Cation Self-Diffusion and Nonstoichiometry of Lanthanum Manganite

J. Phys. Chem. C 2007, 111, 813-822

813

Cation Self-Diffusion and Nonstoichiometry of Lanthanum Manganite Studied by Diffusion Couple Measurements Maria´ n Palcut, Kjell Wiik, and Tor Grande* Department of Materials Science and Engineering, Norwegian UniVersity of Science and Technology, 7491 Trondheim, Norway ReceiVed: July 7, 2006; In Final Form: October 11, 2006

Reaction kinetics between dense, polycrystalline pellets of La2O3 and Mn3O4 was investigated at temperatures of 1370-1673 K and oxygen partial pressures of 40 Pa to 50 kPa. The formation of a single product phase, nonstoichiometric La1-xMn1-yO3(δ, was confirmed by X-ray diffraction and electron microprobe analysis. The solid solubility limits of La1-xMn1-yO3(δ determined by wave dispersive spectroscopy were in good agreement with previous reports, and equilibrium was achieved at the phase boundaries in the diffusion couples. Vacancies at the La and O sub-lattices are proposed to be the dominating point defects in the product layer. The growth of the product phase followed the parabolic rate law. The location of Pt markers demonstrated that diffusion of Mn cations in La1-xMn1-yO3(δ dominated over diffusion of La3+. The diffusion coefficient of Mn3+ was determined from the parabolic rate constant, and an activation energy of 280 ( 40 kJ mol-1 was found. The results are discussed in relation to cation diffusion in other LaBO3(δ oxides (B ) Cr3+, Mn3+, and Fe3+).

Introduction Perovskite-type lanthanum manganite and its substituted derivates attracted a lot of attention since the discovery of their electrical and magnetic properties.1-3 Investigations on the giant magnetoresistance4,5 and potential applications in solid oxide fuel cell technology (SOFC)6,7 have been widely reported. Strontium-doped lanthanum manganites (LSM) are still one of the most attractive cathode materials in SOFC. In addition to the mixed conducting properties, a nearly perfect thermal expansion match with the electrolyte (yttria stabilized zirconia, YSZ) can be obtained by tailoring the Sr content in LSM.8 Moreover, since Mn is generally less reducible than other transition metals (e.g., Co and Fe), LSM exhibits little or no chemical expansivity.9 The chemical compatibility between LSM and YSZ has been studied thoroughly.10-13 Reaction proceeds by the diffusion of Mn and La ions into YSZ leading to the formation of La2Zr2O7, while Y3+ and Zr4+ ions remain in YSZ. These studies demonstrate that the interdiffusion and the formation of secondary phases at the cathode/electrolyte interface will, over time, reduce the performance of SOFCs. Cation mobility, although very low in perovskites, determines also the rate of sintering14,15 or creep.16,17 The phase equilibrium in the La-Mn-O system is well established.18-23 The major ternary phase is LaMnO3 solid solution. Several studies confirm that beside the perovskitetype phase also other ternary phases are present.24 However, they are either stable under the reducing conditions and temperatures above 1650 K or at the pressures over 30 kbar. The LaMnO3 phase exhibits oxygen nonstoichiometry and also a certain degree of deviation from the cation molar ratio 1:1.18 Crystal structure and defect chemistry at elevated temperatures under oxidizing and reducing conditions have been widely * Corresponding author. E-mail: [email protected].

reported.25-33 Lanthanum manganite can crystallize either with orthorhombic or rhombohedral structure. All three sublattices are defective, and randomly distributed vacancies rather than interstitials are the major point defects. Specific properties and extensive nonstoichiometry of manganites are caused by the variety of stable valence states of manganese. Lattice distortions result from a large reduction in ionic radius from Mn3+ to Mn4+ and from the charge ordering due to the static Jahn-Teller distortion. Some authors suggest that manganese cations can also occupy vacant lanthanum lattice positions.34,35 One therefore naturally expects specific transport properties of lanthanum manganite compared to other LaBO3 oxides. Regardless of the fundamental importance of this issue, the experimental information about cation transport in LaMnO3 is still lacking. Cation transport in ternary oxides has been studied by tracer annealing,36-39 inter-diffusion between two ternary oxides40 or following the diffusion-controlled solid-state reaction kinetics of two binary oxides. The bulk diffusion of a tracer exhibit significantly lower activation energy, and the determined diffusion coefficients are of several orders of magnitude lower than coefficients from diffusion couple measurements.41 Kinetic studies, recently applied to the diffusion of LnCrO3 (Ln ) La,42 Y,43 and Nd44) and LnFeO3 (Ln ) La,45 Y,46 and Gd47), show a diffusion-controlled process. The reaction pathway can be rather complex, involving a single transport of the A-site or B-site cations or a coupled transfer of negatively and positively charged ions in the rate-limiting step. The study of the reaction between powders of La2O3 and Mn2O3, reported recently,48 disabled the authors to study cation diffusion thoroughly due to the complexity of the powder reaction kinetics, especially with respect to boundary conditions. In the present paper, we report our kinetic studies on the formation of lanthanum manganite following the solid-state reaction between dense polycrystalline bodies of La2O3 and Mn3O4 in close and immediate contact at temperatures of 13701673 K and oxygen partial pressures of 40 Pa to 50 kPa. This

10.1021/jp0642746 CCC: $37.00 © 2007 American Chemical Society Published on Web 11/29/2006

814 J. Phys. Chem. C, Vol. 111, No. 2, 2007

Palcut et al.

