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Electronic properties of polycrystalline LaFeO3. Part I: Experimental results and the qualitative role of Schottky defects
Solid State Ionics 176 (2005) 2783 – 2790 www.elsevier.com/locate/ssi
Electronic properties of polycrystalline LaFeO3. Part I: Experimental results and the qualitative role of Schottky defects Ivar Wærnhus a, Per Erik Vullum b, Randi Holmestad b, Tor Grande a, Kjell Wiik a,* a
Department of Materials Science and Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway b Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 13 August 2004; received in revised form 14 July 2005; accepted 24 August 2005
Abstract The isothermal electrical conductivity of La1y FeO3d ( y = 0.003, 0.000 and + 0.003) ceramics has been investigated at 1000 -C in oxygen partial pressures from 1 to 10 17 atm, and found to be essentially independent of the composition ( y). Both La2O3-rich and Fe2O3-rich secondary phases were identified by transmission electron microscopy in the non-stoichiometric materials ( y = 0.003 and + 0.003), and a narrow homogeneity range for La1Ty FeO3d ( y < 3 I 10 3) was inferred. The materials exhibited n-type conductivity at low oxygen partial pressures due to the reduction of Fe3+ to Fe2+ and formation of oxygen vacancies, consistent with previous reports. The rate of the reduction was controlled by oxygen diffusion and a time independent conductivity was established relatively fast. For oxygen pressures between 10 11 and 10 4 atm, the time independent conductivity was essentially independent of variations in the oxygen pressure. This was explained by a fully occupied oxygen lattice, implying that the material could not be further oxidized without formation of new oxygen sites. At the highest oxygen partial pressures ( P O2 > 10 4 atm), p-type conductivity was evident. However, in this regime, the conductivity was time dependent on a time scale of days or weeks, inconsistent with previous reports. Possible mechanisms for the p-type conductivity and the slow change in the conductivity at high oxygen partial pressures are discussed, and a new defect model is put forward, which includes formation of thermally activated Schottky defects. The model accounts qualitatively for the time dependent conductivity and points out the importance of cation vacancies and cation diffusion at high oxygen partial pressures. D 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Cc; 61.72.Ji; 68.35.Dv; 68.55.Ln Keywords: LaFeO3; Electrical conductivity; Schottky defects; Cation vacancies
1. Introduction Lanthanum ferrite based oxides such as La1x Srx Fe1y Coy O3d are materials becoming increasingly more important due to their electrochemical properties. High ionic and electronic conductivity [1– 3] in these materials make them potential candidates for use as SOFC cathode materials, gas sensors and oxygen permeable membranes [4]. The basic component in the actual system, LaFeO3, prepared as thin films, is also a promising candidate material for use as an oxygen sensor [5]. The isothermal conductivity of Sr-doped LaFeO3 has previously been reported by Mizusaki et al. [1] and Kim et
* Corresponding author. Tel.: +47 73 59 40 82; fax: +47 73 59 08 60. E-mail address: [email protected] (K. Wiik). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.08.012
al. [6]. In both contributions, the concentrations of chemical defects were successfully modelled as an ideal solution, indicating that interaction between defects is insignificant. The electrical conductivity was described by localized electrons and holes hopping between the Fe ions, and the concentration of Fe2+ and Fe4+ constituted the charge carrier concentrations. The isothermal conductivity passed a minimum where the average Fe valence was three, from where it was increased by both increased and reduced oxygen pressure. At this state, the level of oxygen vacancies (d) was defined by the level of Sr doping (x), given as d = x / 2. At higher oxygen pressures, when all oxygen sites were occupied, the isothermal conductivity reached saturation on a level defined by the Sr content. According to this model, p-type conductivity will not become dominant in undoped LaFeO3 for any oxygen pressures, the conductivity is n-type as long as oxygen
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vacancies are present, and then saturates at the minimum level, when all oxygen sites are occupied. However, Mizusaki et al. reported a similar isothermal conductivity in pure LaFeO3 as in the Sr-doped materials [7], and explained the observations with the formation of cation vacancies due to a none unity ratio between La and Fe. It was reasoned that the cation vacancies acted as acceptors and had the same effect on the material as a small level of Sr-doping, and thus accounted for the p-type conductivity. Of vital importance for the use of LaFeO3 as oxygen sensor is the knowledge about the conductivity and oxygen transport mechanism. We have recently applied a 4-point DC technique to determine such data by conductivity relaxations [8], and the isothermal conductivity data are presented in this contribution. The focus has been in particular on the influence of the microstructure and small variations in the overall chemical composition of the materials. Surprisingly, the electrical conductivity in the p-type regime did not fit into the expected model with p-type conductivity saturating at high oxygen pressures, but was time dependent on the time scale of days, corresponding to an apparent equilibrium conductivity not consistent with data reported by Mizusaki et al. In the present article, the model for the conductivity and oxygen stoichiometry in LaFeO3 is re-evaluated qualitatively. Possible physical processes, which can account for the observations reported in this contribution, are discussed with particular attention to Schottky defects. 2. Experimental 2.1. Preparation The powders were prepared by spray drying (Bu¨chi, Mini Spray-Drier B-191) of aqueous glycine– nitrate solutions using La(NO3)3I6H2O (Fluka p.a.) and Fe(NO3)3I9H2O (Riedel-de Hae¨n, p.a.) as starting materials. In order to obtain a high accuracy in the La / Fe ratio, the metal concentrations were calibrated gravimetrically with three parallels for each metal nitrate. The difference in the metal concentrations between the extreme parallels, D = (c max c min) / c avg, was 0.001 for both elements, giving a high accuracy for the La / Fe ratio in the final product. Three compositions of La1Ty FeO3d were synthesized, one nominally stoichiometric ( y = 0.000), one with a small iron deficiency ( y = + 0.003) and one with a small lanthanum deficiency ( y = 0.003). These compositions are referred to as the nominal stoichiometric, the Fe2O3-excess and the La2O3excess compositions, respectively. To optimize the control of the La to Fe ratio, the nominal stoichiometric solution was first prepared and then split into three parallels. The La- and Feexcess solutions were prepared by adding the actual metal nitrate to the respective solution. Glycine (Merck p.a.) was added as fuel for the combustion process. The solutions were spray dried to a dry powder precursor, and fine-grained LaFeO3 powders were prepared by dropping the precursor through a hot tube, preheated to 700 -C, where the precursor ignited. The resulting powders were then ball milled for 12 h with Si3N4 grinding balls and calcined at 1000 -C for 24 h. Rectangular
bars were formed by uniaxial pressing, followed by cold isostatic pressing at 200 MPa and finally sintered at 1300 -C for 10 h. The thicknesses of the samples were in the interval 1.5 to 2.1 mm, and the two other dimensions were 8.0 and 23 mm. Densities of 95% of theoretical density were achieved for all compositions. Prior to the conductivity measurements, the bars were polished with a diamond spray containing 3 Am particles. One stoichiometric bar was also sintered a second time at 1500 -C for 6 h in order to produce a material with larger grain size. 2.2. Characterization The powders were characterized with XRD (Siemens D5005, 2h range: 20– 70-, step 0.02-, count time 11 s) and the cell parameters and the crystallographic density were calculated by Rietveld refinement [9]. The micrographs were taken on polished samples, etched at 1300 -C prior to analysis (SEM, Hitachi S-3500N). The TEM samples were prepared from 3 mm discs which were mechanically grounded, polished and dimpled to a central thickness of ¨20 Am. The discs were ion-beam thinned using a Gatan duo-mill with liquid nitrogen cooling, operating at 3.5 kV and with a thinning angle of 12-. TEM was performed using a Philips CM 30 microscope with an EDAX DX4 EDS system, and all examinations were conducted at a beam voltage of 200 kV. 2.3. The conductivity measurements The conductivity was measured by a 4-point technique enabling both current (I) and voltage (V) to be measured independently (Keithly D500). Two Pt electrodes were attached with Pt paste at each end of the sample, and an Al2O3 clamp pulled the sample down on two other Pt electrodes placed at a distance d = 5.4 mm apart. The conductivity (r) was calculated from: r¼
I d U A
ð1Þ
where A was the area of the cross section normal to the current. The measurements presented in this work have all been carried out at 1000 -C, applying a current between 1 and 2 mA. The sample temperature was monitored using a thermocouple type S located in the vicinity of the bar. The thermocouple was calibrated in accordance with the melting point of gold and silver. The gas was introduced with a continuous flow through an alumina tube placed 5 mm from the sample, the partial pressure of oxygen was controlled by mixing O2 and N2 or CO and CO2 controlled by four mass flow meters (Brooks 5850S, 50 and 500 ml), and the oxygen partial pressure was continuously monitored by a ZrO2 sensor, provided by Riso¨ National Laboratory. 3. Results 3.1. Phase composition and microstructure All three materials appeared phase pure according to the XRD diffractograms. The dimensions of the orthorhombic unit
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
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Fe-excess materials are given in Fig. 2. In all three compositions, an oxide phase containing La and Si was observed by EDS. SiO2 impurities are frequently observed in oxide ceramics as a major contamination introduced during preparation, for instance, many minute amounts of silica have been brought in from the Si3N4 grinding balls during ball milling. SiO2 will then react with the perovskite during heat treatment to form a La2O3 –SiO2 phase, for instance, La9.33(SiO4)6O2 [11], and if the homogeneity range in LaFeO3 is narrow, Fe2O3 should precipitate according to the reaction: 6SiO2 þ 9:33LaFeO3 ¼ La9:33 ðSiO4 Þ6 O2 þ 4:66Fe2 O3
ð2Þ
The La2O3 –SiO2 inclusions were too small and too few to have any direct influence on the conductivity. However, the reaction between SiO2 and LaFeO3 could result in formation of La-vacancies, which may have significant effects on the conductivity. In the Fe-excess composition, traces of Fe2O3 were relatively frequently encountered, but also in the stoichiometric composition, traces of Fe2O3 were observed. It indicated that even minute amount of excess Fe will precipitate from the perovskite phase and form Fe2O3. The Fe2O3 precipitations in the nominally stoichiometric sample may both be a result of minute Fig. 1. Secondary electron SEM micrographs of nominal stoichiometric LaFeO3 (La : Fe = 1 : 1) sintered at 1300 -C (a) and at 1500 -C (b).
