occur on a length scale too small to be observed by X-ray diffraction. It is also likely that the reduction of the valence state of Fe induces a spin transition from a low spin Fe4+ (d4) to high spin Fe3+ (d5), which also would contribute to the volume expansion, but this effect is already accounted for in the linear model suggested by Chen and Adler.24,60 The data presented here clearly show that anisotropic chemical expansion is more pronounced for the unit cell parameter ch than ah, which is in a good agreement with the previous report for La 1−xSrxCoO 3−δ .37 Compared with isostructural oxygen excess (or more precisely cation deficient) perovskite materials such as La1−xSrxMnO3+δ (LSM),36 the thermal expansion of oxygen deficient LSM, LSF, and LSC is

Figure 10. Octahedral rotation angles (a) and octahedral strain parameters (b) of La1−xSrxFeO3−δ (x = 0.3, 0.4, 0.5) as a function of temperature and atmosphere. The dotted lines are guides to the eye. H



Article

where the pseudocubic lattice parameters apc and cpc become equal. The evolution of the transition temperature in La1−xSrxCoO3−δ and La1−xSrxMnO3±δ system are also included in Figure 11 for comparison. The second order phase transition temperature from the ferroelastic phase to paraelastic phase is intensely reduced with increasing Sr-substitution level. At ambient temperature the substitution of La with Sr is mainly charge compensated by oxidation of the transition metal, leading to an increasing Goldschmidt tolerance factor63 and a decreasing rhombohedral distortion from cubic crystal structure. Consequently, the phase transition temperature is rapidly reduced with increasing Sr content. At elevated temperature thermal reduction of the transition metal occurs, which decreases the Goldschmidt tolerance factor because of the increasing ionic radii of the transition metal with decreasing oxidation state.57 It would therefore be tempting to suggest that the reduction of the transition metal would increase the crystal distortion, but the effect of introducing oxygen vacancies dominates over the change in the ionic radii of the B-cation. As a result the phase transition temperatures of LSF and LSC are strongly dependent on the partial pressure of oxygen. The corresponding phase transition of LSM does not depend on the partial pressure of oxygen since the oxygen non-stoichiometry of LSM is relatively independent of the partial pressure of oxygen at these conditions. It is well accepted that the twinning due to ferroelasticity can result in toughening of ceramics.33,64,65 Figure 11 demonstrates that the ferroelasticity would be tailored by changing the second order phase transition temperature through adjustment of the Sr content and partial pressure of oxygen. The strong influence of the chemistry on the properties of these perovskite materials opens up both the transport properties and the mechanical properties for tailoring through chemical modification of the ferroelastic phase transition.

with respect to X-rays, the oxygen position could be determined by the Rietveld refinements, mainly because of the intensity of the rhombohedral super-reflection caused by the antiferrodistortive tilting. A roughly linear relationship between η and temperature was observed, and η becomes 1 at the phase transition. The octahedral rotation angle displays a more complicated temperature dependence and becomes zero at the phase transition. The attempt to fit the order parameters to a physical model of the type (Tc − T)n was not successful, but it should be mentioned that the onset of oxygen nonstoichiometry will influence the order parameters and they do deviate to some degree from the expected behavior for an isostructural material with constant composition, as show previously for LaAlO3.51 The molar volume of La1−xSrxFeO3−δ perovskites was shown to be strongly dependent on the Sr-substitution level at ambient temperature (Figure 6), while at high temperature the molar volume mainly depends on the partial pressure of oxygen or the oxidation state of Fe. Similar type of behavior has also been reported for La1−xSrxCoO3‑δ.37,54,55 The molar volume at elevated temperatures is therefore mainly determined by the average oxidation state of Fe or Co and not the concentration of the oxygen vacancies (Figure 7). The ratio of the number of moles of Fe4+/Fe3+ is determined by the point defect equilibrium, involving the redox chemistry of Fe, eq 2. The ratio of the concentration of Fe in the two oxidation states can be found from the expression of the equilibrium constant, eq 3, and the expression is ⎛ δ ⎞1/2 [Fe•Fe] 1/2 ⎜ ⎟ = P K O2 OX ⎝3 − δ ⎠ [Fe×Fe]