Figure 1. Cross sectional view of a diffusion couple and details of the reaction interfaces in the backscatter mode. (a) Phases from the left are lanthanum oxide (light gray), epoxy resin (black), lanthanum manganite (gray) and manganese oxide (dark gray). Sample was heated for 60 h at 1573 K and p(O2) ) 1.0 × 103 Pa. (b) Phases from the left: lanthanum oxide, lanthanum manganite. Sample was heated for 60 h at 1573 K and p(O2) ) 50 × 103 Pa. (c) Phases from the left: epoxy resin (black), lanthanum oxide(light gray), manganese oxide (dark gray). Bright particles at the interface between manganese oxide and lanthanum manganite are platinum markers. Sample was heated for 100 h at 1573 K and p(O2) ) 20 × 103 Pa.

procedure reduces the complex kinetic problem to a onedimensional study. It will be elaborated further that the growth of lanthanum manganite follows a parabolic rate law. It is therefore possible to find a relation between the rate constant and diffusion coefficient of the rate-limiting species in LaMnO3 solid solution. Experimental Section Starting materials, La2O3 (99.99% purity, KEBOLab) and MnCO3 (99.9% purity, Merck), were calcined for 5 h at 800 and 620 °C, respectively, before use. Fine ball-milled powders of La2O3 and Mn2O3 were uniaxially pressed into cylindrical pellets (15 mm in diameter and 5-7 mm high) by applying a force of 10 kN. A small amount of ethylcellulose (0.7 wt %) was added to improve the green body quality. Sintering of La2O3 at 1600 °C for 5 h in air resulted in pellets of 96-98% relative density. Sintered bodies of Mn3O4 (94-96% relative density) were obtained after the heat treatment of Mn2O3 at 1450 °C for 5 h in air. The pellets were ground and finally polished using a 1 µm diamond abrasive. The reaction couples were made by facing the polished planes of La2O3 and Mn3O4 between two alumina plates and pressed together by a load of 65 kPa. The initial interface was marked by a thin layer of colloidal platinum paint. Reactants were heat-treated in dry and CO2-free air in a vertical tube furnace controlled at 1370-1673 K for 10-100 h. The heating and cooling rates were both 200 K/h. Samples were also kept at 1573 K for 10-60 h in three different gas mixtures of oxygen and nitrogen. The oxygen partial pressure was monitored by the type DS oxygen probe with the SIRO2 oxygen sensor (Australian Oxytrol systems) installed inside the furnace near the reactants. After each annealing, samples were mounted

in the epoxy resin, cut perpendicular to the reaction interface, and polished by a 1 µm diamond abrasive in the final step. The product phase was characterized by X-ray diffraction (SIEMENS D5005, Siemens Germany) with Cu KR radiation (λ ) 1.5418 Å). The microstructure was investigated by a low vacuum scanning electron microscope (Hitachi S3500N) with a solid-state backscattered detector. Accelerating voltage for the electron beam was 15 kV. The element distribution in the product phase was studied by wave-dispersive spectroscopy (JEOL JXA-8900). Three to four line scans of different positions across the diffusion couple were obtained by applying the accelerating voltage of 15 kV for the electron beam. Line scanning was kept perpendicular to the reaction interfaces. Step size was 1 µm, and the scanning started in the bulk of one of the reacting phases. The standard for the electron probe microanalysis (EPMA) was lanthanum manganite prepared by spray pyrolysis. The precursor was prepared from the nitrate solutions of Mn-EDTA and La-EDTA complexes (EDTA ) ethylenediamine tetraacetic acid) mixed exactly in the molar ratio 1:1. The powder from pyrolysis was then calcined at 900 °C for 24 h in air. Dense pellets of lanthanum manganite were prepared by conventional sintering at 1300 °C for 4 h in air (93% relative density). Results Typical cross sectional views of the diffusion couples are shown in Figure 1. A single product layer is evident. Its thickness varies from 10 to 100 µm according to annealing conditions. Product layer is uniform without any discrepancy between the thickness of the interior and edge of the samples (Figure 1a). Signs of nucleation or early stage growth were not detected at any experimental temperature. Due to the thermal