cell in the nominal stoichiometric material were calculated to ˚ , b = 7.861 A ˚ , c = 5.560 A ˚ , and were in good a = 5.570 A agreement with literature data [10]. Within the uncertainty, identical unit cells were observed for all three compositions. Micrographs of two stoichiometric materials sintered at 1300 and 1500 -C, respectively, are given in Fig. 1. The average grain diameters and densities for the two samples were 6.4 Am, q = 96%, and 40 Am, q = 93%, respectively. According to Fig. 1 the morphologies of the two samples are apparently quite different. The variation in morphology is mainly due to sample preparation and thermally etching time. Whereas Fig. 1a shows a polished surface exposed a long time in air at 1300 -C, Fig. 1b shows a polished surface exposed at the same conditions for only a short time (approx. 10 min), sufficient for grain boundaries to appear. It is also evident in Fig. 1b that the microstructure contains some residual porosity and that some grains have been pulled out during polishing. The residual porosity might be due to either Ostwald pore ripening or to green body inhomogeneities. More carefully controlled experiments are, however, necessary in order to give a more fundamental discussion on the evolution of the microstructure. For samples with different compositions sintered at identical temperatures, no significant differences neither in the microstructures nor the densities were observed. The microstructure was also examined both prior to and after the experiments, and no significant changes were found to take place during the conductivity measurements. The TEM investigations revealed the presence of small inclusions (0.2 – 2 Am) of secondary phases at triple points between the grains, typical examples from the La-excess and
Fig. 2. TEM images showing secondary phases at grain boundaries in LaFeO3. Examples of Fe2O3 in the Fe2O3-excess material (a) and La2O3 – SiO2 phase in the La2O3-excess material (b).
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
log(σ / cm s-1)
0,0
1st down
2nd down
-0,5
1st up
3rd up -1,0 -15
-10
-5
0
log(PO2 / atm) Fig. 3. Conductivities of LaFeO3 at 1000 -C measured stepwise, annealing for one hour at each P O2. Start in pure O2, 1st day down and 1st day up were recorded the first day, 2nd day down and 3rd day up recorded the two following days.
quantities of excess Fe from the powder preparation, as well as a result of the reaction between SiO2 and the perovskite (Eq. (2)). In the material which was prepared with excess of La2O3, only the La2O3 – SiO2 phase was observed in addition to the perovskite phase. The La to Si ratio of the EDS intensities in this phase was also significant higher than the corresponding ratio found in the La / Si inclusions observed in the Fe-excess compositions. The ratio between the intensities, I La / I Si, was 3.8 and 2.2 in the La-excess and Fe-excess materials, respectively. The numbers should not be evaluated as absolute values, since the EDS-analysis was not subjected to a standard calibration procedure. However, the analysis verifies the relative difference between the I La / I Si-ratio in the precipitations found in the different materials. The higher La content observed in the precipitates in the nominally La-rich material indicated that these essentially originated from excess La2O3. Thus, the TEMinvestigation points toward no traceable solid solution interval in LaFeO3 on any of the sides of the stoichiometric composition. The possible deviation in the La to Fe ratio in the perovskite phase is less than 3 I 10 3, and even in a nominally stoichiometric material, excess Fe or La may precipitate as oxides, rather than contribute to form cation vacancies. 3.2. Isothermal electrical conductivity The first results from conductivity measurements on nominally stoichiometric materials and at constant T = 1000 -C are given in Fig. 3. The conductivity was first measured in pure oxygen and the oxygen pressure was subsequently reduced stepwise to P O2 = 10 17 atm (‘‘1st day down’’) before stepwise oxidizing the material all the way up to pure oxygen (‘‘1st day up’’). The material was held for one hour at each partial pressure, and the reported conductivity was the conductivity recorded immediately before changing the partial pressure. After the ‘‘1st day up’’ series, the sample was annealed in oxygen for twelve hours before the reduction series ‘‘2nd day down’’ was performed in the same manner as described above. The material
was subsequently annealed in CO/CO2 ( P O2 å 10 13 atm) for another 12 h before the ‘‘3rd day up’’ series was recorded. At P O2 > 10 12 atm, the conductivity was p-type. However, the p-type conductivity is seen to vary between all the series. After the first reduction and oxidation cycle, the conductivity observed in pure oxygen had decreased with more than half an order of magnitude. During the twelve hours of annealing in pure oxygen the following night, the conductivity was slowly increasing to the initial value recorded in pure oxygen for the ‘‘2nd day down’’ series. The ‘‘2nd day down’’ series was terminated with a 12 h residence time at P O2 = 10 13 atm, before the ‘‘3rd day up’’ series was performed. The final conductivity recorded in oxygen was even lower than after the ‘‘1st day up’’ series. Evidently, some kind of background process was taking place in the sample affecting the conductivity in the p-type regime. However, the conductivity observed in the n-type region, for P O2 < 10 12 atm, was reproduced, and a time independent conductivity was quickly obtained. Fig. 4 shows the measured time independent conductivity for the nominally stoichiometric LaFeO3 sample. The measurements at low oxygen pressures started at P O2 = 10 17 atm, where the sample was held for several days performing conductivity relaxations, before these conductivity measurements were carried out. In the n-type region, the conductivity attained a time independent state in less than 30 min. For oxygen pressures between 10 10 and 10 7 atm, the conductivity was found to be virtually independent of the oxygen partial pressure; no changes were observed even after 12 h monitoring the conductivity. The measurements at P O2 > 10 4 atm were carried out in the following order: The sample was first annealed in air for one week before measuring the conductivity. Subsequently, the oxygen pressure was reduced to 5 I 10 4 atm and then increased to 10 2 atm, annealed for four days at each partial pressure while monitoring the slowly relaxing conductivity. The conductivities at P O2 = 10 2 atm and in pure oxygen were measured in later experiments with annealing times of one week at each oxygen pressure. The time independent conductivity was also measured for the La2O3 and Fe2O3 excess materials, for oxygen pressures
0,5
log(σ / S cm-1)
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0,0 n=2δ
p = 3 Vcat
-0,5
-1/6 -1,0
-15
n=p
-10
-3/16
-5
0
log(PO2 / atm) Fig. 4. The time independent isothermal conductivity of LaFeO3 at 1000 -C. The solid line is a guide to the eye.