(14)

The equation shows that the ratio is mainly determined by the partial pressure of oxygen and the equilibrium constant. The thermodynamics of the redox chemistry in La1−xSrxFeO3−δ and La1−xSrxCoO3−δ62 have shown that the enthalpy and entropy of reaction 2 are not strongly dependent on the Sr content, which gives essentially the same KOX independent of the Sr content. The oxidation state of Fe is essentially determined by the partial pressure of oxygen at elevated temperature. The structural phase diagram of La1−xSrxFeO3−δ as a function of temperature in pure O2 and N2 is summarized in Figure 11. The second order rhombohedral to cubic phase transition temperature, Tc, was deduced from the HTXRD data (Table 3). The transition temperature corresponds to the temperature

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CONCLUSION The crystal structure and anisotropic and nonlinear thermal and chemical expansion of Sr-substituted LaFeO3 are reported based on an in situ HTXRD study in O2 and N2 atmospheres. At low ambient temperature Sr substitution is charge compensated by oxidation of Fe. The deviation from cubic symmetry with increasing Sr content can be rationalized by the Goldschmidt tolerance factor. At elevated temperature the dependence of the molar volume of the Sr content vanishes, and is mainly controlled by the partial pressure of oxygen and the average oxidation state of Fe. A strong anisotropy and nonlinearity of the chemical expansion of the materials were demonstrated below the ferroelastic to paraelastic phase transition temperature in analogy with the strong anisotropy of the thermal expansion. The second order rhombohedral to cubic phase transition temperature is strongly suppressed by increasing substitution level of Sr and reducing partial pressure of oxygen. The strong anisotropic thermal and chemical expansion can be rationalized by the strong rectification of the antiferrodistortive tilting of the octahedra in the perovskite structure. The order parameters of the phase transition were confirmed to be the octahedral rotation angle and the compression of the octahedra. Finally, there is apparently no simple physical explanation for the strong nonlinearity of the chemical expansion with respect to the oxygen vacancy concentration.

Figure 11. Structural phase diagram of La1−xSrxMO3±δ (M = Mn, Co, Fe). The data for pure LaCoO3 is taken from ref 66. I