Reaction Kinetics between La2O3 and Mn3O4

J. Phys. Chem. C, Vol. 111, No. 2, 2007 815

Figure 2. Rhombohedral (top) and orthorhombic (bottom) X-ray diffraction patterns of lanthanum manganite formed at 1573 K and p(O2) ) 5 × 104 Pa and 40 Pa respectively. Due to a certain depth penetration of the X-ray beam there are also remaining patterns of the starting oxides (MnO, 9; Mn3O4, 2) and Pt marker (b).

mismatch of the materials, the reaction couples fractured usually along the La2O3/La1-xMn1-yO3(δ interface. Since the samples were mounted in the epoxy resin after the experiment, the amorphous black layer clearly separates mismatched phases (Figure 1a). The layer sometimes appeared porous close to the La2O3/La1-xMn1-yO3(δ interface (Figure 1b). The layer at the Mn3O4/La1-xMn1-yO3(δ interface, on the other hand, was always dense (Figure 1c). The platinum markers, indicators of the position of initial interface in the moving diffusion zone, were present only at the Mn3O4/La1-xMn1-yO3(δ contact plane (Figure 1c). A single product phase was confirmed by electron dispersive spectroscopy and X-ray diffraction. Diffraction patterns taken from reaction interfaces are displayed in Figure 2. The single product phase is rhombohedral or orthorhombic lanthanum manganite, La1-xMn1-yO3(δ. Orthorhombic modification was present only at the lowest oxygen partial pressure. The phase transition of Mn3O4 to MnO occurs at 1573 K and p(O2) ) 40 Pa in agreement with the literature.49 Chemical composition of the product phase was investigated by wave-dispersive spectroscopy. Two different product oxides were analyzed, one prepared at p(O2) ) 50 × 103 Pa and T ) 1573 K and another one grown at p(O2) ) 40 Pa and T ) 1573 K. The composition, given as the La/Mn atomic ratio Versus the actual position inside the layer (L/L0), is displayed in Figure 3. Our measurements started in the bulk of La2O3 phase, continued across the product layer, and ended in the bulk of Mn3O4/MnO phase or in the layer of epoxy resin. Scanning was kept normal to reaction interfaces. Three independent line scans from different parallel positions of the sample are shown in Figure 3. The chemical composition profiles coincide. Since the element distribution is independent of the perpendicular coordinate, the studied transport phenomenon is strictly onedimensional. Cation distribution in the layer is clearly not

Figure 3. La:Mn molar ratio across the lanthanum manganite phase. The starting oxides are on the left (La2O3) and on the right (Mn3O4 respectively MnO) side of the sample. Full symbols refer to the product layer prepared during the 60 h long thermal anneal at T ) 1573 K and p(O2) ) 50 × 103 Pa. Open symbols refer to the phase annealed at T ) 1573 K and p(O2) ) 40 Pa for 30 h. Three independent measurements for each composition are given. Nominal composition (nLa/nMn ) 1) is given by the dashed line.

constant. The composition gradually changes from the slight La-excess to significant La-deficiency. Oxygen content was also measured (Figure 4). However, since the EPMA resolution for light elements is low, only qualitative results for oxygen content were obtained (Figure 4). Absolute oxygen content in the reaction layer increases with increasing oxygen partial pressure and increasing Mn content. The concentration gradients were developed during the experiment, and their slopes vary with the applied oxygen partial pressure.


Palcut et al.

Figure 4. Oxygen content (in atomic percents) across the lanthanum manganite phase. The starting oxides are on the left (La2O3) and on the right (Mn3O4 respectively MnO) side of the sample. Full symbols (9, 2, [) refer to the product layer prepared during the 60 h long thermal anneal at T ) 1573 K and p(O2) ) 50 × 103 Pa. Open symbols (0, 4, ]) refer to the phase obtained during the annealing at T ) 1573 K and p(O2) ) 40 Pa for 30 h. Three independent measurements for each composition are given. Nominal composition (60 atom. %) is given by the dashed line.

Figure 5. Experimental gas oxygen supply (solid line) and the calculated oxygen consumption (dashed line) during the heat treatment of the diffusion couples at 1573 K and p(O2) ) 40 Pa.

amount of product oxide at 1573 K and p(O2) ) 40 Pa are compared in Figure 5. The growth kinetics of the lanthanum manganite layer is shown in Figure 6. It is described by the parabolic rate law

Based on our observations we establish the following overall reaction

x2 ) 2kpt + C

1-x 1-y La2O3(s) + Mn3O4(s) + 2 3 1 δ 9x + 8y ( + O2(g) ) La1-xMn1-yO3(δ(s) (1) 12 2 12

where kp is the parabolic rate constant, t is the dwelling time of the thermal anneal, and C is an integration constant. Reaction kinetics is thus diffusion-controlled, and it reflects the solidstate diffusion of ions in the lanthanum manganite phase. This observation also evidences that the interface reactions were significantly faster and they did not constitute the rate-limiting step. The heating time was not counted in our experiments since only a small deviation of C from zero was observed for the thermal anneal at 1673 K (Figure 6b). The heating rate of 200 K/h was sufficient to achieve the desired dwelling temperature in a reasonably short time. The growth of the layer during heating can be neglected. Parabolic rate constant in air exhibits an Arrhenius-type of behavior with the activation energy EA ) 280 ( 40 kJ mol-1 (Figure 7). The time evolution of the thickness of the product phase at four different oxygen partial pressures at T ) 1573 K is shown in Figure 8. Diffusion-controlled character of the reaction is maintained at all experimental conditions, but the reaction rate, indicated by the slope, clearly decreases with increasing p(O2) (Figure 9).