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
LaFeO3 + La2O3
log(σ / S cm-1)
LaFeO3 + Fe2O3 0,0
-0,5
-1,0
-15
-10
-5
0
log(PO2 / atm) Fig. 5. Time independent conductivity of the La2O3-excess and Fe2O3-excess LaFeO3. The solid line represents the conductivity in nominal stoichiometric LaFeO3. The dashed line is the expected conductivity assuming a permanent number of cation vacancies due to a non-unity ratio between La and Fe in LaFeO3.
lower than 10 7 atm and in air. Prior to the measurements in air, the materials were annealed for one week in the same atmosphere. The slow relaxations were also observed in these materials for P O2 > 10 4 atm, however, these relaxations were not held for sufficient long time to report the final conductivity. The measurements at low oxygen pressures were performed the same way as for the stoichiometric material, and the results are included in Fig. 5. Conductivity relaxations were also carried out in the p-type region for materials with different grain size. Two materials with nominally stoichiometric composition and average grain size of 6.4 and 40 Am, respectively, were initially annealed at 1000 -C in air for three days, before the oxygen partial pressure were reduced by one order of magnitude and held for seven days. During this process, the conductivity was continuously monitored, and the relaxations are given in Fig. 6. The increasing conductivity prior to t = 0 for the fine-grained material indicates that the material was not in complete equilibrium at the given oxygen pressure. Evidently, the relaxation in the fine-grained material was completed after approximately four days, while the conductivity in the coarsegrained material was still decreasing after seven days. However, given that the equilibrium conductivity is independent of the microstructure, both materials should end up with the same conductivity given a sufficient annealing time. Whether the steadily decreasing conductivity observed for the coarse grained material eventually will coincide with the fine grained material is yet to be experimentally verified. 4. Discussion The seeming lack of correspondence between conductivity data reported in this work and data formerly reported in the literature by Mizusaki et al. [7] will be discussed with reference to Fig. 3. Recording the conductivity by keeping the oxygen partial pressure constant for only a short time (typically one
hour) at each pressure gives a behaviour quite similar to observations reported by Mizusaki et al. [7]. However, reducing the sample in CO/CO2 for 12 h and subsequently reoxidizing in pure oxygen did not reproduce the conductivity, but resulted in a conductivity half an order of magnitude lower than the initial conductivity. The overnight annealing in pure oxygen evidently showed the presence of two processes taking place simultaneously in the p-type region: One relatively fast process due to oxygen diffusion and another considerably slower process with a time constant of several days. The total time for the conductivity relaxations in the p-type region was also observed to increase significantly with the grain size (Fig. 6). This may explain why Mizusaki et al. did not observe the slow relaxation processes taking place during the time scale of his experiments because his materials were sintered at 1600 -C and consequently resulted in materials with large grain size. 4.1. The time independent conductivity An ideal LaFeO3 crystal consists of La3+, Fe3+ and O2 occupying all sites in the perovskite structure. At elevated temperatures, vacancies are introduced in the material and compensated by the formation of electronic defects such as Fe2+ (electrons) or Fe4+ (holes), localized on the Fe sites. Assuming that the ionic conductivity in LaFeO3 is much less than the electronic contribution, the electrical conductivity is given by: r¼
F ð uh p þ ue nÞ Vm
ð3Þ
In this equation, n and p are the site fractions of electrons and holes, u e and u h are the electric mobility of each specie, F is Faraday_s constant and V m is the molar volume of LaFeO3. The following defect model will account qualitatively for the time independent isothermal conductivity in the material, with
-0,25 Grain size: 40 µm
log(σ / S cm-1)
0,5
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-0,30
Grain size: 6.4 µm
-0,35
-0,40
0
48
96
144
time / hours Fig. 6. Conductivity relaxations for LaFeO3 in the p-type region, after imposing a step in P O2 from 0.2 to 0.02 atm at 1000 -C. The two materials with nominal stoichiometric composition were sintered at different temperatures to obtain different grain sizes.
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a set of chemical reactions written in the Kro¨ger – Vink notation [12]. A change in the oxygen pressure will be followed by a change in the average Fe-valence when oxygen is incorporated or removed from the material. These processes are described by the following equations, including the corresponding equilibrium expressions: Reduction: x 0 2FeFe þ OOx ¼ 2FeFe þ VO¨ þ 1 = 2O2 ðgÞ
Kred
pffiffiffiffiffiffiffiffi n2 d PO2 ¼ 2 FexFe OxO
ð4Þ ð5Þ
Oxidation:
x þ VO¨ þ 1 = 2O2 ðgÞ ¼ 2FeFe þ OOx 2FeFe
ð6Þ
p2 OxO Kox ¼ 2 pffiffiffiffiffiffiffiffi FexFe d PO2
ð7Þ
n = 2d. By eliminating d in Eq. (5), the following expression is established for the electron concentration: 2 1=2 ð11Þ n3 ¼ 2Kred FexFe OxO PO2 x ] nor [OOx ] changes significantly Since neither K red, [FeFe with the oxygen pressure, and assuming an electronic mobility independent of the electron concentration, the n-type conductivity must follow:
1=6
r / n / PO2
If there also is a large number of cation vacancies present in the n-type region, the cation vacancies must be included in the charge neutrality conditions, which then becomes 2[V O&&] å 3[V cat ]. By eliminating d in Eq. (5) with this expression, the expression for the electron concentration becomes: 2 1=2 1 n2 ¼ 2=3Kred ½Vcat FexFe OxO PO2 ð13Þ and the relation between conductivity and oxygen pressure becomes instead 1=4
Starting with a material with only 3-valent iron, oxygen vacancies and localized electrons will be formed if the oxygen pressure is reduced (reaction (2)), while oxygen vacancies will be occupied and localized electron holes formed at increasing oxygen pressure (reaction (4)). Notice that the last process requires the presence of oxygen vacancies. Adding reactions (2) and (4) leads to the disproportionation reaction of iron, describing the relation between the electronic species:
x 0 2FeFe ¼ FeFe þ FeFe
ð8Þ
with the corresponding equilibrium expression: nIp
Ki ¼ 2 FexFe
ð9Þ
The concentrations of the different species are also restricted by the mass and site balance, however, since the quantity of electronic species and vacancies may be regarded as small for all oxygen pressures, the concentrations of La3+, Fe3+ and O2 are assumed to be unity. Finally, local charge neutrality must be obeyed: n þ 3½Vcat ¼ p þ 2d
ð10Þ
] represents the total number of cation vacancies Here, [V cat on the Fe and La sites. Eqs. (4) – (10) constitute the defect model that Mizusaki et al. put forward to describe the defect chemistry in LaFeO3 [7]. The model will be evaluated qualitatively by comparing the relations between the conductivity and the oxygen pressure within different regions where the conductivity is following relations of the form r ” P O2n . For performing this evaluation, no estimate of the electronic mobility is required. At sufficient low oxygen pressures, there will be a majority of oxygen vacancies and electrons, and the charge neutrality is given by
ð12Þ
r / n / PO2
ð14Þ
The time independent conductivity in Fig. 4 shows a P O2 dependency corresponding to a slope of approximately 1 / 6 in the n-type region. This applies well with Eq. (12), indicating that the population of cation vacancies is insignificant. However, if there exists a region with p-type conductivity in LaFeO3, there must be cation vacancies present to maintain charge neutrality according to Eq. (10). Thus, the concentration of electron holes is found by eliminating d from Eq. (7): 2 1 1=2 p2 ¼ 0:5Kox FexFe OxO ð3½Vcat pÞPO2 ð15Þ The relation between p and P O2 will then depend on the ratio between [V cat ] and p. When 3 I [V cat ] å 2d > >p, typical for the situation at the beginning of the p-type regime close to the n – p transition, the p-type conductivity will follow: 1=4
r / p / PO2
ð16Þ
This corresponds to regular p-type conductivity observed in several ternary oxides, such as BaTiO3 [13]. At higher oxygen pressures, the oxygen vacancies are consumed and the charge neutrality is approximated to p å 3 I [V cat ]. Thus, the conductivity will be independent of P O2 given that the concentration of cation vacancies remains constant. In the virtual absence of cation vacancies, no p-type region will appear, and the P O2 independent regime will merge with the conductivity minimum where the populations of the electronic species (n and p) are equal. The conductivity data given in Fig. 4 give evidence to the assumption that the material is fully oxidized already at P O2 = 10 10 atm. This is also expected from thermodynamics, because the enthalpy of formation of LaFeO3 from La2O3 and Fe2O3 is exothermic, stabilizing the 3-valent state of Fe [14]. An increase in the oxygen pressure from this level up to 10 5 atm has virtually no effect on the conductivity, and is consistent with a fully oxidized state. Fig. 7 shows a qualitative estimate
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Average Fe valence
vacancies and electron holes, giving a charge balance ] + 3[V Fe ] å p. Additionally, the concenapproximated to 3[V La trations of the two types of cation vacancies are assumed to be equal. The cation vacancies are eliminated from Eq. (20), giving: 6 3 3=2 p8 ¼ 36Kcat FexFe OxO PO2 ð21Þ Thus, the p-type conductivity controlled by the Schottky reaction follows the relation: Schottky defects 3=16
r / p / PO2
No cat. vac.