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(26) Kharton, V. V.; Kovalevsky, A. V.; Viskup, A. P.; Jurado, J. R.; Figueiredo, F. M.; Naumovich, E. N.; Frade, J. R. J. Solid State Chem. 2001, 156, 437. (27) Ma, W.; Xie, G.; Wang, H. J. Mater. Sci. Technol. 2002, 18, 286. (28) Julian, A.; Juste, E.; Geffroy, P. M.; Tessier-Doyen, N.; Del Gallo, P.; Richet, N.; Chartier, T. J. Eur. Ceram. Soc. 2009, 29, 2603. (29) Kuhn, M.; Hashimoto, S.; Sato, K.; Yashiro, K.; Mizusaki, J. Solid State Ionics 2011, 195, 7. (30) Kharton, V. V.; Yaremchenko, A. A.; Patrakeev, M. V.; Naumovich, E. N.; Marques, F. M. B. J. Eur. Ceram. Soc. 2003, 23, 1417. (31) Atkinson, A.; Ramos, T. M. G. M. Solid State Ionics 2000, 129, 259. (32) Chou, Y. S.; Stevenson, J. W.; Armstrong, T. R.; Pederson, L. R. J. Am. Ceram. Soc. 2000, 83 (6), 1457. (33) Fossdal, A.; Einarsrud, M. A.; Grande, T. J. Eur. Ceram. Soc. 2005, 25, 927. (34) Hilpert, K.; Steinbrech, R. W.; Boroomand, F.; Wessel, E.; Meschke, F.; Zuez, A.; Teller, O.; Nickel, H.; Singheiser, L. J. Eur. Ceram. Soc. 2003, 23, 3009. (35) Lein, H. L. Doctoral Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2005. (36) Grande, T.; Tolchard, J. R.; Selbach, S. M. Chem. Mater. 2012, 24 (2), 338. (37) Chen, X.; Grande, T. Chem. Mater. 2013, 25 (6), 927. (38) Fossdal, A.; Menon, M.; Wærnhus, I.; Wiik, K.; Einarsrud, M. A.; Grande, T. J. Am. Ceram. Soc. 2004, 87, 1952. (39) Selbach, S. M.; Tolchard, J. R.; Fossdal, A.; Grande, T. J. Solid State Chem. 2012, 196, 249. (40) Geller, S.; Raccah, P. M. Phys. Rev. B 1970, 2, 1167. (41) Battle, P. D.; Gibb, T. C.; Lightfoot, P. J. Solid State Chem. 1990, 84, 271. (42) Battle, P. D.; Gibb, T. C. J. Solid State Chem. 1989, 79, 75. (43) Battle, P. D.; Gibb, T. C.; Lightfoot, P. J. Solid State Chem. 1990, 84, 237. (44) Hodges, J. P.; Short, S.; Jorgensen, J. D.; Xiong, X.; Dabrowski, B.; Mini, S. M.; Kimball, C. W. J. Solid State Chem. 2000, 151, 190. (45) Mizusaki, J.; Okayasu, M.; Yamauchi, S.; Fueki, K. J. Solid State Chem. 1992, 99, 166. (46) Takeda, Y.; Kanno, K.; Takada, T.; Yamamoto, O.; Takano, M.; Nakayama, N.; Bando, Y. J. Solid State Chem. 1986, 63, 237. (47) Rietveld, H. M. J. Appl. Crystallogr. 1969, 2, 65. (48) Dann, S. E.; Currie, D. B.; Weller, M. T. J. Solid State Chem. 1994, 109, 134. (49) van Hassel, B. A.; Kawada, T.; Sakai, N.; Yokokawa, H.; Dokiya, M.; Bouwmeester, H. J. M. Solid State Ionics 1993, 66, 295. (50) Søgaard, M.; Hendriksen, P. V.; Mogensen, M. J. Solid State Chem. 2007, 180, 1489. (51) Howard, C. J.; Kennedy, B. J.; Chakoumakos, B. C. J. Phys.: Condens. Matter 2000, 12, 349. (52) Hayward, S. A.; Redfern, S. A. T.; Salje, E. K. H. J. Phys.: Condens. Matter 2002, 14, 10131. (53) Hayward, S. A.; Morrison, F. D.; Redfern, S. A. T.; Salje, E. K. H.; Scott, J. F.; Knight, K. S.; Tarantino, S.; Glazer, A. M.; Shuvaeva, V.; Daniel, P.; Zhang, M.; Carpenter, M. A. Phys. Rev. B 2005, 72, 054110. (54) Mastin, J.; Einarsrud, M. A.; Grande, T. Chem. Mater. 2006, 18, 1680. (55) Mastin, J.; Einarsrud, M. A.; Grande, T. Chem. Mater. 2006, 18, 6047. (56) Kröger, F. A.; Vink, H. J. Solid State Physics; Seitz, F., Turnbull, D., Eds.; Academic Press: New York, 1956; Vol. 3, p 307. (57) Shannon, R. D. Acta Crystallogr., Sect. A: Cryst. Phys. Diffr., Theor., Gen. Crystallogr. 1976, 32, 751. (58) Howard, C. J.; Kennedy, B. J. J. Phys.: Condens. Matter 1999, 11 (16), 3229. (59) Howard, C. J.; Kennedy, B. J.; Woodward, P. M. Acta Crystallogr. 2003, B59, 463. (60) Chen, X.; Yu, J.; Adler, S. B. Chem. Mater. 2005, 17, 4537.

ASSOCIATED CONTENT

S Supporting Information *

Further deatils are provided in Figure S1 and Tables S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication has been produced with support from the BIGCCS Centre, performed under the Norwegian research program Centres for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Aker Solutions, ConocoPhillips, Det Norske Veritas, Gassco, Hydro, Shell, Statoil, TOTAL, GDF SUEZ, and the Research Council of Norway (193816/S60). Dr. Julian Tolchard is acknowledged for assistance in the HTXRD experiments and Assoc. Prof. Sverre M. Selbach is acknowledged for the discussion of the point defect chemistry and crystallography.

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K


Anisotropic and Nonlinear Thermal and Chemical Expansion of La1

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