(

)

where the nonstoichiometry of lanthanum manganite is expressed as La1-xMn1-yO3(δ. The actual formation of lanthanum manganite takes place at the La2O3/ LaMnO3 phase boundary. The defect reaction at the La2O3/ LaMnO3 interface may be written as

1 3 X 3 •• La O ) LaXLa + V/// Mn + OO + VO 2 2 3 2 2

(2)

The oxygen and manganese diffuse from the Mn3O4/LaMnO3 phase boundary and annihilate with the corresponding vacancies at the La2O3/ LaMnO3 interface. The following two equations describe this process in two steps. The defect reaction taking place at the Mn3O4/LaMnO3 interface can be written as

2 1 4 5 1 Mn O ) MnX + Mn/ + OX + V•• + V/// La (3) 3 3 4 3 Mn 3 Mn 3 O 3 O The defect annihilation at the La2O3/ LaMnO3 interface may be given as follows:

1 1 1 1 1 O (g) + Mn/Mn + V••O ) OXO + MnXMn 12 2 3 6 6 3

(4)

The sum of eqs 2-4 gives eq 1 with x ) y ) δ ) 0. Deviations from stoichiometry will be discussed later. Due to the presence of Mn(II) in manganese oxide, O2(g) is also taking part in the reaction. The oxygen transport takes place preferably via pores along the La2O3/product interface (Figure 1b). Since the perpendicular transport of oxidant could be the rate controlling step in the layer growth at low oxygen partial pressures, the oxygen supply in our experiments was set to be of orders of magnitude higher than the amount needed. The experimental oxygen supply and oxygen consumption calculated from the

(5)

Discussion 1. Cation Nonstoichiometry and Solid Solubility of La1-xMn1-yO3(δ. EMPA concentration profiles provided in Figure 3 clearly demonstrate the extensive solid solubility region of La1-xMn1-yO3(δ. The composition limits at the boundaries with La2O3 and Mn3O4(MnO) phases, extracted from the cation distribution profiles at 1573 K, are shown in Figure 10. The agreement with previously published data18,21,22 is excellent. This observation strongly supports our preliminary conclusion, based on the bulk diffusion-controlled kinetic behavior, that the immediate equilibrium was achieved at the two phase boundaries. The composition limit at the La-deficient side is La0.89(0.01MnO3(δ, and it does not vary significantly with temperature and oxygen partial pressure. The composition at the Mn-deficient phase boundary, on the other hand, is temperature- and



Figure 8. Parabolic plot of the product thickness vs the annealing time at p(O2) ) 40 ([), 1 × 103 (9), 20 × 103 (2), and 50 × 103 Pa (b), T ) 1573 K.

Figure 6. Parabolic plot of the product thickness Versus the annealing time at 1370 (b), 1478 (2), 1573 (9), and 1673 K ([), p(O2) ) 20 × 103 Pa. The appropriate resolution for the high- (a) and low-temperature data (b) is given.

Figure 9. Logaritmic plot of the parabolic rate constant vs the oxygen partial pressure at 1573 K.

one to give the cation content per formula unit. The temperature dependence of the solubility range in air predicts that the lanthanum manganite phase may become unstable with respect to formation of La2O3 at temperatures above 1700 K. This agrees well with the formation of La2Zr2O7 at LSM/YSZ interfaces, which is usually prevented by the use of La-deficient LSM in SOFC.50 The possible decomposition of stoichiometric lanthanum manganite is perhaps also the main difficulty in the accurate measurements of the melting point of this phase.18 The extensive solid solubility region stresses the particularly interesting point defect chemistry of lanthanum manganite. Point defects are most likely related to a Schottky type equilibrium, leading to the mass action expression /// •• 3 KS ) [V/// La][VMn][VO]

Figure 7. Temperature dependency of the parabolic rate constant at p(O2) ) 20 × 103 Pa.

p(O2)-dependent. The solid solubility limits at 1573 K are LaMn0.97(0.01O3(δ (p(O2) ) 50 × 103 Pa) and LaMn1.03(0.01O3(δ (p(O2) ) 40 Pa) where either La or Mn content was scaled to

(6)