ð22Þ
Frozen cat. vac.
log(PO2 / atm) Fig. 7. A qualitative description of the variation in the average Fe-valence in terms of P O2 according to different defect models. Only the Schottky model accounts for both the n- and p-type conductivity.
for the average valence of Fe as a function of logP O2 (arbitrary scale) according to the present model. The dashed line shows the situation in the absence of cation vacancies, whereas the dotted line illustrates the behaviour in the presence of a constant population of cation vacancies. The first alternative accounts for the n-type regime and the oxygen independent region in Fig. 4, but not the p-type region, while the second alternative accounts for a p-type conductivity which saturates at sufficiently high P O2. Neither of the alternatives describes the observed time independent conductivity for LaFeO3 in the whole P O2-region. The discussion so far indicates that the cation vacancy concentration is not independent of the oxygen pressure. This is also known from LaMnO3, where La and Mn vacancies are formed with increasing P O2 [15,16]. Here, we propose that cation vacancies also can be formed in LaFeO3 according to the Schottky reaction [17]: 0 ¼ VLa VVV þ VFe VVV þ 3VO¨
ð17Þ
3 VVV ½VFe VVV VO¨ KSchottky ¼ ½VLa
ð18Þ
Reaction (17) is combined with reaction (6) to describe how the p-type conductivity behaves in terms of the oxygen pressure:
000 000 6FexFe þ 3 = 2O2 ðgÞ ¼ VLa þ VFe þ 6FeFe þ 3OOx
Kcat ¼
3 ½VLa VVV ½VFe VVV p6 OxO x 6 3=2 FeFe PO2
ð19Þ ð20Þ
According to this reaction, holes and cation vacancies are formed with increasing oxygen pressure without the presence of oxygen vacancies, instead, new oxygen sites are formed along with the formation of the cation vacancies. Hence, the relation between the p-type conductivity and the oxygen pressure may be calculated from Eq. (20), using the same method as previously shown. Here, the major defects are cation
This expression agrees well with the obtained p-type conductivity reported in Fig. 4. The assumption of Schottky defects being dependent on the oxygen pressure is also consistent with the conductivity measurements at medium and low oxygen pressures. As the P O2 decreases, the population of cation vacancies will become insignificant, and the conductivity will correspond to a material without cation vacancies. A qualitative estimate of the average valence state of Fe, including the presence of Schottky defects, is also given in Fig. 7 (solid line). A more quantitative treatment of the defect chemistry in LaFeO3 will be presented in a separate paper [18]. 4.2. The La to Fe ratio The observed time independent conductivity in the materials with La2O3 or Fe2O3 excess is given in Fig. 5. Because the conductivity was independent of small variations in the La to Fe ratio, the model applied for the stoichiometric sample should also be valid for the off-stoichiometric samples. If there was a significant solid solubility region in LaFeO3, the excess Fe2O3 or La2O3 in the materials should result in the formation of a permanent population of cation vacancies. The conductivity would accordingly follow the dashed line given in Fig. 5, with saturated p-type conductivity at high oxygen partial pressures defined by the concentration of cation vacancies. Both of the off-stoichiometric materials showed a pressure independent conductivity at intermediate oxygen partial pressures, which ruled out the presence of cation vacancies in this region, giving evidence to a narrow solid solubility range. However, it should also be considered that the cation vacancies not necessarily are formed in equal numbers, as follows from reaction (19). Assuming the presence of excess Fe2O3, the formation of La-vacancies may take place as described by the following reaction:
x 000 4FeFe þ 3 = 2O2 ðgÞ þ Fe2 O3 ðsÞ ¼ 2VLa þ 6FeFe þ 6OxO
ð23Þ The number of La-vacancies will increase with increasing P O2, and assuming a constant activity of Fe2O3, the same proportionality with the oxygen pressure as found for reaction (19) is expected, r ” P O23 / 16. It is also seen from Eq. (19) that the proportionality between conductivity and P O2, r ” P O23 / 16, will remain the same whether the cation
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vacancies formed are V La + V Fe , 2V La or 2V Fe . That is, we are not able to distinguish between the type of cation vacancies formed. 4.3. The relaxation rate The formation of Schottky defects involves the formation of new lattice sites and, hence, additional unit cells corresponding to an overall material expansion. This process is probably initiated by nucleation at surfaces and along grain boundaries, and the further distribution of vacancies into the grains takes place by diffusion of cations in the opposite direction. Cation diffusion in perovskites is a slow process, which explains the slow relaxation rate, even if the typical diffusion path is within the dimensions of the grains [19]. The increased relaxation time with grain size, which is shown in Fig. 6, is also in accordance with a process controlled by cation diffusion through the grain. In principle, chemical diffusion coefficients for cation diffusion may be obtained from the conductivity relaxations observed in these experiments. However, because the materials were not in a clearly defined state at the start of the relaxation, such calculations were not carried out. Conductivity relaxations controlled by cation diffusion have previously also been reported for BaTiO3 doped with 0.5% La [20] and TiO2 doped with 9.5% Nb [21]. The material sintered at 1500 -C resulted in a coarse-grained microstructure and a high conductivity due to a high population of cation vacancies (Fig. 6). A consequence of the large grains is a long diffusion path, thus, the cation vacancies will not relax to equilibrium on a normal time scale at 1000 -C. Hence, the population of cation vacancies is characterised as frozen. Instead of relaxing to equilibrium, a quasi time independent state is reached, which does not correspond to the equilibrium state. It is suggested that the effect of frozen vacancies, caused by a high sintering temperature and correspondingly large grain size, explains why Mizusaki et al. reported a p-type conductivity behaviour different from the present work [7]. 5. Conclusion The present investigation concluded that La1Ty FeO3 has a narrow solid solution interval. Both TEM analysis and conductivity measurements indicated a solid solution interval y 0.003. Hence, off-unity ratios between La and Fe will result in precipitations of La2O3 or Fe2O3 at the grain boundaries. Given small volume fractions of the precipitates, the conductivity will not be affected. Precipitations may also be caused by the presence of impurities such as SiO2, resulting in the formation of stable La – Si– O phases and subsequent formation of Fe2O3. The time independent conductivity for LaFeO3 in terms of the oxygen pressure has been measured at 1000 -C. The required time to obtain a time independent state varied from less than 30 min at low oxygen pressures to several days at high oxygen pressures. Even longer time was required for large grained materials. The present results contradict previously
reported results for the p-type conductivity behaviour [7]. Here, it is proposed that the p-type conductivity at high oxygen partial pressures is due to the formation of Schottky defects. The number of cation vacancies will increase with the oxygen pressure, giving the following conductivity behaviour: r ” P O23 / 16. The total conductivity relaxation time in the p-type regime was found to increase with the grain size. The extended relaxation times are consistent with cation diffusion being the rate controlling process for the oxidation of LaFeO3 at high P O2. Acknowledgements The authors wish to thank senior scientist Finn Willy Poulsen at The Danish National Laboratory, Riso¨ , for permission to use his worksheet for performing defectchemistry calculations. Prof. Mari-Ann Einarsrud at Department of Materials Science and Engineering, NTNU, is gratefully acknowledged for her helpful guidance with experimental preparations and The Norwegian Research Council is acknowledged for the financial support. References [1] J. Mizusaki, T. Sasamoto, W.R. Cannon, H.K. Bowen, J. Am. Ceram. Soc. 66 (1983) 247. [2] J.E. ten Elshof, H.J.M. Bouwmeester, H. Verveij, Solid State Ion. 81 (1995) 97. [3] J.E. ten Elshof, H.J.M. Bouwmeester, H. Verveij, Solid State Ion. 89 (1996) 81. [4] K. Huang, H.Y. Lee, J.B. Goodenough, J. Electrochem. Soc. 145 (1998) 3220. [5] I. Hole, T. Tybell, J.H. Grepstad, I. Wærnhus, K. Wiik, T. Grande, Solid State Elec. 47 (2003) 2279. [6] M.C. Kim, S.J. Park, H. Haneda, J. Tanaka, S. Shirasaki, Solid State Ion. 40 (1990) 239. [7] J. Mizusaki, T. Sasamoto, W.R. Cannon, H.K. Bowen, J. Am. Ceram. Soc. 65 (1982) 363. [8] I. Wærnhus, T. Grande, K. Wiik, Grain Boundary Engineering of Electronic Ceramics, Maney Publishing, London, 2003, p. 19. [9] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [10] S.E. Dann, D.B. Currie, M.T. Weller, M.F. Thomas, A.D. Al-Rawwas, J. Solid State Chem. 109 (1994) 134. [11] U. Kolitsch, H.J. Seifert, F. Aldinger, J. Solid State Chem. 120 (1995) 38. [12] F.A. Kro¨ger, The Chemistry of Imperfect Crystals, Nort-Holland, Amsterdam, 1974. [13] J. Nowotny, M. Rekas, Solid State Ion. 49 (1991) 135. [14] T. Nakamura, G. Petzow, L.J. Gauckler, Mater. Res. Bull. 14 (1979) 649. [15] J.H. Kuo, H.U. Anderson, D.M. Sparlin, J. Solid State Chem. 83 (1989) 52. [16] J. Mizusaki, N. Mori, H. Takai, Y. Yonemura, H. Minamiue, H. Tagawa, M. Dokiya, H. Inaba, K. Naraya, T. Sasamoto, T. Hasimoto, Solid State Ion. 129 (2000) 163. [17] C. Wagner, W. Schottky, Z. Phys. Chem., B Chem. Elem.Proz. Aufbau Mater. 11 (1931) 163. [18] I. Wærnhus, T. Grande and K. Wiik, Solid State Ion. (in press). [19] I. Wærnhus, N. Sakai, H. Yokokawa, T. Grande, M.-A. Einarsrud, K. Wiik, Solid State Ion. 175 (2004) 69. [20] R. Wernicke, Philips Res. Rep. 31 (1975) 526. [21] M. Radecka, M. Rekas, J. Phys. Chem. Solids 56 (1995) 1031.