/// where KS is the equilibrium constant and [V/// La], [VMn], and •• [VO] are the concentrations of the point defects. Interstitials are not expected in perovskites due to the high atomic packing.51 The defect chemistry of La1-xMn1-yO3(δ(ss) is also dependent on the valence state of Mn, which can vary from +II to +IV under the conditions of the present study. Finally, anti-site defects such as Mn cations on La sublattice sites may be also


Figure 10. Solubity limits of La1-xMn1-yO3(δ (ss). Results from the present work are compared to previous observations from the literature: ∇, present work (T ) 1573 K, p(O2) ) 50 kPa); O, present work (T ) 1573 K, p(O2) ) 40 Pa); 9, ref 18; b, ref 21; [, ref 22. Shift of the La-rich phase boundary with decrease in oxygen partial pressure is indicated by an arrow.

of relevance since A-site deficiency is generally more frequent than the B-site deficiency in ABO3 perovskites. The results of independent investigations suggest that major ionic defects formed in La1-xMn1-yO3(δ (ss) are La and Mn vacancies.52-55 Structural defects, however, have been only recently studied by neutron diffraction. Wołcyrz et al. investigated three different samples with La:Mn ratios 0.91, 1, and 1.11.56 They were able to determine the sublattice occupation for the La-deficient sample. It can be described as [La0.922Mn0.013]MnO3 (i.e., by excess Mn ions in the La sublattice). The structure of the Mn-deficient sample was not resolved. Effects of cation vacancy distribution in substituted LaMnO3+δ were recently investigated by Malavasi et al.57 The authors correlated the structural information from neutron difractometry measurements with magnetic properties of Na- and Casubstituted lanthanum manganites. It is clearly shown that the 57 formal and real concentration of V/// Mn are not identical. From these observations and from our data, we conclude that Mn cations may occupy vacant La positions. Since it has been alreadypossibletosynthesizeahighlycation-deficientLa1-xMn1-yO3(δ (ss) with x,y > 0.12 under extreme conditions,58 more information is expected to appear in the future. A complete defect model, however, is beyond the scope of the present work, but in the following paragraphs, we will discuss our experimental findings in relation to the dominant point defects at respectively La-deficient and Mn-deficient phase boundaries. The measured oxygen content of cation stoichiometric LaMnO3(δ at p(O2) ) 50 × 103 Pa and 1573 K from EPMA is 3 ( δ ) 2.88. This indicates that the measured oxygen molar fraction in our measurements is underestimated with about 0.1. Although the accuracy of EMPA at high p(O2) is low (Figure 4), we may still get an estimation of the overall composition of the product layer. The absolute nominal chemical compositions at the phase boundaries in the diffusion couples at 1573 K in p(O2) ) 50 × 103 Pa are according to EPMA LaMn0.97O2.51 and La0.89MnO3.02, respectively. Corresponding compositions obtained in p(O2) ) 40 Pa are La0.95MnO2.5 and La0.89MnO2.48. If we assume that the oxidation states of La and O in the perovskite are restricted to +III and -II respectively, the data

Palcut et al.

Figure 11. Principle of the marker experiment illustrated on the sample heated at 1573 K for 60 h at p(O2) ) 50 × 103 Pa. Platinum marker indicates the position of the initial interface after the reaction and thus reflects the direction of mass transport. Phases: 1 ) La2O3, 2 ) Mn3O4, and 3 ) La1-xMn1-yO3(δ (ss). The dark region is epoxy resin.

demonstrate that the average oxidation state of Mn is strongly dependent on p(O2) for La-deficient materials and it varies from above +III to considerably below +III. The oxidation state decreases from the phase boundary with Mn3O4/MnO to the phase boundary with La2O3. The average oxidation state of Mn is considerably below +III at both Mn-deficient and La-deficient phase boundaries at low p(O2). The strong dependency of the overall stoichiometry on temperature and p(O2) also demonstrate that the thermal history of lanthanum manganite is of paramount importance with respect to defect chemistry of these materials. The absolute oxygen content decreases with decreasing p(O2) and increasing La content (Figure 4). We may therefore conclude that oxygen vacancies are present in considerable quantities except for La-deficient materials at high p(O2). Based on these findings, the following point defects at T g 1573 K are dominant: •• La-deficient phase boundary: V/// La and VO at low partial pressure of O2 /// V/// La and VMn at high partial pressure of O2 •• Mn-deficient phase boundary: V/// Mn and VO Cation nonstoichiometry is also known for NdMnO3.59-61 Solubility limits at 1673 K and p(O2) ) 21 × 103 Pa are Nd0.88MnO2.92 and Nd1.05MnO2.72.61 This composition range is comparable to our data at 1573 K and p(O2) ) 50 × 103 Pa. Since the oxygen content in NdMnO3 samples was accurately measured, a useful composition-defect structure map divided into four quadrants, each with a principal defect structure, was provided.61 In line with our conclusions, most data on nonstoichiometric LnMnO3 (Ln ) La, Nd) fall within the quadrant with dominant O and Ln vacancies. 2. Diffusion of Mn Cations in La1-xMn1-yO3(δ. The Mn3+ diffusion from the Mn-rich side in La1-xMn1-yO3(δ (ss) dominates over La3+ diffusion in the opposite direction (Figure 11). The most remarkable conclusion from the previous section is, however, that vacant sites in the Mn sublattice are only present in a thin part of the product layer close to the La2O3/