Electronic properties of polycrystalline LaFeO3. Part I: Experimental results and the qualitative role of Schottky defects Ivar Wærnhus a, Per Erik Vullum b, Randi Holmestad b, Tor Grande a, Kjell Wiik a,* a
Department of Materials Science and Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway b Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 13 August 2004; received in revised form 14 July 2005; accepted 24 August 2005
Abstract The isothermal electrical conductivity of La1y FeO3d ( y = 0.003, 0.000 and + 0.003) ceramics has been investigated at 1000 -C in oxygen partial pressures from 1 to 10 17 atm, and found to be essentially independent of the composition ( y). Both La2O3-rich and Fe2O3-rich secondary phases were identified by transmission electron microscopy in the non-stoichiometric materials ( y = 0.003 and + 0.003), and a narrow homogeneity range for La1Ty FeO3d ( y < 3 I 10 3) was inferred. The materials exhibited n-type conductivity at low oxygen partial pressures due to the reduction of Fe3+ to Fe2+ and formation of oxygen vacancies, consistent with previous reports. The rate of the reduction was controlled by oxygen diffusion and a time independent conductivity was established relatively fast. For oxygen pressures between 10 11 and 10 4 atm, the time independent conductivity was essentially independent of variations in the oxygen pressure. This was explained by a fully occupied oxygen lattice, implying that the material could not be further oxidized without formation of new oxygen sites. At the highest oxygen partial pressures ( P O2 > 10 4 atm), p-type conductivity was evident. However, in this regime, the conductivity was time dependent on a time scale of days or weeks, inconsistent with previous reports. Possible mechanisms for the p-type conductivity and the slow change in the conductivity at high oxygen partial pressures are discussed, and a new defect model is put forward, which includes formation of thermally activated Schottky defects. The model accounts qualitatively for the time dependent conductivity and points out the importance of cation vacancies and cation diffusion at high oxygen partial pressures. D 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Cc; 61.72.Ji; 68.35.Dv; 68.55.Ln Keywords: LaFeO3; Electrical conductivity; Schottky defects; Cation vacancies
1. Introduction Lanthanum ferrite based oxides such as La1x Srx Fe1y Coy O3d are materials becoming increasingly more important due to their electrochemical properties. High ionic and electronic conductivity [1– 3] in these materials make them potential candidates for use as SOFC cathode materials, gas sensors and oxygen permeable membranes [4]. The basic component in the actual system, LaFeO3, prepared as thin films, is also a promising candidate material for use as an oxygen sensor [5]. The isothermal conductivity of Sr-doped LaFeO3 has previously been reported by Mizusaki et al. [1] and Kim et
* Corresponding author. Tel.: +47 73 59 40 82; fax: +47 73 59 08 60. E-mail address: [email protected] (K. Wiik). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.08.012
al. [6]. In both contributions, the concentrations of chemical defects were successfully modelled as an ideal solution, indicating that interaction between defects is insignificant. The electrical conductivity was described by localized electrons and holes hopping between the Fe ions, and the concentration of Fe2+ and Fe4+ constituted the charge carrier concentrations. The isothermal conductivity passed a minimum where the average Fe valence was three, from where it was increased by both increased and reduced oxygen pressure. At this state, the level of oxygen vacancies (d) was defined by the level of Sr doping (x), given as d = x / 2. At higher oxygen pressures, when all oxygen sites were occupied, the isothermal conductivity reached saturation on a level defined by the Sr content. According to this model, p-type conductivity will not become dominant in undoped LaFeO3 for any oxygen pressures, the conductivity is n-type as long as oxygen
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vacancies are present, and then saturates at the minimum level, when all oxygen sites are occupied. However, Mizusaki et al. reported a similar isothermal conductivity in pure LaFeO3 as in the Sr-doped materials [7], and explained the observations with the formation of cation vacancies due to a none unity ratio between La and Fe. It was reasoned that the cation vacancies acted as acceptors and had the same effect on the material as a small level of Sr-doping, and thus accounted for the p-type conductivity. Of vital importance for the use of LaFeO3 as oxygen sensor is the knowledge about the conductivity and oxygen transport mechanism. We have recently applied a 4-point DC technique to determine such data by conductivity relaxations [8], and the isothermal conductivity data are presented in this contribution. The focus has been in particular on the influence of the microstructure and small variations in the overall chemical composition of the materials. Surprisingly, the electrical conductivity in the p-type regime did not fit into the expected model with p-type conductivity saturating at high oxygen pressures, but was time dependent on the time scale of days, corresponding to an apparent equilibrium conductivity not consistent with data reported by Mizusaki et al. In the present article, the model for the conductivity and oxygen stoichiometry in LaFeO3 is re-evaluated qualitatively. Possible physical processes, which can account for the observations reported in this contribution, are discussed with particular attention to Schottky defects. 2. Experimental 2.1. Preparation The powders were prepared by spray drying (Bu¨chi, Mini Spray-Drier B-191) of aqueous glycine– nitrate solutions using La(NO3)3I6H2O (Fluka p.a.) and Fe(NO3)3I9H2O (Riedel-de Hae¨n, p.a.) as starting materials. In order to obtain a high accuracy in the La / Fe ratio, the metal concentrations were calibrated gravimetrically with three parallels for each metal nitrate. The difference in the metal concentrations between the extreme parallels, D = (c max c min) / c avg, was 0.001 for both elements, giving a high accuracy for the La / Fe ratio in the final product. Three compositions of La1Ty FeO3d were synthesized, one nominally stoichiometric ( y = 0.000), one with a small iron deficiency ( y = + 0.003) and one with a small lanthanum deficiency ( y = 0.003). These compositions are referred to as the nominal stoichiometric, the Fe2O3-excess and the La2O3excess compositions, respectively. To optimize the control of the La to Fe ratio, the nominal stoichiometric solution was first prepared and then split into three parallels. The La- and Feexcess solutions were prepared by adding the actual metal nitrate to the respective solution. Glycine (Merck p.a.) was added as fuel for the combustion process. The solutions were spray dried to a dry powder precursor, and fine-grained LaFeO3 powders were prepared by dropping the precursor through a hot tube, preheated to 700 -C, where the precursor ignited. The resulting powders were then ball milled for 12 h with Si3N4 grinding balls and calcined at 1000 -C for 24 h. Rectangular
bars were formed by uniaxial pressing, followed by cold isostatic pressing at 200 MPa and finally sintered at 1300 -C for 10 h. The thicknesses of the samples were in the interval 1.5 to 2.1 mm, and the two other dimensions were 8.0 and 23 mm. Densities of 95% of theoretical density were achieved for all compositions. Prior to the conductivity measurements, the bars were polished with a diamond spray containing 3 Am particles. One stoichiometric bar was also sintered a second time at 1500 -C for 6 h in order to produce a material with larger grain size. 2.2. Characterization The powders were characterized with XRD (Siemens D5005, 2h range: 20– 70-, step 0.02-, count time 11 s) and the cell parameters and the crystallographic density were calculated by Rietveld refinement [9]. The micrographs were taken on polished samples, etched at 1300 -C prior to analysis (SEM, Hitachi S-3500N). The TEM samples were prepared from 3 mm discs which were mechanically grounded, polished and dimpled to a central thickness of ¨20 Am. The discs were ion-beam thinned using a Gatan duo-mill with liquid nitrogen cooling, operating at 3.5 kV and with a thinning angle of 12-. TEM was performed using a Philips CM 30 microscope with an EDAX DX4 EDS system, and all examinations were conducted at a beam voltage of 200 kV. 2.3. The conductivity measurements The conductivity was measured by a 4-point technique enabling both current (I) and voltage (V) to be measured independently (Keithly D500). Two Pt electrodes were attached with Pt paste at each end of the sample, and an Al2O3 clamp pulled the sample down on two other Pt electrodes placed at a distance d = 5.4 mm apart. The conductivity (r) was calculated from: r¼
I d U A
ð1Þ
where A was the area of the cross section normal to the current. The measurements presented in this work have all been carried out at 1000 -C, applying a current between 1 and 2 mA. The sample temperature was monitored using a thermocouple type S located in the vicinity of the bar. The thermocouple was calibrated in accordance with the melting point of gold and silver. The gas was introduced with a continuous flow through an alumina tube placed 5 mm from the sample, the partial pressure of oxygen was controlled by mixing O2 and N2 or CO and CO2 controlled by four mass flow meters (Brooks 5850S, 50 and 500 ml), and the oxygen partial pressure was continuously monitored by a ZrO2 sensor, provided by Riso¨ National Laboratory. 3. Results 3.1. Phase composition and microstructure All three materials appeared phase pure according to the XRD diffractograms. The dimensions of the orthorhombic unit
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
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Fe-excess materials are given in Fig. 2. In all three compositions, an oxide phase containing La and Si was observed by EDS. SiO2 impurities are frequently observed in oxide ceramics as a major contamination introduced during preparation, for instance, many minute amounts of silica have been brought in from the Si3N4 grinding balls during ball milling. SiO2 will then react with the perovskite during heat treatment to form a La2O3 –SiO2 phase, for instance, La9.33(SiO4)6O2 [11], and if the homogeneity range in LaFeO3 is narrow, Fe2O3 should precipitate according to the reaction: 6SiO2 þ 9:33LaFeO3 ¼ La9:33 ðSiO4 Þ6 O2 þ 4:66Fe2 O3
ð2Þ
The La2O3 –SiO2 inclusions were too small and too few to have any direct influence on the conductivity. However, the reaction between SiO2 and LaFeO3 could result in formation of La-vacancies, which may have significant effects on the conductivity. In the Fe-excess composition, traces of Fe2O3 were relatively frequently encountered, but also in the stoichiometric composition, traces of Fe2O3 were observed. It indicated that even minute amount of excess Fe will precipitate from the perovskite phase and form Fe2O3. The Fe2O3 precipitations in the nominally stoichiometric sample may both be a result of minute Fig. 1. Secondary electron SEM micrographs of nominal stoichiometric LaFeO3 (La : Fe = 1 : 1) sintered at 1300 -C (a) and at 1500 -C (b).
cell in the nominal stoichiometric material were calculated to ˚ , b = 7.861 A ˚ , c = 5.560 A ˚ , and were in good a = 5.570 A agreement with literature data [10]. Within the uncertainty, identical unit cells were observed for all three compositions. Micrographs of two stoichiometric materials sintered at 1300 and 1500 -C, respectively, are given in Fig. 1. The average grain diameters and densities for the two samples were 6.4 Am, q = 96%, and 40 Am, q = 93%, respectively. According to Fig. 1 the morphologies of the two samples are apparently quite different. The variation in morphology is mainly due to sample preparation and thermally etching time. Whereas Fig. 1a shows a polished surface exposed a long time in air at 1300 -C, Fig. 1b shows a polished surface exposed at the same conditions for only a short time (approx. 10 min), sufficient for grain boundaries to appear. It is also evident in Fig. 1b that the microstructure contains some residual porosity and that some grains have been pulled out during polishing. The residual porosity might be due to either Ostwald pore ripening or to green body inhomogeneities. More carefully controlled experiments are, however, necessary in order to give a more fundamental discussion on the evolution of the microstructure. For samples with different compositions sintered at identical temperatures, no significant differences neither in the microstructures nor the densities were observed. The microstructure was also examined both prior to and after the experiments, and no significant changes were found to take place during the conductivity measurements. The TEM investigations revealed the presence of small inclusions (0.2 – 2 Am) of secondary phases at triple points between the grains, typical examples from the La-excess and
Fig. 2. TEM images showing secondary phases at grain boundaries in LaFeO3. Examples of Fe2O3 in the Fe2O3-excess material (a) and La2O3 – SiO2 phase in the La2O3-excess material (b).
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
log(σ / cm s-1)
0,0
1st down
2nd down
-0,5
1st up
3rd up -1,0 -15
-10
-5
0
log(PO2 / atm) Fig. 3. Conductivities of LaFeO3 at 1000 -C measured stepwise, annealing for one hour at each P O2. Start in pure O2, 1st day down and 1st day up were recorded the first day, 2nd day down and 3rd day up recorded the two following days.
quantities of excess Fe from the powder preparation, as well as a result of the reaction between SiO2 and the perovskite (Eq. (2)). In the material which was prepared with excess of La2O3, only the La2O3 – SiO2 phase was observed in addition to the perovskite phase. The La to Si ratio of the EDS intensities in this phase was also significant higher than the corresponding ratio found in the La / Si inclusions observed in the Fe-excess compositions. The ratio between the intensities, I La / I Si, was 3.8 and 2.2 in the La-excess and Fe-excess materials, respectively. The numbers should not be evaluated as absolute values, since the EDS-analysis was not subjected to a standard calibration procedure. However, the analysis verifies the relative difference between the I La / I Si-ratio in the precipitations found in the different materials. The higher La content observed in the precipitates in the nominally La-rich material indicated that these essentially originated from excess La2O3. Thus, the TEMinvestigation points toward no traceable solid solution interval in LaFeO3 on any of the sides of the stoichiometric composition. The possible deviation in the La to Fe ratio in the perovskite phase is less than 3 I 10 3, and even in a nominally stoichiometric material, excess Fe or La may precipitate as oxides, rather than contribute to form cation vacancies. 3.2. Isothermal electrical conductivity The first results from conductivity measurements on nominally stoichiometric materials and at constant T = 1000 -C are given in Fig. 3. The conductivity was first measured in pure oxygen and the oxygen pressure was subsequently reduced stepwise to P O2 = 10 17 atm (‘‘1st day down’’) before stepwise oxidizing the material all the way up to pure oxygen (‘‘1st day up’’). The material was held for one hour at each partial pressure, and the reported conductivity was the conductivity recorded immediately before changing the partial pressure. After the ‘‘1st day up’’ series, the sample was annealed in oxygen for twelve hours before the reduction series ‘‘2nd day down’’ was performed in the same manner as described above. The material
was subsequently annealed in CO/CO2 ( P O2 å 10 13 atm) for another 12 h before the ‘‘3rd day up’’ series was recorded. At P O2 > 10 12 atm, the conductivity was p-type. However, the p-type conductivity is seen to vary between all the series. After the first reduction and oxidation cycle, the conductivity observed in pure oxygen had decreased with more than half an order of magnitude. During the twelve hours of annealing in pure oxygen the following night, the conductivity was slowly increasing to the initial value recorded in pure oxygen for the ‘‘2nd day down’’ series. The ‘‘2nd day down’’ series was terminated with a 12 h residence time at P O2 = 10 13 atm, before the ‘‘3rd day up’’ series was performed. The final conductivity recorded in oxygen was even lower than after the ‘‘1st day up’’ series. Evidently, some kind of background process was taking place in the sample affecting the conductivity in the p-type regime. However, the conductivity observed in the n-type region, for P O2 < 10 12 atm, was reproduced, and a time independent conductivity was quickly obtained. Fig. 4 shows the measured time independent conductivity for the nominally stoichiometric LaFeO3 sample. The measurements at low oxygen pressures started at P O2 = 10 17 atm, where the sample was held for several days performing conductivity relaxations, before these conductivity measurements were carried out. In the n-type region, the conductivity attained a time independent state in less than 30 min. For oxygen pressures between 10 10 and 10 7 atm, the conductivity was found to be virtually independent of the oxygen partial pressure; no changes were observed even after 12 h monitoring the conductivity. The measurements at P O2 > 10 4 atm were carried out in the following order: The sample was first annealed in air for one week before measuring the conductivity. Subsequently, the oxygen pressure was reduced to 5 I 10 4 atm and then increased to 10 2 atm, annealed for four days at each partial pressure while monitoring the slowly relaxing conductivity. The conductivities at P O2 = 10 2 atm and in pure oxygen were measured in later experiments with annealing times of one week at each oxygen pressure. The time independent conductivity was also measured for the La2O3 and Fe2O3 excess materials, for oxygen pressures
0,5
log(σ / S cm-1)
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0,0 n=2δ
p = 3 Vcat
-0,5
-1/6 -1,0
-15
n=p
-10
-3/16
-5
0
log(PO2 / atm) Fig. 4. The time independent isothermal conductivity of LaFeO3 at 1000 -C. The solid line is a guide to the eye.
I. Wærnhus et al. / Solid State Ionics 176 (2005) 2783 – 2790
LaFeO3 + La2O3
log(σ / S cm-1)
LaFeO3 + Fe2O3 0,0
-0,5
-1,0
-15
-10
-5
0
log(PO2 / atm) Fig. 5. Time independent conductivity of the La2O3-excess and Fe2O3-excess LaFeO3. The solid line represents the conductivity in nominal stoichiometric LaFeO3. The dashed line is the expected conductivity assuming a permanent number of cation vacancies due to a non-unity ratio between La and Fe in LaFeO3.