J. Phys. Chem. C, Vol. 111, No. 2, 2007 819 TABLE 1: Experimental Parabolic Rate Constants for the Layer Growth of Lanthanum Manganite in Air Compared to the Manganese and Oxygen Diffusion Data T/ K

0 -∆G(A7) /(RT)a

kp/ cm2 s-1

DO/ cm2s-1 b

DMn/ cm2s-1 c

1370 1478 1573 1673

5.08 4.60 4.23 3.88

2.37 ( 0.25 × 10-12 6.20 ( 0.46 × 10-12 5.83 ( 0.23 × 10-11 1.66 ( 0.10 × 10-10

1.86 × 10-11 1.22 × 10-10 5.14 × 10-10 1.96 × 10-9

2.38 × 10-12 6.26 × 10-12 5.92 × 10-11 1.70 × 10-10

a Extrapolated from ref 71. b Extrapolated from ref 66. c Calculated using formula (A9).

Figure 12. Illustration of possible jumps of Mn cations between the La and Mn sublatices projected in the (110) direction. Grey circles represent O2-, black circles Mn cations and square represents vacant La position.

LaMn1-yO3(δ interface (Figure 3). At lower p(O2) the product phase becomes La-deficient in the entire range and vacancies on both La and O sublattices are dominant. The vacant sites available for Mn3+ diffusion are therefore most likely the La vacancies. One of the possible migration paths is illustrated in Figure 12. One may ask if a combination of La vacancies and Mn antisite defects on the La sublattice can explain qualitatively the increase of the parabolic rate constant with decreasing p(O2). On the basis of our concentration profiles (Figure 3 and 4), one may see that the La-vacancy concentration becomes more pronounced with decreasing p(O2) and the average valence of Mn is also decreasing with decreasing p(O2). Based on size arguments too, the presence of Mn on La site is favored by a lower valence of manganese since the ionic size increases with decreasing valence.62 Enhanced diffusion of Mn in the diffusion couples at lower partial pressure of oxygen is reasonably explained based on these considerations. The diffusion-controlled growth of ternary compounds from binary oxides was first quantitatively described by Wagner in the case of spinel AB2O4.63 Application of the theory to other ternary compounds with narrow ranges of nonstoichiometry was later developed by Buscaglia et al.46,47 and others.42-45,64 Oxide growth occurs by the counter-diffusion of cations or by unidirectional diffusion of anions and cations. Since lanthanum manganite is a p-type semiconductor,65 oxide growth may occur also by diffusion of cations and electron holes. The parabolic rate constant is related to the standard Gibbs energy of formation of the ternary compound and the diffusion coefficients of the ions taking part in the reaction. Since the oxide grows between two other compounds in close and immediate contact, the phase boundary moves as the reaction proceeds. The presence of the Pt marker at the vicinity of the La1-xMn1-yO3(δ /Mn3O4 contact plane evidences that diffusion of Mn dominates (Figure 10). We thus conclude that the diffusion of La3+ in La1-xMn1-yO3(δ is 1 or 2 orders of magnitude lower than diffusion of Mn cations in these materials. Oxygen tracer diffusion data for stoichiometric and Ladeficient lanthanum manganites in temperatures of 979-1251 K were recently reported by Berenov et al.66 Activation energies (240 kJ mol-1 for LaMnO3(δ and 294 kJ mol-1 for La0.9MnO3(δ) agree well with the activation energy from the present study. Extrapolated DO values in the 1370-1673 K temperature range, however, are about 1 order of magnitude higher than the parabolic rate constant. We would also expect the thickness of the layer to be thicker at the edges if the diffusion of oxygen

were the rate-limiting step. Since the product layer was always homogeneous in thickness across the entire profile of diffusion couples, we conclude that DO . DMn. Parabolic rate constant is therefore related only to the Mn diffusion coefficient, DMn

kp ) -

Vm RT

∫µµ

Mn(La)

Mn(Mn)