lower than 10 7 atm and in air. Prior to the measurements in air, the materials were annealed for one week in the same atmosphere. The slow relaxations were also observed in these materials for P O2 > 10 4 atm, however, these relaxations were not held for sufficient long time to report the final conductivity. The measurements at low oxygen pressures were performed the same way as for the stoichiometric material, and the results are included in Fig. 5. Conductivity relaxations were also carried out in the p-type region for materials with different grain size. Two materials with nominally stoichiometric composition and average grain size of 6.4 and 40 Am, respectively, were initially annealed at 1000 -C in air for three days, before the oxygen partial pressure were reduced by one order of magnitude and held for seven days. During this process, the conductivity was continuously monitored, and the relaxations are given in Fig. 6. The increasing conductivity prior to t = 0 for the fine-grained material indicates that the material was not in complete equilibrium at the given oxygen pressure. Evidently, the relaxation in the fine-grained material was completed after approximately four days, while the conductivity in the coarsegrained material was still decreasing after seven days. However, given that the equilibrium conductivity is independent of the microstructure, both materials should end up with the same conductivity given a sufficient annealing time. Whether the steadily decreasing conductivity observed for the coarse grained material eventually will coincide with the fine grained material is yet to be experimentally verified. 4. Discussion The seeming lack of correspondence between conductivity data reported in this work and data formerly reported in the literature by Mizusaki et al. [7] will be discussed with reference to Fig. 3. Recording the conductivity by keeping the oxygen partial pressure constant for only a short time (typically one
hour) at each pressure gives a behaviour quite similar to observations reported by Mizusaki et al. [7]. However, reducing the sample in CO/CO2 for 12 h and subsequently reoxidizing in pure oxygen did not reproduce the conductivity, but resulted in a conductivity half an order of magnitude lower than the initial conductivity. The overnight annealing in pure oxygen evidently showed the presence of two processes taking place simultaneously in the p-type region: One relatively fast process due to oxygen diffusion and another considerably slower process with a time constant of several days. The total time for the conductivity relaxations in the p-type region was also observed to increase significantly with the grain size (Fig. 6). This may explain why Mizusaki et al. did not observe the slow relaxation processes taking place during the time scale of his experiments because his materials were sintered at 1600 -C and consequently resulted in materials with large grain size. 4.1. The time independent conductivity An ideal LaFeO3 crystal consists of La3+, Fe3+ and O2 occupying all sites in the perovskite structure. At elevated temperatures, vacancies are introduced in the material and compensated by the formation of electronic defects such as Fe2+ (electrons) or Fe4+ (holes), localized on the Fe sites. Assuming that the ionic conductivity in LaFeO3 is much less than the electronic contribution, the electrical conductivity is given by: r¼
F ð uh p þ ue nÞ Vm
ð3Þ
In this equation, n and p are the site fractions of electrons and holes, u e and u h are the electric mobility of each specie, F is Faraday_s constant and V m is the molar volume of LaFeO3. The following defect model will account qualitatively for the time independent isothermal conductivity in the material, with
-0,25 Grain size: 40 µm
log(σ / S cm-1)
0,5
2787
-0,30
Grain size: 6.4 µm
-0,35
-0,40
0
48
96
144
time / hours Fig. 6. Conductivity relaxations for LaFeO3 in the p-type region, after imposing a step in P O2 from 0.2 to 0.02 atm at 1000 -C. The two materials with nominal stoichiometric composition were sintered at different temperatures to obtain different grain sizes.
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a set of chemical reactions written in the Kro¨ger – Vink notation [12]. A change in the oxygen pressure will be followed by a change in the average Fe-valence when oxygen is incorporated or removed from the material. These processes are described by the following equations, including the corresponding equilibrium expressions: Reduction: x 0 2FeFe þ OOx ¼ 2FeFe þ VO¨ þ 1 = 2O2 ðgÞ
Kred
pffiffiffiffiffiffiffiffi n2 d PO2 ¼ 2 FexFe OxO
ð4Þ ð5Þ
Oxidation:
x þ VO¨ þ 1 = 2O2 ðgÞ ¼ 2FeFe þ OOx 2FeFe
ð6Þ
p2 OxO Kox ¼ 2 pffiffiffiffiffiffiffiffi FexFe d PO2
ð7Þ
n = 2d. By eliminating d in Eq. (5), the following expression is established for the electron concentration: 2 1=2 ð11Þ n3 ¼ 2Kred FexFe OxO PO2 x ] nor [OOx ] changes significantly Since neither K red, [FeFe with the oxygen pressure, and assuming an electronic mobility independent of the electron concentration, the n-type conductivity must follow:
1=6
r / n / PO2
If there also is a large number of cation vacancies present in the n-type region, the cation vacancies must be included in the charge neutrality conditions, which then becomes 2[V O&&] å 3[V cat ]. By eliminating d in Eq. (5) with this expression, the expression for the electron concentration becomes: 2 1=2 1 n2 ¼ 2=3Kred ½Vcat FexFe OxO PO2 ð13Þ and the relation between conductivity and oxygen pressure becomes instead 1=4
Starting with a material with only 3-valent iron, oxygen vacancies and localized electrons will be formed if the oxygen pressure is reduced (reaction (2)), while oxygen vacancies will be occupied and localized electron holes formed at increasing oxygen pressure (reaction (4)). Notice that the last process requires the presence of oxygen vacancies. Adding reactions (2) and (4) leads to the disproportionation reaction of iron, describing the relation between the electronic species:
x 0 2FeFe ¼ FeFe þ FeFe
ð8Þ
with the corresponding equilibrium expression: nIp
Ki ¼ 2 FexFe
ð9Þ
The concentrations of the different species are also restricted by the mass and site balance, however, since the quantity of electronic species and vacancies may be regarded as small for all oxygen pressures, the concentrations of La3+, Fe3+ and O2 are assumed to be unity. Finally, local charge neutrality must be obeyed: n þ 3½Vcat ¼ p þ 2d
ð10Þ
] represents the total number of cation vacancies Here, [V cat on the Fe and La sites. Eqs. (4) – (10) constitute the defect model that Mizusaki et al. put forward to describe the defect chemistry in LaFeO3 [7]. The model will be evaluated qualitatively by comparing the relations between the conductivity and the oxygen pressure within different regions where the conductivity is following relations of the form r ” P O2n . For performing this evaluation, no estimate of the electronic mobility is required. At sufficient low oxygen pressures, there will be a majority of oxygen vacancies and electrons, and the charge neutrality is given by
ð12Þ
r / n / PO2
ð14Þ
The time independent conductivity in Fig. 4 shows a P O2 dependency corresponding to a slope of approximately 1 / 6 in the n-type region. This applies well with Eq. (12), indicating that the population of cation vacancies is insignificant. However, if there exists a region with p-type conductivity in LaFeO3, there must be cation vacancies present to maintain charge neutrality according to Eq. (10). Thus, the concentration of electron holes is found by eliminating d from Eq. (7): 2 1 1=2 p2 ¼ 0:5Kox FexFe OxO ð3½Vcat pÞPO2 ð15Þ The relation between p and P O2 will then depend on the ratio between [V cat ] and p. When 3 I [V cat ] å 2d > >p, typical for the situation at the beginning of the p-type regime close to the n – p transition, the p-type conductivity will follow: 1=4
r / p / PO2
ð16Þ
This corresponds to regular p-type conductivity observed in several ternary oxides, such as BaTiO3 [13]. At higher oxygen pressures, the oxygen vacancies are consumed and the charge neutrality is approximated to p å 3 I [V cat ]. Thus, the conductivity will be independent of P O2 given that the concentration of cation vacancies remains constant. In the virtual absence of cation vacancies, no p-type region will appear, and the P O2 independent regime will merge with the conductivity minimum where the populations of the electronic species (n and p) are equal. The conductivity data given in Fig. 4 give evidence to the assumption that the material is fully oxidized already at P O2 = 10 10 atm. This is also expected from thermodynamics, because the enthalpy of formation of LaFeO3 from La2O3 and Fe2O3 is exothermic, stabilizing the 3-valent state of Fe [14]. An increase in the oxygen pressure from this level up to 10 5 atm has virtually no effect on the conductivity, and is consistent with a fully oxidized state. Fig. 7 shows a qualitative estimate
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Average Fe valence
vacancies and electron holes, giving a charge balance ] + 3[V Fe ] å p. Additionally, the concenapproximated to 3[V La trations of the two types of cation vacancies are assumed to be equal. The cation vacancies are eliminated from Eq. (20), giving: 6 3 3=2 p8 ¼ 36Kcat FexFe OxO PO2 ð21Þ Thus, the p-type conductivity controlled by the Schottky reaction follows the relation: Schottky defects 3=16
r / p / PO2
No cat. vac.