DMncMn dµMn

(7)

where Vm is the molar volume of reaction product formed by transport of Mn, cMn is the molar concentration of Mn and µMn(Mn) and µMn(La) are the chemical potentials of Mn cations at the interfaces. The diffusion of manganese occurs preferably via a vacancy mechanism since the interstitial defects in La1-xMn1-yO3(δ are unfavorable.51 Flux of manganese cation is equal to that of manganese vacancy

cMnDMn ) [V/// Mn]DV

(8)

where [V/// Mn] is the concentration of manganese vacancies and DV is the diffusion coefficient of manganese vacancies. The cation nonstoichiometry of the product layer demonstrates that the concentration of available vacant sites for Mn diffusion must necessarily vary across the layer. The diffusion coefficient extracted from the parabolic rate constant represents the average transport property of Mn cations in La1-xMn1-yO3(δ, and it must be treated strictly in this manner. In the Appendix, we shall present the approach how to estimate the Mn diffusion coefficient in the oxygen-excess region of La1-xMn1-yO3(δ. In this region, relevant for air measurements, the concentration of vacant Mn sites is reasonable and thus the single hopping of Mn cations in the Mn sublattice is probable. 3. Cation Diffusion in LaBO3 Oxides (B ) Cr, Mn, and Fe). The parabolic rate constant and, correspondingly, the diffusion coefficient of Mn3+ in La1-xMn1-yO3(δ are expressed as

( )

DMn ) D0MnpOn 2 exp -

EA RT

(9)

with n ) -0.108 ( 0.034 and EA ) 280 ( 40 kJ mol-1 determined by diffusion couple experiments. Values are given in Table 1. For the sake of comparison, oxygen diffusion coefficients are also included. The diffusion coefficient of Mn3+ is p(O2)-dependent and decreases with increasing oxygen partial pressure. Apart from our measurements, the retardation effect of increasing oxygen partial pressure has been already observed in the diffusional creep of La1-xSrxMnO3.17 Cation self-diffusion in lanthanum manganite has not been previously investigated. Only estimates based on creep measurements16,17 have been made. The diffusion coefficient of Mn3+ determined by us represents the first experimental data available. The diffusional creep of (La1-xSrx)1-yMnO3+δ, x ) 0.3, reported

820 J. Phys. Chem. C, Vol. 111, No. 2, 2007 in ref 17, reflects the mobility of the slowest cation. Although the authors were unable to determine which cation was slower, based on the defect model, they suggested La3+. Since the Mn3+ cation is faster than La3+ as based on our marker experiments, the conclusion is reasonable. Many papers dealing with the stability of La1-xSrxMnO3-YSZ composites report that the penetration of manganese cations causes a degradation of YSZ and formation of new phases.10-13 A recent kinetic study,67 for instance, shows that the diffusion of Mn3+ in YSZ is higher by about 1 order of magnitude than La3+ or Sr2+. Since the activation energy of Mn3+ transport in YSZ is low and close to the activation energy for O2- transport, the authors suggest that the Mn3+ diffusion in YSZ is a complex process occurring by ambipolar diffusion of Mn-O pairs. Activation energies for O2- and Mn3+ transport in La1-xMn1-yO3(δ are comparable. Coupled diffusion of Mn-O pairs could be relevant beside the single diffusion of Mn3+. However, since it is a coupled transport process, it is limited by the diffusion of Mn3+ cations. Cation diffusion in several La3+B3+O3 perovskite-type oxides has been investigated previously by three different techniques: diffusion-controlled solid-state reaction kinetics,42,45 tracer diffusion,36-39 and interdiffusion studies.40 The present work concentrates on the diffusion-controlled reaction kinetics, and we can therefore mainly compare our data to similar experiments reported in the literature. Data on tracer diffusion in La3+B3+O3type oxides exhibit significantly lower activation energies, and thus, they cannot be directly related to diffusion coefficients from kinetic measurements. Parabolic rate constants for diffusion-controlled growth of La1-xMn1-yO3(δ (ss), LaFeO3,45 and LaCrO342 are compared in Figure 13. Apart from the LaCrO3 system, the diffusion of the B3+ cation is dominant. The Cr3+ transport is slower than La3+ diffusion, and thus, it cannot be determined by this technique. Data reported by Akashi et al.42 reflect the diffusion of the La3+ cation. Similar reports on YCrO3 and NdCrO3 are again related to the A3+ diffusion.43,44 The Cr3+ diffusion coefficient was determined by tracer annealings.68 It is 10-2times smaller than the A3+ tracer diffusion coefficient.69 Since LaCrO3 has a different mobility of cations, it certainly has a different defect structure than the two remaining oxides. Diffusion coefficients of Fe3+ in LaFeO3 and Mn3+ in La1-xMn1-yO3(δ (ss) are comparable. Activation energy for Mn3+ transport is only slightly lower than that of LaFeO3. This is understandable since LaFeO3 does not have a dramatic cation nonstoichiometry and Fe3+ probably does not occupy vacant La sites. The authors report a negligible p(O2)-dependency of parabolic rate constants. The precision of this investigation, however, can be doubted. According to our measurements in air, the thickness of the layer at 1423 K is in the range of 1015 µm. Within the typical experimental uncertainty, given mainly by the final polishing step ((1-2 µm), it is not easy to register the effect of oxygen partial pressure. A higher temperature needed to be selected for this investigation. La3+ diffusion has been studied by interdiffusion experiments between LaFeO3 and NdFeO3.40 The bulk diffusion of La3+ is about 1 order of magnitude lower than Fe3+ diffusion from kinetic measurements. A similar difference between A3+ and B3+ tracer diffusion coefficients in LaFeO3 was also observed by I. Wærnhus et al.41 Since there are no data available on A3+ diffusion in lanthanum manganite, neither chemical nor tracer, one can take these estimates also for La1-xMn1-yO3(δ (ss).