ð22Þ
Frozen cat. vac.
log(PO2 / atm) Fig. 7. A qualitative description of the variation in the average Fe-valence in terms of P O2 according to different defect models. Only the Schottky model accounts for both the n- and p-type conductivity.
for the average valence of Fe as a function of logP O2 (arbitrary scale) according to the present model. The dashed line shows the situation in the absence of cation vacancies, whereas the dotted line illustrates the behaviour in the presence of a constant population of cation vacancies. The first alternative accounts for the n-type regime and the oxygen independent region in Fig. 4, but not the p-type region, while the second alternative accounts for a p-type conductivity which saturates at sufficiently high P O2. Neither of the alternatives describes the observed time independent conductivity for LaFeO3 in the whole P O2-region. The discussion so far indicates that the cation vacancy concentration is not independent of the oxygen pressure. This is also known from LaMnO3, where La and Mn vacancies are formed with increasing P O2 [15,16]. Here, we propose that cation vacancies also can be formed in LaFeO3 according to the Schottky reaction [17]: 0 ¼ VLa VVV þ VFe VVV þ 3VO¨
ð17Þ
3 VVV ½VFe VVV VO¨ KSchottky ¼ ½VLa
ð18Þ
Reaction (17) is combined with reaction (6) to describe how the p-type conductivity behaves in terms of the oxygen pressure:
000 000 6FexFe þ 3 = 2O2 ðgÞ ¼ VLa þ VFe þ 6FeFe þ 3OOx
Kcat ¼
3 ½VLa VVV ½VFe VVV p6 OxO x 6 3=2 FeFe PO2
ð19Þ ð20Þ
According to this reaction, holes and cation vacancies are formed with increasing oxygen pressure without the presence of oxygen vacancies, instead, new oxygen sites are formed along with the formation of the cation vacancies. Hence, the relation between the p-type conductivity and the oxygen pressure may be calculated from Eq. (20), using the same method as previously shown. Here, the major defects are cation
This expression agrees well with the obtained p-type conductivity reported in Fig. 4. The assumption of Schottky defects being dependent on the oxygen pressure is also consistent with the conductivity measurements at medium and low oxygen pressures. As the P O2 decreases, the population of cation vacancies will become insignificant, and the conductivity will correspond to a material without cation vacancies. A qualitative estimate of the average valence state of Fe, including the presence of Schottky defects, is also given in Fig. 7 (solid line). A more quantitative treatment of the defect chemistry in LaFeO3 will be presented in a separate paper [18]. 4.2. The La to Fe ratio The observed time independent conductivity in the materials with La2O3 or Fe2O3 excess is given in Fig. 5. Because the conductivity was independent of small variations in the La to Fe ratio, the model applied for the stoichiometric sample should also be valid for the off-stoichiometric samples. If there was a significant solid solubility region in LaFeO3, the excess Fe2O3 or La2O3 in the materials should result in the formation of a permanent population of cation vacancies. The conductivity would accordingly follow the dashed line given in Fig. 5, with saturated p-type conductivity at high oxygen partial pressures defined by the concentration of cation vacancies. Both of the off-stoichiometric materials showed a pressure independent conductivity at intermediate oxygen partial pressures, which ruled out the presence of cation vacancies in this region, giving evidence to a narrow solid solubility range. However, it should also be considered that the cation vacancies not necessarily are formed in equal numbers, as follows from reaction (19). Assuming the presence of excess Fe2O3, the formation of La-vacancies may take place as described by the following reaction:
x 000 4FeFe þ 3 = 2O2 ðgÞ þ Fe2 O3 ðsÞ ¼ 2VLa þ 6FeFe þ 6OxO
ð23Þ The number of La-vacancies will increase with increasing P O2, and assuming a constant activity of Fe2O3, the same proportionality with the oxygen pressure as found for reaction (19) is expected, r ” P O23 / 16. It is also seen from Eq. (19) that the proportionality between conductivity and P O2, r ” P O23 / 16, will remain the same whether the cation
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vacancies formed are V La + V Fe , 2V La or 2V Fe . That is, we are not able to distinguish between the type of cation vacancies formed. 4.3. The relaxation rate The formation of Schottky defects involves the formation of new lattice sites and, hence, additional unit cells corresponding to an overall material expansion. This process is probably initiated by nucleation at surfaces and along grain boundaries, and the further distribution of vacancies into the grains takes place by diffusion of cations in the opposite direction. Cation diffusion in perovskites is a slow process, which explains the slow relaxation rate, even if the typical diffusion path is within the dimensions of the grains [19]. The increased relaxation time with grain size, which is shown in Fig. 6, is also in accordance with a process controlled by cation diffusion through the grain. In principle, chemical diffusion coefficients for cation diffusion may be obtained from the conductivity relaxations observed in these experiments. However, because the materials were not in a clearly defined state at the start of the relaxation, such calculations were not carried out. Conductivity relaxations controlled by cation diffusion have previously also been reported for BaTiO3 doped with 0.5% La [20] and TiO2 doped with 9.5% Nb [21]. The material sintered at 1500 -C resulted in a coarse-grained microstructure and a high conductivity due to a high population of cation vacancies (Fig. 6). A consequence of the large grains is a long diffusion path, thus, the cation vacancies will not relax to equilibrium on a normal time scale at 1000 -C. Hence, the population of cation vacancies is characterised as frozen. Instead of relaxing to equilibrium, a quasi time independent state is reached, which does not correspond to the equilibrium state. It is suggested that the effect of frozen vacancies, caused by a high sintering temperature and correspondingly large grain size, explains why Mizusaki et al. reported a p-type conductivity behaviour different from the present work [7]. 5. Conclusion The present investigation concluded that La1Ty FeO3 has a narrow solid solution interval. Both TEM analysis and conductivity measurements indicated a solid solution interval y 0.003. Hence, off-unity ratios between La and Fe will result in precipitations of La2O3 or Fe2O3 at the grain boundaries. Given small volume fractions of the precipitates, the conductivity will not be affected. Precipitations may also be caused by the presence of impurities such as SiO2, resulting in the formation of stable La – Si– O phases and subsequent formation of Fe2O3. The time independent conductivity for LaFeO3 in terms of the oxygen pressure has been measured at 1000 -C. The required time to obtain a time independent state varied from less than 30 min at low oxygen pressures to several days at high oxygen pressures. Even longer time was required for large grained materials. The present results contradict previously
reported results for the p-type conductivity behaviour [7]. Here, it is proposed that the p-type conductivity at high oxygen partial pressures is due to the formation of Schottky defects. The number of cation vacancies will increase with the oxygen pressure, giving the following conductivity behaviour: r ” P O23 / 16. The total conductivity relaxation time in the p-type regime was found to increase with the grain size. The extended relaxation times are consistent with cation diffusion being the rate controlling process for the oxidation of LaFeO3 at high P O2. Acknowledgements The authors wish to thank senior scientist Finn Willy Poulsen at The Danish National Laboratory, Riso¨ , for permission to use his worksheet for performing defectchemistry calculations. Prof. Mari-Ann Einarsrud at Department of Materials Science and Engineering, NTNU, is gratefully acknowledged for her helpful guidance with experimental preparations and The Norwegian Research Council is acknowledged for the financial support. References [1] J. Mizusaki, T. Sasamoto, W.R. Cannon, H.K. Bowen, J. Am. Ceram. Soc. 66 (1983) 247. [2] J.E. ten Elshof, H.J.M. Bouwmeester, H. Verveij, Solid State Ion. 81 (1995) 97. [3] J.E. ten Elshof, H.J.M. Bouwmeester, H. Verveij, Solid State Ion. 89 (1996) 81. [4] K. Huang, H.Y. Lee, J.B. Goodenough, J. Electrochem. Soc. 145 (1998) 3220. [5] I. Hole, T. Tybell, J.H. Grepstad, I. Wærnhus, K. Wiik, T. Grande, Solid State Elec. 47 (2003) 2279. [6] M.C. Kim, S.J. Park, H. Haneda, J. Tanaka, S. Shirasaki, Solid State Ion. 40 (1990) 239. [7] J. Mizusaki, T. Sasamoto, W.R. Cannon, H.K. Bowen, J. Am. Ceram. Soc. 65 (1982) 363. [8] I. Wærnhus, T. Grande, K. Wiik, Grain Boundary Engineering of Electronic Ceramics, Maney Publishing, London, 2003, p. 19. [9] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [10] S.E. Dann, D.B. Currie, M.T. Weller, M.F. Thomas, A.D. Al-Rawwas, J. Solid State Chem. 109 (1994) 134. [11] U. Kolitsch, H.J. Seifert, F. Aldinger, J. Solid State Chem. 120 (1995) 38. [12] F.A. Kro¨ger, The Chemistry of Imperfect Crystals, Nort-Holland, Amsterdam, 1974. [13] J. Nowotny, M. Rekas, Solid State Ion. 49 (1991) 135. [14] T. Nakamura, G. Petzow, L.J. Gauckler, Mater. Res. Bull. 14 (1979) 649. [15] J.H. Kuo, H.U. Anderson, D.M. Sparlin, J. Solid State Chem. 83 (1989) 52. [16] J. Mizusaki, N. Mori, H. Takai, Y. Yonemura, H. Minamiue, H. Tagawa, M. Dokiya, H. Inaba, K. Naraya, T. Sasamoto, T. Hasimoto, Solid State Ion. 129 (2000) 163. [17] C. Wagner, W. Schottky, Z. Phys. Chem., B Chem. Elem.Proz. Aufbau Mater. 11 (1931) 163. [18] I. Wærnhus, T. Grande and K. Wiik, Solid State Ion. (in press). [19] I. Wærnhus, N. Sakai, H. Yokokawa, T. Grande, M.-A. Einarsrud, K. Wiik, Solid State Ion. 175 (2004) 69. [20] R. Wernicke, Philips Res. Rep. 31 (1975) 526. [21] M. Radecka, M. Rekas, J. Phys. Chem. Solids 56 (1995) 1031.