Palcut et al.

Figure 13. Temperature (a) and pressure dependency (b) of parabolic rate constant for LaBO3 oxides: 2, La1-xMn1-yO3(δ (present work); b, LaCrO3;42 9, LaFeO3.45

Conclusion The main conclusions of the present paper may be given as follows: 1. The reaction kinetics between dense and polycrystalline La2O3 and Mn3O4 was a diffusion-controlled process regardless of temperature and oxygen partial pressure. A single homogeneous phase, La1-xMn1-yO3(δ (ss), was formed. 2. Significant deviations from the cation molar ratio 1:1 in the product phase were observed. Solubility limits of La1-xMn1-yO3(δ (ss) with La2O3 and Mn3O4(MnO) were in line with the previously reported data for lower temperatures. The composition of the La-deficient phase boundary did not change with temperature or oxygen partial pressure. The composition of the La-rich phase boundary, on the other hand, shifted toward La-deficiency with decreasing oxygen partial pressure. The solid solubility range thus became thinner with increasing temperature and decreasing partial pressure of O2. 3. Point defects present in La1-xMn1-yO3(δ (ss) are V/// La, /// in unequal amounts. Most of the solid solution VMn, and V•• O lies in the region with dominant vacancies in the lanthanum and oxygen sublattice. Concentration of the vacancies in the Mn sublattice is reasonable only at high oxygen partial pressures. Manganese cations are present in different oxidation states and probably occupy also vacant La sites. 4. The diffusion of Mn3+ in La1-xMn1-yO3(δ (ss) dominates over the La3+ diffusion. Appendix At fixed oxygen partial pressure, the equilibrium constant of reaction 2 is represented by


K2 )

•• 3/2 [V/// Mn][VO] [LaXLa][OXO]3/2 1/2 aLa 2 O3


(A1)

By rearranging, we may express the concentration of manganese vacancies

[V/// Mn] )

K2

a1/2 •• 3/2 X X 3/2 La2O3 [VO] [LaLa][OO]

(A2)

The expression of diffusion coefficient of Mn3+ cations (eq 8) becomes straightforward

DMn )

[V/// Mn] /1/2 D ) D/MnaMn La2O3 cMn V

(A3)

X X 3/2 3/2 with D/Mn ) K2DV/(cMn[V•• O] [LaLa][OO] ). This equation can be substituted into eq 7. Since the molar volume of transported Mn3+ cations is Vm ) 1/cMn, the relation between parabolic rate constant and diffusion coefficient of Mn3+ becomes

kp ) -

D/Mn RT

∫µµ

1/2 aLa dµMn 2O3

Mn(La)

Mn(Mn)

(A4)

The change in chemical potential of manganese is related to the change in chemical potential of La3+ and, correspondingly, to that of La2O3

2dµMn ) -dµLa2O3 ) -RT d ln aLa2O3

(A5)

Equation A4, after substitution and integration, becomes 1/2 1/2 - aLa ) kp ) D/Mn(aLa 2O3(La) 2O3(Mn)

(A6)

Activity of La2O3 at the Mn3O4(MnO)/La1-xMn1-yO3(δ interface can be, in principle, estimated from the Gibbs free energy of the following hypotetical reaction42-45

1 1 La O + Mn O f LaMnO3 2 2 3 2 2 3

(A7)

At the La2O3/La1-xMn1-yO3(δ interface it is assumed to be 1 (i.e., the same as in the bulk of La2O3). The parabolic rate constant then becomes

(

kp ) D/Mn 1 - exp

( )) ∆G0(A7) RT

(A8)

0 ∆G(A7) values are taken from ref 71. The diffusion coefficient, correspondingly, is given by

D/Mn

(

) kp 1 - exp

( )) ∆G0(A7) RT

-1

(A9)

Equation A9 represents the diffusion coefficient of Mn3+ in La1-xMn1-yO3(δ when aLa2O3 ) 1 (i.e., at the La2O3/La1-xMn1-yO3(δ interface). Acknowledgment. M.P. thanks Mrs. Eli Beate Jakobsen for the help with the construction of the high-temperature furnace and to Mr. Morten Peder Raanes for the performace of EPMA analysis. The award of a research grant by Research Council of Norway (Grant no. 158517/431, Functional oxides for energy technology) is also fully acknowledged. A preliminary version of this work was presented at 26th Risø International Sympo-

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Cation Self-Diffusion and Nonstoichiometry of Lanthanum Manganite

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